1. An arch in the shape of a semicircle is to be set up at the entrance of a festival.
The distance around the arch is about 110 feet. What is the height of the arch, in
feet? Round your answer to the nearest whole number.​

Answer:

x = -14

Step-by-step explanation:

Look at the image attatched. I have labeled the angles for better explanation.

We know that angle 1 is 54 degrees as is rests on a straight line with its adjacent angle at 126 degrees. This means that angle 1 would be 180 - 126 degrees, or 54 degrees. We also know that angle 1 and 3 must be congruent as the sides of the triangle opposite those angles are congruent as well. This means that both those angles are 54 degrees. Since the sum of all angles in a triangle must equal 180 degrees, we can get that angle 4 is 180 - (2*54) degrees, or 72. Since angle two and angle 4 both lie on a straight line, they must add up to 180 degrees. This means that the value of angle 2 would be 180 - 72, or 108 degrees. Since angle 2 is also equal to x+122, we get the equation:

108 = x + 122.

We then solve this by getting:

x = 108 - 122

which gives us the answer of

x = -14

Answer: x = -14

Step-by-step explanation:

a) Top triangle, top angle: Using the Linear Pair Postulate, 180° - 126° = 54°

b) Top triangle, bottom left angle: Congruent sides implies congruent angles = 54°

c) Bottom triangle, top left angle: Using the Complimentary Angles Postulate, 90° - 54° = 36°

d) Bottom triangle, bottom angle: Congruent sides implies congruent angles = 36°

Triangle Sum Theorem states that the sum of the three angles must equal 180°.

36° + ∠2 + 36° = 180°

36° + (x + 22) + 36° = 180°

x + 194 = 180

         x = -14

Answer:

[tex]9[/tex]

Step-by-step explanation:

[tex]x \div 4=9/4[/tex]

[tex]x=9/4 \times 4[/tex]

[tex]x=36/4[/tex]

[tex]x=9[/tex]

Answer:

9

Step-by-step explanation:

x/4=9/4

x=9 (multiply both sides by 9)

Answer:

5.1

Step-by-step explanation:

Before we calculate  the y value for the point Q that is located two thirds the distance from point P to point R, we need to get the distance of point p from point R using the formula for calculatingf the distance between two points

D = √(x2-x1)²+(y2-y1)²

Given P(−2, 7), and R(1, 0)

RP = √(1-(-2))²+(0-7)²

RP = √3²+(-7)²

RP = √9+49

RP =√58

To get the y value for point Q that is located two thirds the distance from point P to point R, this will give

PQ = y = 2/3 of √58

= 5.1

Answer: I Believe its 2.3

Step-by-step explanation:

P is located at (-2,7)

R is located at (1,0)

Look at the y coordinates

P(-2,7)  R(1,0)

7 to 0= distance of 7

multiply 2/3 by 7 = 4.7      (it was originally 4.666666665 but i couldnt find the answer with just 4.6 so i rounded it to 4.7)

Now plug in the info we know:

.y axis = 7 - 4.7 = 2.3

Hope this helped! Im taking the test and ill be back if this is wrong

Answer:

there are fourteen 4-point questions and twenty six 2-point questions.

Step-by-step explanation:

Given : A 40-question test has 108 possible points.

There are m 4-point questions and n 2-point questions.

So , equation for total number of questions in the test :

m + n = 40 | 4n + 2n = 108

Multiplying (i) by 2 , we get

2m + 2n = 80

Subtract (iii) from (ii) , we get

2m = 28

⇒ m = 28/ 2 = 14

Using value of m in (i) , we get

14 + n = 40 ⇒ n = 26

from this we get there are fourteen  4-point questions and twenty six 2-point questions.

hope this helped!

Answer:

108

Step-by-step explanation:

Answer:

it is longer than 1/3

Step-by-step explanation:

Answer:

A = 90.25π

Step-by-step explanation:

Area of a circle = [tex]\pi r^2[/tex]

r = 9.5

A = 90.25π

Answer:

[tex]\pi \times 9.5 {?}^{2} [/tex]

Answer:

x = -7/2, y=2

Step-by-step explanation:

2x + 5y = 3

-2x - y = 5​

Add the two equations together to eliminate x

2x + 5y = 3

-2x - y = 5​

------------------------

     4y = 8

Divide each side by 4

4y/4 = 8/4

y =2

Now find x

2x +5y =3

2x +5(2) =3

2x+10 =3

Subtract 10

2x = -7

Divide by 2

2x/2 = -7/2

x = -7/2

Answer:

2

Step-by-step explanation:

A factor is a number that can evenly divide into another number.

Let’s list all the factors of both numbers.

26: 1, 2, 13, 26

14: 1,2, 7, 14

Now find the GCF, or greatest common factor. The biggest number that is a factor of both 26 and 14 is 2.

Therefore, the GCF of 26 and 14 is 2.

Answer:

(5x²+2y² + 2xy)(5x²+2y²-2xy)

Step-by-step explanation:

25x⁴+4x²y²+4y⁴= (5x²)²+2*5x²*2y²+(2y²)² - 16x²y²= (5x²+2y²)² - (4xy)²= (5x²+2y² + 2xy)(5x²+2y² - 2xy)

Answer:

The second figure is the correct figure.

Step-by-step explanation:

Graph (ii) is solution of system of equation.

We have to given that,

System of equations are,

2x + y = 3

3y = x - 12

Now, Solve the equations and find the solution,

Here, Equations are,

2x + y = 3  .. (i)

3y = x - 12  .. (ii)

From (i);

y = 3 - 2x

Substitute in (ii);

3 (3 - 2x) = x - 12

9 - 6x = x - 12

9 + 12 = 6x + x

7x = 21

x = 3

And from (i);

2 × 3 + y = 3

6 + y = 3

y = - 6 + 3

y = - 3

Hence, Solution is, (3, - 3).

So, Graph shown in option (ii) has intersection point (3, - 3)

Thus, Graph (ii) is solution of system of equation.

Learn more about systems of equations at:

brainly.com/question/14323743

#SPJ2

Answer:

C.

Step-by-step explanation:

= [tex]\sqrt[3]{8}^{x}\\[/tex]

= Since [tex]\sqrt[3]{} = ^{1/3}[/tex]

= So, It becomes :

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

Answer:

$7.50

Step-by-step explanation:

Since there is a 50% chance that the card is odd, the expected payoffs would be $15 * 50%=0.5*15=7.5. Hope this helps!

Step-by-step explanation:

It might be easier thinking of "rate of change" as the slope. Since you'll be finding a slope, then, use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the values.

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{20-12}{8-6}\\m=\frac{8}{2} \\m=4[/tex]

Answer:

[tex]m=\frac{4}{1}[/tex] or [tex]m=4[/tex]

Answer:

[tex]-3(x+2)+5x=-9\\-3x-6+5x=-9\\-3x+5x=-9+6\\2x=-3\\x=-\frac{3}{2}[/tex]

Answer:

27 miles

Step-by-step explanation:

2/3rds of the way home is 18 miles

2/3 d = 18

Multiply each side by 3/2

3/2 * 2/3 = 18 *3/2

d = 27

The distance is 27 miles

Answer:

The median is 47

Step-by-step explanation:

that line in the middle of the box is directly on 47

Answer:

7

Step-by-step explanation:

y=mx+b

b= y-intercept

So 7 is your answer

235.5 units^2 or 75π

Here is why:

The formula for the surface area of a cone is...

[tex]SA=\pi r^2+\pi rl[/tex]

Since you didn't specify if you wanted an exact or approximate answer, I will be doing both. The lateral height is l, so I'm going to assume the height you gave is the lateral height. We can now plug everything in.

[tex]SA=(3.14*5*5)+(3.14*5*10)[/tex]

[tex]SA=78.5+157[/tex]

[tex]SA=[/tex]

235.5

Now that we have the approximate answer, we will find the exact answer or the answer in pi.

[tex]SA=(\pi *5*5)+(\pi *5*10)[/tex]

[tex]SA=25\pi +50\pi[/tex]

[tex]SA=[/tex]

75π

~

The approximate answer for the surface area of the cone is 235.5 units^2 and the answer in terms of pi is 75π.

Answer:

The government loses $1000 per tax payer, according to the following function:

[tex]y(x) = -1000*x[/tex]

Where "y" is the total money earned by the government and "x" is the number of tax payers.

Step-by-step explanation:

Let's call the monetary balance of the government after one year "y", where "x" is the number of tax payers. Since each tax payer, "x", pays a total of $1500 every year, but the government spends $2500 with each one of them, then we can build a function "y(x)", with the value of collected tax being positive while the cost of each tax payer is negative, as shown below:

[tex]y(x) = 1500*x - 2500*x\\y(x) = x*(1500 - 2500)\\y(x) = -1000*x[/tex]

The government loses $1000 per tax payer.

Answer:

The relationship between the angles is alternate exterior angles.

Step-by-step explanation:

Exterior means outside.

Alternate means every other or in this case across form each other.

These angles represent alternate exterior angles because they are on the outside of the transversal and they are alternating each other.

Answer:

27

Step-by-step explanation:

given value of Z=9

so, 3×9=27

Answer:

A.

Step-by-step explanation:

Plug it in:

3 + 5 = 8

TRUE

Answer:

4x+6

Step-by-step explanation:

P=2L+2W

P= 2(x+2) +2(x+1)

P= 2x+4+2x+2

P= 4x+6

Answer:

Since the slope of the line is (31/4 - 25/4) / (5/4 - 3/4) = 3 that means that for every 1 that x increases, y increases by 3 so an example could be 1 3/4 for x and 9 1/4 for y.

Answer:

a) 4, 7, 12, 19

b) 2, 8, 18, 32

Step-by-step explanation:

Sequence is just number line sir, so to begin with you get n=1, then n=2, then n=3, then n=4, these are the first 4 terms

Answer:

a) 4, 7, 12, 19

b) 2, 8, 18, 32

Step-by-step explanation:

In order to find the first 4 terms, you have to substitute 1 to 4 into n for both expressions :

[tex]a) {n}^{2} + 3[/tex]

[tex]1st \: term \\ {1}^{2} + 3 = 4[/tex]

[tex]2nd \: term \\ {2}^{2} + 3 = 7[/tex]

[tex]3rd \: term \\ {3}^{2} + 3 = 12[/tex]

[tex]4th \: term \\ {4}^{2} + 3 = 19[/tex]

[tex]b)2 {n}^{2} [/tex]

[tex]1st \: term \\ 2( {1}^{2} ) = 2[/tex]

[tex]2nd \: term \\ 2( {2}^{2} ) = 2(4) = 8[/tex]

[tex]3rd \: term \\ 2( {3}^{2} ) = 2(9) = 18[/tex]

[tex]4th \: term \\ 2( {4}^{2} ) = 2(16) = 32[/tex]

Answer:

Probability ≈ 0.1071

Step-by-step explanation:

Consider steps below;

[tex]Total Possible Outcomes - 8C5,\\\\8! / 5! ( 8 - 5 )!,\\1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 / ( 1 * 2 * 3 * 4 * 5 )( 1 * 2 * 3 ),\\\\6 * 7 * 8 / 6 = Combinations - 56,\\\\[/tex]

[tex]Number Of Outcomes - 6C5,\\\\6! / 5! ( 6 - 5 )!,\\1 * 2 * 3 * 4 * 5 * 6 / ( 1 * 2 * 3 * 4 * 5 ) ( 1 ),\\720 / 120 * 1,\\\\Outcomes - 6[/tex]

[tex]Conclusion ; Solution - 6 / 56 = ( About ) 0.1071\\Hope That Helps![/tex]

Solution; Probability ≈ 0.1071

Answer:

The probability is 0.107

Answer:

solo la conosco como ipotenuza

Step-by-step explanation:

Answer:

flank right-angled triangle right triangle

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I got it on the test

The measure of ∠ABC in the triangle below is 60°

Triangle is a polygon with three sides and three angles. The sum of angles in a triangle is 180°.

∠ACB + 135 = 180° (Sum of angles in a straight line)

∠ACB = 45°

In triangle ABC:

∠ABC + ∠ACB + ∠CAB  = 180° (Sum of angle in a triangle)

∠ABC + 75 + 45 = 180

∠ABC = 60°

The measure of ∠ABC in the triangle below is 60°

Find out more on Triangle at: https://brainly.com/question/23945265