An 18-foot flagpole casts a shadow 12 feet long forming a triangle as shown in the diagram. You are 5.75 feet tall and cast a shadow as shown. How long is the shadow you cast given the triangles shown are similar?

A. 3.83

B. 8.63

C. 11

Answer:

y = 4x -18

Step-by-step explanation:

y-2 = 4(x-5)

y = 4x -20+2

y = 4x -18

Answer:

y = 4x-18

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 4x+b

Substitute the point in the equation and solve for b

2 = 4(5)+b

2 = 20+b

2-20 = b

-18 =b

y = 4x-18

Given:

The table of values is:

x :     -7          -5         -3           -1

y :      5           9         13          17

To find:

Whether the given data is linear and then find the equation.

Solution:

The given data is linear if the slope and rate of change is constant.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the slope formula. we get

[tex]\dfrac{9-5}{-5-(-7)}=2[/tex]

[tex]\dfrac{13-9}{-3-(-5)}=2[/tex]

[tex]\dfrac{17-13}{-1-(-3)}=2[/tex]

Since the rate of change is constant, i.e., 2, therefore the given data is linear.

The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-5=2(x-(-7))[/tex]

[tex]y-5=2(x+7)[/tex]

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

Adding 5 on both sides, we get

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

[tex]y=2x+19[/tex]

Therefore, the equation for the given data is [tex]y=2x+19[/tex].

Answer:

32 cars

Step-by-step explanation:

we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32

Math step-by-step:

30-14=16

16×2=32

Answer:

5x-6

Step-by-step explanation:

f(x) = 2x + 3

g(x) = 3x - 9

f(x) + g(x) = 2x + 3  + 3x-9

               = 5x-6

Answer: -5, -1

Step-by-step explanation:

Answer:

44.4

Step-by-step explanation:

Using SOH

sin(x)=7/10

x= 44.427

Answer:

x ≈ 44.4°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{10}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{7}{10}[/tex] ) ≈ 44.4° ( to the nearest tenth )

Answer:

See attachment

Step-by-step explanation:

A function is given to us and we need to tell which graph represents the given function. The function given to us is,

[tex]\tt: \implies f(x) = -( x + 3 )( x + 1 ) [/tex]

Let's find out at which points do the graph Intersects x axis / finding the roots. For that substitute f(x) = 0 , we have ,

[tex]\tt: \implies -(x +3)( x + 1 ) = 0 [/tex]

Equate each factor by 0 ,

[tex]\tt: \implies \boxed{\blue{ \tt x = -1,-3 }} [/tex]

Therefore the graph will intersect x axis at x is equal to -1 and x is equal to -3 .

On looking at the given graphs in the options the second graph intersects x axis at -1 and -3 .

Hence the second option is correct .

{ See attachment }

The graph of the function is graph (b)

The function is given as:

f(x) = -(x + 3)(x + 1)

The above equation means that:

Hence, the graph of the function is graph (b)

Read more about quadratic functions at:

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Answer:

here

Step-by-step explanation:

Answer:

a. 2,727

b. (85.6%, 87.6%)

Step-by-step explanation:

The percentage of the adults aged 57 through 85 that used at least one prescription medication = 86.6%

a. The expected number of the 3,149 subjects aged 57 through 85 that used at least one prescription medication = 3,149 × 86.6/100 = 2,727.034 ≈ 2,727 (subjects)

b. The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is given as follows;

[tex]CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p} \cdot (1-\hat{p})}{n}}[/tex]

Where;

[tex]\hat p[/tex] = 86.6/100= 0.866

n = 3,149

z = The z-value at 90% confidence level = 1.645

Therefore, we get the following confidence interval of the percentage of adults (rounded to one decimal place as required);

[tex]\left (0.866 - 1.645\times \sqrt{\dfrac{0.866 \times (1-0.866)}{3,149}}\right) \times 100 \% \approx 85.6 \%[/tex]

[tex]\left( 0.866 + 1.645\times \sqrt{\dfrac{0.866 \times (1-0.866)}{3,149}} \right) \times 100 \% \approx 87.6 \%[/tex]

The 90% confidence interval, of the percentage C.I. ≈ (85.6%, 87.6%).

Answer:

A point.

Step-by-step explanation:

An object in geometry that has width, length or height is simply a point. A point is yet just a dot.

Answer:

top left questions answer is B

the area of the triangle is A

Volume of the cylinder is B

The area of the triangle for q 17 is A

Answer:

1. b

2.a

17.c

Step-by-step explanation:

Answer:

5.7

Step-by-step explanation:

First find the coordinates of the points

A ( 2,2)

B ( -2,-2)

The distance is

d = sqrt(  (x2-x1)^2 + (y2-y1)^2)

  = sqrt(  (-2-2)^2 + (-2-2)^2 )

   = sqrt( (-4)^2 + (-4) ^2)

   = sqrt( 16+16)

  = sqrt( 32)

  =5.656854249

To the nearest tenth

5.7

Answer:

5.65

Step-by-step explanation:

(2,2) (-2,-2)

√(x2 - x1)² + (y2 - y1)²

√(-2 - 2)² + (-2 - 2)²

√(-4)² + (-4)²

√(16) + (16)

√32

= 5.65

Answer:

i dont see anything

Step-by-step explanation:

Correct question is;

The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the cheetah ran in hours. Solve (f/g)(3), and interpret the answer.

Answer:

26 is the cheetahs rate in miles per hour.

Step-by-step explanation:

We are given;

f(x) = 6x + 8

g(x) = x − 2

Thus;

f/g = f(x)/g(x)

> (6x + 8)/(x − 2)

Since we are looking for (f/g)(3), then we have;

> (6(3) + 8)/((3) − 2) = 26

Since f(x) is distance and g(x) is time, then, we know that distance/time = speed. Thus, the interpretation is 26 mph which is the speed of the cheetah.

Answer:

26; the cheetah's rate in miles per hour

Step-by-step explanation:

I just took the test

Answer:

[tex]x^3 - 12x^2 - 2x + 24[/tex]

[tex]x^2(x - 12) - 2(x -12)[/tex]

[tex](x - 12)(x^2 -2)[/tex]

Step-by-step explanation:

Answer:

[tex](x^2-2)(x-12)=0[/tex]

Step-by-step explanation:

Factoring by grouping is a way of determining the factors of a polynomial equation. One firsts groups terms by putting them in parenthesis. Then one will take a common factor out of the parenthesis. Finally, one will group the coefficients and the grouped terms respectively, thus rewriting the polynomial equation as the product of its factors.

One is given the following equation:

[tex]x^3-12x^2-2x+24=0[/tex]

Group the different terms in the equation:

[tex](x^3-12x^2)+(-2x+24)=0[/tex]

Factor, write a common factor that both terms in the parenthesis share, outside of the parenthesis.

[tex]x^2(x-12)-2(x-12)=0[/tex]

Factor the equation again. Group the like terms together, and the coefficients together.

[tex](x^2-2)(x-12)=0[/tex]

Answer: 4 Shirts

Step-by-step explanation:

Given

Person has [tex]\$80[/tex]

Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]

Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts

Spent money must be equal or less than the total money. The inequality becomes

[tex]\Rightarrow 80\geq29x+12y[/tex]

For 1 pair of pants that is, 1 pants

[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]

That is maximum number of shirts that can be bought are 4.

Answer:

sin X = 21/ 29

Step-by-step explanation:

Since this is a right triangle

sin X = opp side/ hypotenuse

sin X = 21/ 29

Answer:

[tex]\boxed{\sf sinX =\frac{21}{29}}[/tex]

Step-by-step explanation:

We need to find out the value of sinX using the given triangle . Here we can see that the sides of the triangle are 21 , 29 and 20.

We know that the ratio of sine is perpendicular to hypontenuse .

[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]

Here we can see that the side opposite to angle X is 21 , therefore the perpendicular of the triangle is 21. And the side opposite to 90° angle is 29 . So it's the hypontenuse . On using the ratio of sine ,

[tex]\sf\longrightarrow sinX =\dfrac{ p}{h}=\dfrac{ZY}{ZX}[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ X =\dfrac{21}{29}}}[/tex]

Hence the required answer is 21/29 .

Answer:

157 miles

Step-by-step explanation:

total cost = flat fee + cost per mile * miles

133.17 = 16.99 + .74 * m

Subtract 16.99 from each side

116.18 = .74m

Divide each side by .74

116.18 / .74 = .74m/.74

157 = m

Answer:

Acute and scalene

Step-by-step explanation:

All the three interior angles of triangle are less than 90 then it is an acute triangle.

All the sides have different length then it is Scalene triangle. In Scalene triangle, all the sides have different length and so all the angles are of different

Explanation:

You have the right idea. The triangle is acute since all three angles are less than 90 degrees. The triangle is also scalene because all three sides are different lengths.

For a triangle to be equilateral, the three sides must be the same length. So we can rule out choice A.

We can rule out choice B since none of the angles are larger than 90 degrees. This contradicts choice E.

We can rule out choice C because we don't have exactly two sides the same length. This contradicts choice D.

We can rule out choice F because we don't have a 90 degree angle. This contradicts choice E.

Answer:

4       :  5

Step-by-step explanation:

boys : girls

12          15

Divide each by 3

12/3 :  15/3

4       :  5

Answer: 4:5

Step-by-step explanation:

To simplify the ratio 12:15, divide both numbers by the GCF of the 2 numbers (3). This gives you the simplified ratio, 4:5.

Answer:

[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]

Answer:

base area=16π in² height=6 in ⇒ base area= πr²

16π²=π(r)²

r=4 in

v=1/3 ×π (4)²×(6)

v=32π in²

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

v=1/3 π(12/2)²×5

v=1/3π(31)×5=

v=60π in³

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

v=1/3 π×(25×4)=

v=100π/3 in³

OAmalOHopeO

Answer:

Step-by-step explanation:

I answered this in your question from yesterday. See #24317186

Answer:

5 : -1.5

10: -4

y =  1 -.5x

noticed the pattern of subtracting .5 .... then plugged in x = 4

and saw that -2 had to be combined with "1" to end up with a "-1"

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

x + 40 + 100 + x=360. (sum of angles at a point)

2x+140=360

2x=360-140

2x=220

x=220/2

x=110⁰

Answer:

3 x plus 8 minus 8 equals 14 minus 8

Step-by-step explanation:

3x+8 = 14

Step 1 subtract 8 from each side

3x+8-8 = 14-8

Answer:450

Step-by-step explanation:

The correct answer is option (F) 450 cm

For a circle with radius 'r' and the central angle 'θ' (in radians), an arc length 's' is,

s = r × θ

C = 2 × π × r

We have been given that the length of xy (the minor arc) is 15 cm and angle = 12°.

⇒ θ = 0.209 radians

Let r be the radius of the circle.

xy = 15

⇒ r × θ = 15

⇒ r × 0.209 = 15

⇒ r = 71.77 cm

The circumference of the circle is,

C = 2 × π × r

⇒ C = 2 × π × 71.77

⇒ C = 450.95

⇒ C ≈ 450 cm

Therefore, the circumference of the circle is option (F) 450 cm

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Answers:

=========================================

Explanation:

In this exercise we have to use the knowledge of angles, in this way we can say that:

A) Right angles

B) Substitution

C) Congruence

So punctuating some necessary definitions we have that:

A) This alternative is a right angle, that is, an angle that has 90 degrees.

B) The substitution property allows us to replace one thing for another, as long as the two things are equal.

C) IIn this alternative, we are dealing with congruent angles, that is, angles that have the same measure, normally less than 90 degrees.

See more about angles at brainly.com/question/15767203

Answer:

2x+8w

I hope this will help you