r=7/8cosθ+2sinθ
Which of the following gives the Cartesian form of the equation above?
Select the correct answer below:


x2+y2=7/10
y=−1/4x+7/8
y=−4x+7/2
8x2+2y2=7

SOLUTION

DILATION BY SCALE FACTORN OF 1/2

REFLECTED OVER THE X-AXIS

MIDPOINT OF THE FINAL IMAGE

Answer:

Option A) The volume is multiplied by 1/8.

Step-by-step explanation:

For the first volume problem involving the rectangular pyramid, the normal volume formula is V = 1/3 (l)(w)(h).  Since all 3 dimensions are being multiplied by 1/2, this involves multiplying the original formula by (1/2)(1/2)(1/2) which, put together, is multiplying by 1/8, so the volume will be 1/8 of what it was with the original dimensions.

The volume of the rectangular pyramid is multiplied by ( 1/8 )

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the length of the rectangle be L

Let the width of the rectangle be W

Let the height of the rectangle be H

Now , the volume of rectangle be V = L x W x H

And , when the length , width and height are multiplied by ( 1/2 ) , we get

L' = L/2

W' = W/2

H' = H/2

So , the volume V' = ( L' x W' x H' )

The volume of rectangular pyramid V' = ( 1/8 ) V

Hence , the volume is multiplied by ( 1/8 )

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Answer:

Hey Mate...

Step-by-step explanation:

All that the slope-intercept form (the equation to describe linear equations) is, is an equation (y=mx+b) where m (the number that multiples x) is the slope and b (the number that is not multiplying a variable on the right-hand side of the equation) is the y-intercept.

The value of x is -15

Functions are simply defined as expressions or rules showing the relationship between two variables.

These variables are listed as;

From the information given, we have that;

g(x) =x  -1, if g(x) = -16

Now, we have to equate the two functions, we get;

x - 1 = -16

collect the like terms, we get;

x =-16 + 1

add the values, we have;

x = -15

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The complete question:

Given g(x) =x  -1, if g(x) = -16, find x.

Answer:

2

Step-by-step explanation:

Let

P = percentage of those that text and drive

S = percentage of those that do not text and drive

P + S = 1

S = 1 - P

S = 1 - 0.52

S = 0.48

The expected number would be:

1/0.48 = 2.08

Which is approximately 2.

Therefore the expected number of people the police officer would expect to pull over until she finds a driver not texting is 2.

The number of people should a police officer expect to pull over until she finds a driver NOT texting while driving is; 2 people

A geometric random value is one that gives a discrete time as to the the first success of an event.  

Now, we are told that it is estimated that 52% of drivers text while driving. Thus, the success is a driver that is not texting, and the probability (p) is 0.52.

This means that the expected value of a geometric random variable is expressed as 1/p.  

Therefore, In this question;

geometric random variable = 1/0.52

⇒ 1.923 ≈ 2

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Answer:

4a

Step-by-step explanation:

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

3.99s + 15.20 = 95.00

Step-by-step explanation:

you would put 's' next to the 3.99 because that's what your multiplying or having more than 1 of, then you would add the 15.20 because it's just a one time delivery fee.

Answer:

The answer is 20

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: s≥20

Interval Notation: [20,∞)

Answer: 1.6

Step-by-step explanation:

each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces

Answer:

shown below

Step-by-step explanation:

golf balls per ounce = 5/8 or 0.625

ounces per gold ball = 8/5 or 1.6

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answer:

Step-by-step explanation:

Answer:

x= 7/20

Step-by-step explanation:

(5+2×8)/6=x(4+6)

(5+16) /6 = 4x+6x

21/6=10x (divide 21/6 by 3)

7/2=10x

7/2×1/10= x

x= 7/20

Hope this helps :)

Keep Smiling

Answer:

C  -3 < x ≤ 4

Step-by-step explanation:

-9 < 4x + 3 ≤ 19.

Subtract 3 from all sides

-9-3 < 4x + 3-3 ≤ 19-3

-12 < 4x  ≤ 16

Divide by 4

-12/4 < 4x/4 ≤ 16/4

-3 < x ≤ 4

Step-by-step explanation:

First add outer numbers then add inner numbers theninus inner number from outside number I think I had learnt it on grade 1 now I am on 7th standard

Supplementary: N and M

Supplementary angles: A pair of angles that when combined are equal to 180°.

Vertical: M and I

Vertical angles: A pair of opposite angles that are made by two intersecting lines.

Complimentary: None

Complimentary angles: A pair of angles that when combined are equal to 90°.

Hope this helps! Good luck! :D

The value of x with the given condition is 10

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

D(7,2), E(1, 9), F(4,8), and G(x, 1),

Also, we have

DE || FG

This means that the lines DE and FG are parallel lines and they have equal slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(9 - 2)/(1 - 7) = (1 - 8)/(x - 4)

Evaluate the difference

-7/6 = -7/(x - 4)

So. we have

x - 4 = 6

Evaluate

x = 10

Hence. the value of x is 10

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Answer: 3/2

Step-by-step explanation:

3x - 2y = 14

-2y = 14-3x

y = 3/2x-7  divide both sides by -2

From the attached image, it can be seen that triangle PQR is an isosceles triangle and therefore option (A), option (B), option (C)  and option (D) are all correct.

An isosceles triangle has 2 sides equal meaning 2 opposite angles are also equal.

Let us assume the following:

PR = 1cm

QR = 1cm

PQ = 2cm

cos P = adj/hyp

         = PR/PQ = 1/2

cos Q = adj/hyp

          = QR/PQ = 1/2

Therefore cos P and cos Q are equal.

sin P = opp/hyp

        = QR/PQ = 1/2

sin Q = opp/hyp

         = PR/PQ = 1/2

Also sin P and sin Q are equal.

From this analogy, we can deduce the following:

sin P = sin Q = 1/2

cos P = cos Q = 1/2

sin P = cos Q = 1/2

cos P = sin Q = 1/2

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The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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Answer:

First answer is infinitely many.  It doesn't matter what x is.

Second answer is x = -5.

Step-by-step explanation:

8 + x = 3

x = - 5

Answer: p = 1

Step-by-step explanation:

2/5 + p = 4/5 + 3/5p

-2/5        -2/5

      p = 2/5 + 3/5p

-3/5p            -3/5p

2/5p = 2/5

Divide both sides by 2/5

p = 1

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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The statement that is not true: The arc is not a semicircle.

The diagram shows an arc that is formed by two points, point a and point b, with the same radius. The arc does not appear to be a semicircle because it is not a complete circle and the two points, a and b, do not appear to be the same distance from each other.

This means that the statement “The arc is a semicircle” is not true. Additionally, the arc could be an ellipse or some other curved shape, depending on the location of the two points, a and b, relative to each other.

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Given:

The data set is 17, 21, 26, 28, 31, 33, 41, 46, 52.

To find:

The five-number summary for the given data set.

Solution:

We have, the values

17, 21, 26, 28, 31, 33, 41, 46, 52

Divide the data values into 2 equal parts.

(17, 21, 26, 28), 31, (33, 41, 46, 52)

Divide each parenthesis into 2 equal parts.

(17, 21), (26, 28), 31, (33, 41), (46, 52)

Now,

Minimum value = 17

The first quartile is:

\(Q_1=\dfrac{21+26}{2}\)

\(Q_1=\dfrac{47}{2}\)

\(Q_1=23.5\)

Median = 31

The third quartile is:

\(Q_3=\dfrac{41+46}{2}\)

\(Q_3=\dfrac{87}{2}\)

\(Q_3=43.5\)

Maximum value = 52

Therefore, the five-number summary for the given data set is 17, 23.5, 31, 43.5, 52.

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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Answer: A. 7

Step-by-step explanation:

189.24 - 99.99 = 89.25

89.25 ÷ 12.75 = 7

Based on the information given the number of months did she pay is (A)7.

First step is to calculate the fee amount paid

Amount=$189.24 -$99.99

Amount=$89.25

Second step is to calculate for number of months

Number of months=$89.25 ÷ $12.75

Number of months= 7 months

Inconclusion the number of months did she pay is (A)7.

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Answer:

Bree hikes for 4 kilometers per hour

Answer:

D

Step-by-step explanation:

x represents time and y represents disrtance in relation to time.

(when you look at 1 sec you can tell that the y value is 4 meaning that the realtion is y=4x)

The amount of cups of lemonade sold by Abbie is 6 x 8 = a.

Hence, option A is correct.

Use the concept of multiplication defined as:

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that,

Number of lemonade cups sold by Lust = 8

Number of lemonade cups sold by Abbie =  6 times of lust

Let 'a' represents the number of cups sold by Abbie,

Therefore,

6 x 8 = a

Hence,

The correct expression is 6 x 8 = a which is option A.

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The complete question is:

Luct sold 8 cups of lemonade Abbie sold 6 times as many cups of lemonade. Which equation helps us find how many cups Abbie sold if the number of cups sold by Abbie is 'a'.

A. 6x8 = a

B. 8xa = 6

C. 6xa = 8

the answer is 6 minutes and 46 seconds