Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each graph to the inequality it represents.

Drag The Tiles To The Correct Boxes To Complete The Pairs. Not All Tiles Will Be Used.Match Each Graph
Drag The Tiles To The Correct Boxes To Complete The Pairs. Not All Tiles Will Be Used.Match Each Graph
Drag The Tiles To The Correct Boxes To Complete The Pairs. Not All Tiles Will Be Used.Match Each Graph
Drag The Tiles To The Correct Boxes To Complete The Pairs. Not All Tiles Will Be Used.Match Each Graph
Drag The Tiles To The Correct Boxes To Complete The Pairs. Not All Tiles Will Be Used.Match Each Graph

Answers

Answer 1

The graphs and their inequalities are

Graph 1 ⇒ 3x + 4y > 6Graph 2 ⇒ 2x - 7y ≥ 14Graph 3 ⇒ 3x + 4y < 6Graph 4 ⇒ 7x + 2y ≥ 14

How to match the inequalities?

The inequalities are given as:

2x - 7y ≤ 14

7x + 2y ≥ 14

2x - 7y ≥ 14

3x + 4y < 6

4x - 3y > 6

3x + 4y > 6

To represent the inequalities on a graph, we use the following guides:

> uses a dotted line, and the upper parts are shaded< uses a dotted line, and the lower parts are shaded≥ uses a thick line, and the upper parts are shaded≤ uses a thick line, and the lower parts are shaded

Using the above as a guide, we have:

Graph 1 ⇒ 3x + 4y > 6

Graph 2 ⇒ 2x - 7y ≥ 14

Graph 3 ⇒ 3x + 4y < 6

Graph 4 ⇒ 7x + 2y ≥ 14

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Related Questions

Helen got a 7% reduction in the price of a pair jeans that are normally $32. What is the approximate percent in the price?

Answers

A percentage is a way to describe a part of a whole. The approximate percent decrease in the price is 21.87%, thus, the correct option is B.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given the reduction in the price is $7, while the original cost is $32. Therefore, the approximate percent decrease in the price is,

Percentage decrease = 7/32  × 100%

                                     = 21.87%

Hence, the approximate percent decrease in the price is 21.87%, thus, the correct option is B.

The correct question is:

Helen got a $7 reduction in the price of a pair of jeans that are normally $32. What is the approximate percent decrease in the price?

The percent decrease is approximately 15%.

The percent decrease is approximately 21%.

The percent decrease is approximately 43%.

The percent decrease is approximately 78%

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Solve the following proportion by cross multiplying:
( x - 3 ) / 4 = ( 2x + 2 ) / 6

Answers

Answer:

- 13

Step-by-step explanation:

Solving

[tex] \frac{(x - 3)}{4} = \frac{(2x + 2)}{6} \\ \\ cross \: multiplying \\ 6 \times (x - 3) = 4 \times (2x + 2) \\ 6x - 18 = 8x + 8 \\ 6x - 8x = 8 + 18 \\ - 2x = 26 \\ dividing \: bothsides \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{26}{ - 2} \\ x = - 13[/tex]

Solution :

[tex] \implies \: \sf{ \dfrac{x \: - \: 3}{4} \: = \: \dfrac{2x \: + \: 2}{6} } \\ \\ \implies \: \sf{6( x \: - \: 3) \: = \:4(2x \: + \: 2)} \: \\ \\ \implies \: \sf{6 \times ( x \: - \: 3) \: = \: (2x \: + \: 2)}\\ \\ \implies \: \sf{6x \: - \: 18 \: = \:8x \: + \: 8}\\ \\ \implies \sf{6x \: - \: 8x \: = \:18\: + \: 8}\\ \\ \implies \sf{ - 2x \: = \:18\: + \: 8}\\ \\ \implies \sf{ - 2x \: = \: 26}\\ \\ \implies \sf{ - x \: = \: \dfrac{26}{2} }\\ \\ \implies \sf{ - x \: = \: \cancel{\dfrac{26}{2} }}\\ \\ \implies \sf{ - x \: = \: 13}\\ \\ \implies \red{\bf{ x \: = \: - 13}}[/tex]

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.

What is an equation?

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

Given the inequality:

–3(2x – 5) < 5(2 – x)

= -6x + 15 < 10 - 5x

= -x < -5

= x > 5

The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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Answer: The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right. What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.Given the inequality:–3(2x – 5) < 5(2 – x)= -6x + 15 < 10 - 5x= -x < -5= x > 5The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Step-by-step explanation:

Find an equation for the line that passes through the points (6,1) and (-4,3)

Answers

Answer: $$y=-2/3x+2$$

Explanation:  Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.

A membership committee of three is formed from four eligible members. let the eligible members be represented by a, b, c, and d. the possible outcomes include s = {abc, abd, acd, bcd}. which statements about the situation are true? select three options.

Answers

The correct statements are:

There are four ways to choose the committee.

There are three ways to form the committee if person D must be on it.

If persons B and C must be on the committee, there are two ways to form the committee.

It is given that:

A membership committee of three is formed from four eligible members.

1)

There are four ways to choose the committee.

This statement is true.

since we have to choose 3 members out of the 4 members so we can use the method of combination.

2)

There are three ways to form the committee if person D must be on it.

This statement is also true.

since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.

3)

If seven members are eligible next year, then there will be fewer combinations.

This statement is wrong.

Since we have to choose 3 members out of 7 members so the number of possible combinations will be:

i.e. there are 35 combinations possible.

4)

If persons B and C must be on the committee, there are two ways to form the committee.

if B and C have to be in the committee then we have to choose just one person out of the two people left.

Hence, the statement is true.

5)

If persons A and C must be on the committee, then there is only one way to form the committee.

If A and C have to be in the committee then as in last option we have to choose any one of the two person left.

so possible number of ways are 2.

Hence, the statement is false.

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How do the areas of the parallelograms compare? the area of parallelogram abcd is 4 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is 2 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is equal to the area of parallelogram efgh. the area of parallelogram abcd is 2 square units less than the area of parallelogram efgh.

Answers

option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.

What is parallelogram?

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The area of the parallelogram is:

A = b×h

Here b is the base length and h is the height

In ABCD parallelogram:

A = (3)×(3)

A = 9 square units

EFGH parallelogram:

a = (3)×(3)

A = 9  square units

The area of parallelogram ABCD is equal to the area of parallelogram EFGH.

Thus, option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.

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Please help me solve this.

Answers

Answer:

I think that is a FORMULA.

it can't be solved if we don't know the values of atleast one of the x and y.

Hope this helps.

Good luck ✅.

Urgent! I really need help

Answers

Answer:

  58.0°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides of a right triangle and trig functions of the acute angles.

Application

Here, the hypotenuse of the triangle is given (17 cm), as is the side adjacent to angle x (9 cm). This suggests using the relation ...

  Cos = Adjacent/Hypotenuse

  cos(x) = (9 cm)/(17 cm) = 9/17

The angle for this cosine value is found using the inverse trig function.

  x = arccos(9/17)

  x ≈ 58.034°

Rounded to the nearest tenth, the angle is ...

  x = 58.0°

__

Additional comment

Of course, the angle y is the complement of this:

  y = 32.0°

Which set of systems of equations represents the solution to the graph?

an upward opening parabola decreasing from negative 3 comma 4 to a minimum at negative one comma zero and then increasing to 1 comma 4 and a downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3

Answers

The correct graph for the given sets of equation is given attached below.
Equation no 2 gives the perfect solution to the graph.

What is a parabola?

A parabola, is cross section cut out of the cone and represented by an equation [tex]Y=4ax^2[/tex]

Clearly, by property of the parabola, the curve of parabola should symmetric to its axis. From this property set of Equation (2) i.e. downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3 Holds the property of the parabola

Thus, the required solution for the sets of equation (2) is given in the attachment.

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Select the correct answer from each drop-down menu.


The slope of the line in the graph is [ ]. The y-intercept is [ ]. The equation of the line is y= [ ], and x is [ ]

BOX 1:
A. 2
B. 3
C. -2
D. -3

BOX 2:
A. -3
B. 3
C. 4
D. -4

BOX 3:
A. 2
B. 3
C. -2
D. -3

BOX 4:
A. -3
B. +3
C. +4
D. -4

Answers

For the linear function in the graph, we have that:

The slope is of 3.The y-intercept is of -4.The equation of the line is: y = 3x - 4.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line goes through point (0,-4), hence:

The y-intercept is of -4.

The function also goes through point (2,2), hence the slope is:

m = (2 - (-4))/(2 - 0) = 6/2 = 3.

Then, the equation of the line is:

y = 3x - 4.

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what is the slope of this line?
y-9=1/5(x-2)

Answers

The slope of the line is 1/5

Answer: D) 1/5

Step-by-step explanation:

Format for point-slope form:  y-y₁=m(x-x₁)

x1, y1 is a point on the line

m is the slope

So in this equation, m = 1/5

so, the slope is 1/5

hope this helps!

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.

Answers

Considering the given equation of the circle, the true statements are given as follows:

The radius of the circle is of 3 units.The center of the circle lies on the x-axis.The circle has the same radius as the circle with equation x² + y² = 9.

What is the equation of a circle?

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation given is:

x2 + y² - 2x - 8 = 0.

Completing the squares, the equation is given as follows:

(x - 1)² + y² = 8 + 1

(x - 1)² + y² = 9.

Researching the problem on the internet, the true statements are:

The radius of the circle is of 3 units.The center of the circle lies on the x-axis([tex]y_0 = 0[/tex]).The circle has the same radius as the circle with equation x² + y² = 9.

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Please answer with everything needed i appreciate everyones help:)

Answers

Answer:

Hey there....

Step-by-step explanation:5

This is ur answer....

Expression : -x + 5

Working :-

x = Unknown number

x + 5 = Sum of the number and Five

x + 5 - 2x = Previous sum decreased by the the twice of the unknown number.

-x + 5 = combine the terms

Hope it helps!

Brainliest pls!

Have a good day!^^

Step-by-step explanation:

x is the number.

(x + 5) - 2x : the sum of the number and 5 decreased by twice the number.

or simplified without the brackets

x + 5 - 2x = 5 - x

it is not clear if you need the general expression showing both conditions (the first up there), or the then simplified result

5 - x

What is the radius of a hemisphere with a volume of 4635 ft 3 , 4635 ft 3 , to the nearest tenth of a foot?

Answers

Step-by-step explanation:

Hemisphere Formulas in terms of radius r:

V = (2/3)πr.

Hereof, What is the radius of a hemisphere? As latter is 4πr2 , curved surface area of a hemisphere of radius r is 2πr2 . and hence total surface area of hemisphere is 2πr2+πr2=3πr2 . Hence, radius of hemisphere is 4 cm.

Mass (kg)
45
61
57
78
68

Length (cm)
112
138
133
180
175

Which of the options is the most appropiate to suow data in the table?

Pictogram
Pie chart
Bar chart
Line Graph
Scatter Graph​

Answers

Answer:

Line or scatter graph.

Step-by-step explanation:

I prefer line, although some of the points deviate a bit.  But the line shows a definite relationship between mass and length.

See attached graph.

if y= 2x-3 were chnged to y=2x+5 how would the graph of the new function compare with the original

Answers

Answer: +8
I think that is what you asked

The new function moved up by 8 units from the original.

The only difference in the functions is the y-intercept. The slope remained the same ([tex]2[/tex]), but the y-intercept went up by 8, meaning the function moved up 8 units.

See the attached image for a graph of both functions. The new function is the solid blue line.

Which set of data does not have a mode?

(A) 1, 2, 5, 6, 8
(B) 1, 3, 5, 5, 6
(D) 1, 1, 1, 2, 2
(C) 1, 5, 5, 5, 5

Answers

A, because it does not repeat any numbers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\textbf{Which set of data does not have a mode?}[/tex]

[tex]\huge\textbf{The choices that you have provided:}[/tex]

[tex]\textbf{(A) 1, 2, 5, 6, 8}[/tex]

[tex]\textbf{(B) 1, 3, 5, 5, 6}[/tex]

[tex]\textbf{(C) 1, 5, 5, 5, 5}[/tex]

[tex]\textbf{(D) 1, 1, 1, 2, 2}[/tex]

[tex]\huge\textbf{Okay, so let's get the understanding}\\\\\huge\textbf{of the word mode is:}[/tex]

[tex]\large\textbf{The best way to understand what \boxed{\bf mode} it is known as}\\\\\large\textbf{the number you see MORE THAN once. }[/tex]

[tex]\huge\textbf{Now that we got that information out of}\\\\\huge\textbf{the way, we can answer your question by}\\\\\huge\textbf{doing process of elimination.}[/tex]

[tex]\huge\textsf{Option A.}[/tex]

[tex]\textbf{1, 2, 5, 6, 8}[/tex]

[tex]\large\textbf{None of the numbers r.e.p.e.a.t so this cann be your}\\\\\large\textbf{answer.}[/tex]

[tex]\huge\textsf{Option B.}[/tex]

[tex]\textbf{ 1, 3, 5, 5, 6}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{3}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}\\\large\textbf{6}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}[/tex]

[tex]\large\textbf{Just because majority of your numbers r.e.p.e.a.t.e.d}\\\\\large\textbf{once that doesn't mean it does have a mode rarely.}\\\\\\\\\\\large\textbf{So, Option B. isn't your answer because it has a mode.}[/tex]

[tex]\huge\textsf{Option C.}[/tex]

[tex]\textbf{ 1, 5, 5, 5, 5}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d four times}[/tex]

[tex]\large\textbf{Option C. isn't your answer because it has a mode.}[/tex]

[tex]\huge\textsf{Option D. }[/tex]

[tex]\textbf{1, 1, 1, 2, 2}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d three times}\\\large\textbf{2}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}[/tex]

[tex]\large\textbf{Just because we have like two modes, it still doesn't mean}\\\large\textbf{you don't have a mode. It 's kind of cool that you have more}\\\large\textbf{than once mode.}[/tex]

[tex]\large\textbf{Option D. isn't your answer because it has a mode though}\\\large\textbf{because it has like 2 sets of modes.}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{Option\ A. 1, 2, 5, 6, 8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Find the value of x.

Answers

The value of 'x' is 25.00

How to determine the value of x

The given figure is a triangle

To find the value of 'x', first find the value of the other side

Using

Hypotenuse square = opposite square + adjacent square

16^2 = 10^2 + y^2

256 = 100 + y^2

Make y subject of formula

y = √ 256- 100

y = √ 156

y= 12. 49

To find 'x'

28^2 = x^2 + 12.59^2

784 = x^2 + 158. 51

x^2 = 784 - 158. 51

x^2 = 625. 49

x =√ 625. 49

x = 25.00

Thus, the value of 'x' is 25.00

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I'm not very good at solving these problems

Answers

1 atom of C has a mass of 12 amu (atomic mass unit).

1 atom of O has a mass of 16 amu.

1 molecule of CO₂ thus has a mass of 12 + 2×16 = 44 amu.

C thus makes up 12/44 ≈ 0.27 of the total mass of CO₂, while O makes up the remaining 32/44 ≈ 0.73.

Then in a 2 kg = 2000 g block of CO₂, carbon makes up about 12/44 × 2000 ≈ 545 g.

The point P(x, y) is on the terminal ray of angle Theta. If Theta is between Pi radians and StartFraction 3 pi Over 2 EndFraction radians and = Negative five-halves, what are the coordinates of P(x, y)?
P(Negative StartRoot 21 EndRoot, –2)
P (StartRoot 21 EndRoot, –2)
P(–2, StartRoot 21 EndRoot)
P(–2, Negative StartRoot 21 EndRoot)

Answers

The coordinates of P(x, y) is: A. P(Negative StartRoot 21 EndRoot, –2)

Coordinates of P(x, y)

Given:

Radians=3π/2

theta=-5/2

Hence:

Hypotenuse = - 5

Altitude = 2

Using  Pythagorean theorem

Hypotenuse² =  Altitude² + Base²

-5²= 2²  + Base²

25 ² - 4 ² = Base²

Base = √21

Thus P(x,y) :

= P(-√21 : -2)

Therefore the correct option is A.

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Duane rode his bike at 14 miles per hour for 3 hours, then put the bike down and began walking at miles 2 per hour. Elizabeth started jogging at 5 miles per hour along the same path at the same time that Duane started biking. When she reached the bike, she began riding it at 10 miles per hour. How many hours will it have been since they started when Elizabeth catches up to Duane

Answers

Elizabeth will take 9 hours and 45 minutes to catch up with Duane using the given speed-distance-time values.

The speed-distance-time relations are:

Speed = Distance/Time, Distance = Speed*Time, and Time = Distance/Speed.

The distance traveled by Duane on the bike at 14 miles per hour for 3 hours = 14*3 miles = 42 miles.

The time that Elizabeth takes to cover 42 miles jogging at 5 miles per hour = 42/5 hours = 8.4 hours.

The distance traveled by Duane in the extra time which Elizabeth took to reach his bike (8.4 - 3 = 5.4 hours) walking at 2 miles per hour = 2*5.4 = 10.8 miles.

Now, the distance between Elizabeth and Duane is 10.8 miles, before Elizabeth starts riding the bike.

Keeping the distance constant, we calculate the relative speed to calculate the time to cover this distance.

Relative speed = Elizabeth's speed - Duane's speed {As Elizabeth is moving towards Duane, that is, covering the distance but Duane is moving away from Elizabeth, that is, increasing the distance}.

or, Relative speed = 10 - 2 = 8 miles per hour.

Time taken to cover the distance = 10.8/8 = 1.35 hours.

Therefore, the total time taken by Elizabeth to catch up with Duane = 8.4 + 1.35 hours = 9.75 hours or 9 hours and 45 minutes.

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Harry decided to buy some candy bars that
cost $2.19 each. He also bought a drink for
$3.55. Harry paid a total of $10.12. Write an
equation to find how many candy bars Harry
purchased.

Answers

If its 3.55 for for the drink 3.55 - 10.12 is 6.57 and if each candy bar is 2.19 x 3 is 6.57 so you can get 3 candy bars

Which of the following are solutions to the equation below?
Check all that apply.
9x² - 6x + 1 = 7
☐ A. x = -√7 +1
3
B. X=
=
C. x=
☐ D. x=
= 2√2
2√2
3
☐ E. X=
-√7
3
☐ F. x =
<=
X= √²+1
3
+1
+1

Answers

Step-by-step explanation:

therefore A is the correct answer

20 points. The length of a rectangular room is 4.5 m and it’s width is 9.6 m. Find the area of the room

Answers

Answer:

43.2 m square is ur answer .

Answer:

43.2 m^2

Step-by-step explanation:

The area of a rectangle is the width times the length.

Area = (9.6 m)*(4.5 m)

Area = 43.2 m^2

HELP ASAP
Given: ABCD is a parallelogram.
Prove: A is congruent to FCE.

Answers

Answer:

Step-by-step explanation:

C is equal to A. Because angle FCE is on the other side with C, it has to be equal to A

ABCD is a parallelogram (Given)

As opposite angles of a parallelogram are equal

<A=<BCD--(1)

Also

<BCD=<FCE(Opposite angle)-(2)

From (1) and (2)

<A is congruent to <FCE

A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime is the image of △ A B C △ABCtriangle, A, B, C under a rotation about the origin, ( 0 , 0 ) (0,0)left parenthesis, 0, comma, 0, right parenthesis.

Answers

The angle of rotation of triangle ABC to A'B'C is 105°

How to illustrate the information?

It should be noted that the rotation from ABC to A'B'C is in a clockwise direction.

Point B is also on the x axis and point B' is in the second quadrant.

In this case, the angle that depicts the second quadrant is 105°.

In conclusion, the correct option is D.

The complete question is:

Triangle A’ B’ C’ is the image of A B C under a rotation about the origin, (0,0)

Determine the angle of rotation

A. -105 degrees

B. -75 degrees

C. 75 degrees

D. 105 degrees

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If the side lengths of a polygon are: 4x, 6x, 12, and 18 what is the value of x if the perimeter is 118?

Answers

The value of x for given polynomial is 8.8.

What is Polygon?

The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.

Here, the length of sides of given Polygon are:

    4x, 6x, 12, 18

Perimeter of polygon = 118 units.

We know that,

Perimeter of polygon = Sum of all sides

                             118 = 4x + 6x + 12 + 18

                             118 = 10x + 30

                             118 - 30 = 10x

                               10x = 88

                               x = 88/10

                               x = 8.8

Thus, the value of x for given polygon is 8.8.

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Find the inverse of the function

y = log₂ (x-3)

Answers

h(x)=2^(x-3)

replace h(x) with y:

y=2^(x-3)=(2^x)*(2^-3)=(2^x)/(2^3)=(2^x)/8

y=2^x/8

solve for x:

8y=2^x

log2(8y)=x

Answer:

[tex]f^{-1}(x)=2^x+3[/tex]

Step-by-step explanation:

Given:

[tex]y=\log_2(x-3)[/tex]

To find the inverse of the given function, make x the subject.

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 2^y=x-3[/tex]

Add 3 to both sides:

[tex]\implies x=2^y+3[/tex]

Swap x for [tex]f^{-1}(x)[/tex] and y for x:

[tex]\implies f^{-1}(x)=2^x+3[/tex]

6) Stacie was solving the triangle below. Can you find her mistake?

Answers

Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.

What is triangle?

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

Solution is supposed to be


[tex]tan_ (-1) (28/21) = 53.33[/tex]

Thus,Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.

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una fracion reducicion a su minima expresion en igual a 1/8 . si la suma de sus terminos es 72. hallar la diferencia entre ellos

Answers

La diferencia entre el denominador y el númerador de la fracción es:

64 - 8 = 56.

¿Como encontrar la fracción?

Tendremos una fracción de la forma:

[tex]\frac{a}{b}[/tex]

Tal que:

[tex]\frac{a}{b} = \frac{1}{8}[/tex]

[tex]a + b = 72[/tex]

Eso es un sistema de ecuaciones

Primero, podemos reescribir la primer ecuación como:

[tex]8a = b[/tex]

Ahora podemos reemplazar "b" en la segunda ecuación por "8a", así obtenemos:

[tex]a + 8a = 72\\\\9a = 72\\\\a = 72/9 = 8[/tex]

Ahora podemos obtener el valor de b:

[tex]b = 8a = 8*8 = 64[/tex]

La diferencia entre a y b es:

[tex]b - a = 64 - 8 = 56[/tex]

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