Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)
We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.
Hence the area is
[tex]\dfrac{x(y+z)}2[/tex]
(which is identical to what you have).
graph x=4y , x+y=7.0
Answer:
First find the x and y intercepts. Recall that intercepts intersect the x and y axis of a graph, therefore either the x or y value of a coordinate point must be 0 in order for it to be an intercept.
After you find the intercept, plot the them on the cartesian coordinate system and draw a straight line (it’s a linear equation) going through the two intercepts.
Side note: Not sure how credentials work on Quora yet. I meant to say I am a student
The equation of the lines can be plotted on the graph after calculating the coordinates on each line.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two linear equation:
x = 4y
x + y = 7.0
To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.
For the equation of line:
x = 4y
x 0 1 2 3 -1 -2 -3
y 0 4 8 12 -4 -8 -12
For the equation of line:
x + y = 7.0
x 0 1 2 3 -1 -2 -3
y 7 6 5 4 8 9 10
Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.
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evaluate question 3 only
Step-by-step explanation:
(4²-x²)³/²
or,(4+X) (4-X)
Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to
[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]
Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and
[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]
(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])
So, the integral we want transforms to
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]
Expand the integrand using the identity
[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]
to write
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]
Now integrate to get
[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]
Recall the double angle identity,
[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]
[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]
By the Pythagorean identity,
[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]
Finally, put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]
h(x)=x²-5
Find h(-7)
Simplify your answer.
Answer:
h(-7) = 44
Step-by-step explanation:
h(x) = h (-7) means x= -7
h(x) = (-7)² - 5
49 - 5
44
what is the domain of the ordered pair shown in the graph?
Answer:
D.
Step-by-step explanation:
It is the only one that contains all the x-values of the points. (Domain is the set of x-values).
y 2 +2y+1 Identify a= b= c= Factor m= Factor n= Factored Form :
Answer:
a = 1
b = 2
c = 1
Factored form: (y + 1)^2 or (y + 1)(y + 1)
Step-by-step explanation:
Using the diagram, if angle 3 + angle 4 is a straight line then what is the total
measure?
Answer: 180 degrees
Step-by-step explanation:
Angles on a line add to 180 degrees since they form a straight angle.
Match each fraction to a reasonable estimate.
(-6/11)
(-7/9)
(-3/13)
(-1/4)
(-3/4)
(-1/2)
Which one goes with each?
Answer:
-6/11 goes with -1/2
-7/9 goes with -3/4
-3/13 goes with -1/4
Step-by-step explanation:
6/11 is close to 6/12 which is the same as 1/2, so -6/11 goes with -1/2
7/9 is close to 6.75/9 which is 3/4, so -7/9 is close to -3/4
3/13 is close to 3/12 which is the same as 1/4, so -3/13 goes with -1/4
Need help with number 2 please!!!
Answer:
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Step-by-step explanation:
The graph of function f(x) is the parent function.
(Parent functions are the simplest form of a given family of functions).
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=x^3[/tex]
Step 1
Multiply the parent function by 6:
[tex]\implies 6f(x)=6x^3[/tex]
Therefore, this is a vertical stretch by a factor of 6.
Step 2
Now make the function negative:
[tex]\implies -6f(x)=-6x^3[/tex]
Therefore, this is a reflection in the x-axis.
Step 3
Finally, add 2 to the function:
[tex]\implies -6f(x)+2=-6x^3+2[/tex]
Therefore, the function has been translated 2 units up.
Conclusion
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
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Given (x – 7)2 = 36, select the values of x.
Answer:
x = 25
Step-by-step explanation:
Solve by isolating x:
(x-7)2 = 36
x-7 = 18
x = 25
A sample of size 400 was drawn and sample mean was found t
be 99. Test whether this sample could have come from a normal
population with mean 100 and variance 64 at 5%
significance.
Answer:
etrf4f3dvef3rf3rfr2wrgwrf2rg3rf3rgerferferfef I'm
Solve for x in the inequality |2x + 5| ≤ 11. (If this is an "and" inequality, give your answer as a single compound inequality. If this is an "or" inequality, separate your answers using a comma.) Solve for x in the inequality | 2x + 5 | ≤ 11. ( If this is an " and " inequality , give your answer as a single compound inequality . If this is an " or " inequality , separate your answers using a comma . )
|2x + 5| ≤ 11
x = 3
2(3) + 5
6 + 5
11 ≤ 11
The solution for the x in the inequality |2x + 5| ≤ 11 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3}
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
|2x + 5| ≤ 11
To find the solution for the x, solve the inequality,
|2x + 5| ≤ 11
-11 ≤ 2x + 5 ≤ 11
Subtract 5 from whole the expression,
-11 - 5 ≤ 2x + 5 - 5 ≤ 11 - 5
-16 ≤ 2x ≤ 6
-8 ≤ x ≤ 3
The value of x for the given inequality varies from -8 to 3.
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Find the midpoint of the line segment whose endpoints are given. (9,3), (10,- 10)
Answer:
Step-by-step explanation:
(xm , ym ) = x1 + x2 / 2 and y1 + y2 / 2
= 9 +3 / 2 = 10 -10 / 2
= 12/2 = 0/2
= 6 = 0
So midpoints are (6 , 0)
Answer:
midpoint = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Step-by-step explanation:
To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.
• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]
= [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]
= [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]
= [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Two buses leave a station at the same time and travel in opposite directions. One bus travels12m/hrslower than the other. If the two buses are 765 miles apart after 6 hours, what is the rate of each bus?
distance = speed * time
the first bus speed = x
second bus = x - 12
the sum of distance = 765 miles
first distance = 6x
second distance = 6 (x -12)
6x + 6(x-12) = 765
x + x -12 = 127.5
2x = 139.5
x = 69.75 mi/h which is the faster bus
the second bus speed = 57.75 mi/h
Steve bought a new car for $22,000 but paid 93% of the list price. How much was the list price
Answer:
approximately $23,655.91 (rounded to the nearest hundredths place)
Step-by-step explanation:
[tex]22,000=0.93x\\x=23,655.91[/tex]
Answer:
Step-by-step explanation:
let the list price=x
93% of x=22,000
x=22,000 ×100/93
≈23,655.91 $
what is the fourth term in the binomial expansion (a+b)^6)
Answer:
[tex]20a^3b^3[/tex]
Step-by-step explanation:
Binomial Series
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
Therefore, the fourth term in the binomial expansion (a + b)⁶ is:
[tex]\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3[/tex]
[tex]\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3[/tex]
[tex]\implies \dfrac{6!}{3!3!}a^{3}b^3[/tex]
[tex]\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3[/tex]
[tex]\implies \left(\dfrac{120}{6}\right)a^{3}b^3[/tex]
[tex]\implies 20a^3b^3[/tex]
Suppose that prices of recently sold homes in one neighborhood have a mean of $220,000 with a standard deviation of $7450. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $197,650 and $242,350? Round your answer to one decimal place.
The minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.
What is Mean ?Mean is the ratio of the sum of all the data points to the number of data points.
It is given that
mean of $220,000 with a standard deviation of $7450.
The range is given , let the range is represented by x - --y
It is given that x = 197650 and y = 242350
Let the number of homes sold is k
To determine the value of k
upper level = (y-mean)/standard deviation = (242350-220000)/7450 = 3
lower level = (mean-x)/standard deviation = (220000-197650)/7450 = 3
probability = 1-(1/k²)
k= 3
= 1 - (1/3^2)
= 1 - 1/9
= 0.889 or 88.9%
So, the minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.
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Which expression can be used to calculateof formalin needed make this batch of 3200 pd the amount? The batch sugar 3% water 39% formalin 44% melamine 14% total 100 amount of pounds equal 3200
The appropriate expression to identify the amount of formalin is: x = 3200 ÷ 100 × 44%
How to identify the amount of formalin?To calculate the amount of formalin in this substance we must perform the following mathematical operation:
3200 ÷ 100 = 3232 × 44% = 1,408According to the above, the mathematical expression would be:
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−3x(4x² − 81) (x² + 64) = 0
Answer: [tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]-3x(4x^2-81)(x^2+64)=0\\[/tex]
multiply the terms together
[tex]-12x^5-525x^3+15552x=0[/tex]
factor left side of the equation
[tex]3x(-x^2-64)(2x+9)(2x-9)=0[/tex]
set factors equal to 0
[tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]
Which of the following best describes the slope of the line below?
A. Negative
B. Undefined
C. Positive
D. Zero
PLEASE HELP
Answer:
A. negative
Step-by-step explanation:
It is clear from the accompanying graph that the value of y decreases as the value of x grows. The line has a negative slope, and the right answer is C, as shown by the inverse connection between the values of x and y.
Reasoning for other incorrect options:
The slope is positive if the connection between x and y is positive (y rises as x rises, and vice versa). As a result, choice A is incorrect.It is an undefined slope if the value of y varies without the value of x changing. A horizontal line is used to symbolize it. Option B is thus untrue.The slope of a line is zero and is determined by a vertical line if the value of x varies but the value of y stays the same. So, the option D is incorrect.If slope is denoted by m, then the line with various slopes is depicted in the picture below.Wei Xun bought 8 pieces of chocolates and 10 lollipops for $17. The average price of a piece of chocolate was S$1. What was the average price of a lollipop?
Answer:
$0.90
Step-by-step explanation:
If each piece of chocolate is $1, then 8 pieces is $8. Wei Xun bought 8 pieces of chocolate and 10 lollipops, which came out to $17. The chocolate was $8 total, leaving $9 for the 10 lollipops. 9/10 = 0.9. So, each lollipop was $0.90, or 90 cents.
A consultant needs to make at least $600 this week. She earns $120 for each
new written piece and $60 for each review. Which of the following inequalities
represents the possible combinations of reviews and new written pieces that
she must complete?
OA. 120x+60 y ≤ 600
OB. 120x+60y < 600
O C. 120x+60y 2 600
OD. 120x+60y > 600
SUBMIT
Find the missing side of this right
triangle.
19
X
X =
16
✓[?]
Answer:
x = sqrt(105)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
16^2 + x^2 = 19^2
256 + x^2 = 361
x^2 = 361 -256
x^2 =105
Take the square root of each side
sqrt(x^2) = sqrt(105)
x = sqrt(105)
See photo for questions.
Answer:
1. "a" [tex]u'=6x[/tex]
2. "d" [tex]v'=15x^2[/tex]
3. "b" [tex]y'=75x^4+30x^2+6x[/tex]
Step-by-step explanation:
General outline:For parts 1 & 2, apply power ruleFor part 3, apply product rulePart 1.
Given [tex]u=3x^2+2[/tex], find [tex]\frac{du}{dx} \text{ or } u'[/tex].
[tex]u=3x^2+2[/tex]
Apply a derivative to both sides...
[tex]u'=(3x^2+2)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]u'=(3x^2)'+(2)'[/tex]
Scalars factor out of derivatives...
[tex]u'=3(x^2)'+(2)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]u'=3(2x)+0[/tex]
Simplify...
[tex]u'=6x[/tex]
So, option "a"
Part 2.
Given [tex]v=5x^3+1[/tex], find [tex]\frac{dv}{dx} \text{ or } v'[/tex].
[tex]v=5x^3+1[/tex]
Apply a derivative to both sides...
[tex]v'=(5x^3+1)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]v'=(5x^3)'+(1)'[/tex]
Scalars factor out of derivatives...
[tex]v'=5(x^3)'+(1)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]v'=5(3x^2)+0[/tex]
Simplify...
[tex]v'=15x^2[/tex]
So, option "d"
Part 3.
Given [tex]y=(3x^2+2)(5x^3+1)[/tex]
[tex]\text{Then if } u=3x^2+2 \text{ and } v=5x^3+1, y=u*v[/tex]
To find [tex]\frac{dy}{dx} \text{ or } y'[/tex], recall the product rule: [tex]y'=uv'+u'v[/tex]
[tex]y'=uv'+u'v[/tex]
Substituting the expressions found from above...
[tex]y'=(3x^2+2)(15x^2)+(6x)(5x^3+1)[/tex]
Apply the distributive property...
[tex]y'=(45x^4+30x^2)+(30x^4+6x)[/tex]
Use the associative and commutative property of addition to combine like terms, and rewrite in descending order:
[tex]y'=75x^4+30x^2+6x[/tex]
So, option "b"
The admission fee at a local zoo is $1.50 for children and $5.00 for adults. On a certain day, 3000 people enter the zoo and $9, 400.00 is collected. How many children and how many adults attended?
1600 children and 1400 adults attended
How to determine the number of adults?Let the children be x and adult be y.
So, we have the following equations:
x + y = 3000
1.5x + 5y = 9400
Make x the subject in x + y = 3000
x = 3000 - y
Substitute x = 3000 - y in 1.5x + 5y = 9400
1.5(3000 - y) + 5y = 9400
Expand
4500 - 1.5y + 5y = 9400
Evaluate the like terms
3.5y = 4900
Divide both sides by 3.5
y = 1400
Substitute y = 1400 in x = 3000 - y
x = 3000 - 1400
Evaluate
x = 1600
Hence, 1600 children and 1400 adults attended
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(1 point)Let S be the part of the plane 2x+2y+z= 1 which lies in the first octant, oriented upward. Find the flux of the vector field
F = 2i+2j + 2k across the surface S.
The flux is 9.
What is Flux?Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.
Given:
2x+2y+z= 1
F = 2i+2j + 2k
Now,
r = xi + yj + z( 1-2x-2y) K
dr/dx= i - 2k
dr/dy = j-2k
dr/dx* dr/dy
= ( i - 2k) * (j-2k)
= 2i + 2j + k
F(x)= 2i+2j + 2k
F(x). da = 4 +4 +2 = 10 dxdy
Hence, flux
= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]
= [tex]\int\limits^1_0[/tex] 10(1-2y) dx
= [tex]\int\limits^1_0[/tex] 10-2y
= 10(1) - (1)²
=9
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The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function
[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization
[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]
where [tex]p_i[/tex] denote the given points.)
The normal vector to [tex]S[/tex] is
[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]
Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,
[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]
[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]
julie ran a race 2 minutes faster than teri did. if teri ran the race in 28 minutes, what equation would be used to find the number of minutes teri took to run the race
Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.
How many minutes did it take Teri to run the race?Addition is a mathematical operation that is used to determine the sum of two or more numbers.
The total minutes run by Julie = minutes ran by Teri + 2
28 = m + 2
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Need help with Graphs. please help!!
The ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5
Median weekly earningsThe median weekly earnings on the graphs are
High school diploma = $750Bachelor's degree = $1250Represent as a ratio
Ratio = $750 : $1250
Divide by 250
Ratio = 3 : 5
Hence, the ratio of the median weekly earnings is 3 : 5
The ratio of the area in graph AIn (a), we have:
Ratio = 3 : 5
The horizontal scale is given as:
Ratio = 1 unit : 1 grid mark
The rectangles in graph A have a width of 1 unit.
So, we have:
Ratio = 3 * 1: 5 * 1
Ratio = 3 : 5
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5
The ratio of the area in graph BRecall that:
Ratio = 3 : 5
Ratio = 1 unit : 1 grid mark
From the graph, we have the following widths:
Red = 3 units
Blue = 5 units
So, we have:
Ratio = 3 * 3 : 5 * 5
Simplify
Ratio = 9 : 25
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25
The ratio of the volume in graph CRecall that:
Ratio = 3 : 5
Ratio = 1 unit : 1 grid mark
From the graph, we have the following widths:
Red = 3 units
Blue = 5 units
Since the base are squares, we have:
Ratio = 3 * 3 * 3 : 5 * 5 * 5
Simplify
Ratio = 27 : 125
Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125
The most misleading graphThe most misleading graph is graph B.
This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
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consider the parabola given by the equation:
f(x)=2x^2+12-9
find the following for this parabola:
a) the vertex
b) the vertical intercept is the point
c) find the coordinates of the two x-intercept of the parabola and write them as a list, separated by commas
Answer:
First simply it as 2x²+3
(a) vertex (0,3)
(b)f(0)=3
(c) no x-intercept
How many solutions exist for the given equation?
3(x - 2) = 22 -x
Answer:
One solution
Step-by-step explanation:
The equation can be rewrite as 3x - 6 = 22 - x
so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7
Mountain Climbing Gym has a gym registration fee of $30 and then charges $55 per month for all access climbing.
Susie wanted to model what she has spent in total on the climbing gym at any given month in the future.
Fill in the blanks for the equation if C = total Cost and m = number of months.
Answer:
C=55m + 30
Step-by-step explanation:
You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.
