can anyone help? i don’t understand this !

Answer: The above answer is correct.

1. C

2. B

Step-by-step explanation: I got this right on Edmentum.

The vertices of the hyperbola will be (–20, 41) and (–20, 1). Then the correct option is C. The foci of the hyperbola will be (–20, 50) and (–20, –8). Then the correct option is B.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

The equation of the hyperbola is given below.

[tex]\rm \dfrac{(y-21)^2}{20^2}-\dfrac{(x+20)^2}{21^2}=1[/tex]

The vertices (h, k + a), (h, k – a) are the two bending points of the hyperbola with center (h, k).

The center of the hyperbola will be at (-20, 21).

The value of a and b will be 20 and 21, respectively.

Then the vertices of the hyperbola will be

(–20, 21 + 20) and (–20, 21 – 20)

(–20, 41) and (–20, 1)

Then the correct option is C.

The foci (h, k + c), (h, k – c) are the two bending points of the hyperbola with center (h, k).

c² = a² + b²

c² = 20² + 21²

c = 29

Then the foci of the hyperbola will be

(–20, 21 + 29) and (–20, 21 – 29)

(–20, 50) and (–20, –8)

Then the correct option is B.

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Answer:

The president's approval rating in 2014 is 60.9%

Step-by-step explanation:

The parameters given are;

President's approval rating in 2015 = 42%

President's approval rating in 2015 = 31% less than 2014 president's approval rating

Therefore, whereby the president's approval rating in 2014 = x, we have;

42% = x - 31% of x = x - 0.31·x = 0.69·x

Hence, x% = 42% ÷ 0.69 = 60.8696 ≈ 60.9%

The president's approval rating in 2014 = 60.9%.

his approval rating in 2014 is 60.9%

Here we assume the president's approval rating in 2014 = x

So,  

42% = x - 31% of x

= x - 0.31·x

= 0.69·x

Now  

Hence, x% [tex]= 42\% \div 0.69[/tex] = 60.8696 ≈ 60.9%

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Answer:

Ambos cometas coincidirán en 2016.

Step-by-step explanation:

(The following exercise is presented in Spanish and for such reason explanation will be held in that language).

Sean [tex]t_{1}[/tex] y [tex]t_{2}[/tex] los años en los que se hacen visibles los cometas, respectivamente. Se sabe que los cometas coinciden cuando se pueden ver el mismo año, ese año estaría asociado al mínimo común múltiplo de ambos intervalos de tiempo, el cual sería igual a 72 años. Entonces, ambos cometas volverán a coincidir en 2016.

Answer:

2/5

Step-by-step explanation:

0.4 = 4/10 which in simplest form is 2/5

Answer:

2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

When the question comes with answer choices, please share them.   In this case it sounds like there were four graphs from which to choose.

f(x) = |x^2 − x − 2| is always zero or greater, due to the absolute value function.

x^2 − x − 2 = 0 factors to (x - 2)(x + 1) = 0, so the zeros of f(x) are {-1, 2}.

Plot x-intercepts {-1, 2}.  The axis of symmetry is the vertical line x = 1/2, which is precisely halfway between the x-intercepts.  If we now choose the test number x = 0, we find the value of f(0) to be |-2}, which tells us that the y-intercept is (0, |-2|), or (0, 2), so we have a parabolic curve opening down between x = -1 and x = 2 and touching (but not crossing) the x-axis at those x-values. To the left of x = -1 the curve increases steadily from y = 0 in Quadrant II; to the right of x = 2, the curve increases steadily from y = 0 in Quadrant I.

The graph for the given function is plotted below.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=|x²-x-2|.

Graph the absolute value using the vertex and a few selected points.

Put x= -2, -1, 0 and 1 in the given function, we get

When x=0

y= |0-0-2|

y=0

When x=1

y=|1-1-2|

y=2

When x=-2

y=|4+2-2|

y=2

Now, plot points (-2, 4), (-1, 0), (0, 2) and (1, 2) on graph

Therefore, the graph for the given function is plotted below.

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Answer:

4 km -> 400,000 mm

put a decimal point at the end of 4 and move it to the left 6 times because we know that 1 km is equal to 100,000 and it has zeros.

hence, it is proven that 4 km is equal to 4000,000.

Answer:

258 cm

Step-by-step explanation:

Given:

Distance from the base of the pole to the base of a tent guy line is [tex]2\frac{1}{2}[/tex]

Length of a tent guy line is 359 cm

To find: Height of the upright tent pole

Solution:

Let AB denotes the pole and AC denotes a tent guy line.

According to Pythagoras theorem, in a right angled triangle, square of hypotenuse is equal to sum of squares of other two sides.

[tex]AC^2=AB^2+BC^2[/tex]

[tex]AC=359 cm\\AB=x\\BC=2\frac{1}{2}\,m=\frac{5}{2}\,m=\frac{5}{2}\times 100=250\,cm[/tex]

Therefore,

[tex](359)^2=x^2+(250)^2\\128881=x^2+62500\\128881-62500=x^2\\66381=x^2\\x=257.6\,cm\approx 258\,cm[/tex]

Answer:

........................ 260

Answer:

260

Step-by-step explanation:

Write 65% as

65/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

65/100 of 400 = 65/100 × 400

=260

Answer:

B

Step-by-step explanation:

These lines are parallel so they have no solutions

Answer:

Infinite Solutions

Step-by-step explanation:

When graphed, the lines overlap with each other. This means that the system has an infinite number of solutions.

Answer:

x = -4

Step-by-step explanation:

6 -x = 5x + 30

6 - 30 = 5x + x

-24 = 6x

divide both sides by 6 to get x = -4

Answer:

[tex]=-4[/tex]

Step-by-step explanation:

[tex]6-x=5x+30\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\6-x-6=5x+30-6\\\mathrm{Simplify}\\-x=5x+24\\\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}\\-x-5x=5x+24-5x\\Simplify\\-6x=24\\\mathrm{Divide\:both\:sides\:by\:}-6\\\frac{-6x}{-6}=\frac{24}{-6}\\Simplify\\\frac{-6x}{-6}=\frac{24}{-6}\\\mathrm{Simplify\:}\frac{-6x}{-6}:\quad x\\\frac{-6x}{-6}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{6x}{6}\\\mathrm{Divide\:the\:numbers:}\:\frac{6}{6}=1\\=x[/tex]

[tex]\mathrm{Simplify\:}\frac{24}{-6}:\quad -4\\\frac{24}{-6}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{6}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{6}=4\\=-4\\[/tex]

Answer:

[tex]8x^2-10x-3[/tex]

Step-by-step explanation:

[tex](2x-3)(4x+1)[/tex]

[tex]2x(4x+1)-3(4x+1)[/tex]

[tex]8x^2+2x-12x-3[/tex]

[tex]8x^2-10x-3[/tex]

Answer:

[tex]-4y-1[/tex]

Step-by-step explanation:

[tex](5y+-y+-8y)+(8+-8+-1)[/tex]

[tex]-4y-1[/tex]

Answer:

5y + 8 - 1y - 8 - 8y - 1

variables = -4y

numbers = -1

Answer:

i need help

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Let the two matrix A and [tex]A^{-1}[/tex] are,

A = [tex]\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}[/tex] and [tex]A^{-1}[/tex] = [tex]\frac{1}{(-1)}[/tex][tex]\begin{bmatrix}2 &-3\\-3 & 4\end{bmatrix}[/tex]

Therefore, [tex]A^{-1}[/tex] = [tex]\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}[/tex]

Now [tex]A.A^{-1}[/tex] = [tex]\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}.\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}[/tex]

                   = [tex]\begin{bmatrix}(-8+9) & (12-12)\\(-6+6) & (9-8)\end{bmatrix}[/tex]

                  = [tex]\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}[/tex]

Therefore, Option (B) will be the answer.

Answer:

153 members

Step-by-step explanation:

Given;

117 had used treadmills

N(A) = 117

89 had used stationary bikes

N(B) = 89

53 had used both types of equipment

N(A∩B) = 53

The number of members that had used treadmills, stationary bikes, or both is;

N(A or B) = N(A) + N(B) - N(A∩B)

N(A or B) = 117 + 89 - 53

N(A or B) = 153

The number of members that had used treadmills, stationary bikes, or both is 153

Answer:

8km

Step-by-step explanation:

1:100000

8 : x

x = the distance travelled in cm = 8 x 100000 = 800000cm

convert cm to km = 800000/100000 = 8km

Hope this helps.

Good Luck

Answer:

3.1 ≤d≤183.1

Step-by-step explanation:

d = 4.5t + 3.1

Since this is a line, we can find the range by putting in the minimum and maximum of the domain

domain = 0≤t≤40

Let t =0

d = 0+3.1  so the minimum of the range is 3.1

Let t = 40

d = 4.5(40)+3.1

d = 183.1 so the maximum is 183.1

The range is 3.1 ≤d≤183.1

Answer:

[tex]\frac{1}{5x-5}[/tex]

Step-by-step explanation:

=> [tex]\frac{x-1}{5(x-1)^2}[/tex]

=> [tex]\frac{x-1}{5(x-1)(x-1)}[/tex]

Cancelling (x-1)

=> [tex]\frac{1}{5(x-1)}[/tex]

=> [tex]\frac{1}{5x-5}[/tex]

The simplified form of the expression (x-1)/5(x-1)² is 1/(5x-5).

The given expression is (x-1)/5(x-1)²

To simplify the expression (x-1)/5(x-1)², we can first cancel out the common factor of (x-1) in the numerator and denominator:

(x-1)/(5(x-1)²) = 1/[5(x-1)]

The expression simplifies to 1 divided by 5 times (x-1), which can be written as:

1/(5x-5)

So, the simplified form of (x-1)/[5(x-1)²] is 1/(5x-5).

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Answer:

(-1, 4)

Step-by-step explanation:

In the figure attached,

Ordered pair representing point P is (3, 4) [parallel to y-axis]

If this point has been reflected across a line x = 1

New point after reflection across x = 1 will be,

P(3, 4) → P'(-1, 4)

Since point P and P' will be equidistant from the line (x = 1), so the x ordinate of P' will be = 3 - 4 = -1

And y-ordinates of point P' will be same as y = 4

Answer:

a) 1 and 7 = congruent

b) 2 and 5 = supplementary

c) 4 and 6 = congruent

d) 3 and 8 = supplementary

Step-by-step explanation:

Congruent angles are the same, but in different forms. So they might be flipped around, but they are still the same angle and they have the same number of degrees.

Supplementary angles are 2 angles that add up to 180 degrees.

For example, you know that 2 + 3 = 180 degrees, because its sitting on a straight line, and so they are supplementary. They have been cut unevenly which makes 2>3. Same goes for all the other pairs of angles. Using this, you can determine which ones are supplementary and congruent.

So, even though they haven't given you exact values for each of the angles, just by looking at the shape, you can often tell very easily what kind they are:

*acute angles = angles that are less than 90 degrees

*obtuse angles = angles more than 90 degrees, but less than 180 degrees.

a) 1 and 7 have the same shape. Both are acute angles, just flipped upside down.

b) 2 and 5 are complementary. 5 is an acute angle, like 1 and 7. 2 is an obtuse angle, like 6 and 8. If you look at it closely, you can tell that they add up to 180 degrees.

c) 4 and 6 are congruent. They are both obtuse angles.

d) 3 and 8 are supplementary. 3 is an acute angle and 8 is obtuse.

Hope this helped : )

Answer:

[tex]\frac{3y+4}{2-6y} = -\frac{2}{5} \\y=-8[/tex]

Answer:

y = -8

Step-by-step explanation:

[tex]\frac{3y+4}{2-6y} = \frac{-2}{5}[/tex]

5 ( 3y + 4) = -2 ( 2 - 6y)

15y + 20 = -4 + 12y

15y - 12y + 20 = -4 + 12y -12y

3y + 20 = -4

3y + 20 - 20 = -4 -20

3y = -24

y = -8

Hope this helps ^-^

Answer:

6 = 2 * 3 so it is composite

22 = 2 * 11 so it is composite

29 is a prime number

Step-by-step explanation:

Answer:29

Step-by-step explanation:

6 = 2 and 3

22 = 2 and 11

29 = 1 and 29

therefore 29 is the composite number

Answer:it would be D

Step-by-step explanation:

Input would be the x and output the y

Answer: D

Step-by-step explanation: The input is X, Output is Y

Answer:

x = -3, y = 7.

Step-by-step explanation:

 x + 3y = 18  

-3x -  12y = -75

Multiply the first equation by 3:

3x + 9y = 54

Adding the last 2 equations to eliminate x:

-3y = -21

y = 7.

Substitute y = 7 into the first equation:

x + 3(7) = 18

x + 21 = 18

x = 18 - 21

x = -3.

Answer:

Below in bold.

Step-by-step explanation:

6 hours 12 minutes = 6.2 hours

7 hours 18 minutes = 7.3 hours.

Average speed = distance / time

So for West to East,  average speed =  3800 / 6.2 = 612.9 km/hour.

- and  for East to West,  average speed =  3800 / 7.3  = 520.5  km/hour.

These values are correct to the nearest tenth.

Answer: V=1008π units³

Step-by-step explanation:

The formula for volume is [tex]V=\pi r^2h[/tex]. We can plug in our values to find volume.

[tex]V=\pi (12)^2(7)[/tex]

[tex]V=1008\pi[/tex]

Answer:

2

Step-by-step explanation:

10a² : 5a² = 10 : 5 = 2

Answer:

..........................