h(x) = x2 + 3x – 2; 12 - h(7)10​

Answer:

y=3/2x-16

Step-by-step explanation:

The equation of the line passing from points (10, -1) is y = 3x/2 - 16.

A straight line's equation is a mathematical formula that describes the relationship between the coordinate locations along the line. It conveys the slope, x-intercept, and y-intercept of the line and can be expressed in a variety of ways. Y = mx + c and axe + by = c are the two versions of the equation of a straight line that are most frequently employed.

Given slope = 3/2 and points (10, -1)

equation of line is given by y = mx + c

m = 3/2

y = 3/2x + c

substitute points,

-1 = 10*3/2 + c

c = -16

equation of line is y = 3x/2 - 16

Hence the equation is y = 3x/2 - 16.

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Answer:

Area of a triangle is 1/2B x H

In this case, BH = 0.5(3x-5)·4x

A = 4/2 · (3x²-5x)

Answer:

82 is the answer

Step-by-step explanation:

hope it help you

Answer: 18 miles

explanation: set up a proportion. (2 over 1/9 = x over 1). cross multiply, 2x1=2, then divide 2/(1/9)=18.

Answer:

I think it is 4 but, im not sure

Answer:

A. 190/5.

Step-by-step explanation:

Adele made 190 cookies, which is five times the amount of cupcakes she made. To find the amount of cupcakes she made, we must divide 190 by 5. By doing this we get the answer: 38 cupcakes.

Hope this helps! Let me know!

Answer:

They make 4 approximately tons of oxygen each year.

Step-by-step explanation:

( 250lbs × 32 ) ÷ 2000 = 4t

250 pounds because each tree makes about 250 pounds of oxygen a year.

× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.

÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.

Answer: 61.6

Step-by-step explanation:

17.6 X 3.5 = 61.6

Answer:

Kyle threw the baseball 61.6 meters

Step-by-step explanation:

You multiply 17.6 by 3.5 which results in 61.6

Answer:

4

Step-by-step explanation:

because 2+2+2+2=8 pretty self explanatory

Answer:

13

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

Exterior angles are equal.

7x - 3 = 6x + 17

Add 3 and subtract 6x to both sides.

x = 20 is the answer.

Answer:

1

Step-by-step explanation:

h

Answer:

I know it is 1

Step-by-step explanation:

Answer:

Option c is the answer

Step-by-step explanation:

3/5 = 0.6

2 divided by 0.6 = 3.3333333

3.33333 = 10/3

10/3 = 3 1/3

Hope this helps :)

Answer:

3 1/3 or 3, depending on if he can play a fraction of a match

Step-by-step explanation:

The question is asking us how many times 3/5 can go into the whole number 2. to find this we can multiply the denominator of the fraction (5) by the whole number we are trying to get with the fraction (2), and this results in 10. if we put this over the denominator, we get 10/5, which results in 2. to find how many times 3/5 can go into 10/5, we will divide 10/5 by 3/5. this results in 3 and 1/3. so he can play 3 1/3 matches.

Answer:

(6400-8700)/(8700)*100

Step-by-step explanation:

percent of change = (new value - old value)/(old value) * 100

percent of change = (6400 - 8700)/(8700) * 100

Answer:

Step-by-step explanation:

Given principal p =$3500

Time t =1 year

Rate of interest r =2.3%

So annual interest=p×r×t/100

=3500×2×2.3/100

=7000×2.3/100

=16100/100

=161.

So annual interest is $161

Answer:

a equal to c 25 b greater than

Step-by-step explanation:

Answer:

As per graph the rate of Printer A is 15 pages per minute.

Missing words are:

The rate for Printer B is greater than the rate for Printer A because the rate of 25 pages per minute is greater than the rate of 15 pages per minute for Printer A.

========================================================

Explanation:

The general equation

y = ax^2 + bx + c

has the vertex (h,k) such that

h = -b/(2a)

In this case, a = -16 and b = 147. This means,

h = -b/(2a)

h = -147/(2*(-16))

h = 4.59375

The x coordinate of the vertex is x = 4.59375

Plug this into the original equation to find the y coordinate of the vertex.

y = -16x^2+147x+118

y = -16(4.59375)^2+147(4.59375)+118

y = 455.640625

The vertex is located at (h,k) = (4.59375, 455.640625)

The max height of the rocket occurs at the vertex point. Therefore, the max height is y = 455.640625 feet which rounds to y = 455.6 feet

Answer: Silver

Step-by-step explanation:

Answer:silver

Step-by-step explanation: I did it

Answer: 5 minutes

Step-by-step explanation:

a. Jason's mother to catch him after time of 5minutes.

b. Jason biked for distance of 3miles when his mother catches him.

c.  Mother has to drive with speed of 60mph to catch him at the school door, if Jason's school is 2.5 miles from his apartment.

" Speed is defined as the total distance travelled per unit time."

Formula used

[tex]Speed = \frac{total distance travelled}{total time taken}[/tex]

According to the question,

Speed of Jason bike = 12mph

1hour = 12miles

60minutes = 12miles

1minutes = [tex]\frac{12}{60}[/tex] miles

Speed of Jason's mother bike = 36mph

Time after mother found the homework = 10 minutes

After 10 minutes

Jason is at distance =  [tex]\frac{12}{60} (10)[/tex]

                                 =2miles

After 15 minutes = [tex]\frac{12}{60} (15)[/tex]

                            = 3miles

To cover three miles mother has to drive for

1hour = 36miles

60minutes = 36miles

1miles = [tex]\frac{60}{36}[/tex] minutes

3miles = [tex]\frac{60}{36} (3)[/tex]

           = 5minutes    

If Jason's school is 2.5 miles from his apartment,

Time taken by Jason to reach school door = [tex]\frac{2.5}{12.5} (60)[/tex] minutes

                                                                        = 12.5 minutes

Time in which mother has to cover distance of 2.5miles

= [tex](12.5-10)[/tex]minutes

= 2.5minutes

Substitute the value in the formula we get,

Speed of mother's bike =  [tex]\frac{2.5}{2.5} (60)[/tex] mph

                                       = 60mph

Hence,  

a. Jason's mother to catch him after time of 5minutes.

b. Jason biked for distance of 3miles when his mother catches him.

c.  Mother has to drive with speed of 60mph to catch him at the school door, if Jason's school is 2.5 miles from his apartment.

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Answer:

A fair six-sized die is rolled. Find the probability of getting at least a 4.

There are 6 outcomes and three of them are 4, 5 or 6, so the probability of greater than or equal to 4 is 3/6=½.

Answer:

210 minutes

Step-by-step explanation:

120/4 = 30

30*7 = 210

210 minutes

Answer:

210 minutes

Step-by-step explanation:

120/4=30

30*7=210

Answer:

1586

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Least Common Multiple (LCM) of 14 and 22 is 154.

Answer:

Least Common Multiple (LCM) of 14 and 22 is 154.

The standard form for expressing the equation of a straight line is

y = mx + b

Given the functions from the question f(x)  = 3x + 4

If h(x) = f(x+3)

Replace x with x+3 in the function f(x) to have;

h(x) = 3(x+3) + 4

h(x) = 3x + 9 + 4

h(x) = 3x + 13

Hence the required graph for both functions are attached below;

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Answer:

Division

Step-by-step explanation:

3x = 3 times x so, you must do the opposite of multiplication to get rid of the 3, which is division.

The solution of the equation with a single variable  3x = 15 will be 5.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

3x = 15

Divide the equation by 3 into both sides, then we have

3x / 3 = 15 / 3

x = 5

The solution of the equation with a single variable  3x = 15 will be 5.

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Answer:

(3,-6)

Step-by-step explanation:

  [1]    x - 2y = 15

  [2]    2x + 4y = -18

Graphic Representation of the Equations :

   -2y + x = 15        4y + 2x = -18  

Solve by Substitution :

// Solve equation [1] for the variable  x

 [1]    x = 2y + 15

// Plug this in for variable  x  in equation [2]

  [2]    2•(2y+15) + 4y = -18

  [2]    8y = -48

// Solve equation [2] for the variable  y

  [2]    8y = - 48

  [2]    y = - 6

// By now we know this much :

   x = 2y+15

   y = -6

// Use the  y  value to solve for  x

   x = 2(-6)+15 = 3

Solution :

{x,y} = {3,-6}

Answer:

[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]

Step-by-step explanation:

From the information given:

Lets first change the given relations into polar coordinates

So, the region of the inner circle into polar coordinates is as follows:

(x - 4)² + y² = 16

x² + y² - 8x = 0

r² - 8r cos θ = 0

r = 8 cos θ

For the outside circle:

x² + y² = 16

r² = 16

Thus, the intersection point are:

64cos²θ = 16

cos²θ = 1/4

θ = -(π/3) , (π/3)

Now: if we are to represent the sketch on a graph, the region of the integration D will be:

[tex]D = \bigg \{ (r,\theta )\bigg |-\dfrac{\pi}{3}\leq \theta \leq \dfrac{\pi}{3}, 4 \leq r \leq 8 cos \theta \bigg \}[/tex]

Therefore, the are of the required region can now be computed as follows:

[tex]A = \int \int _D \ dA[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \int ^{8 \ cos \theta}_{4} \ r dr d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \bigg (\dfrac{r^2}{2} \bigg ) ^{8 \ cos \theta}_{4} \ d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{1}{2} \bigg (64 \ cos ^2 \theta - 16 \bigg ) \ d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{16}{2} \bigg (4 \ cos ^2 \theta - 1 \bigg ) \ d \theta[/tex]

[tex]A = \dfrac{16}{2} * 2 \int ^{\pi/3}_{0} \bigg (4 \bigg ( \dfrac{ 1+ cos 2 \theta}{2} \bigg) - 1 \bigg ) \ d \theta[/tex]

[tex]A = 16 \int^{\pi/3}_{0} (1 + 2 cos 2 \theta ) d \theta[/tex]

[tex]A =16 ( \theta + sin2 \theta )^{\pi/3}_{0}[/tex]

[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) - (0-0) \end {bmatrix}[/tex]

[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) \end {bmatrix}[/tex]

[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]

The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.

The double integral formula for the area of a given curve is described below:

[tex]A = \iint\,r(\theta) \,dr\,d\theta[/tex] (1)

Where:

We notice that [tex]r \in [4, 8\cdot \cos \theta][/tex] and [tex]\theta \in \left[-\frac{\pi}{3}, \frac{\pi}{3} \right][/tex], then we have the following integral:

[tex]A = \int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \int \limits_{r= 4}^{r = 8\cdot \cos \theta}\,r\,dr\,d\theta[/tex]

Now we proceed to integrate the expression:

[tex]A = \frac{1}{2}\int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \,(64\cdot \cos^{2}\theta -16)\,d\theta = 32 \int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \,\cos^{2}\theta \, d\theta - 8\,\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]

[tex]A = 16\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } {\cos 2\theta} \, d\theta + 8\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]

[tex]A = 8\sqrt{3}+\frac{16\pi}{3}[/tex]

The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.

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