2. Given R (6, -2) and S (8, 12), find the midpoint of RS.

Answer:

D

Step-by-step explanation:

Because subjects were not assigned randomly to a control or an experimental group, the design of the experiment was flawed.

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As a result, the value of x is 20. Vertically opposite angles are formed by two straight intersecting lines that are opposite one another at a specific vertex.

Here to find y,

∠A = ∠B ( vertically opposite angles are equal ).

5y - 8 = 42

5y = 42 +8

5y = 50

y = 10

To find ∠A,

∠ A = 5y - 8

        = 5 x 10 - 8

        = 50 -8

         = 42°.

we know that angle on a straight line is 180°.

So , ∠A + ∠C = 180°

       42 + ∠C = 180°

       ∠C = 180 - 42

       ∠ C = 138°.

Since ∠C = ∠D (vertically opposite angle ).

          ∠D = 138°

As a result, the value of x is 20.

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Answer:

a

Step-by-step explanation:

\(y\leq\frac{1}{2}x+2 \\\\1\leq \frac{1}{2}(0)+2\\\\1\leq 0+2\\\\1\leq 2\)

This statement is true

Hope this helps!

The linear inequality represented by the graph is y ≤ 1/2x + 2

From the graph, we have the following highlights:

Next, we calculate the slope (m) using:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

Using the points on the graph, we have:

\(m = \frac{4 -2}{4 -0}\)

Evaluate

m = 1/2

The first highlight implies that the y-intercept is 2.

So, the linear inequality is:

y ≤ mx + c

This gives

y ≤ 1/2x + 2

Hence, the linear inequality represented by the graph is y ≤ 1/2x + 2

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Answer:

x = 60

Step-by-step explanation:

(x + 50)° + (x + 10)° = 180° (interior angles on the same side of transversal)

(2x + 60)° = 180°

2x + 60 = 180

2x = 180 - 60

2x = 120

x = 120/2

x = 60

Answer:

introduction of a business invironment

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Answer:

Step-by-step explanation:

sinθ = 13.8/14

θ = arcsin(13.8/14) = 80.3°

The ladder is not safe at that angle.

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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Answer:

Step-by-step explanation:

\(\sqrt{14}/\sqrt{18}\)= \(\sqrt{14*18} /18=\sqrt{2*7*2*3*3} /18=\)6\(\sqrt{7} /18\)=\(\sqrt{7}/3\)

a. The interest for the first payment is $40.

b. The interest for the seventh payment is $29.27.

In financial accounting and management, interest refers to the finance charge for obtaining or giving a loan or credit.

The interest payment or revenue is based on the interest rate applied to the principal or loan balance.

Loan = $3,200

Monthly payment = $199.68

Interest rate = 15%

Loan balance after 6 payments = $2,341.45

Interest for the first payment = $40 ($3,200 x 15% x 1/12)

Interest for the seventh payment = $29.27 ($2,341.45 x 15% x 1/12)

Thus, while the interest for the first payment is $40, the interest for the seventh payment is $29.27.

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Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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The observation of the pattern is discussed below.

When we calculate the squares of the numbers from 1 to 10 and observe the digits at the one's place of each square, we notice a pattern:

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

If we focus on the digits at the one's place, we can see that they form a repeating pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. This pattern repeats itself as we calculate the squares of higher numbers.

This observation is known as the "digit at one's place pattern" or the "units digit pattern." It occurs because the square of any number depends only on the digit at the one's place of that number. Hence, when we square numbers that have the same digit at the one's place, we get the same digit at the one's place in the result.

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Answer:

Part of a train timetable is shown.

Aberystwyth

Shrewsbury

Birmingham

08 30

10 17

12 30

14 19

13 55

16 05

17 20

a)

Bob catches the 12 30 train from Aberystwyth. He arrives in Shrewsbury 8 minutes late. What time does he arrive in Shrewsbury?

b) How long is Bob's journey from Aberystwyth to Shrewsbury? Give your answer in minutes.

minutes

11 30

15 30

Judy catches the 12 30 train from Aberystwyth.

She arrives in Shrewsbury on time.

She attends a job interview.

She gets back to Shrewsbury station 1 hour and 50 minutes later. Is she back in time to catch the 16 05 train to Birmingham?

You must show your working.

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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x = -3y - 9 is the answer to the equation x+3y+9=0

Mathematics a number or values that, when used as a substitution for one or more variables inside an equation, makes the equation true. For instance,\(x^{2} = 4\) has two solutions, which are 2 & -2.

Because it is not a system, the single equation in a set of linear equations cannot be solved.

There are two or more multiple-variable equations in a linear equation system. The location that simultaneously fulfills all of the lines in the system, which each equation represents as a line, is the system's solution.

In the case of a single equation with a single variable, the answer can be obtained by solving for the variable. By removing 3y & 9 both from sides of the equation, x = x + 3y plus 9 = 0, we may find the value of x.

x = -3y - 9

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Answer:

the answer is 14

Step-by-step explanation:

7+7=14

I hope this help

Answer:

14

Step-by-step explanation:

Answer:

5.25 minutes

Step-by-step explanation:

a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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The least common multiple of 598 and 45 is 26, 910

To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.

This gives:

598 prime factorization :

2 x 13 x 23 = 598

45 prime factorization :

3 x 3 x 5 = 45

The least common multiple is;

= 2 x 13 x 23 x 3 x 3 x 5

= 26, 910

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

What is division?

A division in mathematics is the process of dividing a specific amount into equal parts. The division is the inverse of multiplication.

We can find a division fact if we know a multiplication fact: For instance, 3 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Here given that,

We have to divide 87/7,

By dividing,

we know that 8/7 gives reminder 1, and a quotient of 1.

Then divide 14 by 7,

which gives reminder 0 and quotient 2.

So by dividing 84 / 7 we get reminder 0 with a quotient of 12.

Therefore the correct option is option A. With a quotient of 12.

Hence, When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

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Answer: 3/4 is greater than 1/2  

                                   >

Step-by-step explanation:

Given:

Base of a triangle 24m and height = 30m

Required:

Find the area of a triangle.

Explanation:

We have formula for area of triangle

Now,

Answer:

The area of triangle is 360 meter square.

The graph of a function f(x) is translated up when a positive number is added to the y-value of the function by 3 units that is the graph g(x) that is g(x) = f(x) + 3.

The correct option that illustrate the transformation that gives g(x) that has a y-intercept at 3, is the option B;

g(x) = f(x) + 3

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

The graph of the function f(x) = x, as an illustration is attached

The transformation of linear functions are:

Horizontal shifts;

f(x + h); A shift of h units left

f(x - h); A shift of h units right

Vertical shifts;

f(x) + m; A shift of m units up

f(x) - m; A shift of m units down

Whereby the y-intercept of f(x) is 0, we have;

Let f(x) = x, therefore;

g(x) = f(x) + 3

      = x + 3

The graph has to be shifted 3 places up to get g(x), therefore;

The function that gives g(x) from f(x) is the option;

B. g(x) = f(x) + 3

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The equivalent of the expressions are solved to given the following

The distributive property of multiplication is applied to find the equations as follows

2(4x + 3y) - 2x - 2y

= 2(4x + 3y - x - y)

= 2(3x + 2y)

hence the given equation can be rewritten as 2(3x + 2y)

2(4x + 3y) + 2(x + y)

= 2(4x + 3y) + 2x + 2y)

= 2(4x + 3y + x + y)

= 2(5x + 4y)

hence the given equation can be rewritten as 2(5x + 4y)

2(4x + 4y) - 2x + y

= 8x + 8y - 2x + y

= 6x + 9y

= 3(2x + 3y)

hence the equivalence of the given equation is 3(2x + 3y)

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Answer:

52

Step-by-step explanation:

First,do whats in the parenthessis,giving me 13.Then,mukltiply by 4,giving us 53.

Answer:

52

Step-by-step explanation:

The scatter plot shows a [positive linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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