Proving triangles similar

The simplified exponential function is determined as x⁴.

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

To simplify an exponential function, we will apply the rules of exponent as shown below;

The given exponential function;

= (∛ x² )⁶

The given expression is simplified as follows;

= [tex](x^2) ^{\frac{1}{3} \times 6}[/tex]

= ( x² )²

= x⁴

Thus, the simplified exponential function is determined by applying the rules of multiplication of powers.

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Answer:

For [tex]x = -2[/tex]

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = x^2 - 2x[/tex]

[tex]g(x) = 6x + 4[/tex]

[tex]f(x) + g(x) = (f+g)(x)  = x^2 - 2x + 6x + 4 = x^2 + 4x + 4[/tex]

Which is a value of x does (f+g)(x) =0

[tex]x^2 + 4x + 4[/tex]

Quadratic equation with [tex]a = 1, b = 4, c = 4[/tex]

So

[tex]\Delta = 4^{2} - 4*1*4 = 0[/tex]

[tex]x_{1} = \frac{-4 + \sqrt{0}}{2} = -2[/tex]

[tex]x_{2} = \frac{-4 - \sqrt{0}}{2} = -2[/tex]

For [tex]x = -2[/tex]

Answer:

A

Step-by-step explanation:

Answer:

x= -6 ,1

Step-by-step explanation:

B is the answer

x= -6 ,1

Answer:

Volume uses cubic ___  

A mile or kilometer is to big

So an cubic centimeter is about right

C

Answer:

0.79

Step-by-step explanation:

Answer:

139284 238

Step-by-step explanation:

Answer:

equal

alternate exterior angles

Step-by-step explanation:

The measure of given angles are equal to each other because they are alternate exterior angles,

Answer:

There is nothing.

Step-by-step explanation:

Answer:

A line that starts at with a constant positive slope

Step-by-step explanation:

Hope it makes sense!!

Answer:

PQR and RQP

Step-by-step explanation:

We name the angle by providing 3 points - the middle point needs to be the tip of the angle, the other two should lie on the sides. The order of the sides doesn't matter (unless we define it to), so both PQR and RQP are valid names for this angle.

Step-by-step explanation:

This question is very straightforward.

Angle names always has a format: angle aBc

, where the middle letter is always the angle you want to use or find the value of.

Therefore in this case, you can name the angle , as angle RQP or angle PQR.

Answer:

Both students scored in the top 10% of their classes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Top 10% = Above the 100 - 10 = 90th percentile.

The 90th percentile of scores is X when Z has a pvalue of 0.9, that is, Z = 1.28.

So, the student who had a z-score above 1.28 scored in the 90th percentile of their class.

In student A's class the mean was 78 and the standard deviation of 5. He scored 87.

We have that [tex]\mu = 78, \sigma = 5, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 78}{5}[/tex]

[tex]Z = 1.8[/tex]

1.8 > 1.28, so student A scored in the top 10% of his/her class.

Student B's class the mean was 76 with a standard deviation of 4. Scored 87.

We have that [tex]\mu = 76, \sigma = 4, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 76}{4}[/tex]

[tex]Z = 2.75[/tex]

2.75 > 1.28, so student B also scored in the top 10% of his/her class.

Both students scored in the top 10% of their classes.

Answer:

D. 11

Step-by-step explanation:

Midsegment theorem:

The length of the midsegment of a triangle is half the length of it's third side.

In this question:

Third side: 3x - 5

Midsegment: 14m

So

[tex]\frac{3x - 5}{2} = 14[/tex]

[tex]3x - 5 = 28[/tex]

[tex]3x = 33[/tex]

[tex]x = \frac{33}{3}[/tex]

[tex]x = 11[/tex]

The correct answer is given by option D.

Answer:

Step-by-step explanation: 0.5

The Wendy spent $27.78 on a silver necklace online.To calculate the total cost of the silver necklace, we need to add the cost of the necklace to the shipping and handling charges.

The cost of the necklace is given as $23.15.

Wendy bought a silver necklace online. It cost $23.15 plus 20% shipping and handling.

What was the total cost?When purchasing a silver necklace online, Wendy spent $23.15, but she had to pay for shipping and handling as well, which cost 20% of the total price of the item.

To find the total cost of the necklace, follow these steps:

1. Determine the cost of shipping and handling: $23.15 × 0.20 = $4.632

Add the cost of shipping and handling to the cost of the necklace:$23.15 + $4.63 = $27.78

The total cost of the necklace is $27.78.

It's important to consider the additional charges such as shipping and handling when calculating the total cost of an online purchase to have an accurate understanding of the amount spent.

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Answer:

They are all correct.

Step-by-step explanation:

1.

1/2(b)(h)

1/2(4)(6)

1/2(24)

12

2. l x w

7 x 5

35

3. (b)(h)

(8)(4)

32

Answer:

The answer to the question provided is 7.

Step-by-step explanation:

[tex]7x + 9 = 8x + 2 \\ \frac{ - 8x \: \: \: \: = - 8x}{ - 1x + 9 = 2 } \\ \frac{ \: \: \: \: \: \: \: \: - 9 = - 9}{ \frac{ - 1x}{ - 1} = \frac{ - 7}{ - 1} } \\ x = 7[/tex]

[I apologize if this isn't the answer]

Answer:

4/x = [tex]\frac{\pi }{6}[/tex], 5 [tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

Sorry if I am wrong

The average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].

The average Rate of Change of the function f(x) can be calculated as;

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]

The given function is f(x) = 2sin(1/2)x on the interval [0, π]

Here a = 0

b = π

f(a) = 2sin(1/2)a

f(0) = 0

f(b) = 2sin(1/2)π = 2

Step 2: Find Average

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\f(x) = \dfrac{2- 0}{\pi }\\\\f(x) = \dfrac{2}{\pi }\\[/tex]

Therefore, the average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].

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Answer:

64 m²

Step-by-step explanation:

Area of the trapezoid = ½(a + b)h

Where,

a = 6 m

b = 10 m

h = 8 m

Plug in the values

Area = ½(6 + 10)*8

Area = ½(16)*8

Area = 8*8

Area = 64 m²

Answer:478.85 in2

Step-by-step explanation:

Just divide LOL

The percentage of debit shoppers has increased.

21% (2006) < 40% (2009)

In 2006, the percentage of debit shoppers is 21%.

In 2009, the percentage of debit shoppers is 40%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

In 2006:

A sample of 200 in-store shoppers showed that 42 paid by debit card.

The percentage of debit shoppers in 2006.

= 42/200 x 100

= 42/2

= 21%

In 2009:

A sample of the same size showed that 80 were paid by debit card.

The percentage of debit shoppers in 2009.

= 80/200 x 100

= 40%

Thus,

The percentage of debit shoppers has increased.

21% (2006) < 40% (2009)

In 2006, the percentage of debit shoppers is 21%.

In 2009, the percentage of debit shoppers is 40%.

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Answer:

720 boysss

Step-by-step explanation:

Yep thts the answerrr...

Answer:

42°

Step-by-step explanation:

According to Exterior Angle Theorem,

an exterior angle of a ∆ is equal to the sum of the opposite interior angles.

So,

h+96°=138°

h=138°-96°

h=42°

Answer:

2/5 or 0.4

Step-by-step explanation:

convert -14/5 / (-7)

divide 14/5 / 7  ( two negatives equal a positive)

equals 2/5 or 0.4 in decimal

Answer:

3 for vowles and two for number

Step-by-step explanation:

I also need help on this one just need points

Answer:

6. (a-4)(a+9)

7. (3p+4)(p-2)

8. Will explain below.

9. (5b+4)(5b-4)

Step-by-step explanation:

HELLOOO IM BACK

6. -4*9 = -36 (the variable), 9-4 = 5 (a) , so a^2 +5a - 36 is fulfilled.

7. 4*-2 = -8, 4-2 = 2, so 3p^2 - 2p - 8 is fulfilled.

9. 25b^2 = (5b)^2

16 = 4^2

Using the difference of squares formula, a^2-b^2= (a+b)(a-b)

Answer:

D. 270 cm2

Step-by-step explanation:

2*(15*5 + 15*3 + 5*3) = 270 cm2

Using the context surrounding the word trough in line 9 of "Concrete Mixers," explain what a trough looks like and what it does on a concrete mixer. .

sorry I can't delete it this not answer your question

Answer:

799.99999 or 800 miles.

Step-by-step explanation:

You first need to find the conversion rate, so you divide 500 by the number representing it on the map, that being 1.7 feet. Once you've done this, you will get a conversion rate of 294. Now that you have the conversion rate, you multiply your second number, 2.72. This will give you your answer of 799.68 miles, which can be rounded up to 800 miles.

Answer:

40 square units

Step-by-step explanation:

This is a rhombus, so you multiply the two diagonals and divide by 2.

8x10÷2=40

Answer:

x=48°

Step-by-step explanation:

We two lines cross over each other, making four angles, the angles opposite each other are equal. They're called vertically opposite angles.