Consider the relation y = −3|x + 5| − 6. What are the coordinates of the vertex?

Hello there. To solve this question, we'll simply have to make x => x + 5 in the function.

Given the function:

We have to determine f(x + 5)

By making x => x + 5 in this function, we get:

Now remember the binomial expansion of order 2:

Therefore we have:

Multiply the terms inside parentheses and calculate the square.

Apply the distributive property

Multiply and add the numbers

This is the answer we're looking for.

A way of showing this is the correct answer is to make x = 1 and x = 6 in the former function:

Then making x = 1 in the expression we found after:

As expected.

The combined triangles will look as shown below:

It can be observed that the lengths of the three sides fit alongside one another perfectly. This means that the lengths are equal.

Also, the middle piece of the three triangles has no space when it aligns with the other two triangles. This means that all the angles add up to 180°.It would also be a safe assumption that the angles are equal to each other, therefore the measure of each angle will be:

Therefore, it can be observed that the sides and angles of the three triangles are equal.

As per given by the question,

There are given that;

Now,

Solve the given equation for the value of y.

So,

The given equation can be written as,

Then,

So,

Hence, the value of y is;

ANSWER:

18.1 ft³

STEP-BY-STEP EXPLANATION:

Given:

Radius (r) = 1.2 ft

Height (h) = 4 ft

We can determine the volume of the cylindrical barrel using the following formula:

We substitute each value and calculate the volume, like this:

The volume of the barrel is 18.1 ft³

From the graph given,

It is an absolute function

The following statements are true about the graph

i) The vertex is located at (2, -2)

ii) The graph has two zeros

ii) The range is [-2, ∞)

Let's start by drawing the situation:

According to this, one of the dimensions of the box is 40-2x. The other one is 30-2x and the last one, that we could say it's the height, is x.

The volume of a box is given by the product of the three dimensions:

Use the given value of the volume to find x:

Factoring this expression we have that:

One of the possible dimensions of the square is 3. Now, solve the quadratic expression (third factor) to find the other 2 options:

It means that the squares can have 3 different dimensions, which are:

Nevertheless, the second possible option is not coherent since it's value is close to 23 and the dimensions of the cardboard are 30 and 40. It means that the possible dimensions are 3 and (32-sqrt(208))/2.

Answer:

technically it's both

Step-by-step explanation:

because if you have the answer plus 18 and if it works and you get 44 that will be the answer

The area of the circle is given by:

So, the area of a circle is basically:

It can be seen as the number of squares inside of the circle

We have the function:

The domain is the set of values of x for which f(x) is defined. In this case, f(x) is defined only for non-negative values of x, so the domain is D:{x≥0}.

The range is the set of values that f(x) can take for the domain in which it is defined. In this case, f(x) will only take non-negative values, so the range can be defined as R: {y≥0}.

For the linear function f(x) = 3x+2, we don't have restrictions for the domain and the the range: both x and y can take any real value, so the domain and range are D: {x: all real numbers} and R: {y: all real numbers}.

Answer:

For the function f(x) = √x, the domain is D:{x≥0} and the range is R: {y≥0}.

For the function f(x) 3x+2, the domain is D: {x: all real numbers} and the range is R: {y: all real numbers}.

The value of the digit 2 in the quotient is 200

We know that,

Place value is the value of each digit in a number.

From the question, we have

392,000/10 = 39200

The value of the digit 2 in the quotient is 2 hundreds, or 200

Divide:

The simplest definition of split is to divide into two or more equally sized pieces, locations, groups, or divisions. Simply put, to divide something is to give it to a group in equal portions or to cut it into equal pieces. Consider a diagonal that creates two triangles with equal areas from a square. A division operation could result in an integer or it could not. Decimal numbers may be used to express the outcome occasionally.

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ANSWER:

Candy bar A: 264 calories

Candy bar B: 259 calories

STEP-BY-STEP EXPLANATION:

Let x be the number of calories in candy bar A and y be the number of calories in candy bar B.

We can establish the following system of equations according to the data of the statement:

We substitute the first equation into the second and solve for y, just like this:

Therefore:

Candy bar A contains 264 calories and candy bar B contains 259 calories

The equation of a circle with center (h, k) and radius r is given by the following expression:

In this case, the center of the circle is located at (6, -4), and its radius equals 6, then by replacing 6 for h, -4 for k and 6 for r, we get:

Then, the last option is the correct answer: (x - 6)^2 + (y + 4)^2 = 36

We know that AC is 10 centimeters long, and M is the midpoint of AC.

If we move point A as the problem says, we have.

As you can observe, the length of AC is triple.

Problem

Solution

For this case we can find the perimeter of the figure with the following operation

Then the final answer would be:

The expression

means "n takes values less than -3 but without taking the 3", for the symbol <.

Then, the number line that shows the solutions of the expression is

Explanation:

Ezra has a square brick patio where x represents the length of one side of this square patio:

And hee wants to reduce the width by 6 feet, and increase the length by 6 feet.

The new width is x-6,

The new length is x+6.

Then, we need to find the area of the new patio:

We multiply the length by the width. The area is:

And finally, if the original measure of the sides is x=13 ft, the area of the new patio is:

Since it represents the area the units are square feet:

133 square feet.

These results are shown in option B.

Answer:

Given the coordinates;

The slope m of the line MN is;

The slope of a line parallel to the line MN must have a slope equal to line MN, that is;

The slope of a line perpendicular to line MN has a slope of negative reciprocal of line MN, that is;

Using the distance formula to find the length of MN, the formula is given as;

step 1

Find out the area of the complete pie

r=30/2=15 ft ----> the radius is half the diameter

substitute

Remember that the area of a complete circle, subtends a central angle of 360 degrees

so

Applying proportion

Find out the area for a central angle of 42 degrees

The rate of work obtained from the 240 and 400 minutes it takes for the large and small pumps to remove the water alone respectively, gives the duration it takes for the two pumps to remove the water working together as 150 minutes.

The rate of work in completing a project is given by the reciprocal of the time it takes to complete the project.

The given parameters are;

The time it takes the larger pump to remove the water, A = 240 minutes

The time it takes the smaller pump to remove the water, B = 400 minutes

The rate of doing work by the larger pump = [tex]\frac{1}{240}[/tex]

The work rate of the smaller pump = [tex]\frac{1}{400}[/tex]

The rate of work of the two pumps combined, [tex]\frac{1}{r}[/tex], is therefore;

[tex]\dfrac{1}{A} +\dfrac{1}{B} = \dfrac{1}{r}[/tex]

Where;

r = The time it takes for the two pumps to remove the water together

Which gives;

[tex]\dfrac{1}{240} +\dfrac{1}{400} = \dfrac{1}{150} = \dfrac{1}{r}[/tex]

∴ r = 150

The time it takes for the two pumps to remove the water together is 150 minutes

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Answer: 150 min

(I completed the question)                  

Since we can apply Rolle's Theorem:

Take the inverse sine of both sides:

Since it is for the interval:

The solutions are:

Answer:

Given:

for the ultra-safe treasury bills:

For riskier corporate bonds:

she needs $12,000 per year, so:

grandma has $250000 to invest, therefore:

Let:

Replace y into (3):

Therefore, grandma needs to invest $150000 in ultra-safe treasury bills, and

The equiation of parabola in vertex form is:

where (h, k) are the coordinates of the vertex and a is a constant. In our case we have:

add 4 to both sides:

Resolving:

Therefore we already have it in the vertex form and we have to:

Therefore the answer is c. (-1, 4)

Explanation:

We know that AB = CD and that ∠ABD = CBD because it is given information.

Then, we have that BD = BD because a side is congruent to itself. It is called the reflexive property of congruence.

Now, we can say that ΔABD = ΔBDC by SAS (Side - Angle - Side) because we have two congruent sides and the angle between them is also congruent

Finally, ∠A = ∠C because the corresponding sides of congruent triangles are congruent

Answer:

Therefore, the answer is

1) A rolled die has just 6 outcomes; from 1 to 6

Number of total events for a die = 6

Let's begin by identifying key information given to us:

Given:

a grid 2/3 of the squares are shaded with color.

And 1/4 of the squares on the grid is shaded blue

So, to Find the fraction of the Shaded squares are blue squares ​

Multiply both fractions

So,

so, the answer will be 1/6 of the Shaded squares are blue squares ​

The diffrentiated function will be

RULES FOR DIFFERENTIATION

Also

Also

we know that

14-7=7 --------> given problem

so

we have

14-8

Rewrite the expression

14-(7+1)

14-7-1

Remember that

14-7=7

substitute

7-1

6

we have

12-6=6

so

12-7

rewrite

12-(6+1)

12-6-1

substitute

6-1

5

we have

13-6

13-(3+3)

13-3-3

10-3

7