" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function ⇒ D
Step-by-step explanation:
The form of the linear function is f(x) = mx + b, where
m is the slope (rate of change) of the functionb is the y-intercept (initial amount) of the function∵ f(x) = 37 x + 20 models the total cost for Rachel to be a member
at a gym for x months
∵ f(x) = m x + b
∴ m = 37 and b = 20
∵ m represents the rate of change
- That means she must to pay 37 per month for x months
∴ Rachel must pay $37 per month to use the gym
∵ b represents the initial amount
- That means she pays a fixed amount one time
∴ Rachel must pay a $20 membership fee to join the gym
" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function
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Choose the point-slope form of the line passing through (3,5) with a slope of -3.
O y -3'= -3 (ix – 5)
0 -3(y – 5) = x - 3
y - 5 = -3 (0 - 3)
O 3x - 5y = -3
O
Answer:
answer is y-5=-3(x-3)
Step-by-step explanation:
your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3). The equation put together correctly would be y-5=-3(x-3)
Answer:
y-5=-3(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-3(x-3)
help a girl out
(2a^3−5a)−(7a+3a^2)
For this case we must simplify the following expression:
[tex](2a ^ 3-5a) - (7a+ 3a ^ 2) =[/tex]
By definition of the law of multiplication signs we have to:
[tex]- * + = -[/tex]
Rewriting the expression we have:
[tex]2a ^ 3-5a-7a-3a ^ 2 =[/tex]
We add similar terms taking into account that:
Equal signs are added and the same sign is placed.
[tex]2a ^ 3-3a ^ 2-12a[/tex]
ANswer:
[tex]2a ^ 3-3a ^ 2-12a[/tex]
a 20.00 pair of jeans is discounted 20%. What is the final price of the jeans?
Answer:
16.00
Step-by-step explanation:
When you divide twenty percent(0.20) to 20.00 you will get sixteen or 4.00 dollars off
3.3(x – 8) - x = 1.2
Answer:
3.3 x - (3.3*8) - x = 1.2
2.3 x - (3.3*8) = 1.2
2.3 x - 26.4 = 1.2
2.3 x - 26.4 + 26.4 = 1.2 + 26.4
2.3 x = 27.6
2.3 x / 2.3 = 27.6 / 2.3
x = 12
Which fraction is the reciprocal of 2 5/7 ASAP!!!
7/19
bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19
Answer:
7/19
Step-by-step explanation:
2 5/7=19/7
which formula can be used to find an ?
Answer:
Step-by-step explanation:
an = 6n - 13
If n = 10 , a10 = 6*10 - 13 = 60-13 = 47
If n = 11 , a11 = 6*11 - 13 = 66-13 = 53
If n = 12 , a12 = 6*12 - 13 = 72-13 = 59
The formula to find the nth term of the sequence an, is a(n) = -13 + 6n
How to determine the formula to find an ?From the question, we have the following parameters that can be used in our computation:
a(10) = 47
a(11) = 53
a(12) = 59
a(13) = 65
The nth term of an arithmetic sequence can be represented as
a(n) = a(1) + (n - 1) * d
Where,
common difference,
d = 6
So, we have
a(n) = a(1) + (n - 1) * 6
Using the 12th term, we have
a(1) + (12 - 1) * 6 = 59
a(1) = 59 - 66
a(1) = -7
So,, we have
a(n) = -7 + (n - 1) * 6
Expand
a(n) = -13 + 6n
Hence, the formula to find an is a(n) = -13 + 6n
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the rate of watering is Rs. 4 per ll.
6) Find the area of the cardboard required to make a closed box of length
25cm, 5m and height 15cm.
dim deep is to be made. It is open at the
Answer:
The area of cardboard required is 40750 cm².
Step-by-step explanation:
Given:
Length (L) = 25 cm
Width (W) = 5 m = 5 × 100 = 500 cm
Height (H) = 15 cm
Area of the cardboard is same as the total surface area of the closed rectangular box.
Total surface area of the rectangular box is given as:
[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]
So, the area of cardboard required is 40750 cm².
A rectangular prism with a volume of 555 cubic units is filled with cubes with side lengths of \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit.
How many \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit cubes does it take to fill the prism?
135 cubes are required to fill the prism
Solution:
Given that a rectangular prism with volume of 5 cubic units is filled with cubes with side lengths of [tex]\frac{1}{3}[/tex] units
Then the number of cubes required to fill the prism will be given by:
[tex]\text { number of cubes }=\frac{\text {volume of rectangular prism}}{\text {volume of cube}}[/tex]
Volume of rectangular prism = 5 cubic units
[tex]\text{ Volume of cube}=(\text { side })^{3}$[/tex]
[tex]\text { Volume of cube }=\left(\frac{1}{3}\right)^{3}=\frac{1}{27}[/tex]
Therefore number of cubes required to fill the prism are:
[tex]\text { number of cubes }=\frac{5}{\frac{1}{27}}=5 \times 27=135[/tex]
Therefore 135 cubes are required to fill the prism
Answer:
135
Step-by-step explanation:
What is the slope of the line shown below?
Answer:
B
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line
m = [tex]\frac{-4-8}{2+1}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 → B
Answer:
The slope of the given line is -4.
So, option (B) is correct.
Step-by-step explanation:
We know that, slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now, the given line passes through the point (-1, 8) and (2,-4).
So, (x₁, y₁) = (-1, 8) and (x₂, y₂) = (2, -4)
So, by using the above formula, we get
Slope(m) of the given line passing through (-1, 8) and (2, -4) is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{-4-8}{2-(-1)}[/tex]
[tex]\implies\;m = \frac{-12}{3}=-4[/tex]
∴The slope of the given line is -4.
Hence, option (B) is correct.
Please help! A chemist has 100ml of 25% acid solution. How much of the solution does she need to drain and replace with 70% acid solution to obtain 100ml of 60% acid solution?
Answer:
77.78
Step-by-step explanation:
Answer:
77.78
Step-by-step explanation:
i had this ? on rsm student portal.
Determine the y-intercept of x 12 + y 3 = 2
The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]
To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.
To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:
[tex]\[12(0) + y^3 = 2\][/tex]
[tex]\[y^3 = 2\][/tex]
To solve for y, we take the cube root of both sides:
[tex]\[y = \sqrt[3]{2}\][/tex]
So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]
Coordinates of centroid of a triangle with vertices of (0,1) (2,6) (7,2)
Answer:
The centroid is located at (3,3)
Step-by-step explanation:
Centroid Of A Triangle
The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.
Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are
[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]
[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]
The vertices are (0,1) (2,6) (7,2), thus
[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]
[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]
The centroid is located at (3,3)
The coordinates of centroid are (3,3)
Step-by-step explanation:
The coordinates of centroid of a triangle are calculated by finding average of x-coordinates of vertices and the average of y-coordinates of vertices.
Given vertices are:
(0,1) (2,6) (7,2)
So,
x-coordinate of centroid:
[tex]x = \frac{0+2+7}{3}\\=\frac{9}{3}\\= 3[/tex]
y-coordinate of centroid:
[tex]y = \frac{1+6+2}{3}\\=\frac{9}{3}\\= 3[/tex]
Hence,
The coordinates of centroid are (3,3)
Keywords: Triangle, centroid
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Is x-4 equivalent to x3•x-7
Answer:
No.
Step-by-step explanation: Assuming you mean x^3*x-7, these two equations do not produce the same line.
Answer:
YESStep-by-step explanation:
[tex]x^3\cdot x^{-7}=x^{3+(-7)}=x^{-4}\\\\\text{used}\ a^n\cdot a^m=a^{n+m}\\\\\text{Other way}\\\\a^{-n}=\dfrac{1}{a^n}\\\\x^3\cdot x^{-7}=x^3\cdot\dfrac{1}{x^7}=\dfrac{x^3}{x^7}=\dfrac{x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1}{x\!\!\!\!\diagup_1\cdot x\!\!\!\!\diagup_1 \cdot x\!\!\!\!\diagup_1 \cdot x\cdot x\cdot x\cdot x}=\dfrac{1}{x^4}=x^{-4}[/tex]
Someone please help!
Answer:
See explanation
Step-by-step explanation:
1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.
2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.
3. Angles 2 and 7 are congruent (see 1)
Angles 2 and 10 are congruent (see 2)
Hence, angles 7 and 10 are congruent by transitive property.
A candy store sells caramels and milk chocolate by the pound the table below shows the total cost in dollars for a pound of each type of candy the store sells
Caramels: $10.28
Milk Chocolate: $13.85
How much more is the cost for 1 3/4 pounds of milk chocolate than the cost for 1 3/4 pounds of caramels?
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
Step-by-step explanation:
Given,
Cost of one pound of Caramels = $10.28
Cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel = [tex]10.28*1\frac{3}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99[/tex]
Cost of one pound of chocolate milk = $13.85
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]13.85*1\frac{3}{4}=13.85*\frac{7}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]\frac{96.95}{4}=\$24.24[/tex]
Difference = 24.24 - 17.99 = $6.25
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
Keywords: difference, multiplication
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Final answer:
The cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels, after calculating the total cost of each based on their per pound price.
Explanation:
To find out how much more the cost for 1 3/4 pounds of milk chocolate is than the cost for 1 3/4 pounds of caramels, we first need to calculate the cost of 1 3/4 pounds of each type of candy. Since the cost per pound of caramels is $10.28 and the cost per pound of milk chocolate is $13.85, we can set up our calculations as follows:
Total cost of caramels = 1.75 (pounds) * $10.28 (per pound) = $17.99
Total cost of milk chocolate = 1.75 (pounds) * $13.85 (per pound) = $24.24
Now, we subtract the total cost of caramels from the total cost of milk chocolate to find the difference:
Cost difference = $24.24 - $17.99 = $6.25
So, the cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels.
Janet charges an upfront fee of $20 plus $7.50 an hour for babysitting. Lisa does not charge an upfront fee, but charges $8.75 an hour. After how many hours will their charge be equal?
After 16 hours, the charges will be same.
Step-by-step explanation:
Given,
Janet's upfront fee = $20
Charges per hour = $7.50
Let,
x be the number of hours.
J(x) = 7.50x+20
Lisa has no upfront fee.
Charges per hour = $8.75
L(x) = 8.75x
For the charges to be equal;
J(x) = L(x)
[tex]7.50x+20=8.75x\\20=8.75x-7.50x\\20=1.25x\\1.25x=20[/tex]
Dividing both sides by 1.25
[tex]\frac{1.25x}{1.25}=\frac{20}{1.25}\\x=16[/tex]
After 16 hours, the charges will be same.
Keywords: function, division
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Is the following relation a function?
Answer:
No
Step-by-step explanation:
A function is a relation in which no two ordered pairs have the same first element.
A function associates each element in its domain with one and only one element in its range.
Graph the inequality.
Match the graph to the correct inequality below.
(attatched)
x > 5
x < 5
x ≥ 5
x ≤ 5
Answer:
x<=5
Step-by-step explanation:
Two things
direction its pointing is always how the sign will look likeif the circle is shaded it will have an "or equals to" sign; if its blank, there is only the "greater/lesser" signTwo-thirds of a number added to itself is 20. What is the number?
Answer:
12
Step-by-step explanation:
2/3 x + x = 20
2/3 x + 3/3x = 20
5/3 x = 20 ... times 3/5 both sides
x = 12
check: 2/3 x 12 + 12 = 8 + 12 = 20
here is an inequality 2x + 5 > 50 explain the steps you would use to solve the equation for x what would the graph look like
Answer:
[tex]x>22.5[/tex]
Step-by-step explanation:
Given linear inequality:
[tex]2x+5>50[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 5.
[tex]2x+5-5>50-5[/tex]
[tex]2x>45[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}>\frac{45}{2}[/tex]
∴ [tex]x>22.5[/tex]
The graph of the inequality is shown below.
The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.
HELP PLEASE!
Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the given function?
Y= |6x-2|-7
A.)(1/3,7);x=1/3; translated to the right 1/3 unit and up 7 units
B.) (1/3,7);x=1/3; translated to the left 1/3 unit and down 7 units
C.) (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units
D.) (1/3,-7);x=1/3; translated to the left 1/3 unit and up 7 units
Answer:
C. (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
Step-by-step explanation:
The function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The parent function is:
g(x) = IxI
And we have:
f(x) = I6x - 2I - 7
Rearranging the function:
f(x) = 6Ix - 1/3I - 7
Then, now let's define some transformations:
If we start with g(x), a translation of N units to the right is:
f(x) = g(x - N)
if we start with g(x), a translation of N units up is:
f(x) = g(x) + N
A translation down would be:
f(x) = g(x) - N
And a vertical dilation of scale factor A is written as:
f(x) = A × g(x)
Then in this case we have:
A translation to the right of 1/3 units.
A dilation of scale factor 6.
A translation down of 7 units.
And the axis of symmetry will be when the absolute value part is equal to zero, or when
6Ix - 1/3I = 0
And that is when x = 1/3.
Therefore, the function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.
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Which number line best shows how to solve −8 − (−6)?
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to negative 8.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 6. Another arrow points from negative 6 to 2.
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Answer:
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Step-by-step explanation:
find the number line best shows how to solve −8 − (−6)
In the number line first we start with -8 . negative and negative becomes positive
from -8 move 6 units to the right. So it ends at -2
A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.
Linda owns 4 shares of a certain stock. Yesterday the total value of her shares went down by 32 dollars. What was the change in value for each share?
Answer:
The value of each share decreased by $8.
Step-by-step explanation:
Number of shares of a certain stock Linda owned = 4
Total value of shares went down by = $32
So find the change in value of each share.
Solution:
Let the total value of each share in dollars be = [tex]x[/tex]
Value of 4 shares in dollars will be = [tex]4x[/tex]
The total value of shares went down by $32
So, new value of 4 shares = [tex]4x-32[/tex]
New value of each share = [tex]\frac{New\ value\ of\ total\ shares}{4}[/tex]
⇒ [tex]\frac{4x-32}{4}[/tex]
Splitting the denominators.
⇒ [tex]\frac{4x{{4}-\frac{32}}{4}[/tex]
⇒ [tex]x-8[/tex]
Original value of each share in dollars was = [tex]x[/tex]
New value of each share in dollars = [tex]x-8[/tex]
Thus, we can see that the value of each share decreased by $8.
PLEASE HELP! 20 POINTS!
What is the apparent solution to the system of equations? y=1/2x+2y=2x−1 Graph the system of equations using the Line tool. Plot a point at the apparent solution to the system using the Point tool.
Answer:
y=x/2−1/2
Step-by-step explanation:
How many 3/4 cup servings are in 12 cups of cherries?
Answer:
16 serving.
Step-by-step explanation:
Given: 3/4 cup servings.
Now, computing the number of serving in 12 cups of cherries.
Using unitary method to solve.
∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]
Number of serving in one cup is [tex]\frac{4}{3}[/tex]
Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]
Number of serving in 12 cups= [tex]16\ serving[/tex]
∴ There are 16 serving is possible in 12 cups of cherries.
Final answer:
To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.
Explanation:
To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.
First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.
Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.
To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).
The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.
solve the inequality for x: -3(2x+5) < -45
Answer:
x>5
Step-by-step explanation:
-3(2x+5)<-45
2x+5<-45/-3
2x+5<15
2x<15-5
2x<10
x<10/2
x<5
x>5
What is the point (5, -3) after a rotation of 90 degrees counterclockwise
Answer:
It would be (3,5)
Step-by-step explanation:
On a coordinate plane it would be changed in which the 2nd number becomes first & the + or - changes. Same for the first number.
Absolute value of 225
225
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Answer: 3x-x+2=4
Step-by-step explanation:
absolute value of 225 = | 225 | = 225
3x + 4x − 2x = − 76 + 96
Answer:
4
Step-by-step explanation:
first add up the xs that gives you 5x because first 3x+4x gives you 7 then minus that with 2x that gives you five,
now add the numbers -76+96 that gives you 20 now the equation becomes
5x=20
now divide 20 by 5 that gives you 4
The base of a triangle is 10 cm greater than the height. The area is 28 cm2. Find the height and the
base.