Complete proofs 3-5 using Angle-Angle-Side (AAS).
3. Given: ZKJL = ZLMK, ZJKL ZMLK
Prove: AJKLAMLK
1.
2.
3.
4.
Statements
1.
2.
3.
4.
K
Reasons
L
M
Gina Wilson (All Things Algebra, LLC), 2014-2020

The area and the perimeter of the various given figures above are listed below:

1.) area=70 cm²

perimeter = 29cm

2. area= 80mm²

perimeter = 36mm

3.) area=108m²

perimeter = 42m

4.) area=72cm²

perimeter = 34cm

For figure 1;

The area of the given figure = length×width.

Where;

Length = 7cm, width = 10

area = 7×10 = 70 cm²

The perimeter = summation of the whole sides.

= 10+7+5+4+3

= 29cm

For figure 2;

The area of the given figure = length×width.

Where;

Length = 8 mm; width = 10mm

area = 8×10 = 80mm²

The perimeter = 6+8+6+10+(8-6)+(10-6)

= 6+8+6+10+2+4

= 36mm

For figure 3;

The area of the given figure = length×width.

Where;

Length= 6+3 = 9m

width ,= 8+5 = 12m

area = 9×12 = 108m²

The perimeter: 2( 9+12) = 42m

For figure 4;

The area of the given figure = length×width.

Where;

Length= 8cm

width = 4+5 = 9cm

area = 8×9 = 72cm²

The perimeter = 6+4+5+8+(5+4)+(8-6)

= 6+4+5+8+9+2

= 34cm.

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1. The values of x in the equation are 1 and 10.

2. The values of x are 1 and -4.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

1. y = x²

y = 11x - 10

Combine both variables

x² - 11x + 10

x² - x - 10x + 10

x(x - 1) - 10(x - 1)

x - 10 and x - 1 = 0

x = 10 and 1

2. y = x².

y + 3x = 4

x² + 3x - 4

x² +4x - x - 4

x(x + 4) - 1(x + 4)

(x - 1)(x + 4)

x = 1 and -4

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Answer:

(1-5n)(25m^2+5n+1

Step-by-step explanation:

The volume of the cone is 64π

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

Height, h = 12 m

Radius, r = 4 m

The volume is calculated s

V = 1/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 1/3π * 4² * 12

Evaluate

V = 64π

Hence, the volume is 64π

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Answer:

2 boys must be vegetarian.

If all 34 girls were vegetarian, there would have to be 2 boys to add up to 36.

The equation that represents the situation is m= 1/8s-10

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

When

s= 0, m= -10

When

s= 80, m= 0

[tex]\frac{0-(0-10)}{80-0} = \frac{10}{80} = \frac{1}{8}[/tex]

m-0 = 1/8(s-80)

m= 1/8s-10. The equation

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Answer: its 270.1087 degrees

Step-by-step explanation:

Answer:

y= 6x+50

Step-by-step explanation:

y= 6x+50

The cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.

Two or more expressions with an Equal sign is called as Equation.

Plan A costs $30 plus an additional $0.03 for each minute of calls.

This can be expressed in equation as

y=30+0.03x

Plan B has no initial fee but costs $0.18 for each minute of calls.

y=0.17x

Now we have to find the cost when the two plans cost the same for a set number of minutes

30+0.03x=0.18x

30=0.18x-0.03x

30=0.15x

Divide both sides by 0.15

x=200

when the number of minutes of calls is 200, the two plans cost the same.

To find the cost when the two plans cost the same,

we can substitute x = 200 into either expression for Cost_A or Cost_B:

Cost_A = 30 + 0.03(200) = $36

Cost_B = 0.18(200) = $36

Therefore, the cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.

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The intersection point of the exponential and linear equation is at (3.748, 14.993).

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The equations are given below.

[tex]\rm y = 2 \left ( \dfrac{1}{5} \right )^{x - 5}[/tex]

The graph of the exponential equation is drawn.

y = 4x

The graph of the linear equation is also drawn.

From the graph, the intersection point of the exponential and linear equation is at (3.748, 14.993).

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Answer:

-2

Step-by-step explanation:

?

First we need to select the subject to create the great paper outline template. Then follow the steps to create a paper.

Step 1: Choose the topic for the paper.

Step 2: Make a list of all the concepts you wish to discuss or incorporate.

Step 3: Separate similar concepts into smaller groupings.

Step 4: Put your concepts in order of importance: What ought the reader to discover first? What matters the most? Which conclusion will best suit your paper?

Step 5: Make good headers and subheadings for your documents.

Step 6: Format the outline in decimal, full-sentence, or alphanumeric form.

Step 7: State and review the paper by oneself first.

Follow all the steps to create the great paper outline template.

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The answer is that it depends on the specific countable sets being considered and how they are being combined.

The union of countably infinite sets can be countable, as in the case of the union of all positive integers and all negative integers, which is also countable.

However, the union of countably infinite sets can also be uncountable. For example, consider the union of all the intervals [n, n+1) for n = 1, 2, 3, .... Each of these intervals is countable (since it contains all the real numbers between two integers, which is a countable set), but the union of these intervals is the uncountable set of all real numbers greater than or equal to 1. Therefore, the union of these countably infinite sets is uncountable.

So the answer is that it depends on the specific countable sets being considered and how they are being combined.

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The population be 1,152 hours from now will be 17200

Exponential growth is a process of increasing a quantity over time. It occurs when the rate of change of a quantity with respect to time is proportional to the itself.

Given that, the number of bacteria in a colony doubles every 384 hours and there is currently a population of 2,150 bacteria,

The exponential growth law for this problem is :-

p(t) = 2150(2)ⁿ/₃₈₄

where t is in hours. Plug t = 1152 into the equation and evaluate.

p(1152) = 2150(2)¹¹⁵²/₃₈₄

= 2150(2)³

= 17200

Hence, the population be 1,152 hours from now will be 17200

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Answer:

After 3 hours.

Step-by-step explanation:

60 + 30x = y

40x = y

Beach Shack:

60, 90, 120, 150, 180, 210

Surf Shop:

40, 80, 120, 160, 200

Answer:

since p is irrational it is not expressible as a ratio of two integers and has an infinite and nonrecurring expansion when expressed as a decimal

Step-by-step explanation:

so a

The number of birds they can take care on that day is zero.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 2.5b + 5r = 80.

Where, b represents the number of birds and r represents the number of reptiles.

On a given day. If the business cares for 16 reptiles, Therefore,

2.5b + 5(16) = 80.

2.5b + 80 = 80.

2.5b = 0.

So, They can not take care of any birds during the day.

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Answer:

4.72

Step-by-step explanation:

for essy calculation remove the decimal point

[tex] \frac{0.18}{100} [/tex]

=

[tex] \frac{18}{100} [/tex]

then multiply by 4

you will get

[tex] \frac{18 }{25} [/tex]

= 4.72

Answer:

VII

Step-by-step explanation:

The simplified form of the expression √50 - √2 is 4√2.

Given the expression in the question;

√50 - √2

To evaluate, first we simplify each term

√50 - √2

Factor out 25 from 50

√( 25(2) ) - √2

Now, rewrite 25 as 5²

√( 5²(2) ) - √2

Take the square root of 5² to pull it out of the radical

5√2 - √2

Now, subtract √2 from 5√2

4√2

Therefore, the simplified form is 4√2.

Option C) 4√2 is the correct answer.

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The measure of the central angle subtended by minor arc ab, to the nearest degree is 67.

A minor arc is a part of a circle that is created by two points on the circumference of the circle.

To find the measure of the central angle subtended by the minor arc ab, we need to use the formula for the circumference of a circle, which is C = 2πr. The length of the minor arc ab is 12 feet, which is a part of the circumference of the circle. So, we can write an equation:

12 = C * (arc ab / C)

where C is the circumference of the circle and arc ab is the length of minor arc ab. We know that the radius of the circle is 10 feet, so we can find the circumference of the circle using the formula for circumference:

C = 2πr = 2π * 10 = 20π

Substituting the value of C in the equation above, we get:

12 = 20π * (arc ab / 20π)

Dividing both sides of the equation by 20π, we get:

12 / 20π = (arc ab / 20π)

We can now find the central angle subtended by the minor arc ab by using the formula:

Central angle = 2 * arctan(arc ab / 2r)

Substituting the values, we get:

Central angle = 2 * arctan(12 / (2 * 10)) = 2 * arctan(0.6)

Using a calculator, we can find that the value of arctan(0.6) is about 33.7 degrees. Hence, the central angle subtended by minor arc ab is:

Central angle = 2 * 33.7 = 67.4 degrees

Rounding off to the nearest degree, we get that the central angle subtended by minor arc ab is 67 degrees.

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The mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.

To find the mean distance that the heavy ball was thrown, we need to calculate the sum of all the distances and then divide by the total number of throws:

(20+25+25+31+33+34+41+41+45+50+56+67)/12 = 467/12 ≈ 38.92

So, the mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.

This means that on average, the ball was thrown a distance of 3.24 feet. However, it's important to note that the mean can be influenced by outliers, which in this case is the one throw of 6.7 feet.

So, while the mean is a useful measure of central tendency, it's important to also consider other measures such as the median and mode to get a complete picture of the data.

The mean is the sum of all the values in a dataset divided by the total number of values. It provides an estimate of the central location of the data and can be a useful summary statistic for describing a dataset. However, the mean can be influenced by outliers, which are values that are significantly different from the rest of the data.

In this case, the one throw of 6.7 feet is an outlier because it is much further than any other throw, and it will increase the mean value.

For this reason, it's important to consider other measures of central tendency such as the median and mode. The median is the middle value in a dataset, and it's not affected by outliers. The mode is the value that appears most frequently in a dataset and can provide useful information about the typical or most common value in the data.

By considering all three measures (mean, median, and mode), we can get a more complete picture of the data and make better inferences or conclusions about it.

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Answer:

[tex]\dfrac{1}{12}[/tex]

See the explanation for more details

Step-by-step explanation:

Not sure if you want this as a word problem or not. So here goes anyway

3 friends decided to share 1/4 of a pizza equally. How much of the original pizza portion did each get

In equation form:
[tex]\dfrac{1}{4} \div 3[/tex]

When dividing, flip the divisor so it is the reciprocal of the original divisor

Then multiply both the dividend and the flipped value

[tex]\textrm{Reciprocal of 3 = }[/tex] [tex]\dfrac{1}{3}[/tex]

[tex]\dfrac{1}{4} \div 3 = \dfrac{1}{4} \times \dfrac{1}{3}[/tex]

[tex]= \dfrac{1 \times 1}{4 \times 3} \\\\= \dfrac{1}{12}[/tex]

This is the quotient

Answer:

162cm²

Step-by-step explanation:

Formula of square with diagonals=1/2*d²

=1/2*(18)²

=1/2*324cm²

we get,

=162cm²

The volume of the cone with a base diameter of 6in and height of 6in is 6π in³.

The volume of a cone is expressed as;

V = (1/3)πr²h

Where r is radius of the base, h is the height of the cone and π is constant pi.

Given the data in the diagram;

Plug the given values into the above formula and solve for the volume of the cone.

V = (1/3) × π × r² × h

V = (1/3) × π × ( 3in )² × 6in

V = 18π/3 in³

V = 6π in³

Therefore, the volume of the cone is 6π cubic inches.

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Answer:

Reese will first need to use point slope Formula to plug in- 4   for x1,  8 for y1, and 3 for the m

Reese's final answer will be y = 3x + 20, which is written in slope intercept Form.

Step-by-step explanation:

The answers in terms of the choices and order in which the blanks appear are

H. Point Slope

E. -4

I. 8

B. 3

C. y=3x+20

G. Slope Intercept

The point slope form for a line
y - y1 = m(x - x1)

Pugging in x1 = -4, y1= 8 and m = 3 gives
y -8 = 3(x - (-4))

y - 8 = 3x + 12  Move -8 to right side
y = 3x +12 + 8
y = 3x + 20

A. 63

The angle shown is 90 degrees, if you take 90 and subtract 27 you get 63.

The probability that the number cube and the card have the same number is 2/39.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Outcomes of cube = { 1, 2, 3, 4, 5, 6}

Outcome of Card = {1, 2, 3} from each group.

So, we have three number both in common as {1, 2, 3}

So, the probability that the number cube and the card have the same number is

= 1/6 x 16/52

= 8/156

= 2/39

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The algebraic fraction which is an equivalent fraction with the denominator 24a^3b^2 is 15b/24a^3.

To find an equivalent fraction with the denominator 24a^3b^2, we need to find a common denominator for the two fractions 5b and 8a^3. This common denominator is 24a^3b^2.

To find an equivalent fraction for 5b, we can multiply both the numerator and denominator by the same factor to obtain the desired denominator. To do this, we need to find a factor that would give us a denominator of 24a^3b^2 when multiplied with 8a^3.

The factor that would give us a denominator of 24a^3b^2 is 3.

So, the equivalent fraction for 5b with the denominator 24a^3b^2 is (5b * 3)/(8a^3 * 3) = 15b/24a^3.

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