Instructions: Match the linear equation with its graph. Label the given point on the graph and the slope. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12).

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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Answer:

Step-by-step explanation:

183,883,72

Answer:

18388372

Step-by-step explanation:

1 )Use the algorithm method.

      3 2 1 7

×              5      7      1      6

        1      1       1      4                      

        1      9      3      0     2            

        3 2  1  7 0

  2 1  1     4  

  2 2 5    1       9      0     0

1  1     3

1  6 0 8   5       0      0     0

      1  1    1

1  8 3 8   8       3       7     2

2 )Therefore, 3217 × 5716 = 18388372.

18388372

Answer:

Variable rate of change.

Step-by-step explanation:

Plot the points and you'll see that the graph is not a straight line, therefore the rate of change is variable.

Rate of change is variable in the given data.

"Variable is a quantity which shows the change in value as per the conditions apply on it."

"Rate of change is defined as when there is a change in one quantity or variable with respect to another quantity or variable."

According to the question,

Change in time interval is constant with the difference of 1 second.

Change in distance is vary as time increases.

From the graph we can conclude the rate of change is not constant as graph is not a straight line.

Hence, rate of change is variable in the given data.

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Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Layla should by not more than 4 outfits in order not to exceed her budget

The inequality expression is n  ≤ 4

price of a new bicycles = $418.55

2 bicycle reflectors = $19.39

a pair of bike gloves = $27.23

new biking outfits = $38.86 each

Nora's total money to spend at a bicycle store = $38.86

Layla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items

We write the expression as;

$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86

where n represents the number of the new biking outfits

$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86

( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) /  $38.86≥ n

( $640 - $484.56 ) /  $38.86 ≥ n

( $155.44) /  $38.86  ≥ n

4  ≥ n

Layla should by not more than 4 outfits in order not to exceed her budget

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Answer:

21 cupcakes

Step-by-step explanation:

6 = $7

18 = 6 x 3

18 = 7 x 3

18 = $21

Answer:

21

Step-by-step explanation:

We can use proportions to solve

6 cupcakes        18 cupcakes

------------------- = -----------------

7 dollars               x dollars

Using cross products

6x = 7* 18

6x =126

Divide by 6

6x/6 =126/6

x =21

The probability that the traffic light is not green is 0.65

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

If the traffic light is not green it can either be red or yellow.

The probability that the traffic light is not green = probability that the light is red + probability that the light is yellow

55% + 10% = 65% = 0.65

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Answer:

To find a fraction between two fractions, all we need to do is make the sum of the numerators be the new numerator, and the sum of the denominators be the new denominator. then write down the number of rational number you want. if you need more then multiply the denominator and numerator by 10,100.

Step-by-step explanation:

Answer:

21/12

Step-by-step explanation:

You can multiply the number: 1 4/6  1 5/6

10/6  and  11/6

20/12 and 22/12

21/12

I think I am not sure, I have not learned it.

According to the Angle Addition Postulate, the measure of m∠ABD = 202°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠ABC=37°,

and m∠⁡C⁣B⁣D= 165⁢°.

So, according to the angle addition postulate;

m∠ABD = m∠ABC + m∠CBD

Substituting the values,

m∠ABD = 37° + 165⁢°

m∠ABD = 202°

Therefore, the angle measure of m∠ABD = 202°.

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Answer:

good morning but will wait to hear the direction of economics class and concerns about human resources

Answer:

The diameter of the specimen in centimeters is 103 cm.

Step-by-step explanation:

In order to determine the diameter in centimeters of the largest specimen of jellyfish, knowing that said diameter is 1.03 meters, and that 1 meter is equal to 100 centimeters, the following calculation must be performed:

1.03 x 100 = X

103 = X

Therefore, the diameter of the specimen in centimeters is 103 cm.

The correct value of Z for the solution to true system is -2

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

2x + 3y - z = 4

x - 3y + 2z = -3

3x + y - z = 5

Transform the third equation

So we have

2x + 3y - z = 4

x - 3y + 2z = -3

9x + 3y - 3z = 15

Eliminate y in the equations by subtraction

So we have

x - 3z = 7

10x - z = 12

Multiply x - 3z = 7 by 10

10x - 30z = 70

10x - z = 12

Subtract the equations

-29z = 58

So, we have

z = -2

Hence, the correct value of Z  is -2

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Answer:

24 ft

Step-by-step explanation:

This is modelled as a right triangle with height 5 ft and hypotenuse 13 ft

Base of triangle = radius of circle

Find base length using Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle)

⇒ 5² + b² = 13²

⇒ 25 + b² = 169

⇒ b² = 169 - 25

⇒ b² = 144

⇒ b = √144

⇒ b = 12 ft

Therefore, if b is 12 ft, then the radius is 12 ft.

Diameter of a circle = 2r (where r is the radius)

⇒ diameter = 2 x 12 = 24 ft

Apply Pythagorean theorem

\(\\ \rm\hookrightarrow B^2=H^2-P^2\)

\(\\ \rm\hookrightarrow B^2=13^2-5^2\)

\(\\ \rm\hookrightarrow B^2=12^2\)

\(\\ \rm\hookrightarrow B=12\)

Radius is 12ft

Answer:

6:4:9 Yw❤️

Step-by-step explanation:

To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:

1. Reflect A over the y-axis to get A': (-2, 2)

2. Reflect A' over the x-axis to get A'': (-2, -2)

Therefore, the new point A'' is (-2, -2).

The number line that shows the solution to the inequality is given as follows:

First number line.

The inequality in the context of this problem is defined as follows:

-6x + 5 >= 17

-6x >= 12.

Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:

6x <= -12.

Then the solution is given as follows:

x <= -2.

Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.

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The number line that shows the solution to the inequality is: C. graph C.

In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-6x + 5 ≥ 17

By subtracting 5 from both sides of the equation (inequality), we have;

-6x + 5 - 5 ≥ 17 - 5

-6x ≥ 12

x ≤ 12/6

x ≤ 2 (it would be shaded to the left with a closed circle at 2).

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Answer:

Step-by-step explanation:

The two base angles are equal.

The vertex angle is 8x

The two base angles are 5x + 5x

The sum of all three angles = 180 degrees (all triangles make 180 degrees when their interior angles are added).

5x + 5x + 8x = 180

18x = 180

x = 180/18

x = 10

Therefore the vertex angle is 8*10 = 80 degrees

One of the base angles = 10* 5 = 50 degrees

The other base angle = 50 because the triangle is isosceles.

Answer:

25

Step-by-step explanation:

Difference in miles = difference in odometer reading

d = 68,615 - 68,240 =  375 miles

So, if she used 375 miles by the end of the week, then her mile per gallon will be calculated with this equation below:

375 / 15 = 25

Therefore, the correct answer is 25.

Answer

a. The backpack is $4.50

b. The sweatshirt is $2.70

Step-by-step explanation:

a. 30 x 0.15 = 4.50 (The 0.15 is from the price you are actually paying for the item. Because the item is 85% off, you are paying for 15% of the usual price. 15% as a decimal is 0.15 so you multiply that to the original price to find the amount u will pay.)

b. 18 x 0.15 = 2.70  

Answer:

x=1

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+2=3+1

Step 1: Simplify both sides of the equation.

2x+2=3+1

2x+2=(3+1)(Combine Like Terms)

2x+2=4

2x+2=4

Step 2: Subtract 2 from both sides.

2x+2−2=4−2

2x=2

Step 3: Divide both sides by 2.

2x2=22

x=1

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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Answer:

width = 3/10 mi

Step-by-step explanation:

area = length * width

width = area/length

width = (3/4 mi^2)/(2 1/2 mi)

width = (3/4 mi^2)/(5/2 mi)

width = 3/4 * 2/5 mi

width = 6/20 mi

width = 3/10 mi

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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The measure of the angle x is 70.53 degrees

It is important to know that trigonometric identities are defined as equalities that relate to different trigonometric functions and also holds true for any value of the variable that is in the domain.

There are different trigonometric identities namely;

The ratio for the identity cosine is;

cos θ = adjacent/hypotenuse

substitute the values, we get;

cos x = 4/12

divide the values

cos x = 0. 3333

Take the inverse cosine of the values

x = 70. 53 degrees

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Answer:

The perimeter is 99

Step-by-step explanation:

you do 11x9=99

Answer:

17.65%

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve