What other congruence is needed to prove that △QRP≅△QFP by ASA?
QR≅QF
∠R≅∠F
∠QPR≅∠QPF
PR≅PF

Answer:

2.5

Step-by-step explanation:

We Know

You buy 4 5/8 blue fabric and 2 1/8 green fabric .

4 5/8 = 37/8 = 4.625 blue fabric

2 1/8 = 17/8 = 2.125 green fabric

How much blue than green did you buy?

We Take

4.625 - 2.125 = 2.5

So, you buy 2.5 blue more than green.

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

Answer:

a = 2; b = -1; and c = 3

Step-by-step explanation:

Please see attached image for the step by step answer

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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5a⁶ x e⁷

Answer:

5/2

Step-by-step explanation:

Answer:

The prime factorization of the number 24 is 2 × 2 × 2 × 3.

Answer: 24

Step-by-step explanation:2x2x2x3 is 24

Answer:

Around 0.40

Step-by-step explanation

If she doubles the gift every year, do 18x2=36, 36 rounds to 40 or 0.40.

The total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is  evaluated as 2621.43 dollars

Lets suppose the geometric sequence has its initial term is \(a\), multiplication factor is  r, then, its sum is given as:

\(S_n = \dfrac{a(r^n-1)}{r-1}\)

(sum till nth term)

The sequence would look like \(a, ar, \cdots, ar^{n-1},\cdots\)

For this case, we are specified that:

That shows that the gift amounts each year will form a geometric sequence where a = 1, and r = 2 (as amounts are doubled).

The gift amounts would look like:

\(\\1, 2, 4, \cdots\\or\\1, 2\times 1, 2^2 \times 1, \cdots\)

We have to find these terms' sum till 18th term(18th term is the gift of her 18th birthday).

Thus, we have: n = 18, a = 1, and r = 2.

The sum will be:

\(S_n = \dfrac{a(r^n-1)}{r-1} = \dfrac{1(2^{18}-1)}{2-1} = 2^{18} - 1 = 262143 \: \rm cents\)

There are 100 cents in 1 dollars,

Thus, 1 cent = 0.01 dollars,

and thus, 262143 cents form 2621.43 dollars.

Thus, the total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is  evaluated as 2621.43 dollars

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Answer:

pluto, rhea, theres more but theres a lot but we call them planetoids

Step-by-step explanation:

Answe:

Haumea, Pluto, and Makemake

Step-by-step explanation:

i think

Answer:

m<M= 85° m<N= 85°

Step-by-step explanation:

To find the value of x we should...

Sum of all angles = 360°

95+95+10x-5+8x+13 = 360

198+18x = 360

18x = 360-198

18x = 162

x = 162÷18

x = 9

m<M = (10×9)-5 = 90-5 = 85°

m<N = (8×9)+13 = 72+13 = 85°

PLZZZ MARK ME AS BRAINLIEST PLZZZ

Answer:

x = 9

∠M = 85°

∠N = 85°

Step-by-step explanation:

360 = 95 + 95 + (10x-5) + (8x + 13)

reduce:

18x = 162

x = 9

∠M = 85°

∠N = 85°

The 95% confidence interval for the difference between the two proportions is (0.056, 0.164)

Here, we are given that from the sample information for people under 18-

n₁  =  500

x₁ =  180

⇒ p₁  =  180/ 500    

p₁  =  0.36    

then,  

q₁  =  1 -  p₁    

q₁ =  0.64

Similarly, from the sample information for people over 18, we have-

n₂  =  600

x₂  =  150

⇒ p₂  =  150 / 600  

p₂ =  0,25  

then,

q₂  =  1 - p₂  

q₂ =  1 - 0.25  

q₂ = 0,75

Now, we conduct a hypothesis test as follows-

Null hypothesis (H₀) ⇒  p₁  =  p₂

Alternative Hypothesis (Hₐ) ⇒ p₁  ≠  p₂

Confidence interval =  95 %    

⇒ significance level (α) = 5 %  

α  =  0.05  

and α/ 2  =  0.025  

⇒ z at 95% significance level = 1.96 (from z tables)

Now, we calculate z statistic-

z(s)  =  (p₁ - p₂) / EED

EED = √[(p₁*q₁)n₁  +  (p₂*q₂)/n₂]

EED = √[( 0.36*0.64)/500  +  (0.25*0.75)/600]

EED = √[0.00046  +  0.0003125]

EED = 0.028

and (p₁  -  p₂) = 0.36 - 0.25  

= 0.11

Therefore,

z(s)  =  0.11 / 0.028

z(s) = 3.93

we can see that  z(s) > 1.96

⇒ z(s) is in the rejection region for H₀

Thus, we reject H₀. We can´t support the idea of equals means

Now, CI at 95 %  = (p₁ - p₂) ±  z(c) * EED

CI = (0.11 ± 1.96 * 0.028)

CI = (0.11 ± 0.054)

CI =  (0.056, 0.164)

Thus, the 95% confidence interval for the difference between the two proportions is (0.056, 0.164)

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Your question was incomplete. Check for missing content below-

Q1. Let P, represent the proportion under and p, the proportion over the age of 18. The null hypothesis is:_____.

Q2. The 95% confidence interval for the difference between the two proportions is:____.

The value of n that satisfies the given polynomial expression is 10

From the question, we are to determine determine the corresponding value of n in the simplified expression.

The given expression is

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

First, we will simplify this expression

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

(12x⁵ + 6x³ + x) - (2nx³ + x + 52nx² + 26)

(12x⁵ + 6x³ + x - 2nx³ - x - 52nx² - 26)

Simplify further

(12x⁵ + 6x³ - 2nx³ - 52nx² - 26)

(12x⁵ + (6 - 2n)x³ - 52nx² - 26)

By comparison with (12x⁵ - 14x³ - 520x² - 26)

(6 - 2n)x³ = - 14x³

and

- 52nx² = - 520x²

Solve (6 - 2n)x³ = - 14x³ for n

(6 - 2n)x³ = - 14x³

6 - 2n = - 14

6 + 14 = 2n

20 = 2n

n = 20/2

n = 10

Similarly,

Solve - 52nx² = - 520x² for n

52n = 520

n = 520/52

n = 10

Hence, the value of n is 10

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(1)The break - even sales for last year is $600000.

(2)(a) The operating income for last year is $300000.

(b) The maximum operating income that could have been realized during the year is $337500.

In mathematics, a range refers to the set of all possible values or outputs that a function or relation can produce. It is the collection or set of all values that a function can take on as its output when given various inputs from its domain.

The term "volume" typically refers to the measure of the amount of space occupied by a three-dimensional object. It is a quantitative measure of the capacity or size of a solid shape in three-dimensional space. Volume is often used to describe the amount of space enclosed by an object or the amount of material it can hold.

Cost-Volume-Profit (CVP) Chart for Last Year:

To construct a CVP chart, we need to plot the sales, variable costs, fixed costs, and profit (or operating income) on the y-axis and the number of units sold on the x-axis.

Based on the given information:

Sales = $900,000

Unit selling price = $200

Variable cost per unit = $125

Fixed costs = $225,000

Maximum sales within relevant range = 7,500 units

Using the formula for calculating the break-even point:

Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)

Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units

Now we can construct the CVP chart:

Sales:

The sales line will start from the origin (0,0) and have a slope of $200 per unit, as the unit selling price is $200.

Variable Costs:

The variable costs line will also start from the origin (0,0) and have a slope of $125 per unit, as the variable cost per unit is $125.

Fixed Costs:

The fixed costs line will be a horizontal line parallel to the x-axis, at a height of $225,000, as the fixed costs are constant and do not change with the number of units sold.

Profit (Operating Income):

The profit line can be calculated by subtracting the total variable costs and fixed costs from the total sales. So, the profit line will start from the origin (0,0) and have a slope of ($200 - $125) per unit, which is the difference between the unit selling price and variable cost per unit.

The break-even point will be the point where the profit line intersects the x-axis, which is at 3,000 units. So, the break-even sales for last year is 3,000 units x $200 per unit = $600,000.

Verification using the break-even equation:

Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)

Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units

Operating Income for Last Year and Maximum Operating Income:

Operating Income for Last Year:

Operating Income = Sales - Variable Costs - Fixed Costs

Operating Income = $900,000 - ($125 x Number of Units Sold) - $225,000

Substituting the break-even point of 3,000 units, we get:

Operating Income = $900,000 - ($125 x 3,000) - $225,000

Operating Income = $900,000 - $375,000 - $225,000

Operating Income = $300,000

Maximum Operating Income:

The maximum operating income can be achieved at the maximum sales within the relevant range, which is 7,500 units.

Operating Income = Sales - Variable Costs - Fixed Costs

Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000

Operating Income = $1,500,000 - $937,500 - $225,000

Operating Income = $337,500

Verification using the mathematical approach to CVP analysis:

Plugging in the values for last year's sales of 7,500 units:

Let's calculate the maximum operating income using the mathematical approach to CVP analysis:

Operating Income = (Unit Selling Price x Number of Units Sold) - (Variable Cost per Unit x Number of Units Sold) - Fixed Costs

Given:

Unit Selling Price = $200

Variable Cost per Unit = $125

Fixed Costs = $225,000

Number of Units Sold = 7,500

Putting  the values:

Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000

Operating Income = $1,500,000 - $937,500 - $225,000

Operating Income = $337,500

So, the maximum operating income that could have been realized during the year is $337,500.

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The fraction that can be found on a ruler would be = 1½ inch. That is option C.

Fraction is defined as the expression of a number in the form of numerator and denominator.

The meter rule is the device that is used in the measurement length of an object.

A meter rule can be marked as in centimeter or in inches.

The best fraction that can be seen on a meter rule is 1½in = 1.05in.

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The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).

To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.

There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.

Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.

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Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

Step-by-step explanation:

3 out of 4 students mean

3/4th students were wearing shirts.

Total students = 600

So,

3/4th of 600 students were wearing shirt.

Let us calcualte (3/4)th of 600:

450 students

9514 1404 393

Answer:

  >180° (more than 180°)

Step-by-step explanation:

Angles are classified as ...

It seems that we're looking at definitions:

  obtuse : >90° :: reflex : >180°

The line of reflection that would make A'B'C'D' the image of ABCD is line 3

From the question, we have the following parameters that can be used in our computation:

Rectangles ABCD and A'B'C'D'

Also, we can see that

Both rectangles are in opposite quadrants

This means that the line of reflection must be slant line in the adjacent quadrants

In this case, the line is line 3

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Answer:

Step-by-step explanation:

The formula for the volume of a cone is:

V = (1/3)πr^2h

where V is the volume of the cone, r is the radius of the base, and h is the height of the cone.

Substituting the given values, we have:

V = (1/3)π(10 mm)^2(6 mm)

V = (1/3)π(100 mm^2)(6 mm)

V = (1/3)π(600 mm^3)

V = 200π mm^3

Using a calculator to approximate π to 3.14, we get:

V ≈ 628.32 mm^3

Therefore, the answer is O 628 mm³.

The solutions of the system of equations are:

x = -2, y = 4, z = -2

Here we have the system of equations:

4x - y - 2z = -8

-2x + 4z = -4

x + 2y = 6

To eliminate one variable, we can add the second equation and two times the third equation, we will get:

(-2x + 4z) + 2*(x + 2y) = -4 + 2*6

Now we can simplify that so we get:

4z + 4y = -4 + 12

4*(z + y) = 8

z + y = 8/4  =2

z + y = 2

With that we can write z in terms of y.

z = 2 - y

And with the third equation we can write x in terms of y.

x = 6 - 2y

Replacing that in the first equation we get:

4*(6 - 2y) - y - 2*(2 - y) = -8

Now we can solve this for y.

24 - 8y - y +2y - 4 = -8

20 - 11y = -8

-7y = -28

y = 28/7  = 4

Now that we know the value of y we can find the values of x and z.

x = 6 - 2y = 6 - 2*4 = -2

z = 2 - y = 2 - 4 = -2

The solutions of the system of equations are:

x = -2, y = 4, z = -2

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Answer:35

Step-by-step explanation:

We add or subtract from left to right to find the value of the expression:

3

Because the result is negative, she is below the cave entrance (by 35 feet).

Answer:

25 ft

Step-by-step explanation:

Answer: i thought that i knew the awnser but it was wrong sorry

Step-by-step explanation: