An equilateral triangle has a side length of 1.4x + 2 inches. A regular hexagon has a side length of 0.5x + 2 inches. The perimeters are equal. What is the side length of the triangle? What is the side length of the hexagon? Show your work.

Answers

Answer 1

Answer:

9 inches; 4.5 inches.

Step-by-step explanation:

Given the following data;

Length of sides of the equilateral triangle = 1.4x + 2 inches.

Length of sides of the hexagon = 0.5x + 2 inches.

We know that the perimeter of a hexagon is given by the formula;

P = 6 * length of sides

Substituting into the equation, we have;

P = 6*(0.5x + 2)

P = 3x + 12

Perimeter of an equilateral triangle is given by the formula;

P = 3 * length of sides

Substituting into the equation, we have;

P = 3(1.4x + 2)

P = 4.2x + 6

Since perimeter of hexagon = perimeter of equilateral triangle. Therefore;

3x + 12 = 4.2x + 6

Rearranging the equation, we have;

12 - 6 = 4.2x - 3x

6 = 1.2x

x = 6/1.2

x = 5

I. To find the length of each sides of the equilateral triangle;

Length of a side = 1.4x + 2

Substituting the value of "x" into the equation, we have;

Length of sides = 1.4*(5) + 2

Length of sides = 7 + 2

Length of sides = 9 inches.

II. To find the length of each sides of the hexagon;

Length of sides = 0.5x + 2

Substituting the value of "x" into the equation, we have;

Length of sides = 0.5*(5) + 2

Length of sides = 2.5 + 2

Length of sides = 4.5 inches.

Answer 2

The side length of the equilateral triangle 9 inches.

The side length of the hexagon 4.5 inches.

The side length of the equilateral triangle = 1.4x + 2

So, the perimeter = 3(1.4x + 2) = 4.2x + 6.

The side length of the hexagon = 0.5x + 2

So, the perimeter = 6(0.5x + 2) = 3x + 12.

Given tha the perimeters are equal.

So,

[tex]4.2x+6=3x+12\\4.2x-3x=12-6\\1.2x=6\\x=5[/tex]

Hence,

The side length of the equilateral triangle = 1.4x + 2 = 1.4(5) + 2 = 9

The side length of the hexagon = 0.5x + 2 = 0.5(5) + 2 = 4.5

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The regular price of a pair of sneakers is $80. They are on sale now for $50. What is the percent decrease in the price of sneakers?

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Answer:

62.5% decrease

Step-by-step explanation:

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This is for the first answer and to be honest just use Desmos if you don’t have a graphing calculator

Simplify the expression. (Use the Distributive Property)
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$51.75

Step-by-step explanation:

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Offering Brainliest, a 5 star review, and a like on your answer, Please help.

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Step-by-step explanation:

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(1,1)

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Step-by-step explanation:

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At the Fast-Pack It shipping, the employees can unload 25 trucks in 5 hours. Which of the following is a correct unit rate for this situation? (4 points)

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Answer:

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Step-by-step explanation:

The vertices of a triangle are P(-2, -4), Q(2, -5), and R(-1,-8). Name the vértices of the triangle after reflecting over the x-axis

Answers

Answer:

P(-2,4)

Q(2,5)

R(-1,8)

Step-by-step explanation:

The rule for reflecting points across the x-axis is to keep the x-value the same but "negate" the y-value. So, the points above are your answers.

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Step-by-step explanation:

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A room 9m wide has a span roof which slopes at 34 degrees on one side and 44 degrees on the other. Find the length of the roof slopes, correct to the nearest mm

Answers

Answer:

Slope sides are;

5.07 m and 6.39 m

Step-by-step explanation:

I've attached a drawn diagram showing a triangle representing the roof slopes and I have attached it.

From the image attached, the missing angle is θ.

From sum of angles in a triangle,

θ = 180 - (44 + 34)

θ = 102°

Now, a & b represent the slopes of the roof.

Thus, using law of sines which is that;

a/sin A = b/sin B = c/sin C, we can solve as follows;

a/sin 34 = 9/sin 102

a = (9 × sin 34)/sin 102

a = (9 × 0.5512)/0.9781

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(Identify the type of sampling method used.) A candidate for the senate creates an automated message that calls every third listed phone number and reminds them to vote for him in the upcoming election.

Convenience Sampling
Cluster Sampling
Systematic Sampling
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Answer:

Systematic Sampling

Step-by-step explanation:

Systematic sampling is one of the types of probability sampling method. It is an advanced form of simple random sampling. In this form, from the population of members, sample members are selected randomly. In this random selection, a starting point is fixed. The sample is created when the members are selected from the fixed intervals.  

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Solve and explain (x^2+2xy+y^2)(x+1)

A. x^3 + 2x^2y + x^2 + y^2 + xy^2

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Step-by-step explanation:

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an angle measures 94°. what is the measure of its supplement?

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Step-by-step explanation:

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Find the domain of the vector function. (Enter your answer in interval notation.) r(t) = t − 2 t + 2 i + sin(t)j + ln(36 − t2)k

Answers

Answer:

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

Step-by-step explanation:

The given vector function  can be correctly expressed as:

[tex]r(t) = \dfrac{t-2}{t+2}i + sin \ tj + In(36-t^2) k[/tex]

The domain of the given function can be determined by finding the domain of each respective component.

To start with [tex]\dfrac{t-2}{t+2}[/tex]

Not defined, t = -2

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No restriction on t

The 3rd component of the function is ㏑(36 - t²)

Let recall that natural is defined for +ve numbers,

i.e.

36 - t² > 0

(6 + t) (6 - t) > 0

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The third domain = (-6,6)

Overall;

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

Domain of a function is the set all possible inputs for that function.The domain of the given vector function is,

[tex](-6, -2) \cap (-2,6)[/tex]

What is domain?

Domain of a function is the set all possible inputs for that function.

Given information-

The vector function given in the problem is,

[tex]r(t)=\dfrac{t-1}{t+2} \hat i++sin(t)\hat j+ln(49-t^2)\hat k[/tex]

To find the domain of the above vector function, we need to find the domain of each function of vector quantity.

Lets find the domain of [tex]\hat i[/tex] first which is given by,

[tex]\dfrac{t-2}{t+2}[/tex]

This function is defined at all values except, t equals to -2 as the function is not defined at,

[tex]t=-2[/tex]

Hence the domain of component [tex]\hat i[/tex] is,

[tex](-\infty, -2) \cap (\infty,2)\\[/tex]

Lets find the domain of [tex]\hat j[/tex] first which is given by,

[tex]\sin(t)[/tex]

Two trigonometry function sine and cosine defined for all real number.

This function is defined at all real numbers. Hence the domain of component [tex]\hat j[/tex] is

Lets find the domain of [tex]\hat k[/tex] first which is given by,

[tex]\ln(36-t^2)[/tex]

Set the above argument greater than zero to find where the expression is defined.Thus,

[tex](36-t^2)>0\\(6+t)(6-t)>0[/tex]

Therefore,

The domain of it should be [tex](-6,6)[/tex]

Hence the domain of the given vector function is,

[tex](-6, -2) \cap (-2,6)[/tex]

Learn more about the domain here;

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Write an equation of the line that passes through each pair of points (- 2, - 3), (4, 5)

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Answer:

y= 4/3x -1/3

Step-by-step explanation:

Find slope: y2-y1/x2-x1 = 5-(-3)/4-(-2) = 8/6 = 4/3

Use point slope to find the equation:

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y = 4/3x + 8/3 + (-3)

y = 4/3x + 8/3 - 9/3

y= 4/3x -1/3

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Step-by-step explanation:

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yup

Step-by-step explanation:

2/3 (x - 7) = -2

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Answer: x=4

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

[tex]\frac{2}{3} (x-7)=-2\\[/tex]

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[tex]\frac{2}{3}x=\frac{3}{8}[/tex]

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The slope of a line on the coordinate plane can be calculated using any two points on the line and one outside point.
O True
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Answer:

true i think

Step-by-step explanation:

Yes I believe that it is also true

quiz 4-1 : classifying and solving for sides/angles in triangles gina wilson (all things algebra) URGENT

Answers

Answer:

14.

[tex]x = 11[/tex]  [tex]m<B = 108[/tex]   [tex]m<C= 36[/tex]   [tex]m<D = 36[/tex]

15.

[tex]x = 4[/tex]     [tex]WX = 25[/tex]     [tex]XY = 17[/tex]     [tex]WY = 25[/tex]

Step-by-step explanation:

Solving (14):

[tex]BC = BD[/tex]

[tex]m<B = 13x - 35[/tex]

[tex]m<C = 5x - 19[/tex]

[tex]m<D = 2x + 14[/tex]

First, we solve for x.

Since sides [tex]BC = BD[/tex], then

[tex]m<C = m<D[/tex]

This is so because the theorem of ASA (Angle-Side-Angle)

So, we have:

[tex]5x - 19 = 2x + 14[/tex]

Collect Like Terms

[tex]5x - 2x = 19 + 14[/tex]

[tex]3x = 33[/tex]

Divide both sides by 3

[tex]x = 11[/tex]

Solving for m<B, m<C and m<D.

We simply substitute 11 for x in their respective expressions.

[tex]m<B = 13x - 35[/tex]

[tex]m<B = 13*11 - 35[/tex]

[tex]m<B = 143 - 35[/tex]

[tex]m<B = 108[/tex]

[tex]m<C = 5x - 19[/tex]

[tex]m<C= 5*11 - 19[/tex]

[tex]m<C= 55 - 19[/tex]

[tex]m<C= 36[/tex]

[tex]m<D = 2x + 14[/tex]

[tex]m<D = 2*11 + 14[/tex]

[tex]m<D = 22 + 14[/tex]

[tex]m<D = 36[/tex]

Solving (15):

[tex]<X = <Y[/tex]

[tex]WX = 9x - 11[/tex]

[tex]XY = 4x + 1[/tex]

[tex]WY = 7x - 3[/tex]

First, we solve for x.

Since [tex]<X = <Y[/tex], then

[tex]WX = WY[/tex]

This is so because the theorem of SAS (Side-Angle-Side)

So, we have:

[tex]9x - 11 = 7x - 3[/tex]

Collect Like Terms

[tex]9x - 7x = 11-3[/tex]

[tex]2x = 8[/tex]

Divide both sides by 2

[tex]x = 4[/tex]

Solving for WX, WY and XY

We simply substitute 4 for x in their respective expressions.

[tex]WX = 9x - 11[/tex]

[tex]WX = 9 * 4 - 11[/tex]

[tex]WX = 36 - 11[/tex]

[tex]WX = 25[/tex]

[tex]XY = 4x + 1[/tex]

[tex]XY = 4 * 4 + 1[/tex]

[tex]XY = 16 + 1[/tex]

[tex]XY = 17[/tex]

[tex]WY = 7x - 3[/tex]

[tex]WY = 7 * 4 - 3[/tex]

[tex]WY = 28 - 3[/tex]

[tex]WY = 25[/tex]

Anyone know- I need help.

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Answer: 5on x axis 2 on the y axis

Answer:

The answer would be (5,2)

:D Have a Great Day :D

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Answer:

148 i thk i did 16x-12

Step-by-step explanation:

Graph y=-3x+4
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Answer:

(-2,10)

(-1,7)

(0,4)

(1,1)

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Step-by-step explanation:

Answer:

your anwer is x=-1/3y+4/3

Step-by-step explanation:

John has 8 coins, all of which are quarters and nickels. In all, they're worth $1.00. How many of each kind of coin does John have?

Answers

Answer:

you will need 3 quarters and 5 nickel  

Step-by-step explanation:

3 quarters is 75     and 5 nickels is 25 =1.00

Liza and Kelly rode their bikes everyday for five days. They each rode the same distance everyday. Lisa rode 60 miles in all and Kelly rode 25 miles in all. How many more miles per day did Lisa ride than Kelly?​

Answers

Answer:

60/5=12  25/5=5   7 more miles a day

Step-by-step explanation:

plzz mark brainiest

Rewrite in simpliest terms-

−0.2(3p−0.9)+0.4(−0.9p−5)

Answers

Answer:

-0.96p - 1.82

Step-by-step explanation:

There are 40 boys in 6th grade. The number of girls in 6th grade is 30. Carly says that means the ratio of the number of boys in 6th grade to the number of girls in 6th grade is 4:7. Is Carly correct? If not, what is the correct answer?

Answers

Answer:

Carly is wrong. The correct answer is 4:3

Step-by-step explanation:

40/10=4

30/10=3

Answer:

Carlie is wrong

Step-by-step explanation:

The correct answer is 4:3

Can some please help me! No one has helped me out yet, please do this is you can

Answers

Answer:

Please check the explanation below.

Step-by-step explanation:

We know that a binary relation between two sets is termed as a function which associates every element of the first set to exactly one element of the second set.

In other words, in order for relation to be a function, we must make sure there must be no repetition of 'x' coordinate values, as it would violate the fundamental definition of a function.

A) (2, 5), (5, 7), (7, 9)

Here, the x-coordinates are: 2, 5, and 7

At x = 2, y = 5

At x = 5, y = 7

At x = 7, y = 9

As there is no repetition of x-coordinates.

Thus, the coordinate pairs (2, 5), (5, 7), (7, 9) represent the function.

B) (2, 3), (1, 4), (2, 8),(0, 1)

Here, the x-coordinates are: 2, 1, 2 and 0

At x = 2, y = 3

At x = 1, y = 4

At x = 2, y = 8

At x = 0, y = 1

Please observe that the x-coordinate values i.e. x=2 are repeated.

Thus, the coordinate pairs (2, 3), (1, 4), (2, 8),(0, 1) does not represent the function.

C) (4, 8), (5, 8), (6, 8)

Here, the x-coordinates are: 4,5 and 6

At x = 4, y = 8

At x = 5, y = 8

At x = 6, y = 8

As there is no repetition of x-coordinates.

Thus, the coordinate pairs (4, 8), (5, 8), (6, 8) represent the function.

Please note that it does not matter if y-values are repeated. Just remember, we can not have repeated x-values.

D) (-1, 4), (0, -1), (8, 3)

Here, the x-coordinates are: -1, 0, and 8

At x = -1, y = 4

At x = 0, y = -1

At x = 8, y = 3

As there is no repetition of x-coordinates.

Thus, the coordinate pairs (-1, 4), (0, -1), (8, 3) represent the function.

E) (1, 8), (8, 1), (1, 3)

Here, the x-coordinates are: 1, 8, and 1

At x = 1, y = 8

At x = 8, y = 1

At x = 1, y = 3

Please observe that the x-coordinate values i.e. x=1 are repeated.

Thus, the coordinate pairs (1, 8), (8, 1), (1, 3) does not represent the function.

F) (9, 0), (9, 1), (9, 2), (9, 3)

Here, the x-coordinates are: 9, 9,9 and 9

At x = 9, y = 0

At x = 9, y = 1

At x = 9, y = 2

At x = 9, y = 3

Please observe that the x-coordinate values i.e. x=9are repeated.

Thus, the coordinate pairs (9, 0), (9, 1), (9, 2), (9, 3) does not represent the function.

g(x) = -4x2 + 4x – 2
What is the maximum or minimum step by step

Answers

Ok for this answer you use a calculator for the times part and for g x you get the times you count too

We want the maximun or minimum of [tex]g(x)=-4x^2+4x-2[/tex]

Firstly, notice that we have a leading coefficient of -4, wich means our parabola is concave down. Thus, our function will have a maximum.

To find what is the maximum, let's firstly find on wich value of x it happens. We'll start by taking the first derivative of the function:

[tex]g'(x)=-8x+4[/tex]

To find the extremes of the function, we just need to find where the derivative equals zero. Setting g'(x)=0 we have

[tex]0 = -8x+4\\8x=4\\x=\frac{1}{2}[/tex]

So we found that the x coordinate of the maximum is x=1/2. To find the y coordinate we just need to substitute the value of x into the original function.

[tex]g(1/2)=-4(1/2)^2+4(1/2)-2\\g(1/2)=-1+2-2\\g(1/2) = -1[/tex]

Therefore, the maximum point [tex]M[/tex] of the function is

[tex]\boxed{M=(0.5,-1)}[/tex]

 Glad to help! Wish you great studies.

If you found this helpful consider giving this answer brainliest ;)

The video game store is having a 25% off sale on all video games. How much money will Sandra save if she buys a game that originally
cost $49.952

Answers

49.952 * 0.25 = 12.488
She saves $12.488
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