11. Determine whether the triangles are similar. If so, what is the similarity statement and the
postulate or theorem used?

(please answer ASAP if you have the all of the questions for the semester exam I'll take them too please)

A.>TRS~>TPQ;SSS~
B.>TRS~>TPQ;SAS~
C.>TRS~>PQR;SAS~
D.The triangles are not similar ​

It is not possible to fill a smaller rectangular prism with larger 14-inch cubes.

However, there is a typo in the question because the cubes with an edge length of 14 inches cannot fit inside a rectangular prism of smaller dimensions.

Hence, it is impossible to fill the rectangular prism with cubes of 14-inch edge lengths.

Answer:

x=60

Step-by-step explanation:

As the sides of the triangle are doubled (21 to 42 and 44 to 88) that means that the side of 30 is doubled to 60

Answer:

x=60

Step-by-step explanation:

It's B A(n)= 350 + (n - 1) (0.04 · 350); $504.00

Answer:

Option B.

Step-by-step explanation:

Gracie invest $350 at the beginning of the year 1 at annual simple interest rate of 4%.

the balance at the beginning of the year 12. Interest will be calculated for 11 years.

Formula for simple interest : A = P(1 + rt)

By putting the value : A = 350(1 + 0.04 × 11)

                                   A = 350 ( 1.44 ) = $504.00

So the best answer would be option B.

Answer:

hello : x = 2 +√17    or  x = 2 -√17

Step-by-step explanation:

(5x-2)^2=17

5x-2 = √17     or 5x-2 =  - √17

x = 2 +√17    or  x = 2 -√17

Answer:3*6

Step-by-step explanation: It is (40*6)+(3*6) you have to break it down

Answer:

x² + 8x + 16

Step-by-step explanation:

(x + 4)² = (x + 4)(x + 4)

Each term in the second parenthesis is multiplied by each term in the first parenthesis, that is

x(x + 4) + 4(x + 4) ← distribute both parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16 ← perfect square trinomial

So first you have to find the volume of the entire tank using the height of 6cm. Then you have to find the volume of just the water using the height of 4 cm. Then you subtract both of your volumes and that will represent the volume of the part of the tank that isn't filled with water

Answer:

432cm³

Step-by-step explanation:

First we need to find the volume.

Use the volume formula.

[tex]V=l*w*h[/tex]

Plug in the values.

[tex]V=18*12*6\\ \\ V=1296[/tex]

Now find the volume of water we filled up.

[tex]V=18*12*4\\ \\ \\V=864[/tex]

Now we can subtract to find how much more water we need.

[tex]V=1296-864\\ \\ \\V=432[/tex]

432cm³ of water is needed to fill up the tank completely.

Answer:

226.2 feet

Step-by-step explanation:

The fence around the dog's house is a circle, with a radius of 12 meters.

To calculate the distance the dog runs, we need to find the circumference of that circle, which is given by the formula:

C = 2 π r, since we know r, the calculation is easy:

C = 2  π 12 = 24 π = 75.4 feet.

The dog makes three laps around the circle before calming down... so he runs 3 times 75.4 feet.

Dogs run = 3 x 75.4 ft = 226.2 feet

Answer:

Option D. ET=IT

Step-by-step explanation:

we know that

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

In this problem

the included angle ∠ETK of triangle TEK is congruent with the included angle ∠KTI of triangle TIK

the side KT is a common side both triangles

therefore

ET must be equal to IT to prove that triangles TEK and TIK are congruent by SAS postulate

Answer:

241

Step-by-step explanation:

Answer:

The sides of the new triangle compared to the original are 4 times smaller.

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z-----> the scale factor

x----> the corresponding side of new triangle

y----> the corresponding side of the original triangle

[tex]z=\frac{x}{y}[/tex]

we have

[tex]z=\frac{1}{4}[/tex]

substitute

[tex]\frac{1}{4}=\frac{x}{y}[/tex]

[tex]x=\frac{1}{4}y[/tex]

therefore

The sides of the new triangle compared to the original are 4 times smaller.

Answer:

C

Step-by-step explanation:

The correct answer is B.

1/9 can be converted into 2/18. 2/3 can be converted into 12/18. 2/18 + 12/18 + 5/18 = 19/18. The answer is B

Answer:69.38

Step-by-step explanation: Sue = 15.5 allie = 23.25 carol = 15.5+32.25 - 8.12 2.   15.5+32.25=38.75-8.12=  30.63 now all together 23.25+15.5+30.63= 69.38

The girls danced for a total of 30 minutes and 33 seconds.

First, we need to calculate the total time Sue and Allie danced combined:

Sue danced for 15.5 minutes, which can be written as [tex]\(\frac{155}{10}\)[/tex] minutes.

Allie danced for 23.25 minutes, which can be written as [tex]\(\frac{2325}{100}\)[/tex] minutes.

To combine these times, we need a common denominator, which is 100:

Sue's time in minutes: [tex]\(\frac{155 \times 10}{100} = \frac{1550}{100}\)[/tex]

Allie's time in minutes: [tex]\(\frac{2325}{100}\)[/tex]

Now we add Sue's and Allie's times:

[tex]\(\frac{1550}{100} + \frac{2325}{100} = \frac{3875}{100}\)[/tex]

Converting this back to mixed numbers:

[tex]\(\frac{3875}{100} = 38\)[/tex] minutes and [tex]\(\frac{75}{100}\)[/tex] minutes, which is 45 seconds.

Now, Carol danced for 8 minutes and 12 seconds less than the combined time of Sue and Allie. We need to subtract this time from the total time Sue and Allie danced:

[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds.

Subtracting the minutes:

[tex]\(38 - 8 = 30\)[/tex] minutes.

Subtracting the seconds:

[tex]\(45 - 12 = 33\)[/tex] seconds.

Therefore, Carol danced for 30 minutes and 33 seconds. Since Sue and Allie's combined time was 38 minutes and 45 seconds, and Carol danced for 8 minutes and 12 seconds less, the total time the girls danced altogether is:

[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds [tex]\(=\) \(30\)[/tex] minutes and [tex]\(33\)[/tex] seconds.

Thus, the girls danced for a total of 30 minutes and 33 seconds.

The answer is y=1/2x-2

Answer:

[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]

Step-by-step explanation:

Given quadratic equation is [tex]4x^2-x+3=0[/tex].

Compare with [tex]ax^2+bx+c=0[/tex], we get:

a=4, b=-1, c=3

Now plug these values into quadratic formula :

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-\left(-1\right) \pm \sqrt{\left(-1\right)^2-4\left(4\right)\left(3\right)}}{2\left(4\right)}[/tex]

[tex]x=\frac{1 \pm \sqrt{1-48}}{8}[/tex]

[tex]x=\frac{1 \pm \sqrt{-47}}{8}[/tex]

[tex]x=\frac{1 \pm \sqrt{47}i}{8}[/tex]

Hence final answer is

[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]

Answer:

Solution of given quadratic equation,

x = [1 + 6.86i]/8 or x = [1 - 6.86i]/8

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given a quadratic equation, 4x²-x+3=0

To find the solution using quadratic formula

Here a = 4, b = -1 and c = 3

We have,

x = [-b ± √(b² - 4ac)]/2a

x = [--1 ± √((-1)² - 4*4*3)]/2*4

 = [1 ± √(1 - 48)]/8

 = [1 ± √(-47)]/8

 = [1 ± 6.86i]/8

x = [1 + 6.86i]/8 or

x = [1 - 6.86i]/8

The least amount would be 0.146 because the tenths digits is the smallest.

The least amount among the given different amounts is 0.146

Least amount of something means the smallest amount or number.

To find the least number or amount among the list of numbers we first go through the whole list of numbers and compare their values one after the other. And we arrange these numbers or amount in ascending order and find the least one.

According to the given question

We have different amounts

0.146, 2.0102, 0.45, 1.09, 2.001

For finding the least amount, arrange all the given amount in the ascending order.

So, the required ascending order is

0.146, 0.45, 1.09, 2.001, 2.0102

Hence, the least amount among the given different amounts is 0.146.

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Answer:

Mike is not right

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the enlarged rectangular prism

y-----> surface area of the original rectangular prism

[tex]z^{2}=\frac{x}{y}[/tex]

so

In this problem we have

[tex]z=2[/tex]

substitute

[tex]2^{2}=\frac{x}{y}[/tex]

[tex]4=\frac{x}{y}[/tex]

[tex]x=4y[/tex]

so

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism

therefore

Mike is not right

Verify with an example

we have a rectangular prism

[tex]L=5\ m[/tex]

[tex]W=2\ m[/tex]

[tex]H=3\ m[/tex]

The surface area of the prism is equal to

[tex]SA=2(LW)+(2L+2W)H[/tex]

substitute the values

[tex]SA=2*(5*2)+(2*5+2*2)*3=62\ m^{2}[/tex]

If he doubles each dimension of any rectangular prism

then

the new dimensions will be

[tex]L=5*2=10\ m[/tex]

[tex]W=2*2=4\ m[/tex]

[tex]H=3*2=6\ m[/tex]

The new surface area will be

[tex]SA=2*(10*4)+(2*10+2*4)*6=248\ m^{2}[/tex]

[tex]248/62=4[/tex]

therefore

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism

Answer:

They will each have painted 8 km. This goal will be met on Day 4.

Step-by-step explanation:

Group A | Group B

Start: 2   | Start: 5                               Day 1

2 + 2 = 4 | 5 + 1 = 6                            Day 2

4 + 2 = 6 | 6 + 1 = 7                             Day 3

6 + 2 = 8 | 7 + 1 = 8                            Day 4

The first group and second group of workers will each have painted 8 kilometers of the bridge after 3 days.

This question is related to the concept of linear equation in one variable. To solve such a problem, we typically set up an equation that relates the two groups and the amount they have painted to find out when they have painted an equal amount.

The equation representing the painting work of the first group is: 2 + 2d = x, where d is the number of days and x is the total distance painted. For the second group, the equation is 5 + d = x. We can set up these equations because each new day adds certain kilometers to the existing painted distance.

To find when these two equations are equal, we can simply equate them: 2 + 2d = 5 + d. Solving this equation, we get d = 3 days. Substituting d = 3 into either of the group's equations, we get x = 8 kilometers.

So, after 3 days, both groups would have painted 8 kilometers each.

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Answer:

-1/2

Step-by-step explanation:

To find the slope we know that:

Slope = (Y2-Y1)/(X2-X1)

Then, given the two points, we have that:

(X1, Y1) = (-2,-2)

(X2, Y2) = (2, -4)

Then:

m= (Y2-Y1)/(X2-X1) = (-4-(-2))/(2-(-2)) = -4+2/2+2 = -2/4 = -1/2

So the slope of the function that passes through those points is: -1/2

Answer: Option D

[tex]P (B | A) =\frac{4}{5}[/tex]

Step-by-step explanation:

Call A to the event in which a student advances to the second round.

We know that:

[tex]P (A) = 75\% = 0.75[/tex]

Call B the event in which a student advances to the third round.

We know that:

[tex]P (B) = 60\% = 0.6[/tex]

We then look for the probability of B given A. This is:

[tex]P (B | A) =\frac{P(B\ and\ A)}{P(A)}[/tex]

In this case, the probability of B and A is equal to the probability of B, since the students who advance to the third round also advanced to the second round before

[tex]P (B | A) =\frac{P(B)}{P(A)}[/tex]

[tex]P (B | A) =\frac{0.6}{0.75}[/tex]

[tex]P (B | A) =\frac{4}{5}[/tex]

Answer:

45,000

Step-by-step explanation:

Apex is the source

Answer: the answer is $ 45,000 APEX

The ratio of dry rice to water is 1 to 2. This means that water is two times more than dry rice. Since the chef uses 9.5 cups of dry rice, the chef needs 19 cups of water.

You can check by using fractions. 9.5 / 19 in simplified form is 1/2, which is 1:2 in ratio.

It would be 9.5:19 just multiply 9.5 by 2

Answer:

a

Step-by-step explanation:

math

5/8, 8/12, and 3/4 are ordered from least to greatest.

Write all the fractions so that they have a common denominator in order to arrange them in ascending order. By comparing the numerators and sorting the fractions, determine which fraction is the smallest. Rewrite the numbers in the order of size that they appear in the question.

Given

5/8, 8/12, 3/4

Least common multiple of 8, 4, and 12 is 24

[tex]\frac{5*3}{8*3} , \frac{8*2}{12*2} ,\frac{3*6}{4*6} \\\\\frac{15}{24} , \frac{16}{24} .\frac{18}{24}[/tex]

therefore, 5/8, 8/12, and 3/4 are ordered from least to greatest

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The answer is:

[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]

To solve the problem, we need to perform the operations and then, add like terms.

We need to apply the distributive property, which is defined by the following way:

[tex]a(b+c)=ab+ac[/tex]

Also, we need to remember how to add like terms. Like terms are terms that share the same exponent and the same variable, for example:

[tex]3x+5x+x^{2}=8x+x^{2}[/tex]

We were able to add only the first two terms since they are like terms, both are sharing the same exponent and the same variable.

So, we are given the expression:

[tex]-2(2x+5)-3(x-1)[/tex]

Then, solving we have:

[tex]-2(2x+5)-3(x-1)=-4x-10-(3x-3)\\\\-4x-10-(3x-3)=-4x-10-3x+3\\\\-4x-10-3x+3=-4x-3x-10+3\\\\-4x-3x-10+3=-7x-7[/tex]

Hence, we have that the answer is:

[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]

Have a nice day!

D) Arc wx and arc yz is the correct answer because both arcs are equal to 27

Answer:

Option D is correct.

Step-by-step explanation:

Arcs are said to be equal if it subtends equal angles at the center

here we can see that  arcs WX and ZY subtends equal angle and its measure is 27 degrees.

therefore option D is correct answer

Since we are not given the angles subtended by WY and XZ in the center

so we cannot say for option A

Likewise we cannot say  for rest of the option.

Answer:

(z-6)(z+3)

Step-by-step explanation:

Answer:

The factored form of the given expression is (z-6)(z+3).

Step-by-step explanation:

The given expression is

[tex]z^2-3z-18[/tex]

The middle term can by written a -6z+3z.

[tex]z^2-6z+3z-18[/tex]

[tex]z(z-6)+3(z-6)[/tex]

[tex](z-6)(z+3)[/tex]

Therefore the factored form of the given expression is (z-6)(z+3).

Answer:

B. 0.22

Step-by-step explanation:

8/36 = 0.2222

B is the correct answer

Answer:

t^2/3

Step-by-step explanation:

Interest=Principal×Rate×Time

I=PRT/100

I= 79000×15×1

100

I= 1185000

100

I= $11850

To confirm

11850/79000 ÷ 100

= 0.5 ×100

= 15% (rate)

The interest of one year is $11850.

easy interest is based on the essential amount of a loan or the primary deposit in a savings account.

calculation:-

Amount of money borrowed by Linda = $79000

rate of interest =15%

Interest amount= $79000*15/100

  The interest of the year =$11850

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Answer:

4th option is correct; Each distribution has a different mean and a different standard deviation

Step-by-step explanation:

For the mean to be same in all three distributions, all graphs must be centered around the same number, so mean is not same.

The width of each graph shows how much data deviate from the mean. Since the width is different in all three distributions, standard deviation is different in all three distributions

Answer:

D

Step-by-step explanation:

E2020