What is the range of the function f(x) = –2|x + 1|?

all real numbers
all real numbers less than or equal to 0
all real numbers less than or equal to 1
all real numbers greater than or equal to 1

Answer:

4x/9

Step-by-step explanation:

The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9).

The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9). Here, 'x' represents the unknown number. To calculate the value of this expression, you would multiply 4 with 'x' and then divide the result by 9. For example, if the unknown number is 6, the expression would evaluate to (4 * 6)/9 = 24/9 = 2.67.

In the realm of algebraic expressions, the quotient derived from four times an unspecified number divided by nine takes on the simple yet versatile form of (4x/9), with 'x' standing in as the variable denoting the unknown quantity. The computation entails a straightforward process wherein you multiply the value of 'x' by 4 and subsequently divide the outcome by 9. For instance, if 'x' were to represent the value 6, the expression's evaluation would unfold as follows: (4 * 6)/9 = 24/9 = 2.67. This straightforward algebraic framework empowers us to efficiently compute the result based on the specific value attributed to 'x,' facilitating various calculations and problem-solving endeavors.

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Answer:

3c-8

Step-by-step explanation:

Answer:

Monday: 70

Tuesday: 64

Wednesday: 50

Thursday: 55

Friday: 76

Step-by-step explanation:

Equations

Let's call x to the number of sandwiches ordered for Thursday's meeting. We know that for Wednesday’s, we'll need x-5 sandwiches, for Monday's, we'll need 20 more, i.e. (x-5+20)=x+15 sandwiches. For Tuesday's it will be 6 fewer than x+15, or x+9. Finally, for Friday's, it will be 12 more than x+9 or x+21. Summarizing:

Monday: x+15

Tuesday: x+9

Wednesday: x-5

Thursday: x

Friday: x+21

The fewest of them all is x-5 and is must be equal to 50

[tex]x-5=50[/tex]

[tex]x=55[/tex]

The number of sandwiches per day is

Monday: x+15=70

Tuesday: x+9=64

Wednesday: x-5=50

Thursday: x=55

Friday: x+21=76

Answer:

72 cubes

Step-by-step explanation:

Attached is the picture drawn (though not great one), showing 6 cube on length of prism, 3 cubes on width and 4 cubes on height of prism.

Given: Length of prism= 6

           Width= 3

            Height= 4

To know the number of cubes, which can fill the entire prism, we need to find volume of prism.

∴ Volume of prism= [tex]length\times width\times height[/tex]

Volume of prism= [tex]6\times 3\times 4= 72[/tex]

∴ 72 units of cube can fill the entire prism.

The conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]

Solution:

Given that average person's speed when riding a bike along a street is 18 kilometers per hour

To find: conversion factor used to convert the given speed to meters per hour

Given average speed = 18 km per hour

From the conversion parameters:

1 km = 1000 meters

or

[tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]

So, we can use the above conversion factor to convert average speed into meters per hour

18 km per hour = 18000 meter per hour

So the conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]

Thus option C is correct. 1000 meters for 1 kilometers

Answer:

its c

Step-by-step explanation:

The expression 13 - (-21) simplifies to 34.

The expression 13 - (-21) can be simplified as follows:

So, the expression 13 - (-21) is equivalent to 34.

To find the equivalent expression for \(13 - (-21)\), you can simplify the subtraction of a negative number, which is the same as adding its positive counterpart. Therefore:

\[ 13 - (-21) \]

is equivalent to:

\[ 13 + 21 \]

Among the given choices, the expression that matches this result is:

\[ \text{(Choice D) } 13 + 21 \]

Final answer:

The expression 13 - (-21) is equivalent to 13 + 21 because we change the subtraction of a negative number to addition. The final result is 34.

Explanation:

The expression 13 - (-21) involves subtracting a negative number from a positive number. According to the rules for subtracting integers, we change the sign of the number being subtracted and then follow the rules for addition as follows:

Therefore, the expression 13 - (-21) is equivalent to 13 + 21, which simplifies to 34.

Answer:

x = 13.7

Step-by-step explanation:

This is a right triangle so we use the trig ratios. We need an angle of reference (not the right angle) and any side (which is given, hypotenuse = 47).

We can either find the angle at the top or the right to be the angle of reference, Θ (theta).

Angle at the top:

The two angles, 17° and the unknown interior angle add to 90° because they are complementary.

∠Θ = 90° - 17° = 73°

Now use the trig ratio cosine.

cosΘ = adjacent ÷ hypotenuse

cos(73°) = x / 47

x = 47cos(73°)

x = 13.74147.....    Round down the exact answer to nearest tenth

x ≈ 13.7                Answer

The value of x is the same as the side adjacent to the angle of reference I chose.

If I chose the other missing angle to be the angle of reference, I would use sine and x would be opposite.

Answer:

slope of parallel line and perpendicular line are 5 and -1/5 espectively

equation of parallel and perpendicular line are y = 5x + 22 [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex] respectively

Step-by-step explanation:

y = 5x - 4 is in the form

y = mx + c

where m is the slope of the line and c is the y intercept of thr line

therefore slope of the line = 5 and y intercept = -4

when an another line is parallel to the given line then the slope of both the lines are equal

therefore the slope the parallel line = 5

equation of a line passing through a given point [tex](x_{1} ,y_{1})[/tex] with slope m is given by [tex]y-y_{1} = m(x-x_{1} )[/tex]

given [tex](x_{1} ,y_{1})[/tex]= (-4,2)

therefore equation of line y-2 = 5(x+4)

therefore y = 2+ 5x+20

y = 5x + 22is the eqaution of required line.

when two lines are perpendiculer then

[tex]m_{1} m_{2}=-1[/tex]

where [tex]m_{1} and m_{2}[/tex] are slope of the lines therefore

m×5=-1

therefore m= [tex]\frac{-1}{5}[/tex]

therefore eqaution of line passing through (-4,2) and with slope m= [tex]\frac{-1}{5}[/tex] is given by [tex]y - 2= \frac{-1}{5} (x+4)[/tex]

[tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex]

We can see here that the line perpendicular to the given line, passing through (-4, 2), is (0, -6).

Let's first verify the given information and then find the point on the line perpendicular to the given line passing through (-4, 2).

Given line: y = 0.5x - 4

Slope of a line parallel to the given line:

The slope of the given line is 0.5. Parallel lines have the same slope. Therefore, the slope of a line parallel to the given line is also 0.5.

A point on the line parallel to the given line, passing through (-4, 2):

Since the slope of the parallel line is 0.5, and we know a point (-4, 2) that lies on it, we can find the equation of the parallel line using the point-slope form of a line.

Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.

Substitute the values: y - 2 = 0.5(x + 4)

Now, let's find a point on the line perpendicular to the given line, passing through (-4, 2):

Slope of a line perpendicular to the given line:

Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 0.5, so the slope of the line perpendicular to it is -1/0.5 = -2.

A point on the line perpendicular to the given line, passing through (-4, 2):

Using the point-slope form again, we can find the equation of the perpendicular line passing through (-4, 2).

Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.

Substitute the values: y - 2 = -2(x + 4)

Now, we can find another point on the perpendicular line by setting x = 0:

y - 2 = -2(0 + 4)

y - 2 = -8

y = -6

So, another point on the line perpendicular to the given line, passing through (-4, 2), is (0, -6).

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Answer:

B,C, and E

Step-by-step explanation:

A histogram is a graphical illustration of information in bars of diverse heights. A histogram displays the shape and spread of continuous sample data. The true statements about the data essay scores for high school sophomores and juniors in a contest are; the juniors tended to have higher essay scores than the sophomores, the medians of both data sets are equal and the histogram is the best way to show that both distributions are nearly symmetric.

Answer:

bce

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

Find the ratio of the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout and simplify it

25:10+25+15

25:50

1:2

Answer:

1 to 2

1:2

1/2

Step-by-step explanation:

Ratios can be written in three forms:

A to B

A:B

A/B

Ratios are also simplified by reducing to lowest terms like fractions are.

This problem's ratio is:

minutes lifted weights to total minutes workout

The number of minutes lifting weights is in the question: 25.

To find the total minutes of his workout, add the number of minutes he spent for all of the activities:

Total minutes = warm-up + lifting weights + treadmill

Total minutes = 10 + 25 + 15

Total minutes = 50

The ratio before simplifying is 25/50.

This ratio can be reduced to lowest terms. Both sides are divisible by 25.

25/25 = 1

50/25 = 2

The ratio in lowest terms is 1/2.

It can also be written as 1 to 2 or 1:2.

Answer:

x = 25

y = 60

Step-by-step explanation:

Angles with meauseres 80° and 4x° are the same-side interior angles when two parallel lines are cut by transversal. This means the sum of the measures of these angles is equal to 180°.

[tex]80^{\circ}+4x^{\circ}=180^{\circ}\\ \\4x=180-80\\ \\4x=100\\ \\x=25[/tex]

Angles with measures 4x° and (2y - 20)° are vertical angles, so they are congruent:

[tex]4x^{\circ }=(2y-20)^{\circ}\\ \\4\cdot 25=2y-20\\ \\2y-20=100\\ \\2y=100+20\\ \\2y=120\\ \\y=60[/tex]

Hope it helps u............

Answer:

x-intercept = (-1,0)

y-intercept = (0,-3)

Explanation:

x-intercepts are points where the line crosses the x-axis.

y-intercepts are points where the line crosses the y-axis.

Answer:

D

Step-by-step explanation:

Final answer:

Using a system of equations, it's found that Mo's farm stand sold 65 pounds of peaches, with the total sales of apples and peaches being 165 pounds and revenue $337.50.

Explanation:

To determine how many pounds of peaches Mo's farm stand sold, we can set up a system of equations based on the given information about total weight and revenue from apples and peaches. The weight equation can be written as A + P = 165, where A is the weight of apples sold and P is the weight of peaches sold. The revenue equation is 1.75A + 2.50P = 337.50.

Let's solve for A using the weight equation: A = 165 - P. Substitute A in the revenue equation: 1.75(165 - P) + 2.50P = 337.50. Upon solving, we get: 288.75 - 1.75P + 2.50P = 337.50, which simplifies to 0.75P = 48.75. Therefore, P, the weight of peaches sold, is 65 pounds.

Answer:

Angle M = 98 degrees

Step-by-step explanation:

All triangle angles add up to 180.

Set up equation like this:

(x+6)+(3x-16)+(x)=180

Combine like terms.

5x-10=180

Add on both sides.

5x=190

Divide 5 both sides.

x=38

Solve for angle M.

3(38)-16=98

Answer:

x = y

Step-by-step explanation:

7x = 5y + 2x

Subtract 2x from both sides

5x = 5y

x = y

Answer:

-5x - 6x ≤ 8 - 8x - x

-11x ≤ 8 - 9x

-2x ≤ 8

x ≥ -4

Answer:

y=-2x-3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-3))/(1-0)

m=(-5+3)/1

m=-2/1

m=-2

y-y1=m(x-x1)

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

y+3=-2(x)

y+3=-2x

y=-2x-3

Answer:

$3.70

Step-by-step explanation:

divide 1.48 by 4 = .37

multiply by 10

Answer:

One notebook costs $2.50

Step-by-step explanation:

The cost of notebook is $2.50.

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions.

Given:

let the number of pen be x

let the number of notebooks be y.

So, the equation can be written as

3x + 5y= 13.75....(1)

x - y = 1.25

3x- 3y = 3.75 ....(2)

Solving above 2 equation we get

8y = 10

y= 10/8

y= 5/4

y= 1.25

and, x= 1.25+1.25=2.50

Hence, the notebook costs $2.50.

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The required equations that represent the sum and difference of numbers are: x + y = 77 and [tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]

Solution:

Let the two consecutive numbers be "x" and "y"

Where "x" is the smaller number and "y" is the larger number

Given that sum of two consecutive numbers is 77

Therefore we frame a equation as:

x + y = 77

Also given that The difference of half of the smaller number and one-third of the larger number is 6

Therefore we frame a equation as:

half of the smaller number - one-third of the larger number = 6

half of x - one third of y = 6

[tex]\frac{1}{2}x - \frac{1}{3}y = 6\\\\\frac{x}{2} - \frac{y}{3} = 6[/tex]

Therefore the required equations that represent the sum and difference of numbers are:

x + y = 77

[tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]

Answer: (x + 1 )(x+5)

Step-by-step explanation:

Given :

[tex]x^{2}[/tex] + 6x + 5

Compare with the general quadratic equation:

a[tex]x^{2}[/tex] + bx + c

To factorize , you are  to find two numbers that multiply to give ac , and add to give b.

After which you will re - write the middle number with those numbers.

From the given question , ac = 5[tex]x^{2}[/tex] , we are to find two numbers that will multiply to give 5[tex]x^{2}[/tex] and add to give 6x.

The numbers are 1x and 5x.

We will then replace the middle number by the two numbers , that is

[tex]x^{2}[/tex] + x + 5x + 5

x(x+1) +5( x +1)

(x+1)(x+5)

Answer:

15 girls

Step-by-step explanation:

Answer:

15 girls

Explanation:

You first set up the ratio of boys to girls (4/5) as a fraction. Then you look. You make another fraction next to the 4/5 fraction to figure out how many girl are in the class.  You know that you are trying figure out how many GIRLS are in the classroom if their are 12 boys. So on the other fraction the DENOMONATER is going to have an x on it because you don't know how many girls their are and girls (according to the fraction boys to girls (4/5) are on the bottom. So, now you cross multiply. 12x5 is 60 and 60/4 is 15. Therefore, you get 15 as your answer.

Ok, so 27 is >, 30 is <, 13/5 is 2 3/5, 5 2/7 is 37/7, 9 3/4 is 39/4, and 23/3 is      7 2/3

I did not do #27 and #30, just did the table.

Answer:

x=4.8

Step-by-step explanation:

5x+3=27

   -3     -3

5x=24

/5  /5

x = 4.8

Answer:

Sam has 27 pencils. He has 3 loose pencils and 5 packs of pencils with x pencils in each pack.

Step-by-step explanation:

14 bags of fertilizer are needed

Solution:

Given that You need to buy fertilizer for a circular flower bed with a diameter

of 13 feet

Diameter = 13 feet

[tex]radius = \frac{diameter}{2}[/tex]

[tex]radius = \frac{13}{2} = 6.5[/tex]

Therefore radius of circular flower bed is 6.5 feet

Area of circle is given as:

[tex]\text{ area of circle } = \pi r^2[/tex]

Substitute r = 6.5

[tex]\text{ area of circle } = 3.14 \times 6.5^2 = 132.665[/tex]

Given that one bag will fertilize 10 square feet

1 bag = 10 square feet

Then number of bags needed are:

[tex]\rightarrow \frac{132.665}{10} = 13.2665[/tex]

Thus approximately 14 bags of fertilizer are needed

Answer:

3/10, 3:10

Step-by-step explanation:

3 to 10 : 3/10, 3:10

The largest possible height of the plant is 1 inch, the smallest possible height is 0 inches, and the largest possible percent error in Jada's measurement is -25%.

To find the largest possible height of the plant, we need to round up the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 1 inch. Therefore, the largest the actual height of the plant could be is 1 inch.

To find the smallest possible height of the plant, we need to round down the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 0 inches. Therefore, the smallest the actual height of the plant could be is 0 inches.

The percent error in Jada's measurement can be found by calculating the difference between the approximate measurement and the actual measurement, dividing it by the actual measurement, and then multiplying by 100. In this case, the approximate measurement is 3/4 inch and the actual measurement could be between 0 and 1 inch. So, the largest possible percent error would be (3/4 - 1) / 1 * 100 = -25%, and the smallest possible percent error would be (3/4 - 0) / 1 * 100 = 75%.

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Answer:

They are supplementary

Step-by-step explanation:

Two Angles are Supplementary when they add up to 180 degrees.