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3 years ago

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The diagonals of rhombus ABCD intersect at point E. The area of ABCD is 168 in If ED = 8 inches, find AC. A. 16 inches B. 21 inc

hes C. 24 inches D. 42 inches

1 answer:

ziro4ka [17]3 years ago

3 0

The answer is D) Hope I helped you out

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crimeas [40]

Answer:

The zeros are:

$x =4, x=2, x = 5$

The function has three distinct real zeros.

Hence, option (B) is true.

Step-by-step explanation:

Given the expression

$h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)$

Let us determine the zeros of the function by putting h(x) = 0 and solving the expression

$0=\left(x-4\right)^2\left(x^2-7x+10\right)$

switch sides

$\left(x-4\right)^2\left(x^2-7x+10\right)=0$

as

$x^2-7x+\:10=\left(x-2\right)\left(x-5\right)$

so

$\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0$

Using the zero factor principle

$\mathrm{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

so

$x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0$

$x =4, x=2, x = 5$

Thus, the zeros are:

$x =4, x=2, x = 5$

It is clear that there are three zeros and all the zeros are distinct real numbers.

Therefore,

The function has three distinct real zeros.

Hence, option (B) is true.

4 0

3 years ago

Find the volumes of the solids generated by revolving the triangle with vertices (2, 2), (2, 6), and (5, 6) about a) the x-a

Vesna [10]

About the $x$ -axis (washer method):

$\displaystyle\pi\int_2^5\left(6^2-\left(\frac43x-\frac23\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(20+x-x^2)\,\mathrm dx=\boxed{56\pi}$

About the $y$ -axis (shell method):

$\displaystyle2\pi\int_2^5x\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5x(5-x)\,\mathrm dx=\boxed{36\pi}$

About $x=7$ (shell method):

$\displaystyle2\pi\int_2^5(7-x)\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5(35-12x+x^2)\,\mathrm dx=\boxed{48\pi}$

About $y=2$ (washer method):

$\displaystyle\pi\int_2^5\left((6-2)^2-\left(\frac43x-\frac23-2\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(5+4x-x^2)\,\mathrm dx=\boxed{32\pi}$

7 0

3 years ago

What is the slope for y = 4 + 3x? *<br> Your answer

Leto [7]

Answer:

3

Step-by-step explanation:

5 0

2 years ago

Im not sure how to find the missing angle

LuckyWell [14K]

Answer:

Step-by-step explanation:

the question is asking for the length of the side labeled x

use Pythagoras' theorem to find that side

where c = x because c represents the hypotenuse in the theorem and x is on the hypotenuse in this problem

c = $\sqrt{a^{2} + b^{2} }$

sooo plug in a = 14 and b = 10

c = $\sqrt{14^{2} + 10^{2} }$

c = $\sqrt{196+100}$

c = $\sqrt{296}$

c= 17.20465..... ( that's the approx. length of side x in the problem )

since this is a right triangle we could use trigonometry to find the two angles use SOH CAH TOA to remember how those functions fit on the triangle.

Sin(Ф)=Opp/Hyp Cos(Ф)=Adj/Hyp Tan(Ф)=Opp/Adj

since we know the Hyp (hypotenuse) and the side adjacent will be the side with the 10 soooo...

Cos(Ф)=10/17.20465

Ф = arcCos(10/17.20465)

Ф = 54.4623° is the angle on the side with 10

the side with 14 then has an angle of 35.5376°

:)

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3 years ago

How to write "360.124" in expanded.and exponential

weeeeeb [17]

Answer:

360.124 in expanded and exponential form :

300+60+1/10+2/100+4/1000

6 0

3 years ago