What is the slope of the line on the graph

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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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]

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:

The 200 sound cards represent the sample if they are randomly selected from a large production line.

A sample in statistics can be defined as a small part or subset of a population or group that intends to represent what the whole population is like. A sample may be randomly selected or may be selected non-randomly.

In this case, the whole production line of the sound card can be considered as a population. Out of this population of sound cards, 200 are randomly selected to estimate the average lifetime thus determining the characteristic of the whole population, therefore it is said to be the sample of the sound cards and the 5 years is the value of the statistic.

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In  linear equation, y = -6 is the output .

What is a linear equation example?

We want to find the y value on the graph when x = -7

Got to x = -7 and find the value  of the blue line

y = -6

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The complete question is -

Find the output, y, when the input, x, is -7​

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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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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The trigonometric functions for the angle of 195º are given as follows:

1. cos(195º) = -0.9659.

2. sin(195º) = -0.2589.

3. tan(195º) = 0.2680

The identity is verified at the end of the answer.

One of the functions have to be given/found using a calculator, hence:

cos(195º) = -0.9659.

The sine and the cosine of the same angle are related according to the following identity:

sin²(x) + cos²(x) = 1.

Hence:

sin²(195º) + cos²(195º) = 1

sin²(195º) + (-0.9659)² = 1

sin²(195º) + 0.93296281 = 1

sin²(195º) = 1 - 0.93296281.

sin(195º) = ±sqrt(1 - 0.93296281)

sin(195º) = -0.2589. (the angle of 195º is on the third quadrant, where both the sine and the cosine are negative).

The tangent of an angle is given by the sine of the angle divided by the cosine of the angle, hence:

tan(195º) = sin(195º)/cos(195º) = -0.2589/(-0.9659) = 0.2680. (negative divided by negative is positive)

The identities for the sine of the sum and of the subtraction are given as follows:

Hence the subtraction is:

sin(x + y) - sin(x - y) = (sin(x)cos(y) + cos(x)sin(y)) - (sin(x)cos(y) - cos(x)sin(y))

sin(x + y) - sin(x - y) = sin(x)cos(y) + cos(x)sin(y) - sin(x)cos(y) + cos(x)sin(y)

sin(x + y) - sin(x - y) = 2cos(x)sin(y).

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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

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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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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[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 ❞

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 linear equation represented in the table is:

y = -3x + 20

A general linear equation of the form is:

y = a*x + b

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

slope = (y₂ - y₁)/(x₂ - x₁)

Here we can use the last two points on the table:

(-2, 26) and (-4, 32)

Then the slope is:

slope = (26 - 32)/(-2 + 4) = -6/2 = -3

So this is like:

y = -3*x + b

To find the value of b we can use one of the points, i will use (-2, 26), then:

26 = -3*-2 + b

26 = 6 + b

26 - 6 = b = 20

The linear equation is y = -3x + 20

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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

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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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.

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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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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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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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 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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a) 14.81 J of work is needed to stretch the spring from 29 cm to 31 cm.

b) 2 cm far beyond its natural length will a force of 15 N keep the spring in stretched position.

It is mentioned that 3 J of work is needed to stretch a spring from its natural length of 24 cm to 33 cm.

We know the work done on the spring is expressed by the following given equation:

[tex]W=\frac{1}{2} ke^{2}[/tex]

Where, W = workdone that is done on the spring

k = elastic constant

e = extension of the given material

So, Work (W) = 3 J and e = 33 cm - 24cm = 9 cm = 0.09 m

So, putting the above values we calculate the value of 'k' as below:

[tex]W=\frac{1}{2} ke^{2}[/tex]

⇒ [tex]3=\frac{1}{2} k(0.09)^{2}[/tex]

⇒ 3 x 2 = 0.0081k

⇒ k =  [tex]\frac{6}{0.0081}[/tex] N/m

⇒ k = 740.74 N/m

a) Now using the same formula for work, we will determine the amount of work that is needed to stretch the spring from 29 cm to a length of       31 cm.

k =  740.74 N/m

e = 31 cm - 29 cm = 2 cm = 0.02 m

[tex]W=\frac{1}{2} ke^{2}[/tex]

⇒ W = [tex]\frac{1}{2} (740.74) (0.02)^{2}[/tex]

⇒ W = 14.81 J

The work that is done to stretch the spring from 29 cm length to 31 cm is   14.81 J.

b) From the Hooke's law we have, F = ke, where F is the force applied on the spring. Now here we have been given that a force of 15N is applied and we have to find the 'e' that is the extennsion in the natural length of the given spring.

k = 740.74 N/m

F = 15 N

F = ke

⇒ 15 N = 740.74 x e

⇒ e = [tex]\frac{15}{740.74}[/tex] m

⇒ e = 0.02 m = 2 cm

Therefore the natural length of the spring will be stretched by a length of 2 cm when a force of 15 N is applied.

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The solution of the system of equation is as follows:

The system of equation can be solved algebraically using substitution method.

The system of equation can be solved when we find the value of x and y as follows:

y = 4x + 1

6x - 2y = 3

Let's substitute the equation(i) in equation(ii)

6x + 2(4x + 1) = 3

6x + 8x + 2 = 3

14x + 2 = 3

14x = 3 - 2

14x = 1

x = 1 / 14

let's find y as follows:

y = 4(1 / 14) + 1

y = 4 / 14 + 1

y = 2 / 7 + 1

y = 2 + 7 / 7

y = 9 / 7

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The slope of the line that passes through the points (-7, -10) and (-19,-10) is 0.

Slope is simply expressed as change in y over the change in x.

It is expresses as;

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1 ( -7, -10 )

Point 2 (-19,-10)

Plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -10 - (-10) )/( -19 - (-7) )

Slope m = ( -10 + 10 )/( -19 + 7 )

Slope m = ( 0 )/( -12 )

Slope m = 0/-12

Slope m = 0

Therefore, the slope of the line is 0.

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[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:

8 pens = 32

1 pen = 32 ÷ 8

= 4

Cost of one pen is $4.

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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