Choose the definition for the function.
A.
C.
√4x - if x < 0
3
2x + 2
if x ≥ 0
2x - 2
--4
if x ≤ 0
if x > 0
B.
D.
2x + 2
x + 4
x + 4
2x + 2
if x ≤ 0
if x > 0
if x ≤ 0
if x > 0

Answer:

d equals to -3, so in every expression we substitute d with -3.

2d(-3d)

2(-3) x (-3x-3)

-6 x 9 = -54

12d - 28

12(-3) - 28

-36-28 = -64

-3d

-3x(-3) = 9

-5d-8

-5x(-3)-8

15-8 = 7

8d+14

8x(-3) + 14

-24 + 14 = -10

hope it helps.

According to the given a two-column proof bellow the EFI = 40°

A two-column geometric proof is made up of a set of claims and the reasons why we know they are true. The statements are stated in the left column, while the reasons for making them are mentioned with in right column.

Given:

GFI = 128°where

9x - 2 = 128°

EFI = 40° And

4x = 40

So,

GFI = 128°where

9x - 2 + 4x = 128°

13x = 130

x = 10

putting the value x = 10 in EFI = 40° And  4x = 40:

So,

4x = 40

4(10) = 40

40 = 40

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The cost of running only half of the fleet for 6 hours each would be $7687.2 .

The company runs full fleet of 16 trucks at 8 hours each.

Which means total hours of running on full fleet = 128 Hours

So, The cost of running 128 hours =  $20,500

Then, cost of running 1 hour = $20,500 ÷ 128

                                             = $160.15

Now we will determine the cost of running trucks on half fleet for 6 hours each.

As we already know that

Full fleet = 16 Trucks

Then, Half fleet = 8 Trucks

Total hours of trucks running on half fleet = 8 × 6

                                                                 = 48

The cost of running 48 hours = 48 × $160.15

                                              =  $7687.2

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The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.

Given X is not a negative number and conjecture X is a positive number.

A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases.

Given X is not a negative number

Conjecture X is a positive number

If X is 0, which is neither positive nor negative.

So, the statement is false.

The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.

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Answer:

m = 0

Step-by-step explanation:

- 10 = - 10 + 7m ( add 10 to both sides )

0 = 7m ( divide both sides by 7 )

0 = m

Answer:

[tex]\frac{-5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{-3}{4}[/tex] - [tex]\frac{-1}{3}[/tex]  Subtracting a negative number is the same as adding a positive

[tex]\frac{-3}{4}[/tex] + [tex]\frac{1}{3}[/tex]  Rewrite each fraction with a common denominator.  Let's use 12 as our new denominator.

[tex]\frac{-3}{4}[/tex] = [tex]\frac{-9}{12}[/tex]  multiple the top and the bottom of the first fraction by 3 to get the equivalent fraction [tex]\frac{-9}{12}[/tex]

[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{12}[/tex]  Multiple the top and bottom of the first fraction by 4 to get the equivalent fraction [tex]\frac{4}{12}[/tex].

Now, add the two fractions

[tex]\frac{-9}{12}[/tex] + [tex]\frac{4}{12}[/tex] = [tex]\frac{-5}{12}[/tex]  The denominator stays the same and you add the numerators.

Answer:

m = 2

Step-by-step explanation:

Find LCM.

[tex]7,\:14\\14=7\cdot \:2\\=2\cdot \:7\\=7\cdot \:2\\=14\\[/tex]

Multiply

[tex]\frac{2m}{7}\cdot \:14+\frac{3m}{14}\cdot \:14=1\cdot \:14[/tex]

Simplify(AA)

[tex]\frac{2m}{7}\cdot \:14\\=\frac{2m\cdot \:14}{7}\\=\frac{28m}{7}\\=4m[/tex]

Simplify(AB)

[tex]\frac{3m}{14}\cdot \:14\\=\frac{3m\cdot \:14}{14}\\=3m[/tex]

Simplify(AC)

[tex]1\cdot \:14\\= 14[/tex]

Divide

[tex]=7m = 14\\\frac{7m}{7}=\boxed{\frac{14}{7}}\\= 2[/tex]

Based on the given task content, the quotient of - 80 and - 16 is 5

Quotient refers to the number resulting from the division of one number by another. Such as: the quotient of 12 divided by 4 is 3.

The divisor

The number or expression that another is to be divided by.

In "42 ÷ 3" the divisor is the 3.

The dividend

These refers to numbers or expressions that is to be divided by another.

In "42 ÷ 3" the dividend is the 42.

= - 80 / - 16

= 5

Therefore, the quotient of -80 and -16 is 5

Complete question:

what is the quotient of -80 and -16

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Based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex]

The product rule of exponents says that if two quantities that are multiplied together have the same base, we will add their exponents together to get the product.

Given the following:

a^4 * a^6

Applying the product rule of exponents, we will have:

a^4 * a^6 = a[tex]^{(4 + 6)}[/tex]

a^4 * a^6 = [tex]a^{10}[/tex].

Therefore, based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex].

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Trymaine is 20 years old and Sunny is 13 years old.

GIven, Trymaine is 7 years older than Sunny.

In 3 years the sum of their ages will be 39.

Let the age of Trymaine be a and age of Sunny be b.

we have,

a = b ₊ 7

a ₊ 3 ₊ b ₊ 3 = 39

a ₊ b = 39 ₋ 6

a ₊ b = 33 .... eq(2)

therefore a = b ₊ 7

a ₋ b = 7 ....eq(1)

solve eq (1) and eq(2)

2a = 40

a = 20

and a ₋ b = 7

20 ₋ b = 7

₋b = 7 ₋ 20

₋b = ₋13

b = 13

hence Trymaine is 20 years old , whereas Sunny is 13 years old.

hence we get the ages of Trymaine and Sunny as 20 and 13 respectively.

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In simplest radical form, the values are,

(1) The missing length = 48

(2) The missing length = 48

(3) The missing length = 140

(4) The missing length = 25

(1) : In triangle,

ΔADB ≅ ΔABC

∠A = ∠A

∠ABC = ∠ABD

So, ΔADB ≅ ΔABC

AD/AB = AB/AC

AD = 64 AND AC = 100 substitute in this equation,

64/AB = AB/100

AB * AB = 64*100

[tex]AB^{2}[/tex] = 6400

AB = [tex]\sqrt{6400}[/tex]

AB = 80

Because,

∠ADB = 90°

So,

[tex]AD^{2} +BD^{2} =AB^{2}[/tex]

[tex]BD^{2} = AB^{2} -AD^{2}[/tex]

BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]

BD = [tex]\sqrt{6400-4096}[/tex]

BD = [tex]\sqrt{2304}[/tex]

BD = 48

Therefore,

The missing length is BD = 48

(2) : In triangle,

ΔADB ≅ ΔABC

∠A = ∠A

∠ABC = ∠ABD

So, ΔADB ≅ ΔABC

AD/AB = AB/AC

AD = 64 AND AC = 100 substitute in this equation,

64/AB = AB/100

AB * AB = 64*100

[tex]AB^{2}[/tex] = 6400

AB = [tex]\sqrt{6400}[/tex]

AB = 80

Because,

∠ADB = 90°

So,

[tex]AD^{2} +BD^{2} =AB^{2}[/tex]

[tex]BD^{2} = AB^{2} -AD^{2}[/tex]

BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]

BD = [tex]\sqrt{6400-4096}[/tex]

BD = [tex]\sqrt{2304}[/tex]

BD = 48

Therefore,

The missing length is BD = 48

(3): In triangle BDC

tanθ = BC/DC

tanθ = 60/36

θ  = [tex]tan^{-1}[/tex](60/36)

θ  = [tex]tan^{-1}[/tex](1.66)

θ = 53.16

And,

[tex]BD^{2} =BC^{2} +CD^{2}[/tex]

[tex](BD)^{2}[/tex] = 60*60 + 36*36

[tex](BD)^{2}[/tex] = 3600+1296

[tex](BD)^{2}[/tex] = 4896

BD = 69.97

In big triangle, ABC

cosθ = BC/AC

cosθ = 60/(36+u)

cos69.97 = 60/(36+u)

0.342 = 60/(36+u)

36+u = 60/0.342

36+u = 195.4

u = 195.4 - 36

u = 139.4

u = 140

Therefore,

The maximum length u = 140

(4) : In ΔABC and  ΔDAB

∠B = ∠B   (Common)

∠A = ∠D = 90°

Hence, ΔBAC ≅ ΔBDA

AB/BC = BD/AB

15/x = 9/15

x = (15*15)/9

x = 225/9

x = 25

Therefore,

The missing length x = 25

Hence,

(1) The missing length = 48

(2) The missing length = 48

(3) The missing length = 140

(4) The missing length = 25

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The expression that best represents the cost of shirts plus shipping is 20b + 5.

An expression is a statement that is made up of at least two numbers or variables and at least one mathematical operation. An expression usually does not have an equal to sign.

The first step is to determine the cost of a shirt and the cost of shipping.

a + b = 25 equation 1

a + 2b = 45 equation 2

Where:

a = cost of shipping

Subtract equation 1 from equation 2

b = 20

a = 25 - 20

a = 5

Thus, the cost of one shirt is 20. The cost of shipping is 5. The cost of shirts increases with the number of shirts bought while the cost of shipping remains constant.

The expression is: 20b + 5

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a: The centripetal acceleration of the child = 1.60 m/s².

b: The net horizontal force exerted on the child = 40N.

The parameters provided;

Part a: The child's centripetal acceleration is calculated as follows:

a = v²/r

Put the values;

a = 1.65²/1.7

a = 1.60 m/s²

Thus, the child's centripetal acceleration is 1.60 m/s².

Part b: The child's net horizontal force is calculated as follows:

F = ma

F = 25×1.60

F = 40 N

Thus, child's net horizontal force is 40 N.

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The complete question is-

A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.65 m/s.

a. Calculate the centripetal acceleration of the child

b. Calculate the net horizontal force exerted on the child

Mass of child = 25 kg.

The weight of each baby based on the information will be:

Martin = 2.9 kg

Daniel = 3.5kg

Kevin = 3.9 kg

Martin = x

Daniel = x + 0.6

Kevin = x + 1

Total weight = 10.3 kg

Therefore, this will be solved as:

x + x + 0.6 + x + 1 = 10.3

3x + 1.6 = 10.3

3x = 10.3 - 1.6

3x = 8.7

Divide

x = 8.7 / 4

x = 2.9

Therefore, the weights will be:

Martin = x = 2.9 kg

Daniel = x + 0.6 = 2.9 + 0.6 = 3.5kg

Kevin = x + 1 = 2.9 + 1 = 3.9 kg

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The values of the functions are:

f(-2) = -6

f(0) = 0

f(3) = 9

Given the function, f(x) = 3x, to find the values of f(-2), f(0), and f(3), solve as shown below.

Find f(-2) by substituting x = -2 into the function, f(x) = 3x:

f(-2) = 3(-2)

f(-2) = -6

The value of f(-2) for the given function is: -6

Find f(0) by substituting x = 0 into the function, f(x) = 3x:

f(0) = 3(0)

f(0) = 0

The value of f(0) for the given function is: 0

Find f(3) by substituting x = 3 into the function, f(x) = 3x:

f(3) = 3(3)

f(3) = 9

The value of f(3) for the given function is: 9

Thus, the values of the functions are:

f(-2) = -6

f(0) = 0

f(3) = 9

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Answer:

Choice C; degree is 3

Step-by-step explanation:

The degree of the polynomial is the greatest of the exponents (powers) of its various terms.

So the degree of this polynomial is 3  which is choice C

Considering the definition of perpendicular line, the equation of of perpendicular line is y= -3/4x + 5/2.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 3y= 4x +7. Expressed in the form y = mx + b, you get:

y= (4x +7)÷ 3

y= 4/3x -+7/3

The line has a slope of  4/3. If you multiply the slopes of two perpendicular lines, you get –1, then:

4/3× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 4/3

slope perpendicular line= -3/4

So, the perpendicular line has a form of: y= -3/4x + b

The line passes through the point (6, -2). Replacing in the expression for parallel line:

-2= (-3/4)×6 + b

-2= -9/2 + b

-2+ 9/2= b

5/2= b

Finally, the equation of of perpendicular line is y= -3/4x + 5/2.

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Using Bernoulli's principle, the thing that we know about the ocean and the coast is that E. There is more air pressure over the ocean than over the coast.

According to Bernoulli's principle, which governs fluid dynamics, a fluid's speed increases concurrently with a reduction in pressure or potential energy.

The Bernoulli principle establishes a connection between a fluid's elevation and speed and its pressure. In water, air, or any other fluid with a very low viscosity, these characteristics can be approximated using Bernoulli's equation.

Since the weatherwoman is on the news explaining that there will be high winds on the central coast coming in from the ocean, it implies that there is more air pressure over the ocean than over the coast.

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Increase in the length is 3.64 ft.

What is area of square?

The area of square is the product of side of the square.

i.e., Area of square =  side * side

Given that;

Yossi has garage whose area =262 ft²

And, 50% area is incremented.

Now, the New Area is calculated as;

Area = 262 × 150%

       = 393 ft²

As we know that;

Area of Square = (Length) × (Length)

Length = √393 = 19.82 ft

Also,

Length of garage = √262 = 16.18 ft

Hence, Increase in the length = 19.82 - 16.18 = 3.64 ft.

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Answer: x∈[-4,3)     y∈(-5,5)

Step-by-step explanation:

[tex]Domain:x\in[-4,3)\\Range\ of\ y:\ y\in(-5,5)[/tex]

Answer:

Step-by-step explanation:

Round each number individually,

276.93 Rounded up -> 277

69.24 Rounded Down -> 69

102.56 Rounded up -> 103

73.69 Rounded up -> 74

Total = 523

Anything 0.50 to 0.99 gets rounded up

Anything 0.01 to 0.49 gets rounded down

When to the nearest dollar

Answer:

3h+6 inches

Step-by-step explanation:

Step-by-step explanation:

f(g(x)) means g(x) is embedded in f(x) as the argument or input value for f(x).

therefore,

f(g)x)) = 4(x² - 1) - 7 = 4x² - 4 - 7 = 4x² - 11

c. is the right answer

g(f(x)) is now the other way around. now f(x) is the only value for g(x) :

g(f(x)) = (4x - 7)² - 1 = 16x² - 56x + 49 - 1 = 16x² - 56x + 48

a. is the right answer

The value of x is 74

Surekha Washburn has scores of 61, 65, 77, and 81 on her algebra tests.

a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 72 or higher, given that the final exam

counts as two tests.

let score on final exam is x

two test are 2x

then we get the value of x

[tex]\frac{61 + 65 + 77 + 81 + 2x}{6}[/tex] = 72

[tex]\frac{284 + 2x}{6}[/tex]  = 72

284 + 2x =432

2x = 432 - 284

x = [tex]\frac{148}{2}[/tex]

x = 74

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Average Formula in Maths

The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. Hence, the average formula in Maths is given as follows:

Average = Sum of Values/ Number of values

Suppose, we have given with n number of values such as x1, x2, x3 ,….., x n. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+x n)/n

How to Calculate Average?

We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values.

Average can be calculated using three simple steps. They are:

Step 1: Sum of Numbers:

The first step in finding the average of numbers is to find the sum of all the given numbers.

Step 2: Number of Observations:

Next, we have to count how many numbers are in the given dataset.

Step 3: Average Calculation:

The final step in calculating the average is to divide the sum by the number of observations.

Now, let us consider an example to calculate the average.

If there are a group of numbers say, 20, 21, 23, 22, 21, 20, 23. Then find the average of these values.

By average formula, we know,

Average = (Sum of values)/No. of values

= (20+21+23+22+21+20+23)/7

= 150/7

=21.42

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Answer:

-1

Step-by-step explanation:

Answer:

-1 is the answer

Step-by-step explanation:

The equation in slope-intercept form is y = x - 6.

What is in slope-intercept form?

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line p is

y = 8x + 2

Comparing with the slope intercept form, slope = 8

If two lines are parallel, it means that they have the same slope. Therefore, the slope of line q passing through ( -1 , -2 ) is 8

To determine the y intercept, we would substitute m = 8, x = - 1 and

y = -2 into y = mx + c. It becomes

-2 = 8 × - 1 + c

-2 = - 8 + c

c = - 8 + 2 = -6

The equation becomes

y = x - 6

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Answer:

7

Step-by-step explanation:

3 goes into 21 7 times leaving no remainder which means: 3 x 7 = 21

The constant of variation k for the direct variation in 4x = –6y will be 1.5.

It should be noted that a direct variation simply means the mathematical relationship that exists between two variables which can be expressed by an equation such that a variable is equal to another one.

Therefore, the constant of variation k for the direct variation in 4x = –6y will be:

4x = –6y

Divide through by 4

4x / 4 = -6y / 4

x = -1.5y

Therefore, the constant of variation is 1.5.

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Using proportions, the person who earned the most commission is given by:

B. Bridget.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The commission is given by:

Rate(as a decimal) x Number of Items x Cost of Each Item.

Hence, for Bridget, the commission is given by:

B = 0.045 x 18 x 50 = $40.5.

For Curtis, the commission is given by:

C = 0.0375 x 11 x 80 = $33.

For Gloria, the commission is given by:

G = 0.0475 x 5 x 140 = $33.25.

For Hugo, the commission is given by:

H = 0.0425 x 13 x 60 = $33.15.

Hence Bridget earned the most commission and option B is correct.

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According to the given statement

Quadratic equation for x2+8x−5=0 is x=-4± √21

Second-degree algebraic expressions of the type ax2 + bx + c = 0 are known as quadratic equations.

There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (, ) and are also known as the roots of the quadratic equations.

According to the given value;

For this equation: a=1, b=8, c=-5

1x2+8x+−5=0

Step 1: Use quadratic formula with a=1, b=8, c=-5.

x=

−b±√b2−4ac

2a

x=

−(8)±√(8)2−4(1)(−5)

2(1)

x=

−8±√84

2

x=−4+√21 or x=−4−√21

Hence,quadratic equation for x2+8x−5=0 is x=-4± √21

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