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3 years ago

1

Mathematics

1 answer:

Setler [38]3 years ago

5 0

Answer:

135 small cubes fill the prism

Step-by-step explanation:

Find the volume of the prism.

V = l * w * h

l = 2 1/4 = 2.25

w = 3/4 = 0.75

h = 1 1/4 = 1.25

V = 2.25 * 0.75 * 1.25

V = 2.109375

I wouldn't round this quite yet.

V of 1 small cube = 1/4 * 1/4 * 1/4 = .015625

So divide the volume of the prism by the volume of the small cube

2.109375/0.015625 = 135

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The circle described by the equation <img src="https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%20%2B%28y%2B4%29%5E%7B2%7D%3D9" id="T

ElenaW [278]

Answer:

The point at which center of the image circle located is (-2, -3) so second option is correct.

Step-by-step explanation:

Given equation of circle is:

$(x-3)^{2} + (y+4)^{2} = 9$ (i)

The general equation of circle is mentioned below,

$(x-h)^{2} + (y-k)^{2} = r^{2}$ (ii)

Here 'r' represents the radius of the circle and (h,k) shown the center of the circle.

By comparing equation (i) and equation (ii), we get

r^2 = 9

r = 3

$(x-3)^{2} = (x-h)^{2}$

$(x-3) = (x-h)$

$h = 3$

$(y+4)^{2} = (y-k)^{2}$

$(y+4) = (y-k)$

$k = -4$

So the center of given circle is (h,k) = (3,-4)

Also, the circle is translated 5 units left, that is towards the -x-axis. Therefore h = 3 - 5 = -2

Also, the circle is translated 1 unit up, that is towards the +y-axis. Therefore k = -4 + 1 = -3

Hence, the point at which center of the image circle located is (-2, -3) so second option is correct.

6 0

3 years ago

Read 2 more answers

Find the discriminant of the following equation. 4x2 + 12x + 9 = 0

oksano4ka [1.4K]

For
ax^2+bx+c=0
discriminatn is b^2-4ac

a=4
b=12
c=9
discriinat is
12^2-4(4)(9)=
144-144
0

the discrminat is 0

8 0

3 years ago

A mountain gorilla weighs 135 pounds and is gaining pound each week. An eastern gorilla

Tju [1.3M]

Answer:

njnnnnnnn

Step-by-step explanation:

nmkm

6 0

3 years ago

Given The following Graph: a.)Evaluate f(0). b.) Solve for f(x) = -3

dlinn [17]

Answer:

see explanation

Step-by-step explanation:

f(0) means find the value of y when x = 0

That is f(0) = 1 ← the point (0, 1) on the graph

When f(x) = - 3 means what are the values of x corresponding to y = - 3

From the graph when y = - 3 there are 2 corresponding values of x, that is

x = - 2 or x = + 2

The solution to f(x) = - 3 is x = ± 2

3 0

4 years ago

Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and thr

Sindrei [870]

Answer:

The rental rate for the Fords is of $12 per day.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the cost of a Nissan.

y is the cost of a Ford.

z is the cost of a Chevrolet.

Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.

This means that:

$3x + 2y + 4z = 106$

Two Nissans, four Fords, and three Chevrolets cost $107 per day

This means that:

$2x + 4y + 3z = 107$

Four Nissans, three Fords, and two Chevrolets cost $102 per day.

This means that:

$4x + 3y + 2z = 102$

From the first equation:

$4z = 106 - 3x - 2y$

$2z = 53 - 1.5x - y$

$z = 26.5 - 0.75x - 0.5y$

Replacing into the third equation:

$4x + 3y + 53 - 1.5x - y = 102$

$2.5x + 2y = 49$

From the second equation:

$2x + 4y + 3z = 107$

$2x = 107 - 4y - 3z$

$x = 53.5 - 2y - 1.5z$

$x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)$

$x - 1.125x = 53.5 - 2y - 39.75 + 0.75y$

$-0.125x = 13.75 - 1.25y$

$0.125x = 1.25y - 13.75$

$x = \frac{1.25y - 13.75}{0.125}$

$x = 10y - 110$

Find the rental rate for the Fords.

We have to find y, so:

$2.5x + 2y = 49$

$2.5(10y - 110) + 2y = 49$

$25y - 275 + 2y = 49$

$27y = 324$

$y = \frac{324}{27}$

$y = 12$

The rental rate for the Fords is of $12 per day.

3 0

3 years ago