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3 years ago

Find the quotient when x2 + 10x + 21 is divided by x + 7

Mathematics

1 answer:

Alja [10]3 years ago

5 0

Answer:

The quotient is $x+3$

Step-by-step explanation:

We first use the remainder theorem to determine whether $x+7$ is divisible by

$x^2+10x+21$ :

$(-7)^2+10(-7)+21\\ = 49 - 70+21 = 0$

the remainder is zero which means $x^2+10x+21$ is divisible by $x+7$ .

Now, we could do polynomial long division to find the quotient, but in this case, it turns out that guessing is easier.

$x^2+10x+21$

is factored as

$x^2+10x+21 = (x+7)(x+3)$

which means

$\dfrac{x^2+10x+21}{x+7} =(x+3)$

which means the quotient is $x+3.$

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1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an

Musya8 [376]

Given:

• AB = 6 cm

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

$\begin{gathered} AM=\sqrt{AB^2-BM^2} \\ \\ AM=\sqrt{6^2-3^2} \\ \\ AM=\sqrt{36-9} \\ \\ AM=\sqrt{27} \\ \\ AM=5.2\text{ cm} \end{gathered}$

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

$SO=\sqrt{SM^2-MO^2}$

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

$\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\ \\ SO=\sqrt{15-6.76} \\ \\ SO=2.9\text{ cm} \end{gathered}$

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

$A=\frac{1}{2}*BC*AM$

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*6^*5.2 \\ \\ A=15.6\text{ cm}^2 \end{gathered}$

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

$SA=\frac{1}{2}*p*h$

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\ \\ A=34.86\text{ cm}^2 \end{gathered}$

• (5). Total surface area:

To find the total surface area, apply the formula:

$TSA=base\text{ area + area of side surface}$

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

$V=\frac{1}{3}*area\text{ of base *height}$

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

$\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\ \\ V=15.08\text{ cm}^3 \end{gathered}$

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

• 2.) 2.9 cm

• 3.) 15.6 cm²

• 4.) 34.86 cm²

• (5). 50.46 cm²

• 6). 15.08 cm³.

7 0

1 year ago

Find the value of x that makes m||n

beks73 [17]

Answer:

x = 6

Step-by-step explanation:

In order for m to be parallel to n 16x - 6 would have to equal 90. We can demonstrate that using an equation.

16x - 6 = 90

Let's solve for x:

First add 6 to both sides to isolate the 16x:

16x - 6 + 6 = 90 + 6

16x = 96

Now divide both sides by 16 to isolate the x:

16x/16 = 96/16

x = 6

The value of x has to be 6 in order for m to be parallel to n.

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3 years ago

A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per

aleksley [76]

The volume of a rectangular prism is given by
area of base × height
The rate at which the tank is being filled is 1 liter per minute which we need to convert
1 liter = 1 dm³
But 1 dm = 10 cm. Hence
1 liter = (10 cm)³ = 1000 cm³
The height h of the water is related to the volume by
volume = area of base × h
In one minute the volume increases by 1 liter or 1000 cm³ and the height increases by
h = volume / area of base = 1000 cm³ / 100 cm² = 10 cm <span>
</span>

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3 years ago

The perimeter of a rectangle is 72. The width is 4 less than the length.

likoan [24]

Answer:

The perimeter =72

The width = 16

The length = 20

Step-by-step explanation:

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3 years ago

What is a constant of proportionality? What does the constant of proportionality tell me?

asambeis [7]

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