Answers
The equation that passes through the point (7, -2) and (11, 5) is y = 4/7x - 9
Equation of the line:
The standard form of the equation of the line is written as
y = mx + b
here
x and y represents the coordinates of the equation
m refers the slope of the equation
b refers the y intercept of the equation
Given,
Here we have the points (7, -2) and (11, 5).
Now we have to find the equation that passes through this points.
If you want to find the equation of the line, we have to find the slope and the intercept of the line.
The slope of the line is calculated by using the given point (7, -2) and (11, 5),
=> m = (11 - 7) / ( 5 - (-2))
=> m = 4/7
Now, we have to use the slope and the point (11, 5) to find the value of y intercept of the equation,
=> 5 = (4/7) (11) + b
=> 35 = 44 + b
=> b = -9
Therefore, the equation that passes through the points is y = 4/7x - 9
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Related Questions
What are the tep to writing the equation of a line, parallel or perpendicular, to a given line through a given point? Parallel line have the _____ lope. Perpendicular line have _____
Answers
Answer:
parallel line: a(x-h) +b(y-k) = 0, or y-k = m(x -h); same slopeperpendicular line: b(x-h) -a(y-k) = 0, or y-k = (-1/m)(x -h); opposite reciprocal slopeStep-by-step explanation:
You want the steps to writing the equation of a line parallel or perpendicular to a given line through a given point.
EquationsGiven line ax+by=c and point (h, k), you can write equations for the desired lines using the forms:
a(x -h) +b(y -k) = 0 . . . . . . parallel line
b(x -h) -a(y -k) = 0 . . . . . . . perpendicular line
If you eliminate parentheses and collect terms, you will have the general form equation of the desired line(s). If you solve for y, you will have the slope-intercept form of the equation.
To use these forms, it is helpful to start with the equation of the given line in standard form, as shown. (It could also be in general form ax+by-c=0.)
StepsUsing the above solution, the steps are ...
Write the equation of the given line in standard form or general form.Identify the coefficients 'a' and 'b'.Fill in the coefficients and given point coordinates in the relevant equation above.Rearrange the result to whatever form you need.You will note that the same coefficients are used on the same variables for a parallel line. This is because parallel lines have the same slope.
The coefficient of the variables are swapped, and one of them is negated in the equation for the perpendicular line. This is because perpendicular lines have opposite reciprocal slope.
Slope-intercept formWhen the given line is in slope-intercept form, y = mx +b, the slope is readily identified as m, the coefficient of x. For the parallel line, this slope can be used directly in the point-slope equation for a line through a given point:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
This can be rearranged to the slope-intercept form:
y = mx +(k -mh)
The perpendicular line has opposite reciprocal slope. The line perpendicular to the given line with slope m will have slope -1/m. Then the two forms of equation are ...
y -k = -1/m(x -h) . . . . . . . . . point-slope form
y = (-1/m)x +(k +h/m) . . . . . slope-intercept form
__
Additional comment
A standard form equation (ax +by = x) has mutually prime integer coefficients, with a positive leading coefficient. When you have written your equation, you may find it necessary to multiply the equation by some value to put it in this form. For example, -2x +4y = -8 must be multiplied by -1/2 to get the standard form equation x -2y = 4.
You need to be aware of the form required by your grader. The wording "the equation" often means slope-intercept form, or the form matching the given equation or the answer box format.
Which expression is equivalent to 9^3/3^3
Answers
Answer:
3^3
Step-by-step explanation:
Exponents
9^3 can be rewritten as
3^2 ^3
Using exponent rules a^b^c = a^ (b*c)
3^2^3 = 3^6
3^6 / 3^3
We know that a^b / a^c = a^(b-c)
3^6 / 3^3 = 3^(6-3) = 3^3
Answer:
2nd answer is correct
Step-by-step explanation:
We know that,
[tex] \rightarrow \sf {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \rightarrow \sf \frac{{x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ \rightarrow \sf( {x}^{a} )^{b} = {x}^{ab} [/tex]
Accordingly, let us solve it now.
[tex] \sf \frac{ {9}^{3} }{ {3}^{3} } \\ \\ \sf \frac{ {3}^{2 \times 3} }{ {3}^{3} } \\ \\ \sf\frac{ {3}^{6} }{ {3}^{3} } \\ \\ \sf {3}^{6 - 3} \\ \sf {3}^{3} [/tex]
(3xy^(2))^(3)*(-(2)/(3)x^(2)y^(3))^(4)
Answers
Answer:
its B!!
Step-by-step explanation:
I took the test and got it wrong but the review said it was B
Which is the smallest number. 0.5 0.17 0.07 1.7 0.071
Answers
The smallest number among the given options is 0.07.
To determine the smallest number, we compare the given options. Among the numbers 0.5, 0.17, 0.07, 1.7, and 0.071, the smallest number is 0.07. This can be determined by examining the decimal places. The number 0.07 has the fewest decimal places and is the smallest value.
When comparing decimal numbers, the digits after the decimal point are crucial.
In this case, we observe that 0.07 has the smallest digit in the hundredths place, while the other numbers have larger digits in that place. Therefore, 0.07 is the smallest number among the given options.
It is important to note that the order of magnitude (the number before the decimal point) does not affect the comparison when determining the smallest number among decimal values.
In summary, by comparing the decimal places, we find that 0.07 is the smallest number among the given options.
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Find the slope and y-intercept of each equation *Please*:
1.) 8x-4y=24
2.) y= -5x+16
Answers
Answer:
1) Slope: 2 ; y-intercept: (0, -6)
2) Slope: -5; y-intercept: (0, 16)
Step-by-step explanation:
8x-4y=24 is also y=2x-6
Slope: 2
y-intercept: -6
y= -5x+16
Slope: -5
y-intercept: 16
A watusi, a Ubangi, and a Pigmy compare the speeds at which ech can run.
The sum of the speeds of the natives is 30 miles per hour (mph). The Pigmy's
speed plus one-third of the Watusi's speed is 22 miles per hour more that the
Ubangi's sped. Four times the Watusi's speed plus three times the Ublani's
speed minus twice the Pigmys' speed is 12 miles per hour. Find out how fast
each can run. Then, tell what is unfortunate about the Ubangi.
*write system of equations
Answers
There is Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x represent Watusi's speed,
y represent Ubangi's speed,
And z represents Pigmy's speed.
According to the given information, we can write the system of equations as
x + y + z = 30 .....(i)
z + 2x/3 = 22 - y .....(ii)
4x + 3y - z = 12 .....(iii)
The above system of equations gives the values of x, y, and z when solving
x = 6, y = 3, z = 21
This means Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.
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The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the the domain of the inverse function.
Answers
The given descriptions "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.
First, let us understand the logarithmic function:
The inverses of exponential functions are logarithmic functions, and any exponential function could be represented in logarithmic form.
The given description fully stated about the logarithmic function.
Thus, the given description "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.
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Reese is installing an in-ground rectangular pool in her backyard. Her pool will be 30 feet long, 14 feet wide, and have an average depth of 8 feet. She is installing two pipes to bring water to fill the pool; these pipes will also be used to drain the pool at the end of each season. One pipe can fill and drain the pool at a rate that is 1 more than 2 times faster than the other pipe. If both pipes are open and working properly, it will take 3.5 hours to fill the pool.
Use this information and what you know about solving rational equations to answer the questions below.
1. When Reese opens the pipes to fill the pool, she finds that only the slower pipe is working. Write a rational equation that you can use to find out how long it will take to fill the pool under these circumstances. Explain how you came up with your equation.
2. Solve the equation that you wrote in question 1. You can round your final answer(s) to the nearest hundredth. Show all your work.
3. Interpret your answer(s) to question 2 in context of the problem. What do the number(s)
Answers
The 30 feet by 14 feet by 8 feet, filled in 3.5 hours by two pipes in which one pipe is 1 more than twice the other, indicates;
1. The rational equation from which the time the smaller pipe takes to fill the pool is; [tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]
2. The solution of the equation is t ≈ 10.51 hours
3. The time it takes to fill the pool using only the small pipe is about 10.51 hours
What is a rational equation?Rational equation are equations that have rational polynomial expressions.
The dimensions of the pool are;
Length = 30 feet
Width = 14 feet
Depth = 8 feet
1. Let x represent the flow rate of the slower pipe
The flow rate of the faster pipe = 2·x + 1
Time it will take both pies to fill the pool = 3.5 hours
The volume of the pool, V = 30 × 14 × 8 = 3360
The volume of the pool is 3360 cubic feet
The rate equation is therefore;
[tex]\dfrac{x}{3360} +\dfrac{2\cdot x+1}{3360} =\dfrac{1}{3.5}[/tex]
[tex]\dfrac{x}{3360} =\dfrac{1}{3.5} - \dfrac{2\cdot x+1}{3360}[/tex]
From the rate equation above, the time it takes the smaller pipe to fill the pool is; t = 3360/x therefore;
[tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]
2. Solving for x from the volume of water in the pool, V, therefore;
The volume of water that fills the pool, V, is found from the equation;
V = 3.5 × (2·x + 1 + x) = 10.5·x + 3.5
V = 10.5·x + 3.5
Therefore;
3360 = 10.5·x + 3.5
[tex]x = \dfrac{3360-3.5}{10.5} =319.\overline 6[/tex]
t = 3360/319.[tex]\overline 6[/tex] ≈ 10.51
The time it takes to fill the pool using only the smaller pipe is approximately 10.51 hours
Aliter;
[tex]\dfrac{3\cdot x}{3360} =\dfrac{1}{3.5}-\dfrac{1}{3360}[/tex]
[tex]t = \dfrac{3360}{x} =\dfrac{3}{\left(\dfrac{1}{3.5}-\dfrac{1}{3360}\right)} \approx 10.51[/tex]
3. The interpretation of the solution is that it takes about 10.51 hours for the smaller pipe working alone to fill the pool
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PLEASE HELP FAST! 2. Find the volume of the following figure. Use 3.14 for pi. Show work please
Answers
Answer:
Step-by-step explanation:
the equation of the cone is given already
r=6 inches
h=7 inches
Substitute in the equation =84pi=263.89
for the sphere substitute the radius r= 6 inches in the equation, and then divide by 2. This is because the spherical shale in top of the cone is half a sphere, as it can be clearly seen.
So It’s 288pi= 904.78 /2 =452.39
add the volume of cone and volume of sphere
The final answer is 716.28 inches^3
Riley walked 6 players in 3
innings. How many players is
he likely to walk in 5 innings?
Answers
m -10
-------- = 0
-2
What is the answer
Answers
1) multiply each side by -2 for m-10 = 0
2) add ten to each side for m = 10
A delivery truck is coming from San Antonio with avocados. The avocados are boxed in 2 different boxes small and large. The weight of both small and large boxes is 75lb. If the truck has 70 large boxes and 55 small boxes with a total weight of 4800 lb. How much does each type of box weigh?
Answers
x= weight of a large box
y = weight of a small box
We write the system of equations:
X + y = 95
50x + 65y = 5275
The solution to the system of equations by the graphic method is:
x = 60
y = 35
Note: see attached image.
Answer:
each type of box weigh:
weight of a large box = 60 pounds
weight of a small box = 35 pounds
Hope this helps <33
Please I need help please
Answers
The value of x in the given triangle is x = 2 .
In the question ,
it is given that ,
a triangle is given ,
let us name the triangle as triangle ABC ,
So , By Basic Proportionality Theorem , which states that ,
The line drawn parallel to one side of triangle and cuts the other two sides divides the other two sides in equal proportion.
So , By Basic Proportionality Theorem
AD/AB = AE/AC
substituting the value from the triangles , we get
4/12 = 6/(6+6x)
1/3 = 1/(1+x)
1 + x = 3
x = 3 - 1
x = 2
Therefore , The value of x in the given triangle is x = 2 .
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If A ⊂ B, then A ∩ B = ∅. true or false
Answers
The statement if A ⊂ B, then A ∩ B = ∅ is false.
First, let us understand the set:
A set is a mathematical model for a collection of different things; a set contains elements or members that can be any mathematical object: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
We are given;
A ⊂ B
We need to find A ∩ B.
Let us understand the given set;
A ⊂ B means A is a proper subset of B.
All the elements of set A are in set B.
So, A ∩ B = A
But, A ∩ B = ∅ is given.
So, the statement is false.
Thus, the statement if A ⊂ B, then A ∩ B = ∅ is false.
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Roberto has already run 16 of 26. 2 miles of a marathon. Rounded to the nearest whole number, what percent of the marathon has he completed?.
Answers
Answer: Alright, lets get started.
Roberto has already run miles = 16
Total miles for marathon = 26.2
As per percentage formula :
So, percentage completed =
Rounding the answer to whole number 62 %
62 percent of the marathon he has completed. : Answer
Hope it will help :)
Step-by-step explanation:
Kiara and Lee are collecting violas in a ratio of 2:5 . If they collected 266 violas altogether , how many violas did Kiara collect?
Answers
The quantity of violas Kiara collected is 76
Calculating quantity of violas collectedFrom the question, we are to determine the quantity of violas Kiara collected.
From the given information,
"Kiara and Lee are collecting violas in a ratio of 2:5"
First, we will determine the sum of ratios
Sum of ratios = 2 + 5 = 7
Also, from the given information
The total number of violas they collected is 266
Thus,
The quantity of violas Kiara collected will be
2/7 × 266
= 2 × 38
= 76
Hence, the quantity she collected is 76
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Multiply. (-5 5/8) • (-2 1/3) What is the product?
Answers
Answer:
105/8 = 13 1/8 = 13.125
Step-by-step explanation:
The first step is to turn the (-5 5/8) into a mixed number. The mixed number you should be getting is - 45/8. The second step is to convert the (-2 1/3) into a mixed number as well, your second mixed number should be -7/3. Next multiply the two fractions, - 45/8 x (-7/3) = 315/24.
We can simplify 315/24 by dividing by 3, so you'll divide 315 divided by 3 and 24 divided by 3 and you should get ... 105/8. So 105/ 8 is equal to
13 1/8. If you need this fraction in decimal form it is 13.125.
PLEASEEEE HELP 100 POINTS AND I WILL MARK BRAINLIEST PLEASE
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C(t) = −2t^2 + 8t, where the time, t, is hours after injection.
Part A: What are the domain and range of the function C(t) based on the context of the problem? Show all necessary calculations.
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.
Answers
Answer:
See below
Step-by-step explanation:
First, graph the function to see that the domain ( the values of x the function can have in this context goes from 0 to 4 hours ( after four hours the concentration goes negative.....can't happen in the real world)
and the range is 0 to max of 8 mg/L
Here is the graph :
Use the spinner shown. It is equally probable that the pointer will land on
any one of the six regions. If the pointer lands on a borderline, spin again. If
the pointer is spun twice, find the probability that it will land on
grey and then purple
Find the probability that the spinner will land on grey and then purple.
Answers
The probability that the spinner will land on grey and then purple is 1/18.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of grey regions = 1
Number of purple regions = 2
Total number of regions = 6
Now,
The probability that the spinner will land on grey.
= Number of grey regions / Total number of regions
= 1 / 6
The probability that the spinner will land on purple.
= Number of purple regions / Total number of regions
= 2 / 6
The probability that the spinner will land on grey and then purple.
= 1/6 x 2/6
= 1/6 x 1/3
= 1/18
Thus,
The probability that the spinner will land on grey and then purple is 1/18.
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Which of the following is a polynomial with roots:-√3,√3, and 3?
x3-2x²-3x+6
x3-3x2-3x+9
x3+2x²-3x-6
x3+3x²-3x-9
Answers
Answer:
[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]-3x+9
Step-by-step explanation:
(x-3)([tex]x^{2}[/tex]-3) = 0
x = -[tex]\sqrt{3}[/tex], [tex]\sqrt{3}[/tex], 3
what is the y-intercept of the line given by the equation below?
y=4x-6
A. (4, 0)
B. (0, 4)
C. (-6, 0)
D. (0, -6)
Answers
Answer:
D: (0,-6)
Step-by-step explanation:
the y intercept in an equation is the "b" value in y=mx+b
Answer:
(0,-6)
Step-by-step explanation:
you can look at the last term in the equation which is -6
Or you can set x to 0
y=4(0)-6
y=-6
Hopes this helps please mark brainliest
How many laps around the lake does Latrell jog? Write your answer as a whole number of laps plus a fraction of a lap.
Answers
The number of laps around the lake that Latrell jogs is 5 1/4 laps.
What is a fraction?A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
From the information he jogs 7 miles and each lap is 4/3 miles. The number of laps will be:
= Total laps / Number of miles
= 7 ÷ 4/3
= 7 × 3/4
= 21 / 4.
= 5 1/4 laps.
He jogs 5 1/4 laps.
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NEED ANSWER SOON PLEASE
The graph shows how many cnetimeters a bamboo plant can grow and the number that the plant has been growing. Determine the constant of proportionatlity and explain what it means.
The numbers below are what the dots are plotted-
10,50
20,100
30,150
40,200
50,250
Answers
The constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.
We know that the constant of proportionality is nothing but the slope of the line.
The slope of the line is given by;
Slope = Change in y-coordinate / change in x-coordinate
We are given:
The numbers below are what the dots are plotted-
10, 50
20, 100
30, 150
40, 200
50, 250
Take any two points.
Let us choose (20, 100) and (30, 150).
Put the values in the slope formula;
Slope = (150 - 100) / (30 - 20) = 50 / 10 = 5
So, the slope of the line is 5.
Thus, the constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.
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A recipe for whole grain bread calls for 1 oz of rye flour for every 4 oz of whole wheat flour. How many ounces of each kind of flour should be used to make a loaf of bread weighing 22 oz?
Answers
In the making of 22 oz of bread rye flour and whole wheat requirements are 4.4 0z and 17.6 oz.
What is the different method of writing a ratio?A ratio is a comparison between two quantities in simplest form.
A ratio of the from a : b can be written as a/(a + b) and b/(a + b).
Given, A recipe for whole grain bread calls for 1 oz of rye flour for every 4 oz of whole wheat flour.
∴ In the making of 22 oz of bread rye flour needed is 1/(1 + 4)×22
= (1/5)×22.
= 4.4 oz.
In the making of 22 oz of bread whole wheat needed is 4/(1 + 4)×22.
= (4/5)×22.
= 17.6 oz.
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Lesson
Cool Down: Off by a Little Bit?
Clare
estimates that her brother is 4 feet tall. When they get measured at the doctor's
office, her brother's height is 4 feet, 2 inches.
1. Should Clare's or the doctor's measurement be considered the actual height?
Explain your reasoning.
2. What was the error, expressed in inches?
3. What was the error, expressed as a percentage of the actual height?
Answers
Answer:
See belowStep-by-step explanation:
GivenEstimated value - 4 feet,Measured value - 4 feet, 2 inchesSolution1. The measured height is the exact value therefore it is to be considered as actual height.
2. The error is the difference between actual and estimated values:
4 feet 2 inches - 4 feet = 2 inches3. Percent error is:
Error / Actual value * 100%or
2 in / 4 ft, 2 in *100% = 2 in / (4*12 + 2) in * 100% = convert ⇒ 1 foot = 12 inches2 in / 50 in * 100% = 4%A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer. Write the specification as an absolute value inequality.
Answers
The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1 .
In the question ,
it is given that ,
the specification of the furniture , is 17.9 ≤ w ≤ 18.1 ,
where w is the width of the desk drawer in inches .
we need to write the given inequality in absolute inequality form ,
we know that the a-b < x < a+b , then the absolute inequality is |x-a|<b ,
On comparing the given inequality with a-b < x < a+b ,
we get
a - b = 17.9 and
a + b = 18.1
adding both the equations , we get
2a = 36
a = 36/2
a = 18
Substituting a = 18 in a + b = 18.1 , we get
18 + b = 18.1
b = 18.1 - 18
b = 0.1
The required inequality is |x-a| ≤ b .
|x - 18| ≤ 0.1
Therefore , The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1 .
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A CFL Factory uses 24,325.208 litre of water in 4 hours. How much water does the factory use in 3 hours
Answers
Answer:
18243.906
Step-by-step explanation:
Find how much water is used in 1 hour and then multiply that by 3
24325.208/4
6081.302
6081.302x3
18243.906
according to city reports, it was found that the mean age of the prison population in the city was 26 years. marc wants to test the claim that the mean age of the prison population in his city is less than 26 years. he obtains a random sample of 25 prisoners and finds a mean age of 24.4 years and a standard deviation of 9.2 years. at a significance level of 0.05, what should his conclusion be? note: the p-value
Answers
The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.
According to the question we will set up Hypothesis
Null, H0: U=26
Alternate, H1: U<26
Test Statistic
Population Mean(U)=26
Sample X(Mean)=24.4
Standard Deviation(S.D)=9.2
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/√(n))
to =24.4-26/(9.2/√(25))
to =-0.87
| to | =0.87
Critical Value
The Value of |t α| with n-1 = 24 d.f is 1.711
We got |to| =0.87 & | t α | =1.711
According to this, we have to make a decision
Hence Value of |to | < | t α |
P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658
Hence Value of P0.05 < 0.19658
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How many angles are formed by the intersection of the diagonals?
Answers
The number of angles that are formed by the intersection of the diagonals is 4.
What is a square?A square is a four-equal-sided figure with diagonals cut perpendicular to each other, with a total of four angles formed by diagonals.
It is a geometrical figure with four sides, each of which must be equal, and an angle of 90 degrees between two adjacent sides.
Square area = Side²
The square's perimeter = 4 sides
Every square contains two diagonals. The intersection angle of both diagonals is 90 degrees. The number of diagonal angles equals four.
Therefore, the correct option is 4.
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Complete question
How many angles are formed by the intersection of the diagonals in a square?
Solve for z.
Assume the equation has a solution for z.
a⋅(t+z)=45z+67
Answers
[tex]a(t+z)=45z+67\implies at+az=45z+67\implies az=45z+67-at \\\\\\ az-45z=67-at\implies \stackrel{common~factoring}{z(a-45)}=67-at\implies z=\cfrac{67-at}{a-45}[/tex]