Answer:
Step-by-step explanation:FIGURE A FIGURE B FIGURE C FIGURE D 2.1.1. Calculate the area of figure A 2.1.2. Calculate the area of figure 2.1.3. Calculate the area of figure C
Sure, here are the calculations for the area of each figure:
Figure A is a rectangle with a length of 4 cm and a width of 3 cm. The area of a rectangle is calculated by multiplying the length and the width, so the area of Figure A is 4×3=12 square centimeters.
Figure B is a triangle with a base of 4 cm and a height of 3 cm. The area of a triangle is calculated by multiplying the base and the height and dividing by 2, so the area of Figure B is (4×3)/2=6 square centimeters.
Figure C is a trapezoid with a top base of 4 cm, a bottom base of 6 cm, and a height of 3 cm. The area of a trapezoid is calculated by averaging the top and bottom bases and multiplying by the height, so the area of Figure C is (4+6)/2×3=15 square centimeters.
Figure D is a circle with a radius of 2 cm. The area of a circle is calculated by multiplying the square of the radius by π, so the area of Figure D is 2
2
π=4π square centimeters.
Question
The histogram shows the numbers of concerts choir students at a school have performed in. How many choir students have performed in at least 3 concerts?
The number of choir students that performed in at least 3 concerts is given as follows:
16 students.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed, or the number of observations in each range of a data-set.
Hence, for this problem, the meaning of the histogram is given as follows:
8 students performed in between 0 and 2 concerts.9 students performed in between 3 and 5 concerts.4 students performed in between 6 and 8 concerts.3 students performed in between 9 and 11 concerts.Hence the number of choir students that performed in at least 3 concerts is given as follows:
9 + 4 + 3 = 16 students.
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The names eben , evelyn , eunice, frieda and frank are to be randomly chosen, and each has the same probability of being selected. Use events E,F,G and H to determine the probabilities in part A to E .
A: Find P(e) in simple fraction form
B: find p(f) In simplest fraction form
C : find p(g) In simplest fraction form
D: find p ( E U F) simplest fraction form
A. P(E) = 1/5
B. P(F) = 1/5
C. P(G) = 1/5
D. The probability of selecting either "Eben" or "Frank" is 2/5.
A: To find the probability of selecting the name "Eben," we need to determine the fraction of the total possible outcomes that result in selecting "Eben." Since there are a total of five names to choose from, the probability of selecting "Eben" can be expressed as:
P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case, there is only one favorable outcome (selecting "Eben"), and there are five possible outcomes (choosing any of the five names). Therefore:
P(E) = 1/5
B: Similarly, to find the probability of selecting the name "Frank," we can apply the same approach. The probability of selecting "Frank" can be expressed as:
P(F) = (Number of favorable outcomes) / (Total number of possible outcomes)
Again, there is only one favorable outcome (selecting "Frank"), and there are five possible outcomes (choosing any of the five names). Thus:
P(F) = 1/5
C: To find the probability of selecting the name "Evelyn," we follow the same method as above. The probability of selecting "Evelyn" is:
P(G) = (Number of favorable outcomes) / (Total number of possible outcomes)
Once again, there is only one favorable outcome (selecting "Evelyn"), and there are five possible outcomes (choosing any of the five names). Therefore:
P(G) = 1/5
D: To find the probability of selecting either event E or event F (P(E U F)), we can add their individual probabilities and subtract the probability of their intersection (P(E ∩ F)). The probability of the union can be calculated as follows:
P(E U F) = P(E) + P(F) - P(E ∩ F)
Since event E and event F are independent, the probability of their intersection is zero (no name can be both "Eben" and "Frank" simultaneously). Therefore:
P(E U F) = P(E) + P(F) - 0
= P(E) + P(F)
= 1/5 + 1/5
= 2/5
Thus, the probability of selecting either "Eben" or "Frank" is 2/5.
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The city’s Emergency Task Force is putting together emergency kits for some of its residents. Karen used 84 batteries for 12 flashlights and 6 radios. Jin used 50 batteries for 5 flashlights and 10 radios. How many batteries does each radio and flashlight need?
Learning Goal: I can use the substitution method to solve linear systems of equations.
Each radio requires 2 batteries, and each flashlight requires 6 batteries.
To solve this problem using the substitution method, we need to determine how many batteries each radio and flashlight need. Let's assume the number of batteries needed for a flashlight is represented by 'f', and the number of batteries needed for a radio is represented by 'r'.
From the given information, we can create two equations:
Equation 1: 12f + 6r = 84 (Karen's usage of batteries)
Equation 2: 5f + 10r = 50 (Jin's usage of batteries)
To solve the system of equations, we can use the substitution method. First, we'll solve Equation 1 for 'f' in terms of 'r':
12f = 84 - 6r
f = (84 - 6r)/12
f = 7 - (r/2)
Now, we substitute this expression for 'f' into Equation 2:
5(7 - (r/2)) + 10r = 50
35 - 5(r/2) + 10r = 50
35 - (5r/2) + 10r = 50
35 + (20r - 5r)/2 = 50
35 + 15r/2 = 50
15r/2 = 15
15r = 30
r = 2
Now that we have the value of 'r' as 2, we can substitute it back into Equation 1 to find the value of 'f':
12f + 6(2) = 84
12f + 12 = 84
12f = 72
f = 6
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1/4
Homework Progress
22 / 77
P and Q are points on the line 3y - 4x = 12
a) Complete the coordinates of P and Q.
P (0,4
,0)
b) Plot points P and Q on the graph.
Use the tool to plot the coordinates.
c) Draw the line 3y - 4x = 12 for values
of x from -3 to 3.
8
7
6
5
4
3
2
1
Answer:
Step-by-step explanation:Homework Progress
22 / 77
P and Q are points on the line 3y - 4x = 12
a) Complete the coordinates of P and Q.
P (0,4
,0)
b) Plot points P and Q on the graph.
Use the tool to plot the coordinates.
c) Draw the line 3y - 4x = 12 for values
of x from -3 to 3.
HELP!!!
The quadrilateral is in a circle with a radius of 2cm. The maxium possible area of the quadrilateral....
A. 2cm^2
B. [tex]2\sqrt{2} cm^2[/tex]
C. 4cm^2
D. 4[tex]\sqrt{2}[/tex]cm^2
E. 4[tex]\sqrt{3}[/tex]cm^2
Answer:
C. 4 cm²
Step-by-step explanation:
You want the maximum possible area of a quadrilateral inscribed in a semicircle.
AreaThe figure is symmetrical about a vertical line, so the area will be maximized when the area of half the quadrilateral is maximized. The area of the quadrilateral in the right half of the figure is the product of the x- and y-coordinates of the corner point on the circle.
For coordinates (x, y), the area is A=xy. The graph of this function is a hyperbola, symmetric about the line y=x. The larger the value of A, the farther the graph is from the origin.
The maximum possible value of A will be found where the graph of xy=A is tangent to the circle. That point of tangency will lie on the circle and on the line y = x.
Corner pointThe equation for the semicircle is ...
x² +y² = 2²
When x=y, this is ...
x² +x² = 4
x² = 2
This is the area of the quadrilateral in the right half of the figure.
The entire quadrilateral has an area twice this, or 2·2 = 4 (square cm).
The maximum possible area of the quadrilateral is 4 cm².
__
Additional comment
You will notice the figure is half of a figure of a whole circle with a square inscribed. This is not a coincidence.
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A TV at Best Buy is , and they charge sales tax. What is the amount of tax you would pay for the TV?
Answer:
you would still pay the normal amout of tax of other normal technology. The tax would change depending on e=what state your in tho
Step-by-step explanation:
Which statement must be true?Choose all that apply.
From the attached image, it can be seen that triangle PQR is an isosceles triangle and therefore option (A), option (B), option (C) and option (D) are all correct.
Understanding Isosceles TriangleAn isosceles triangle has 2 sides equal meaning 2 opposite angles are also equal.
Let us assume the following:
PR = 1cm
QR = 1cm
PQ = 2cm
cos P = adj/hyp
= PR/PQ = 1/2
cos Q = adj/hyp
= QR/PQ = 1/2
Therefore cos P and cos Q are equal.
sin P = opp/hyp
= QR/PQ = 1/2
sin Q = opp/hyp
= PR/PQ = 1/2
Also sin P and sin Q are equal.
From this analogy, we can deduce the following:
sin P = sin Q = 1/2
cos P = cos Q = 1/2
sin P = cos Q = 1/2
cos P = sin Q = 1/2
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For each value of y , determine whether it is a solution to -5 = 9 - 7y
Hello !
-5 = 9 - 7y
-5 + 7y = 9
7y = 9 + 5
7y = 14
y = 14/7
y = 2
so no for all except for y = 2
Point P is on a bearing of 135° and 320° respectively from point Q and R.If PQ=25km and PR=40km,find
a)QR
b)bearing of Q from P
(a). The distance QR is equal to 45.3 using the cosine rule.
(b) Bearing of Q from P is 315°
What is bearing?Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.
(a). Let ∆PQR be the triangle formed with bearings so that:
angle P = 45° + 40° {alternate angles from Q and R respectively to P}
angle P = 85°
PQ = 25km
PR = 40km
The distance QR is calculated using the cosine rule as follows:
QR² = 25² + 40² - 2(25)(40)cos85° {cosine rule}
QR² = 2225 - 174.3115
QR = √2050.6885 {take square root of both sides}
QR = 45.2845
(b) Bearing of point Q from P is the angle measured from the north of P to the straight line distance between Q and P
Bearing of Q from P = 45° + 270° = 315°
Therefore, the distance QR is equal to 45.3 using the cosine rule. Bearing of Q from P is 315°
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The police went on a wild chase to catch a man speeding through town in a black pick-up truck. At times their speeds exceeded eighty-five miles per hour. At that rate, how many miles would the car go in 20 minutes? (round to the nearest whole mile)
Answer: About 28 miles.
Step-by-step explanation:
First, we will find the rate of miles per minute.
85 miles / 60 minutes = 1.41666667 miles per minute
Next, we will multiply this rate by 20 minutes:
20 minutes * 1.41666667 miles per minute ≈ 28 miles
Answer:
Step-by-step explanation:
To find out how many miles the car would go in 20 minutes, we need to determine the distance covered in one minute and then multiply it by 20.
Given that the car's speed exceeded 85 miles per hour, we can calculate the distance covered in one minute by dividing 85 by 60 (since there are 60 minutes in an hour).
85 miles/hour ÷ 60 minutes/hour = 1.4167 miles/minute
Therefore, the car would travel approximately 1.4167 miles in one minute.
To find the distance covered in 20 minutes, we multiply the distance covered in one minute by 20:
1.4167 miles/minute × 20 minutes = 28.3334 miles
Rounding to the nearest whole mile, the car would go approximately 28 miles in 20 minutes.
find the value of q,r&s in the triangle below
The values of angle Q,R, S are 90°, 53.1° and 36.9° respectively.
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
sin(θ) = opp/hyp
cos(θ) = adj/hyp
sin(θ) = opp/adj
Finding angle R;
sinR = 8/10
sinR = 0.8
R = 53.1°
Q is a right angle , therefore Q is 90°
therefore to find angle S
angle S = 90- 53.1
= 36.9°
Therefore the values of angle Q,R, S are 90°, 53.1° and 36.9° respectively.
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2
2780-4
Which is more, the average of the 4 even whole numbers from 8 to
15 or the average of the 4 odd whole numbers from 8 to 15?
After calculating the average of numbers here, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.
The step-by-step solution to this is given below:
To determine which average is greater, let's calculate the averages of the even and odd numbers separately.
The four even numbers from [tex]8 \ to \ 15 \ are \ 8, 10, 12, and \ 14[/tex]. To find their average, we sum them up and divide by [tex]4[/tex]:
[tex]\[\text{Average of even numbers} = \frac{8 + 10 + 12 + 14}{4} = \frac{44}{4} = 11\][/tex]
The four odd numbers from [tex]8 \ to \ 15 \ are \ 9, 11, 13, and \ 15.[/tex] Similarly, we calculate their average:
[tex]\[\text{Average of odd numbers} = \frac{9 + 11 + 13 + 15}{4} = \frac{48}{4} = 12\][/tex]
Now, the next step will be comparing the two averages, we find that the average of the four odd numbers, [tex]12[/tex], is greater than the average of the four even numbers, [tex]11[/tex].
Therefore, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.
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solve the equation x²+2x-3=0
Answer:
x = - 3, x = 1
Step-by-step explanation:
x² + 2x - 3 = 0
consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (+ 2)
the factors are + 3 and - 1 , since
3 × - 1 = - 3 and + 3 - 1 = + 2 , then
(x + 3)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
x - 1 = 0 ( add 1 to both sides )
x = 1
solutions are x = - 3 , x = 1
7. Fatima plans to solve the system below using elimination. Which is a
reasonable first step Fatima could take?
-3x + 4y = -14
x + 2y = -12
A. Multiply the 2nd equation by -3
B. Multiply the 2nd equation by -2
C. Multiply the 2nd equation by 2
D. Any of the above
Answer:
Step-by-step explanation:
D is the answer. See attachment for reason.
PUT THE NUMBERS LEAST TO GREATEST AND EXPLAIN WHY. i will mark you brainliest
Answer:
The answer is
-5.79×10²³,6.88×10‐²³,5.73×10²³,57.8×10²²,5.83×10²³
Step-by-step Explanation:
(Polynomials (all operations)) Find the *
area of the triangle below with base
length -6x + 3.
4(x - 2)
Please help
The area of a triangle is:
12x² -18x - 12
How to find the area of the triangle?The area of a triangle can be calculated using the formula:
A = 1/2 * b * h
where b is the base and h is the height of the triangle
We have:
b = -6x + 3
h = 4(x - 2) = 4x - 8
substituting into the formula:
A = 1/2 * (6x + 3) * (4x - 8)
A = 1/2 * (24x² -48x + 12x - 24)
A = 1/2 * (24x² -36x - 24)
A = 12x² -18x - 12
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Please Help !!!
A local hamburger shop sold a combined total of 686 hamburgers and cheeseburgers on Saturday. There were 64 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Saturday?
hamburgers
X
The number of hamburger is 375 and the number of cheeseburger is 311.
Here,
It should be noted that an expression is simply used to show the relationship between the variables.
In this case, the local hamburger shop sold a combined total of 686 hamburgers and cheeseburgers on Saturday and there were 64 fewer cheeseburgers sold than hamburgers.
Let Cheeseburger = x
Hamburger = x + 64
This will be:
x + x + 64 = 686
2x + 64 = 686
2x = 686 - 64
2x = 622
x = 622/2
x = 311
Cheeseburger = 311
Hamburger = x + 64 = 311 + 64 = 375
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Which expression is equivalent
Answer:
4th option
Step-by-step explanation:
using the rule of exponents
• [tex]a^{m}[/tex] ×[tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
then
[tex]x^{9}[/tex] × x = [tex]x^{9}[/tex] × [tex]x^{1}[/tex] = [tex]x^{(9+1)}[/tex] = [tex]x^{10}[/tex]
Then
[tex]\sqrt[3]{x^{10} }[/tex] ≡ [tex]\sqrt[3]{x^9 . x}[/tex]
An angle with an initial ray pointing in the 3-o'clock direction measures theta radians (where 0 less than or equal to 0 less than or equal to 2pi) the circles radius is 3 units long and the terminal point is located at (-2.69, -1.33)
a. The terminal point it how many radius lengths to the right of the circles vertical diameter
h= ____ radius lengths
b. When we evaluate cos^-1(h) the value returned is _____ radians
c. therefore, theta =
a) The terminal point is 0.896 radius length.
b) The value returned is -0.896.
We have,
The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)
a. Since the circle's radius is 3 units long, we divide the x-coordinate by 3:
x-coordinate of terminal point: -2.69
Number of radius lengths to the right: -2.69 / 3 ≈ -0.896
However, since the angle is measured from the 3-o'clock direction, we consider it to be in the clockwise direction.
Thus, the number of radius lengths to the right is
Number of radius lengths to the right: -(-0.896) = 0.896
Therefore, the terminal point is 0.896 radius length.
b. Using Trigonometry
cos(h) = x-coordinate of terminal point / radius length
cos(h) = -2.69 / 3 ≈ -0.896
c. As, θ = h. From the given information, we have:
θ ≈ -0.896 radians
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b. Express log2 24 in terms of prime factors and leave answer in the most simplified form using properties of logarithms. (2 Marks)
log₂ 24 can be expressed as 3 + log₂ 3 in terms of prime factors, using the properties of logarithms.
To express log₂ 24 in terms of prime factors, we can use the properties of logarithms and the fact that any positive integer can be expressed as a product of prime factors.
First, let's find the prime factorization of 24.
24 can be divided by 2, so we have 24 = 2 × 12.
12 can be divided by 2, so we have 12 = 2 × 6.
6 can be divided by 2, so we have 6 = 2 × 3.
Therefore, the prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3.
Now, using the properties of logarithms, we can express log₂ 24 as the sum of logarithms of its prime factors.
log₂ 24 = log₂ (2³ × 3)
According to the properties of logarithms, we can separate the factors inside the logarithm as individual terms:
log₂ (2³ × 3) = log₂ 2³ + log₂ 3
Since log₂ 2³ is equal to 3, we can simplify the expression further:
log₂ (2³ × 3) = 3 + log₂ 3
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Divide.
(x²+10x+16)÷(x+3)
Your answer should give the quotient and the remainder.
Answer: quotient: x+7 remainder: -5
A small class has 10 students, of whom are 5 girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the teacher will choose two girls? Write your answer as a fraction in simplest form
2/9 is the probability that the teacher will choose two girls
To calculate the probability of choosing two girls from the class
we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes: Since the teacher is choosing two students from a class of 10, the total number of outcomes is given by the combination formula C(10, 2), which is calculated as:
C(10, 2) = 10! / (2!(10 - 2)!) = 10! / (2! × 8!) = (10 × 9) / (2 × 1) = 45
Number of favorable outcomes
We want to choose two girls from the 5 girls in the class.
The number of ways to choose 2 girls from 5 is given by the combination formula C(5, 2), which is calculated as:
C(5, 2) = 5! / (2! × (5 - 2)!) = 5! / (2! × 3!) = (5× 4) / (2× 1) = 10
Therefore, the number of favorable outcomes is 10.
The probability of choosing two girls is given by the number of favorable outcomes divided by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes = 10 / 45 = 2 / 9
Hence, the probability that the teacher will choose two girls is 2/9.
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He buys a jewel for $180 then sells it for $216 find his percentage profit
The difference between the selling price and the cost price is the profit he earned.
Profit = Selling Price - Cost Price
Profit = $216 - $180
Profit = $36
To find the percentage profit, we need to calculate what proportion of the cost price the profit represents, and express that as a percentage :
Percentage Profit = (Profit : Cost Price) * 100%
Percentage Profit = ($36 : $180) * 100%
Percentage Profit = 0.2 * 100%
Percentage Profit = 20%
Therefore, his percentage profit is 20%.
5. A $1,500 loan grows at 5.5% simple interest.
a) Develop a formula to calculate the amount after n months.
b) What is the amount owed after 14 months?
(a) A formula to calculate the amount after n months: 1,500(1 + nx0.0046)
(b) the amount owed after 14 months = $1596.6
Given that,
Principal amount = P = $1,500
interest of grown = R = 5.5%
Now we can write is,
5.5% = 5.5/100
= 0.055
We know that,
The simple interest formula,
A = P(1 + rt)
Where,
A represents Amount after T years
R represents rate of interest
T is time in year
Now,
Since 1 month = 1/12 years
= 0.084
Therefore amount after 1 month be
A = 1,500(1+0.055x0.084)
= 1,500(1+0.0046)
= 1506.93
Amount after 2 month be
A = 1,500(1+ 2 x 0.055x0.084)
= 1,500(1+2x0.0046)
Amount after 3 month be
A = 1,500(1+ 2 x 0.055x0.084)
= 1,500(1 + 3x0.0046)
Hence amount of n months = 1,500(1 + nx0.0046)
Hence,
The amount after 14 months,
= 1,500(1 + 14x0.0046)
= $1596.6
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What is the meaning of "The Separation Axioms are too weak to develop set theory with its usual operations and constructions"?
The statement means that the Separation Axioms, a set of principles in mathematics, are not sufficient on their own to build acomprehensive framework for settheory that includes its typical operations and construction.
What are Separation Axioms?The Separation Axioms are a collection of axioms that define the basic properties of topological spaces. They are not strong enough to develop set theory with its usual operationsand constructions.
One reason forthis is that the Separation Axioms do not allow us to distinguish between different points in a topological space. For example, in a T0 space, we can say that two points are distinct if there is an open set that contains one point but notthe other.
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In the pyramid and prism below, the height is the same and the sides of the pentagon bases are the same. If the volume of the pyramid is 435.7 cm3, what is the volume of the prism?
Step-by-step explanation:
volume of any type of pyramid :
1/3 × base area × height
FYI (not needed to solve the problem) :
base area is a pentagon.
the area of a pentagon is
1/2 × p × a
p is the perimeter (5 × side length) of the pentagon.
a is the apothem (the direct - right-angled- distance from the center of the pentagon to the center of a side).
volume of any type of regular prism :
base area × height
since the sides of the pentagon are the same, also their base areas are the same.
the height is the same.
so, when we compare both formulas, we see that the only difference is the factor 1/3.
the volume of the pyramid is 1/3 the volume of the prism.
therefore,
volume prism = volume pyramid × 3 = 435.7 × 3 =
= 1,307.1 cm³
The midpoint between (8, 3) and (12, -7) is
hello
the answer to the question is (10, - 2)
Answer:
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex]
Midpoint = [tex](\frac{8+12 }{2} , \frac{3+(-7)}{2} )[/tex]
Midpoint = [tex](\frac{20 }{2} , \frac{-4)}{2} )[/tex]
Midpoint = (10, -2)
Select the correct answer. Joel and Kevin are each putting money in a savings account to buy a new bicycle. The amount, in dollars, in Joel's savings account, x weeks after the start of the year, is modeled by function j. The amount of money in Kevin's account, at the same time, is modeled by function k. j(x) = 25 + 3x k(x) = 15 + 2x Which function correctly represents how much more money, in dollars, is in Joel's account than in Kevin's account x weeks after the start of the year? O A. (j − k)(x) = 40 + 5x (j − k)(x) = 40 + x (j-k)(x) = 10 + 5x (j-k)(x) = 10 + x O B. C. O D. Reset dtry Next
The correct answer is (j - k)(x) = 10 + x.
To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).
(j - k)(x) = (25 + 3x) - (15 + 2x)
= 25 - 15 + 3x - 2x
= 10 + x
This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.
Therefore, the correct function is (j - k)(x) = 10 + x.
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What number is halfway between
a. Three point six and nine point six
b. One point one and one point five
c. Seven point two six and seven point two eight
a. The number halfway between 3.6 and 9.6 is 6.6.
b. The number halfway between 1.1 and 1.5 is 1.3.
c. The number halfway between 7.26 and 7.28 is 7.27.
To find the number halfway between 3.6 and 9.6, we can add the two numbers and divide by 2:
(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6
The number halfway between 3.6 and 9.6 is 6.6.
To find the number halfway between 1.1 and 1.5, we can use the same approach:
(1.1 + 1.5) / 2 = 2.6 / 2 = 1.3
The number halfway between 1.1 and 1.5 is 1.3.
To find the number halfway between 7.26 and 7.28, we can apply the same method:
(7.26 + 7.28) / 2 = 14.54 / 2
= 7.27
The number that is between 3.6 and 9.6:
(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6
6.6 is the number that falls between 3.6 and 9.6.
We can apply the same strategy to determine the value that lies between 1.1 and 1.5:
(1.1 + 1.5) / 2 = 2.6 / 2
= 1.3
1.3 is the number that falls between 1.1 and 1.5.
We can use the same procedure to determine the number that is halfway between 7.26 and 7.28:
(7.26 + 7.28) / 2 = 14.54 / 2
= 7.27
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determine the inclination of the following straight line
1. y=x+3 2) 3x-2y = 6
The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.
To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.
The inclination represents the ratio of how much y changes with respect to x.
Equation: y = x + 3
In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.
This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.
Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.
Equation: 3x - 2y = 6
To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.
First, isolate y:
-2y = -3x + 6
Divide the entire equation by -2 to solve for y:
y = (3/2)x - 3
Now we can observe that the coefficient of x is 3/2.
This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.
The inclination can be expressed as 3/2.
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