A chord is 22 cm long. It is 60 cm from the center of the circle.
What is the radius of the circle?

B is the assertion that captures the final behavior of the function f(x) = 3|x 7| 7. As x moves closer to zero, f(x) moves closer to positive infinity.

An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate

From the question,

\(f(x) = 3|x − 7| − 7\\when x = -101\\then, f(x) = 3|-101 − 7| − 7\\f(x) = 3|-108| − 7\\\)

f(x) = 3 × 108 − 7

f(x) = 324 -7

\(f(x) = 317\\Also, when x = -3000\\then, f(x) = 3|-3000- 7| - 7\\f(x) = 3|-3007| - 7\\f(x) = 3 × 3007 - 7\\\)

f(x) = 9021 - 7

f(x) = 9014

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To write an absolute value equation that satisfies a given solution set, we need to determine the expression within the absolute value function based on the given solutions.

1. Solution set: {-3, 3}

An absolute value equation that satisfies this solution set is |x| = 3. This equation means that the absolute value of x is equal to 3, and the solutions are x = -3 and x = 3.

2. Solution set: {-2, 2}

An absolute value equation that satisfies this solution set is |x| = 2. This equation means that the absolute value of x is equal to 2, and the solutions are x = -2 and x = 2.

3. Solution set: {0}

An absolute value equation that satisfies this solution set is |x| = 0. This equation means that the absolute value of x is equal to 0, and the only solution is x = 0.

In summary:

1. |x| = 3

2. |x| = 2

3. |x| = 0

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Answer:

Sum of angles of a triangle is 180, so x + y + w = 180

Straight angle is 180 , so y + z = 180

From the first 2 conditions :

=>x + y +w = y + z

=> x + w = z  

Option 1, 2, 5

The equations which are true are given by,

Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.

From angle sum property of triangle says that the sum of all interrior angles of a triangle is 180.

Here all interrior angles of triangle are x,y,w

So, x+y+w = 180

Hence first option is correct.

Again the exterrior angle of a triangle is equal to the sum of the opposite two interrior angles.

here exterrior angle is z and opposite two interrior of z are x,w

So, w+x = z

Hence last option is correct.

Again y+z = y+w+x

so second option is also true.

Hence correct options or equations are given by:

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Answer: ß

Step-by-step explanation:

The mode of a sample is the value that appears most often in the data set. It can be larger, smaller or equal to the mode of the population, depending on the sample size and the distribution of the population.

The mode of a sample is not necessarily equal to the mode of the population if the sample is truly random, as there is no guarantee that the most frequent value in the population will appear in the sample.

For example, let’s say the population has a mode of 10. If the sample size is 50, the probability of the sample having a mode of 10 is 0.2. The probability of the sample having a mode of 11 or larger is 0.4. The probability of the sample having a mode of 9 or smaller is also 0.4.

This means that the mode of the sample can be larger, smaller or equal to the mode of the population. It does not have to be equal to the mean of the population, as the mean is an average of all the values in the population and is not necessarily the most frequent value. Furthermore, the mode of the sample cannot be 500, as this is the size of the population, not a value that appears in the data set.

The mode of the sample can be larger, smaller or equal to the mode of the population, and cannot be equal to the mean of the population or equal to the size of the population.

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Answer:

x = 12

Step-by-step explanation:

-17x = -204 (Given)

x = 12 (division)

Negative x negative = positive

The equivalent value of the expression is x = 12

Given data ,

Let the equation be represented as A

Now , the value of A is

-17x = -204

On simplifying the equation , we get

-17x = -204

So , the left hand side of the equation is equated to the right hand side by the value of ( -204 )

Opening the parenthesis on both sides , we get

-17x = -204

Divide by ( -17 ) on both sides , we get

x = -204 / -17

x = 204 / 17

On further simplification , we get

x = 12

Therefore , the value of x = 12

Hence , the expression is x = 12

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(a) The function y1 of t, which is the solution of the second-order linear homogeneous differential equation 4y'' - 25y = 0, with initial conditions y1(0) = 1 and y1'(0) = 0, is given by y1 = cos(5t).

(b) To find y2 of t with initial conditions y2(0) = 0 and y2'(0) = 1 for the same differential equation, we differentiate the function y1 = cos(5t) to obtain y1' = -5sin(5t). Therefore, y2 = -5sin(5t).
(a) The given differential equation is a linear homogeneous differential equation of second order with constant coefficients. Its characteristic equation is 4r^2 - 25 = 0, which can be factored as (2r - 5)(2r + 5) = 0. Solving for r, we get two distinct roots: r1 = 5/2 and r2 = -5/2.
Since the roots are distinct, the general solution of the differential equation is y(t) = c1e^(r1t) + c2e^(r2t). Applying the initial conditions, y1(0) = 1 and y1'(0) = 0, we find c1 = 1 and c2 = 0, resulting in y1 = e^(5/2)t.
(b) To find y2 with initial conditions y2(0) = 0 and y2'(0) = 1, we differentiate y1 = cos(5t) to obtain y1' = -5sin(5t). By comparing y1' with the initial condition y2'(0) = 1, we see that y2' = y1' = -5sin(5t). Integrating y2' with respect to t, we obtain y2 = -5sin(5t) + c3. Using the initial condition y2(0) = 0, we find c3 = 0, yielding y2 = -5sin(5t).
Therefore, the solutions to the differential equation with the given initial conditions are y1 = cos(5t) for part (a) and y2 = -5sin(5t) for part (b).

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To factor 1 out of 3 we divide 3 by 1

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

For example to factor out 4 out of 20. It shows that 4 is a factor of of 20 and to get the other factor we divide 20 by 4. This means that 20/4 = 5. This shows that 4 and 5 are factors of 20.

Similarly to factor out 1 over 3, we divide 3 by so as to get the other factor. This means that 3/1 = 3.

This shows that 3 and 1 are factors of 3

Therefore to factor a number(x) over another number(y) we divide the y by x

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Answer:

B

Step-by-step explanation:

Two 90 degree angles add up to 180, a supplementary angle

Correction: The answer is B, I have made a mistake. Sorry.

Answer:

10 $20 bills and 20 $5 bills

Step-by-step explanation:

The entered points belong to a vertical line. There is no slope.

Equation: x = -19.

The standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

To calculate the standard deviation of the sampling distribution of sample means, we need to use the formula for the standard deviation of a sample mean. This formula states that the standard deviation of the sampling distribution (σ) is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n).

Given that the population standard deviation (σ) is 5.9 pounds and the sample size (n) is 72, we can plug these values into the formula:

Standard Deviation of the Sampling Distribution (σ) = σ / √n

σ = 5.9 pounds

n = 72

Substituting these values, we get:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / √72

To find the standard deviation of the sampling distribution, we need to evaluate the square root of 72. Using a calculator or mathematical software, we find that √72 is approximately 8.49.

Now, let's calculate the standard deviation of the sampling distribution:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / 8.49 ≈ 0.695 pounds (rounded to two decimal places)

Therefore, the standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

This value represents the average amount of variation or dispersion in the means of different samples taken from the population. It indicates how much the sample means are likely to deviate from the population mean.

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Let's analyze the given information and the statements provided.

We are told that the integers r, s, and t all have the same remainder when divided by 5. This means that these integers can be written in the form:

r = 5n + k

s = 5m + k

t = 5p + k

where n, m, and p are integers representing quotients and k is the common remainder.

Statement (1) r + s = t:

If r + s = t, we can substitute the expressions for r and s:

(5n + k) + (5m + k) = 5p + k

Combining like terms:

10n + 10m = 5p

Dividing both sides by 5:

2n + 2m = p

From this equation, we can see that p must be an even number. However, we cannot determine the exact value of t based on this equation alone. Statement (1) is not sufficient to answer the question.

Statement (2) 20 ≤ t ≤ 24:

This statement provides a range for the possible values of t. Since t has the same remainder when divided by 5 as r and s, it must be congruent to k modulo 5. From the given range, the only number that satisfies this condition is t = 20.

However, we need to consider the combined information from both statements to reach a conclusion.

By considering both statements, we find that the only value that satisfies both conditions is t = 20.

the value of t is 20.

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Answer:

➢ Calculating Area of Sector :-

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ \theta \: }{360 \degree \: } \times \pi \: {r}^{2} \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 80 \: }{360 \degree \: } \times \frac{22}{7} \times\: {5}^{2} \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 8 \: }{36 \degree \: } \times \frac{22}{7} \times \: 5 \times 5 \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 8 \: }{36 \degree \: } \times \frac{22}{7} \times\: 25 \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 4 \: }{18 \degree \: } \times \frac{22}{7} \times \: 25 \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 2\: }{9 \degree \: } \times \frac{22}{7} \: \times 25 \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 2 \times 22 \times 25\: }{9 \times 7 \: } \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 44 \times 25\: }{9 \times 7 \: } \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = \frac{ 1100\: }{63 \: } \\ \)

\( \sf \longrightarrow \: Area \: of \: Sector \: = 17.5 \: \: {m}^{2} \\ \)

____________________________

Option D :- 17.5 m²

Answer:

Step-by-step explanation:

If z is any integer then the next integer to z would be: z+1

And the next:  z+1+1 = z+2 (the largest)

Their sum is 39 so:

z + z+1 + z+2 = 39

3z + 3 = 39

3z = 36

z = 12

z+2 = 12 + 2 = 14

check:

z+1=12+1=13,

14+13+12 = 39

Answer:

B.

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

The slope of the line that passes through the points (0, - 4) and (30, -9) is -1/6.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-9 + 4)/(30 - 0)

Slope, m = -5/30

Slope, m = -1/6.

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Answer: What are the answers to your question?

Step-by-step explanation:

X, and Y they are both axis's so most likely you might be using a grid but the arn't showing so make a grid and find the coordinats

Answer:

Ito

Step-by-step explanation:

Make them to their closest common multiple which is twelve.

Next times 7 by 4 as 3*(4) is 12

Then time 9 by 3 as 3*(4) is 12

7*4=28

9*3=27

Therefore ito washes at a faster rate

Answer:

ITO

Step-by-step explanation:

ITO

He can wash 7 cars in 3 hours.

a) 3 x 60 min = 180 minutes

b) 180\7 = 25.71 minutes per car

JOAN

She can wash 9 cars in 4 hours

a) 4 x 60 = 240 minutes

b) 240\9 = 26.66 minutes per car

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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Answer:

Step-by-step explanation:

2x-3y=12

y=2/3x-4

Answer: diffrent form so i can help you better

Step-by-step explanation:

Answer: 33.375 feet

Step-by-step explanation:

To find the maximum height, we need to find the vertex of the parabolic function h = 16t² + 12t + 30.

The vertex of a parabola with equation y = ax^2 + bx + c is located at x = -b/2a and y = c - b^2/4a.

In this case, a = 16, b = 12, and c = 30.

So,

t = -b/2a = -12/(2*16) = -3/8

h = 16(-3/8)² + 12(-3/8) + 30 = 33.375

Therefore, the maximum height reached is 33.375 feet.

Answer:

(12, 9)

Step-by-step explanation:

Answer:

the shape of the box is a rectangular prism.The way to solve this is by using the formula V=l*w*h

we only have 20(l) and 10(h) so here's a clue it said that the base of the box was squared so the width would also be 10 in. so....

V=20*10*10

                ₃      

=2000 in

Step-by-step explanation:

Answer:

\(y=\frac{1}{2}x+1\)

The slope is 1/2.

The y-intercept is 1.

Step-by-step explanation:

We have:

\(x-2=2(y-3)\)

Let’s divide both sides by 2. This gives us:

\(\frac{x}{2}-\frac{4}{2}=y-3\)

Simplify:

\(\frac{1}{2}x-2=y-3\)

Add 3 to both sides:

\(\frac{1}{2}x+1=y\)

Flip:

\(y=\frac{1}{2}x+1\)

This is in the slope-intercept form:

\(y=mx+b\\\)

Where m is the slope and b is the y-intercept.

Hence, our slope m is 1/2 and our y-intercept b is 1.