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PilotLPTM [1.2K]
2 years ago
9

Find the area of the prism 14 in. 4 in. 9in.

Mathematics
1 answer:
RSB [31]2 years ago
8 0

Answer:

504 in cubed

Step-by-step explanation:

I am assuming this is a rectangular prism, since you did not show a picture.

l x w x h

14 x 4 x 9

14 x 36

504

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Find the quadratic function y=​f(x) whose graph has a vertex ​(−3​,4​) and passes through the point ​(−7​,0). Write the function
olganol [36]

Answer:

Step-by-step explanation:

This is a parabola since a quadratic is a parabola.  The standard form for a parabola is y = ax² + bx + c

but before we do that, we will use the vertex form, since it will make our work easier at the beginning.  

First and foremost, when we plot the vertex and the given point, the vertex is higher up than is the point; that means that this parabola opens upside down, and its vertex form will be

y=-|a|(x - h)² + k

The absolute value is out in front of the a, so we know that the value of a is positive, but the quadratic itself is negative (upside down) and we will find that math takes care of that negative that needs to be out front.  So we need to solve for a by filling in the x, y, h, and k values from the point and the vertex:  x = -7, y = 0, h = -3, k = 4

0 = a(-7 - (-3))² + 4 and

0 = a(-7 + 3)² + 4 and

0 = a(-4)² + 4 and

0 = a(16) + 4 and

0 = 16a + 4 and

-4 = 16a so

a=-\frac{1}{4}

Now that we know a, we can plug it back into the vertex form and then put it into standard form from there.

y=-\frac{1}{4}(x+3)^2+4

Now we will FOIL out what's inside the parenthesis to get

y=-\frac{1}{4}(x^2+6x+9)+4

Simplify by distributing the -1/4 into the parenthesis:

y=-\frac{1}{4}x^2-\frac{3}{2}x-\frac{9}{4}+4

Combine like terms to get

y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{7}{4}

And there you go!

5 0
3 years ago
HELPPPP PLEASEEE IM BEGGING SOMEONE PLEASE PLEASE HELP
pychu [463]

Given:

The figure of a rhombus QRST.

To find:

A. The value of x.

B. The measure of angle RQP.

Solution:

A. We need to find the value of x.

We know that the diagonals of a rhombus are perpendicular bisectors. It means the angles on the intersection of diagonals are right angles.

m\angle RPS=90^\circ                       [Right angle]

(5x+15)^\circ=90^\circ

(5x+15)=90

5x=90-15

5x=75

Divide both sides by 5.

x=\dfrac{75}{5}

x=15

Therefore, the value of x is 15.

B. We need to find the measure of angle RQP.

From the given figure, it is clear that

m\angle RQP=(2x+3)^\circ

Putting x=15, we get

m\angle RQP=(2(15)+3)^\circ

m\angle RQP=(30+3)^\circ

m\angle RQP=33^\circ

Therefore, the measure of angle RQP is 33 degrees.

8 0
2 years ago
Which function BEST expresses the linear relationship displayed by the scatter plot?
Harrizon [31]

Answer:

C

Step-by-step explanation:

We want a line of best fit, which means we want to create a line that the data points will lie closest to.

One thing we can do is find the slope between the bottom-leftmost point and the top-rightmost point. This is because if we were to draw a line connecting these two, it will cut through the data quite well.

Those two points are (9, 15) and (16, 18), so the slope is change in y divided by the change in x:

(18 - 15) ÷ (16 - 9) = 3 ÷ 7 ≈ 0.4

Eliminate A and B.

Now we need to determine the y-intercept. This needs no calculations; simply look at the graph: there's no way a line cutting through the y-intercept point of (0, 18) will perfectly match the data points; instead it must be a y-intercept lower than 18. So, eliminate D.

The answer is C.

6 0
3 years ago
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Artist 52 [7]
16 because 8 rooms have 8-11, 5 rooms have 4-7, and 3 rooms have 0-3 guests.
8 0
3 years ago
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Look at the picture attached :)
Karolina [17]
I think it is B
Not sure
4 0
3 years ago
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