Question

Help please❤️❤️❤️ Urgently I’m crying and panicking so plz help with my math

Answer 1

Step-by-step explanation:

1. In fully simplified form, $(16c^9d^{-6})^{\frac{1}{2}}(3c^{-1}d^5)^2$ is equivalent to

First, we can remove the exponents outside of each set of parenthesis. Recall that when you have exponents inside the parenthesis and an exponent on the outside, you can multiply the powers to remove the parenthesis.

$(16c^9d^{-6})^{\frac{1}{2}}(3c^{-1}d^5)^2\\\\(\sqrt{16}c^{\frac{9}{2}}d^{-3})(9c^{-2}d^{10})$

Now we can combine like terms. Recall that when you multiply two powers with the same base, you add the powers.

$(4c^{\frac{9}{2}})(9c^{-2})(d^{-3})(d^{10})\\\\36c^{\frac{5}{2}}d^7$

So our answer is B.

2. In fully factored form $-3x^3-3x^2+126x$ is equivalent to $-3x(x-A)(x+B)$. One of the correct factors is

First, we need to factor out $-3x$ from this expression

$-3x^3-3x^2+126x\\\\-3x(x^2-x-42)$

Now, we need to factor the expression $x^2-x-42$

This means that we are looking for two numbers that add together to get -1 and multiply to get -42. These two numbers would be 6 and -7.

This means that the factored form is

$(x-7)(x+6)$

So our fully factored form would be

$-3x(x-7)(x+6)$

So our answer is B.

3. The Chrysler Building is 319 metres tall. An artist is looking to draw a scale drawing of the Chrysler Building at a scale of 1: 5000. How tall should she draw the Chrysler Building?

From this problem, we can set up the following proportion:

$\frac{319}{5000}=\frac{h}{1}$

This means that

$h=0.0638$ meters.

We have to move the decimal 2 places, which means that we have to modify the units as well. This means that our units become millimetres.

This gives us

$h=6.38$ mm

The last thing we need to do is round this number. As 8 is larger than 5, we can round the 3 to a 4.

This gives us our answer of

$h=6.4$ mm

So our answer is D.

4. The cube has a surface area of $3313.5$ $cm^2$. The volume of the cube, to the nearest cubic centimeter, is

The equation for the surface area of a cube is

$s_a=6s^2$

This means that we can solve for the side length of the cube, s.

$6s^2=3313.5\\\\s^2=552.25\\\\s=\sqrt{552.25}\\\\s=23.5$

Recall that the volume of a cube is

$v=s^3$

This means that

$v=(23.5)^3\\\\v=12977.875$

When rounded to the nearest cubic centimeter, this value becomes

$v=12978$ $cm^3$

So our answer is B.

5. The area of the shaded region above can be written as which of the following polynomial expressions?

The area of this shaded region is everything within the rectangle that is not within the smaller rectangle. This means that we can take the difference of the area of each to find our answer.

Let us begin with finding the area of the larger rectangle. As the area of a rectangle is equal to the length multiplied by the width, the area of the rectangle would be

$(4x+3)(4x-5)\\\\16x^2-8x-15$

And now for the area of the smaller rectangle

$(3x)(2x-3)\\\\6x^2-9x$

Now, we can take the difference of each of these equations

$(16x^2-8x-15)-(6x^2-9x)\\\\16x^2-8x-15-6x^2+9x\\\\10x^2+x-15$

So our answer is B.