The measures of two angles in a triangle are 48° and 71°. What is the measure of the third angle?

Answer:

The area of the orange ​band is 576 + 48x square inches

Step-by-step explanation:

Step 1: Area of the green square

The area of the green square =[tex]side^2[/tex]

The area of the green square  =  [tex]x^2[/tex] square inches

Step 2: Area of the orange square

The area of the orange square =[tex]side^2[/tex]

The side of the orange square  =  12+12 + x = 24 +x

Now the area of the orange square  =[tex](x+24)^2[/tex]

Step 3: The area of the orange ​band

Area of the orange ​band =  area of the orange square - area of the green square

Area of the orange ​band =   [tex](x+24)^2 - x^2[/tex]

expanding and solving the equation we get

[tex]x^2 + 24^2 +48x - x^2[/tex]

[tex]576 + 48 x[/tex] square inches

Final answer:

The area of the orange band surrounding the central green square on the rug is found by subtracting the area of the green square from the area of the entire rug. The formula for the area of the orange band is 48x + 576 square inches, where x represents the side length of the green square.

Explanation:

To find the area of the orange band on the rug, we need to calculate the area of the entire rug and subtract the area of the central green square. The width of the orange band is given to be 12 inches. Therefore, each side of the orange rug is increased by 2 times 12 inches (for both the left and the right side of the green square), making the total length of the rug's side x + 2(12) inches.

The area of the entire rug, which is a larger square, is[tex](x + 24)^2[/tex] square inches. The area of the central green square is [tex]x^2[/tex]square inches. To find the area of the orange band, we subtract the area of the green square from the area of the entire rug which is: [tex](x + 24)^2 - x^2[/tex].

Expanding the squared term we get: [tex]x^2 + 48x + 576 - x^2[/tex], which simplifies to 48x + 576 square inches. That's the area of the orange band surrounding the green square.

Answer: 200%

Step-by-step explanation:

We are asked to find the percent increase in student fees. The amount of increase in student fees is given by

final amount − initial amount = increase

12,000 − 4,000 = 8,000

We can now find the percent increase by finding what percent the amount of increase is of the initial amount. In other words, we want to find what percent 8,000 is ... of 4,000.

Let p be the percent. The question can be translated into an equation.

8,000  {is}  {what percent}     {of}  4,000

8,000  {=}   {          P          }     {x}   4,000

To solve for p, we can now divide each side by 4,000 and simplify.

8,000 = 4,000p

p=2

To convert p to a percent, multiply 2 by 100.

2 x 100

=200%

It follows that the percent increase in student fees was 200%.

Answer:

200%

Step-by-step explanation:

Find the amount of change.

12,000−4,000=8,000

Find the percent.

Change is what percent of the original amount?

Let p= the percent.

8,000 is what percent of 4,000?

Translate to an equation and simplify.

8,000 = p⋅ 4,000=

8,000 = 4,000p

Divide both sides by 4,000 and change to percent form.

2=p

200%=p

Answer:

The answer is 23.22

Step-by-step explanation:

The reason why is because all you have to do is multiply the length that the snail travels per minute by the amount of minutes.

Answer:

a) angle 4 = 60°

b) angle 6 = 120°

c) angle 8 = 60°

Step-by-step explanation:

a) angle 4 =

angle 3 = 120

angle 4 = 180 - 120 = 60

b) angle 6 =

c) angle 8 =

angle 8 = 180 - 120 = 60

Angles 4, 6, and 8 in the given parallel line scenario would all measure 120 degrees because they are alternate interior, corresponding, and vertical angles to angle 3 respectively.

When dealing with parallel lines and transversals in geometry, certain angles have specific relationships. Given that lines l and m are parallel and angle 3 measures 120 degrees, we can deduce the following:

Remember that in parallel line angle relationships, alternate interior, corresponding, and vertical angles provide a dependable method to find missing angle measures.

Answer:

-20

Step-by-step explanation:

-20 divided by -4 is 5.

Answer:

-20

Step-by-step explanation:

x/-4 = 5

x = 5*-4

x = -20

Answer:

b

Step-by-step explanation:

bc i just did it

Answer:

The interest rate was 2.5% per year.

Step-by-step explanation:

Answer:

Number of students who went on the field trip = N - 6 .

We subtract 6 from the total number of students to get the number of students who went on the field trip.

Step-by-step explanation:

i) let the number of students in the club be = N

ii) If all but 6 students went on the trip then to we can write an expression for the number of students on the field trip by subtracting 6 from N. Therefore we can write the expression as

number of students who went on the field trip = N - 6

Answer:

Step-by-step explanation:

[tex]A_{5}=4+(-1)^5=4-1=3[/tex]

The fifth term of the sequence is 3.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Given to us,

Sequence,

An=4+(-1)^n

For fifth term,

n = 5,

now, we have,

Subsituting the value of n we get,

An=4+(-1)^n

A_5 = 4+(-1)^5

A_5 = 4+(-1)

A_5 = 4 -1

A_5 = 3

Hence, the fifth term of the sequence is 3.

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An area of rectangle: a · b

a = 0.4 km

b = 0.07 km

a · b = 0.4 km · 0.07 km = 0.028 km²

The area of the rectangular plot of land is found by multiplying the length (0.4 km) by the width (0.07 km), resulting in an area of 0.028 square kilometers.

To find the area of a rectangular plot of land, you multiply the length by the width. The given rectangular plot is 0.4 kilometers long and 0.07 kilometers wide. To calculate the area, we do the following multiplication:

The area of the rectangular plot of land is 0.028 square kilometers.

Answer:

[tex](-2,\frac{5}{3})[/tex]

Step-by-step explanation:

[tex]Given\ y=\frac{2}{3}x+3,\ and\ x=-2\\\\Substitute\ the\ value\ of\ x\\\\y=\frac{2}{3}\times (-2)+3\\\\y=-\frac{4}{3}+3\\\\y=\frac{-4+9}{3}\\\\y=\frac{5}{3}\\\\Hence\ (-2,\frac{5}{3})\ satisfies\ the\ equation.[/tex]

Answer:11 tbs for 33 ounces of water

Step-by-step explanation:

Answer:

Step-by-step explanation: because i did 33 divided 2 to get the answer for the questions which equal 16.5 for 33

Answer:

The percent increase in the price of the car is 31.36%.

Step-by-step explanation:

Given:

A car dealer buys a luxury car for $65,200 and sells it for $85,650.  

Now, to find the percent increase in the price of the car.

Cost price of the luxury car = $65,200.

Sell price of the luxury car = $85,650.

So, the price of the car increased by:

Sell price of the luxury car - Cost price of the luxury car.

[tex]=\$85,650-\$65,200\\\\=\$20,450.[/tex]

Thus, the price of car increased by $20,450.

Now,to get the percent increase in the price of the car:

[tex]\frac{20450}{65200} \times 100[/tex]

[tex]=0.3136\times 100[/tex]

[tex]=31.36\%.[/tex]

Therefore, the percent increase in the price of the car is 31.36%.

Answer:

Step-by-step explanation:

Example:  (cx)×(ax + b) comes out to acx^2 + bcx, which is a linear quadratic (highest power of x is 2).

the product of a linear monomial and a linear binomial will be

[tex]\rm = (cx)\times(ax + b)[/tex]   which will comes out to  [tex]\rm acx^2 + bcx[/tex] that is a linear quadratic higgest power of x

Lets understand,

A Linear monomial is an Expression that has only one given term & whose power or highest degree is one. It cannot take any addition or subtraction signs monomial is an linear expression that has only a single non-zero term. Monomials can be numbers, variables, or numbers multiplied with variables.

Examples of linear monomial:-

For example, [tex]\rm 2, ab, and\; 42\;xy[/tex] are examples of a monomial. A few other examples of monomials are [tex]\rm 5x, 5x^3 , 7xy,x^5 .[/tex]

Therefore, the product of a linear monomial and a linear binomial will be

[tex]\rm = (cx)\times(ax + b)[/tex]   which will comes out to  [tex]\rm acx^2 + bcx[/tex] that is a  quadratic with higgest power of x.

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For a.

Since there are already two angles given for the triangle, we can measure the last angle using this formula:

90 + 55 + a = 180

Now solve for "a".

90 + 55 + a = 180

145 + a = 180

a = 180 - 145

a = 35°

For b.

From the picture above, the two triangle's tip are touching and having to form vertical angles. This means that the angles are congruent to each other.

Now that we have two angles in the second triangle(35 and 120), we can use the same formula:

35 + 120 + b = 180

Now solve for "b":

35 + 120 + b = 180

155 + b = 180

b = 180 - 155

b = 25°

Answer:

a = 35     b = 25

Step-by-step explanation:

Triangles always add up to 180 degrees.  Knowing this we can first solve the triangle with the right angle.

55 + 90 + a = 180

Before we solve this, keep in mind that the reflective property will be used on angle a, giving the answer to the third angle in the second triangle.

145 + a = 180

-145        -145

a = 35

Now that we have a solved use the reflective property to get it on the second triangle.

120 + 35 + b = 180

155 + b = 180

-155        -155

b = 25

There you have your two angles.

Hope this helped you out.

Answer:

[tex]x=4\sqrt{6}\ units[/tex]

[tex]y=4\sqrt{2}\ units[/tex]

[tex]z=4\sqrt{3}\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

In the right triangle ABD

Applying the Pythagorean Theorem

[tex]x^2=y^2+(12-4)^2[/tex]

[tex]x^2=y^2+64[/tex]

[tex]y^2=x^2-64[/tex] ----> equation A

step 2

In the right triangle BDC

Applying the Pythagorean Theorem

[tex]z^2=y^2+4^2[/tex]

[tex]z^2=y^2+16[/tex]

[tex]y^2=z^2-16[/tex] ----> equation B

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

[tex]12^2=x^2+z^2[/tex]

[tex]144=x^2+z^2[/tex] ----> equation C

step 4

Equate equation A and equation B

[tex]x^2-64=z^2-16[/tex]

[tex]x^2=z^2+48[/tex] -----> equation D

step 5

substitute equation D in equation C

[tex]144=z^2+48+z^2[/tex]

solve for z

[tex]2z^2=144-48[/tex]

[tex]2z^2=96[/tex]

[tex]z^2=48[/tex]

[tex]z=\sqrt{48}\ units[/tex]

simplify

[tex]z=4\sqrt{3}\ units[/tex]

Find the value of x

[tex]x^2=z^2+48[/tex]

[tex]x^2=48+48=96[/tex]

[tex]x=\sqrt{96}\ units[/tex]

[tex]x=4\sqrt{6}\ units[/tex]

Find the value of y

[tex]y^2=z^2-16[/tex]

[tex]y^2=48-16[/tex]

[tex]y^2=32[/tex]

[tex]y=\sqrt{32}\ units[/tex]

[tex]y=4\sqrt{2}\ units[/tex]

Answer:  

Look at her flexible expenses and prioritize

Step-by-step explanation:

Take the flexible-expense section of your budget and list the categories in the order of their importance to you.

The best option for Tricia would be look at her flexible expenses and prioritize. The correct option is d.

Budgeting is the process of developing a financial plan. It entails assessing your income and expenses and deciding how to allocate your resources.

Examine her variable expenses and prioritize. Tricia needs to re-evaluate her budget and see where she can cut costs to save more money for her emergency needs and long-term savings goals.

By examining and prioritizing her flexible expenses, she can identify areas where she can cut back on spending and redirect those funds to her savings goals.

Tricia must avoid incurring additional debt by using a credit card and must continue to cover her basic needs, such as food, by budgeting appropriately.

Thus, the correct option is d.

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Your question seems incomplete, the probable complete question is:

Tricia saved money, but the amount she saved didn't meet both her emergency needs and savings for her goal. Which of these would be BEST for Tricia to do next?

a.) Delete her food budget

b.) Incur more debt and use a credit card

c.) Spend more money on flexible expenses

d.) Look at her flexible expenses and prioritize

Answer:

Step-by-step explanation:

(f-g)(x)​ = f(x)- g(x)

= 3x - 1 - ( x + 2)

=3x - 1 - x - 2

= 2x - 3

Answer:

What

Step-by-step explanation:

What is the missing variables

Answer:

C - 8

Step-by-step explanation:

153 - 81 = 72

72 ÷ 9 = 8

Answer:

C) 8

I looked at the other answer at the bottom.

Answer:

The scale factor is 3.

Step-by-step explanation:

Let the origin O(0,0) is the reference point and the coordinates of the point A are given by (3,-6).

Therefore, the distance OA is given by [tex]\sqrt{(3 - 0)^{2} + (- 6 - 0)^{2}} = 3\sqrt{5}[/tex] units.

Again, the coordinates of point A' are (1,-2).

Therefore, the distance OA' is given by [tex]\sqrt{(1 - 0)^{2} + (- 2 - 0)^{2}} = \sqrt{5}[/tex] units.

Hence, the scale factor is [tex]\frac{OA}{OA'} = \frac{3\sqrt{5} }{\sqrt{5}} = 3[/tex]. (Answer)

The proportion that could be used to solve for the variable is [tex]\frac{16}{40}=\frac{3}{h}[/tex] ; h = 7.5 ⇒ answer b

Step-by-step explanation:

A proportional relationship: one variable is always a constant value times the other, that constant is called the constant of proportionality

The number of walls and the number of hours are increased or decreased together

∴ The number of walls and the number of hours are proportion

∵ 16 walls in 40 hours

∵ 3 walls in h hours

- By using the second rule above

∴ [tex]\frac{16}{40}=\frac{3}{h}[/tex]

The proportion that could be used to solve for the variable is  [tex]\frac{16}{40}=\frac{3}{h}[/tex]

Let us solve it to find h

∵  [tex]\frac{16}{40}=\frac{3}{h}[/tex]

- By using cross multiplication

∴ 16 × h = 3 × 40

∴ 16 h = 120

- Divide both sides by 16

∴ h = 7.5

The value of h is 7.5 hours

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Answer:

The product of 5x + 3 and 8x2 - 2x + 5 is 3x2 and 8 + 3x + 5

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 ((5x +  (3and8 • x2)) -  2x) +  5

Step  2  :

Trying to factor a multi variable polynomial :

2.1    Factoring    3x2and8 + 3x + 5

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

 3x2and8 + 3x + 5

Processing ends successfully

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Answer:

40X^3 - 34X^2 + 4X + 15

Step-by-step explanation:

Using Algebraic expansion, the first number in bracket with its coefficience multiplies the second bracket. Equally , the second number in the first bracket is also used to multiply the second bracket, taking note of the sign (addition and minus sign)

5x(8x^2 -2x +5) +3 (8x^2 -2x +5)

= 40X3 - 10X^2 + 10X -24X^2 - 6X + 15

= 40X^3 - 34X^2 + 4X + 15

Answer:

The total of ways the buildings can be painted are  = 4 [tex]\times[/tex] 3  [tex]\times[/tex] 2  [tex]\times[/tex] 2  [tex]\times[/tex] 1 = 48 ways.

Step-by-step explanation:

i) color five buildings that are in a row.

ii) any two neighboring buildings must be different colors

iii) the first third and fifth buildings must be different colors.

iv) the number of ways to paint the fist building are 4.

v) the number of ways to paint the second building are 3.

vi) the number of ways to paint the third building are 2.

vii) the number of ways to paint the fourth building are 2.

viii) the number of ways to paint the last building are 1.

ix) therefore the total of ways the buildings can be painted are

   = 4 [tex]\times[/tex] 3  [tex]\times[/tex] 2  [tex]\times[/tex] 2  [tex]\times[/tex] 1 = 48 ways.

Answer:

84

Step-by-step explanation:

we can split it into 2 cases: 1 case is when you choose the last building first and the second case is when you choose it last: so it is 4x2x2x3 for the first case and 4x3x3x1 for the last. So it’s 36+48=84 total cases.

Answer:

StartFraction pi Over 4 EndFraction times StartFraction 180 degrees Over pi EndFraction.

Step-by-step explanation:

We know the relation between radian and degree is that, π radians = 180°.

Then we have to calculate the degree that is equivalent to [tex]\frac{\pi }{4}[/tex] radians.

Now, using the unitary method, we can calculate the degree value.

Therefore, [tex]\frac{\pi }{4}[/tex] radians is equivalent to [tex]\frac{\pi }{4} \times \frac{180}{\pi } = \frac{180}{4} = 45 ^{\circ}[/tex].

So, it is StartFraction pi Over 4 EndFraction times StartFraction 180 degrees Over pi EndFraction. (Answer)

After evaluating the expression with the given values for x, y, and z by following the order of operations, the final result of the expression is 28.

To evaluate the expression given x=4, y=9, and z=7, we follow the order of operations, which means we perform the operations inside the parentheses first before multiplying by x.

First, calculate the value inside the parentheses as follows:

y + z - 3 squared

= 9 + 7 - 32

= 9 + 7 - 9

= 16 - 9

= 7

Now, multiply this result by x:

x(y + z - 3 squared)

= 4(7)

= 28

So, the evaluated expression equals 28.

Answer: Angle X = 30

Step-by-step explanation: First and foremost, we should recognize that an isosceles triangle has two sides equal and the two angles subtended by the two equal sides are also equal in measurement.

This means. In the diagram on the left, line DE = line DF and that is 10cm.

The similar angles are the ones subtended by the lines identified as being equal, that is

Angle E = angle F and that is 75. If both angles measure a combined total of 150 the third angle can be derived simply as

180 - (75+ 75)

{Sum of angles in a triangle = 180}

180 - (150)

= 30

Therefore angle D = 30.

However having been given in the question that both triangles are similar and are isosceles, then

Angle D = Angle X and that is 30

Answer:

Answer:

es mi amigos senior le si nueve diez veite treinta Cien si onu fose locas

Step-by-step explanation:

Answer: 6.99 times.55x

Step-by-step explanation: