Determine the rule of a quadratic function in factored
form given the following information:
.
the zeros are (-2,0) and (4,0)
it passes through the point (5,14)
.

Answer:

domain [-1, ∞)

range [ -3, ∞)

Step-by-step explanation:

Step-by-step explanation:

Asymptote: y = 2 y-intercept: (0,8)

Step-by-step explanation:

The given function is

f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)

x

+2

This function is of the form:

f(x) = a {b}^{x} + cf(x)=ab

x

+c

where y=c is the horizontal asymptote.

By comparing , we have c=2 hence the horizontal asymptote is

y = 2y=2

To find the y-intercept, we put x=0 into the function to get:

f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)

0

+2=6+2=8

Therefore the y-intercept is (0,8).

Answer: About 6.321 cm

Step-by-step explanation:

[tex]tan(x)=\frac{opposite}{adjacent}[/tex]

[tex]tan(36)=\frac{x}{8.7} \\\\x=8.7*tan(36)=6.3209...[/tex]

Answer:

Step-by-step explanation:

let the horizontal distance be x

(17.8-1.5)/x = tan 38

or x = 16.3/tan38

or x = 20.863

Answer:

F

Step-by-step explanation:

add all the numbers and divide them by how many numbers there is(in this case 15) to find the average of the prices

Answer:

$1.05 per yard

Step-by-step explanation:

5.25 ÷ 5 = 1.05

Answer:

$1.05 per yard.

Step-by-step explanation:

find unit rate; (cost / quantity)

5.25 / 5 = 1.05

Answer:

c = 9.7

Step-by-step explanation:

Using the law of sines

sin 55       sin 82

---------- = ---------------

8                    c

Using cross products

c sin 55 = 8 sin 82

c = 8 sin 82 / sin 55

c=9.67115

To the nearest tenth

c = 9.7

Hi there!

[tex]\large\boxed{r\approx 10.6 cm}[/tex]

Solve for the radius using the pythagorean theorem:

a² + b² = c²

We know the lengths of the hypotenuse and one leg, so:

a = 12

b = ?

c = 16

Plug these into the equation:

12² + b² = 16²

Simplify:

144 + b² = 256

Subtract both sides by 144:

b² = 112

Take the square root:

b ≈ 10.6

Thus the radius is about 10.6 cm.

Answer:

55, 23, x+y =78; x-y =32

Step-by-step explanation:

-the system of equation

x+y = 78

x-y = 32

-solve by elimination

x-y = 32, add y to both sides

x= y+32

x +y =78, substitute x= y+32

y+32+y = 78, subtract 32 from both sides

y+y = 78-32, combine like terms

2y = 46, divide both sides by 2

y = 23

x +y =78, substitute y = 23

x+ 23 =78, subtract 23 from both sides

x = 78-23, combine like terms

x = 55

Answer:

The equation:

x + y = 78

x - y = 32

The answers:

x= 55

y = 23

Step-by-step explanation:

Call the first number (x) and the second number (y). Take is as a given that (x) is larger than (y). One is given the following information:

"The sum of two numbers is 78"

"Their difference is 32"

Rewrite this in numerical terms:

x + y = 78

x - y = 32

The process of elimination is a way of solving a system of equations. First one manipulates one of the equations such that one variable has an inverse coefficient of its like term in the other equation. This step one does not need to be performed, as the coefficients of the term (y) are inverses in the equations. Next, one adds the equations. Then one uses inverse operations to solve for the remaining variable. Finally, one back solves for the value of the eliminated variable by substituting the value of the solved variable into one of the equations, and simplifying.

Add the equations,

x + y = 78

x - y = 32

____________

2x = 110

Inverse operations,

2x = 110

x = 55

Back solve,

x + y = 78

x = 55

55 + y = 78

y = 23

Answer:

A =27 cm^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the base and h is the height

A = 1/2 (9) (6)

A =27 cm^2

Answer:

I assure you the person above is perfectly right. The area of a triangle is:

A = 1/2bh

Step-by-step explanation:

Have a good day.

Answer:

m+5

Step-by-step explanation:

4m + 5 - 3m

Combine like terms

4m-3m  +5

m+5

Answer:

This equation simplified is [tex]m+5[/tex]

Step-by-step explanation:

To simplify this expression subtract 3m from 4m to get 1m or m.

Answer:

3p^2 - 12p - 12p + 16 + 24p - 16

3p^2 -24p +24

p^2 -8p +8

Answer:

The number is -6.

Step-by-step explanation:

Variable x = a number

Set up an equation:

3x + 12 = -6

Isolate variable x:

3x = -18

x = -6

Check your work:

3(-6) + 12 = -6

-18 + 12 = -6

-6 = -6

Correct!

Answer:

3x +12=-6

3x=-6-12

3x=-18

x=-18/3

x=-6

Answer:

A

Step-by-step explanation:

khan

Answer:

These are the intervals of the people who are at least adults and are mature enough to take the survey seriously and answer correctly

Step-by-step explanation:

Answer:

1 term

Step-by-step explanation:

Writing an expression of 5 terms such that all 5 terms are like terms ;

Using the analogy :

x, 2x, 4x, 3x, 5x

Writing as an expression :

x + 2x + 4x - 3x + 5x

7x - x + 5x

6x + 5x

11x

The least number of terms in its equivalent expression is 1 ;

As the expression x + 2x + 4x - 3x + 5x is equivalent to 11x

Answer:

y + 1 = 2/3 (x - 8)

Step-by-step explanation:

y2 - y1 / x2 - x1          -5 - (-1) / 2 - 8      -4/-6      2/3

y + 1 = 2/3 (x - 8)

Answer: Choice C. 110ft

Step-by-step explanation:

Near a 30,60,90 triangle, multiply by [tex]\sqrt{3}[/tex] to approximate the distance from point B to the tree.

Answer:

82

Step-by-step explanation:

I want to say 82 but i am not positive

Answer:

a) 7085g

b) 6346g

c) 5342g

Step-by-step explanation:

1kg = 1000g

Answer:

10/3 days  or 3 1/3 days

Step-by-step explanation:

Let d = number of days total

75% of the days is 10

.75 d = 10

d = 10/.75

d = 40/3 days

We want to know how man is 25% of d

d * 25%

(40/3) *.25

10/3 days

Answer:

Option C, sin Y = 38/63

Step-by-step explanation:

sin Y = Opposite/Hypotenuse

sin Y = 38/63

Answered by GAUTHMATH

Answer:

45in³

Step-by-step explanation:

6 x 5 x 3 = 90/2 = 45in³

So you pretty much have all you need. 1/3 represents slope, and slope is m. Initial value would be your y intercept which is b.

y=1/3x-3

Answer:

y = x/3 - 3

Step-by-step explanation:

x/3 is the equivalent of 1/3(x)

you just have to divide the value by 100 and then multiply by 3 (the order doesn't matter tho) so,

131000/100 = 1310 x 3 = 3930

the commission is $3930.00

hope it helps :)

Answer:

17.1

Step-by-step explanation:

tan(35)=12/x, x=17.1

Answer:

x ≈ 17.1

Step-by-step explanation:

The angle is 35 degrees, so we do tan(35)

Which equals the side divided by x.

tan(35) = 12 / x

So x ≈ 17.1

Answer:

No, it doesn't indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company

Step-by-step explanation:

Let's first state the hypotheses.

Null hypothesis; H0: p = 0.68

Alternative hypothesis; Ha: p > 0.68

A random sample of 53 claims showed that 41 were made by single people under the age of 25.

Thus; p^ = 41/53 = 0.7736

Let's find the test statistic from the formula;

z = (p^ - p_o)/√(p_o(1 - p_o)/n)

z = (0.7736 - 0.68)/√(0.68(1 - 0.68)/41)

z = 0.0936/0.07285

z = 1.28

From online p-value from z-score calculator, using z = 1.28, one tail hypothesis and significance level of 0.05,we have;

P(z > 1.28) = 0.100273

The p-value gotten is greater than the significance value and so we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

Answer:

1508527.582 cm³/min

Step-by-step explanation:

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 6800 cm³/min,

dV/dt = k - 6800

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

Answer:

the answer will be

184.31