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2 years ago

I have this problem in Algebra that I cannot figure out :(

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

8 0

The answer is -4

Solution:

f(x) = 3x - 7
g(x) = 2x^2 - 3x + 1

(fog)(0)

= f(2(0)^2 - 3(0) + 1)
= f(2x^2 - 3x + 1)
= f(1)

= 3x - 7
= 3(1) - 7
= -4

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A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.

melisa1 [442]

Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.

$\overline{OB}:\overline{AB} = 1:2$
$\overline {OB}:10 = 1:2$
$\overline{OB} = \frac{1}{2}(10) = 5$

Similarly, we have

$\overline{AO}:\overline{AB} = \sqrt{3}:2$
$\overline {AO}:10 = \sqrt{3}:2$
$\overline{AO} = \frac{\sqrt{3}}{2}(10) = 5\sqrt{3}$

Now, to find the lengths of the diagonals,

$\overline{AD} = 2(\overline{AO}) = 10\sqrt{3}$
$\overline{BC} = 2(\overline{OB}) = 10$

So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units

8 0

3 years ago

Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins

Zanzabum

The expression Hallie wrote is not clear, because if 0 is the only number that satisfies p = 4l + 4w + 4h = l + w + h.

But if you meant to write:

p = 4l + 4w + 4h

p/4 = l + w + h

then she could get something different.

Answer:

The expression (w + h) + p/4 should follow the subtraction if Hallie's equation is

p = 4l + 4w + 4h

p/4 = l + w + h

h = -

Step-by-step explanation:

Let us solve Hallie's problem.

She can use the equation:

p = 4l + 4w + 4h

to determine the sum of the lengths of the edges of a rectangular prism. Because she begin to solve the equation for h, let us solve for h.

This means we are trying to make h the subject of the formula.

p = 4l + 4w + 4h

When you factor out 4 on the right hand side, you have

p = 4(l + w + h)

Dividing both side by 4, we have

p/4 = l + w + h

Now, subtracting (l + w) from both sides, we have

p/4 - (l + w) = h.

This can be written as:

h = - (l + w) + p/4

And that is what Hallie wanted to obtain.

7 0

3 years ago

Read 2 more answers

The distance from Neptune to Mars is 4.272\times 10^{9}4.272×10 9 kilometers. How long would it take a rocket, traveling at 4.8\

just olya [345]

The time taken is $8.9 * 10^4hrs


$

<h3>Distances</h3>

Given the following information:

Distance from Neptune to Mars = $4.272\times 10^{9}$
Time is taken = $4.8\times 10^{4}km/hr$

Get the time taken:

Time = Distance/Speed

Time = $\frac{4.272\times10^9}{4.8\times 10^4}$

Time = 0.89 * 10^5

Time = 8.9 * 10^4hrs

Hence the time taken is $8.9 * 10^4hrs


$

Learn more on distance here: brainly.com/question/4931057

6 0

2 years ago

What is the highest common factor of 72 and 90

Zina [86]

Answer:

Step-by-step explanation:

5 0

2 years ago

Parallelogram R S T U is shown. Angle S is 70 degrees.

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

The opposite angles of the parallelogram are the same.

From the diagram;

<S = <U and <R = <T

Given

<S = 70°

Since <S = <U, hence <U = 70°

Since the sum of angles in a quadrilateral is 360 degrees, hence;

<R+<S+<T+<U = 360

Since <R = <T, then;

<Y+<S+<T+<U = 360

2<T + 70+70 = 360

2<T = 360-140

2<T = 220

<T = 220/2

<T = 110°

Since <T = <R, then < R = 110°

Hence m∠R = 110°, m∠T = 110°, m∠U = 70°. Option B is correct

4 0

3 years ago

Read 2 more answers