What is the range of this function?

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

[tex]\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2[/tex]

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Answer:

First, the graph is overall decreasing with two local maximums and two local minimums.

Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.

Considering the above observations we can state that:

Cara's first error occurred when she simplified the expression (negative 4) squared.

According to the order of operations (PEMDAS/BODMAS), exponentiation should be performed before any other operations. However, Cara incorrectly squared only the negative sign and not the entire number.

As a result, she obtained a value of positive 4 instead of 16.

To correct the error, Cara should have squared the entire value of -4. Squaring a negative number yields a positive result. Thus, (-4) squared is equal to 16. By failing to correctly apply this rule, Cara ended up with an incorrect value in her expression.

The correct evaluation of the expression should have been:

StartFraction 4 (7 minus 13) over 3 EndFraction + (negative 4) squared minus 2 (6 minus 2) = StartFraction 4 (-6) over 3 EndFraction + 16 minus 2 (4) = -8 + 16 - 8 = 0.

Therefore, Cara's first error was in incorrectly squaring only the negative sign and obtaining a value of 4 instead of 16.

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The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Answer:

60%

Step-by-step explanation:

To find percent error, use the following equation:

Percent error = [tex]\frac{prediction-actual}{actual}[/tex]×100

=[tex]\frac{16-10}{10}[/tex]

=[tex]\frac{6}{10}[/tex]×100

=0.6×100

Drake's percent error is 60%.

Answer:

45 inches represent 55 miles on the scale drawing.

Step-by-step explanation:

To solve this proportion, we can set up the following ratio:

9 inches / 11 miles = x inches / 55 miles

We can cross-multiply to solve for x:

9 inches * 55 miles = 11 miles * x inches

495 inches = 11 miles * x inches

Now, we can isolate x by dividing both sides by 11 miles:

495 inches / 11 miles = x inches

Simplifying the expression:

45 inches = x inches

Answer:

I can't understand the language but try people who can

Answer:

$248.00

Step-by-step explanation:

Hours worked on Friday:  6 hr and 30 min = 6.5 hr

Money earned on Friday:  $15.5/hr x 6.5 hr = $100.75

Hours worked on Saturday:  6.5 hr - 1.167 hr = 5.33   *10 min = 10/60 = 0.1667 hr

Money earned on Saturday:  $15.50 x 5.33 hr = $82.67

Hours worked on Monday:  4.167 hr

Money earned on Monday:  $15.50/hr x 4.167 hr = $64.58

Total money made:  100.75 + 82.67 + 64.58 = $248.00

Answer:

Step-by-step explanation:

I understand your confusion. Let's go through the steps together to solve the equation correctly:

Given equation: 5 + x - 12 = 2x - 7

Combine like terms on the left side and the right side of the equation:

x - 7 = 2x - 7

Now, let's isolate the variable x. Subtract x from both sides of the equation:

x - x - 7 = 2x - x - 7

Simplifying:

-7 = x - 7

Next, add 7 to both sides of the equation:

-7 + 7 = x - 7 + 7

Simplifying:

0 = x

Therefore, the solution to the equation is x = 0.

If you need to use the values x = -4, 0, and 5, you can substitute each value into the original equation to check if it satisfies the equation. Let's do that:

For x = -4:

5 + (-4) - 12 = 2(-4) - 7

-11 = -15 - 7

-11 = -22

The equation is not satisfied for x = -4.

For x = 0:

5 + 0 - 12 = 2(0) - 7

-7 = -7

The equation is satisfied for x = 0.

For x = 5:

5 + 5 - 12 = 2(5) - 7

-2 = 3

The equation is not satisfied for x = 5.

Therefore, the correct solution to the equation is x = 0. The values x = -4 and x = 5 do not satisfy the equation.

In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.

To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.

First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.

Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.

To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.

Since the number of students must be a whole number, we round down to 1428 students.

Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.

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Answer:

she mixed up the slope and y- intercept in step 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

she correctly calculated the slope as m = - 4 and the y- intercept b = - 3

thus equation she should have is

y = - 4x - 3

Brooke's error was that she found the incorrect slope in step 1.  

The slope formula is:  m = (y₂ - y₁) / (x₂ - x₁)  

Using the given points:  m = (13 - 25) / (-4 - (-7))  m = -12 / 3  m = -4  

So, the slope is -4, not -12/3 as Brooke calculated in step 1.  

The correct equation for the line passing through the points (-7, 25) and (-4, 13) is: y = -4x - 3 (as found in step 3)

Answer:  [tex]x=200[/tex]

Step-by-step explanation:

    [tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]

[tex]\frac{1}{5}x-\frac{2}{3}(15)=30[/tex]

    [tex]\frac{1}{5}x-10=30[/tex]

            [tex]\frac{1}{5}x=40[/tex]

              [tex]x=\frac{40}{\frac{1}{5}}[/tex]

             [tex]x=40*\frac{5}{1}[/tex]

             [tex]x=200[/tex]

Answer:

You multiply each coordinate by 4

Step-by-step explanation:

Rule: (x, y) to (4x, 4y)

A: (-6,5) to A' (-24, 20)

B: (-4, 2) to B' (-16, 8)

C: (-6, 2) to C' (-24, 8)

By algebra properties, the simplified form of the complex fraction is - (x - 4) / [120 · (x - 1)].

In this problem we find the case of a complex fraction that must be simplified by algebra properties. A simple fraction must be found. First, write the entire expression:

[1 / (3 · x² - 3)] / [5 / (x + 1) - (x + 4) / (x² - 3 · x - 4)]

Second, factor the parts of the fraction:

[1 / [3 · (x - 1) · (x +1)]] / [5 / (x + 1) - (x + 4) / [(x - 4) · (x + 1)]]

[1 / [3 · (x - 1) · (x +1)]] / [[5 · (x - 4) - (x + 4)] / [(x - 4) · (x + 1)]]

Third, eliminate the rational fraction:

[(x - 4) · (x + 1)] / [- 120 · (x - 1) · (x + 1)]

Fourth, eliminate common binomials:

- (x - 4) / [120 · (x - 1)]

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Hello!

V

= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)

= 1,620cm³ + 630cm³

= 2,250cm³

The correct value of volume of the pyramid is 48 cubic inches.

To find the volume of the solid oblique pyramid, we can use the formula V = (1/3) * Base Area * Height. The base of the pyramid is a triangle, and the height is given as 6 inches.The formula for the area of a triangle is (1/2) * base * height. In this case, the base length is 8 inches and the height is 6 inches. Base Area = (1/2) * 8 * 6 = 24 square inches

Now, we can calculate the volume of the pyramid:

V = (1/3) * Base Area * Height

V = (1/3) * 24 * 6

V = 48 cubic inches

Therefore, the volume of the pyramid is 48 cubic inches.

None of the provided options (a, b, c, d) match the calculated volume of 48 cubic inches. Please double-check the given options or provide the correct options for further comparison.

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If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.

Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:

Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.

Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.

This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.

This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.

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Answer:

Step-by-step explanation:

Certainly! I'm here to assist you.

The given function is f(x) = -2(x - 3).

To simplify this expression, we can distribute the -2 to the terms inside the parentheses:

f(x) = -2 * x - (-2) * 3

Simplifying further:

f(x) = -2x + 6

Therefore, the simplified form of the function f(x) = -2(x - 3) is f(x) = -2x + 6.

The equation to determine the initial amount of money Cecilia had is x = 0.

Let's denote the initial amount of money Cecilia had as "x" dollars.

According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.

Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.

Since she had $8 left, we can set up the equation:

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

To simplify the equation, we can first combine like terms:

(x - (1/4)x - (1/2)x + 8) = 8

Now, let's solve the equation step by step:

(x - (1/4)x - (1/2)x + 8) = 8

Multiplying the fractions by their common denominator, which is 4, we get:

(4x - x - 2x + 32) = 32

Simplifying further:

(x + 32) = 32

Subtracting 32 from both sides:

x = 0

Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.

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The opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.

The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:

Situation 1: Temperature Change

If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.

Situation 2: Financial Gain

Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.

Additional situations that can be represented by the opposite of -5:

Situation 3: Distance Traveled

If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.

Situation 4: Weight Gain

Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.

In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.

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Answer:

3

Step-by-step explanation:

parallel lines have the same gradient

Answer:

$150

Step-by-step explanation:

Original Savings (Year 0): $1,000

Convert Interest rate into a decimal: 3 / 100 = 0.03

therefore the interest rate is 1.03

How much will be added each year?

5 years = $30 x 5 = $150

Final sum: $1,000 x $150 = $1,150

Suzy will have $1,150 in her account at the end of a five year period.

The value of x that makes lines c and d parallel when cut by transversal p is 99 (option d).

To determine the value of x, we need to analyze the relationship between the given lines and transversal.

Recall that when two lines are cut by a transversal, the corresponding angles are congruent if the lines are parallel.

Since lines c and d are cut by transversal p, we need to find the corresponding angles that should be congruent.

Let's assume that angle 12 corresponds to angle 18. In order for lines c and d to be parallel, angle 12 must be congruent to angle 18.

However, angle 12 and angle 18 do not have equal values (12 ≠ 18). Therefore, we need to explore other possible values of x.

Let's try x = 81. With this value, angle 12 corresponds to angle 81. But again, angle 81 is not congruent to angle 18 (81 ≠ 18). Thus, x = 81 does not make lines c and d parallel.

Finally, let's try x = 99. With this value, angle 12 corresponds to angle 99. If angle 99 is congruent to angle 18, then lines c and d will be parallel.

Since 99 = 99, we can conclude that when x = 99, lines c and d are parallel when cut by transversal p.

Therefore, the value of x that makes lines c and d parallel when cut by transversal p is 99. Thus, the correct option is d.

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Answer:

5) tan A = 0.42

6) Acute angle is less than 90°

7) Right angle is exactly 90°

8) Obtuse angle is greater than 90° but less than 180°

9) Straight angle is exactly 180°

10) Complementary angles add up to 90°

11) Supplementary angles add up to 180°

Step-by-step explanation:

tan A = opposite / adjacent

= 5/12

= 0.42

The antiderivative of ∫[[tex]x^\frac{1}{11}[/tex] - 7sin(x)]dx is:

[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex]

The indefinite integral, denoted as ∫f(x)dx, represents the antiderivative of a function f(x). It involves finding a function whose derivative is equal to the given function f(x).

Let's evaluate the indefinite integral of [tex]\int [x^\frac{1}{11} - 7sin(x)]dx[/tex]

To find the antiderivative of [tex]x^\frac{1}{11}[/tex], we add 1 to the exponent and divide by the new exponent:

[tex]\int x^\frac{1}{11} dx = (11/12)x^\frac{12}{11} + C_1[/tex], where C₁ is the constant of integration.

∫7sin(x)dx:

To find the antiderivative of 7sin(x), we use the trigonometric identity that the antiderivative of sin(x) is -cos(x):

∫7sin(x)dx = -7cos(x) + C₂, where C₂ is another constant of integration.

Combining the two results, the indefinite integral of [tex]\int[x^\frac{1}{11} - 7sin(x)]dx[/tex] is:

[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex],

where C = C₁ + C₂ represents the constant of integration.

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The correct statement is the first one:

f(0) = 2

g(-2) = 0

Here we can see the graph of two quadratic equations.

The orange one is g(x), and we can see that it has the vertex at (-2, 0).

And the blue one is f(x), we can see that the vertex is at (2, 0)

From, that, we coclude that:

g(-2) = 0

f(2) = 0

We also can see that the two have the sa,me y-intercept (0, 2), so:

f(0) = g(0) = 2

Then the correct statement is the first one:

f(0) = 2

g(-2) = 0

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Answer:

23.6°

Step-by-step explanation:

The angle of depression, x, is congruent to the bottom right angle of the triangle.

sin x = opp/hyp

sin x = 100/250 = 0.4

x = sin^-1 0.4

x = 23.6°

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.