If all the values in a set of data are the same, which of the following is true? (Check all that apply.)

(A) The median and mode are the same.
(B) The range is zero.
(C) The range and mode are the same.
(D) The low and high values are the same.

The equation for the ellipse centered at the origin is C. x²/4 + y²/49 = 1.

Let the equation of the ellipse be:

x²/b² + y²/a² = 1

The co vertices are at (2, 0) and (-2, 0). The major axis is 14 units. Therefore, 2a = 14. This implies that a = 7 and a² = 7 × 7 = 49.

Therefore, since x²/b² + y²/a² = 1, this will be x²/4 + y²/49 = 1.

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Answer:

B) [tex]-5\leq y\leq -1[/tex]

Step-by-step explanation:

The range is the lowest point to the highest point on the graph.

Remember this:

1. domain (x-axis) LEFT –> RIGHT

2. range BOTTOM (y-axis) –> TOP

when this equation is graphed over the domain, it limits the range to being (8,–5) and (–8,–1) and since with range you only look at the y-coordinates that means that the range is [–5,–1]

The number 0.7 / 8 is given by the fraction 7 / 80 when expressed in its simplest form

An equation is an expression that shows the relationship between two or more variables and numbers.

A fraction in its simplest terms is given as a/b, where a is the numerator and b is the denominator.

Hence:

0.7 / 8 = 7 / 80

The number 0.7 / 8 is given by the fraction 7 / 80 when expressed in its simplest form

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Answer:

(a) x = 0

(b) g(2) = -5

Step-by-step explanation:

Another way of representing g(x) is with the variable "y". In other words, the value of g(x) is the value on the y-axis (vertical axis).

(a) The question is asking you to give the "x" value when the line crosses y = -4. The only value which satisfies this is x = 0.

(b) When 2 is placed inside the parentheses of g(x), it is asking you to find the "y" value of the line at x = 2. The only value which satisfies this is y = -5.

Answer:

approximately 8.5

Step-by-step explanation:

So you can use the distance formula: [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\[/tex] which is derived from the Pythagorean theorem because normally x2-x1 would kind of give the distance length between x2 and x1 except sometimes it would be negative which wouldn't make much sense right? but it doesn't matter because it's being squared so the value ultimately becomes positive, and the same thing goes for the y-value. the distance between x2 - x1 really represents the base and y2-y1 represents the height and then adding them together gives the hypotenuse squared which is why you take the square root over the entire thing to find the distance, since the hypotenuse is the shortest distance between two points

Now all you have to do is plug the values in to get

[tex]\sqrt{(-7 - (-4))^2 + (-8 - 0)^2}\\\sqrt{(-3)^2 + (-8)^2}\\\sqrt{9 + 64}\\\sqrt{73}\\distance \approx 8.5[/tex]

Answer:

C

Step-by-step explanation:

because it just make sence

Answer:

McKenna runs all the way home from school ...

Step-by-step explanation:

In this distance v time graph, a negative slope means going from school to home, a positive slope means going from home to school, and a flat section means staying at a particular location without moving.

Answer:

7 ÷ 15 = 0.46666666666667

Step-by-step explanation:

Answer:

0.47

Step-by-step explanation:

To turn any fraction into a decimal, we must simply divide the numerator by the denominator. 7 divided by 15 is equal to 0.466666...

If we round this number to the nearest hundredth, we get 0.47.

Answer:

3. Increase

Step-by-step explanation:

If more people are being born compared to the number of deaths, then you have population growth.

Answer:

3. increase

Explanation:

When birth rate is higher than the death rate, it is called natural increase.

The formula for natural increase is:

[tex]natural \space\ increase = \frac{Crude \space\ Birth \space\ Rate \space\ - \space\ Crude \space\ Death \space\ Rate}{100}[/tex]

Answer: y = -2/3x+23/3

Step-by-step explanation:

Parallel is the key point here. They gave points (7,3), 7 is the x value, 3 is the y value.

Take your equation

y = -2/3x+3 and substitute the 7 for the x value and 3 for the y value.

Like this...

3 = -2/3(7)+b

3 = -14/3 +b

Add 14/3 to 3

The answer is 23/3

So y = -2/3x+ 23/3

***Don't change -2/3 because it's asking for parallel***

***If 2 lines are parallel their slopes are equal***

Ly has 15 dimes, 12 nickels and 30 quarters given that he has 3 more dime than nickels and twice as many quarters than dimes and the value of these coins is $9.60. This can be obtained by giving variables to each represent the number of each coin and adding the values to equate with the total value of coins.

Let number of dimes be y

Given that,

3 more dime than nickels ⇒ Number of nickel = y - 3

twice as many quarters than dimes ⇒ Number of quarters = 2y

9.60 = 0.1y + 0.05(y-3) + 0.25(2y)

9.60 = 0.1y + 0.05y - 0.15 + 0.5y  

9.60 = 0.1y + 0.05y - 0.15 + 0.5y  

9.60 + 0.15 = 0.65y

y = 9.75/0.65 = 15

y = 15

Therefore the number of each coin,

Hence Ly has 15 dimes, 12 nickels and 30 quarters given that he has 3 more dime than nickels and twice as many quarters than dimes and the value of these coins is $9.60.

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Using the Factor Theorem, the inequality that represents the given region is:

[tex]y < \frac{(x + 40)(x - 50)}{21}[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

The roots are given as follows:

[tex]x_1 = -40, x_2 = 50[/tex]

Hence:

y = a(x + 40)(x - 50)

It includes the point (-55,-75), hence:

-75 = a(-55 + 40)(-55 - 50)

a = 75/(15 x 105)

a = 1/21

Hence the region less than the equation is:

[tex]y < \frac{(x + 40)(x - 50)}{21}[/tex]

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Answer:

D

Step-by-step explanation:

In accordance with the definitions of rigid transformation and translation, the correct rule for the translation is defined by (x, y) → (x - 3, y + 4). (Right choice: A)

Mathematically speaking, transformations are rigid transformations that are modelled according to the following formula:

P'(x, y) = P(x, y) + (h, k)     (1)

Where:

Hence, a leftward translation indicates that h < 0. The correct rule for the translation is defined by (x, y) → (x - 3, y + 4).

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Answer:

a

Step-by-step explanation:

the picture

The number of steps that Julissa walked each hour is 3409.6 steps per hour.

According to this question, Julissa works in the warehouse of a large online retailer. She walked 20,458 steps on Tuesday from 9:00 a.m. to 3:00 p.m.

9:00 a.m to 3:00pm is 6 hours difference. This means that Julissa walked 20,458 steps in 6 hours.

Therefore, Julissa walked 20,458 steps ÷ 6 = 3409.6 steps per hour.

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Answer:

it's A

Step-by-step explanation:

Answer: X = 12.1 units

Step-by-step explanation:

Solving the side x of the triangle just requires the Pythagorean theorem.

x^2 + 7^2 = 14^2

x^2 + 49 = 196

subtract 49 on both sides, to cancel the 49 on the left side.

x^2 = 147 units

extract the square root of each side.

X = 12.1 units

Hope I Helped!

Answer:

Step-by-step explanation:

The attached image shows the figure of rotation generated by rotating a triangular shape about the x-axis.

When the given line is rotated about the x-axis, each point on the line traces a circle in the y-z plane. Those together will make a cone shape. The radius of the circle is the distance of the point from the x-axis.

The base of the cone will be the circle obtained by rotating the y-intercept about the x-axis. As above, the radius of that circular base is the y-value of the y-intercept: 8 units.

The height of the cone will be the x-value of the point where the radius is zero, at x=6.

The cone has a height of 6 units and a radius of 8 units.

Answer:

x = - [tex]\frac{5}{p}[/tex]

Step-by-step explanation:

px + 17 = 12 ( subtract 17 from both sides )

px = - 5 ( isolate x by dividing both sides by p )

x = [tex]\frac{-5}{p}[/tex] = - [tex]\frac{5}{p}[/tex]

Answer:

can't see anything in this photo because this photo is not clear

Step-by-step explanation:

We have a dilation because we are multiplying the pre image by some constant,

Since dilations doesn't preserve side length, they are a non rigid motion.

According to the rule, we multiply the x values by 3 and the y values by 2.

So our new points are

A'(9,10)

B'(15,6)

C'(6,4)

The measure of the angles are 105 degrees

The sum of the angles is given as 210 degree

Alternate angles are equal.

So, we have:

x + x = 210

This gives

2x = 210

Divide by 2

x = 105

Hence, the measure of the angles are 105 degrees

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Answer:

32°, 58°

Step-by-step explanation:

Let one acute angle measure x.

The other acute angle measures 2x - 6.

The sum of the measures of the acute angles of a right triangle is 90.

x + 2x - 6 = 90

3x - 6 = 90

3x = 96

x = 32

2x - 6 = 2(32) - 6 = 58

Answer: 32°, 58°

This shows that the food will only last 1 1/3 meals

Fractions are written as a ratio of two integers. Given the following

Total pounds of food bought = 24 pounds

Amount fed each per meal = 3/4 * 24 pounds = 18 pounds

Remains = 24 - 18

Remaining = 6 pounds

This shows that the food will only last 1 1/3 meals

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Answer:

19

Step-by-step explanation:

Given:

To find how many full bags of sweets the machine can fill, divide the total number of sweets by the number of sweets per full bag:

⇒ 4275 ÷ 28 = 152.6785714...

Therefore, the machine can fill 152 full bags.

To calculate how many sweets are left, subtract the product of the number of full bags and the number of sweets per bag from the total number of sweets:

⇒ 4275 - (152 · 28)

⇒ 4275 - 4256

⇒ 19

Therefore, there are 19 sweets left after the machine has filled as many bags as possible.

Answer:

276 feet

Step-by-step explanation:

The best way to do this is to complete the square, which puts the quadratic in vertex form. The vertex of a negative parabola, which is what this is, is the highest point of the function...the max value.  The k coordinate of the vertex will tell us that highest value.  To complete the square, we will first set the quadratic equal to 0, then move the constant over to the other side:

The rule for completing the square is that the leading coefficient must be a positive 1.  Ours is a negative 16, so we have to factor out -16:

Now the next thing is to take half the linear term, square it, and then add it to both sides.  Our linear term is 7, half of that is 7/2.  Squaring 7/2 gives you 49/4.  So we add 49/9 into the parenthesis on the left.  However, we can't forget that there is a -16 out front there that refuses to be ignored.  We have to add then (-16)(49/4) onto the right:

The purpose of this is to create a perfect square binomial that serves as the h value of the vertex (h, k).  Stating that perfect square on the left and doing the addition on the right:

Now we finalize by moving the constant back over and setting it back equal to y:

The vertex is

That translates to "at 3.5 seconds the particle is at its max height of 276 feet".

Transformation is a process in which the size and/or orientation of a given figure are/is adjusted. The appropriate answers are:

i. equal to

ii. congruent to

iii. the same distance to

Transformation is the process required to either increase or decrease the size of a given shape, or change the orientation of a given shape. The methods of transformation are dilation, reflection, rotation, and translation.

Thus the required statements to complete the reflection across a line as required in the question are:

i. equal to

ii. congruent to

iii. the same distance to

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The value of discriminant [tex]b^{2} -4ac[/tex] of the equation [tex]-2x^{2} -3x+8=0[/tex] is equal to 73.

Given equation [tex]-2x^{2} -3x+8=0[/tex] and we have to find the value of determinant and the number of roots of the equation.

Determinant is the quantity that depends on the coefficients of variables.

To find out the value of determinant we have to put the values in [tex]b^{2} -4ac[/tex] in which b=-3, a=-2 and c=8

[tex]b^{2} -4ac[/tex]=[tex]-3^{2} -4*(-2)*8[/tex]

=9+8*8

=9+64

=73

And because the value of discriminant is one so the number of real solution that [tex]-2x^{2} -3x+8=0[/tex] is 2. If the discriminant is equal to zero then there is exactly one real root.

Hence the value of determinant of the equation [tex]-2x^{2} -3x+8=0[/tex] is 73.

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Answer:

baahsuslskissisudjxnxnx