A triangle has an angle that measure 36.6° and a second angle that measures 59.3°. What is the
measure of the third angle?
2 pts

Answer:

x = 3.5units

Step-by-step explanation:

Congruent means the same length, so set the given lengths equal to each other.

8x - 17 = -2x + 18

Add 2x to both sides.

10x -17 = 18

Add 17 to both sides.

10x = 35

Divide by 10

x = 3.5

When x is 3.5, KL and ST are the same length. Check.

8(3.5) - 17 = 11

and

-2(3.5) + 18 = 11

The size of the angle x = 54 degrees

The regular pentagon is given

Number of sides of the pentagon = 5

O is the center  of the pentagon

The sum of all the angle around a point is 360 degrees

From the figure we can see that the it equally divided by 5 parts

The measure of each angle = 360/5

= 72 degrees

Consider the corresponding triangle

Sum of all the interior angles of the triangle is 180  degrees and the two sides of the triangle is equal, therefore it is an isosceles triangle

Then,

x + x+ 72 = 180

2x + 72 = 180

2x = 180- 72

2x = 108
x = 108/2

x = 54 degrees

Hence, the size of the angle x = 54 degrees

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The probability for Jacie or Robyn would consume cheese on a random day is 0.15.

The likelihood of Jacie eating cheese on any particular day is 0.6.

The likelihood of Robyn eating cheese on any particular day is 0.25.

Both events are independent.

As a result, the probability for Jacie or Robyn would consume cheese on a random day is;

P(Jacie or Robyn)  = P(Jacie). P(Robyn)

P(Jacie or Robyn)  = 0.6 x 0.25

P(Jacie or Robyn)  = 0.15

Thus, the probability for Jacie or Robyn would consume cheese on a random day is 0.15.

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Bruce paid $17 and $55 respectively for each of the books

From the question, we have the following statements:

Represent the books with the variables x and y

So, we have the following equations

x = 4 + 3y

x + y = 72

To start with;

We can substitute 4 + 3y for x in the equation x + y = 72

So, we have the following representation

4 + 3y + y = 72

Evaluate the like terms

4 + 4y = 72

Collect the like terms in the above equation

So, we have the following equation

4y = 72 - 4

Evaluate the like terms

4y = 68

Divide both sides by 4

So, we have

y = 17

Recall that x = 4 + 3y

Substitute 17 for y in the equation x = 4 + 3y

x = 4 + 3 * 17

Evaluate the products

x = 4 + 51

Evaluate the sum

This gives

x = 55

Hence, the cost of the books are $17 and $55

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Possible question

Bruce bought two books, one book costs $4 more than three times than the other. They both equal $72.

What is the cost of each book

If x + y = L and [tex]x^2+y^2[/tex] = M and the vales of L and M are constants, then the value of [tex]x^3+y^3[/tex] in terms of L and M is [tex]x^3+y^3=L^3-3(\frac{L^2-M}{2} )(L)[/tex]

The given values are

x + y = L

[tex]x^2+y^2[/tex] = M

We know the value of

[tex](x+y)^3=x^3+y^3+3xy(x+y)[/tex]

Rearrange the terms and convert to the suitable form

[tex]x^3+y^3=(x+y)^3-3xy(x+y)[/tex]

The value of x + y = L

Substitute the value of x + y in the equation

[tex]x^3+y^3=L^3-3xy(L)[/tex]

Here we have to find the value of xy

We know

[tex](x+y)^2=x^2+y^2+2xy[/tex]

Rearrange the terms and convert to suitable form

[tex]2xy=(x+y)^2-(x^2+y^2)[/tex]

Substitute the values in the equation

2xy = [tex]L^2-M[/tex]

xy = [tex]\frac{L^2-M}{2}[/tex]

Substitute the value of xy in the equation

[tex]x^3+y^3=L^3-3(\frac{L^2-M}{2} )(L)[/tex]

Hence, if x + y = L and [tex]x^2+y^2[/tex] = M and the vales of L and M are constants, then the value of [tex]x^3+y^3[/tex] in terms of L and M is [tex]x^3+y^3=L^3-3(\frac{L^2-M}{2} )(L)[/tex]

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Answer:

Is this an arithmetic sequence?

Yes.

Is there a common difference and if so, what is it?

Yes, there is a common difference : 1

The common difference is 1

The quadratic function has only maximum value :

[tex]F(x)_{min}[/tex] = 30

x = 3

There is no minimum value of the quadratic function.

Given,

In the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Determine whether the following quadratic function has a maximum or a minimum value. Then find  the maximum and minimum value of the function.

Now, According to the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Take out the leading coefficient

F(x) = -3[tex](x^2-6x)+3[/tex]

Complete the square:

F(x) = [tex]-3(x^2+(2(-3))x + (-3)^2)+(3-(-3)^2))[/tex]

Express the function in vertex form

F(x) = [tex]-3(x-3)^2+30[/tex]

To  find the maximum value

[tex]F(x)_{min}[/tex] = 30

x = 3

For Minimum value:

F(x) = [tex]-3x^2 +18x +3[/tex]

Rewrite the function by completing the square

F(x) = [tex]-3(x-3)^2+30[/tex]

The graphs always open downwards

So, There is no minimum value of the quadratic function.

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The equation of the graph in vertex form is: y = 1x – 3| + 5.

The graph in the diagram above is a graph of an absolute value equation. The equation can be expressed as y = a|x – h| + k (vertex form), where the vertex is represented as (h, k).

The vertex of the graph is the coordinate of the point where the two straight lines meet.

Given the graph above, the vertex is at point (3, 5). Therefore:

h = 3

k = 5

The graph opens up, so the value of a = 1.

Substitute h = 3 and k = 5 into y = a|x – h| + k:

y = 1|x – 3| + 5

y = 1x – 3| + 5

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Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.

In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).

Step-by-step explanation:

Answer:

y=2x+9

Step-by-step explanation:

Fill in the equation

5=2(-2)+b

Solve for b

5 = -4+b

9 = b

Put the original equation

y=2x+9

Answer:

56%

Step-by-step explanation:

112/200 as a percentage

112/200 = 0.56

0.56 as a percentage:

0.56 * 100 = 56%

Answer::

To do percentages with fractions,

divide the numerator by denominator to get a decimal,

so for example, your question, 112/200

112/200 is 0.56 decimal, and then to make it percent,

we multiply by 100,

how does that work?

you move two places to the right because 100 has two zeros

so 0.56 would be 56,

therefore the percent of 112/200 would be 56%

Have a good day! <3

Answer: K is greater than or equal to 18

Step-by-step explanation:

Answer:k>=-18

Step-by-step explanation:

Rewrite so k

is on the left side of the inequality.

2/5⋅(k−2)≥−8

Multiply each term in

2/5⋅(k−2)≥−8 by 5/2 to eliminate the fractions.

k−2≥−20

Move all terms not containing

k to the right side of the inequality.

k≥−18

The result can be shown in multiple forms.

Inequality Form:

k≥−18

Answer: he will be left with 31.74 dollars

Step-by-step explanation:

i first put 55.00 - 4.50 = 50.5

then you subtract 50.5 with 6.25  3 times so the and is 31.74

hope this helped !!

There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.

Take into account the details offered.

43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.

Consequently, p= 8/43.

If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.

q= 35/43

Let X represent how many presidents have passed away while in office.

The probaility that at least one student will choose a president who passed away in office is:

P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)

P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸

By using  Combinations Formula,

By solving we get,

P(X[tex]\geq[/tex]1 ) = 0.97541

As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.

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The system of inequalities for this situation are

Cost inequality = $4x + $6y ≤ $100

Time inequality = 30x + 60 ≤ 900

And  the retailer should make 10 single layer and 10 2-layer mask by using the available time and cost.

System of inequalities

When two or more algebraic expressions are compared using the mathematical symbols like <, > ≤, or ≥, then they form an inequality. They are the mathematical expressions in which both sides are not equal.

Given,

A retail store manager makes cotton cloth facemasks for his employees during Covid. He has enough money to buy $100 worth of fabric. Fabric costs $4 for a single layer mask and $6 for a mask with 2 layers of fabric. It takes him 30 minutes to make a single layer mask and 1 hour to make double layer mask. He only has 15 hours available to work on masks. He wants to maximize his time and resources.

Here we need to find the system of inequalities and we also need to find each type of mask should he make.

Let us consider x be the number of single layer mask and y be the number of 2 layer mask.

Then based on the given cost, the cost inequality is written as,

$4x + $6y ≤ $100.

Here we know the time taken for each mask making, so, in the inequality form, it can be written as,

We know that,

1 hour = 60 minutes

So, 15 hours = 900

Therefore, the inequality of time is written as,

30x + 60 ≤ 900

While we plot these values on the graph then we get the graph like the following,

Here the blue line represent the time inequality and the red line represents the cost inequality.

Through the given graph, we have identified that the retailer should make 10 single layer and 10 2 layer mask by using the available time and cost.

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As a result of using all values in the data set to calculate an average, the mean is the most widely used measure of central tendency.

A measure of central tendency, also known as a measure of center or a measure of central placement, is a summary statistic that seeks to summarize an entire collection of data by using a single number that corresponds to the middle or center of the distribution.

You are probably most familiar with the central tendency measure known as the mean, which is the arithmetic average. It is fairly easy to determine the mean. Simply add up all the values then divide by the dataset's observation count.

The teacher can get a mathematical breakdown of how well the children are doing through measures of central tendency.

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A quadrilateral is a polygon with four sides, the length of BC for the given quadrilateral will be 8.1.

A quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.

In other meaning, a quadrilateral is a kind of polygon in which four sides, for example, rectangle, square, and parallelogram are quadrilateral.

As per the give quadrilateral,

In triangle ACD.

Apply Pythagoras' theorem,

BD = √(5²+7.5²) = 9.0123

In triangle BDC by cosine law,

Cos38° = ((DB)²+(DC)² - (BC)²)/(2×DB×DC)

Cos38° = (9.0123²+13²- (BC)²)/(2×9.0123×13)

Cos38° = (250.25- (BC)²)/(234.32)

(250.25- (BC)²) = 184.646

(BC)² = 65.60

BC = 8.1

Hence, "A quadrilateral is a polygon with four sides, the length of BC for the given quadrilateral will be 8.1".

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Complete question attached below ;

The equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Given:

(1,-5) with slope m = -1

The standard slope intercept form is y = mx + c.

substitute m = -1 and (1,-5)

-5 = -1(1) + c

-5 = -1 + c

c = -4.

y = mx + c

y = -1(x) + (-4)

y = -x - 4.

Therefore the equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Therefore equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

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Answer: 721 ft

Step-by-step explanation:

formula for area is a=l*w

Given: w=103, length=7

103*7=721

Answer: The answer 721. When you are finding an area of something you must multiply the length and the width so the information given.

103 x 7 = 721 feet long

Here is the real problem:

It's sloppy as long as you understand the concept : )

Each section of a highway has length of 1.5 miles.

In this question, Ms. Galindo’s class has adopted two equal sections of a highway to keep clean.

We need to find the length of each section.

Let each section measures x mile.

The combined length of the two sections is 6/8 of a mile.

So, we get an equation x + x = 6/8

We solve above equation to find the value of x.

2x = 6/8

x = (6/8) / 2

x = 6/4

x = 1.5

Therefore, each section of a highway has length of 1.5 miles.

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The height of the triangle is 15 feet.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the interior angles of a triangle add up to 180 degrees. It is the polygon with the fewest sides.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest side of the three sides, known as the hypotenuse, is the third side.

The formula for the area of a right-angle triangle is A = (½)×b×h square units.

Let the height of the triangle be h

Given:- The area (A) of the triangle is 120 ft^2.

            The base (b) of the triangle is 16 feet.

From the formula, we know that area of the triangle is:-

A = (½)×b×h

By substituting the values of A and b

[tex]120=\frac{1}{2}*16*h\\ h=(120*2)/16\\h=15[/tex]

Hence the height of the triangle is 15 feet.

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The colour code needed is silver, green, red and blue for the tolerance of ± 10% on the 4 color band resistor.

For the given question;

Since it is silver in this instance, the resistor colour code table indicates a tolerance of  ± 10% .

Thus, the colour code needed is silver, green, red and blue for the 0.34

Ohm resistor with tolerance of ± 10%.

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Answer:

4/7

Step-by-step explanation:

32:56

32÷2=16

56÷2=28

16:28

16÷2=8

28÷2=14

8:14

8÷2=4

14÷2=7

4:7

32:56 ~ 32/56

=4/7

Step-by-step explanation:

so, after clarification from your side, we know

f(x) = 12500 × (0.82)^x

so, with every new year we are multiplying the value of the previous year by 0.82.

in other words

f(n) = f(n-1) × 0.82

with f(0) = 12500

because anything to the power of 0 equals 1.

A

so, the price is decreasing every year, because any multiplication with a positive value smaller than 1 decreases the original number.

multiplying an amount by a decimal number like 0.82 creates exactly 82% of the original amount because 1 represents 100%.

that means the value decreases every year by 100 - 82 = 18% compared to the value of the previous year.

B

1 5600

2 3136

3 1756.16

4 983.45

remember, Part A showed always an 18% decrease over the previous year.

from 5600 to 3136, this was a change of

100% = 5600

1% = 100%/100 = 5600/100 = $56

the price difference was 5600 - 3136 = 2464

how many % was that decrease ?

as many as how often 1% fits into 2464 :

2464 / 56 = 44%

that was much more than Part A.

from 3136 to 1756.16, this was a change of

100% = 3136

1% = $31.36

the price difference was 3136 - 1756.16 = $1,379.84

how many %

1,379.84 / 31.36 = 44%

again.

from 1756.16 to 983.45, this was a change of

100% = 1756.16

1% = $17.5616

the price difference was 1756.16 - 983.45 = 772.71

hire many %

772.71 / 17.5616 = 43.99997722...%

and again 44% (just a little rounding uncertainty).

so, product B recorded a much greater percentage change in value over the previous year than product A :

44% to 18%

Answer:

equation: y= -2x-1

Step-by-step explanation:

y= -2x+b

-3= -2(1)+b

-3= -2+b

b= -1

equation: y= -2x-1

Answer:

25

Step-by-step explanation:

First, we add 50, 12, and 16, which gives us 78. Then, we remove 3 from the answer, giving us 75. Then, divide 75 by 3.

Answer = 25.

(ps: sorry for any spelling mistakes, i dont really type answers alot)

If you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, You win 50 tickets, 12 tickets, and 16 tickets at an arcade. You are able to buy 3 of the same item with 3 tickets left over.

Number of tickets won,

= 50 + 12 + 16

= 78 tickets

Number of items bought = 3 items

Let the cost of 1 item be 'x' tickets.

The cost of 3 items = 3x

By the amount, we can buy 78 tickets as,

3x = 78

x = 26

Thus, if you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.

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Answer:

The red symbol drawn over ∠2 and ∠3 indicates that the two angles total 90°. Therefore:

[tex]m\angle{2}+m\angle{3}=90^{\circ}[/tex]

The old monthly payment was =  9.27 x 50 = 463.5

The new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is 1.947%

Given,

Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on his original loan

According to the question:

So, per thousand value of $65000 is 50000/1000 =50

Now, the old monthly payment was =  9.27 x 50 = 463.5

She decides to renew and will now pay $11.10 monthly per thousand on his loan.

So, the new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is= 11.10 /9.27 - 1 x 100

19.7411 % and to nearest tenth it is 1.947%

Hence, the old monthly payment was =  9.27 x 50 = 463.5

the new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is 1.947%

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The equations y=3+2 and y=2x+1 both will meet at x=3

Acc to our question-

Hence,The lines y=3x−2 and y=2x+1 both will intersect at x=3

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