Which system of inequalities is represented by the graph?

Step-by-step explanation:

1 + 1 + 1 - 1 - 5 - 5r - 3 - 3 --2 - 6 --4

3 - 1 - 5 - 5r - 3 - 3 -- 2 - 6 -- 4

2 - 5 - 5r - 3 - 3 -- 2 - 6 -- 4

-3 - 5r - 3 - 3 -- 2 - 6 -- 4

-5r - 6 - 3 + 2 - 6 + 4

-5r - 9 + 2 - 6 + 4

-5r - 7 - 6 + 4

-5r -13 + 4

-5r - 9

This is the furthest it can be reduced to if you're not trying to find the value of r.

Hope this helps! :)

The sampling distributions reach a normal distribution as sample sizes increase.

For the given statement in the question-

As sample sizes grow larger, sampling distributions reach a normal distribution.

The mean of the sampling distribution equals the population mean (µ) (with "infinite" numbers of the successive random samples).

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Answer: 34

Step-by-step explanation:

Vertical angles are congruent.

Answer:

It goes

1.) C

2.) A

3.) B

A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas.  

A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v=Dt) and the area of a circle (A=r2). In this part, we resolve straightforward one-variable equations.

Alternatively,

Ax +By = C

Any sign that crosses over equal(=) signs always change

In this case, Ax crosses over to C

By = C - Ax

To eliminate y from By, then

By/y = (C - Ax) /y

y cancel out y on the left side

B  = (C - Ax) /y

The complete question is,

Solve for B in the literal equation Ax+By=C

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ax^2 + bx + c = 0

a=1

b=4

c=-8

x^2 + 4x - 8 = 0

(I thought I was wrong but I might be correct lol)

The scale factor from the ΔABC to ΔDEF is 3/2 cm.

Given that, in triangle ABC, side AB measures 12 cm and is the longest side and in triangle DEF, side DE measures 8 cm and is the longest side.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.

The scale factor from the triangle ABC to triangle DEF is 12/8 = 3/2 cm

The scale factor from the triangle DEF to triangle ABC is 8/12 = 2/3 cm

Therefore, the scale factor from the ΔABC to ΔDEF is 3/2 cm.

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Answer:

B 36

Step-by-step explanation:

36 = 6×6 = 6^2

6^2 is a perfect square

Answer:

x = 20

Step-by-step explanation:

4x + 1 and 2x + 41 are alternate exterior angles and are congruent , then

4x + 1 = 2x + 41 ( subtract 2x from both sides )

2x + 1 = 41 ( subtract 1 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

The total amount accrued, principal plus interest, from simple interest on a principal of $1,500.00 at a rate of 3.5% per year for 30 years is $3,075.00. With a principal of £1,500.00 and an interest rate of 3.5% over a 30-year period, Sarah-Jane will save UK £1,575.00. It is undoubtedly a wise investment because the original UK £1,500 doubled.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.

A = P(1 + RT)

A=Final Amount

P = Principal

R = Rate of Interest

T = Time period

Here,

A = $3,075.00

I = A - P = $1,575.00

A = P(1 + rt)

First, converting R percent to r a decimal

r = R/100 = 3.5%/100 = 0.035 per year.

Solving our equation:

A = 1500(1 + (0.035 × 30)) = 3075

A = $3,075.00

$3,075.00 is the total amount accrued from simple interest on a principal of $1,500.00 at a rate of 3.5% per year for 30 years (principal plus interest). In a 30-year loan with a £1,500.00 principal and a 3.5% interest rate, Sarah-Jane will save UK £1,575.00. The original UK £1,500 doubled, so it is unquestionably a smart investment.

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The proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Karyn proofreads 15 pages in 2 hours for $40. The rate will be calculated as:-

Rate of reading = ( 15 / 2 )

Rate of reading = ( 7.5 ) pages per hour

The cost will be calculated as:-

For 2 hours = $40

For 1 hour = ( 40 / 2 )

For 1 hour = $20

Therefore, the proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.

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The angle ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62° for the given quadrilateral by using different laws for angle and lines.

A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. 

A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curved. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.

∠1=62° by parallel line properties.

∠2=71° by alternate angles.

∠3=109° by alternate angles

∠4=35° by triangle properties

∠5=109° by alternate angles

∠6=29° by triangle properties

∠7=47° by parallel line properties.

∠8=62° by parallel line properties.

for the given quadrilateral by using different laws for angle and lines, The angles are ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62°.

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The given expression is equivalent to the third option -19.5b - 6.9. We get this on solving the algebraic expression.

The given expression in the question is

3(-4.5b-2.1) - (6b +0.6)

= -13.5b - 6.3 - 6b - 0.6         (multiplying 3 and -1 respectively with the elements in the bracket)

= -19.5b - 6.9

Therefore we can see that on solving the given algebraic expression we get that it is equivalent to -19.5b - 6.9

Hence the third option which is -19.5b -6.9 is the correct answer.

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Answer: 6w^3-3+18u^2

Step-by-step explanation:

The most appropriate choice for area of rectangle will be given by-

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 [tex]cm^2[/tex]

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is given by

Area of rectangle = [tex]l \times b[/tex]

Here,

Area of rectangle 1 = 60.81 [tex]cm^2[/tex]

Area of rectangle 2 = 61.44 [tex]cm^2[/tex]

Area of rectangle 3 = 35.52 [tex]cm^2[/tex]

Area of rectangle 4 = 47.88 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 2 =

                                                                                             (61.44 - 60.81)[tex]cm^2[/tex]

                                                                                            = 0.63 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 3 =

                                                                                            (60.81 - 35.52)[tex]cm^2[/tex]

                                                                                             = 25.29 [tex]cm^2[/tex]

Difference between Area of rectangle 1 and rectangle 4 =

                                                                                             (60.81 - 47.88)[tex]cm^2[/tex]

                                                                                            = 12.93 [tex]cm^2[/tex]

Difference between Area of rectangle 2 and rectangle 3 =

                                                                                             (61.44 - 35.52)[tex]cm^2[/tex]

                                                                                            = 25.92 [tex]cm^2[/tex]

Difference between Area of rectangle 2 and rectangle 4 =

                                                                                            (61.44 - 47.88) [tex]cm^2[/tex]

                                                                                            = 13.56 [tex]cm^2[/tex]

Difference between Area of rectangle 3 and rectangle 4 =

                                                                                           (47.88 - 35.52) [tex]cm^2[/tex]

                                                                                            = 12.36 [tex]cm^2[/tex]

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 [tex]cm^2[/tex]

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The value of the function operation of each one is represented below.

To solve this problem, we have to perform the operation on each one.

1) (fg)(x)

[tex](fg)(x) = 2x^3 + 12x^2 + 24x + 16[/tex]

2) (hg)(x)

[tex](hg)(x) = x^4 + 4x3 -16x -16[/tex]

3)

(fh)(2)

[tex](fh)(2) = 0[/tex]

4) (gh)(x)

[tex](gh)(x) = x^4 + 4x^3 - 16x -16[/tex]

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Explanation:

The LCM of 5 and 9 is 5*9 = 45

This is the LCD of the two fractions.

So,

3/5 + 2/9 = 27/45 + 10/45 = 37/45

Answer:

7 soloists

Step-by-step explanation:

10%   is  .1 in decimal form

70  x  0.1 = 7 soloists

Answer:

Step-by-step explanation:

Answer:

p = 55485

Step-by-step explanation:

p =  53600 + 145 n

n = 2022 - 2009 = 13 years

so, p =  53600 + 145(13)

p = 55485

we need to verify for each equation if x=3 is a solution. If we replace x by 3 in the first equation we get

so the answer is letter A

not that bad

goodluck tho :)

The equation of the line passes through (2, -10) and to parallel to 14x +2y =  6 is 7x + y = 4

In the above question,

The equation of the line = 14x + 2y = 6

2y = 6 - 14x

y = [tex]- \frac{14x - 6}{2}[/tex]

y = -(7x - 3)

y = -7x + 3

The inclination of a line with respect to the horizontal is measured numerically is called as Slope

Slope of the given line = -7

The slope of a line parallel to the given line would be the same as they both are parallel to each other, hence the needed line's slope is also -7

The point through which is passes = (2, -10)

We need to find the equation of the line which passes through (2, -10) and to parallel to 14x +2y =  6

The equation of a line parallel to the given 14 x + 2 y = 6, and passing through the point (2, -10) is

[y - (-10)] = (-7)[x - 2]

y + 10 = -7x + 14

7x + y = 14 - 10

7x + y = 4

Hence, the equation of the line passes through (2, -10) and to parallel to 14x +2y =  6 is 7x + y = 4

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The expression 400 + 0.1s represents her total weekly earnings.

An expression is written in the form of variables and constants separated by the operation of addition and subtraction. There are many types of expressions some of them are algebraic expression, trigonometric expression, logarithmic expressions, and many more.

Given Tasha earns $400 per week plus a commission of 10% on her weekly sales.

She also saves one-fourth of her earnings.

Assuming the amount she makes on sales is s.

∴ The expression that represents her total weekly earnings is,

= 400 + 0.1s.

As 10% in decimal can be written as (10/100) = 0.1.

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Answer:

8

Step-by-step explanation:

To solve this problem you multiply 4 by 100 and then divide the total by 50 as follows: (4 x 100) / 50

The equation that can be solved to determine the number of days when both jobs would have the same cost is 120d + 1,500 = 110d + 2,500.

The equations that would be formed would be linear equations. A linear equation is an equation that has a single variable that is raised to the power of one. A linear equation is a straight line when it is drawn on a graph.

The equation that represents the total bonus of the first job is: fixed pay + total variable pay

1,500 +( $120 x d)

1,500 + 120d

The equation that represents the total bonus of the second job is: fixed pay + total variable pay

$2,500 + ($110 x d)

$2,500 + $110d

When the amount at both jobs are equal, the two above linear functions would be equal

$2,500 + $110d = 1,500 + 120d

Combine similar terms together:

$2,500 - $1,500 = $120d - $110d

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Answer:

0.2

Step-by-step explanation:

For the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.

As given in the question,

In the given figure of rectangle RSTW,

Conditions satisfies the criteria of the rectangles are as follow:

a. m ∠SRZ = 40°

Line segment SR is parallel to TW. TR is the transversal.

m ∠SRT = m ∠WTR ( Alternate interior angles)

T -Z - R

m ∠SRZ = m ∠WTZ = 40°

Given criteria is satisfies the criteria of rectangles.

b. m ∠STZ = 40°

All the interior angles of rectangle are of measure 90°

m ∠STW = 90°

m ∠WTZ = 40° (given)

m ∠STZ + m ∠WTZ = 90°

⇒ m ∠STZ = 50°

Given option does not satisfies the criteria of rectangles.

c. m ∠SRW = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

d. m ∠TWR = 80°

All the interior angles of rectangle are of measure 90°

Given option does not satisfies the criteria of rectangles.

Therefore, for the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to  m ∠SRZ = 40°.

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Answer: b c

Step-by-step explanation:

Answer:

She earned $42,000 in the previous year

Step-by-step explanation:

9% can be rewritten as 0.09

0.09x is 4050

divide both sides by 0.09

0.09x becomes x

4050 becomes 45,000

then we subtract 3,000 from 45,000 to find the previous years salary

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

[tex]g(f(2)) = -9[/tex]

=======================================================

Explanation:

Let's compute g(f(x))

We do this by starting with the outer function g(x). Then replace every x with f(x). Then plug in the definition of f(x) as shown below.

[tex]g(\text{x}) = \text{x}-1\\\\g(f(\text{x})) = f(\text{x})-1\\\\g(f(\text{x})) = 4-3\text{x}^2-1\\\\g(f(\text{x})) = -3\text{x}^2+3\\\\[/tex]

At this point, we then plug in x = 2 so we can find that...

[tex]g(f(\text{x})) = -3\text{x}^2+3\\\\g(f(2)) = -3(2)^2+3\\\\g(f(2)) = -3(4)+3\\\\g(f(2)) = -12+3\\\\g(f(2)) = -9\\\\[/tex]