Instructions: For the given piecewise function, evaluate for
the specified value of x.
S3, x < -4
g(x) =
2x + 4, 2 > -4
Evaluate when = – 2
g(-2) =

Answer:

-8

Step-by-step explanation:

Divide -6 on both sides: x=48/-6   =   x=-8

Answer:

At a map scale of 1:100000, 1 millimeter on the map is equivalent to 1 kilometer on the ground

Answer:

1000 or 1/1000

Step-by-step explanation:

The scale is 1000 or 1/1000 as there are 1000 cm in 1 km

Answer:

8.6

Step-by-step explanation:

omni cal.cu.lator

branliest PLEASE

The total distance travelled by Kyle is 210 m.

Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².

The given length of the field is 84 m.

And, the width is 35 m.

Now, the diagonal of the field can be calculated using Pythagoras theorem as below,

Diagonal = √((84)² +(35)²)

               = 91

Then, the total length is found by summing the length, width and the diagonal as below,

= 84 + 35 + 91

= 210

Hence, Kyle run for the distance of 210 m.

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The sketch of the front elevation and the side elevation of the prism are added as an attachment

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

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

K = 3/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

k−9=5(k−3)

k+−9=(5)(k)+(5)(−3)(Distribute)

k+−9=5k+−15

k−9=5k−15

Step 2: Subtract 5k from both sides.

k−9−5k=5k−15−5k

−4k−9=−15

Step 3: Add 9 to both sides.

−4k−9+9=−15+9

−4k=−6

Step 4: Divide both sides by -4.

-4k/-4 = -6/-4

K = 3/2

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Answer: Option 1

Step-by-step explanation:

\(|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2\)

Solve Absolute Value.

| x + 4 | = 2

We know either x + 4 = 2 or x + 4 = −2

x + 4 = 2 (Possibility 1)

x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)

x = -2

x + 4 = −2 (Possibility 2)

x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)

x = -6

Answer: x = - 2 or x = -6

Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.

Answer:

1.75 + 1.25 + 1.50 + .75(3) = $6.75 total

Step-by-step explanation:

Make sure to multiply .75 x 3 because there are 3 bags of chips. That gives you $2.25 in chips to add to the hotdog, popcorn, and soda total.

Step-by-step explanation:

first of all, all answer options are basically wrong, because an area is always measured in units² (and not just in units).

the blue colored area is the area of the whole square minus the area of the circle.

the side length of the square is 2 times the radius of the circle (the diameter) : 2×12 = 24 units.

so, the area of the square is

24² = 576 units²

the are of the circle is

pi×r² = pi×12² = 144pi units²

so, the blue area is

576 - 144pi = 123.6106579... ≈ 124 units²

therefore, D is the right answer.

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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Answer:

The refund was $29.40 off hope this helps!

The equation that is used to determine the amount c, in pounds, of the cinnamon flavored coffee, and the amount h, in pounds, of the hazelnut flavored coffee is c + h = 20 and 6c + 9h = 20(8)

An equation is an expression that shows the relationship between two or more variables and numbers.

Let c represent the amount of cinnamon flavored coffee, and h represent the amount in pounds, of the hazelnut flavored coffee.

The required blend is 20 pounds:

c + h = 20    (1)

Also:

6c + 9h = 20(8)  (2)

From eqn 1 and 2:

The equation that is used to determine the amount c, in pounds, of the cinnamon flavored coffee, and the amount h, in pounds, of the hazelnut flavored coffee is c + h = 20 and 6c + 9h = 20(8)

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Egbert must deposit $19,602.52 as a lump sum in order to have $40,000 in the fund at the end of 10 years.

To calculate the required lump sum deposit, we can use the formula for compound interest:

A = P\((1+r/n)^{nt}\)

Where:

A = the future value (desired amount in the fund) = $40,000

P = the initial principal (lump sum deposit we need to find)

r = the annual interest rate in decimal form = 7% = 0.07

n = the number of compounding periods per year = 4 (quarterly compounding)

t = the number of years = 10

Plugging in these values, the formula becomes:

$40,000 = P\((1+(0.07/4)^{(4*10)}\)

Simplifying further:

$40,000 = P\((1.0175)^{40}\)

Now we can solve for P by dividing both sides of the equation by

P = $40,000 /\((1.0175)^{40}\)

Using a calculator to evaluate the expression, we find:

P ≈ $19,602.52

Therefore, Egbert must deposit approximately $19,602.52 as a lump sum in order to have $40,000 in the fund at the end of 10 years.

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The surface area of the complex solid is 530 square yards.

In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:

A = w · h

Where:

The surface area of the complex solid is:

A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)

A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²

A = 530 yd²

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Answer:

There is no graph attached.

Step-by-step explanation:

Check the question again.

Answer:

not just you

Step-by-step explanation:

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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Answer: 55%

Step-by-step explanation:

total: 40 questions

part A: 20

part B: 20

15/40 needed to pass

aka 37.5%

20% of 20 is 4

she needs 11 (15-4) questions correct to pass in part B

11/20 = .55 * 100 = 55% of the questions right in part B

Step-by-step explanation:

part A has 20 questions.

20% are correct, that means

100% = 20

20% = 100%/5 = 20/5 = 4

so, she has 4 questions correctly answered in part A.

she needs 15 correctly answered questions in total.

therefore, she needs to answer 11 questions correctly on part B.

part B has also 20 questions. how many % are 11 questions ?

100% = 20

1% = 100%/100 = 20/100 = 0.2

11 are a many % as 1% fits into 11 :

11/0.2 = 55

she needs to answer 55% of the questions correctly in part B.

Answer:

Choice D

Step-by-step explanation:

Since it is a straight one line, the y-intercept (3) stays the same. For the x, it changes so you will have to add both x intercept (2 and 10) and divide by 2. So that gives 12/2 =6 (the x intercept), and since it's one straight line the y intercept remains the same (3)

Answer:

D(6,3)

step-by-step explanation.

In a right triangle, the length of side "a" is 12.

The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, can be used to find the length of side "a" in a right triangle with sides of 13 and 5 units.

Let's assign "a" as the unknown side. According to the Pythagorean theorem, we have the equation: \(a^{2}\) = \(13^{2}\) - \(5^{2}\).

Simplifying the equation, we get \(a^{2}\) = 169 - 25, which becomes \(a^{2}\) = 144.

To solve for "a," we take the square root of both sides: a = √144.

The square root of 144 is 12. Therefore, side "a" has a length of 12 units.

In summary, using the Pythagorean theorem, we determined that side "a" in the right triangle with side lengths 13 and 5 units has a length of 12 units.

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Answer:

5 miles/day

Step-by-step explanation:

This is a division problem.

(60 miles)/(12 days) = 5 miles/day

Hence, these lines are perpendicular to each other.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Draw the graph by using the given equation is

(24)

line \(a: y = 5x - 6\)

line \(b: x + 5y = 5\)

Graph is of the form:-

(25)

line \(a: 2x = y = 10\)

line \(b: -6x - 3y = 3\)

line \(c: x - 2y = 8\)

Graph is of the form:-

Hence, these lines are perpendicular to each other.

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Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

The transformation of f(x) = 2ˣ⁺⁹ + 7 includes a horizontal shift of 9 units to the left and a vertical shift upward by 7 units.

The transformation of the function f(x) = 2ˣ⁺⁹ + 7 can be described as a vertical shift upward by 7 units and a horizontal shift to the left by 9 units.

The original function f(x) = 2ˣ is a basic exponential function. By adding 9 to the exponent, the function is shifted 9 units to the left. This means that the graph of f(x) = 2ˣ⁺⁹ is shifted horizontally to the left by 9 units compared to the graph of f(x) = 2ˣ.

Additionally, by adding 7 to the entire function, the graph is shifted vertically upward by 7 units. This means that every y-coordinate of the graph of f(x) = 2ˣ⁺⁹ is increased by 7 compared to the graph of f(x) = 2ˣ.

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