Answer: q1=11 q2=15 q3=20
Step-by-step explanation:
The physician orders 150 mg/5 kg. The patient’s weight is 75 kg. How many grams of medication has the physician ordered?
Answer: 2.25 grams
Step-by-step explanation:
In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.
[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex] [cross multiply]
[tex]11250=5x[/tex] [divide both sides by 5]
[tex]x=2250mg[/tex]
We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.
[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex] [cross multiply]
[tex]1000y=2250[/tex] [divide both sides by 1000]
[tex]y=2.25[/tex]
Therefore, we need to give 2.25 grams.
1.1.2 Quiz: What Is Health?
Question 2 of 10
In order to maintain wellness, the parts of the health triangle always need to
be
Select two responses.
and
A. working together
B. apart from one another
C. independent of one another
D. in balance
Answer:
The World Health Organization (WHO) defines health as 'a state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'
Find 45% of 60???????
Answer:
27
Step-by-step explanation:
To find 45% of 60, you can multiply 60 by 0.45
60 x 0.45 = 27
45% of 60 is 27.
Rewrite in simplest terms: 9(-6p-4)+3(3p-5)9(−6p−4)+3(3p−5)
The expression in the simplest form is -90p - 102
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We are given an expression as 9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)
Then Rewrite in simplest terms:
9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)
2 [ 9(-6p-4)+3(3p-5) ]
Solve the like terms;
2 [-54p - 36 + 9p - 15]
2 [-54p + 9p - 15 - 36]
2 x ( -45p - 51)
-90p - 102
To know more about an expression follow;
brainly.com/question/19876186
#SPJ1
PLEASE HELP FRACTION S EASY!! A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses pounds of gravel. For each pound of gravel, he uses pound of cement. He is making enough concrete that he needs to use 3 pounds of sand.
How many pounds of cement does he use?
The pound of cement used based on the information will be C. 2 pounds.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.
The pound of cement used will be:
Gravel = 1 2/3 × 3
= 5 pounds
Cement used will be:
= 2/5 × 5.
= 2 pounds.
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
a radio caller won the grand prize, where the caller gets to
spin a wheel with prizes of $500, $750, $1,250, $21500,
$5,000, $10,000, and $25,000 on a wheel. The probability
the wheel lands on $500 is }, landing on $750 is
crIN
landing on $1,250 is 25,
, landing on $2,500 is 25, landing
on $5,000 is 25, landing on $10,000 is 25, and landing on
$25,000 is
25 •
What is the expected amount of money
the radio caller should win if the caller gets to spin the
wheel once?
O $5,050
O $6,450
O $4,100
O $3,650
Answer: To find the expected amount of money the radio caller should win, you can multiply the prize amount by the probability of winning that prize, and add those products for each prize. The expected value is also known as the mean value.
$500 * 1/8 = $62.50
$750 * 1/8 = $93.75
$1,250 * 1/8 = $156.25
$2,500 * 1/8 = $312.50
$5,000 * 1/8 = $625.00
$10,000 * 1/8 = $1250.00
$25,000 * 1/8 = $3,125.00
Total expected value = $62.50 + $93.75 + $156.25 + $312.50 + $625.00 + $1250.00 + $3,125.00 = $5,050.00
So, the expected amount of money the radio caller should win if the caller gets to spin the wheel once is $5,050.
It's worth to mention that the probability for each prize is the same, but the prizes are not the same so each prize win will be different according to the prize amount.
The expected value doesn't assure that the prize will be won, but it's a good approximation of the prize the caller could win.
Step-by-step explanation:
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Orange marble selection has a 0.33 experimental probability.12 over 60 is the experimental probability of landing on a number smaller than 2
what is probability ?Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.
given
In each of the three studies, Sandy's experimental probability matched the theoretical probability to the letter.
The theoretical likelihood of landing on orange is one-fourth, but the actual likelihood is 20%.
Orange marble selection has a 0.33 experimental probability.
12 over 60 is the experimental probability of landing on a number smaller than 2.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface for the dish and are reflected to the focus, where the receiver is located. The satellite dish has a diameter of 14 feet and a depth of 3 feet. How far from the base of the dish should the receiver be placed? Round your answer to the nearest tenth.
Answer:
Given that we know the base of the parabola is at the origin, and that it is symetrical about the y-axis, we can simplify the equation to
y=ax2=14px2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=ax2=14px2y=ax2=14px2
which corresponds to the given equation a=14p" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=14pa=14p given above.
Since y=6" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=6y=6 when x=2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">x=2x=2,
6=a(2)2=4a" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">6=a(2)2=4a6=a(2)2=4a
and
a=32" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=32a=32
Thus we have
32=14p12p=2p=16" role="presentation" style="display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 3.337em; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; width: 10000em; position: relative;">32=14p12p=2p=1632=14p12p=2p=16
So, the receiver should be placed 16" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1616 of a foot, or 2 inches, above the base.
Simplify (-8-r)+(2r-4) Plato question
Answer:
−12r+32−2r 2
Step-by-step explanation:
(−8−r)(2r−4)
Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.
−16r+32−2r
2
+4r
Combine −16r and 4r to get −12r.
Answer:
R-12
Step-by-step explanation:
Open the parenthesis, then solve
-8-r + 2r-4
-r+2r-8-4
r-12
Your answer will be R-12
15 points help please solve each equation for both variables
Answer:
I hope this helps. Let me know if you have any doubts. Have a nice day!!
Y= 25x + 115
What is the rate of change and what does it represent?
Answer:
Step-by-step explanation:
y= 265
The rate of change of the equation is 25.
The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.
Given that the linear equation is y = 25x + 115. The rate of change of the equation is represented by the slope or gradient of the equation of the line.
Here in the equation y = 25x + 115 the rate of change is 25. Which is equivalent to the slope of the line.
To know more about the rate of change follow
https://brainly.com/question/25184007
#SPJ2
8. Laurie graphed two lines, as shown on the right.
One line has a slope of -2 and the other has a slope of
1/2. Laurie noticed that although the slopes are
negative reciprocals of each other, the lines do not
appear to be perpendicular. Explain why this result
occurs, even though she graphed the lines correctly.
It's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle,
What are the slopes of the two lines?
The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter m.
The slopes of the two lines that Laurie graphed, -2 and 1/2, are negative reciprocals of each other, which means that their product is -1.
In a Cartesian coordinate system, lines that are perpendicular to each other will have slopes that are negative reciprocals of each other, and the product of their slopes will be -1.
However, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle.
The two lines could be skew lines that never intersect and thus cannot be perpendicular.
Another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
When working with slope, we always assume that the lines are defined on a 2D Cartesian coordinate system, if that is not the case, it could cause the lines to not appear as perpendicular.
Hence, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle, another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
To learn more about the slopes of the two lines visit,
https://brainly.com/question/29250482
#SPJ1
In 3 billion repetitions of an experiment, a random event occurred in 500 million cases.
The probability of the event is 1.
True or False
The probability of the event is 0.
True or False
What is the expected probability of this event?
What is the expected probability of the complement of the event?
Answer:
The probability of the event is 1. False
The probability of the event is 0. False
What is the expected probability of this event?
The probability of the event is (500 million successful events) / (3 billion total repetitions) = 0.1667 or 16.67%.
What is the expected probability of the complement of the event?
The complement of the event is the event not happening. The probability of the event not happening is (3 billion total repetitions - 500 million successful events) / (3 billion total repetitions) = 0.8333 or 83.33%.
Uday Tahlan
please answer this is due at 11:59PM!!!
Answer:
Step-by-step explanation:
An explanatory variable is what you manipulate or observe changes in while a response variable is what changes as a result (e.g., reaction times). The words “explanatory variable” and “response variable” are often interchangeable with other terms used in research.
help pls fractionsss tyy
The amount of syrup she needs is 3/4 cups of syrup. Option A
What is a fraction?A fraction can be described as the part of a whole variable, element or number.
The several types of fractions are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsAlso, proportion can be defined as a mathematical comparison between two numbers
From the information given, we have that;
6 cups of soap = 1 /4 cup of syrup
Then 18 cups of soap = x cups of syrup
cross multiply, we get;
6x = 18(1/4)
multiply the values
6x = 18/ 4
Divide both sides by the coefficient of x , we get;
x = 18/ 4 × 1/6
x = 3/ 4 cup of syrup
Hence, the value is 3/4
Learn more about proportion here:
https://brainly.com/question/1781657
#SPJ1
In a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Triangle with vertices labeled golfer and spectator and hole, with the distance from the golfer to the spectator measuring 140 yards and the distance from the golfer to the hole measuring 200 yards and the vertex of the spectator measuring 120 degrees
If the spectator has an angle of 120° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
60.0°
59.6°
37.3°
22.7°
The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Let the angle that the golfer has between the spectator and the hole be x
Here, sin 120°/200 =sin x/140
0.8660/200 =sin x/140
0.00433 = sin x/140
sin x=0.866
x=60°
Therefore, option A is the correct answer.
Learn more about the sine rule here:
https://brainly.com/question/22288720.
#SPJ1
Hi hi! The answer would be 22.7°, I took the test a while ago.
In the diagram below,
ZCAB≈ ZCDE. Solve for x. Round
your answer to the nearest tenth if
necessary.
14
A
D
X
с
18.7
E
9.3
B
Answer:14 a
Step-by-step explanation:
The explanation is that it is E
5. Two Friends Kofi and tayo own a Store. The ratio of kofi Share to tayo's Share Is N120.00, Its 11:9 Of Tayo's Calculate the value of the Store
Answer:
Step-by-step explanation:
Can somebody help me? I need help please
By using concept of angle relationship, we get x equal to 27°.
What are angle relationships defined as?We compare the position, measurement, and congruence of two or more angles when we talk about angle relationships. For instance, two pairs of vertical angles are created when two lines or line segments intersect.
∠BAF+∠EAF=180°
∠EAF=180° - 138°
∠EAF=42°
Since, ∠EAF and ∠BAC are vertically opposite angle,
Hence,
∠EAF = ∠BAC =42°
Again,
∠EAD+∠DAC+BAC=180°
4x+30°+42°=180°
4x=180°-72°
4x=108°
x=27
To know more about angle visit:-
brainly.com/question/30147425
#SPJ1
Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
The following statements are true based on the diagram below
I is a vertex of right angleK is a vertex of right angleWhat is vertex?When two or more curves, lines, or edges come together, it is called a vertex (plural: vertices or vertexes) in geometry. As a result of this definition, polygonal and polyhedral corners as well as the intersection of two lines to form an angle are referred to as vertices.
The vertex of an angle is the point at which two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location.
Learn more about vertex
https://brainly.com/question/29030495
#SPJ1
noah's family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry,blueberry,and peach
Answer: 8
Step-by-step explanation:
Im guessing this is your question
Noah's family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags. Use the tape diagrams to determine how many fruit bars were originally in each box.
Answer:
Step-by-step explanation:
x-5
me bye u see okay later
Idil owns a small business selling clothing. She knows that in the last week 3
customers paid cash, 25 customers used a debit card, and 53 customers used a credit
card.
with
Based on these results, express the probability that the next customer will pay
cash or a credit card as a percent to the nearest whole number.
The probability that the next customer will pay cash or a credit card is 56%, since 3 customers paid cash and 53 customers used a credit card out of a total of 81 customers.
What is customers?Customers are individuals or organizations who purchase goods and services from a business. They play an important role in a company's success as they provide the revenue needed to sustain and grow the business. Customers become loyal to a business when they are provided with quality products, excellent customer service, and competitive prices. Companies that focus on customer satisfaction often develop long-term relationships with their customers, as they understand the importance of customer loyalty. Companies must strive to continually meet the changing needs of their customers in order to remain successful in the long term.
To learn more about customers
https://brainly.com/question/27155914
#SPJ1
6. Larry earns $840 per pay period, plus a commission of 8% on his sales. During the last pay period, Larry earned
a total of $2,440.00. What were Larry's total sales during the pay period?
A. $784
B. $22,500
C. $30,500
D. $38,500
7. Tom's bill at a local restaurant was $19.47. If he wants to leave a 15% tip, approximately how much should he
leave?
A. $0.15
B. $3
C. $4
D. $15
6. Larry's total sales during the pay period is $20,000.
7. Tom should leave $3 (approximate)
What is the meaning of total sales?
Total sales revenue usually referred to as gross sales is the sum of the value of the products and services a company provides to its clients over the course of a given reporting period.
Given that Larry earns $840 per pay period, plus a commission of 8% on his sales.
Assume that Larry sale $x during the last pay period.
The total earn is 840 + 8% of x
= 840 + 0.08x
According to the question:
840 + 0.08x = 2,440.00
Subtract 840 from both sides:
0.08x = 2,440 - 840
0.08x = 1600
Divide both sides by 0.08
x = 1600/0.08
x = 20,000
The sales is $20,000.
7. Given that, Tom's bill at a local restaurant was $19.47. He leaves 15% of the total bill as a tip.
15% of $19.47
= 15/100 × $19.47
= 2.920
≈ 3 (approximate)
Tom should leave $3.
To learn more about percentages, click on the below link:
https://brainly.com/question/28978848
#SPJ1
identify the part of following expression 4x-2y + 6/ 2x
Coefficients:
Constants:
Variable Terms:
Like Terms:
identification of the expression 4x- 2y + 6 = 2x is
Coefficient: 4, -2, 2Constant: 6Variable term: 4x, -2yLike terms: 4x and 2xWhat is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, a linear expression 4x-2y + 6 = 2x
Coefficient:
Coefficients are the numbers by which the variables in an equation are multiplied
Thus, the Coefficient terms for this equation = 4x, -2y, 2x
Constants:
the constant is the part of the expression that does not vary with the value of x and y.
Thus, constant terms for this equation = 6
variable terms:
These are the terms that vary at the different values of x and y.
Thus, variable terms for this equation = 4x, -2y
Like terms:
Terms that have identical variable parts (same variable(s) and same exponent(s))
thus, Like terms for this expression = 4x, 2x
Learn more about Expressions here:
https://brainly.com/question/14083225
#SPJ1
y is inversely proportional to x
when y = 7, x = 9
a) work out an equation connecting y and x
b) work out the value of y when x = 21
The equation connecting y and x is y = 63/x and the value of y when x =21 is 3
a) work out an equation connecting y and xFrom the question, we have the following parameters that can be used in our computation:
Variation = inverse variation
y = 7, x = 9
An inverse variation is represented as
k = xy
Where k is the constant of proportion
Substitute the known values in the above equation, so, we have the following representation
k = 7 * 9
Evaluate
k = 63
So, we have the following representation
xy = 63
Make y the subject
y = 63/x
b) work out the value of y when x = 21Substitute the known values in the above equation, so, we have the following representation
y = 63/21
Evaluate
y = 3
Hence, the solution is 3
Read more about inverse variation at
https://brainly.com/question/11177292
#SPJ1
Lucas hosted a New Year's dinner for his employees.
The total bill was $1,011.50. He left the server a 20%
tip. How much money did Lucas tip the server?
Round your answer to the nearest hundredth.
Answer:
$202.30
Step-by-step explanation:
You want to know the value of a 20% tip on a bill of $1011.50.
TipThe tip amount can be found by multiplying the bill amount by the tip percentage:
20% · $1011.50 = $202.30
Lucas tipped the server $202.30.
__
Additional comment
You know that 10% of the amount can be found by moving the decimal point one place: $101.15.
20% of the amount will be double this value: $202.30. You can do this math mentally.
Photo attached someone please help
thanks
By drawing the line x + y = 2, one of the solution to the given system of equations is (0, 2).
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided, we have the following system of equations:
x² + y² = 9 ......equation 1.
x + y = 2 .............equation 2.
Next, we would use an online graphing calculator to plot the given system of equations and then highlight (read) the point of intersection, which is the ordered pair (0, 2).
Read more on equation of a circle here: brainly.com/question/17028215
#SPJ1
PLEASE HELP ME THIS IS DUE RIGHT NOW HELP ASAP
============================================================
Explanation:
We'll need to find the slope of the line through the two given points.
[tex](x_1,y_1) = (-3,17) \text{ and } (x_2,y_2) = (2,-3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-3 - 17}{2 - (-3)}\\\\m = \frac{-3 - 17}{2 + 3}\\\\m = \frac{-20}{5}\\\\m = -4\\\\[/tex]
The slope is -4.
Think of -4 as -4/1. The reciprocal is -1/4, and it flips in sign to +1/4 or simply 1/4.
The original slope -4 leads to the perpendicular slope 1/4. The two slopes multiply to -1. This is true of any perpendicular lines where neither is vertical nor horizontal.
------------------------
In short, the answer equation will involve a slope of 1/4. This points us directly to choices A and E as two answers so far.
Something like choice B is not an answer since it has slope 4. Choice C is ruled out because 4x+y = -8 solves to y = -4x-8. It has a slope of -4.
Choice D on the other hand has x-4y = 2 solve to y = (1/4)x - 1/2, and this has a slope of 1/4 that we want. This means choice D is another answer.
Choice F and choice G are ruled out because they involve slopes of 4 and -4 respectively.
------------------------
Summary: The 3 answers are choices A, D and E
Step-by-step explanation:
the slope of a line is the ratio
y coordinate change / x coordinate change
when going from one point on the line to another.
so for (-3, 17) and (2, -3) we get
x changes by +5 (from -3 to 2).
y changes by -20 (from 17 to -3).
the slope is
-20/+5 = -4/1 = -4
now, a perpendicular slope (90° to the original slope) is putting the slope fraction upside-down and flips the sign :
+1/4 or simply 1/4.
the slope in an equation of the form "y = ..." is always the factor of x.
y + 2 = (1/4)(x - 1)
yes, there are only some constant additions or subtractions to get to a or "y = ..." form, so 1/4 is indeed the factor of x and the slope of this line.
y = 4x + 12
4 <> 1/4, so, no, it is not.
4x + y = -8
y = -4x - 8
-4 <> 1/4, so, no, it is not.
x - 4y = 2
-4y = -x + 2
y = (1/4)x - 2/4
1/4 is indeed 1/4, so, yes, it is.
y = (1/4)x - 15
1/4 is indeed 1/4, so, yes, it is.
y + 3 = 4(x - 2)
similar to the first one, but 4 <> 1/4, so, no, it is not.
y = -4x + 3
-4 <> 1/4, so, no, it is not.
Rashaad has
x
x dimes and
y
y nickels, having no less than 18 coins worth at most $1.50 combined. At least 4 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
Answer:
see attached for a graph4 dimes, 22 nickelsStep-by-step explanation:
You want to solve graphically the system of inequalities expressing that Rashaad has no less than a total of 18 dimes (x) and nickels (y) with a combined value of at most $1.50, of which at least 4 are dimes.
InequalitiesAn inequality can be written for each of the constraints:
x + y ≥ 18 . . . . . . . no less than 18 coins
0.10x +0.05y ≤ 1.50 . . . . . . at most $1.50 in value
x ≥ 4 . . . . . . . . . . at least 4 dimes
GraphA graph of these inequalities is attached. The marked points are the vertices of the triangular solution space. Each is a possible solution, along with all of the grid points inside the triangle.
One possible solution is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.
Using graph to solve the system of linear inequality the most likely solutions will be 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50
What is System of Linear InequalitySystems of linear inequalities are equations with two or more linear inequalities that contain two or more variables. These equations can be used to represent real-world problems and to find the solutions of such problems. The solutions of a system of linear inequalities are all the points that are common to all of the linear inequalities in the system.
In this problem, we have to define our variables and then solve this using graphical method. The point of intersection between the two lines lies the solution to the linear inequality.
Let;
x = dimesy = nickelx + y ≥ 18
0.1x + 0.05y ≤ 1.50
x ≥4
Using a graphing calculator to solve this,
The possible solutions is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.
Learn system of linear inequality here;
https://brainly.com/question/23093488
#SPJ1
The functions each model the number of students S is that played an online video game d days after each video game was released. S^1(d)= 0.45d^3-3d^2 + 4.75d +16
S^2(d)=0.09d^3-1.31d^2 +7.25d +18
Use a graphing calculator to determine the number of days after the games release that were played by the same number of students.
0.36d³ - 4.31d² - 2.5d - 2 = 0 is the function and the graph of the function is given below -
What is function?function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable).
y = x² is an illustration of this. Any input for x yields a single output for y. Because x represents the input value, one can state that y is a function of x.
To determine the number of days after the game's release that was played by the same number of students for the two functions S^1(d) and S^2(d).
Here, the functions each model the number of students S.
played an online video game d days.
We need to set the two functions equal to each other and solve for d.
S^1(d) = S^2(d)
or, 0.45d³ - 3d² + 4.75d + 16 = 0.09d³ - 1.31d² + 7.25d + 18
Subtracting 0.09d³ - 1.31d² + 7.25d + 18 from both sides we get:
or, 0.36d³ - 4.31d² - 2.5d - 2 = 0
So, the graph becomes:
To know more about function refer to:
https://brainly.com/question/11624077
#SPJ1