Solve the compound inequality.
- 3x≤ - 9 or 5x-18 ≥ 12

The answer to all the subparts of the congruency of triangles is shown:

In ΔABC and ΔPQR  

Thus from SSS congruence, we get ΔABC ≅ ΔPQR  

In ΔGHJ and ΔUVW

Thus from SSS congruence, we get ΔGHJ ≅ ΔUVW

However, ΔGHJ and ΔPQR are not congruent because there are no two sides that are equal.

Also, ΔPQR and ΔUVW are not congruent because of the same reason mentioned above.

Therefore, the answer to all the subparts of the congruency of triangles is shown:

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The correct answer is option D

3(c) - 2 represents the total cost of three dance tickets at a cost of c each, less a one-time $2 discount.

         y = mx+b, where m is the slope and b is the y-intercept.

Based on the question. We have the parameters listed below.

The total cost of three dance tickets is 3c (at c for each)

One-time offer = $2

Because discounts are always subtracted from the total cost,

the equation represents,

the total cost of three dance tickets at a cost of c each, less a one-time discount $2

=  3(c) - 2

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The statement that correctly compares two numbers is: A. 3.02 = 3.020

An inequality can be defined as a mathematical relation that compares two (2) or more numbers such as integers, and variables in an equation based on any of the following arguments (symbols):

Next, we would evaluate the given inequalities in order to determine the correct statement as follows:

3.02 = 3.020 (True).

4.05 < 4.05 (False) because 4.05 is equal to 4.05.

5.17 < 5.07 (False) because 5.17 is greater than 5.07.

6.08 > 6.08 (False) because 6.08 is equal to 6.08.

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Answer:

B

Step-by-step explanation:

Let's go through each, step-by-step and simplify to see if we find a true number sentence:

A)

[tex]3\frac{1}{3} < \sqrt{7}?[/tex]

[tex]3.3333 < 2.64575?[/tex] Not true

B)

[tex]4.8 < \sqrt{32}?[/tex]

[tex]4.8 < 5.65685?[/tex] True

Knowing B is true, we have found our answer and don't need to go any further.

Given

Values of winning and losing scores

Find

Make a stem and leaf ploy for the given values

Explanation

Final answer

Above is the

y = -3x - 8

Slope-intercept form: y = mx + b

Given: y + 2 = -3(x + 2)

Simplify:

y + 2 = -3x - 6

y = -3x - 6 - 2

y = -3x - 8

We have: m = -3, and b = -8

Answer:

y=-3x-8

Step-by-step explanation:

First make y by itself

y=-3(x+2)-2

Distribute the -3

y=-3x-6-2

Combine like terms

y=-3x-8

Answer: 80%

Step-by-step explanation:

To find percent error all you have to do is divide the estimate by the actual then multiply it by 100

8/10×100=80%

The percent error of the actual measurement of 10 fluid ounces is 25%.

Percent error:

Percent error means the difference between the exact or known value of something and its approximate or actual value, in percentage form.

The formula to calculate the percent id defined as

δ = |(A - E)/E| x 100%

Where

δ  = percent error

A  = actual value observed

E  = expected value

Given,

Derek filled the pitcher with 8 fluid ounces of lemonade.

Here we need to find the percent error if the actual measurement was 10 fluid ounces.

According to the percent error formula, the actual value in the given question is 10 and the expected value is 8.

Then we have to apply the value on the formula, then we get,

Percent error = [(10 - 8)/8] x 100%

Percent error = [2/8] x 100%

Percent error = 0.25 x 100%

Therefore, the percent error in the given situation is 25%.

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The system of inequalities has no solution because the lines do not meet at any point

The system of inequalities is given as

y ≥ x² + 3

y < x + 1

From the above system of inequalities, we can see that the function types are

Next, we plot the graph of both inequalities in the system (see attachment for the graph)

From the graph, we can see that the lines and the curves of the functions do not intersect

This means that the system has no solution

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Answer:

(1) Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity. Example, 1, 2, 3, 4,... are natural numbers.

Step-by-step explanation:

(2) Number Trick 1:

Let the single digit be: 1

Multiply by 2: 1 x 2 = 2

Add 8 to your answer: 2 + 8 = 10

Divide your answer by 2: 10 ÷ 2 = 5

Subtract original number: 5 - 1 = 4

(3) Final result is 4.

The trick will always work for all NATURAL NUMBERS.

Answer:

[tex](g \circ f)(0)=216[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=2x+6\\g(x)=x^3\end{cases}[/tex]

(g o f)(x) is a composite function.  

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function (g o f)(0) means to substitute the function f(x) when x=0 in place of the x in function g(x).

[tex]\begin{aligned}\implies (g \circ f)(0)&=g[f(0)]\\& = g(2(0)+6)\\&=g(0+6)\\&=g(6)\\&=6^3\\&=216\end{aligned}[/tex]

Travis should include A. Chicago, St Paul, Bismarck and Fargo on his lost because these cities had temperature of 6°F below zero for the month of January.

The only countries which Travis is including on his list are those which has a temperature of 6 degrees Fahrenheit   below zero in the month of January.

The correct choices are provided in the option A.

He should include Chicago, St. Paul, Fargo and Bismarck.

He should add these cities because they all had temperature of 6 degrees Fahrenheit below zero for the month of January.

These cities are very cold because of their geological location.

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Answer:

1/25 or 0.04

Step-by-step explanation:

evaluated in fraction and decimal form i hope this helped :)

Answer:

x = 9.629 meters

Step-by-step explanation:

x / 10.25 = 1.55 / 1.65

x = 1.55 / 1.65 * 10.25

x = 9.629 meters

The biggest  area of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.

GIVEN:

SOLVING:

Area of the quadrilateral is

hence,The biggest  area  of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.

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The amount of the insurance agent's sales for the month is 11,000.

The total income can be modelled as a linear equation. A linear equation is an equation that has one variable that is raised to the power of one. The form of a linear equation is:

y = mx + b

Where:

530 = base salary + (percentage x value of sales over 2000)

530  = 200 + 3% x s

530 = 200 + 0.03s

530 - 200 = 0.03s

330 = 0.03s

s = 330 / 0.03

s = 11,000

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The names of the polygons are;

a. Heptagon

b. Octagon

c. Pentagon

d. Hexagon

A polygon can be defined as a plane figure described by a known number of straight line segments which are connected to form a closed chain.

Polygon are also described as figures which are enclosed by line segments known as sides.

It is important to note that polygons are 2- dimensional shapes.

Depending on the number of sides, the types of polygons are;

a. It has seven sides = Heptagon

b. It has eight sides = Octagon

c. It has five sides = pentagon

d. It has six sides = Hexagon.

Hence, the number of sides determines the name.

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Angle 6, Angle 16 and Angle 11 are not congruent.

We need to check ∠5 is not equal to which angle from the figure.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Here,

Angle 5 = Angle 2 (Vertically opposite angles)

Angle 5 = Angle 7 (corresponding angles are equal)

Angle 5 = Angle 13 (corresponding angles are equal)

Therefore, Angle 6, Angle 16 and Angle 11 are not congruent.

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Answer:

B)  Angle 6

C)  Angle 16

E)  Angle 11

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Corresponding Angles Theorem

When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.

According to the corresponding angles theorem:

According to the vertical angles theorem:

Therefore:

As angle 5 is not a right angle, the angles that angle 5 is not equal to are:

Answer:

45 large dogs

Step-by-step explanation:

Step 1:

60 x 3 = 180

180 ÷ 4 = 45

[tex]\textit{area of a rectangle}\\\\ A=bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=2x^2+5x+4\\ h=5x^3 \end{cases}\qquad \begin{array}{llll} \\\\\\ A~~ = ~~ \end{array} \begin{array}{cllll} 2x^2+5x+4\\\\ \times ~~ 5x^3\\\cline{1-1} 10x^5+25x^4+20x^3 \end{array}[/tex]

Answer:

98 ÷ 98 = 1 OR 98 ÷ 1 = 98

Step-by-step explanation:

Division is breaking something up into equal parts. The "dividend" is the whole you start with, the "divisor" is what you use to divide up the whole, and the "quotient" is the answer like this: Dividend ÷ Divisor = Quotient. So, the quotient of 98 and a number would be represented as such: 98 ÷ 1 = 98 or 98 ÷ 98 = 1

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The number of the students should be sampled to be within 0.25  alcoholic drinks of population mean with 95% probability is 62.

α is the result of subtracting one from confidence interval as well as dividing by two.

α =  (1 - 0.95) ÷ 2 = 0.25

Find z in the Z-table because z does have a p-value of 1 - α.

As a result, the p-value of z is  (1 - 0.025) = 0.975.

Thus, z  = 1.96

Now find M as;

M = z × (σ ÷ √n)

In which,

When M = 1,

The standard deviation, in accordance with the question, is approximately 1.

σ = 1

M = z × (σ ÷ √n)

0. 25 = 1.96 × (1 ÷ √n)

√n = 1.96 × (1 ÷ √n)

Squaring both sides,

(√n)² = ((1.96 × 1) ÷ 0.25)²

n = (7.84)²

n = 61.4656

n ≈ 62

Thus, the number of the students should be sampled to be within 0. 25 alcoholic drink of population mean with 95% probability is 62.

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Answer:

$271.15

Step-by-step explanation:

Assuming that "time-and-a-half for all hours worked over 40 hours" means that all time spent past that is 1.5X the paycheck, then its 40 times 5.80=$232. then (5.8 times 1.5) times 4.5 = $39.15
$232+$39.15=$271.15

Answer:

8 pens = 32

1 pen = 32 ÷ 8

= 4

Cost of one pen is $4.

Answer:

Step-by-step explanation:

rearrange this equation y – 7=3(x−4) into this Ax+By = C

its pretty simple if you think about it :)

firstly, lets multiply the 3 with x - 4

y - 7 = 3x -12

we are going to bring the 3x to the right side to make the arrangement possible

-3x - y = -5 (minus twelve plus seven)

therefore, A is -3, B is -1 and C is -5

In the given question, the following information is given

Sandra music player randomly selects music from her playlist. Sandra’s playlist contains:

traditional country songs = 3

traditional rock songs = 6

hip-hop rap songs = 4

contemporary country songs' = 5

Latin rap song = 1

traditional pop songs = 3

Total sample space = 3 + 1+ 5 + 4+ 6+3 = 22 songs

We need to find the probability, that her music player will play a rap song = [tex]\frac{Number of sample sample space for rap song}{Total space} \\[/tex]

= [tex]\frac{4 + 1}{22}[/tex] = [tex]\frac{5}{22}[/tex]

P (traditional), that is, the probability that the player will randomly select traditional music of any kind = [tex]\frac{Number od sample space for traditional song}{total sample space}[/tex]

= [tex]\frac{3 + 6+3}{22}[/tex]

= [tex]\frac{12}{22}[/tex] = [tex]\frac{6}{11}[/tex]

P (traditional pop) = [tex]\frac{sample space for pop songs}{total sample space}[/tex]

= [tex]\frac{3}{22}[/tex]

P  (country), the probability that the next song is country music = [tex]\frac{Sample space fpr country music}{total sample space}[/tex]

= [tex]\frac{8}{22}[/tex]

= [tex]\frac{4}{11}[/tex]

P (not country), the probability that the next song is NOT country music.=

1 - [tex]\frac{4}{11}[/tex]

= [tex]\frac{11 -4}{11}[/tex]

= [tex]\frac{7}{11}[/tex]

Hence, this is the final answer.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{3}{4}x - 9[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 9x +12y = -108[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y = - 108- 9x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ -108}{12} - \frac{9x}{12} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{3}{4}x - 9[/tex]

And this the equation of same line in its slope intercept form, where slope (m) = -3/4 and y - intercept = -9

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time. When the total principal amount and the rate of interest for a certain amount of time surpass the due date for payment, this is known as compound interest.

Total to Calculate Interest on - $150

Annual Interest Rate - 4%

Monthly interest -  $0.50

Yearly interest -  $6.00

Total to Calculate Interest on - $180

Annual Interest Rate - 3.5

Monthly interest -  $0.53

Yearly interest - $6.30

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The given figure is a Rhombus hence the last diagram is correct.

In planar Euclidean geometry, a rhombus—also known as a rhombi or rhombus—is a quadrilateral having four sides of equal length.

The given figure is a rhombus. All the sides are equal but the angles are not 90°. Hence its is not a square or a rectangle.

The correct diagram is attached below.

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If Justin bought a calculator and a binder that were both 15% off the original price. The original price of the binder was $6.20. Justin spent a total of $107.27. Then $120 the original price of the calculator

A percentage is a number or ratio expressed as a fraction of 100.

Let,

x be the original price of the calculator

y be the original price of the binder

we know that

15%=15/100=0.15

(x+y)(1-0.15)=$107.27

(x+y)(0.85)=$107.27....(1)

y=6.20....(2)

substitute the value of y in the equation A and solve for x

(x+6.20)(0.85)=107.27

(x+6.20)=107.27/0.85

x=107.27/0.85-6.20

x=126.20-6.20

x=120

Hence the original price of calculator is $120.

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