Two Step problem:STEP 1: 7x^2 = -4using the standard form ax^2 +bx + c =0 of the given quadratic equation, factor the left hand side of the equation into two linear factors. STEP 2: 7x^2 = -4xsolve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary. PICTURE OF ANSWER BOX ATTACHED: is for step #2

we have that

interval (-infinite,0) ------> f(x)=5x+4

interval [0, infinite) ------> f(x)=x+7

Part B

f(0)

For x=0 ------> belong to the interval [0, infinite)

so

f(x)=x+7

substitute

f(0)=0+7

Part C

f(3)

For x=3 ---> belong to the interval [0, infinite)

so

f(x)=x+7

substitute

f(3)=3+7

OPTION C

A quartic function is a fourth-degree polynomial: a function that has, as its highest order term, a variable raised to the fourth power.

From our question, it was easy to

the graph of this equation is:

Let us make part of the table corresponding to this graph

To calculate the maximum distance that the ball takes, we can use the first and second derivatives of y to find out this. We have:

Using the second derivative criterion, we have that y'' < 0, therefore, we have a maximum in the root of the first derivative. For that, we get the following:

Therefore, at x=28 is where the maximum distance is. Now we only substitute x=28 in y to find out:

Finally, we have that the ball will go 59 feet from the child

In order to calculate the product of a pair of conjugate terms, we can use the pattern below:

So we have:

To find the angles 1 and 2:

In the above triangle, the angles opposite to the equal sides are equal.

Let us take,

So, using the angle sum property of a triangle

Hence, the angles are

Answer:

To graph a line you have to find two points on the line, one way of doing this is first setting x=0 and solving for y, as follows:

With the above calculations, we got that the point (0,-1) is on the line.

Now, to find another point on the line we set y=0 and solve for x:

With the above calculations, we got that the point (-4/3,0) is on the line.

Once we have those points we draw the line that passes through those points.

The graph of the given equation is:

Given:

⇒There are 61 students in total.

⇒12 of them got an A while 32 of them got a B.

⇒In total, 44 students did not get a C.

⇒So, 44 out of 61 students did not get a C.

Convert 44/61 into decimal form.

Answer:

The probability that a randomly chosen student did not get a C is 0.721 approximately.

One way to find the least common multiple of two numbers is to first list the prime factors of each number.

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.

Types of correlation:

Based on the types of correlation, we can see that the best description of the data given is a positive correlation.

Answer: A positive correlation.

a For any relation to be a function, an independent variable x cannot produce different dependent varible y

From the table,

when x = 5, y = 2

Also, when x = 5, y = 5

and when x = 5, y = 7

We can see that x= 5 produces 3 different values of y ( that is 2, 5, and 7). This has disobeyed the rule of a function

Hence, the table is not a function

The answer is False

Answer:

D. 8pi yd^2

Explanation:

Area of a sector is expressed as;

r is the radius of the circle

theta is the angle substended at the centre

Given the following

r = 9yd

theta = 360-200

theta = 160degrees

Substitute

A = 160/360 * pi(9)^2

A = 4/9*18pi

A = 72pi/9

A = 8pi yd2

Hence the area of the shaded sector is 8pi yd2

Answer:

which question you want to be answered

Answer:

[tex]\textsf{13.\;a)}\quad d=\dfrac{P}{0.5 \pi +1}[/tex]

[tex]\textsf{13.\;b)}\quad d=14\; \sf inches[/tex]

Step-by-step explanation:

The perimeter, P inches, of a semicircle of diameter, d inches, is represented by the equation:

[tex]\boxed{P=0.5 \pi d+d}[/tex]

Part (a)

To express d in terms of P, rearrange the equation to isolate d.

Factor out the common term d from the right side of the equation:

[tex]\implies P=d(0.5 \pi +1)[/tex]

Divide both sides by (0.5π + 1):

[tex]\implies \dfrac{P}{0.5 \pi +1}=\dfrac{d(0.5 \pi +1)}{0.5 \pi +1}[/tex]

[tex]\implies \dfrac{P}{0.5 \pi +1}=d[/tex]

[tex]\implies d=\dfrac{P}{0.5 \pi +1}[/tex]

Part (b)

Given:

Substitute the given values into the equation derived in part (a) and solve for d:

[tex]\implies d=\dfrac{36}{0.5 \left(\frac{22}{7}\right) +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +1}[/tex]

[tex]\implies d=\dfrac{36}{\frac{11}{7} +\frac{7}{7}}[/tex]

[tex]\implies d=\dfrac{36}{\frac{18}{7}}[/tex]

[tex]\implies d=36 \times \dfrac{7}{18}[/tex]

[tex]\implies d=\dfrac{252}{18}[/tex]

[tex]\implies d=14[/tex]

Therefore, the diameter is 14 inches.

ANSWER

EXPLANATION

Given;

Recall, the general formula for slope - intercept form is;

comparing the given equation with the standard slope intercept form formula;

Hence, the graph of the given equation is;

Answer:

(x+4)(x-5)

Step-by-step explanation:

Second order polynomial in the following format:

ax² + bx + c = 0

Has roots x¹ and x².

Can be factored as:

(x - x¹)(x - x²)

So, we have to find the roots.

Finding the roots:

Bhaskara formula, which is:

In the polynomial given in this question:

a = 1, b = -1, c = -20

So

The roots are:

The factored form is:

(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)

The daily rate can be found by dividing the total number of books over the number of calendar days.

15,260 / 28 = 545

545 books per day

Given: (x² + 5x - 2)-(3x²-x+4)

Remove the parentheses:

Add like terms:

Answer:

Let the number of attendees be a.

ak=c , where k=constant of variation.

6k=30

k=30/6

k=5

Find a when c=$50

5a=50

a=50/5

a=10

There will be 10 attendees for a bu

We have a 345 gallon hot tub that fills at a rate of 3.61 gallons/min.

To calculate filling time, we need to divide as it follows:

in that way we can find how much time does it take in minutes

now, if we want to determine time in hours, we must divide by 60, because there are 60 min. in one hour.

Then, it would take approximately 1.59 hours to fill the hot tub.

x is an unknown number

twice a number means: 2x

and twice a number minus 19 means: 2x - 19

Using the distributive property, the maximum number of players that can be in the NBA is; 450 players

The distributive property is a property of algebra that states that you can distribute the contents of one parentheses into another to find an answer. For example;

a(b + c) = ab + ac

Now, we are told that there are 30 teams in the national basketball association and that each team has 12 healthy players plus three on injured reserve. Thus;

Number of players on each team = (12 + 3)

Now, for the 30 teams;

Total number of players for the teams = 30(12 + 3)

Applying distributive property, we have;

(30*12 + 30*3) = 450

Read more about distributive property at; https://brainly.com/question/2807928

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1) Let's calculate that. Start by multiplying the factors 7, and 5.

After that, we use the property of the exponents when multiplying. Repeat the base and then add the exponents -8 + (-5) = -8 -5 = -13.

We are asked to determine the total amount paid for 6 batteries and 4 folders. To do that we need to determine the unit price of each item. We do that by dividing the amount spent by the number of items that were bought. That is:

Now we multiply the desired number of items by each of the corresponding unit prices:

Solving the operations:

Therefore, the total amount paid is $11.

we have:

h = hour

the equation is

answer: 3 hours

Question:

Solution:

Let the following trigonometric equation:

Subtract the root of 3 from both sides of the equation:

solve for sin(x):

Applying the trigonometric circle on the given interval, we obtain that the correct answer is:

Let:

A = Getting a 7

a = Number of sides with 7

N = Number of sides

so:

SOLUTIONS

What is the multiplicity of each of the roots of this graph?

Factorise f(x) by the options

(a) According to the option we have -3 is a root of so x+3 is a factor

(b) 1 is a root too so x - 1 is a factor

Therefore the correct answer = Option A

The square root of 2 is irrational

Here, we want to check if the square root of 2 is rational or not

When we talk of rational numbers, we mean numbers that can be expressed as the ratio of two integers

Roots of non-perfect squares such as two are not rational. They are referred to as irrational numbers. The special name they are called is surd

we have the following:

solving for x: