I can’t figure out how to solve this

Step by step process needed! Thank you!


Simplify Radicals

Since the domain is restricted to one side of the axis of symmetry of the full graph of f(x), an inverse does exist.

Letting [tex]f(x)=y[/tex],

[tex]x=y^2 +y-6\\\\x=\left(y+\frac{1}{2} \right)^2 -\frac{25}{4}\\\\x+\frac{25}{4}=\left(y+\frac{1}{2} \right)^2[/tex]

Since the domain is restricted to the right hand side of the axis of symmetry, and since the range of the inverse is the same as the domain of the original function, we take the positive square root.

[tex]\sqrt{x+\frac{25}{4}}=y+\frac{1}{2}\\\\y=f^{-1}(x)=\sqrt{x+\frac{25}{4}}-\frac{1}{2}[/tex]

The domain of the inverse is the range of the original function, which is [tex]\left[-\frac{25}{4}, \infty \right)[/tex].

The range of the inverse is the domain of the original function, which is [tex]\left[-\frac{1}{2}, \infty)[/tex],

Answer:

a square root is basically any number multiplied by itself to get another number. there are 2 types, perfect and non perfect, perfect is when the number being multiplied by itself is an a whole number, while the non perfect is when the number that is being multiplied by itself is a decimal or fraction

Step-by-step explanation:

The Complement rate where Trade discount rate is 15% = 100 - 15 = 85%.

Thanks

Answer: The answer is that 50 ÷ (-8) is greater

Answer:

-6 x 1.5 < 50 ÷ (-8)

-6 x 1.5 = -9

50 / -8 = -6.25

50 divided by -8 is greater than -6 times 1.5p

Step-by-step Explanation:

=D

Answer:

Htel Htel will hear the sounds again at 9:00 AM

we have that

B=5 degrees

C=125 degrees

b=200 units

step 1

Find out the measure of angle A

Remember that

the sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180

substitute given values

A+5+125=180

A=180-130

A=50 degrees

step 2

Applying the law of sines

Find out the value of a

substitute given values

solve for a

a=1,757.9 units

step 3

Find out the value of c

substitute given values

The new triangle A'B'C' shown in the attached graph has the coordinates of B' are (2, 8), A' are (1, 6), and  C' (4, 6).

Two triangles are said to be congruent if their corresponding sides and angles are equal.

The given triangle ABC shown in the graph has:

The coordinates of B are (-7, 6),

The coordinates of A are (-8,4),

The coordinates of C are (-5, 4)

If B' is the translated position of B.

The new triangle A'B'C' shown in the attached graph has:

The coordinates of B' are (2, 8)

The coordinates of A' are (1, 6)

The coordinates of C' are (4, 6)

Length of AB = A'B' = √5

Length of BC = B'C' = 2√2

Length of CA = C'A' = 3

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Answer:

the answer is C..........

The sample standard deviation formula is

square root {(Σ(X - mean)²) / (N - 1)}

What the student did wrong?

The square root sign was not included in their calculation

The correct value of the sample standard deviation is = 3.08

Standard deviation shows the by how much the values differs from the mean.

The calculation is done by forming the table and calculating the required variables as below:

X        (X - mean)²

8              25

1                 4

3                0

0                9

3                0

ΣX = 15

mean = ΣX/N = 15/5 = 3

Σ(X - mean)² = 38

Σ(X - mean)² / (N-1)

= 38 / 4

= 9.5

Sample standard deviation = √9.5

= 3.08

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For the given question,

The coordinates of the three lines are given with the end points.

Part a: The slope  piece wise rule for defined graph is-

Part b: calculate the three equations-

First find the slope for the three given lines;

slope (blue line);

coordinates - (0, -4) and (1, -1)

m = (-1 + 4)/(-1 - 0)

m = -3

Equation of line;

y + 4 = -3(x -0)

y = -3x - 4

slope (red line);

coordinates - (1, 4) and (5, 8)

m = (8 - 4)/(5 - 1)

m = 4/4

m = 1

Equation of line;

y - 4 = 1(x - 1)

y = x + 3

slope (green line);

coordinates - (5, 8) and (8, 8)

m = (8 - 8)/(8 - 5)

m = 0

Equation of line;

y - 8 = 0(x - 5)

y = 8

Thus, the three equation of line are found.

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Answer:

Step-by-step explanation:

SOLUTION

The following sequence is a geometric series and we have been provided with the formula

Here a1 is the first term = 40,

r is the common ratio = -0.4 (to get r, divide the second term by the first term)

n = number of terms = 9. Now let's solve

The sum to the nearest hundredth becomes = 28.58

Given:

Mr. Cumme has 8 3/4 yards of material for her class.

he needs to use 1/3 of the material to make an example.

To find the number of yards of material that he will need, we will multiply 1/3 by 8 3/4 to get the answer.

So, the answer will be 2 11/12 yards.

Let x = the number of seats

Let y = the number of rows.

Since the auditorium is rectangular and it has 1,749 people, then we can say that:

Then, if the number of seats "x" exceeds the number of rows "y" by 20, then we can say that:

Now we have two equations. To solve for x, let's use the substitution method.

1. Rewrite the equation 2 x = y + 20 into y = x - 20.

2. Replace the value of "y" in equation 1 by x - 20.

2. Multiply x and x - 20.

3. Transfer the constant term 1749 on the left side of the equation. When transferring over the equal sign, the operation will change. From +1749, it becomes -1749.

4. To solve this quadratic equation, let's find the factors of -1749 that sums to -20.

a. 3 and -583 = -580

b. 11 and -159 = -148

c. 33 and -53 = -20

As we can see above, the factors of -1749 that sums to -20 are 33 and -53. Hence, the quadratic equation above can be factored to:

5. Equate each factor to zero and solve for x.

Since the value of x cannot be negative, then the value of x is 53.

Therefore, the number of seats in each row is 53. In addition, there are 33 rows in the auditorium.

Let's solve the system of equations using elimination:

4x + 5y = 14

-4x -2y = -8

First, we need to get rid of one variable.

Sometimes we multiply them by some factors to have the same number on one variable, but in this case, we can subtract the x variable

4x +5y =14

-4x-2y = -8

----------------------

4x-4x =0, 5y -2y = 3y and 14-8=6

------------------------------

0+3y = 6

Solve the equation for y

Divide by 3 into both sides

3y/3 = 6/3

y = 2

Then, replace this variable on one equation, whichever you want:

4x + 5y = 14

4x +5(2) = 14

4x +10 = 14

and solve the equation for x

4x +10 = 14

Subtract 10 on both sides

4x +10-10 = 14-10

4x = 4

Divide by 4 into both sides

4x/4 = 4/4

x = 1

You can replace both variables to confirm the results:

4x +5y =14

4(1) +5(2) = 14

4 +10 = 14

14 = 14

---------------------------------

-4x -2y = -8

-4(1) -2(2) = -8

-4-4 = -8

-8 = -8

The result is correct, so my ordered pair is (x,y) = (1,2)

Both lines AB and CD are secant lines beacuse in two points they are touching the circunference. There is a Theorem which says the following

Since the distance from the center of the circle to each secant line is the same (5 units), we could assume that the both secant lines are similar. saying:

Then the lenght of CD is:

,By following these steps, we can find the value of this expression:

first we multiply both -2 and 3 by their corresponding fractions, we do this by just multiplying the numbers with the numerator of the fraction, like this:

Now simplify the fractions:

To sum fractions, we have to make sure that the denominators are the same, this is not the case, we can make their denominators the same by dividing and multiplying the two by two, like this:

Now, we just have to sum up the numerators, like this:

Then, the value of this expression is:

The required value of t is (-∞, -6) U (4, ∞).

What is a linear inequality and how is it solved?
Expressions with linear inequalities compare any two values using inequality symbols like "<" and ">." The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. Polynomial inequality, rational inequality, and absolute value inequality are the several types of inequalities that exist in mathematics.
First, create an equation for the inequality. The given equation must be solved for one or more values. Represent all of the values that you found on the number line now. On the number line, use open circles to symbolize the excluded values. the interval, then. To determine whether the values satisfy the inequality equation, substitute any random value from the interval into the inequality equation. The solutions of the given inequality equation are intervals that fulfil the inequality equation.

Given, the linear inequalities are t + 1 < -5 and t + 1 > 5
Solving the first inequality, t + 1 < -5 ⇒ t < -5 -1 ⇒ t < -6
Again, solving second inequality, t + 1 > 5 ⇒ t > 5 - 1 ⇒ t > 4
Combining the solution of both the inequalities, we have;
the value of t can take any value in (-∞, -6) U (4, ∞).
Therefore, the required value of t is (-∞, -6) U (4, ∞).

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Answer:

1/4

Step-by-step explanation:

1/2 - 1/4 = 2/4 - 2/4 = 1/4

We know that the sum of the interior angles of a triangle equals 180, then,in this case we have the following equation:

then, solving for b, we get:

now that we have that b = 41, we can find the measure of each angle:

We are given a table with values of "x" and associated values of "y". Let's remember that direct variation implies that each value of "y" will be related with its corresponding value of "x" according to the following relationship:

Where "k" is the constant of proportionality. If the table shown has direct variation the same constant should apply for each value. Let's take the first value of the table, that is, x = 3 and y = 6. Substituting we get:

Dividing both sides by 3 we get:

Solving the operations:

Now we substitute in the relationship:

Now, for the second value of "x", that is x = 6:

Since we did not get the corresponding value of "y" in the table, this means that the constant of proportionality doesn't work for this value, and therefore, "y" does not vary directly with "x".

Answer:

if f(-4) = -31

then

f(-2) = -7

f(0) = 1

f(1) = -1

f(3) = -17

Step-by-step explanation:

You have to replace the x of the f(x) equation with said number in the left column. Then plug it into your calculator and your golden :]

f(x) = -2x²+1

= -2(-4)²+1

= -32+1

f(x) = -2x²+1

= -2(-2)²+1

= -2(4)+1

= -8+1

f(x) = -2x²+1

= -2(0)²+1

= -2(0)+1

= 0+1

f(x) = -2x²+1

= -2(1)²+1

= -2(1)+1

= -2+1

f(x) = -2x²+1

= -2(3)²+1

= -2(9)+1

= -18+1

Answer:

4

Step-by-step explanation:

The solution to the equation means that the coordinate satisfy the equation. Given that the equation is y= x +5, we know the relationship between the y-coordinate (y) and the x-coordinate (-1) of the point.

y= x +5

Substitute the coordinates into the equation:

When x= -1, y= y,

y= -1 +5

y= 4

Thus, the value of y is 4.

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Answer:

-29

Step-by-step explanation:

subtracting the negative 22 from the -17 made it positive until you subtract the 34 which made it -29

Answer:

y + 2 = 2/3(x - 0)

Step-by-step explanation:

The general form of an equation of line with slope m, passing through point (x1, y1) is:

y - y1 = m(x - x1)

substituting values:

y - (-2) = 2/3(x - 0)

simplify

y + 2 = 2/3(x - 0)

Answer:

where

m(Gradient or slope) =2/3

y1=-2

x1=0

hello

to solve this question, we asume it's a right angled triangle and we use pythagorean theorem

pythagorean thorem states that the square of the longest side which is the hypothenus of a triangles is equal to the sum of the square of the two other sides which are the opposite and adjacent

according to pythagorean

now we go through the options

from the first option (3, 4, 5)

the longest side here is 5

let's check if this is true

option 1 is represents a triangle

let's check option 2

(2, 5, 9)

longest side = 9

option 2 does not represents a triangle and it's the right option here