f(x) = 9x² + 5x +4
g(x) = - 8x² - 3x - 4
Find (f + g)(x).

We have a function of which we only know the graph.

We have to find in which intervals the function is decreasing.

We know that a function is decreasing in some interval when, for any xb > xa in the interval, we have f(xa) < f(xb).

This means that when x increases, f(x) decreases.

We can see this intervals in the graph as:

We assume each division represents one unit of x. Between divisions, we can only approximate the values.

Then, we identify all the segments in the graph where f(x) has a negative slope, meaning it is decreasing.

We have the segments: [-3, -1.5), (1,5, 4.5) and (7,9].

Answer:

The right options are:

Between 1.5 and 4.5

Between -3 and -1.5

Between 7 and 9

Hence, the correct option is C: x=5

If the ratio of trucks to trucks is 5 to 8,

then we can use proportions to solve for the number of truck (unknown "x"):

5 / 8 = x / 440

we solve for x by multiplying: by 440 both sides

x = 440 * 5 / 8

x = 275

There are 275 trucks on the freeway.

Given the following question:

y = 116

x = 64

8,22,29,36

between 22 - 8 = 14

divide by 2 ,14/2= 7

now add 8+7 = 15

Then anwer is

Option C) (29-22) + 8 = 7 + 8

L = length

W = width

L = 4 + 3*W

The perimeter of a rectangle is the sum of its sides: 2L + 2W. Since it's 72, we have:

2L + 2W = 72

Now, to solve for L and W, the dimensions of the garden, we can use the first equation (L = 4 + 3*W) into the second one (2L + 2W = 72):

2L + 2W = 72

2 * (4 + 3*W) + 2W = 72

2 * 4 + 2 * 3W + 2W = 72

8 + 6W + 2W = 72

8W = 72 - 8

8W = 64

W = 64/8 = 8

Then we can use this result to find L:

L = 4 + 3W = 4 + 3 * 8 = 4 + 24 = 28

Therefore, the garden has a width of 8 and a length of 28.

If l and m are parallel, then ∠1 must measure 55°.

The addition of the angles of a triangle is equal to 180°, in consequence,

Here we are given a geometrical shape with the following inner and an arc angle as follows:

Property: The inner angle is always the mean of corresponding verticaly opposite arc angles.

We can express the above property in lieu to the geometry question at hand. We see that the two arc angles:

Ther inner vertically opposite angle are:

The property can be expressed mathematically as follows:

Next plug in the respective values of angles and evaluate for the arc angle BG as follows:

Therefore the correct option is:

You have the following inequality:

z/4 ≤ 12

To solve the previous inequality you proceed as follow:

z/4 ≤ 12 multiply both sides by 4

z ≤ 48

Hence, the solution is z ≤ 48

when you want to graph a solution of the form "z lower or equal than", you draw a black point, that means the solution are all number lower than 48, including 48.

Step 1

Given

Required; To convert it to meter

Step 2

1 kilometer is equivalent to 1000 meters

Therefore using ratio we will have

Step 3

Get the conversion to meter

Hence, 0.350km as meters = 350m

We are asked to factor in the following expression:

To do that we will multiply by 3/3:

Now, we use the distributive property on the numerator:

Now we factor in the numerator on the right side in the following form:

Now, in the spaces, we need to find 2 numbers whose product is 12 and their algebraic sum is 7. Those numbers are 4 and 3, since:

Substituting the numbers we get:

Now we take 3 as a common factor on the parenthesis on the right:

Now we cancel out the 3:

Therefore, the factored form of the expression is (3y + 4)(y + 1).

Explanation

We can deduce from the information that MAT 012 has 3 sections, namely:

Our section, and two other sections

Then, we can also infer that MAT012 has a total of:

Our task will be to get the percentage of our section taking MAT 102

Since our section has 23

Then we can calculate the answer as

Thus, the answer is 34.33%

we have the expression

3/4 - 1/2 × 7/8

so

Applying PEMDAS

P ----> Parentheses first

E -----> Exponents (Powers and Square Roots, etc.)

MD ----> Multiplication and Division (left-to-right)

AS ----> Addition and Subtraction (left-to-right)

First Multiplication

so

substitute

Remember that

3/4 is equivalent to 12/16 (multiply by 4 both numerator and denominator)

substitute

therefore

We will have the following:

First, calcuate the difference in hours:

From 7pm to 6am there are 11 hours.

Then we add the number of minutes, those would be 40 minutes.

So, she slept 11 hours and 40 minutes.

System A

solve the second equation for x

replace in the first equation

The system has no solution.

System B

solve the second equation for x

replace in the first equation

The system has infinitely many solutions, they must satisfy the following equation:

Solution:

Given:

Considering the right triangle KLM,

To get the width (x), we use the Pythagoras theorem.

The area of the bedroom floor is;

Therefore, the area of Felipe's bedroom floor to the nearest tenth is 312.3 square feet.

We must solve for x the following equation:

1) We pass the +25 on the right to left as -25:

2) Now, we can rewrite the equation in the following form:

3) Factoring the last expression, we have:

Factoring the (x+8) in each term:

4) By replacing x = 2 or x = -8 in the last expression, we see that the equation is satisfied. So the solutions of the equation are:

Answer

The solutions are:

• x = 2

• x = -8

We have the tickets sold each weekend:

• Last weekend: 26,675

• This weekend: 24,567

We have to find how many tickets where sold in both weekends by rounding each number to the nearest thousand units. This will let us do the math without a calculator.

Then, we can approximate 26,675 to 27,000 and 24,567 to 25,000.

NOTE: we round the numbers up because the next number is 5 or greater. Then 675 is and 567 are approximated as 1,000.

We then can add them as: 27,000+25,000 = 52,000.

Answer: the solution is about 52,000 tickets sold.

NOTE: the exact solution would have been 51,242

The given expression is

Notice that the hundredth 7 is greater than 5, this means 19.67 is greater than 19.657.

Answer: 6x + 8 = 32

Explanation:

Let x represent the number

6 times the number = 6 * x = 6x

If we add 6x to 8, it becomes

6x + 8

Given that the result is 32, the equation could be used to solve the problem is

6x + 8 = 32

Let the horizontal distance be represented with x

By Trigonometric Ratio,

In order to determine the limit of f(x) when x tends to -4 from the right (4^+), we need to look in the table the value that f(x) is approaching when x goes from -3.9 to -3.99 to -3.999.

From the table we can see that this value is 0.4.

Then, to determine the limit of f(x) when x tends to -4 from the left (4^-), we need to look in the table the value that f(x) is approaching when x goes from -4.1 to -4.01 to -4.001.

From the table we can see that this value is 1.5.

Since the limit from the left is different from the limit from the right, the limit when x tends to -4 is undefined.

Finally, the value of f(-4) is the value of f(x) when x = -4. From the table, we can see that this value is -4.

Answer:

what is the shooting percentage?

Here we must apply the following rule:

Since m ∠NRQ = 42°, we have:

slope intercept form of the required graph:

-8 + 6x = 4y

y = 3/2x - 2

When broken open Austen's jawbreaker will make a hemisphere.

Recall that the total surface area of a hemisphere is given by

Where r is the radius of the hemisphere.

We are given the diameter of the hemisphere that is 16.4 inches.

The radius is half of the diameter.

So, the radius is 8.2 inches

Substitute the radius into the above formula of total surface area

Therefore, the total surface area of the hemisphere is 633.72 square inches.

Please note that if you want to find out only the curved surface area then use the following formula

For the given case, the curved surface area is 453.96 square inches.

We know that

• The mean is 200 pounds.

• The standard deviation is 25 pounds.

• The random sample is 35.

First, let's find the Z value using the following formula

Let's replace the mean, the standard deviation, and x = 210.

Then, using a p-value table associated with z-scores, we find the probability

The table used is shown below

We were provided with a right-angled triangle. For a right-angled triangle, we can use the trigonometric ratios to solve for unknown sides or angles.

First, let's label the triangle to determine the trigonometric ratios to use:

From the diagram above, we are given:

adjacent = 12

angle = 25 degrees

x = oppossite

We are going to use the tangent ratio, which is:

When, we substitute the given data, we have:

Answer: x = 5.6 (option A)

Answer:

y=14000x

Step-by-step explanation:

x represents years after 2020 and y is the number of miles

The required equation for the distance travelled versus number of years after 2020 is given as y = 14000x + 56000.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given problem can be solved as follows,

Suppose the year 2020 represents x = 0.

The distance travelled per year can be taken as the slope of the linear  equation.

This implies that slope = 14000.

And, the distance travelled by January 1, 2020 is 56000.

It implies that for x = 0, y = 56000.

The slope-point form of a linear equation is given as y = mx + c.

Substitute the corresponding values in the above equation to obtain,

y = 14000x + c

At x = 0, y = 56000

=> 56000 = 14000 × 0 + c

=> c = 56000

Now, the equation can be written as,

y = 14000x + 56000

Hence, the required equation for number of miles and years for the car is given as y = 14000x + 56000.

To know more about straight line equation click on,

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Notice that:

(1)

Therefore:

(2)

Therefore:

(3)

Therefore:

Answer: The 3 sets have in common that in each case both fractions represent the same number.