Ideas Math FL B.E.S.T. - Geometry > Checkpoint: Similarity transformations G6J
The side lengths of AGHI are 8, 12, and 16 units. Two of the side lengths of ALMN are 10 and
15 units. If AGHI and ALMN are similar, what is the length of the third side of ALMN?
units

Answer: 1.08g

Step-by-step explanation:

Concentration = Moles/ Volume

Moles = Concentration x Volume

Moles = 0.048 x 250/1000

Moles= 0.012

Moles= Mass / Relative Formula Mass

Mass = Moles x Relative Formula Mass

Mass = 0.012 x 90

= 1.08g

Answer:

angle a = 122°

Step-by-step explanation:

since the opposite angles in a parallelogram are equal, therefore,

Angle a = angle c

therefore,

14x -4 = 15x - 13

-4 +13 = 15x - 14x

x = 9

therefore angle a = 14 x 9 - 4 = 122°

To evaluate the multiplication expression 7*38, we simply multiply 7 and 38 together and the result after multiplication is 266.

Multiplication is a basic arithmetic operation that involves combining two or more numbers to obtain a product. In this case, we are given the expression 738, which involves multiplying the number 7 by the number 38 to obtain a product. To do this, we can use the multiplication operation, which involves adding 7 to itself 38 times.

This can be a time-consuming process when dealing with large numbers, but it is a fundamental skill in mathematics and is used in a wide range of applications, including engineering, science, finance, and computing. In this case, we have evaluated the expression 738 to be equal to 266, which is the product of 7 and 38.

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The greatest common factor of the 24x³ + 36x² is 12x².

It is the greatest factor common to all the numbers given such that there are no greater factors common other than that.

Example:

4 is the gcd of 12, 8, 16.

We have,

24x³ + 36x²

Taking out the common factor.

= 12x² (2x + 3)

Thus,

GCF of the expression is 12x².

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Let's call the length of the longer rope piece x and the length of the shorter rope piece y. We know that:

x + y = 5 (the total length of the rope is 5 feet)

And from the problem statement, we have:

3x - 7 = 5y

Now we can use the first equation to solve for y:

y = 5 - x

Substituting this expression for y into the second equation:

3x - 7 = 5(5 - x)

Expanding the right side:

3x - 7 = 25 - 5x

Adding 5x to both sides:

8x - 7 = 25

Adding 7 to both sides:

8x = 32

Dividing both sides by 8:

x = 4

So the length of the longer rope piece is 4 feet.

Answer:

  G  descends about 8 ft per second

Step-by-step explanation:

You want to know the descent rate of an airplane whose altitude is shown on a graph as being 1500 ft at 0 seconds and 0 ft at 180 seconds.

The airplane descended 1500 feet over a period of 180 seconds. That rate of change is ...

  (-1500 ft)/(180 s) ≈ -8.333 ft/s

The plane descends about 8 feet per second.

__

Additional comment

The slope of the line segment is the change in y divided by the change in x. For computing these changes, it is useful to consider points whose coordinates are obvious. Here, the y-intercept (1500 ft) and the x-intercept (180 seconds) are good choices.

The change in y from 1500 to 0 is a change of -1500. The change in x from 0 to 180 is a change of +180. The ratio of these changes is the slope, which is often designated by the letter m:

  m = -1500/+180 = -25/3 = -8 1/3 . . . . . . about -8

The units of the slope are the ratio of the y-axis units to the x-axis units: feet/second.

The slope of -8 feet/second tells you the plane is descending about 8 feet per second.

For the given matrix A, a 3x2 matrix B such that AB=I, where I is the 2x2 matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex] when AB=I

Given matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₂ₓ₃

B = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₃ₓ₂

In such a way we know that, that AB = I ₂ₓ₂

therefore = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

we can say that [tex]\left[\begin{array}{ccc}a+2c+e&b+2d+f\\a+c+e&b+d+f\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

then, a+2c+e=1

then, when elaborated we get, a+2(-a-e)+e=1

a-2a-2e+e=1

-a-e=1

a+e = -1

2c-c = 1, c = 1 hence we get the value for c

similarly we can do the same steps for the other values

b+2d+f=0

1-d+2d=0

1+d = 0

d = -1

we get the value of d as well now for the value of a and e we can proceed as shown below:

a+c+e=0

c= -a-e

a+e= -c

a+e= -1

a= -2, e=1

similarly we can proceed as shownfor the values of b and f

b+d+f=1

b+f=1-d

b+f=2

b=1, f=1

when we put these values in the correct order and place we get the value for matrix b such as shown below,

therefore, matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex]

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Solution of given inequality is x < -12.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

Given inequality

- (1/2)x > 6
Multiplying with 2 on both sides

- (2/2)x > 6×2

- x > 12

Multiplying with -1 on both sides

x < -12

Hence, x < -12 is the solution of given inequality.

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The restocking fee for an item with an original price of $180 and a restocking fee of 6% is $10.80.

A restocking fee is a fee that is charged when a customer returns an item, usually to cover the costs associated with processing the return and getting the item back in a sellable condition. The fee is typically calculated as a percentage of the original price of the item.

In this problem, we are given that the restocking fee is 6% and the original price of the item is $180. To find the restocking fee, we can use the formula:

Restocking fee = (Percentage fee / 100) x Original price

In this case, the percentage fee is 6% or 0.06 (since 6% is equivalent to 6/100). The original price is $180. Substituting these values into the formula gives:

Restocking fee = (0.06) x $180

Restocking fee = $10.80

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Answer:

y = 2ˣ

Step-by-step explanation:

Since, the question asked which function is best represented by the graph and the function given are:

y = 0.5ˣ

y = 2ˣ

y = 3ˣ

y = 2 * 0.25 ˣ

We can graph each of them to see which is the answer.

Base on the graph below we can see that;

the function that represents the graph is  y = 2ˣ

RevyBreeze

In a case whereby Shana bought sodas and popcorn for the movies. Sodas cost $3 each and popcorn costs the system of equation involving the number of sodas, s, and the bags are:  (3s + 4p )= $26  and s+p = 7 .Then Shana bought 5 sodas and 2popcorn.

We know that :

Sodas cost =$3 each

popcorn costs= $4 per

total =$26

The system of equation can be written as :

(3s + 4p )= $26

We were also told that he bought things equal to the 7 things which can be expressed as:

s+p = 7

Then we can solve the equations as:

3s + 4p = 26 .............................................(1)

s+p = 7................................................................(2)

multiply equation by -3

-3s - 3p =-21  ..................................................................(3)

Then add (1) and 3

4p-3p = 26-21

p=5

Then substitute the value of p into equation 2 we have

s+5 = 7

s= 7-5

=2

s=2

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complete question:

Shana bought sodas and popcorn for the movies .Sodas cost $3 each and popcorn cost $4 per bag . Shana bought 7 things from the concession., all either sodas or bags of popcorn. Shana spent a total of $26 . Write a system of equations involving the number of sodas S ,and the bags of popcorn ,B .Solve the system to see how many of each shana bought

The percentage of decrease in the amount of land that Simon owns is 20.1%.

1,510 - 1,208 = 302

302 / 1,510 = 0.201

0.201 x 100 = 20.1%

Simon recently sold his old farmland, which was 1,510 acres in size, and purchased a new plot of land that is 1,208 acres in size. To calculate the percent of decrease in the amount of land that Simon owns, we subtract the new land size from the old land size and divide the result by the old land size. This number is then multiplied by 100 to get the percent of decrease. In this case, we subtract 1,208 from 1,510 to get 302. We then divide 302 by 1,510 to get 0.201. When we multiply 0.201 by 100, we get 20.1%, which is the percent of decrease in the amount of land that Simon owns now.

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The probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%. We can use the standard normal distribution to find the probability that the next report will weigh less than 45g.

z = (x - mu) / sigma

where z is the standard score, x is the value we want to standardize (45g), mu is the mean (60g), and sigma is the standard deviation (12g).

Substituting the given values, we get:

z = (45 - 60) / 12

z = -1.25

Next, we use a standard normal distribution table (or a calculator) to find the cumulative probability of z being less than -1.25. This gives us:

P(z < -1.25) = 0.1056

Therefore, the probability that the next report will weigh less than 45g is approximately 0.1056 or 10.56%.

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The value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2

We shall evaluate for the value of x to know what makes the algebraic equation true as follows;

3(2x - 5 + 8x) = 5(2x + 5)

3(10x - 5) = 5(2x + 5)

30x - 15 = 10x + 25 {expand bracket}

30x - 10x = 25 + 15 {collect like terms}

20x = 40

x = 40/20 {divide through by 20}

x = 2

Therefore, the value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2.

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Since in the figure, a || b and m∠1 = 34°, the magnitude of m∠5 is equal to 34°.

In Mathematics, parallel lines are two lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to lines a and b, we have the following:

m∠1 ≅ m∠5

m∠5 = 34°.

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The p-value is a measure of the evidence against the null hypothesis (H0)

The correct answer is (a) greater the evidence against H0.

It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming that the null hypothesis is true.

The smaller the p-value, the less likely it is that the observed result is due to chance alone, and the stronger the evidence against the null hypothesis. This means that if the p-value is very small (e.g., less than 0.05), we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis.

In contrast, a large p-value indicates weak evidence against the null hypothesis, and we may not have enough evidence to reject H0. Therefore, the smaller the p-value, the greater the evidence against H0.

Option (b) is incorrect because the chance of committing a Type I error (rejecting the null hypothesis when it is actually true) is related to the level of significance (alpha) and not the p-value. Option (c) is also incorrect because the chance of committing a Type II error (failing to reject the null hypothesis when it is actually false) is related to the power of the test and not the p-value. Option (d) is incorrect because a smaller p-value actually makes it more likely that one will reject H0, assuming that the level of significance is held constant.

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"3 added to 5 is the same as 3 more than 5",  this statement is true. The statement "3 added to 5 is the same as 3 more than 5" means that the expression "3 added to 5" is equal to the expression "3 more than 5".

Another way to express the equality of two mathematical expressions is "3 added to 5 is the same as 3 more than 5".

"3 added to 5" is equivalent to the sum "3 + 5", which equals 8.

"3 more than 5" can be written as "5 + 3," which equals 8 as well.

Because both expressions have the same value of 8, the statement "3 plus 5 equals 3 more than 5" is correct.

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Answer:

The total length of the two straight parts is 80 m x 2 = 160 m.

So, the length of the curved part of the track is 400 m - 160 m = 240 m.

Let the radius of the curved part of the track be "r".

Since there are two curves, each of length "l", in the track, the total length of both curves is 2l.

The length of one curved part can be given by the formula:

l = 2πr, where π is pi (approximately equal to 3.14).

So, 2l = 2 x 2πr = 4πr.

Therefore, 4πr = 240 m.

Dividing both sides by 4π, we get:

r = 240 m / (4π) = 240 / (4 x 3.14) = 15 m.

Hence, the radius of the curved part of the track on both sides is 15 m.

The height of the tree is approximately 156.7 feet.

What is Trigonometry?

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

The height of the tree can be calculated using trigonometry.

Let's call the height of the tree "h".

Then, using the right triangle formed by the height of the tree, the distance from the base of the tree to where Jerome is standing, and the angle between the ground and the top of the tree, we can set up the following equation:

tan(33°) = h / 90

Solving for h, we get:

h = 90 * tan(33°)

Using a calculator to find the value of tan(33°), we get:

h = 90 * 1.730

h ≈ 156.7 feet

So, The height of the tree is approximately 156.7 feet.

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The total cost of an order is $900 if 50 invitations cost is $298.50

To calculate the cost of an order of personalized invitations, you would need to know the cost of each invitation and the one-time design fee.

Let calculate the cost of each invitation and the one-time design fee as follows:

50 Invitations: $298.50 / 50 = $5.97 per invitation

500 Invitations: $2049 / 500 = $4.098 per invitation

Design Fee: ($2049 - ($5.97 × 50)) / 500

= $3.90 one-time design fee

If you wanted to order 150 personalized invitations, the cost would be:

150 Invitations x $5.97 per invitation = $896.50

Plus one-time design fee of $3.90 = $890.40

Total cost = $896.50 + $3.90 = $900.

Hence, the total cost of an order is $900 if 50 invitations cost $298.50

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Answer:

156

Step-by-step explanation:

6(2×3+5×4)

6(6+20)

6×26

156

another way

6(2x+5y)

12x+30y

12×3+30×4

36+120

156

The first term of an arithmetic progression is 5 and the 10th term is 95. The sum of the first 10 terms is 455.

The sum of the first 10 terms of an arithmetic progression (A.P.) can be found using the formula:

S_n = n/2 * (2a + (n-1)d)

where a is the first term, d is the common difference, and n is the number of terms.

Given that the first term is 5 and the 10th term is 95, we can find the common difference (d) using the formula:

a_n = a + (n-1)d

Plugging in n = 10 and a = 5, we get:

95 = 5 + (10 - 1)d

Solving for d, we get:

d = (95 - 5) / (10 - 1) = 9

Now that we know the common difference, we can find the sum of the first 10 terms:

S_10 = 10/2 * (2 * 5 + (10 - 1) * 9) = 10/2 * (10 + 81) = 10/2 * 91 = 455

So, the sum of the first 10 terms is 455.

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The width of standard television set is 16.8 inches.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

We can solve this by using the  Pythagorean theorem which is below:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Or we can say

[tex]w^{2} +h^{2} =d^{2}[/tex]

w = width

h = height

d = diagonal measure

With that said, we know the height is .75 times the width so .75w. We also know d = 21, which is our diagonal measure.

w = don't know yet but need to find

h = .75w

d = 21

[tex]w^{2} +h^{2} =d^{2}[/tex]

[tex]w^{2} +(0.75w)^{2} =21^{2}[/tex]

1.5625 w^2 = 441

w^2 = 441/1.5625

w ^2 = 282.24

w =16.8

The width of standard television set is 16.8 inches.

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If the wax was priced at $1.67 per square foot, it would cost $1,664.99 to wax the entire floor. The right answer is C.

The floor is made up of a trapezoid and a rectangle.

The area of a trapezoid can be calculated as:

A = (b₁ + b₂)/2 x h

Where b₁ and b₂ are the lengths of the bases and h is the height.

The trapezoid is 14 feet tall, and its bases are 33 feet long and (28 - 19) or 9 feet wide. Thus, its area is:

A = (33 + 9)/2 x  14

A = 294 square feet

The rectangle is 37 feet tall with a 19-foot base. Thus, its area is:

A = 19 x 37

A = 703 square feet

The area of the triangle and trapezoid together make up the overall area of the figure.

A = 294 + 703

A = 997 square feet

Finally, to find the cost of the wax, we multiply the area by the cost per square foot:

Cost = 997 * $1.67

Cost  = $1664.99

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Answer:

ASA

Step-by-step explanation:

There are two pairs of congruent angles, and the pair of congruent sides is included between the angles.

4. The value of b is 180+2a (option C)

11. the distance between A and B is 4√2 (option A)

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.

The total angle at a point is 360°

therefore the third angle in the triangle = 180-(a+a) = 180-2a

therefore b = 360-( 180-2a)

b = 360-180+2a

b = 180+2a

If the volume of the cube is 64, then AB = √4²+4²

= √16+16 = √32

AB = √32

AB = √ 16×2

AB = 4√2

Therefore the distance between A and B is 4√2

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The answer in fractions is 59/100

When a statistic is given as a percentage, we assume that the sample size of the survey is

100

persons.

So, in the aforementioned question, we simply need to express the percentage as a fraction where the

numerator

represents the number of people who are in favor of the argument that their teens are addicted to cell phones which is

59

the denominator of the fraction represents the total number of people in the sample survey size which is

100.

simply using the above logic we can deduce the percentage into a fraction which is

59/100

.

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Answer: look at the image for the answer and the solution

Step-by-step explanation:

Answer: a^2 b^2 c^2

Step-by-step explanation:

because that is the pythageoran theorem the rule of it is a^2 + b^2 + c^2 so it's right

Answer:

x + y = -6

Step-by-step explanation:

Just put x and y and add the number on the RHS
Its really not that hard

But i hope it helped