Please Solve this Algebraic Proof for Geometry!!
2 images attached

The equality of the respective angles and the proportionality of the corresponding sides determine if two triangles are comparable.

Triangle A: 53, 71, Triangle B: 53, 71; Similar

Triangle C: 90, 37, Triangle D: 90, 53; Similar

Triangle E: 63, 45 Triangle F:14, 71; Not similar

Triangle G, 121, Triangles H: 70, Not similar

If two of one triangle's angles are congruent with two of the

angles of a different triangle, then the two triangles are comparable.

Similarity hypothesis, angle, and AA

Given that: The interior product of the AA similarity hypothesis

The angle sum property of a triangle states that the angles of a triangle are 180°,

Consequently, the third angle is also congruent when two angles are

congruent

53, 71 in Triangle A and 53, 71 in Triangle B; similar

Based on the AA similarity postulate, the triangles are similar.

Triangles C (90, 37) and D (90, 53) have similar angles.

Supplied that the given angles are identical to each of their complimentary angles, the triangle is similar.

Triangle F: 14, 71 Triangle E: 63, 45; not comparable

There are no parallel triangles.

Triangles H: 70, not identical to Triangle G's 121,

The details are insufficient.

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The price of the jacket in decimals is $ 41.89

The decimal numeral system is widely used to express both integer and non-integer numbers.

Let the price of the jacket be x.

Price of the pair of shoes = x + 7.65

Total cost of both the pieces = x + x + 7.65 = 2x+7.65

But the total cost is $91.43

Hence forming a linear equation we get :

$91.43= 2x+7.65

solving the linear equation for x we get :

x=$ 41.89

hence the cost of the jacket is $ 41.89 .

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Answer:  36 copies per minute

Step-by-step explanation:

126 copies in 3.5 minutes

We want x number of copies per 1 minute

[tex]\frac{126copies}{3.5minutes} = \frac{xcopies}{1minute}[/tex]

Cross multiply and we get

126 = 3.5x

Solve for x.

x = 126/3.5

x = 36

36 copies per minute

Answer:

[tex]1) \:\:\: \dfrac{14x}{y}[/tex]

[tex]2) \:\:\:\dfrac{16x^2}{9y^2}[/tex]

[tex]3)\:\:\:10[/tex]

[tex]4)\:\:\:\dfrac{x-2}{x+4}[/tex]

Step-by-step explanation:

I will provide detailed explanation for the first problem and quicker steps to solve the others. You should be able to figure them out

Dividing a number(integer or fraction) by a fraction is equivalent to multiplying that number by the reciprocal of the divisor fraction

So if you have an expression
[tex]\dfrac{a}{b} \div \dfrac{c}{d}\\\\\implies \dfrac{a}{b} \times \dfrac{d}{c}[/tex]

Question 1

[tex]\dfrac{14x^5}{5y^2}\:\div \dfrac{2x^4}{10y}\\\\= \dfrac{14x^5}{5y^2} \times \dfrac{10y}{2x^4}\\\\[/tex]

[tex]=\dfrac{14x^5\cdot \:10y}{10y^2x^4}[/tex]

10 in the numerator and 10 in the denominator cancel:

[tex]=\dfrac{14x^5y}{y^2x^4}[/tex]

[tex]\dfrac{x^5}{x^4} = x^{5-4} = x \;\;\;\;\;\;\text{Since }\dfrac{x^a}{x^b}=x^{a-b}}[/tex]

Likewise

[tex]\dfrac{y}{y^2} = y^{1-2} = y ^{-1} = \dfrac{1}{y}[/tex]

Therefore
[tex]=\dfrac{14x^5\cdot \:10y}{10y^2x^4} = 14 \dfrac{x}{y} = \dfrac{14x}{y}[/tex]
Answer: Question 1

Question 2

[tex]\left(\dfrac{x}{y}\right)\left(\dfrac{4y}{3x}\right)\:\div \dfrac{6y^2}{8x^2}[/tex]

[tex]\dfrac{x}{y} \cdot \dfrac{4y}{3x} = \dfrac{4}{3}[/tex]

[tex]\dfrac{6y^2}{8x^2} = \dfrac{4y^2}{3x^2}[/tex]'

[tex]\left(\dfrac{x}{y}\right)\left(\dfrac{4y}{3x}\right)\:\div \dfrac{6y^2}{8x^2} \\\\= \dfrac{4}{3} \times \dfrac{3x^2}{4y^2}\\\\= \dfrac{16x^2}{9y^2}[/tex]

Question 3

[tex]\dfrac{\left(5\left(y+6\right)\right)}{2\left(xy-3\right)}\:\div \dfrac{\left(y\:+\:6\right)}{4\left(xy\:-\:3\right)}\\\\\\\dfrac{5(y + 6)}{2(xy-3)} \times \dfrac{4(xy-3)}{y+ 6}\\\\[/tex]

The y + 6 terms cancel out from numerator and denominator as do the xy - 3terms

[tex]= \dfrac{5}{2} \times \dfrac{4}{1}\\\\= \dfrac{20}{2} \\\\= 10[/tex]

Question 4

[tex]\dfrac{x^2-4}{x^2+5x+4}\:\div \dfrac{x+2}{x+1}\\\\=\dfrac{x^2-4}{x^2+5x+4}\:\times \dfrac{x+1}{x+2}[/tex]

[tex]x^2-4 = (x + 2)(x-2) \;\;\;\; \text{Since $a^2-b^2 = (a +b)(a-b)$}[/tex]

[tex]x^2 + 5x + 4\;\;\; \text{can be factored as: }\\\\(x + 1)(x + 4)[/tex]

Therefore
[tex]\dfrac{x^2-4}{x^2+5x+4}\:\div \dfrac{x+2}{x+1}\\\\\\=\dfrac{x^2-4}{x^2+5x+4}\:\times \dfrac{x+1}{x+2}\\\\\\= \dfrac{(x+2)(x-2)}{(x+1)(x+4)} \times \dfrac{x+1}{x+2}\\\\\\\\[/tex]

The x+2 terms cancel out as do the x + 1 terms giving the result
[tex]\dfrac{x-2}{x+4}[/tex]

Answer:

[tex]\textsf{1. \quad $\dfrac{14x}{y}$}[/tex]

[tex]\textsf{2. \quad $\dfrac{16x^3}{9y^2}$}[/tex]

[tex]\textsf{3. \quad $10$}[/tex]

[tex]\textsf{4. \quad $\dfrac{x-2}{x+4}$}[/tex]

Step-by-step explanation:

When dividing two fractions, multiply the first fraction by the reciprocal of the second fraction.  

The reciprocal of a fraction is its inverse (swap the numerator and denominator).

[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$\dfrac{a^b}{a^c}=a^{b-c}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]

[tex]\begin{aligned}\dfrac{14x^5}{5y^2} \div \dfrac{2x^4}{10y} & = \dfrac{14x^5}{5y^2} \times \dfrac{10y}{2x^4}\\\\& = \dfrac{14x^5 \times 10y}{5y^2\times 2x^4}\\\\& = \dfrac{140x^5y}{10x^4y^2}\\\\& = \dfrac{14x^5y}{x^4y^2}\\\\& = 14x^{5-4}y^{1-2}\\\\& = 14x^1y^{-1}\\\\& = \dfrac{14x}{y}\end{aligned}[/tex]

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[tex]\begin{aligned}\left(\dfrac{x}{y} \right)\left(\dfrac{4y}{3x} \right) \div \dfrac{6y^2}{8x^3}&=\dfrac{4xy}{3xy} \div \dfrac{6y^2}{8x^3}\\\\&=\dfrac{4}{3} \div \dfrac{6y^2}{8x^3}\\\\&=\dfrac{4}{3} \times \dfrac{8x^3}{6y^2}\\\\&=\dfrac{4 \times 8x^3}{3 \times 6y^2}\\\\&=\dfrac{32x^3}{18y^2}\\\\&=\dfrac{16x^3}{9y^2}\end{aligned}[/tex]

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[tex]\begin{aligned}\left[\dfrac{5(y+6)}{2(xy-3)} \right] \div \left(\dfrac{y+6}{4(xy-3)}\right) & = \left[\dfrac{5(y+6)}{2(xy-3)} \right] \times \left(\dfrac{4(xy-3)}{y+6}\right)\\\\& = \dfrac{5(y+6) \times 4(xy-3)}{2(xy-3) \times (y+6)}\\\\& = \dfrac{20(y+6)(xy-3)}{2(xy-3)(y+6)}\\\\& = \dfrac{20}{2}\\\\&=10\end{aligned}[/tex]

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Factor the numerator and denominator of the first fraction.

Apply the Difference of Two Squares to the numerator:

[tex]\implies x^2-4=x^2-2^2=(x-2)(x+2)[/tex]

Factor the denominator:

[tex]\begin{aligned}\implies x^2+5x+4 & =x^2+x+4x+4\\ & =x(x+1)+4(x+1)\\ & =(x+1)(x+4)\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\left(\dfrac{x^2-4}{x^2+5x+4}\right) \div \left( \dfrac{x+2}{x+1} \right) & = \left(\dfrac{x^2-4}{x^2+5x+4}\right) \times \left( \dfrac{x+1}{x+2} \right)\\\\& = \left( \dfrac{(x-2)(x+2)}{(x+1)(x+4)} \right) \times \left( \dfrac{x+1}{x+2} \right)\\\\& = \dfrac{(x-2)(x+2)(x+1)}{(x+1)(x+4)(x+2)}\\\\& = \dfrac{x-2}{x+4}\\\\\end{aligned}[/tex]

Answer:

Sometimes, Never, and Always.

(Sounds like a good movie title).

Step-by-step explanation:

See attached image.

[tex] \frac{v}{8} - 4 = - 12 \\ \frac{v}{8} = - 12 + 4 \\ \frac{v}{8} = - 8[/tex]

Now I will use CROSS MULTIPLICATION

[tex]v = 8( - 8) \\ v = -6 4[/tex]

ATTACHED IS THE SOLUTION

Answer: v/8 - 4 = (-12)

-12 + 4 = (-8)

what divided by 8 is 8?

8/8 = 1 so 8 x 8 = 64

this means v = -64

64/8 - 4 = -12

- 64/8 is -8 and that minus 4 is -12

Using algebra, we know that the total number of bees in her hive is 540.

So,

Then,

(A) Work out an estimate for the total number of bees in her hive

The estimated total no. of bees will be 540 bees.

Therefore, using algebra, we know that the total number of bees in her hive is 540.

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Answer:

9/25

0.36

Step-by-step explanation:

Part 1:

You divide 36 by 100 to find the fraction:

36/100

Then, simplify:

36/100 = 9/25

.................................................................................

Part 2:

To find the decimal of a percentage, divide the percent by 100. When dividing by 100, you get the answer by moving the decimal point two spaces to the left.

36% = 0.36

For a sale of $8400 made his gross pay is $373.21

In this question, we have been given Mike Lasueze is guaranteed a minimum salary of $220 per week or 5.5 percent of his total sales, whichever is greater.

We need to find his gross pay for a week in which his total sales were $8,400

weekly pay = $220

commission = 5.5% of sales

                    = 0.055 of sales

let m be the total sale and his gross pay be represented by y

So, we get an equation for the total/gross pay:

y = 0.055x + 220

Required is the gross pay y for x = 8400

y = 0.055(8400) + 220

y = 682

Therefore, for a sale of $8400 made his gross pay is $373.21

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Using percentages we can conclude that the total cost of the dinner was $65.

So, the total cost of dinner:

The tip was 25% of the dinner, then we need to find the 25% of 52 as follows:

The total cost of the diner was $52 + $13 which is $65.

Therefore, using percentages we can conclude that the total cost of the dinner was $65.

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I would tell her that out of all the people who took the verbal section, 23% scored higher than she did and 77% scored at or below her score. For the math section, 94% of those who took the exam scored at or below her score and 6% scored higher than she did.

Here's the complete question:

Suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?

I would tell her that out of all the people who took the verbal section, ___% scored higher than she did and ___ % scored at or below her score. For the math section, ___ % of those who took the exam scored at or below her score and ____ % scored higher than she did.

For the Verbal section: 100 - 77 = 23

For the Maths section: 100 - 94 = 6

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Answer:

C

Step-by-step explanation:

[tex]\frac{8}{12} \times 100 \approx 67[/tex]

Given: A table that shows the result of a survey from 35 randomly selected students at Courtney's school.

Required: To determine the number of votes Rockzilla is expected to receive from a population of 115 students at Courtney's school.

This is achieved thus:

First, we determine the probability of Rockzilla's votes as follows:

Next, we determine the number of votes Rockzilla is expected to receive as follows:

Hence, the answer is:

The original price of the jacket before sale amount is $45.

Original price of the jacket will be calculated by forming the expression relating mentioned price. Let us assume the original price of the jacket to be x.

Writing the equation representing original price, percentage and price after sale

80%×x = 36

Converting percentage to fraction

80/100×x = 36

Shifting the fraction to Right Hand Side of the equation

x = 36×100/80

Cancelling zero as it is common in numerator and denominator and performing division

x = 45

Therefore, according to the sale price, the original price of jacket is $45.

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Using proportions, the coordinates of point P that divides the directed line segment YX in the given ratio are found according to the following rule:

P - X = 3/8(Y - X).

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem relating the variables.

One example of application is for the coordinates of a point dividing a segment, as the distance between one end point and the dividing point is a fraction of the total length of the segment.

In the context of this problem, we have that point P divides segment XY in a 3:5 ratio, meaning that PX is 3/8 of the total distance y/x, hence the following proportional equation is built:

P - X = 3/8(Y - X).

In which:

This equation is used to find both the x-coordinate and the y-coordinate of P, as follows:

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The foci of the given ellipse are (D) (0, 5) and (0, -5).

So, the foci of the ellipse are:

(Refer to the graph attached below)

Therefore, the foci of the given ellipse are (D) (0, 5) and (0, -5).

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The correct question is shown below:

Which are the foci of the ellipse represented by 25x² + 16y² = 400?

A. (-3,0) and (3, 0)

B. (-5, 0) and (5, 0)

C. (0, 3) and (0, -3)

D. (0, 5) and (0, -5)

Answer:

Find the measure of each angle. 1. 23. =70°. 2. 45. 5. 24. 9.48 ... Exterior. ANGLE. ¥180-50=130. 6. 213 2106°. =106°. 44-10+42=180. 44 = 148

Step-by-step explanation:

The classification of the numbers as counterexamples of the conjecture is given as follows:

The next number in the sequence is of 256.

The conjecture is defined as follows:

"Any number divisible by 2 is also divisible by 4"

Hence the counterexamples are the numbers that are divisible by 2 but not by 4, then they are classified as follows:

Each number in the sequence is given by the multiplication of the two previous terms, as:

Then the next number is calculated as follows:

32 x 8 = 256.

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Answer:

I think it's 171.5 in^3 but not sure :)

Step-by-step explanation:

Answer:

A answer is A brainly helps you

Answer:

The answer is 5(30+2)!

The sunflower had a height of 13 inches on day 0 and 13.91 inches on day 1.

Because sunflowers are big feeders and require a slightly alkaline soil (pH 6.0 to 7.5), make sure we put them in nutrient-rich soil. Before planting, we should also make sure the soil is weed-free. Since a sunflower is cultivated in a garden, its height grows by 7% every day. The sunflower is 15.7 inches tall 2.79 days after being planted. To get the sunflower's 1-day growth factor, apply the following calculation:

X x (1 + 0.07) ^ 2.79 = 15.7

X x 1.07 ^ 2.79 = 15.7

1.2077X = 15.7

X = 15.7 / 1.2077

X = 13

13 x 1.07 = 13.91

The sunflower therefore measured 13 inches on day 0 and 13.91 inches on day 1.

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The total weight is 57kg

The perimeter = 2×(8+6)

= 2(14) = 28m

The diagonal = √8²+6²

= √64+36

100 = 10m

The total length of the frame =

28+10 = 38 m

Therefore the total Weight =

38× 1.5 kg = 57 kg

What is the formula for weight?

The force of gravity acting on an item is known as its weight, and it can be determined using the formula w = mg, which equals the mass times the acceleration of gravity.

You must multiply the sectional area, length, and density collectively to determine the weight of your metal. The product must then be divided by 1,000 in order to convert the weight to kilograms. There are several online metal weight calculators that you may use to figure out the weight of your metal product.

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Answer:

#7 m∠4 = 30°  

#8. m∠5 = 150

#22. A'(-6, -3), B'(-3, 4), C'(3, 5)
*** You may just want to put the coordinate points: (-6, -3), (-3, 4), (3, 5) without the A', B', C'. ***

#23. A'(6, -3), B'(3, 4), C'(-3, 5)

Step-by-step explanation:

#7 Angles 30° and ∠4 are corresponding angles and hence equal

#8 ∠4 and ∠5 are supplementary linear angles and add up to 180° So m∠5 = 180 - m∠4 = 180 - 30 = 150°

#22 Reflection about the x-axis means the x-coordinates do not change but the new y-coordinate is the negative of the original y coordinate

In other words, a point(x, y) in the pre-image becomes (x, -y) in the image

#23 With a 180° rotation both x and y axes change signs. (x, y) becomes (-x, -y)

Answer:

-15x - 3

I hope this helps :)

[tex]|x-4|[/tex] is non-negative, and vanishes when [tex]x=4[/tex].

For all [tex]x\in[-2,1][/tex], we have [tex]x<4[/tex], so by definition of absolute value,

[tex]g(x) = |x-4| + 8 = -(x-4)+8 = -x+4[/tex]

which is strictly decreasing on [-2, 1] since [tex]g'(x)=-1<0[/tex]. Then the minimum value of [tex]g[/tex] on [-2, 1] occurs at the endpoint [tex]x=1[/tex], so that

[tex]\min\left\{g(x) \mid -2\le x\le1\right\} = g(1) = |1-4| + 8 = \boxed{11}[/tex]

Step-by-step explanation:

the area of the parallelogram is

baseline × height.

we know the baseline (15 cm), because as parallelogram it must have 2 pays off equal sides. so, the bottom side must be 15 cm too.

15×height = 390

height = 390/15 = 26 cm

now, the height of the triangle on the right is the same height.

and the baseline of this triangle is 25 - 15 = 10 cm.

the area of a triangle is

baseline × height / 2

so, in our case

10 × 26 / 2 = 10×13 = 130 cm²

therefore the area of the trapezium is the area of the parallelogram plus the area of the triangle :

390 + 130 = 520 cm²

Answer:

x < 7/3

Step-by-step explanation:

[tex] - 5 < 9 - 6x[/tex]

[tex] - 14 < - 6x[/tex]

[tex] \frac{7}{3} > x[/tex]

[tex]x < \frac{7}{3} [/tex]

Equivalent ratios are the ratios that are the same when we compare them. Three equivalent ratios are 1/2, 4/8, 3/6 in digits from 1 to 9.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

Equivalent ratios are the ratios that are the same when we compare them.

The digits from 1 to 9 include 1,2,3,4,5,6,7,8,9.

Ratios are nothing but fractions.

Let 1/2 (one by two) is the first ratio.

Now 3/6 (three by six) is the second ratio

4/8 (four by eight) is the third ratio.

If we calculate the value of 1/2 = 0.5

The value of  3/6=1/2=0.5

The value of 4/8= 1/2=0.5

we get the same answer for all the ratios 1/2, 4/8 and 3/6 that is 0.5

That is 0.5 or 1/2.

Hence the three equivalent ratios are 1/2, 4/8, 3/6.

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