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2 years ago

Pls help me, and do not send links. Thanks

Mathematics

1 answer:

ipn [44]2 years ago

8 0

i uploaded a vid on this here

https://www.you tube.com/watch?v=dQw4w9WgXcQ

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The volume of a rectangular prism is b3 + 8b2 + 19b + 12 cubic units, and its height is b + 3 units. The area of the base of the

omeli [17]

Given:

The volume of the rectangular prism is

$b^{3}+8 b^{2} +19b+12$ ,

the height is h=(b+3)

1. The volume of a rectangular prism is (base area)*height

also, notice that the volume is a third degree polynomial, the height is a 1st degree polynomial, so the base area must be a 2nd degree polynomial, whose coefficients we don't know yet.
Let this quadratic polynomial be $(mb^{2}+nb+k)$

2

$b^{3}+8 b^{2} +19b+12=(mb^{2}+nb+k)*(b+3)$

notice that $b^{3}$ is the product of the largest 2 terms: $mb^{2}$ and b, so m must be 1

also, notice that 12 is the product of the constants, k and 3

so k*3=12, this means k=4

3
we write the above equality again:

$b^{3}+8 b^{2} +19b+12=(b^{2}+nb+4)*(b+3)$

$(b^{2}+nb+4)(b+3)= b^{3}+3 b^{2} +nb^{2}+3nb+4b+12$

= $= b^{3}+(n+3)b^{2}+(3n+4)b+12$

4
now compare the coefficient with the left side:

$8 b^{2}=(n+3)b^{2}$

8=n+3

n=5

substituting n=5:

the base area is $b^{2}+5b+4$

Answer: $b^{2}+5b+4$

3 0

2 years ago

2. One angle is one less than six times the measure of

Illusion [34]

The equations used to find the measure of each angle in degrees is x + y = 90 and x = 6y - 1

The two complementary angles are 77 degrees and 13 degrees

<em><u>Solution:</u></em>

Given that two angles are complementary angles

Complementary angles are two angles whose sum is 90 degrees

Let one of the angle be "x" and the other angle be "y"

Therefore,

x + y = 90 ------ eqn 1

Also given that,

One angle is one less than six times the measure of another

one angle = six times the other angle - 1

x = 6y - 1 ------ eqn 2

Substitute eqn 2 in eqn 1

6y - 1 + y = 90

Thus the above equation is used to find the measure of each angle in degrees

Solve the above equation

6y + y - 1 = 90

7y - 1 = 90

7y = 91

y = 13

Substitute y = 13 in eqn 2

x = 6(13) - 1

x = 78 - 1

x = 77

Thus the two complementary angles are 77 degrees and 13 degrees

8 0

3 years ago

How much red paint and blue paint do you use to make 20 cups of purple paint?

Iteru [2.4K]

Answer:

To get 20 cups of purple paint, the table shows that we need 8 cups of blue paint and 12 cups of red paint. We can solve the problem using double (or triple) number lines.

7 0

2 years ago

How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution

AveGali [126]

Answer:

One

Step-by-step explanation:

It is given that,

y = 3x-5 ....(1)

y = -x+4 .....(2)

We can solve the above equations using substitution method. Put the value of y from equation (1) to equation (2) such that,

$3x-5 = -x+4\\\\3x+x = 5+4\\\\4x = 9\\\\x=\dfrac{9}{4}$