Jane construct a four sided wall to wall to surround their castle . The wall has a perimeter of 100 feet. One side measures 16 feet. A different side side measures 22 feet. A third side measures 34 feet. What is the unknown side length

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ahs vertices at points A(-4,-4), B(-1,-2) and C(-1,-4).

1 way: First reflect this triangle across the y-axis to form the triangle A''B''C'' which vertices are at points A''(4,-4), B''(1,-2) and C''(1,-4).

Then translate this triangle 7 units up to form the triangle A'B'C' with vertices:

[tex]A'(4,-4+7)=A'(4,3)\\ \\B'(1,-2+7)=B'(1,5)\\ \\C'(1,-4+7)=C'(1,3)[/tex]

2 way: First translate this triangle 7 units up to form the triangle A''B''C'' which vertices are at points A''(-4,3), B''(-1,5) and C''(-1,3).

Then reflect this triangle across the y-axis to form the triangle A'B'C' with vertices:

[tex]A'(-(-4),3)=A'(4,3)\\ \\B'(-(-1),5)=B'(1,5)\\ \\C'(-(-1),3)=C'(1,3)[/tex]

The measure of the third angle is 119 degrees

Step-by-step explanation:

The given is:

We need to find the measure of the third angle in the triangle

The sum of the measures of the interior angles of a triangle is 180°

∵ The measure of an angle = 26°

∵ The measure of another angle = 35°

∵ The some of measures of the 3 angles = 180°

∴ 26° + 35° + x° = 180°, where x is the measure of the 3rd angle

- Add the like terms in the left hand side

∴ 61° + x° = 180°

- Subtract 61 from both sides

∴ x = 119°

The measure of the third angle is 119 degrees

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Answer:

P = 105°

QR = 11.6

M = 45°

LN = 8.5

Step-by-step explanation:

when reading the order of what is given LMN = PRQ the order DOES matter

so whe looking at what is being asked....

P will equal whatever its place is in the opposite equation. In this case that is L. This means that P = L. Since L = 105° then so does P.

You can do this with the rest of the letters. What ever letter is in it's place in the opposite equation that is what it equals.

Answer:

-15

Step-by-step explanation:

this is the negative scale, so the bigger the smaller

Answer:-15

Step-by-step explanation:

-15 is 15 away from 0 while -5 is only 5 away from 0

Doug have 30 quarters and 15 dimes.

Step-by-step explanation:

Given,

Number of coins = 45

Worth of coins = $9.00 = 9.00*100 = 900 cents

Each quarter = 25 cents

Each dime = 10 cents

Let,

x be the number of quarters

y be the number of dimes

According to given statement;

x+y=45            Eqn 1

25x+10y=900   Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=45)\\10x+10y=450\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](25x+10y)-(10x+10y)=900-450\\25x+10y-10x-10y=450\\15x=450[/tex]

Dividing both sides by 15

[tex]\frac{15x}{15}=\frac{450}{15}\\x=30[/tex]

Putting x=30 in Eqn 1

[tex]30+y=45\\y=45-30\\y=15[/tex]

Doug have 30 quarters and 15 dimes.

Keywords: linear equation, elimination method

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Doug has 30 quarters and 15 dimes.

Let

x = number of quarters

y = number of dimes

The total number of coins is 45. Therefore,

Total amount of the coins is $9. Therefore,

Therefore,

x + y = 45

0.25x + 0.1y = 9

0.1x + 0.1y = 4.5

0.25x + 0.1y = 9

0.15x = 4.5

x = 4.5 / 0.15

x = 30

y = 45 - 30

y = 15

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Answer:

$76.5

Step-by-step explanation:

We have been given that inflation from last year to this year was 2% and a pair of designer jeans sold for $75 last year. We are asked to find the price of pair of designer jeans this year.

An inflation of 2% will increase the price of pair of jeans by 2%, so price of pair of jeans this year would be $75 plus 2% of $75.

[tex]\text{Price of pair of jeans this year}=\$75+\$75\times\frac{2}{100}[/tex]

[tex]\text{Price of pair of jeans this year}=\$75+\$75\times0.02[/tex]

[tex]\text{Price of pair of jeans this year}=\$75+\$1.5[/tex]

[tex]\text{Price of pair of jeans this year}=\$76.5[/tex]

Therefore, the price of pair of jeans would be $76.5 this year.

Answer:

8:32

Step-by-step explanation:

1x+4x=40

5x=40

x=8

1*8:4*8

8:32

Answer:

24

Step-by-step explanation:

Answer:

look at picture shown.

Answer:

5x+2

Step-by-step explanation:

P=2L+2W

14x+4=2(2x)+2W

14x+4=4x+2W

14x+4-4x=2W

14x-4x+4=2W

10x+4=2W

(10x+4)/2=W

5x+2=W

[tex]\boxed{A=50units^2}[/tex]

Hello! Remember you have to write complete questions in order to get good and exact answers. Here you haven't provided any regions so I'll help you assuming a system of inequalities that leads to a shaded region that is a right triangle as shown in the figure below. The system is the following:

[tex]\left\{ \begin{array}{c}x>0\\y>0\\y<-x+10\end{array}\right.[/tex]

From the figure below, the shaded region is a right triangle with base 10 units and height 10 units. So:

[tex]A=\frac{b\times h}{2} \\ \\ \\ A:Area \ of \ the \ triangle \\ \\ b:base \ of \ the \ triangle \\ \\ h:height \ of \ the \ triangle[/tex]

So:

[tex]A=\frac{10\times 10}{2} \\ \\ A=\frac{100}{2} \\ \\ \boxed{A=50units^2}[/tex]

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Answer:

N = 6 - 2

Step-by-step explanation:

Take each part of the word expression and translate it:

"N"   =>  N        ("N" is a variable that represents a number you don't know)

"is the same as"   =>  =       ("the same" means equals)

"6 reduced by 2"   =>  6 - 2          ("reduced" means use subtraction "-")

Put the sentence back together in the same order.

N = 6 - 2

If you wanted to find "N", you can simplify by doing 6 - 2.

N = 4

Answer:its 29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

A- The circumference of the tire is about 7.85 feet

B- The tire will rotate about 672 times to travel 1 mile

Step-by-step explanation:

∵ The diameter of a tire is 2.5 ft

∴ d = 2.5 ft

∵ C = π d, where C is the circumference of tire

∴ C = π(2.5) = 7.85398 ft

∴ C ≅ 7.85 feet

A- The circumference of the tire is about 7.85 feet

∵ The tire have to travel 1 mile

∵ 1 mile = 5280 feet

∴ S = 5280 feet

- To find the number of rotation of the tire divide S by C

∵ n =  [tex]\frac{S}{C}[/tex]

∴ n = [tex]\frac{5280}{7.85}[/tex] ≅ 672 revolution

B- The tire will rotate about 672 times to travel 1 mile

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Answer:

The circumference of the tire is about 7.85 feet

B- The tire will rotate about 672 times to travel 1 mile

Step-by-step explanation:

   The formula of the circumference of a circle is C = π d, where d is the diameter of the circle

   If a circle rotates for n turns and make a distance S, then n =

∵ The diameter of a tire is 2.5 ft

∴ d = 2.5 ft

Step-by-step explanation:

Answer:

11 + 2x

Step-by-step explanation:

First you will want to separate like variables, so (6, 5) and then (-2x, 4x)

Then you will use the signs to do the math. You can move everything to help visualize the solution easier.

6+5+4x-2x

6+5 = 11

4x-2x = 2x

Because you cannot add or subtract a variable with a non variable, and both numbers are positive you end up with

11 + 2x

The expression 6-2x+5+4x simplifies to 11 + 2x by combining like terms: the constants (6+5=11) and the variables (-2x+4x=2x).

To simplify the expression 6-2x+5+4x, we start by combining like terms. Combining the constant terms (6 and 5) and the variable terms (-2x and 4x), we get:

Constant terms: 6 + 5 = 11

Variable terms: -2x + 4x = 2x

Thus, the simplified expression is 11 + 2x.

Answer:

[tex]t = 5[/tex]

Step-by-step explanation:

By the mid-segment theorem of triangles,

[tex]VX= \frac{1}{2} YZ[/tex]

We substitute the expressions in terms of t.

[tex]10t = \frac{1}{2} (t + 95)[/tex]

We multiply through by 2 to get:

[tex]20t = t + 95[/tex]

Subtract t from both sides:

[tex]20t - t = 95[/tex]

[tex]19t = 95[/tex]

Divide both sides by 19:

[tex]t = \frac{95}{19} [/tex]

[tex]t = 5[/tex]

Answer:

2.4

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

4 times 6 =24

Answer:

Ishaan is 2 years old and Ben is 8

Step-by-step explanation:

Ben is 4 x (2) = 8

Ben is 6 + (2) = 8

Answer:

[tex]\$18,453.78[/tex]  

Step-by-step explanation:

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final amount owed  

P is the amount borrowed

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=7\ years\\ P=\$8,000\\ r=12\%=12/100=0.12\\n=12[/tex]  

substitute in the formula above

[tex]A=8,000(1+\frac{0.12}{12})^{12*7}[/tex]

[tex]A=8,000(1.01)^{84}[/tex]  

[tex]A=\$18,453.78[/tex]  

Answer:

390 miles

Step-by-step explanation:

30 mpg means that he gets 30 miles for every gallon.

If he has 13 gallons means that you multiply 30 by 13.

30 * 13 = 390 miles

Final answer:

Mark can travel 390 miles on 13 gallons of gas, as his car gets 30 miles per gallon and distance is calculated by multiplying fuel efficiency by the number of gallons.

Explanation:

To calculate the distance Mark can travel on 13 gallons of gas, we use the formula: Distance = Fuel Efficiency  imes Number of Gallons.

Mark's car gets 30 miles per gallon. Thus, the distance he can cover on 13 gallons of gas is calculated by multiplying 30 miles/gallon by 13 gallons, which equals 390 miles.

This is a straightforward multiplication problem involving units of fuel efficiency (miles per gallon) and quantity of fuel (gallons).

The solution directly gives us the total number of miles Mark can travel on 13 gallons of gas.

Answer:

44-2n

Step-by-step explanation:

Hope it helps!

Final answer:

The expression '44 decreased by twice a number' can be represented as 44 - 2n, where n is the unknown number.

Explanation:

The question involves expressing a given mathematical relationship using a variable. Here, the relationship is '44 decreased by twice a number.' To represent this situation with the variable n, we use the expression 44 - 2n. To simplify further, just substitute the variable 'n' with the unknown number. This represents the original number 44 being reduced by two times the value of some unknown number n.

Answer:

1 1/2 feet

Step-by-step explanation:

We know that she needs 1 3/4 feet of wrapping paper per gift and she has a total of 8 1/2 feet.

The number of gifts she can wrap is:

[tex]8.5/1.75=4.86[/tex]

She can wrap four gifts

Therefore:

[tex]4\cdot{1.75}=7[/tex]

She will use 7 feet of wrapping paper and she has:

[tex]8.5-7=1.5[/tex]

She has 1 1/2 feet of wrapping paper left

Answer:

11/2

Step-by-step explanation:

Answer:

Let the number of balcony seats be b

Let the number of gallery tickets be g

Let the number of main floor tickets be m

b + g + m  = 1020

b = 2g

m = b + 225

The number of balcony tickets = 318

The number of gallery tickets = 159

The number of main floor tickets = 543

Step-by-step explanation:

Let the number of balcony seats be b

Let the number of gallery tickets be g

Let the number of main floor tickets be m

i) Therefore we can write b + g + m  = 1020

ii) there were twice as many balcony tickets sold as gallery tickets

   therefore b = 2g      [tex]\Rightarrow[/tex]  g = 0.5b

iii) there were 225 more main floor tickets than balcony tickets

   therefore m = b + 225

iv) using equation ii) and equation iii) in equation i) we can write

     b + g  + m = b + 0.5b + b + 225  = 1020      [tex]\Rightarrow[/tex] 2.5b  = 795     [tex]\Rightarrow[/tex]  b = 318

v) g  = 0.5 b  = 0.5 [tex]\times[/tex] 318 = 159

vi) m = b + 225 = 318 + 225 = 543

Answer:

D. Gallery: g

Balcony: 2g

Main Floor: 2g+225

Step-by-step explanation:

Gallery is g

Balcony had 2 times as many tickets than Gallery so 2•g (2•gallery)

Main floor had 225 more tickets than Balcony so Balcony’s equation plus 225 tickets. 2g + 225

Answer:

a. 157 cm

Step-by-step explanation:

Multiply the diameter times 3.14

3.14 x 50=157 cm.

answer: 157 cm

To find the circumference of a circle given the diameter, multiply the diameter by π (approximately 3.14). Hence, the circumference of the dartboard is approximately 157 cm.

The subject of the question is Mathematics and it covers a topic generally taught in Middle School. When given the diameter of a circle, you can calculate the circumference using the formula C=πd where C is the circumference, π (pi) is about 3.14, and d is the diameter. In this case, the diameter of the dartboard is 50 cm. So, we simply multiply the diameter (50 cm) by π (3.14) to get the circumference. This means the circumference of the dartboard is approximately

157 cm (Option A)

.

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Answer: you isolate the variable so you can get a equation of y= 10x or something like that

Step-by-step explanation:

Answer:

3x^4-x^2-x^2-5x^4+3

-2x^4-2x^2+3 is the answer

To simplify the given expression, combine like terms by adding or subtracting the coefficients of the same powers of x.

The given expression is 3x4 - x2 - x2 - 5x4 + 3.

To simplify this expression, combine like terms by adding or subtracting the coefficients of the same powers of x.

Combining like terms, we have: -2x2 - 2x4 + 3.

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Answer:

89%

Step-by-step explanation:

Percent is a number out of 100.

If you got 89 out of 100, you got 89%

Answer:

7) -6, -3, 1, 50

9) -18, -11, -8, 11, 18

Answer: No

Step-by-step explanation: 12 x 4 is 48. 12 x 1/4 is the same as dividing 12 by 4, which gives you 3. 3 is not equal to 48.

The correct statement is that the number 3 is not equal to 48.

I do not agree with him.

Simplification is to make something easier to do or understand and to make something less complicated.

Given

Kim says that multiplying 1/4×12 is the same as dividing 12 x 4

The multiplication of 12×4 = 48.

1/4×12 is the same as dividing 12 by 4, which gives you 3.

Therefore, 3 is not equal to 48.

I do not agree with him.

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