Which of these is an exponential parent function?  A. f(x) = 2^x – 3  B. f(x) = 2^x + 2  C. f(x) = 2^x  D. f(x) = 2^x + 1/3

The limit of the expression is determined as 0.

The limit of the expression is calculated as follows;

The given expression = lim (x ---> 9) [ ( x - 9 ) / √x - 3)

For the given limit in the expression, we have x maps to 9 or x tends to 9.

When x tends to 9, we will have;

x ---->9 = (9 - 9 ) / (√9 - 3)

= (0)/(-3 - 3)

note: since √x can be negative or positive, we will choose negative so that our solution will not be undefined.

= 0/-6

= 0

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\(\sf \longrightarrow \: \: \lim_{x\to \: 9} \: \: \: \frac{x \: - \: 9}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ({ \sqrt{x} \: )}^{2} \: - \: {(3)}^{2} }{ \sqrt{x} - 3 } \\ \)

Now , by using Identity:-

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)( \sqrt{x} - 3)}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3) \cancel{( \sqrt{x} - 3)}}{ \cancel{ \sqrt{x} - 3} } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)(1)}{1 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)(1) \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{9} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \sqrt{9} + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 3 + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 6\\ \)

Answer:

x < 5/4

Step-by-step explanation:

divide by 16 on both sides

x < 20/16 = 5/4

The height of the trapezoid is 20 cm.

To find the height of the trapezoid, we can use the formula for the area of a trapezoid:

Area = (1/2) * (major base + minor base) * height

Given that the sum of the major base and minor base is 110 cm and the area is 1100 cm², we can substitute these values into the formula and solve for the height.

1100 = (1/2) * 110 * height

To solve for the height, we can simplify the equation:

1100 = 55 * height

Dividing both sides by 55:

height = 1100 / 55

height = 20 cm

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Note the translated questions is

The sum of the major base and the minor base of a trapezoid is 110cm if the area measures 1100cm2

What is the height of the trapezoid?

Answer: 1:4

Step-by-step explanation:

In order to do this, we have to know that the octagon has an area which is four times less than the other area. Because of this, it shuld be 1:4

Answer:

Step-by-step explanation:

First we are going convert 6 hours to minutes and then seconds

1 hour= 60 mins

6 hours= 6 multiply by 60

           = 360 mins

1 min= 60 secs

360mins to seconds= 360 multiply by 60

                                  =21600

The system of equations as an augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

From the question, we have the following parameters that can be used in our computation:

x                  = 100

   -5m  - 7c  = 350

   -5m  - 9c  = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x    m     c        

1    0      0        100

0   -5    -7        350

0   -5    -9        200

When represented as an augmented matrix, we have

\(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Hence, the augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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The x coordinate of the centroid of triangle ABC with vertices A(-3, 3), B(2, 5), and C(4, -3) is 1

The center of the an object is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together.

For a triangle the formula to find the vertex is

X coordinate: (x₁ + x₂ + x₃)/3  

Y coordinate: (y₁ + y₂ + y₃)/3

substituting for the vertices A(-3, 3), B(2, 5), and C(4, -3)
X coordinate = (x₁ + x₂ + x₃)/3  

X coordinate = (-3 + 2 + 4)/3

X coordinate = 1

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Answer:

11 whole meals

Step-by-step explanation:

Lets say that you have 800 noodles in one box. The serving size would be 80 noodles / meal. Then the question says you eat 7/8 of the recommended meal, which would be 70 noodles. When you divide 800 by 70, you get 11.4285714286 meals. Remember that the question is asking for full meals, so you round down to 11 full meals.

If you want a more algebraic answer:

10 servings (\(\frac{7/8}{1}\)) = 10 (8 / 7) = 80/7 = 11.4285714286 meals.

round down to 11 full meals.

11 complete meals can you get from one box.

Given that, a box of rotini noodles contains 10 servings.

If you eat 7/8 of the recommended serving as a meal, we need to find how many complete meals can you get from one box.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, whereas the whole can be any number, a specific value, or a thing.

Now, the number of complete meals=10÷7/8

=80/7

=11.42≈11

Therefore, 11 complete meals can you get from one box.

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Answer: Q is the answer.

Step-by-step explanation:

Answer:

(-2\(x^{2}\)+3x+1)

Step-by-step explanation:

f(x) = -2x² + 4  g(x) = 3x - 3 find f (4) + g(-6).

f(x)+g(x)

(-2\(x^{2}\)+4) +(3x-3)

(-2\(x^{2}\)+3x+4-3)

(-2\(x^{2}\)+3x+1)

Answer:

Step-by-step explanation:

You want to identify the x-intercepts on the graph.

An "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.

The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...

  (-2, 0) and (3, 0)

<95141404393>

The value of the constant k such that the system has infinitely many solutions is; -2.

It follows from the task content that the system of equations given upon observation are multiples.

Hence, by multiplying the second equation by -2; we have;

-4x +6y = 4

-4x +6y = -2k

Hence, for the system to have infinitely many solutions; 4 = -2k.

Ultimately, k = -2 by dividing both sides of the equation above by -2.

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The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

Answer:

Hello! answer: 175 cm2

Step-by-step explanation:

9 × 7 = 63 63 ÷ 2 = 31.5 31.5 × 4 = 126

7 × 7 = 49 126 + 49 = 175 therefore the area is 175 Hope that helps! And I believe the unuts would be cm2 but don't quote me on it

Answer:

Table needed to help

Step-by-step explanation:

Mean vs Median

The mean (informally, the “average“) is found by adding all of the numbers together and dividing by the number of items in the set: 10 + 10 + 20 + 40 + 70 / 5 = 30.

The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.

Answer:

The expression for the perimeter of the rectangle is: \(P = 4x - 18\)

Step-by-step explanation:

Perimeter of a rectangle:

A rectangle has length l and width w. It's perimeter is given by:

\(P = 2(l + w)\)

In this question:

\(l = x - 9, w = x\)

So

\(P = 2(x - 9 + x) = 2(2x - 9) = 4x - 18\)

The expression for the perimeter of the rectangle is: \(P = 4x - 18\)

Answer:

8x-32

Step-by-step explanation:

Distribute 7 through the parenthesis

x+3+7(x-5)

=x+3+7x-35

Collect the like terms

x+3+7x-35

=8x+3-35

Calculator the difference

8x+3-35

=8x-32

He didn't followed the parentheses method from the beginning itself.

Hope it helps.

The expression that has a value of 26 when a=4 and b=5 is option B: a \((√16+ b) - 10.\)

Let's substitute a=4 and b=5 in each expression and see which one has a value of 26:

An expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can also include exponents, roots, and other mathematical symbols. The value of an expression can vary depending on the specific values of the variables used in the expression.

A) \(a√16+b-10 = 4√16 + 5 - 10 = 4x4 + 5 - 10 = 9\)(not equal to 26)

B)\(a (√16+ b) - 10 = 4(√16 + 5) - 10 = 4(4 + 5) - 10 = 26\) (equal to 26)

C) \(a√16+ (b-10) = 4√16 + (5-10) = 4x4 - 5 = 11\) (not equal to 26)

D)\((a√16) + b-10 = (4√16) + 5 - 10 = 4x4 + 5 - 10 = 9\)(not equal to 26)

Therefore, the expression that has a value of 26 when a=4 and b=5 is option B: \(a (√16+ b) - 10.\)

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The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

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

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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Answer:

Equation: 26-14=(n)

Step-by-step explanation:

If you rest 14 from 26 that is the number of people that still need one.

(The answer is 12)

Answer:

57327392393629324

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The electricity cost $489.76 more than the interest.

Thus, option C is correct.

Interest cost is the total measure of interest a borrower pays on an obligation commitment over the existence of the getting. Interest is paid on the obligation notwithstanding reimbursement of head.

The formula will be:

I = A - P

I = 663(1 + 0.1528/12)^(5*12) - 663

I = 663(1 + 0.1528/12)^60- 663

I = 1416.51 - 663

I = $753.51

The bill for electricity for 7 years and 52 weeks per year  will be

= 7 x 52 x 2.14

= $778.96

The electricity cost is bigger than the interest:

$778.96 is bigger than $753.51 by $25.45:

$778.96 - $753.51 = $25.45.

Therefore, option C is correct.

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The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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      Statement              Reason

1.      LQ ║NP                  Given

2.     ∠Q ≅ ∠N                 ASA Theorem

3.     ∠L ≅ ∠P                   Alternate Interior Angles

4.    ΔLMQ ~ ΔPMN         ASA Similar Theorem

Similar shapes are enlargements of each other using a scale factor.

All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.

The scale factors for length, area and volume are not the same.

From the given diagram,

 Statement              Reason

1.      LQ ║NP                  Given

2.     ∠Q ≅ ∠N                 ASA Theorem

3.     ∠L ≅ ∠P                   Alternate Interior Angles

4.    ΔLMQ ~ ΔPMN         ASA Similar Theorem

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Based on the information given, the null hypothesis states that the newscast reaches 41% of the viewing audience, while the alternate hypothesis states that it does not reach 41% of the audience. So, the correct answer is d. Fail to reject the null hypothesis.

To determine the decision, we need to perform a hypothesis test using the given significance level α = 0.01. This significance level represents the maximum acceptable probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.

In the survey of 100 viewers, 36% indicated that they watch the late evening news on the local CBS station. To test the hypothesis, we can use a one-sample proportion test. We compare this sample proportion to the claimed 41% to see if there is a significant difference.

Using a statistical calculator or software, we calculate the p-value associated with the observed sample proportion. If this p-value is less than α (0.01), we reject the null hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

Based on the decision criteria, if the p-value is less than 0.01, we would reject the null hypothesis and conclude that the newscast does not reach 41% of the audience. However, if the p-value is greater than or equal to 0.01, we would fail to reject the null hypothesis. To summarize, the correct decision, given α = 0.01, would be d. Fail to reject the null hypothesis.

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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The length of the hypotenuse is 7m.

Let the side opposite to 30° be the shortest leg.

The side opposite to 60° is the longest leg.

So, the side opposite to 90° is hypotenuse.

Length of the shortest side is x.

Length of longest side is \(\sqrt{3}x\)

Length of the hypotenuse is 2x.

We know x = 7

So, \(\sqrt{3}(x)=\sqrt{3}(7)\)

Thus, the length of the longer leg is \(\sqrt{3}(7)\) m

Length of hypotenuse = 2x = 2(7) = 14m

\(x^{2} +(\sqrt{3} x)^2 =(2x)^2\\\\(7)^2+(\sqrt{3} (7))^2=(2x)^2\\\\49 + (3(49)) = (2x)^2\\\\49 + 147= (2x)^2\\\\(2x)^2=196\)

Taking square root on both sides:

\(2x = \sqrt{196}\)

2x = 14

x = 7

Therefore, the length of the hypotenuse is 7m.

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If you're looking for x, then:

2 = |x|-1

lxl-1 = 2

lxl-1+1=2+1

lxl=3

so x = -3, x=3