Find each missing measure

The figures are congruent and the corresponding sides are AC = KM, AB = KL and BC = LM

Congruent figures in geometry are identical in shape and size.

In other words, congruent figures are geometric figures that have the same shape and size.

If the figures are polygons, then they are congruent if all the corresponding sides and corresponding angles are congruent.

Therefore, the polygons above are triangles, they are congruent if the corresponding sides and angles are equal.

Therefore, the figures(triangles) are congruent by the following rules:

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Work Shown:

x = number of dimes

y = number of quarters

x+y = 157 coins total

-------------------------------

$26.50 = 2650 cents

1 dime = 10 cents

x dimes = 10x cents

1 quarter = 25 cents

y quarters = 25y cents

total value = 10x+25y = 2650 cents

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We have this system of equations

x+y = 157

10x+25y = 2650

Let's solve for y in the first equation

x+y = 157

y = 157-x

Then plug this into the second equation and solve for x.

10x+25y = 2650

10x+25(157-x) = 2650

10x+25(157)+25(-x) = 2650

10x+3925-25x = 2650

-15x+3925 = 2650

-15x = 2650-3925

-15x = -1275

x = -1275/(-15)

x = 85 is the number of dimes

Then use this to find the value of y

y = 157-x

y = 157-85

y = 72 is the number of quarters

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Check:

85 dimes + 72 quarters = 157 coins total

85 dimes = 85*10 = 850 cents

72 quarters = 72*25 = 1800 cents

850 cents + 1800 cents = 2650 cents = $26.50

This confirms the answers.

Answer:

so 85 dimes and 72 quarter coins are in the box

Step-by-step explanation:

Given; Total number of coin =1557 Total amount money =26.50 To find Number of dimes and quarters in the box. In order to find the solution, make equation of number of coin and amount money. solve for unknown.Let, Number of dimes = x Number of quarters = y As, it is given that total number of coin is 157. x + y = 157 ......(a) Also, the total money is $ 26.50. .. 0.10x+0.25y = 26.50 ..(b)To, solve equation (a) & (b), put value of y from (a) to (b); From (b); From (a); y= 157 0.10x+0.25(157 - x) = 26.50 0.10x+39.25 - 0.25x = 26.50 0.15x+39.25 = 26.50 39.25 26.50 = 0.15x 12.75 = 0.15x 12.75 0.15 = x 85 = x Now, put value of x in equation (a); x + y 85+ y = y= 72

The given statement " If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20" is Hypotesis of a true conditional statement is true, so the conclusion is also true. This is Law of Detachment.

The Hypothesis is the first or “If” portion of the conditional statement or p. The Conclusion is the second or “then” part of the conditional statement or q.

If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, the statement is false.

The following assertion "X + 9 > 20 if x > 12. X has a value of 14. Thus, x + 9 > 20 "The conclusion follows logically from the hypothesized truth of the conditional statement. This is the Detachment Law.

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Answer: to solve this equation, multiply both sides of the equation by 2.

Step-by-step explanation: by multiplying both sides of the equation by 2, you are effectively eliminating the fraction on the left, making the answer x = 16.

2 feet : 12/5 minutes

1/8 foot: 1 2/3 minutes

3 feet : 4 2/3 minutes

1 5/8 feet :2 minutes

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, whereas the ratio of lemons to oranges is 6:8. Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.

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Answer:

4.24ms-²

Step-by-step explanation:

S: x. write suvat and sub in values

u:4.2

v:14.8

a:?

t:2.5

use correct equation

v=u+at

sub values in

14.8=4.2+2.5a

rearrange to get a

10.6/2.5= a

a=4.24

Answer:

Step-by-step explanation:

5) Domain: -3<=x<=2

Range: 4<=y<=-3

6)  Domain: {-3,-2,-1,0,1,2}

Range: {4,3,2,1,0,-1,-2,-3}

Do you need number 7 too?

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Answer:

it's 0

Step-by-step explanation:

i hope this helps you

Answer:

x = 12

Step-by-step explanation:

To justify q || r :

11x - 28 + 7x - 8 = 180 because they would be supplementary angles and their sum would be equal to 180°

add like terms

18x - 36 = 180 add 36 to both sides

18x = 216 divide both sides by 18

x = 12

Answer:

SAS

Step-by-step explanation:

SAS is side, angle, side so two sides are congruent and one angle is congruent.

If you look at the picture the side that is shared by both triangles is equal.(side)

The two sides with the line through them means they're equal.

(side)

The picture shows the two angles are equal.

(angle)

=SSA or SAS

The probability that Cynthia's morning porridge will be just right is 15%.

Probability is defined as the likeliness of an event to happen. It can be determined by dividing the total number of the desired outcome by the total number of samples.

The sum of the probabilities in a probability distribution is always 1.

If there are three outcomes: too cold, just right, and too hot, then the sum of their probabilities is equal to 1 or 100%.

P(too cold) + P(just right) + P(too hot) = 100%

35% + P(just right) + 50% = 100%

P(just right) = 100 - (35 + 50)

P(just right) = 100 - 85

P(just right) = 15%

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We have that the tangents which meet at the same point outside the circle have the same length:

Then, in this case:

Now that we have all the measures, we find the perimeter just by adding them:

6 + 6 + 9 + 9 + 12+ 12 = 54

Answer: the perimeter of the figure is 54

The formula to find the surface area of a cylinder is:

In this case, we have:

B. 140π units²

All the students are paid equal amount of $270. Therefore, no oneis paid more.

For student A, the amount paid for 20 hours will be:

= (67.50 / 5) × 20

= 13.50 × 20

= $270

For student B, the amount paid for 20 hours will be:

= (189/14) × 20.

= $270

For Student C, the amount paid for 20 hours will be:

p = 13.5h

where h = number of hours

p = 13.5 × 20 = $270

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Answer:

D yeyeyeye! <3

Answer:

15 purple beads

Step-by-step explanation:

Calculate total beads

[tex]\frac{9}{\frac{3}{8} } =\frac{72}{3} =24[/tex]

Calculate how many beads are purple

[tex]24-9=15[/tex]

Hope this helps

There are total 15 purple beads.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

given:

Fraction of blue beads = 3/8

Total blue beads = 9

let the total number of beads be x.

So, 3/8x = 9

x= 9. 8/3

x= 72/3

x= 24

So, number of purple beads = 24 -9= 15 beads

Hence, there total 15 purple beads.

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Answer:

C. 152

Step-by-step explanation:

8 × 10 + 6 × 12 = 80 + 72 = 152

Answer:   Median = 5

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Explanation

Given Table of Data

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Size of the shoe} & \text{No. of pair sold}\\\cline{1-2}3 & 4\\\cline{1-2}4 & 18\\\cline{1-2}5 & 25\\\cline{1-2}6 & 12\\\cline{1-2}7 & 5\\\cline{1-2}8 & 1\\\cline{1-2}\end{array}[/tex]

The second column is the set of frequencies. Adding up those frequencies gets us

4+18+25+12+5+1 = 65

There are 65 total shoes.

Divide this in half

65/2 = 32.5

There are 32 values below the median, and 32 values above it. That's 32+32 = 64 values so far. When including the median value itself we have 32+1+32 = 65 values total. This only works when the sample size is odd.

---------------------------

What we'll do is add up the partial sums of the frequency values.

The goal is to get to a sum of 33, or larger, because the median is in the 33rd slot.

Adding the first two frequencies gets us 4+18 = 22. This is not 33 or larger, so we move on.

Adding the first three frequencies gets us 4+18+25 = 22+25 = 47 which is 33 or larger.

What this tells us is that the median corresponds to the third row of the table, since we added the first three frequencies to get to 33 or larger.

The median must be 5.

By using differentials the error in the volume estimation is 7.29 cubic centimeters.

The volume of a cube (V), in cubic centimeters, is equal to the cube of the side length (L), in centimeters, whose formulas are:

V = L³

Now we proceed to estimate the volume differential by using first derivatives:

dV = 3 · L² · dL

Where dL is the length differential, in centimeters.

If we know that L = 9 cm and dL = 0.03 cm, then the error in the computed volume of the cube is:

dV = 3 · (9 cm)² · (0.03 cm)

dV = 7.29 cm³

The error in the volume estimation is 7.29 cubic centimeters.

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The probability that I, Sharon, and Robert are chosen is 0.0012

What is the formula for calculating combinations?

The equation  [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.

The total number of employees=18

The Boss must choose 3 employees to attend the conference.

The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .

The equation  [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.

So, [tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}[/tex]

    [tex]^{18}C_{3}=\frac{18!}{(15)! 3!}[/tex]  

    [tex]^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]

     [tex]^{18}C_{3} =816[/tex]

The probability that I, Sharon, and Robert are chosen is  [tex]\frac{1}{816}[/tex] = 0.0012

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The probability that I, Sharon, and Robert are chosen is 0.0012

What is the formula for calculating combinations?

The equation   [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]    will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.

The total number of employees=18

The Boss must choose 3 employees to attend the conference.

The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex]   .

The equation  [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]    will be used to calculate combinations,.

So,

[tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}^{18}C_{3}=\frac{18!}{(15)! 3!}^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]

[tex]^{18}C_{3}=816[/tex]

The probability that I, Sharon, and Robert are chosen is  = 0.0012

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Answer: 2

Step-by-step explanation:

      We will use the slope formula to find the slope of the line going through these two points.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\displaystyle \frac{0-2}{-5--4} =\frac{-2}{-5+4} =\frac{-2}{-1} =2[/tex]

      The slope of this line is 2.

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Mayumi took 4.5 laps by riding her bike around the park

Distance of each lap around the park = 2/3 miles

Distance covered by Mayumi = 3 miles

Fractions: The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It specifies the number of equal portions of the whole or collection that are taken.

Laps took by Mayumi:

Distance covered by Mayumi on her bike/Distance of each lap around the park

= 3/(2/3)

= 3*3/2

= 9/2 or 4.5 laps

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The approximate length and width of this rectangle to the nearest tenth are 15.6 feet and 31.2 feet respectively.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

A represents the area of a rectangle.

W represents the width of a rectangle.

L represents the length of a rectangle.

Making length (L) the subject of formula, we have:

L = A/W

Substituting the given parameters into the formula, we have;

3x = 489/6x

3x × 6x = 489

18x² = 489

x² = 489/18

x² = 27.2

x = √27.2

x = 5.2

Now, we can determine the length and width of this rectangle as follows:

Width = 6x

Width = 6 × 5.2

Width = 31.2 feet.

Length = 3x

Length = 3 × 5.2

Length = 15.6 feet.

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Answer:

525 miles is that was what was being asked

Step-by-step explanation:

sorry I don't know the quest but the car can travel a total of 525 miles with 15 gallons in the tank

15 times 35=525

Given -

To Find -

Type of Triangle =?

Step-by-Step Explanation -

As we can see we have an obtuse angle in the triangle and also, the two sides are equal.

So,

It is an Obtuse angle triangle.

It is also an isosceles triangle

Final Answer -

B. Obtuse

E. Isoseceles

The value of percent of the decimal .065 is 6.5 %.

We are provided with the value .065 .

The ratio or a number expressed as a fraction of 100 is referred to as percentage. It is  denoted using the percent sign % .

We have, .065 . We need to convert this value in the percentage. certain steps need to be followed to convert this value in the percentage. These steps are mentioned below;

.065

Multiply this above mentioned value by 100 to convert it into percent.

.065 × 100

= 6.5 %

So, percent of the decimal value is  6.5 %.

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Answer:

8 years8 years

Explanation:

Let Eli's age be represented as x

Sydney's age = 11

half on Eli's age = x/2

7 more than half on Eli's age = x/2 + 7

If 7 more than half on Eli's age is Sydney's age, then;

x/2 + 7 = 11

Subtract 7 from both sides

x/2 + 7 - 7 = 11-7

x/2 = 4

Multiply both sides by 2;

x/2 * 2 = 4 * 2

x = 4 * 2

x = 8

Hence Eli is 8 years old

Let's call x to the first number ans y to the second number.

The first of two numbers is twice the second:

x = 2y

Seven more than the second number is equal to 6 less than the first number:

7 + y = x - 6

Isolating x:

7 + y + 6 = x

13 + y = x

Combining last equation with first equation:

2y = 13 + y

2y - y = 13

y = 13

Then:

x = 2*13

x = 26