In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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Answer:

16x + [tex]3y^{2}[/tex] - 26xy

Step-by-step explanation:
PEMDAS

(2x - 3y)(8x - y)
= 16x - 2xy - 24xy + [tex]3y^{2}[/tex]
= 16x + [tex]3y^{2}[/tex] - 26xy

All the values of expressions are,

24. Sin x = 1/√17

25 cos x = 4/√17

26 tan x = 1/4

27. Sin y = 4/√17

28. Cos y = 1/√17

29. Tan y = 4

We have to given that,

A right triangle is shown in figure.

Now, We can simplify all the values,

24. Sin x = Opposite / Hypotenuse

sin x = 2 / 2√17

sin x = 1/√17

25) cos x = Base / Hypotenuse

cos x = 8 / 2√17

cos x = 4/√17

26) tan x = Opposite / Base

tan x = 2 / 8

tan x = 1/4

27. Sin y = Opposite / Hypotenuse

sin y = 8 / 2√17

sin y = 4/√17

28. Cos y = Base / Hypotenuse

cos y = 2 / 2√17

cos y = 1/√17

29. Tan y = Opposite / Base

tan y = 8 / 2

tan y = 4

Thus, All the values of expressions are,

24. Sin x = 1/√17

25. cos x = 4/√17

26. tan x = 1/4

27. Sin y = 4/√17

28. Cos y = 1/√17

29. Tan y = 4

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Answer:

LXXXIX

Step-by-step explanation:

ochenta y nueve es 89.

89 en numero romano es LXXXIX.

41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

We have,

41.

a.

1/3 x 5/6

= 5/18

This means,

Out of the 18 parts, we shade 5 parts

b.

2/9 x 2/3

= 4/27

This means,

Out of the 27 parts, we shade 4 parts

42.

String = 15 feet

Length of each piece = 1/4 feet

Now,

The number of 1/4 feet pieces.

= 15/(1/4)

= 15 x 4

= 60 pieces

43.

Original pizza = 1

Half pizza = 1/2

Number of people = 3

Now,

The fractional part for each person.

= 1/2 ÷ 3

= 1/6

44.

a.

7/6 x 9

= 7/2 x 3

= 21/2

= 10(1/2)

b.

1/7 ÷ 3

= 1/(7 x 3)

= 1/21

c.

4/5 x 3(2/3)

= 4/5 x 11/3

= 44/15

= 2(14/15)

d.

2 ÷ 1/9

= 2 x 9/1

= 18

Thus,

41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

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Answer: Distribute the 10 on the left side of the equation:

10n + 30 = 1,000,000

Subtract 30 from both sides of the equation to isolate the term with n:

10n = 1,000,000 - 30

10n = 999,970

Divide both sides of the equation by 10 to solve for n:

n = 999,970 / 10

n = 99,997

Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.

Step-by-step explanation:

Answer:

4n^4 + 20n^3 - 32n^2

Step-by-step explanation:

We have to distribute 4n2 to each term.

4n2 x n2. We can multiply the two n2 together resulting in 4n^4.

Now we do 4n2 x 5n. Here we multiply 4 x 5 which equals 20. Then, we multiply the n2 and n. Which results in n^3. Now we put them together; 20n^3.

Finally, we multiply 4n2 by -8. Since 8 doesn't have any variables, we just multiply the 4 and -8. Which equals to -32, now we just combine -32 and the variable; -32n2.

Now we combine these terms together. Our final answer is, 4n^4 + 20n^3 -32n^2.

^ represents an exponent.

The length of the arc LM is 8.72 cm.

We have,

The length of an arc is the distance that runs through the curved line of the circle making up the arc.

The length of an arc is expressed as;

l = tetha/360 × 2πr

tetha = R

R = 100°

and, radius = 5 units

so, we get,

l = 100/360 × 2 × 3.14 × 5

l = 8.72 cm (1.dp)

therefore the length of the arc LM is 8.72 cm

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Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by options 2 and 3. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].

the correct answers are, 2 and 3

Answer:

Step-by-step explanation:

it is only moving 3 to the right, so shift the green dot to (3,0)

I used desmos . com for the graph

The value of x is,

⇒ x = 21.65

We have to given that,

A right triangle is shown in image.

Since, The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Hence, We get;

⇒ 25² = 12.5² + x²

⇒ 625 = 156.25 + x²

⇒ x² = 625 - 156.25

⇒ x² = 468.75

⇒ x = 21.65

Thus, The value of x is,

⇒ x = 21.65

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The coordinates of the vertices of the image F'G'H' after reflecting FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

We have,

When reflecting a point across the y-axis, the x-coordinate of the point is negated while the y-coordinate remains the same.

Applying this transformation to each vertex, we get:

F' = (-(-2), -1) = (2, -1)

G' = (-(2), 2) = (-2, 2)

H' = (-(4), -3) = (-4, -3)

Therefore,

The coordinates of the vertices of the image F'G'H' after reflecting FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

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Answer:

8 feet

Step-by-step explanation:

Let b be the length of the base. Then the height is b+6 ft.

The area of the parallelogram is given by:

Area = b(b + 6) = 160

Solving for b, we get,

[tex]b^2 + 6b - 160 = 0[/tex]

Factoring the expression, we get:

(b - 8)(b + 20) = 0

Therefore, b = 8 or b = -20.

Since the base cannot be negative, b = 8.

Therefore, the length of the base of the parallelogram is 8 feet.

The correct options regarding the inequality are:

A. 1 hat, 1 scarf

D. 4 hats, 1 scarf

F. 2 hats, 1 scarf

Based on the time constraint, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:

2h + 3s ≤ 12,

Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.

Phil can knit at most 4 scarves per week, because 4 scarves * 3 hours/scarf = 12 hours.

Phil can use at most 900 yards of yarn, because he has 900 yards of yarn.

Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.

Phil can knit 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.

Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.

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Angle C of the triangle measures 68°.

Side AC = 22.90

Side BC = 14.26

Given triangle,

∠A = 37°

∠B = 75°

AB = 22

Now,

Sum of all the interior angles of triangle is 180.

So,

∠A + ∠B +∠C = 180°

37° + 75° + ∠C = 180°

∠C = 68°

Now,

According to sine rule,

Ratio of side length to the sine of the opposite angle is equal.

Thus,

a/SinA = b/SinB = c/SinC

Let,

BC = a

AC = b

AB = c

So,

a/Sin37 = b/Sin75 = c/Sin68

a/0.601 = b/0.965 = 22/0.927

Solving,

BC = a = 14.26

AC = b = 22.90

Thus with the properties of triangle side length and angles can be calculated.

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x+77=180

x=180-77=103°

x+5y-98=180

=> 103+5y-98=180

=> 5y=180-5

=> y=175/5=35°

Answer:

Volume ≈ 153.93804 cm^3

Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.

Step-by-step explanation:

The test statistic χ² is approximately 1.47.

We have,

To test independence for the contingency table, we need to calculate the test statistic.

The most commonly used test statistic for testing independence in a 2x2 contingency table is the chi-square test statistic.

The chi-square test statistic (χ²) is calculated using the formula:

χ² = Σ [(Observed - Expected)² / Expected]

Where:

Σ represents the sum over all cells of the contingency table.

Observed is the observed frequency in each cell.

Expected is the expected frequency in each cell if the variables were independent.

First, we calculate the expected frequencies for each cell. To do this, we use the formula:

Expected frequency = (row total x column total) / grand total

Grand total = sum of all frequencies = 36 + 17 + 15 + 11 = 79

Expected frequency for the cell "Closed roof - Win" = (53 * 51) / 79 = 34.49

Expected frequency for the cell "Closed roof - Loss" = (53 * 28) / 79 = 18.51

Expected frequency for the cell "Open roof - Win" = (26 * 51) / 79 = 16.51

Expected frequency for the cell "Open roof - Loss" = (26 * 28) / 79 = 9.49

Now, we can calculate the test statistic using the formula:

χ² = [(36 - 34.49)² / 34.49] + [(17 - 18.51)² / 18.51] + [(15 - 16.51)² / 16.51] + [(11 - 9.49)² / 9.49]

Calculating each term and summing them up:

χ² ≈ 0.058 + 0.482 + 0.58 + 0.35 ≈ 1.47

Therefore,

The test statistic χ² is approximately 1.47.

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Step-by-step explanation:

B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).

To factor a quadratic expression, you can use the following steps:

1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).

2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.

In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:

(b+7)(b+1)

This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).

Here is a step-by-step explanation of how to factor B^2+8b+7:

1. The coefficient of the middle term is 8.

2. The constant term is 7.

3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.

4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).

The formulas that represent the linear function in this problem are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The line has a slope of 2/3, hence:

y = 2x/3 + b.

When x = 1, y = 2, hence the intercept b is obtained as follows:

2/3 + b = 2

b = 6/3 - 2/3

b = 4/3.

Hence the slope-intercept equation of the line is given as follows:

f(x) = 2x/3 + 4/3.

The line goes through points (1,2) and (4,4), hence the point-slope equations to the line are given as follows:

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The equation showing the problem is: 4x + 8y = 20

The graph is attached and the y intercept is (0, 2.5)

Assuming that:

Since Pedro walks at a rate of 4 miles per hour, the distance he covers by walking would be

Also Pedro runs at a rate of 8 miles per hour, the distance he covers by running would be

According to the given information, the total distance Pedro covers each week is 20 miles. Therefore, we can write the equation:

4x + 8y = 20

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Answer:

x intercept at( -2)

y intercept at (4)

The x-intercept and the y-intercept are -2 and 4 respectively.

The X-intercept is the point where the line of an equation intersects the X-axis. While y-intercept is the point where the line of an equation intersects the Y-axis. Here, the X-axis is the horizontal axis, and the Y-axis is the vertical axis.

Since the given graph shows the line intersecting the X-axis i.e. the horizontal axis at -2, the x-intercept of the line would be -2. Whereas, since the line intersects the Y-axis at 4, the y-intercept is 4. The points that show these intercepts are (-2,0) for the x-intercept and (0,4) for the y-intercept.

∴ The intercepts are -2,4 respectively.

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Answer:9.5

Step-by-step explanation:

Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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It will take the truck 9 hours to travel from warehouse A to warehouse B.

To determine the time it takes for the truck to travel from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.

First, let's find the vertical distance between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.

Next, we convert the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.

Now, we can calculate the time it takes to travel this distance. We divide the distance by the speed of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.

Therefore, it will take the truck 9 hours to travel from warehouse A to warehouse B.

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Answer:

B. 108 ft³

Step-by-step explanation:

solution given:

We have Volume of solid = Area of base * length

over here

base : 9ft

height : 6 ft

length : 4ft

Now

Area of base : Area of traingle:½*base*height=½*9*6=27 ft²

Now

Volume : Area of base*length

Volume: 27ft²*4ft

Therefore Volume of the solid=108 ft³

log 161 can be expressed as log 7 + log 23 in the form of loga + logb.

To express log 161 in the form of loga + logb, first we need to find suitable values for a and b such that their logarithmic product is equal to log 161.

Let's find the factors of 161 :

161 = 7 * 23

Now, we can express log 161 as product of two logarithms :

log 161 = log (7 + 23)

Using the logarithmic property log(a*b) = log a + log b :

log 161 = log 7 + log 23

Therefore, log 161 can be expressed as log 7 + log 23.

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The equation of the tangent to the circle at point A is 6x + 7y - 93 = 0

The equation of a circle in standard form is (x-h)² + (y-k)² = r²,

(h,k) is the center of the circle

r is the radius.

The radius formula ⇒ √((x₂ - x₁)² + (y₂ - y₁)²).

Here,

x₁ = -1, y₁ = 2 (center of the circle),

x₂ = 5, y₂ = 9 (point A on the circle).

∴

r = √((5 - (-1))² + (9 - 2)²) = √(36 + 49) = √85.

Now, we have the equation of the circle: (x - (-1))² + (y - 2)² = 85, or (x + 1)² + (y - 2)² = 85.

The slope of the radius from the center of the circle to point A ⇒ (y₂ - y₁) / (x₂ - x₁)

= (9 - 2) / (5 - (-1)) = 7/6.

tangent line is the negative reciprocal of the slope of the radius, ∴ -6/7.

The equation of a line in point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

The slope of the tangent line (m) is -6/7 and it passes through point A(5,9). Substituting these values in, it becomes

y - 9 = -6/7 (x - 5).

Multiplying every term by 7 to clear out the fraction and to have the equation in the ax + by + c = 0 form, we get:

7y - 63 = -6x + 30,

or

6x + 7y - 93 = 0.

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