PLEASE HELP!!!!!!! What is the slope of the line?


−53


−35


35


53

By definition of the focus of a parabola, the coordinates of the focus of the parabola - 8 · (x - 5) = (y + 1)² are represented by the point F(x, y) = (3, - 1). (Correct choice: A)

The standard equation of the parabola with an horizontal axis of symmetry is presented below:

[tex]x - h = \frac{1}{4\cdot p}\cdot (y - k)^{2}[/tex]     (1)

Where:

The coordinates of the focus is described by the following expression:

F(x, y) = (h + p, k)

If we know that h = 5, k = - 1 and p = - 2, then the coordinates of the focus are:

F(x, y) = (5 - 2, - 1)

F(x, y) = (3, - 1)

By definition of the focus of a parabola, the coordinates of the focus of the parabola - 8 · (x - 5) = (y + 1)² are represented by the point F(x, y) = (3, - 1). (Correct choice: A)

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Answer:

Part A

1.5 seconds

Part B

By substitution and factorization because h = 0 at ground level

Step-by-step explanation:

Part A

The height from which the soccer player heads the ball, h = 6 feet

The initial velocity of the ball, v = 20 ft./s

The height of the ball in feet, h = -16·t² + 20·t + 6

From the given equation of the ball, we have;

At the initial height, t = 0, from the given equation, h = 6

At the  ground level,  the height, h = 0, therefore, we get;

0 = -16·t² + 20·t + 6

Factorizing using a graphing calculator gives;

0 = 2 × (-8·t² + 10·t + 3) = -2 × (8·t² - 10·t - 3) = -2 × (2·t -3)·(4·t + 1)

∴ (2·t -3)·(4·t + 1) = 0

t = 1.5 or t = -1/4 = -0.25

Therefore;

The time it takes the ball to hit the ground, t = 1.5 seconds.

Part B

The method used in solving the given quadratic equation is by plugging in the value of 'h' as h = 0 in the given equation and factorizing the result because at ground level, the height, h = 0.

Answer:

1/6

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability of choosing dimes twice = total number of dimes / total number of coins

At first pick = 4/9

because there is no replacement, dimes and total coins reduce by 1 and

second pick = 3/8

4/9 x 3/8 = 1/6

Answer:

Solution given:

area of semi circle h=½πr²=½×π×5²=39.27in²

area of rectangle EFHI=l×b=6×3=18in²

area of rectangle CDFG=l×b=17×2=34in²

Total area: 39.27+18+34=91.27 square inches

Answer: Number of hardback = 32

Number of paperback = 117

Step-by-step explanation:

Let the number of hardback books be represented by x.

Let the number of paperback books be represented by y.

Based on the information given, we can form an equation which will be:

x + y = 149 ......... i

3.50x + 0.75y = 199.75 ...... ii

Multiply equation i by 3.50

Multiply equation ii by 1

3.50x + 3.50y = 521.50 ...... iii

3.50x + 0.75y = 199.75 .....iv

Subtract equation iv from iii

2.75y = 321.75

y = 321.75 / 2.75

y = 117

Number of paperback = 117

Since x + y = 149

x = 149 - y

x = 149 - 117

x = 32

Number of hardback = 32

Answer:

Lateral Area = Area of 2 triangle + Area of slant rectangle + area of back rectangle

Lateral Area = (5m)(3m) + (6m) (36m) + (3m) (36m)

LA = 15m² + 216m² + 108m²

LA = 339 m²

SA = (5m)(3m) + (6m) (36m) + (3m) (36m) + (5m)(36m)

SA = 15m² + 216m² + 108m² + 180 m²

SA = 519 m²

Answer:

$28.20

Step-by-step explanation:

11 bumper stickers = $10.34

per sticker = $0.94

30 bumper stickers = 30*0.94

=28.20

30 bumper stickers = $28.20

Answer:

$28.20

Step-by-step explanation:

First, find out how much each bumper sticker costs.

Assuming that the cost of each bumper sticker is the same, the following equation represents how much one number sticker costs.

11x = 10.34

Solve for x [divide both sides by 11]

x = 0.94

So, one bumper sticker costs $0.94

Now, find out how many 30 bumper sticker costs.

The following equation represents how much 30 stickers cost.

30x = y

X represents the cost of one sticker and y represents the cost of 30 stickers.

We already know the value of x [one bumper sticker's cost] which is $0.94, so subsitute that in for x.

30[0.94] = y

28.2 = y

So, 30 bumper stickers cost $28.20.

:)

Answer:N

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

From the 10 cards, only 2 cards have the letter Z.

2/10 = 1/5

Answer:

1/5

Step-by-step explanation:

it is 2/10 so 1/5 thats

the probability that someone picks a card with the letter z on it?

Answer:

[tex]6a - 2[/tex]

Step-by-step explanation:

[tex]a - 2 + 5a[/tex]

[tex]6a - 2[/tex]

Answer:

x = 2

Step-by-step explanation:

2x−3-x+4=3

combine like terms:

x + 1 = 3

x = 2

The equation is true for the value of x = 2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is as given below.

2x − 3 - x + 4 = 3

We have to operate the like terms together.

Here 2x and x are like terms and 3 and 4 are like terms.

(2x - x) - 3 + 4 = 3

x - 3 + 4 = 3

x + 1 = 3

Subtracting 1 on both sides,

x = 3 - 1

x = 2

Hence the equation is true for x = 2.

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Answer:

Either C or A

Step-by-step explanation:

Hope it help you have a good day

Given here is a cube, whose one side is increased by a given percentage. The task is to find percentage increase in the volume of the cube. Below is the implementation of the above approach:

Answer:

The correct answer is that all trapezoids are quadrilaterals. ... Trapezoids are four-sided polygons, so they are all quadrilaterals.

Step-by-step explanation:

hope it helped ( ◜‿◝ )♡

Answer:

Sale price= $26.25

Step-by-step explanation:

Giving the following information:

Selling price= $35

Discount rate= 25%

To calculate the sale price of the sweater, we need to use the following formula:

Sale price= selling price*(1 - discount rate)

Sale price= 35*(1 - 0.25)

Sale price= 35*0.75

Sale price= $26.25

Answer:

3/4a -1/2a=8-4

1/4a=4

a=4/1/4

=16

Answer:

$16

1/2a=8

a=8*2

a=16

Answer:

81

Step-by-step explanation:

(-81)(-1) = 81

Answer:

They are similar by the definition of similarity in terms of a dilation

Step-by-step explanation:

The given vertices of triangle ΔABC are;

A(1, 5), B(3, 9), and C(5, 3)

The vertices of triangle ΔDEF are;

D(-3, 3), E(-2, 5), and F(-1, 2)

Therefore, we get;

The length of segment, [tex]\overline{AB}[/tex] = √((9 - 5)² + (3 - 1)²) = 2·√5

The length of segment, [tex]\overline{BC}[/tex] = √((9 - 3)² + (3 - 5)²) = 2·√10

The length of segment, [tex]\overline{AC}[/tex] = √((5 - 3)² + (1 - 5)²) = 2·√5

The length of segment, [tex]\overline{DE}[/tex] = √((5 - 3)² + (-2 - (-3))²) = √5

The length of segment, [tex]\overline{EF}[/tex] = √((2 - 5)² + (-1 - (-2))²) = √10

The length of segment, [tex]\overline{DF}[/tex] = √((2 - 3)² + (-1 - (-3))²) = √5

∴ [tex]\overline{AB}[/tex]/[tex]\overline{DE}[/tex] = 2·√5/(√5) = 2

[tex]\overline{BC}[/tex]/[tex]\overline{EF}[/tex] = 2·√10/(√10) = 2

[tex]\overline{AC}[/tex]/[tex]\overline{DF}[/tex] = 2·√5/(√5) = 2

The ratio of their corresponding sides are equal and therefore;

ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.

Answer:

P (1 + r/n)^(nt)

Step-by-step explanation:

Answer:

A = P(1+r/n)nt

(note the r/n is a fraction)

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

Answer: The difference is 21

Step-by-step explanation:

first find the volume of the first rectangler prism and write that number down. secound use the same equation but first change the height by 1 and then lastly subtract those two volumes to get your answer.

210-189=21

189+21=210

Answer:

Step-by-step explanation:

Algebra Examples

Popular Problems Algebra Graph y=7x-8

y

=

7

x

−

8

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

7

y-intercept:  

(

0

,

−

8

)

Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

values.

Tap for more steps...

x

y

0

−

8

8

7

0

Graph the line using the slope and the y-intercept, or the points.

Slope:  

7

y-intercept:  

(

0

,

−

8

)

x

y

0

−

8

8

7

0

y=7x-8

Answer:

a) 24

b) 10

c) 12/13

d) 5/13

e) 12/5

Step-by-step explanation:

a) We can see that the leg opposite <C is AB, and we are given AB = 24

b) We can see the leg adjacent to <C is AC, and we are given that AC = 10

c) The trig function sine is equal to

[tex]\frac{opposite}{hypotenuse}[/tex]

The opposite, AB, is 24, and the hypotenuse, BC, is 26. We can plug those numbers in:

[tex]sin(c) = \frac{24}{26} = \frac{12}{13}[/tex]

d)The trig function cosine is equal to

[tex]\frac{adjacent}{hypotenuse}[/tex]

The adjacent, AC, is 10, and the hypotenuse, BC, is 26. We can plug those numbers in:

[tex]cos(c) = \frac{10}{26} = \frac{5}{13}[/tex]

d)The trig function tangent is equal to

[tex]\frac{opposite}{adjacent}[/tex]

The opposite, AB, is 24, and the adjacent, AC, is 10. We can plug those numbers in:

[tex]tan(c) = \frac{24}{10} = \frac{12}{5}[/tex]