suppose you are standing such that a 63-foot tree is directly between you and the sun. if you are standing 240 feet away from the tree and the tree casts a 270-foot shadow, how tall could you be and still be completely in the shadow of the tree?

The equation of the parabola is y = -x² - 2x + 5

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k - p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

The equation of the parabola with the points

A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )

So , from the equation of parabola ,we get

y = ax² + bx + c

Substituting the values of x and y , in the equation of point A , we get

-10 = a ( -5 )² - 5b + c

-10 = 25a - 5b + c   be equation (1)

Substituting the values of x and y , in the equation of point B , we get

2 = a ( -3 )² - 3b + c

2 = 9a - 3b + c   be equation (2)

Substituting the values of x and y , in the equation of point C , we get

-3 = a ( 2 )² + 2b + c

-3 = 4a + 2b + c   be equation (3)

By the method of brute force , we can solve the equations and derive the equation for the parabola

So , the equation for the parabola will be

y = -x² - 2x + 5

Now , substituting the values of x and y from the points , we get

For point A ( -5, -10 )

-10 = - 25 + 10 + 5

-10 = -10

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point B ( -3, 2 )

2 = -9 + 6 + 5

2 = 2

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point C ( 2 , -3 )

-3 = -4 - 4 + 5

-3 = -3

Therefore , the equation is TRUE

Hence , the equation of the parabola is y = -x² - 2x + 5

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Answer:

  $7

Step-by-step explanation:

You want to know the cost of each friend's meal if 5 friends spend $41 on their food, which includes a $6 delivery charge.

For 'a' friends spending 'x' on each meal, the total cost is ...

  6 + ax = 41

Solving for x, we have ...

  ax = 41 -6 = 35

  x = 35/a

When the number of friends is a = 5, the cost of a meal is ...

  x = 35/5 = 7

The cost of each friend's mean when the number of friends is 5 is $7.

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The equation  that can be used to find the number of hotdogs

and sodas sold at the swim meet.

a)x+0.50y=150

b)  y=-2x+300

c)Number of soda sold y =220 if hot dog is 40.

d)  x intercept=150. It is related to the total earnings of soda and hot dogs sold.

f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

What is x-intercept and y-intercept?

An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.

Let us take number of hot dogs sold as x and number of soda sold as y.

Cost of one hot dog = $1.00

Cost of one soda = $0.50

Then , cost of x number of hot dogs sold = 1x

cost of y number of soda sold = 0.50y

Then, . At the end of the day you made $150.

=> 1x+0.50y= 150

a) standard form of the equation is ,

=> x+0.50y=150 ------->1

b) x+0.50y=150

=> x+[tex]\frac{1}{2}[/tex]y=150

=>2x+y=150*2

=>2x+y=300

Then slope intercept form is  y=-2x+300------->2

c) Number of hot dogs sold x=40 and put into 2 ,

then ,  y=-2(40)+300

=> y=-80+300

=>y=220

Number of soda sold y =220

d) To find x intercept put y=0 into 1 , then

=> x+0=150

=>x=150

Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.

e)To find y intercept put x=0 into 1,

=> 0+0.50y=150

=> y = 150/0.50

=> y =300

Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

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The larger bottle will be able to hold a volume of 1372ml

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

This shows that the ratio of the cube of length of the bottle is equal to the the ratio of their volumes

the length of the smaller bottle = 15, the cube of the length= 15^3= 3375

the length of the larger volume = 21, the cube of the length is 21^3=9261

therefore 3375/9261= 500/x

x is the volume of the larger bottle

therefore x= 500×9261/3375

x= 1372ml.

therefore the volume of the larger bottle is 1372ml

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Answer:

x = −22/3 + 5y/3

y = 22/5 + 3x/5

Step-by-step explanation:

The formula used in the situation of sending the emails is distributive property of multiplication and simple addition formula

information gotten from the question

you send e-mails to tell your four friends about the school fair

Then those people send e-mails to four more people

From the first statement the number of emails sent is 4

The second statement says that the 4 persons sent to 4 more people hence each person sent one email

The total number of email sent is solved by

= 4 emails sent by you + 1 email sent by each friend * 4 (distributive property)

= 4 emails sent by you + 4  emails sent by friends

= 8 emails

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Answer: x = -2/3 , 1

Step-by-step explanation:

step 1 (hardest step!) factor by grouping:

(3x + 2)(x-1) = 0

the rest is easy:

3x + 2 = 0  or (x-1) = 0

Solve each for x:

3x + 2 = 0

x = -2/3

x-1 = 0

x = 1

So your 2 solutions for x are -2/3 and 1

Answer:

Step-by-step explanation: 0.2

The length of side x is 6cm

We need to find the scale factor of the shapes below are mathematically similar.

it can be found using the two bases given.

The base of the smaller triangle is 9  and that of large triangle is 12

9/12 = 3/4

The smaller triangle is 3/4 of the larger one.

Multiply the known side by 3/4

X = 8 x 3/4 = 6

X= 6

Therefore, the length of side x is 6cm

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The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds​.

What are the rates?

A rate is a unique ratio where the two words are expressed in several units.

Rate formula

r = d/t

Here, we calculate different rates

a. Per pound price of apples = Total cost / total weights of apples

                                             = 0.80 / 1 = $0.80

Cost of 3 pounds of apples = 3 × 0.80 = $2.4

b. Per pound cost of apples = Total cost / total weights of apples

                                               = 14.50 / 5  = $2.9

Cost of 3 pounds of apples = 3 × 2.9 = $8.7

c. Per pound cost of apples = Total cost / total weights of apples

                                               = 7.50 / 9 = $0.833

Cost of 3 pounds of apples = 3 × 0.833 = $2.49

d. Per pound cost of apples = Total cost / total weights of apples

                                              = 9.60 / 11 = $0.872

Cost of 3 pounds of apples = 3 × 0.872 = $2.61

e. Per pound cost of apples = Total cost / total weights of apples

                                               = 10 / 12 = $0.833

Cost of 3 pounds of apples = 3 × 0.833 = $2.49

Hence, The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds​.

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(a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

In the question ,

it is given that

the rate at which the hamburgers are selling = 160 hamburgers per hour ,

we need to find the rate at which the wraps are selling

From the table ,

we can see that the wraps are sold in an Arithmetic Progression ,

So , at 60 minutes the wraps sold = 2.5 + (n-1)d

= 2.5 + 59×2.5

= 2.5 + 147.5

= 150

So , after one hour , number of wraps sold is 150 and the number of hamburgers sold is 160 .

Similarly , after 2 hours , the number of wraps sold will be 300 and number of hamburgers sold will be 320 .

So, the hamburgers sells faster than wraps .

the slope(steepness)  of the hamburgers = (number of hamburgers sold)/60

= 160/60

= 2.667

the slope(steepness) of the wraps = (number of wraps sold)/60

= 150/60

= 2.5

from the above data , we can see that the steepness of hamburgers is more ,

which means that the hamburgers sells faster than wraps .

the equation that denotes the number of hamburgers sold is y = 2.667x

the equation that denotes the number of wraps sold is y = 2.5x

where x is time in minutes .

The graph that represents the growth rate of hamburger and wraps is shown below .

Therefore , (a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

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Answer: -2

Step-by-step explanation:

since g(x) is a function, x needs to be 0 in order to find the y-intercept. so we plug in 0 to the function. -|0+6|+4=-2 so the y-intercept is -2

Answer:

12 ; 13 ; 14

Step-by-step explanation:

x = sister one

x+ 1 = sister two

x+2 = sister three

2x + 3(x+2) = 4(x+1) + 14

2x + 3x + 6 = 4x + 4 + 14

5x + 6 = 4x + 18

5x - 4x = 18 - 6

x = 12 (sister one)

12 + 1 = 13 (sister two)

12 + 2 = 14 (sister three)

Answer:

$325

Step-by-step explanation:

t +b = 582

t = b - 68

b - 68 + b = 582

2b = 582 + 68

2b = 650

2/2 b = 650 / 2

b = 325

The solution for the intersection point of a triangle is given below.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of angle of a triangle is always 180°

Perpendicular bisectors of the sides is circum center.

The bisector of angles of a triangle is in center.

Intersection point of medians is centroid

The intersection point of altitudes is ortho center.

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300 different (non-equivalent) color schemes are possible.

For starters, there are 49 boxes in total and there are 49[tex]c_{2}[/tex] ways of picking the two yellow boxes which are 1176 ways

clearly, there are far fewer than 1176 "magical" setups

At first, I attempted to brute force this problem but realized that it was too hard to do that

according to a source, there are (1176−24)/4+24/2 =300. This is the same numerical answer as your formula, after simplification.

the system of making something much less complicated and consequently less complicated to do or recognize, or the issue that results from this technique: The corporation advises on the simplification of change strategies. this is a gross simplification of what truly took place. one of the earliest proponents of person simplification was Lufei Kui, who proposed in 1909 that simplified characters need to be used in education.

Bracket (Brackets are solved in order of (), {} and [] respectively. Of Þ multiplication, however, it's miles to be completed earlier than division. So for simplifying expressions, we ought to observe the above collection. in the previously given instance, we first divide 8 through four and upload it to 12 as division (D) is before more than one (M) in BODMAS. Simplification of terms inside the brackets may be achieved immediately. which means we are able to carry out the operations in the bracket inside the order of division, multiplication, addition, and subtraction.

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The value of Y = 17.77 when X = 3, and the value of Y = 16 when X = 3

The equation which represents "Y varies inversely as the square of X"  can be written as:

Y = k/X² where "k" is a constant.

Substitute the values of  X=4 and Y= 10 in the variation equation and solve for k:

⇒ 10 = k/(4)²

⇒ 10 = k/16

⇒ k = 160

The variation equation :

⇒ Y = 160/X²

Substitute the values of X = 3 in the above equation and solve for Y:

⇒ Y = 160/(3)²

⇒ Y = 160/9

⇒ Y = 17.77

Thus, the value of Y = 17.77 when X = 3

The equation which represents "Y Varies inversely as X"  can be written as:

Y = k/X where "k" is a constant.

Substitute the values of Y=8 and X=6 in the variation equation and solve for k:

⇒ 8 = k/(6)

⇒ k = 48

The variation equation :

⇒ Y = 48/X

Substitute the values of X = 3 in the above equation and solve for Y:

⇒ Y = 48/(3)

⇒ Y = 16

Thus, the value of Y = 16 when X = 3

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Answer: x=0  y=4

Step-by-step explanation:

6x - 3(2x + 4) = 12

6x - 6x - 12 = 12

0 = 0

therefore, x = 0

substitute x=0 into y = 2x + 4

y = 2(0) + 4 = 4

Answer:

Step-by-step explanation:

reciprocal of 51/3 is 3/16

Hi you need to change 5 1/3 from mixed number to improper fraction 51/3=(5x3)+1  /3 =16/3

The  reciprocal   of 16/3 is 3/16

The particle will move to the right for t > a .

In the question ,

it is given that ,

a particle moves along the x axis , such that at any time t ≥ 0 ,

its position is given by the equation

x(t) = 12(a−t)²  ,

where a is = positive constant

to find value of the particle moves right ,

we differentiate x(t) , with respect to "x" .

x'(t) = 12×2(a - t)×(-1)

v(t) = -24(a-t)        ..... because x'(t) = v(t)

for particle to move right , v(t) > 0 .

-24(a-t) > 0

dividing both sides by "-24" , we get

a - t < 0

a < t

t > a .

Therefore , The particle will move to the right for t > a .

The given question is incomplete , the complete question is

A particle moves along the x-axis so that at any time t ≥ 0 its position is given by x(t)=12(a−t)² , where a is a positive constant. For what values of t is the particle moving to the right ?  

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Ther right option is that there is not enough evidence to conclude that there is enough association between vaccine location and severe reaction.

Given that,

Children who received the vaccine in the thigh received the first random sample. Children who received the immunization in the arm provided the second random sample.

The chi-square test yields a chi square is 2.0609 with a P value of 0.1511 meaning, the chi square test is not statistically significant.

A,B is therefore out.

C is not also right.

D is what we get when we cannot reject null hypothesis.

Therefore, We cannot conclude that there is dependence.

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The probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

How to calculate the probability?

Given

μ = 41.4

σ = 5.5

First, we need to find the z score when the rainfall 43 inches. So:

z = (x - μ) / σ

z = (43 - 41.4) / 5.5

z = 0.2909

Then, to find out the probability we need to find P(z < 0.2909) in the z score table. So, we get 0.6141 or in percentage is 61.41%.

Thus, the probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

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a. The value of 9.9² × 1.79 is 175.44.

b. The value of ✓97.5 + 1.96 is 11.83

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value of 9.9² × 1.79 will be:

= 9.9² × 1.79

= 98.01 × 1.79

= 175.44

The value of ✓97.5 + 1.96 will be:

= ✓97.5 + 1.96

= 9.87 + 1.96

= 11.83

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Answer:B= 7/9 C=10/9 A=0.62

Step-by-step explanation:

i know this because i multiplyed by 1/3 by 3 to get 3/9 6/9 9/9 for the number line

The system of equations for determining the dollar amount of  phone and computer sales are Sc = Sp + 600 and 0.05Sc + 0.04Sp = 1200

A commission is defined as the compensation paid to a person or entity based on the sale of a product. It is calculated on a percentage basis

Given:

Phone sales commission = 4%

Computer sales commission = 5%

Total commission = $129

Let Sc and Sp represent the dollar amount of phone sales and computer sales respectively

If Houa had $600 more in computer sales than in phone sales, the equation can be written as:

Sc = Sp + 600

Since Houa earns a 4% commission on phone sales and a 5% commission on computer sales, and a total commission of $129. Thus, the equation for the commission can be written as:

0.05Sc + 0.04Sp = 1200

Note:  5% = 5/100 = 0.05 and  4% = 4/100 = 0.04

Therefore, the system of equations for determining phone and computer sales are Sc = Sp + 600 and 0.05Sc + 0.04Sp = 1200

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