Write a quadratic equation in standard form with the given roots. a. Write a quadratic equation with a double root of -5.

In this case,

This difference is made this way:

-2 - (-6) =

-2 +6 = 4

So there we have this identity. The minus before the parentheses turns the minus into plus sign.

The Hooke's law is given by:

F = k*x

Where:

F = force

k = constant factor

x = distance

If F = 20 and x = 20

20 = k*20

Solving for k:

20/20 = k

k = 1

So: how far will a 29 pound mass stretch the spring?

29 = 1* x

Solving for x:

29/1 = x

x = 29 in

Hello

We are given a log funtion to solve and see if it have a solution.

Step 1

we apply log rules

Step 2

Solve for x

From the calculation above, the solution of the set is 13; i.e x = 13

Answer:

14.73%

Step-by-step explanation:

firstly let's divide the phone price into 7 equal parts. by this equation 219.00/7=31.28

So Alec needs to save $31.28 but we want the percentage.

by equation x%*212.34=31.28

x=(31.28*100)/212.34=3128/212.34=14.73

so Alec needs to save 14.73% of 212.34 each week.

Since the probability of Cheetah is 0.4

Since the probability of Tiger is 0.7

Since the probability of Cheetah or Tiger or both is 0.5

Let us draw a figure to show this information

Then we need to find both animals (x)

Since

Add x to both sides and subtract 0.5 from both sides

Divide both sides by 2 to find x

a) The probability of both animals is 0.3

Since the total of probability is 1, then to find the neither subtract (0.4 + 0.7 - 0.3) from 1

b) the probability of neither is 0.2

Events A and B are independent if the equation P(A∩B) = P(A) · P(B)

Since

Since P(Ch) . P(T) = 0.4 x 0.7 = 0.28

Then

c) The events are not independent

The number divisible by 5 is 670.

Numbers divisible by 5 have their last digits as 0 or 5

Answer : 670

Explanation

We are required to determine the pros and cons of using the factorial function on the calculator.

Hence, the answers are:

- Pros

• It makes calculation easier.

• It makes calculations to be done in an efficient manner.

• It helps students to solve complicated questions seamlessly.

- Cons

• It cannot help with large numbers as the calculator has limited space for answer preview.

• It does not help to understand better how the calculation is done.

Explanation

We are required to determine the value of the following:

This is achieved thus:

We know that the combination formula is given as:

Therefore, we have:

Hence, the answer is:

Given the sum of the functions expressed as:

Collecting the like terms:

Group the terms based on their degrees

Simplify the result to determine the final answer:

Hence the required sum of the functions is x^2 - 3x + 7

The domain of the given function corresponds to:

And the range of the function is:

The average rate of change of f over the interval [0,6] is:

Solution

We have the following integral:

We can use the substitution u= 4 +3x² and we have du= 6x dx, then we have this:

First let's find the amount Sonia puts in her account each week.

To do so, let's find the amount increased between weeks 5 and 10:

The account increased $25 in 5 weeks, so for each week, we have:

So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:

So the initial amount is $20.

Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:

So the correct option is the third one.

you have the following equation:

3x - 2 = 2(x+1)

You have to specify the property used in each step to get the solution of the previous equation. You obtain the following:

1. 3x - 2 = 2(x + 1) given

2. 3x - 2 = 2x + 2 distribution prop

3. 3x - 2x - 2 = 2x - 2x + 2 subtraction 2x both sides - subtraction prop

x - 2 = 2

4. x - 2 + 2 = 2 + 2 summation 2 both sides - addition prop

x = 4

Answer:

After tax interest expenses = Interest expenses x (100 - Tax Rate) 

= 70000 x (100 - 30)% 

= 70000 x 70% 

= $49,000.00

Step-by-step explanation:

Let's say x is going to be the number meters of the width of the room:

x: width

Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:

1.8x: lenght

We know that the perimeter of a rectangle is given by

Perimeter = 2· (width + lenght)

We know that the perimeter is 29 meters, then

Perimeter = 29

↓

29 = 2· (width + lenght)

We do know an expression for its width and lenght, we replace them:

29 = 2· (width + lenght)

↓

29 = 2· (x + 1.8x)

Since x + 1.8x = 2.8x:

29 = 2· (x + 1.8x)

↓

29 = 2· (2.8x)

↓ 2· 2.8 = 5.6

29 = 5.6x

↓ dividing both sides by 5.6

29/5.6 = 5.6x/5.6

5.2 = x

Since

x: width

then

Width = 5.2 meters

Since

1.8x: lenght

then

Lenght = 1.8 · 5.2 meters = 9.36 meters

Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

So, tiles needed to cover the wall:

Calculate the area of a tile as follows:

Now, calculate the area of the wall as follows:

Then, tiles needed to cover the wall:

Which means: 80½

Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

Know more about rectangles here:

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The value of the trigonometric function is;  sin(A) =√51/10.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given that  angle A lies in Quadrant IV and cos(A)= 7/10 then;

cos(A)= 7/10

Hence, base = 7

hypotenuse = 10

Therefore, perpendicular

h² = b² + p²

10² = 7² + p²

100 = 49 + p²

p = √51

Then  sin(A = perpedicular/ hypotenuse

sin(A) = √51/10

Hence, the value of the trigonometric function is;  sin(A) =√51/10.

Learn more about trigonometric;

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The equation of the velocity is given by the exponential:

Let us say that the sky driver's velocity will be 47 m/s at t₁. Then, using the expression above:

Solving for t₁:

Answer:

180 miles

Step-by-step explanation:

distance = rate x time

t = time

1st car:

distance = 40t

2nd car:

distance = 60(t - 1,5)

When the car catch up to each other the distances will be the same, so set the equation equal to each other.  Calculate the time and then put the time back into either equation and solve for the distance.

40t = 60(t-1.5)  Distribute the 60

40t = 60t -(60)1.5

40t = 60t - 90  Subtract 60t from both sides of the equation

-20t = -90  Divide both sides by -20

t = 4.5

Now that we know the time, substitue that back into either equaiton and solve for the time

distance = 40 (4.5)

180 miles

Okay let's analyze each triangle

In triangles A, B, and D the angle

f(7) gives 5 1/2.

the position is the 7th term

Explanation:

f(1)= 8 1/2

f(n)= f(n-1) - 1/2

we are looking for the function that gives 5 1/2

We have been given f(1), this means n = 1

f(1) = f(1-1) - 1/2

8 1/2 = f(0) - 1/2

f(0) = 8 1/2 + 1/2

f(0) = 8 + 1 = 9

when n = 2

f(2) = f(2-1) - 1/2

f(2) = f(1) - 1/2

f(2) = 8 1/2 - 1/2

f(2) = 8

when n = 3

f(3) = f(3-1) - 1/2

f(3) = f(2) - 1/2

f(3) = 8 - 1/2

f(3) = 7 1/2

when x = 4

f(4) = f(4-1) - 1/2

f(4) = f(3) - 1/2

f(4) = 7 1/2 - 1/2

f(4) = 7

when n = 5

f(5) = f(5-1) - 1/2

f(5) = f(4) - 1/2

f(5) = 7 - 1/2

f(5) = 6 1/2

f(6) = f(6-1) - 1/2

f(6) = f(5) - 1/2

f(6) = 6 1/2 - 1/2 = 6

when n = 7

f(7) = f(7-1) - 1/2

f(7) = f(6) - 1/2

f(7) = 6 -1/2 = 5 1/2

f(7) gives 5 1/2.

Hence, the position is the 7th term

Given,

Multiplying equation (ii) by 2 as it make the coefficent of x in both equation equal.

Substracting equation (i) from equation (iii) then we get,

The value of y is -2.

Substituting the value of y in equation (i) then,

Hence, the solution of the linear pair (x, y) is (3, -2).

The total of students that study for 3 to 4 h is 147

The total of students that study for 5 to 6 h is 107

Then, the statement: "more students study for 3 to 4 hours than for 5 to 6 hours" is true because 147 students study for 3 to 4 hours and 107 students study for 5 to 6 hours.

B) 4 less than a number.

To find the solution to the system of equation

we will use the elimination method

3x - y = - 5 ----------------------------(1)

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

We will eliminate y and solve for x

multiply equation (1) through by 3

9x - 3y = - 15 ------------------------------------(3)

add equation (2) and equation (3)

11x = -11

divide both-side of the equation by 11

x = -1

substitute x = -1 in equation (1) and solve for y

3x - y = - 5

3(-1) - y = -5

-3 - y = -5

add 3 to both-side of the equation

- y = -5 +3

-y = -2

multiply through byb -1

y = 2

Hence, the correct option is B

Notice that the number of students that got a grade below 80 is:

and the total number of students is:

Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:

Finally, we get that 7 represents the

of 20.

Answer:

First, the pool was filled to 3/4 of its capacity, which is equal to:

Then, 1/9 of the water evaporated remaining 8/9 of the 18000 gal:

Therefore, to fill the pool we need to add:

gallons of water.

Answer: B. 8000.

Could you please send a picture of the inequality you are asked to solve?

I'll be closing the session now if you cannot do it. Please ask your question again, and send the image in the question itself to avoid this problem of your uploaded images and messages not getting to me.

Thank you, and please re-submit your question request.

Answer:

[tex](y+6)=\frac{2}{8} (x+2)[/tex]

Step-by-step explanation:

First, find the slope

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

-4+6=2

6+2=8

m=2/8

With the slop, you have everything you need to stick one of your points in point-slope form.  I chose (-2,-6)

[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]

Really, that's all you need as it is not an equation of a line.  Not the most useful form, but works as an answer.

Let's do the mutiplications:

(3a)(5a) = 15a²

(5p)(2p) = 10p²

(3 inches)(5 inches) = 15 inches²

(5 feet)(2 feet) = 10 feet²mutiplic