Determine whether AGHI and AJKL with the given vertices are similar. Use transformations to explain your reasoning.
G(-2, 3), H(4, 3), I(4, 0) and J(1, 0), K(6.-2), L(1, -2)

Step-by-step explanation:

Just Substitute in place of X

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The coordinates are (0, 3) or (34/5, 3)

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

15x - 10y = -30 _____(1)

5x - 9y = 7 ______(2)

Multiply 3 on (2)

15x - 27y = 21 _____(3)

Using the elimination method we get,

From (1) and (3) we get,

 15x - 10y = -30

 15x - 27y = 21

(-)    (+)        (-)

      17y    = 51

This means,

y = 51/17

y = 3

Now,

Put y = 3 in (1) we get,

15x - 10y = -30

15x- 10 x 3 = -30

15x - 30 = -30

15x = 0

x = 0

Put y = 3 in (2) we get,

5x - 9y = 7

5x - 9 x 3 = 7

5x - 27 = 7

5x = 7 + 27

5x = 34

x = 34/5

Thus,

The coordinates are (0, 3) or (34/5, 3)

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Answer: a = 180 - 63 - 90

Step-by-step explanation:

180 degrees in a triangle

90 degrees in a right triangle

180 = 63 + 90 + a

move 63 and 90 to the other side

a = 180 - 63 - 90

Answer:

x = -8

Step-by-step explanation:

Given equation,

→ (x/4) - 6 = -8

Now the value of x will be,

→ (x/4) - 6 = -8

→ x/4 = -8 + 6

→ x/4 = -2

→ x = -2 × 4

→ [ x = -8 ]

Hence, the value of x is -8.

We have proved that ABCD is a rectangle.

What is the isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.

<EAD=<EDA  ------------------∆AED is isosceles triangle.

<EBC=<ECB    ------------------ ∆EBC is isosceles triangle.

AD= BC   -------------------------Given

<AED=<BEC       ------------------- Vertically opposite angle

<EAD=<ECB                              

2<EAD=180°- <AED

         = 180°-<BEC

            =2<ECB.

∆AED congruent to ∆BEC --------- By A-S-A Congruency.

AE=EC, DE=EB                   ----------Corresponding sides

ABCD is a parallelogram ----------- Diagonals bisect to each other.

AC=BD                                      

AE+EC=DE+EB.

ABCD is a rectangle.   ------------- Diagonals are equal.

Hence, we have proved that ABCD is a rectangle.

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It takes 2 hrs to fill the fountain with both sprinklers operating

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

Given,

A park has two sprinklers that are used to fill a fountain

One sprinkler can fill the fountain in 3 h

second sprinkler can fill the fountain in 6 h

We need to find the time required to fill the fountain by two sprinklers.

Let t = time required with both sprinklers working

t/3+t/6=1

2t+t/6=1

3t/6=1

Apply cross multiplication

3t=6

Divide both sides by 3

t=2

Hence, it takes 2 hrs to fill the fountain with both sprinklers operating

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By power algebra method,

a) [tex]\frac{16}{81}[/tex]

b) [tex]\frac{2xy}{3}[/tex]

c) [tex]\frac{16x^4}{y^8}[/tex]

d) [tex]\frac{3y^2}{x^3}[/tex]

According to the Quotient of Powers Property, you can maintain the base and subtract the exponents when dividing two exponents by the same base. Since you cannot divide by zero, this characteristic will always hold true as long as the base is not zero. For more information on this property, use the interactive below.

The Exponents Power Rule: am*n = (am)n. Multiply the exponent by the power to increase a number with an exponent to that power.

You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).

a) [tex](\frac{2}{3})^4[/tex] = [tex]\frac{2*2*2*2}{3*3*3*3}[/tex] = [tex]\frac{16}{81}[/tex]

b) [tex]\frac{2x^2y}{3x}[/tex] = [tex]\frac{2*x*x*y}{3*x}[/tex] = [tex]\frac{2xy}{3}[/tex]

c) [tex](\frac{2x}{y^2})^4[/tex] = [tex]\frac{2x*2x*2x*2x}{y^2*y^2*y^2*y^2}[/tex] = [tex]\frac{16x^4}{y^8}[/tex]

d) [tex]\frac{3xy^4}{x^3}[/tex][tex].\frac{y}{xy^3}[/tex] = [tex]\frac{3x*y*y*y*y}{x*x*x} . \frac{y}{x*y*y*y}[/tex] = [tex]\frac{3y^2}{x^3}[/tex]

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Answer:

Step-by-step explanation:

The number of bags he can make without having any cookies left over is 4 bags.

Number of chocolate chips = 48

Number of vanilla cookies = 64

Number of raisin cookies = 100

Answer:

Attached

Step-by-step explanation:

this is ur answer

[tex]2y = - 9 \\ y = ( - 9) - 2 \\ y = - 11[/tex]

Answer:

0.6 inches

Step-by-step explanation:

The equation to find the area of a circle is:

[tex]{a} = \pi {r}^{2} [/tex]

however the problem requires you replace π with 3.14.

Using inverse operations you can find the variable r.

Step 1:

Plug in variables.

[tex]0.2826 = 3.14{r}^{2} [/tex]

Step 2:

Solve for r.

[tex]0.2826 \div 3.14 = 3.14 \div 3.14 \times {r}^{2} \\ \sqrt{0.09} = \sqrt{ {r}^{2} } \\ r = 0.3[/tex]

Step 3:

Find diameter from radius.

[tex]0.3 \times 2 = 0.6[/tex]

The diameter of the circle is 0.6 inches.

The elements of the required sets would be:

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

A set, denoted by the curly brackets , is a grouping of items, numbers, elements or objects.

A set of numbers, for instance, is 1, 2, 3, 4.

Solution:

P' = {2, 4, 6, 8, 10}

Q' = {1, 4, 6, 8, 9, 10}

R' = {6, 7, 8, 9, 10}

P∩Q = {3, 5, 7}

R'∪P' = {2, 4, 6, 7, 8, 9, 10}

P∪R = {1, 2, 3, 4, 5, 7, 9}

P∩R = {1, 3, 5}

P∪Q∪R = {1, 2, 3, 4, 5, 7, 9}

P'∩Q'∩R' = S - P∪Q∪R

               = {6, 8, 10}

Now we can find the elements of the required sets:

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

Hence, the elements of the required sets would be

(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}

(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}

(c) Q'∩(P∪R) = {2, 3, 5, 7}

(d) (P∪Q∪R)'∩(P∩R) = ∅

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The probability of the Komets losing their race and the Galaxy winning theirs is

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

The probability of the Galaxy team winning is 22%.

And, The probability of the Komets team winning is 47%.

Now,

Since, The probability of the Galaxy team winning is 22%.

And, The probability of the Komets team winning is 47%.

Hence, The probability of the Komets team losing = 100% - 47%

                                                                              = 53%

                                                                              = 0.53

Then, The probability of the Komets losing their race and the Galaxy winning theirs is = 0.53 × 0.22

                         = 0.1166

Thus, probability of the Komets losing their race and the Galaxy winning theirs is 0.1166.

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Answer:

11.66%

Explanation:

I put 12% as my answer, but I got it wrong. So I talked to my teacher and she said the CORRECT ANSWER WAS 11.66%!!

The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is  1 And the probaility is [tex]\frac{1}{42}[/tex]

Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to signify how many positive findings there are in an experiment with 'n' results. The following formula can be used to determine the likelihood of an event:

Probability (event) equals a favorable result/the total of outcomes divided by n.

The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is  1

And the probaility is -

[tex]\frac{1}{6} X \frac{1}{7}[/tex]

[tex]= \frac{1}{42}[/tex]

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Answer: Open

Step-by-step explanation: the dot is only filled in when the inequallity is "greater than or equal to" or "less than or equal to"

Answer:

  D)  $27

Step-by-step explanation:

You want an estimate of a reasonable amount to pay for 10 gallons of gas at $229 per gallon, and 2 quarts of oil at $1.89 per quart.

For estimating purposes, we like to round numbers to 1 or 2 significant figures.

The cost of 10 gallons of gas is about 10 × $2.30 = $23.

The coast of 2 quarts of oil is about 2 × $2 = $4.

So, the total cost of the gas and oil is about $23 +4 = $27.

You expect the total to be near $27.

__

Additional comment

Part of estimating is estimating the error in your estimate. Here the error is $0.01 per gallon of gas, or $0.10 for 10 gallons. The error is $0.11 per quart of oil, so  $0.22 for 2 quarts. The final estimate of $27 is $0.10 +0.22 = $0.32 too high. $27 is different from the next answer choice by $2, so is still the best answer choice.

Answer:

They are all prime numbers

Explanation:

17, 19, 46, and 55 are all prime numbers. A prime number is a whole number greater than 1 that is only divisible by 1 and itself. Since 17, 19, 46, and 55 are all prime numbers, they have no other factors besides 1 and themselves, which means they cannot be divided evenly by any other number.

The angle of elevation of the ramp to the nearest degree will be 5.71°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that a ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet.

The angle of elevation will be calculated as,

tanθ = ( 1 / 10)

θ = tan⁻¹(1/10)

θ  = 5.7°

Therefore, the angle of elevation of the ramp to the nearest degree will be 5.71°.

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Answer:

3.714

Step-by-step explanation:

26 x ⅐ = 26 / 7

= 3.714 or [tex] 3 \frac{5}{7} [/tex]

The opportunity cost of mowing the lawn is The $15 he earns minus the enjoyment he would have received from watching the football game during that time.

Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them. Making smarter decisions requires an understanding of the possible opportunities lost when a company or person selects one investment over another.

Opportunity Cost =FO−CO where:

FO=Return on best-forgone option

CO=Return on the chosen option

​The formula for calculating an opportunity cost is simply the difference between the expected returns of each option.

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The percentage for blue balls will be 56% and the percentage for red balls will be 44%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

In this situation, there are 4000 balls and 2240 of then are blue while 1760 area red.

The percentage for blue balls will be:

= Number of blue balls / Total balls × 100

= 2240 / 4000 × 100

= 56%

The percentage for red balls will be:

= Number of red balls / Total balls × 100

= 1760 / 4000 × 100

= 44%

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Answer:

[tex]\huge\boxed{\sf h = 130\ m}[/tex]

Step-by-step explanation:

Time = t = 5.2 s

Velocity = v = 25 m/s

Height = h = ?

h = vt

h = 25(5.2)

[tex]\rule[225]{225}{2}[/tex]

Answer:

The valley is 130 m deep.

Step-by-step explanation:

Formula we use,

→ Height = Time × Speed

Now the height will be,

→ Time × Speed

→ 5.2 × 25

→ 130 metres

Thus, valley is 130 m deep.

Answer:

y = -100/13

Step-by-step explanation:

To solve this equation, we can first get all the terms containing the variable y on one side of the equation and all the constant terms on the other side. We can do this by subtracting 25 from both sides of the equation:

5/13y + 25 - 25 = 0 - 25

This gives us:

5/13y = -25

Next, we can divide both sides of the equation by 5/13 to get rid of the fraction:

(5/13y) / (5/13) = (-25) / (5/13)

This simplifies to:

y = -100/13

Therefore, the solution to the equation is y = -100/13.

The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p

Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.

Given that an expression;

2.3p – 10.1 = 6.5p – 4 – 0.01p

Firstly we will simplify the above expression by removing decimals.

For that,

(23 / 10)p – (101 / 10) = (65 / 10)p – 4 – (1 / 100)p

Now we will take LCM,

{ (23 - 101) / (10) }p = {650p - 400 - p} / 100

230p – 1010 = 650p – 400 –p

Therefore The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p.

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Check the picture below.

The true statement about J and K is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

The correct answer is option (c)

In this question, we have been given that a certain statistic will be used as an unbiased estimator of a parameter.

The sample size of J = 40.

and the sample size of K = 100.

We need to find the true statement about J and K.

By central limit theorem, both J and K will have same means.

An expression for standard deviation is:

s = σ/√n

From the above expression standard deviation is inversely proportional to the sample size n. This means, as the sample size increases, the standard deviation decreases.

Thus, the correct statement is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

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The complete question is:

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

Which of the following must be true about J and K ?

a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.

b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.

c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.

e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.

Answer:

143

Step-by-step explanation:

35/55  = 91/x

7/11 = 91/x so 143

Answer:

DB = 143 units

Step-by-step explanation:

In similar triangles, corresponding sides are always in the same ratio.

If ΔDCB ~ ΔDRS then:

[tex]\implies \sf DC : DR = CB : RS = DB : DS[/tex]

From inspection of the given diagram:

Therefore:

[tex]\implies \sf 91 : 35 =DB : 55[/tex]

[tex]\implies \sf \dfrac{91}{35} =\dfrac{DB}{55}[/tex]

[tex]\implies \sf 55 \cdot \dfrac{91}{35} =55 \cdot \dfrac{DB}{55}[/tex]

[tex]\implies \sf 143=DB[/tex]

The shortest side of a triangle is just opposite of the angle 47°.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

All the angle of a triangle are,

⇒ 63°, 47°, 70°

Now,

Since, All the angle of a triangle are,

⇒ 63°, 47°, 70°

We know that;

The smallest side of a triangle is just opposite of the smallest angle.

Thus, The shortest side of a triangle is just opposite of the angle 47°.

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The number of alligators was there in Orange country, Florida in 2001 is equal to 43872.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other words, it is a relationship where the worth of the entire is always considered 100.

As per the given information provided in the question,

Total number of alligators 1992 = 285

Percent increase of alligators every year = 75%

Total number of years from 1992 to 2001,

2001 - 1992 = 9 years

The population of alligators in 2001,

= 285 × (175/100)⁹

= 285 × (7/4)⁹

= 43871.98 or,

= 43872 alligators.

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Answer:

Step-by-step explanation:

To find the number of four-letter words that can be formed using the letters in facetious, you can use the combination formula:

nCr = n! / (r! (n - r)!)

In this case, n is the total number of letters available (9) and r is the number of letters per word (4). Therefore, the number of four-letter words that can be formed is:

nCr = 9! / (4! (9 - 4)!) = 9! / (4! 5!) = (9 x 8 x 7 x 6) / (4 x 3 x 2 x 1) = 126

Therefore, there are 126 four-letter words that can be formed using the letters in facetious.