Read the following prompt and type your response in the space provided.
Explain how to model the division of –24 by –4 on a number line.

ΔABD and ΔBCD are congruent by AAS congruence theorem.

The proof is given below.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure below,

ΔABD and ΔBCD are congruent.

∠BCD = ∠BAD [ 90 degrees ]

∠CDB = ∠ABD [ alternate angles ]

BD = BD [ Common ]

ΔABD ≈ ΔBCD [ AAS ]

Thus,

ΔABD and ΔBCD are congruent by AAS congruence theorem.

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According to the information there are 76 numbers in the sequence between 10 and 238.

To calculate how many  terms there are in the sequence we have to perform the following mathematical operation:

According to the above, there are 76 numbers in the sequence between 10 and 238. Also, we can prove this calculating each number:

10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100...

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The total length of A+C will be 172 cm(unit).

What is a unit?

Units are the tools to measure and compare different things. Comparison becomes easy when all the units for the measurement are the same.  Different units can be classified depending on their use. A few of the units can be classified as:

The seven SI base units (The International System of Units (SI), commonly known as the metric system, is the international standard for measurement) which are comprised of:

Length - meter (m)

Time - second (s)

Amount of substance - mole (mole)

Electric current - ampere (A)

Temperature - kelvin (K)

Luminous intensity - candela (cd)

Mass - kilogram (kg)

Now,

Given B-A=120   -->1

B-C=84              -->2

A+B+C=360      -->3

Therefore, from equations 1,2 and 3

B-120+B+B-84=360

B=188

By putting B=188 in 1 and 2

A=68

C=104

A+C=172cm

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Answer:

41.  (-∞, -1] ∪ [2, 3)

42.  (2, 5) ∪ (5, ∞)

Step-by-step explanation:

Given rational inequality:

[tex]\dfrac{x^2-x-2}{x-3} \leq 0[/tex]

Factor the numerator:

[tex]\dfrac{(x-2)(x+1)}{x-3} \leq 0[/tex]

Find the roots by solving f(x) = 0  (set the numerator to zero):

[tex]\implies (x-2)(x+1)=0[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

[tex]\implies x+1=0 \implies x=-1[/tex]

Find the restrictions by solving f(x) = undefined  (set the denominator to zero):

[tex]\implies x-3=0 \implies x=3[/tex]

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attachment 1).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

For each test value, determine if the function is positive or negative:

[tex]f(-2)=\dfrac{(-2)^2-(-2)-2}{(-2)-3} =\dfrac{+}{-}=-[/tex]

[tex]f(0)=\dfrac{(0)^2-(0)-2}{(0)-3} =\dfrac{-}{-}=+[/tex]

[tex]f(2.5)=\dfrac{(2.5)^2-(2.5)-2}{(2.5)-3} =\dfrac{+}{-}=-[/tex]

[tex]f(4)=\dfrac{(4)^2-(4)-2}{(4)-3} =\dfrac{+}{+}=+[/tex]

Record the results on the sign chart for each region (see attachment 1).

As we need to find the values for which f(x) ≤ 0, shade the appropriate regions (zero or negative) on the sign chart (see attached).

Therefore, the solution set is:

As interval notation:

Given rational inequality:

[tex]\dfrac{\sqrt{x}}{(x-2)|x-5|} > 0[/tex]

Find the roots by solving f(x) = 0  (set the numerator to zero):

[tex]\implies \sqrt{x}=0 \implies x=0[/tex]

Find the restrictions by solving f(x) = undefined  (set the denominator to zero):

[tex]\implies (x-2)|x-5|=0[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

[tex]\implies |x-5|=0 \implies x=5[/tex]

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attachment 1).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

For each test value, determine if the function is positive or negative:

[tex]f(-1)=\dfrac{\sqrt{-1}}{(-1-2)|-1-5|}=\dfrac{\sf unde\:\!fined}{-}=\sf unde\:\!fined[/tex]

[tex]f(1)=\dfrac{\sqrt{1}}{(1-2)|1-5|}=\dfrac{+}{-}=-[/tex]

[tex]f(3)=\dfrac{\sqrt{3}}{(3-2)|3-5|}=\dfrac{+}{+}=+[/tex]

[tex]f(6)=\dfrac{\sqrt{6}}{(6-2)|6-5|}=\dfrac{+}{+}=+[/tex]

Record the results on the sign chart for each region (see attachment 2).

As we need to find the values for which f(x) > 0, shade the appropriate regions (positive) on the sign chart (see attached).

Therefore, the solution set is:

As interval notation:

Answer:

c

Step-by-step explanation:

a.

5+7=13

total amount of apples = 13

green apples = 5

5:13

b.

total amount of apples = 13

red apples = 7

7:13

Bar models can be used to represent the quotient and the product of numbers or expressions that are; y = x + 2 and x = m/4

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the expression as;

y - 2

LEt the expression Represent  y - 2 with x.

y - 2 = x

Add 2 on both sides we get;

y = x + 2

Similalry,

Represent the 4x with m.

4x = m

Divide by 4 on both sides we get;

x = m/4

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The area of the circular sector is equal to 6π square units.

In this question we must determine the area of the circular sector between points H, G and I from given information of the central angle (θ), in degrees, and arc (p). The perimeter and area of the circular sector are described by the following formulae:

Area

A = (θ / 360) · π · r²

Perimeter

p = (θ / 360) · 2π · r

Where r is the radius of the circle.

If we know that p = 2π and θ = 60°, then the area of the circular sector is:

r = (360 / θ) · (p / 2π)

r = (360 / 60) · (2π / 2π)

r = 6

A = (60 / 360) · π · 6²

A = 6π

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The client should invest $8889 in AAA bonds, $4444 in A bonds, and $5667 in B bonds.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x + 4 = 8 is an equation.

We have,

Amount invested in AAA bond = 2x

Amount invested in A bond = y

Amount invested in B bond = x

Now,

Average yield:

AAA bond = 4%

A bond = 5%

B bond = 8%

Now,

Total amount = $19,000

Total yield = $990

Now,

Two equations can be made:

2x + y + x = 19000

3x + y = 19000 _____(1)

0.04 x (2x) + 0.05 x y + 0.08x = 990

0.08x + 0.05y + 0.08x = 990

0.16x + 0.05y = 990 ______(2)

From (1) and (2),

3x = 19000 - y

x = (19000 - y)/3

Substituting in (2)

0.16 x (19000 - y)/3 + 0.05y = 990

0.053 x 19000 - 0.053y + 0.05y = 990

1007 - 0.003y = 990

1007 - 990 = 0.003y

y = 17/0.003

y = 5666.6

y = 5667

Now,

x = (19000 - y)/3

x = (19000 - 5667)/3

x = 4444.333

x = 4444

Now,

x = $4444

y = $5667

2x = $8889

Thus,

Amount invested in AAA bond = $8889

Amount invested in A bond = $5667

Amount invested in B bond = $4444

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The cost of the flowers she bought for her mum alone would be = $18

The items purchased by Emma = flowers and a gift certificate.

The total cost of the flowers and a gift certificate = $68

But, cost of gift certificate= $14 +2x

cost of flower = X

That is 14 + 2x + X = 68

2x + X = 68 - 14

3X = 54

X = 54/3

X= $18

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The least-squares regression line can be used to predict the number of hours of pain relief given a certain dose.

This is done by taking the sum of the squares of the residuals and finding the minimum value. The residuals are the differences between the observed values and the predicted values. The plot of the residuals versus the dose would reveal the variation in the hours of pain relief across the doses.

For example, the formula for finding the least-squares regression line is

Y = b0 + b1X

where Y is the predicted value, b0 is the intercept, b1 is the slope, and X is the dose.

To calculate the residuals, we take the difference between the observed values and the predicted values for each dose.

residual = Y (observed) - Y (predicted)

The plot of the residuals versus the dose would reveal if the variation in the hours of pain relief is not the same across the doses. This is because if the variation is not the same, then the residuals would not be evenly distributed. If the residuals were evenly distributed, then the sum of the residuals would be equal to zero.

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The standard deviation, in dollars, of the probability distribution of p is √(1.50 × 3.6) dollars.

We are given the following parameters -

Expected value = 2.6

Variance = 3.6

Price per doughnut = $1.50

Now we can write the price for the variance of the distribution as -

Price per doughnut × Variance

Variance = $1.50 × 3.6

The formula for the standard deviation of the distribution D in relation to the variance is given by -

Standard deviation = √variance

Standard deviation = √(1.50 × 3.6)

Therefore, the standard deviation of P in dollars will be √(1.50 × 3.6).

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The probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex] Hence, the correct answer is option D.

This probability can be calculated using the normal approximation to the binomial distribution, with the sample proportion (p-hat) being 0.27, the population proportion (p) being 0.22, and the sample size (n) being 300.

The formula for the standard error of a sample proportion is -

[tex]\sqrt{p(1-p)/n}[/tex]

substituting the values, we get,

[tex]\sqrt{(0.27)(0.73)/300}.[/tex]

Then, we use the formula for a standard normal probability -

P(z > (p-hat - p)/standard error),

substituting the values, we get,

[tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex]

Hence, the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex]

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The inequality for the number of lawns he needs to mow is: $50 < $20 + $5n

The correct answer is an option (b)

Let n represents the number of lawns he needs to mow.

Here, Billy needs to make more than $50 between his allowance and the lawns that he mows. This means that an inequality should include 50 <

As Billy will make $5  for each lawn that he mows, for 'n' number of lawns the cost would be = 5n

Based on the mentioned conditions we formulate an inequality,

50 < 20 + 5n

20 + 5n > 50

20 + 5n - 20 > 50 - 20             ...........(subtract 20 from each side)

5n/5 > 30/5                      .............(divide each side by 5)

n > 6

This means, he needs to mow more that 6 lawns.

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The complete question is:

Billy makes $20 a week in allowance plus $5 for each lawn that he mows. this week billy wants to make over $50. select the inequality for the number of lawns he needs to mow.

a) $50 < $20+$5

b) $50 > $20+$5n

c) $50 < $20n+$5

d) $50 > $20n+$5

e) $50 < $20+$5n

The required size of the hole after 10 hours will be 118098 inches.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,

Sally has a leaking faucet in her bathroom. When she first noticed the leak, there was a puddle that was 2 inches in diameter.

According to the given condition

let Y be the size of the hole after 10 hours

Y=2×3¹⁰

Y=118098

Thus, the required size of the hole after 10 hours will be 118098 inches.

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Answer:

Step-by-step explanation:

The answer is 42 MB.If it's round to nearest tenth than it's 40 MB

Since the table shows a proportional relationship between x and y, the unit rate of y per x is equal to 4.

In order to have a proportional relationship and equivalent ratios, the variable (x) and the variable (y) must have the same constant of proportionality.

Next, we would calculate the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/3 = 20/5 = 24/6 = 32/8

Constant of proportionality (k) = 4.

In this context, we can reasonably infer and logically deduce that the unit rate for this proportional relationship is equal to 4.

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Complete Question:

The table shows a proportional relationship between x and y what is the unit rate of y per x (3, 5, 6, 8) (12, 20, 24, 32)?

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.56\%\to \frac{2.56}{100}\dotfill &0.0256\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000[1+(0.0256)(4)] \implies A=3000(1.1024)\implies A = 3307.2[/tex]

Answer:

5$ Per Lawn

Step-by-step explanation:

10$/2=5$

2/2=1

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Answer: the rate she is earning is 5$ per lawn mowed

Step-by-step explanation:

if she earns 10$ after mowing 2 lawns then if you divide 10 and 2 you get 5

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The triangles are proved similar by; D. AA similarity.

When on comparing the sides and measures of internal angles of two or more triangles, if there is a common properties among them, then the triangles are similar. Note that being similar does not imply that they are congruent.

So that on comparing the properties of the two triangles given, it can be inferred that:

the two traingles are similar by Angle-Angle theorem which states that; when two angles of two triangles are the same, then the triangles are similar.

Therefore, the statement to prove that the triangles are similar is giben in option D. AA similarity.

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11.69 is the exact length needed for the mid-segment of the trapezoid with STUV vertices.

The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.

We have,

vertices S(-2,4) ,T(-2,-4) ,U(3,-2) ,V(13,10).

Half of the lengths of the two parallel sides, ST and UV, make up the length of the trapezoid's middle section.

The trapezoid's vertices are S(2, 4), T(2, 4), U(3, 2), and V. (13, 10).

The distance formula is then used to calculate the length of the ST and UV sides;

Length = [tex]\sqrt{x_{2}-x_{1}+y_{2}-y_{1}}[/tex]

Side ST's length is S(-2, 4), T(-2, -4).

ST = [tex]\sqrt{x_{2}-x_{1}+y_{2}-y_{1}}[/tex]

ST = [tex]\sqrt{(-2-(-2))^2+(-4-(4))^2[/tex]

ST = [tex]\sqrt{0 + 64}[/tex]

ST √64

ST = 8

Side UV's length is U(3, 2), V. (13, 10).

UV = [tex]\sqrt{(13-3)^2+(10-(-2))^2[/tex]

UV = [tex]\sqrt{(10)^2+(12)^2[/tex]

UV = √244

UV = 15.62

Therefore,

The mid-segment STUV's length is,

Length of mid-segment = (ST + UV)/2

Length of mid-segment = (8 + 15.62)/2

Length of mid-segment = (23.62)/2

Length of mid-segment = 11.81

Therefore, 11.69 is the exact length needed for the mid-segment of the trapezoid with STUV vertices.

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The icon that points out the Essential Question that you should be able to answer by the end of the lesson is this:

C. A hand icon is shown.

A hand icon is used for the purpose of identifying the important questions that should be answered at the end of the lesson. It shows that the reader should pay careful attention to the indicated question as they may have to provide an answer to it by the end of the lesson.

Icons in reading have different meanings and understanding their purposes will lead to a more immersive reading.

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Answer:

480

Step-by-step explanation:

Lets break this down to make it even easier

(24x2)x10

=(48)x10

=480

Answer:

If you are looking for the simplest form of 24/20 it is basically 6/5.

because if you multiply 6/5 by 4/4 you could get the answer which is 24/20.

and the same thing if you divide

I hope that I helped

The equivalent expressions are B. p-7-p = 22 -, C. p - 7 + 22 = 22 - 7, D. p - 7 + 7 = 22 - 22

Algebraic expressions are simply defined as expressions that comprised of terms. coefficients, factors, constants and variables.

They are also made up of some operations which are arithmetic. They include;

From the information given, we have the equation as;

p- 7 = 22

To solve the equation, collect like terms

p = 22 + 7

Add the like terms

p = 29

Hence, the value is 29

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The complete question:

Which equation is NOT equivalent to p- 7 = 22? Select all that apply.

A. p-p-7 = 22-p

B. p-7-p = 22 -

C. p - 7 + 22 = 22 - 7

O

D. p - 7 + 7 = 22 - 22

Ep-7 + 7 = 22 +7

The solution to the simultaneous equations using Cramer's rule is;

x = 5, y = −1

The simultaneous equations are;

6x + 5y = 25

7x − 9y = 44

We will first find the determinant of the left hand side;

[tex]\left[\begin{array}{ccc}6&&5\\7&&-9\\\end{array}\right][/tex]

|A| = (6 * -9) - (7 * 5)

|A| = -89

Now, will replace the x part of the matrix with the right side values to get;

[tex]\left[\begin{array}{ccc}25&&5\\44&&-9\\\end{array}\right][/tex]

The determinant is;

|A_x| = (25 * -9) - (44 * 5)

|A_x| = -445

Now, will replace the y part of the matrix with the right side values to get;

[tex]\left[\begin{array}{ccc}6&&25\\7&&44\\\end{array}\right][/tex]

The determinant is;

|A_x| = (6 * 44) - (25 * 7)

|A_x| = 89

Thus;

x = |A_x|/|A|

x = -445/-89

x = 5

y = |A_y|/|A|

y = 89/-89

y = -1

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The force with respect to the x and y axes can be calculated as follows:

F_x = 100N cos(30) = 86.6N

F_y = 100N sin(60) = 50N

Let F be the magnitude of the force, (theta) be the angle between the force and the x-axis, and (gamma) be the angle between the force and the y-axis. The components of the force with respect to the x and y axes can be calculated using the following formulas:

F_x = F cos(theta)

F_y = F sin(gamma)

For example, if the magnitude of the force is 100N and (theta) = 30 degrees and (gamma) = 60 degrees, then the components of the force with respect to the x and y axes can be calculated as follows:

F_x = 100N cos(30) = 86.6N

F_y = 100N sin(60) = 50N

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The number of questions that were answered per minute 20 questions

the question reads: Jamie answered 16 questions in 4/5 minutes. How many questions were answered per minute?

You should number that a minute is made up of 60 seconds

This implies that 4/5 of a minute is given as 4/5 * 60

This is equal to 48 seconds

So every 48 seconds, Jamie answers 16 questions

This implies that (16*60)/48 = 20

Therefore in one minute Jamie would answer 20 questions

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As per the elimination method, in order to solve a system of equations when multiplication is necessary to eliminate a variable.

The term equation is known as algebra is a statement of equality that contains one or more unknown quantities or variables.

Here we have given that When using the multiplication method, it is important to multiply all the terms on both sides of the equation, then here we do not just the one term you are trying to eliminate.

According to the rule of elimination method we all know while solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation.

So in order to multiplying to solve linear systems is to find a number to multiply to one or both of the equations so that the x or y terms in one of the equations will have opposite coefficients from the x or y in the other equation.

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The value of x or the expression 56 = -4x + 2 is -27/2.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

56 = -4x + 2

Solve for x.

56 = -4x + 2

Subtract 2 on both sides.

56 - 2 = -4x

54 = -4x

Divide -4 into both sides.

-54/4 = x

x = -54/4

x = -27/2

x = -13(1/2)

Thus,

The value of x is -27/2.

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