A parabola-shaped hill can be modeled by equation
y=-2(x - 3)2 +6, where x and y are measured in
kilometers.
How wide is the bottom of the hill? Assume the r -axis is
ground level. Round to the nearest tenths.
kilometers

Answer:

-4 ≤ y ≤ 7

Step-by-step explanation:

Inequalities

Solve the system of inequalities:

4y - 7 ≤ 3y       [1]

3y ≤ 5y + 8       [2]

A.

Subtracting 3y to [1]:

y - 7 ≤ 0

Adding 7:

y ≤ 7

Subtracting 5y to [2]:

-2y ≤ 8

Dividing by -2 (and flipping the sign):

y ≥ -4

The solution of the system is all the values of y greater or equal to -4 and less or equal to 7.

B.

The solution can be expressed as:

-4 ≤ y ≤ 7

Answer:

It’s B

Step-by-step explanation:

For the shape to be a quadrilateral, then the value of ∠QPS must be (b) 59 degrees

For quadrilateral PQRS to be an actual quadrilateral, then:

[tex]\angle RQP = \angle PSR[/tex] implies that:

[tex]6x + 13 = 7x - 5[/tex]

Collect like terms

[tex]6x - 7x = -13 - 5[/tex]

[tex]-x = -18[/tex]

Multiply both sides by -1

[tex]x = 18[/tex]

[tex]\angle QPS + \angle PSR = 180[/tex] implies that

[tex]\angle QPS + 7x - 5 = 180[/tex]

Substitute 18 for x

[tex]\angle QPS + 7(18) - 5 = 180[/tex]

Collect like terms

[tex]\angle QPS= 180 +5 - 7(18)[/tex]

[tex]\angle QPS= 59[/tex]

Hence, the measure of angle QPS must be (b) 59 degrees

Read more about quadrilaterals at:

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Answer:

the answer is A

Step-by-step explanation:

Answer:

Nickel = 13

Dimes = 8

Quarters = 16

Step-by-step explanation:

Let N denote Nickel,

Let D denote dime

Let Q denote quarter

Now, from online conversions;

1 nickel = 5 cents

Also, 1 dime = 10 cents

Also, 1 quarter = 25 cents

Isabelle has $5.45 which is also 545 cents.

Thus, we have;

5N + 10D + 25Q = 545 - - - (eq 1)

We are told that;

she has five more nickels than dimes, and twice as many quarters than dimes.

Thus;

N = D + 5

Also, Q = 2D

Plugging them for N and Q in eq 1 givens;

5(D +5) + 10D + 25(2D) = 545

5D + 25 + 10D + 50D = 545

25 + 65D = 545

65D = 545 - 25

65D = 520

D = 520/65

D = 8

Thus; N = D + 5 = 8 + 5 = 13

Q = 2D = 2 × 8 = 16

Answer:

answer 24×7

Step-by-step explanation:

answer ia an 409

Answer:

5y^8

Step-by-step explanation:

Simplifies to:

5y^8

=5*y^8

=5*(y*y*y*y*y*y*y*y)

=5y^8

Answer:

There are 182.88  cm in 2 yards.

Step-by-step explanation:

Given that,

1 inch = 2.54 cm

We need to find how many centimeters are there in 2 yards.

We know that,

1 yard = 36 inch

⇒ 2 yards = (2×36) inches

= 72 inches

It means,

72 inches = (72 × 2.54) cm

= 182.88  cm

Hence, there are 182.88  cm in 2 yards.

Answer:

72

Step-by-step explanation:

so he is working 4 day in a week

and 4 day times 18 weeks =18x4=72

Answer:

move decimal one place to the left i think!

Answer:

Step-by-step explanation:

That answer is really simple the answer to the is move decimal one place to the left

Step-by-step explanation:

You add 4 each time:

10+4=14

14+4=18

18+4=22

22+4=26

26+4=30

hope this helps <3

Answer:

Actually it’s d

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Answer: the answer would be 55 but since its says to round to the nearest hundred this would be 50 because its the closest and both lines are equivalent to be the same. plz brainliest plz

Step-by-step explanation:

Answer:

0.48

Step-by-step explanation:

Answer:

can you make the graph bigger please?

Answer:

42.875

Step-by-step explanation:

First you find the x-intercepts and the vertex of the equation.

(-5, 0), (-2, 0), (-3/2, 49/4)

You use those coordinates to find the sides of the triangle and then you use the lengths to find the semiperimeter.

Lastly, you use Heron's formula to compute the area.

The area of the triangle is required.

The area of the triangle is [tex]42.875\ \text{units}^2[/tex]

[tex]y=-x^2-3x+10[/tex]

The x intercepts are

[tex]-x^2-3x+10=0\\\Rightarrow x=\dfrac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\left(-1\right)\times 10}}{2\left(-1\right)}\\\Rightarrow x=-5,2[/tex]

The x intercepts are

[tex](-5,0),(2,0)[/tex]

Distance between them is

[tex]2-(-5)=7\ \text{units}[/tex]

Vertex of a parabola is given by

[tex]x=-\dfrac{b}{2a}\\ =-\dfrac{-3}{2\times -1}\\ =-1.5[/tex]

[tex]y=-(-1.5)^2-3(-1.5)+10=12.25[/tex]

So,

Base = b = 7 units

Height = h = 12.25 units

Area is

[tex]A=\dfrac{1}{2}bh\\\Rightarrow A=\dfrac{1}{2}\times 7\times 12.25\\\Rightarrow A=42.875\ \text{units}^2[/tex]

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Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

10x - 4y=24

7x -4y=12 multiply this equation by -1

-7x+4y=-12 we add it to the first and we get

3x=12

x=12/3=4

replace x with 3 in first equation

40-4y=24

40-24=4y

16=4y

y=4, x=4

Answer:

$36

Step-by-step explanation:

2/3 = $24

divide 24 by 2 to find 1/3

1/3 = $12

3/3 = (12 + 12 + 12 )

3/3 = 36

Answer:

18 students is the amount that passed the test

so the fraction would be 18/24, which can be simplified to 3/4, which is 75% of the class.

75% of the class passed

0.75% of the class passed

Answer:

75%

Step-by-step explanation:

24 x 0.75 (75% as a decimal) = 18

Answer:

slope=7/8

Step-by-step explanation:

8-1/10-2= 7/8

Answer:

its gonna be 1/18

Step-by-step explanation:

I'm pretty good at math honestly tbis was easy

Answer:

she walked 6 miles in the 9 days

Answer:

Step-by-step explanation:

you divide the two to the y, which is x=3/2y

then, you simplify the second equation to y, which is -3y= -4x+12

then, you substitute the x=3/2y into the second equation,

-3y = -6+12

-3y = 6

y = -2

Substitute the y into the first equation, x= 3/2y,

x = -3

Step-by-step explanation:

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

= (-3x + 12) + (2x² + 3x)

= 2x² + 12

= 2(x² + 6).

Answer:

[tex] - 3(x - 4) + x (2x + 3) \\ = - 3x + 12 + 2 {x}^{2} + 3x \\ = 2 {x}^{2} + 12 \\ = 2( {x}^{2} + 6)[/tex]

2(x^2+6) is the right answer.

Answer:

A. less than three batteries were used in five hours.

Answer:

a

Step-by-step explanation:

Answer: C

Step-by-step explanation:

IT IS RIGHT ON -2

Answer:

x = [tex]\frac{12}{5}[/tex]

Step-by-step explanation:

Given

2 = [tex]\frac{1}{2}[/tex] (5x - 8) ( multiply both sides by 2 to clear the fraction )

4 = 5x - 8 ( add 8 to both sides )

12 = 5x ( divide both sides by 5 )

[tex]\frac{12}{5}[/tex] = x

Answer:

The answer is 33,710 euros.

Step-by-step explanation:

Start by multiplying 45,550 by 6%. This will give 2,730. over the next three years the price decreases, so multiply 2,730 by 3, which is 8,190. Finally, subtract 45,550 by 8,190 to get 33,710.