The lines shown below are perpendicular. If the green line has a slope of
-1, what is the slope of the red line?
-5
5
X
O A1/
A.
114
OB. 4
O C. -1
OD. -4

Answer:

To find out how much interest Jenny earns in one year, we can use the formula:

interest = principal x rate x time

where:

the principal is the amount of money in the savings account

rate is the interest rate per year, expressed as a decimal

time is the length of time the money is in the account, in years

In this case, Jenny's principal is $1200, the rate is 3% or 0.03 as a decimal, and the time is 1 year. Plugging these values into the formula, we get:

interest = 1200 x 0.03 x 1

interest = $36

Therefore, Jenny earns $36 in interest in one year.

Answer: h(-8) = 21

Step-by-step explanation:

Answer: 21

Step-by-step explanation:

You equation is h(y)  but you need to find h(-8) which means substitute y for -8 into equation

h(-8)= 4|(-8)+2| -3             do what's inside absolute value first

=4|-6| -3                           for absolute value, take positive of number

=4(6)-3                             multiply

=24-3                               subtract

=21

The quadratic value equation of triangle area is solved and x = 12 m

Given data ,

Let the triangle be represented as ΔABC

Now , the height of the triangle is h = x m

The base of the triangle is = ( x + 6 ) m

Area of triangle = ( 1/2 ) base x height

A = 108 m² = ( 1/2 ) ( x ) ( x + 6 )

216 = x² + 6x

Subtracting 216 on both sides , we get

x² + 6x - 216 = 0

On factorizing the equation , we get

( x + 18 ) ( x - 12 ) = 0

So , the solution is x = 12 m

Hence , the height of the triangle x = 12 m

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Expression used for area of a rectangle is 12x² + 74x + 44 .

Its degree and classification is 2 and quadratic

and demonstration of a closure property is given by product of a polynomial is a polynomial.

Length of the rectangle = (6x + 4) units

and Width of the rectangle = (2x + 11) units.

The area of the rectangle is given by the product of its length and width,

Area = (6x + 4) × (2x + 11)

Find the product,

⇒ Area = 6x × 2x + 6x × 11 + 4 × 2x + 4 × 11

Simplifying this expression, we get,

⇒ Area = 12x² + 74x + 44

The expression that represents the area of the rectangle is 12x² + 74x + 44.

The degree of the expression 12x² + 74x + 44 is 2,

since the highest power of x is 2.

The classification of this expression is quadratic.

Part A demonstrates the closure property for polynomials because the product of two polynomials is also a polynomial.

Here, the area of the rectangle is the product of two polynomials (6x + 4) and (2x + 11).

And the result is also a polynomial (12x² + 74x + 44).

This shows that the set of polynomials is closed under multiplication.

Which is one of the defining properties of a mathematical system.

Therefore, the expression for area of a rectangle is (12x² + 74x + 44) ,

Degree and classification is 2 and quadratic and closure property is demonstrate by product of a polynomial.

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Answer:

There is no square root function mentioned to compare with, but assuming you meant the parent square root function y = sqrt(x), the correct answer is:

A.) "stretched by a factor of 2, reflected over the x-axis, and translated 9 units right"

To see this, note that the equation y = 4x + 38 can be rewritten as y - 38 = 4(x - (-9.5)). This means that the graph of y = 4x + 38 is a transformation of the parent function y = sqrt(x) as follows:

So the correct answer is (a) stretched by a factor of 2, reflected over the x-axis, and translated 9 units right.

Answer:

answer is (a) stretched by a factor of 2, reflected over the x-axis, and translated 9 units right.

Step-by-step explanation:

In 5 seconds of free fall at a speed of 165 feet per second, the parachute user will drop around 122.5 meters.

To convert feet per second (ft/s) to meters per second (m/s), we can use the following conversion factor:

1 m/s = 3.3 ft/s

Therefore, the parachutist's rate of 165 ft/s is equivalent to:

165 ft/s × (1 m/3.3 ft) = 50 m/s

Next, we can use the kinematic equation:

d = 1/2 * a * t²

Here d is the distance traveled (in meters), a is the acceleration due to gravity (9.8 m/s²), and t is the time (in seconds).

For 5 seconds of free fall, we have:

d = 1/2 * 9.8 m/s² * (5 s)² = 122.5 m

Therefore, the parachutist will fall approximately 122.5 meters during 5 seconds of free fall at a rate of 165 ft/s.

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Answer:

jordans van

Step-by-step explanation:

yes satiscal

Answer:for the one in the middle, that one is 5.0, for the one in the top, that one is 7, and for the bottom one, that one is 50

Step-by-step explanation:

The distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.

The distribution of miles ran each week by Elisa is relatively symmetric and centered around 30 miles per week, with a relatively tight spread of about 2.3 miles per week.

We have,

a.

Since the distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.

However, the distribution also has some slight right-skewness, so we may want to consider using the median instead of the mean, depending on the context and purpose of the analysis.

b.

The mean of the distribution is:

= (28 + 29 + 30 + 31 + 32 + 33 + 34)/7

= 30.1

So the center of the distribution is around 30 miles per week.

The standard deviation of the distribution is approximately 2.3 miles per week, which tells us that the spread of the distribution is relatively tight.

Alternatively, we could use the median as a measure of the center.

Since there are 7 data points, the median is the average of the 4th and 5th values (30 and 31):

= (30 + 31)/2

= 30.5

So the center of the distribution is also around 30 miles per week using the median.

Thus,

The distribution is roughly symmetric, we can use the mean as a measure of center and the standard deviation as a measure of spread.

The distribution of miles ran each week by Elisa is relatively symmetric and centered around 30 miles per week, with a relatively tight spread of about 2.3 miles per week.

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The normal curve represents a distribution where the mean, median, and mode are equal to each other.

The normal curve denotes a distribution in which the mean, median, and mode are all equal. As a result, the right answer is:

The curve of a normal distribution is symmetrical and bell-shaped, with the mean, median, and mode placed in the center. The standard deviation is a measure of the data's spread or dispersion around the mean.

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The volume of the cardboard box with given dimensions changes at the fastest average rate over the interval of  option c.  [1,5].

Length of the cardboard box = x + 1

Width of the cardboard box = 5  - x

Height of the cardboard box = x - 1

Volume of the box V (x) =  length × width × height

Substitute the values we have,

V(x) = (x+1)(5-x)(x-1)

Expanding this expression gives,

V(x) = -x³ + 5x² + x - 5

To know where Volume is changing at the fastest average rate,

Find the maximum value of the absolute value of the derivative of V(x) over each of the given intervals.

Taking the derivative of V(x), we get,

V'(x) = -3x²+ 10x + 1

Taking the absolute value of this expression, we get,

|V'(x)| = 3x² - 10x - 1

Now, we can calculate the maximum value of |V'(x)| over each interval,

At [1,2]

|V'(1)| = 8

|V'(2)| = 9

[1,3.5]

|V'(1)| = 8

|V'(3.5)| = 0.75

[1,5]

|V'(1)| = 1

|V'(5)| = 24

[0,3.5]

|V'(0)| = 1

|V'(3.5)| = 0.75

The maximum value of |V'(x)| occurs on interval [1,5].

Therefore, the volume of the box is changing at the fastest average rate over the interval option c . [1,5].

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The above question is incomplete, the complete question is:

A cardboard box manufacturing company is building boxes with length represented by x + 1, width by 5 − x, and height by x − 1. the volume of the box is modeled by the function below. over which interval is the volume of the box changing at the fastest average rate?

a. [1,2]

b. [1,3.5]

c. [1,5]

d. [0,3.5]

Answer:

the answer is (b)

because;

a^2-10a+24

product:24

sum:-10

factor:-6,-4

a(a-6)-4(a-6)

(a-6)(a-4)

therefore:two solutions but only one is given

The larger cube is made up of 384 small cubes, each with a volume of 1/4.

We have,

If we assume that 96 is the total volume of a larger cube made up of smaller cubes, and each small cube has a volume of 1/4.

We can make the following calculation:

Let x be the number of small cubes that make up the larger cube.

The volume of the larger cube = Volume of each small cube x Number of small cubes

96 = (1/4) x

Solving for x.

Multiply 4 on both sides.

96 x 4 = x

x = 384

Therefore,

The larger cube is made up of 384 small cubes, each with a volume of 1/4.

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Answer:

(2, -5)

(4, -3)

(3, -1)

Step-by-step explanation:

When reflected across the X-axis, the sign of the y will change to the opposite.

(x, y) → (x, -y)

Let's solve

(2,5) → (2, -5)

(4,3) → (4, -3)

(3,1) → (3, -1)

So, the missing coordinates are: (2, -5)

                                                       (4, -3)

                                                       (3, -1)

Answer:

0.5 (any number between 0 and 1)

Step-by-step explanation:

34 * 0.5 = 17

34 > 17 > 0

Answer: (10 * 6) + (9 * 6) = 114

Step-by-step explanation:

Using the distributive property, we can write:

19 × 6 = (10 + 9) × 6

= (10 × 6) + (9 × 6) // Distributive property of multiplication over addition

= 60 + 54

= 114

Therefore, 19 × 6 = 114 when using the distributive law.

If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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By translation, the image of the triangle X is equivalent to the triangle E.

Herein we find the representation of a triangle, whose vertices are described below:

A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)

Whose image must be determined by a rigid transformation known as translation:

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

Where:

Now we proceed to determine the images of the vertices of the triangle:

A'(x, y) = (5, 5) + (4, - 3)

A'(x, y) = (9, 2)

B'(x, y) = (5, 6) + (4, - 3)

B'(x, y) = (9, 3)

C'(x, y) = (7, 5) + (4, - 3)

C'(x, y) = (11, 2)

Therefore, the triangle E is the image of the triangle X.

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Rhys will have to pay £6 interest after the first year.

To calculate the interest, we can use the formula:

Interest = Principal x Rate

Where:

Principal = £200

Rate = 3% = 0.03 (in decimal form)

So, the interest Rhys will have to pay after the first year is:

Interest = £200 x 0.03 = £6

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Answer:

(-11,8)

Step-by-step explanation:

To find the coordinates of the fourth corner of the rectangular city block, we need to use the fact that opposite sides of a rectangle are parallel and equal in length.

Let's start by finding the length of one of the sides of the rectangle. We can use the distance formula for that:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For example, if we want to find the length of the side between (2,2) and (2,-4), we have:

d = sqrt((2 - 2)^2 + (-4 - 2)^2) = sqrt(6^2) = 6

We can also see from the given coordinates that the sides of the rectangle are parallel to the x or y axis, which means that their lengths are simply the difference between the corresponding x or y coordinates.

So now we know that the length of the sides of the rectangle are both 6 units. The missing corner must be positioned 6 units away from the given point (-5,-4) along the x-axis, since the fourth side of the rectangle is parallel to the x-axis. Therefore, its x-coordinate is -5 - 6 = -11.

Similarly, the fourth corner must be positioned 6 units away from the given point (2,2) along the y-axis, since the fourth side of the rectangle is parallel to the y-axis. Therefore, its y-coordinate is 2 + 6 = 8.

Therefore, the coordinates of the fourth corner are (-11, 8).

The smallest positive integer n that makes the fourth root of 56n360 an integer is n = 81.

We can start by simplifying the expression inside the fourth root:

56 * n * 360 = [tex]2^{3}[/tex] * 7 * n * [tex]2^{3}[/tex] * [tex]3^{2}[/tex] * 5

= [tex]2^{6}[/tex] * [tex]3^{2}[/tex] * 5 * 7 * n

Taking the fourth root of this expression gives:

[tex](56*n*360)^{(1/4)}[/tex] = [tex](2^{6}*3^{2}*5*7*n) ^{(1/4)}[/tex]

= [tex]2^{(6/4)}[/tex] * [tex]3^{(2/4)}[/tex] * [tex]5^{(1/4)}[/tex] * [tex]7^{(1/4)}[/tex] * [tex]n^{(1/4)}[/tex]

= 4 * [tex]3^{(1/2)}[/tex] * [tex]5^{(1/4)}[/tex] *  [tex]7^{(1/4)}[/tex] * [tex]n^{(1/4)}[/tex]

For the fourth root to be an integer, [tex]n^{(1/4)}[/tex] must be an integer, and since we want n to be as small as possible, we want  [tex]n^{(1/4)}[/tex] to be as small as possible.

The smallest possible value of n that makes  [tex]n^{(1/4)}[/tex]an integer is when n is a fourth power of a prime number. Therefore, we can let n = [tex]p^{4}[/tex], where p is the smallest prime number that makes the expression under the fourth root an integer.

From the expression above, we can see that p must be a factor of 7 and [tex]35^{2}[/tex] in order to make the expression under the fourth root an integer. The smallest prime factor of 7 and [tex]35^{2}[/tex] is 3, so we can let p = 3. Then:

n =  [tex]p^{4}[/tex] = [tex]3^{4}[/tex] = 81

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Answer: Letter C

Step-by-step explanation:

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Since c is saying that congruent arcs associated with chords are perpendicular its wrong.

The coordinate of the resulting point C' after 270-degree rotation clockwise is (-2, -3).

Given that:

Point, C(-3, 2)

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The coordinate of the resulting point C' after 270-degree rotation clockwise is given as,

C' = (-y, x)

C' = (-2, -3)

The coordinate of the resulting point C' after 270-degree rotation clockwise is (-2, -3).

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The measure of the diameter x for the circle is 18.6 units.

A circle is a geometric shape consisting of all points in a plane that are equidistant from a fixed point called the centre. A circle is defined by its radius, which is the distance from the centre to any point on the circle, or by its diameter, which is the distance across the circle passing through the centre and connecting two points on the opposite sides of the circle.

The diameter of a circle is a line segment that passes through the centre of the circle and connects two points on the opposite sides of the circle. The diameter is twice the length of the radius of the circle, and it is often used to express the size or scale of the circle.

The diameter of the circle will be calculated as,

x = 2 ( 3.2 + 6.1)

x = 2 ( 9.3)

x = 18.6 units

Hence, the diameter is 18.6 units.

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If one pound 1.2 euros then 14 pounds is 21 euros.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity

Given that 1 pound is 1.2 euros

We have to find 14 pounds in euros

To do this we just need to multiply 14 with 1.2

14×1.5

21 euros

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t < 8 is the inequality to solve the variable "t" as per the given data.

The cost C (in dollars) of renting the room for t hours can be expressed as:

C(t) = 4t + 18

To spend less than $50, we can set up an inequality:

C(t) < 50

Substituting the expression for C(t), we have:

4t + 18 < 50

Subtracting 18 from both sides, we get:

4t < 32

Dividing both sides by 4, we obtain:

t < 8

Therefore, the chemistry club could rent the meeting room for any number of hours less than 8 in order to spend less than $50.

The inequality solved for t is:

t < 8

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The angle of Z is 63.2 degree.

The word isosceles comes from the Ancient Greek term isosceles which literally means "equal-legged." An isosceles triangle has two of its sides of equal length, which means that the angles opposite these sides would also be of equal measure.

In Triangle ΔXYZ,

∠Y = 83°, XY = 9 and XZ = 10

To find the angle of Z

Using Sine rule :-  sine rule relates the sine of each angle to length of        opposite side.

[tex]\frac{Sin A}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]

Where, A, B , C are the angles of the triangles and a, b, c are the side of the triangles

Then, Apply it:

[tex]\frac{Sin83}{10}=\frac{SinZ}{9}[/tex]

Using cross multiplication:-

Sin 83 × 9 = Sin Z × 10

Sin Z = (Sin 83 × 9)/10

Sin Z = 0.893

∠Z = [tex]Sin^-^1(0.893)[/tex]

∠Z =  63.2°

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222 gallons of milk containing 7% butterfat and 111 gallons of milk containing 4% butterfat must be used to obtain 333 gallons of milk containing 6% butterfat.

Let's assume that x gallons of milk containing 7% butterfat are needed, and y gallons of milk containing 4% butterfat are needed to obtain 333 gallons of milk containing 6% butterfat.

We can set up two equations to represent the given information:

Equation 1: x + y = 333

Equation 2: 0.07x + 0.04y = 0.06(333)

Simplifying Equation 2, we get:

0.07x + 0.04y = 19.98

Multiplying both sides of Equation 1 by 0.04, we get:

0.04x + 0.04y = 13.32

Subtracting this equation from Equation 2, we get:

0.03x = 6.66

Dividing both sides by 0.03, we get:

x = 222

Substituting x = 222 into Equation 1, we get:

222 + y = 333

y = 111

Therefore, 222 gallons of milk containing 7% butterfat and 111 gallons of milk containing 4% butterfat must be used to obtain 333 gallons of milk containing 6% butterfat.

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