If x < 5, then which of the following must be true?

-x < -5
-x > -5
-x < 5
-x > 5

To create an equation for a graph where y depends on x, identify the type of relationship presented by the graph. For a linear relationship, use the formula y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Determine the slope using two points on the line and then solve for 'b' using the slope and one of the points.

Creating an equation for a graph where y depends on x is a common task in algebra. It's essential to identify the type of relation presented by the graph, which may include linear, quadratic, exponential, or logarithmic relationships. Let's assume, for example, that the graph represents a simple linear relationship.

In this case, you would use the formula for a line, which is y = mx + b. 'm' represents the slope of the line, and 'b' stands for the y-intercept.

To find the slope 'm', you can choose two points on the line and calculate the change in y divided by the change in x. Once the slope is determined, plug one of the points' coordinates into the equation and solve for 'b', the y-intercept. This will give you the equation for the line.

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The equation for that graph, where y depends on x can be expressed in slope-intercept form as: y = -2x + 6.

To find the equation of the line, you can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. First, find the slope (m) using any two given points on the graph, i.e. (0, 6) and (4, -2):

[tex]\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} = \frac{{-2 - 6}}{{4 - 0}} = \frac{{-8}}{{4}} = -2 \][/tex]

Now, substitute one of the points (e.g., (0, 6)) and the slope into the equation:

y = mx + b

6 = -2(0) + b

b = 6

So, the equation of the line is y = -2x + 6.

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Supplementary angles, totaling 180 degrees, are demonstrated by ∠2 and ∠4, as well as ∠3 and ∠5, in the context of lines b and c, as depicted in the diagram.

Supplementary angles are pairs of angles whose measures add up to 180 degrees. In the context of lines b and c, the identified supplementary angle pairs are ∠2 and ∠4, as well as ∠3 and ∠5. These pairs satisfy the condition that the sum of their measures equals 180 degrees. Visually, this relationship is evident in the provided diagram, reinforcing the concept of supplementary angles. Specifically, the equation ∠2 + ∠4 = 180° and ∠3 + ∠5 = 180° illustrates the supplementary nature of these angle pairs. Understanding supplementary angles is crucial in geometry, as it provides a fundamental principle for evaluating the relationships between angles formed by intersecting lines. In the given scenario, the angles ∠2, ∠4, ∠3, and ∠5 exhibit supplementary properties, emphasizing their collective role in forming a straight line and contributing to the overall understanding of geometric configurations.

The correct question maybe :-

Given in the attachment

Answer:

D

Step-by-step explanation:

The following steps describes the correct order of steps for constructinf an angle bisector of angle DEF.

(1). Draw a circle with a radius less then the arms of angle.

(2). Draw a line from point of intersections of arc (circle) and arms of the angle.

(3). Draw two circles with radius = distance between point of intersection of circle and arms of angle, center taken as point of intersection of circle and arms. than draw an equilateral triangle.

(4). Use a straightedge to connect the vertex of angle and the right  most vertex of the equilateral triangle.

Hence option D is correct.

Answer:

86

Step-by-step explanation:

Angles in a triangle add up to 180 degrees

add 74 with 20 to get 94

subtract 94 from 180 to get the value of x

180-94=86

The value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.

A triangle is a closed 2-dimensional polygon with three angles and three straight sides.

According to the Triangle Angle Sum Theorem, the sum of the three interior angles in a triangle is always 180°.

Hence,

angleA + angleB + angleC = 180°

Given the data in the question;

We substitute our given values into the expression above.

angleA + angleB + angleC = 180°

74° + 20° + x = 180°

94° + x = 180°

x = 180° - 94°

x = 86°

Hence, the value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.

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Answer:

y =8

Step-by-step explanation:

[tex]y^{2} = 16*4[/tex]

Answer:

(-2,-5)

Step-by-step explanation:

y=1/2x-4 and y=-2x-9

Just substitute one into the other and then solve for x. Then go back to get y.

1/2x-4=-2x-9

Add 4 on both sides

1/2x =-2x-5

Add 2x on both sides

2.5x=-5

Divide both sides by 2.5

x=-5/(2.5)=-2

Plug into y=-2x-9 to find y.

y=-2(-2)-9=4-9=-5.

Answer (-2,-5)

Answer:

A)  (-2,-5)

Step-by-step explanation:

Answer:

the answer is D.126

Step-by-step explanation:

Use the formula A=2(wl+hl+hw)

For this case we have to:

Wednesday:

[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]

Saturday:

He ran [tex]2 \frac {1} {4}[/tex] times more than on Wednesday, that is:

[tex]\frac {20} {3} + \frac {4 * 2 + 1} {4} =\\\frac {20} {3} + \frac {9} {4} =\\\frac {20 * 4 + 9 * 3} {12} =\\\frac {107} {12} =\\8 \frac {11} {12}[/tex]

Thus, on Saturday, he ran [tex]8 \frac {11} {12}[/tex]miles

Answer:

[tex]8 \frac {11} {12}[/tex]

the probability is 1/18

Answer:

C) r3 < r2 < r1

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

ANSWER

[tex]W''(2, - 3)[/tex]

EXPLANATION

The given point bas coordinates

W(-2,3).

The mapping for reflection over the x-axis is

[tex](x,y)\to(x, - y)[/tex]

[tex]W(-2,3)\to \: W'(-2, - 3)[/tex]

This point W'(-2,-3) is then reflected over the y-axis.

The mapping for reflection over the y-axis is

[tex](x,y)\to (-x, y)[/tex]

[tex]W'(-2,-3)\to \: W''(2, - 3)[/tex]

Point W is initially transformed by reflecting it over the x-axis, which inverses the sign of the y-coordinate, followed by a reflection over the y-axis, which inverses the sign of the x-coordinate. The final position of point W" on the coordinate plane is therefore (2, -3).

To answer this mathematics question involving coordinate geometry and reflections, one must understand how reflections in the x-axis and y-axis affect the coordinates of a point.

A reflection of a point across the x-axis changes the sign of the y-coordinate, and a reflection across the y-axis changes the sign of the x-coordinate. Thus, if we start with point W at (-2,3), a reflection over the x-axis to create point W' changes the y-coordinate's sign, yielding point W' at (-2,-3). Then, reflecting W' over the y-axis changes the x-coordinate's sign, yielding our final point W" at (2,-3).

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The desired equation relating the variables is;

Also, a large bag of dog food that contains 210 cups of food will last 140 days according to the equation.

According to the question;

The small dog gets fed 3/4 cups of dog food twice a day.

In essence; The dog is fed twice a day with 3/4 cups of dog food each time.

Therefore; The dog gets fed 2× (3/4) cups of dog food per day

a) The equation is therefore;

b) To determine the number of days a large bag of dog food will last if it contains 210 cups of food;

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Answer:

  a = 20; b = 2√101

Step-by-step explanation:

The triangle at upper left and the one at lower right are similar. Ratios of corresponding sides are equal, so ...

  200/a = a/2

  400 = a^2

  √400 = 20 = a

Then, by the Pythagorean theorem, the value of b can be found:

  b = √(a^2 + 2^2) = √(400 +4) = √4·√101

  b = 2√101

The Box 3 on an electronic W-2 form represents the total wages subject to Social Security tax. To calculate it, look for the 'Social Security wages' value on the form and determine if it exceeds the annual limit set by the Social Security tax.

The Box 3 on an electronic W-2 form represents the total wages that are subject to the Social Security tax. To calculate the amount in Box 3, you can look for the value labeled 'Social Security wages' or 'SS wages' on the form. This value includes all taxable wages and tips that are subject to Social Security taxes, up to a certain limit.

For the year 2020, the Social Security tax is only applied to the first $137,700 of wages. If the 'Social Security wages' value provided on the form is higher than this limit, you should use the limit as the amount in Box 3. If the value is lower than the limit, then the 'Social Security wages' value itself should be used as the amount in Box 3.

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There are two options of x. You have both of them in picture 1.

Answer:

Step-by-step explanation:

x² - 4x +2=0

(x² - 4x +4) - 4+2=0

(x - 2)²= 2

x - 2 = √2   or x- 2 = -√2

x=2+√2 or x=2-√2

note : same solution :Magdaloskotova Beginner

(4+2√2)/2   = 2(2+√2)/2 = 2+√2

(4-2√2)/2   = 2(2-√2)/2 = 2-√2

ANSWER

Phase shift = right 30°, period = 60°

EXPLANATION

See attachment.

Answer:

D

Step-by-step explanation:

The equation given gives y in terms of x, where y is Shaun's savings and x is the number of months.

We want to know the amount he will save in 25 months, so we can plug in x = 25 into the equation and get a value of y, that is the amount he will save. So:

[tex]y = 6x^2 + 75x+200\\y = 6(25)^2 + 75(25)+200\\y=5825[/tex]

D is the correct answer.

Answer:

0.382

0.4

option (a)

Step-by-step explanation:

Formula to calculate probability

a)

probability = number of times event occur  / total number of trials

Experimental probability of landing on white = 191/500 = 0.382

b)

probability = favourable outcome / total outcome

Theoretical probability of landing on white = 2/5 = 0.4

c)

As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.

The student must calculate frequencies, relative frequencies, and probabilities based on the results from spinning a dial. The frequencies are the counts of outcomes, relative frequencies are these counts divided by total spins, and probabilities are based on the assumption of a fair spinner.

The question is about filling in a table with the results from spinning a dial 500 times. This tasks involves calculating frequencies, relative frequencies, and probabilities which are fundamental concepts in probability and statistics. Since we do not have the actual results, I will explain the process of completing the table:

If an outcome occurred 100 times in 500 spins, the frequency is 100. To calculate the relative frequency, divide 100 by 500, which equals 0.2. Round this to the nearest thousandth to get 0.200.

Remember to round all your final calculated values appropriately as per the instructions given in the question.

Answer:

well since there are infinite numbers the probability is hard to solve. is there like a:

what is the probability of selecting a number that is a multiple of 15 in a hat that has paper with numbers from 1- 100

kind of thing?

Step-by-step explanation:

Graphing is overkill... Let [tex]x=0[/tex]. Then [tex]\sec0=1[/tex], while [tex]\tan0=0[/tex]. But [tex]1+1=2\neq0[/tex], so this is not an identity.

Answer:

It is not an identity

Step-by-step explanation:

If you graphic the two equations (left and right) separately, if they are an identity, they will be the same graphic, which is not true in this case.

Another way in order to know if an equation is an identity, you can replace some values ​​at x, for example 2 values:

X=30

X=60

And now we substitute in the equation, like this:

[tex]1+sec^2(30)=tan^2(30)[/tex]

2,33=0,33 this is not equal on both sides

[tex]1+sec^2(60)=tan^2(60)[/tex]

5=3 this is not equal on both sides

And if the results for each number x are the same on both sides of the equation, it is an identity. In this case they are different.

Answer:

The volume of the ball is 256 cm³

Step-by-step explanation:

we know that

The density is equal to the ratio of the mass by the volume

D=m/V

Solve for V

The volume is equal to the ratio of the mass by the density

V=m/D

In this problem we have

m=128 g

D=0.5 g/cm³

substitute

V=128/0.5=256 cm³

Answer:

2

Step-by-step explanation:

Dividing 18 yds into 34 yds yields 2; Adrianna will have 2 pieces 18 yds long, with 8 yds left over.

Answer:

because women are still commonly looked down upon, and men more superior. It is not fair due to the fact that women get paid less and men get hired for more jobs.

Step-by-step explanation:

[tex]S=15\times15+4(7.5\times15)=\boxed{675}[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

Given:

Length of the base rectangle = 15 unit

Width of the  base rectangle = 15 unit

Height of triangle on the side of pyramid = 15 unit

Length of the base of the triangle = 15 unit

Surface are of the rectangular pyramid = Area of Base + 4 × Area of triangle on side.

Area of base = length × width = 15 × 15 = 225 unit²

Area of the triangle = 1/2 × base  × height = 1/2 × 15 × 15 = 112.5 unit²

Surface Area = 225 + 4 × 112.5  = 225 + 450 = 675 unit²

Therefore, Option C is correct.

Answer:

Answer choice B

Step-by-step explanation:

Answer:

The height of the trough is about 1.5 ft

Step-by-step explanation:

If each cubic foot of water contains about 7.5 gallons.

Then; 315 gallons is about [tex]\frac{315}{7.5}=42ft^3[/tex]

Let h be the height of the trough, then

[tex]7\times 4\times h=42[/tex]

This implies that;

[tex]28h=42[/tex]

Divide both sides by 28 to get:

[tex]h=\frac{42}{28}[/tex]

[tex]\therefore h=1.5[/tex]

The height of the trough is about 1.5 ft

the height of the trough is 1.5 feet.

To solve for the height of the trough that holds 315 gallons, we need to use the information that 1 cubic foot of water contains about 7.5 gallons. Since the trough is 7 feet long and 4 feet wide, we can first calculate the volume in cubic feet by dividing the volume in gallons by the gallon-to-cubic-feet conversion factor (315 gallons \/ 7.5 gallons/cubic foot). Then, we use this volume to find the height by dividing the volume by the product of the length and the width of the trough.

Here is a step-by-step approach:

Now, let's calculate:

Therefore, the height of the trough is 1.5 feet.

ANSWER

The correct choice is D.

EXPLANATION

See the attachment for explanation;

Answer:

Option C.

Step-by-step explanation:

Option C. A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.

The correct option is option C.

A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.

The parabola is symmetric about its axis.

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ANSWER

[tex] \sum_{n=1} ^{32} (4n + 1) = 2144[/tex]

EXPLANATION

The given series is

[tex] \sum_{n=1} ^{32} (4n + 1) [/tex]

The first term in this series is

[tex]a_1=4(1) + 1 = 5[/tex]

The last term is

[tex]l = 4(32) + 1 = 129[/tex]

The sum of the first n terms is

[tex]S_n= \frac{n}{2} (a + l)[/tex]

The sum of the first 32 terms is

[tex]S_ {32} = \frac{32}{2} (5 + 129)[/tex]

[tex]S_ {32} =16 \times 134[/tex]

[tex]S_ {32} =2144[/tex]

Therefore,

[tex] \sum_{n=1} ^{32} (4n + 1) = 2144[/tex]

Answer:

Step-by-step explanation:

Left

When a square = a linear, always expand the squared expression.

x^2 - 2x + 1 = 3x - 5                Subtract 3x from both sides

x^2 - 2x - 3x + 1 = -5

x^2 - 5x +1 = - 5                      Add 5 to both sides

x^2 - 5x + 1 + 5 = -5 + 5

x^2 - 5x + 6 = 0

This factors

(x - 2)(x - 3)

So one solution is x = 2 and the other is x = 3

Second from the Left

i = sqrt(-1)

i^2 = - 1

i^4 = (i^2)(i^2)

i^4 = - 1 * -1

i^4 = 1

16(i^4) - 8(i^2) + 4

16(1) - 8(-1) + 4

16 + 8 + 4

28

Second from the Right

This one is rather long. I'll get you the equations, you can solve for a and b. Maybe not as long as I think.

12 = 8a + b

17 = 12a + b         Subtract

-5 = - 4a

a = - 5/-4 = 1.25

12 = 8*1.25 + b

12 = 10 + b

b = 12 - 10

b = 2

Now they want a + b

a + b = 1.25 + 2 = 3.25

Right

One of the ways to do this is to take out the common factor. You could also expand the square and remove the brackets of (2x - 2). Both will give you the same answer. I think expansion might be easier for you to understand, but the common factor method is shorter.

(2x - 2)^2 = 4x^2 - 8x + 4

4x^2 - 8x + 4 - 2x + 2

4x^2 - 10x + 6    The problem is factoring since neither of the first two equations work.

(2x - 2)(2x - 3)     This is correct.

So the answer is D