Write the equation of each circle.
center at (-5,3) , passes through (1,-4)

The length of the indicated side of the trapezoid is as follows:

A trapezoid is quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid. The nonparallel sides are referred to as the legs of trapezoid.

The median of a trapezoid is the segment that joins the midpoints of the nonparallel sides (legs).

The median of a trapezoid is parallel to each base and the length of the median equals one-half the sum of the lengths of the two bases.

Therefore,

ST = 1 / 2 (EF + DG)

19 = 1  /2 (13 + x)

19 = 13 / 2 + x / 2

19 - 6.5 = 0.5x

12.5 = 0.5x

x = 12.5 / 0.5

x = 25

Therefore,

DG = 25

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Step-by-step explanation:

4x - 6 = 2x + 4

2x = 10

x = 5

y = 2x + 4

y = 2(5) + 4

y = 14

Answer:

The value of x is equal to 109

The measure of m∠S is 116.3.

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

Parallelogram QRST.

m∠R = 63.7

Now,

We see that,

m∠R and m∠T are opposite angles.

So,

m∠T = 63.7 _____(1)

And,

m∠Q and m∠S are opposite angles.

So,

m∠Q = m∠S ______(2)

Now,

The sum of the four angles is 360.

So,

m∠R + m∠T + m∠Q + m∠S = 360

From (1) and (2),

63.7 + 63.7 + 2m∠S = 360

127.4 + 2m∠S = 360

2m∠S = 360 - 127.4

2m∠S = 232.6

m∠S = 232.6/2

m∠S = 116.3

Thus,

The measure of m∠S is 116.3.

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Marianne's total candle sales for the week rounded to the nearest

cent is $6539.13.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

From the given information, Let Marianne's total sale be $'x'.

Therefore, $376 is 5.75% of 'x'. which can be numerically expressed as,

(5.75/100)×x = 376.

0.0575x = 376.

x = $6539.13

We also know to obtain percentage change we'll diving the net amount change by the original amount and multiply it by 100%.

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False, sample evidence cannot prove that a null hypothesis is true.

Sample evidence can be used to infer whether a null hypothesis is true or not, but it cannot prove it to be true. The null hypothesis is a statement of no effect or no difference, and it is typically used as a starting point for statistical hypothesis testing. When sample data is collected, it is used to calculate a test statistic, which is then used to make a decision about the null hypothesis.

If the test statistic falls within the acceptance region, meaning that it is not unlikely to occur if the null hypothesis is true, then the null hypothesis is not rejected. However, if the test statistic falls in the rejection region, meaning that it is unlikely to occur if the null hypothesis is true, then the null hypothesis is rejected. The conclusion is that the sample evidence provides a probability that the null hypothesis is true or not, but it cannot prove it to be true.

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The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

We have,

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:

mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6

Next, we calculate the deviation of each data point from the mean:

|4 - 6.6| = 2.6

|5 - 6.6| = 1.6

|7 - 6.6| = 0.4

|9 - 6.6| = 2.4

|8 - 6.6| = 1.4

Then we find the average of these deviations, which gives us the mean absolute deviation:

MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6

Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

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Answer:

B

Step-by-step explanation:

x^2 + 4x + 2 = 0; a=1, b=4, c=2

D= b^2 - 4ac = 16 - 8 = 8>0

-> x1/2= (-b +/- √D)÷2×a= (-4 +/- √8)÷2= 2(-2 +/- √2)÷2

= -2 +/- √2

×1=-2+ √2 ≈ -0.59

×2=-2- √2 ≈ -3.41

therefore, b)

The area of the trapezoid is 30 square inches for the given dimensions and angle.

Given:

Vertical left edge of a trapezoid = 8 inches

Bottom edge of a trapezoid = 4 inches

Vertical right edge of a trapezoid = 11 inches

Top slanted edge of a trapezoid = 5 inches

Now, the formula used:

The formula for the area of a trapezoid is A = (b1 + b2)/2 × h,

where b1 and b2 are the lengths of the parallel bases and h is the height (the perpendicular distance between the bases).

We are given that the vertical left edge of a trapezoid is 8 inches and meets the bottom edge of the trapezoid at a right angle.

Therefore, AB = 8 inches

We are also given that the bottom edge is 4 inches and meets the vertical right edge at a right angle.

Therefore, DC = 4 inches

We are also given that the vertical right edge is 11 inches.

Therefore, CD = 11 inches

We are also given that the top slanted edge measures 5 inches.

Therefore, AB + DC = 8 + 4 = 12 inches is the parallel sides of the trapezoid.

And, h = 5 inches is the height of the trapezoid.

Now, we will use the formula to calculate the area of the trapezoid.

Therefore,

A = (b1 + b2)/2 × h

We know that the parallel sides of the trapezoid are 12 inches and the height of the trapezoid is 5 inches.

Substituting the given values in the formula, we get:

A = (12)/2 × 5A = 6 × 5A = 30

Therefore, the area of the trapezoid is 30 square inches.

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The two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).

Given that, Angle = 60°, v = 8, 6

Consider unit vector a = (x, y)

x² + y² = 1 …. (1)

Now apply the dot product of unit vector with v

a.v = |a||v|cos Ø

a.v = √ (x² + y²) √ (8² + 6²) cos 60º

8x + 6y = 1 × 10 × ½

So we get,

8x + 6y = 5 …. (2)

y = (5 - 8x) / 6

Substituting the value of y in equation (1)

x² + y² = 1

x² + [(5 - 8x)/6]² = 1

x² + 25/36 + 16x²/9 - 20x/9 = 1

25x²/9 - 20x/9 = 11/36

So we get,

4 × (25x² - 20x) = 11

100x² - 80x = 11

100x² - 80x - 11 = 0

Now solve the quadratic equation,

x = { 2/5 ± √5/10}

Substituting the value of x in equation (2)

y = 3/10 ± 2√5/15

Therefore, the two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).

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Hello!

If six friends went to a movie and spent $9 per each ticket and also purchased a small bag of popcorn each with them spending a total of $82.50, the cost of each small bag of popcorn costs $4.75.

Step-by-step explanation:

\(6\) × \(9=54\)

\(82.50-54=28.50\)

\(28.50\) ÷ \(6=4.75\)

Hope this helps!

Answer:

18.5

Step-by-step explanation:

Plug in 13 for r, and 11 for s in the expression.

r + s/2 = 13 + 11/2

Remember to follow PEMDAS.

PEMDAS is the order of operation, and =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, divide:

11/2 = 5.5

Next, add:

5.5 + 13 = 18.5

18.5 is your answer.

~

Answer:

No, the max is $9600.

Step-by-step explanation:

240 x 8=1920.

1920 x 5=$9600.

The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

nCr = n! / [r!(n - r)!]

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

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Answer:

Upper right corner.

Step-by-step explanation:

I took the test and that one was right. Hope this helps!

Answer:

Step-by-step explanation:

let length=l

breadth=b

l×b=660

2(l+b)=104

l+b=104/2=52

b=52-l

l×(52-l)=660

52l-l²=660

l²-52l+660=0

l²-22l-30l+660=0

l(l-22)-30(l-22)=0

(l-22)(l-30)=0

l=22,30

when l=22,b=52-22=30

when l=30,b=52-30=22

l>b

so l=30m

b=22m

Answer:

W = 22 m

L = 30 m

Step-by-step explanation:

given:

area is 660square metre and perimeter is 104metre​

find:

the length and breadth of a rectangular plot

----------------------------------------------------------------

1. area of rectangle (A) = L x W

2. Perimeter of a rectangle (P) = 2L + 2W

where:

A = 660 m²

P = 104 m

solve for L using formula 1.

A = L x W

660 = L x W

L =  660 / W

solve W using formula 2 and use L = 660 / W

P = 2L + 2W

104 = 2 (660)  +  2W

               W

104W = 1320 + 2 W²

-2W² + 104W = 1320

solve W using quadratic equation:

W = 22 m; ( 30 m = L)

plugin W=22 into L =  660 / W to solve L:

L = 660 / 22

L = 30 m

The transformation from the parent quadratic function y = \(1/4 x^2\) involves a vertical stretching by a factor of 1/4 while maintaining the same shape and vertex at the origin.\(1/4 x^2.\)

To describe the transformation from the parent quadratic function, we need to analyze any changes in the equation.

1. Coefficient of\(x^2\): The coefficient 1/4 indicates that the graph is stretched vertically compared to the parent function. It means that the parabola is flatter or less steep.

2. No change in the coefficient of x: Since there is no coefficient attached to the x term \((x^1\)), there is no horizontal stretching or compression. The graph maintains the same shape in the x-direction.

3. No constant term: The absence of a constant term implies that the vertex of the parabola is at the origin (0,0). The vertex is the lowest or highest point on the graph, depending on the direction it opens.

4. Overall transformation: The parent quadratic function y = 1\(/4 x^2\) has been vertically stretched, maintaining the same shape and vertex at the origin.

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Describe the transformation from the parent quadratic function: y equals 1 fourth x squared.

\( \frac{5x}{2} - \frac{3x}{4} = 10 \frac{1}{2} \\ \)

\( \frac{5x}{2} - \frac{3x}{4} = \frac{21}{2} \\ \)

Multiply both sides by 4

\(4 \times ( \frac{5x}{2} - \frac{3x}{4} ) = 4 \times \frac{21}{2} \\ \)

\(10x - 3x = 42\)

\(7x = 42\)

Divide both sides by 7

\( \frac{7x}{7} = \frac{42}{7} \\ \)

\(x = 6\)

There are 28 ways to choose 6 teams for the playoffs if there are 8 college basketball teams in a certain sub-division.

To determine the number of ways to choose 6 teams for the playoffs out of the 8 college basketball teams in a certain Sub-Division, we can use the combination formula. The formula for combinations is given by

nCr = n! / (r! * (n-r)!),

where n represents the total number of teams and r represents the number of teams to be chosen.

In this case, n = 8 and r = 6.

Plugging in these values, we have

8C6 = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 28.

Therefore, there are total 28 ways to choose 6 teams.

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\(\sf\large\underline{\star Given:-}\)

\(\rightarrow\) Radius(r) of cone = \(\sf\pink{6cm.}\)

\(\rightarrow\) Height(h) of Cone = \(\sf\pink{8cm.}\)

\(\rightarrow\) Slant height(l) of cone = \(\sf\pink{10cm}\)

\(\sf\large\underline{\star To \: Find:-}\)

\(\rightarrow\) Length of paper needed to make a cone with above given dimensions (i.e, curved surface area of cone).

\(\sf\large\underline{\star Solution:-}\)

\(\rightarrow\) As we know that,

Curved surface area of cone = \(\sf\blue{πrl}\)

On substituting the value of radius(r) and slant height(l) in this formula we get,

\(\rightarrow\) \(\sf{=\: \frac{22}{7}×6×10}\)

\(\rightarrow\) \(\sf{=\: \frac{22}{7}×60}\)

\(\rightarrow\) \(\sf{=\: \frac{1320}{7}}\)

\(\rightarrow\) \(\sf{=\: 188.57 cm^2.}\)

Therefore, \(\sf\purple{188.57cm^2}\) paper is needed to make a cone of given dimensions.

_____________________________

Hope it helps:)

Step-by-step explanation:

Given:-

To find :-

Concept :-

Solution :-

As we know ,

the formula for finding the curved surface area of cone :- πrl

putting the known values ,

CSA :- 3.14 × 6 × 10 cm²

CSA of cone :- 188.4 cm²

Answer:

5

Step-by-step explanation:

The only way I know how to go about this is to multiply 2 until it becomes 32

2x2=4

4x2=8

8x2=16

16x2=32

Now just count how many 2 I used and I used 5 so the missing exponent is 5

Hopes this helps please mark brainliest

Answer:

oh yeah

Step-by-step explanation:

A radio-controlled helicopter may be purchased for $20, but it requires a lithium battery, which is 25% more expensive. By taking 25% of 20, we can get the battery's cost.

The torque produced by rotating main rotor blades causes the helicopter fuselage to spin in the opposite direction of the blades. Yaw is the tail rotor-controlled rotation of the helicopter about its vertical axis.

The cost of lithium Battery =  \(\frac{25}{100} \times 20\)

The cost of lithium Battery = 5

Let's now calculate the sales tax on the price of the helicopter and the lithium battery.

Total sales tax = \(= \frac{6}{100} \times (20+5)\)

Total sales tax  = 1.5

We can find the total cost of helicopter by adding the cost of helicopter, cost of lithium battery and total amount of sales tax.

The total cost of helicopter \(= 20 + 5+ 1.5\)

The total cost of helicopter= 26.5

Therefore, The total cost of the helicopter = $26.5 The cost of lithium battery = $5. $1.5 is the sales tax amount.

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

A vector graphic consists of a set of instructions for creating a picture is a true statement.

Step-by-step explanation:

A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.

These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.

Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.

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Answer: The inequality given is:

250(1.12)^s > 3750

We want to solve for s, the number of years until the number of mice exceeds 3750. We can begin by dividing both sides of the inequality by 250:

(1.12)^s > 15

Next, we can take the logarithm of both sides of the inequality with base 1.12:

log₁.₁₂ [(1.12)^s] > log₁.₁₂ (15)

s > log₁.₁₂ (15)

Using a calculator, we can evaluate the right-hand side to be approximately 6.27. Therefore:

s > 6.27

Since s must be a whole number, we can round up to the nearest integer to get:

s = 7

Therefore, in 7 years the number of mice will exceed 3750.

The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation: