In the figure below, the segments HI and HJ are tangent to the circle centered at O. Given that OI = 3.9 and OH= 6.5, find HJ.
H
6.5
9
O
HJ = 0
X

By translation, the image of the vertices of the figure A'B'C' are A''(x, y) = (1, - 3), B''(x, y) = (- 2, - 1) and C''(x, y) = (- 3, - 5), respectively.

In this problem we must determine the image of the figure A'B'C', whose vertices are A'(x, y) = (4, - 1), B'(x, y) = (1, 1), C'(x, y) = (0, - 3), by translation, whose definition is shown below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that T(x, y) = (- 3, - 2), then the image of the vertices of the figure A'B'C' are:

A''(x, y) = (4, - 1) + (- 3, - 2)

A''(x, y) = (1, - 3)

B''(x, y) = (1, 1) + (- 3, - 2)

B''(x, y) = (- 2, - 1)

C''(x, y) = (0, - 3) + (- 3, - 2)

C''(x, y) = (- 3, - 5)

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Answer:

Step-by-step explanation:

Answer:

Let x be the length of one side of the first carpet in feet. Then, the area of the first carpet is x^2 square feet.

Let y be the length of one side of the second carpet in feet. Then, the area of the second carpet is y^2 square feet.

From the problem, we know that the sum of the areas of the two carpets is 720 square feet:

x^2 + y^2 = 720

We also know that the difference of the areas of the two carpets is 432 square feet:

x^2 - y^2 = 432

We can solve this system of equations by using the method of substitution. Solving for x^2 in the second equation, we get:

x^2 = y^2 + 432

Substituting this expression for x^2 into the first equation, we get:

y^2 + 432 + y^2 = 720

Simplifying and solving for y, we get:

2y^2 = 288

y^2 = 144

y = 12

Substituting this value of y into the equation x^2 + y^2 = 720 and solving for x, we get:

x^2 + 144 = 720

x^2 = 576

x = 24

Therefore, the dimensions of the first carpet are 24 feet by 24 feet, and the dimensions of the second carpet are 12 feet by 12 feet.

Step-by-step explanation:

Answer:

B)  6

Step-by-step explanation:

Calculate the value of c by substituting point (0, 15) into the quadratic equation formula:

[tex]f(x)=ax^2+bx+c[/tex]

[tex]\begin{aligned}f(0)=a(0)^2+b(0)+c&=15\\0+0+c&=15\\c&=15\end{aligned}[/tex]

Therefore:

[tex]f(x)=ax^2+bx+15[/tex]

Substitute the point (1, 22) into the formula and create an equation for a in terms of b:

[tex]\begin{aligned}f(1)=a(1)^2+b(1)+15&=22\\a+b+15&=22\\a+b&=7\\a&=7-b\end{aligned}[/tex]

Therefore:

[tex]f(x)=(7-b)x^2+bx+15[/tex]

Finally, substitute another point from the table (-3, 6) and solve for b:

[tex]\begin{aligned}f(-3)=(7-b)(-3)^2+b(-3)+15&=6\\(7-b)9-3b+15&=6\\63-9b-3b+15&=6\\78-12b&=6\\-12b&=-72\\b&=6\end{aligned}[/tex]

Therefore, the value of b is 6.

Answer:

6

Step-by-step explanation:

The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range is 0.1487

The total digit of individuals living independently in the area = 31.6

The digit of individuals living in the area who fall within the 25 - 34 age range = 4.7

The probability formula will be applied ed as

P = required outcome / Total possible outcomes

From the information that is provided above the given data is:

P(range 25 - 34) = 4.7 / 31.6

= 0.1487

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The question is incomplete, Complete question probably will be  is:

The table shows the​ distribution, by age and​ gender, of the 31.6 million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 25-34 age range.

The probability is ___.

(Type an integer or decimal rounded to the nearest hundredth as needed.)

The number of players  who included red and purple as their favorite colors is 0.

option A.

The number of people who included red and purple as their favorite colors are calculated as follows;

We are going to determine this number based on the given Venn diagram.

Check the intersection of red and purple, you will notice it is empty, so there is volleyball team member who included red and purple as their favorite colors.

So the answer is zero (0) since the intersection or connection point between red and purple is empty.

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The word problem is given thus: Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?

Four sandwiches were prepared by Mrs. Ericson, each identical in size, for her offspring: Matt, Elisa, Carl, and Riley.

The children consumed varying portions of their respective sandwiches during the shared midday meal.

Post-lunch investigations denoted different fractions residual from each child's original sandwich quantity.

Matt kept 7/8 of his portion while Elisa held on to 3/4 of hers. Meanwhile, two halves (2/4) constitute what remained of Carl's sandwich with Riley retaining 4/8 for himself.

Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?

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The question in English is:

Mrs. Ericson made sandwiches for her 4 children. All the sandwiches had

The same size. After lunch, each child had a fraction left.

different from your sandwich. Matt had, Elisa had

7

3, Carl was 2, and Riley was 8

8

4

Use this information to write a problem comparing two fractions

with the same numerator.

The value of the expression is 28 2/3

To determine the value of addition, we need to know that fractions are described as part of a whole number or variables.

From the information given, we have that;

1/9 times 3 to the 3rd power

This is represented as;

(1/9 × 3)³

Divide the values, we get

(3)³

Find the cube

27

Then, we have;

27 + 2(1/6+2/3)

Solve the bracket

27 + 2( 1+ 4 /6)

27 + 2(5/6)

Divide the values

27 + 5/3

81 + 5/3

86/3

Divide the values

28 2/3

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The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.

The graph of the solution set of -48 < -8t is shown below.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Next, we would determine the solution to the given inequality as follows;

2.5x ≥ 20

x ≥ 20/2.5

x ≥ 8 (Sebastian was wrong)

-48 < -8t

-48/-8 < -8t/-8

6 < t

t > 8

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We can solve this problem using the conservation of momentum and the law of conservation of energy. Here's how:

Let v be the velocity of the 105 kg player just before the tackle. Then the velocity of the 156 kg player just before the tackle is -6 m/s, since he is running south. After the tackle, the two players move at a velocity of 3 m/s north, so we have:

Total momentum before = Total momentum after

(105 kg)(v) + (156 kg)(-6 m/s) = (105 kg + 156 kg)(3 m/s)

Simplifying and solving for v, we get:

v = (105 kg + 156 kg)(3 m/s) + (156 kg)(6 m/s) / 105 kg

v = 2.85 m/s

Therefore, the velocity of the 105 kg player just before the tackle was 2.85 m/s north.

Evaluating the expression (x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1), we get x = 1

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

(x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1)

Evaluating the like terms, we have

(x - 2)/(x - 1) = (x + 1)/(x + 1)(x - 1)

Cancel out the common factors

So, we have

(x - 2) = 1

Add 2 to both sides

x = 3

Hence, the solution is 3

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The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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Answer: C

Step-by-step explanation:

Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.

The Cost of the blue paint that would cover the shaded area = $0.495

The Cost of the white paint that would cover the triangular shapes = $0.6678

Recall the following formulas:

Area of a circle = πr²

Area of a triangle = 1/2 * base * height.

Area the blue paint will cover = 2(1/2 * base * height) = 2(1/2 * 1.5 * 1)

= 1.5 ft²

Cost of the blue paint = 1.5 * 0.33 = $0.495

Area the blue paint will cover = πr² - area of the two triangles

= 3.14 * 1.5² - 1.5 = 5.565 ft²

Cost of the white paint = 5.565 * 0.12 = $0.6678

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Answer:

The Correct answer is D and F

The total cost of the art supplies without the coupon is:

2 paint brushes x $10.50 per brush = $21.00

1 dozen colored pencils x $7.88 per dozen = $7.88

1 sketch book x $16.12 per book = $16.12

Total cost without coupon = $21.00 + $7.88 + $16.12 = $45.00

With the $15.00 off coupon, the total cost becomes:

$45.00 - $15.00 = $30.00

The amount saved by using the coupon is:

$45.00 - $30.00 = $15.00

The percentage saved can be calculated as:

Percentage saved = (Amount saved / Total cost without coupon) x 100%

Percentage saved = ($15.00 / $45.00) x 100%

Percentage saved = 33.33%

Therefore, the customer saved 33.33% by using her coupon.

The triangle with 2 angles as 90° is not possible and the statement is false.

Given data ,

Let the triangle be represented as ∠ABC

Now , the measures of the angles of the triangle are

A triangle has two 90° angles and a side 12 centimeters in length

So , ∠ABC = ∠BAC = 90°

And , For a Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Therefore, a triangle cannot be formed with 2 angles as 90°

Hence, the statement, the third angle is 90° is False

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Answer:

0

Step-by-step explanation:

Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

The probability that fewer than 30% of the rolls result in a two is given as follows:

0.3085 = 30.85%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

2 out of the six faces are two, and there will be 50 trials, thus the parameters n and p are given as follows:

n = 50, p = 2/6 = 1/3 = 0.3333.

The mean and the standard error are given as follows:

The probability that fewer than 30% of the rolls result in a two is the p-value of Z when X = 0.3, hence:

Z = (0.3 - 0.3333)/0.0667

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

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Check the picture below.

Answer: 1/2

Step-by-step explanation:

The fraction equivalent of 0.5 is 1/2.

To convert it into a mixed number, we can divide the numerator by the denominator:

1 ÷ 2 = 0 with a remainder of 1

So, the mixed number is 0 1/2.

The circles are similar because you can translate Circle 1 using the transformation rule (0, -7) and then dilate it using a scale factor of 3/5.

Translation involves moving an object in a straight line without changing its size or shape. In this case, we can translate Circle 1 7 units down to match the y-coordinate of Circle 2. The transformation rule for this translation is (0, -7), since we are not changing the x-coordinate.

Dilation involves uniformly scaling an object, either making it larger or smaller. We can dilate Circle 1 by a scale factor of 3/5 to make it have the same radius as Circle 2. The scale factor is determined by taking the ratio of the radii:

scale factor = radius of Circle 2 / radius of Circle 1

scale factor = 9 / 15

scale factor = 3/5

The center of dilation is the center of Circle 1, since we want to preserve its position.

Therefore, we can transform Circle 1 into Circle 2 by translating it 7 units down and dilating it by a scale factor of 3/5. The transformation rule is:

(0, -7) followed by dilation with a scale factor of 3/5

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The equation for the translated function is the one in option D:

G(x) = (x - 6)² - 4

We start with the parent quadratic function:

F(x) = x²

We apply two translations, one of 6 units to the right which can be written as:

G(x) = F(x - 6)

And a translation of 4 units down, which is written as:

G(x) = F(x - 6) - 4

Replacing F(x) we will get:

G(x) = (x - 6)² - 4

The correct option is D.

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Answer:

Step-by-step explanation:

Let A(-2,-3), B(-4,-4).

Line f(x) = y = ax + b (C)

The line passes through these points so when substituting their coordinates into (C), we get:

-3 = -2a + b

-4 = -4a + b

Solving this set of equations gives us a = 1/2; b = -2.

So the equation of this line is  [tex]f(x)=\frac{1}{2}x-2[/tex]

The width of the brochure is 3/2 inches and the height is 10 inches.

Let's assume that the width of the brochure is x and the height is y.

The area of the brochure is given as 30 square inches:

xy = 30

The perimeter of the brochure is given as 23 inches:

2x + 2y = 23

We can use the second equation to solve for one variable in terms of the other.

2x + 2y = 23

2x = 23 - 2y

x = (23 - 2y)/2

Now we can substitute this expression for x into the equation for the area:

xy = 30

[(23 - 2y)/2]y = 30

23y/2 - y^2 = 60/2

y^2 - 23y/2 + 30 = 0

We can solve for y using the quadratic formula:

y = [23/2 ± sqrt((23/2)^2 - 4(1)(30))]/(2)

y = [23/2 ± sqrt(529/4 - 120)]/2

y = [23/2 ± sqrt(289/4)]/2

y = [23/2 ± 17/2]/2

y = 10 or y = 3/2

Since the height must be greater than the width, we can eliminate y = 3/2 as a solution.

So, y = 10 and

x = (23 - 2y)/2 = (23 - 20)/2 = 3/2

Therefore, the width of the brochure is 3/2 inches and the height is 10 inches.

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The line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

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Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation: