At a certain time of day, the angle of elevation of the sun is 80degree. Find the height of a tree whose shadow is 44 feet long.

Answer:

[tex]x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]

Step-by-step explanation:

[tex]\begin{cases}\alpha -\beta =2\\ \alpha^{2} -\beta^{2} =3\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \left( \alpha +\beta \right) \left( \alpha -\beta \right) =3&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \alpha +\beta =\frac{3}{2} &\end{cases}[/tex]

Then

2α = 2 + 3/2 = 7/2

2β = (3/2) - 2 = -1/2

Then

Then

α = 7/4

β = -1/4

Then

a quadratic equation with root α and β can be :

[tex]\left( x+\frac{1}{4} \right) \left( x-\frac{7}{4} \right) =0[/tex]

[tex]\Longrightarrow x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]

Answer:

It's 3

Step-by-step explanation:

if you go to desmos graphing calculator it'll help you get the solutions for these if you type it in every number and letter and for exponents type ^ its shift then type 6.

Answer:

5th or 6th grade

Step-by-step explanation:

The reason why we learn geography in 5th grade is to prepare us for 6th grade geography. The reason why we learn geography in 6th grade is because Geography helps us understand basic physical systems that affect everyday life. In other words, geography is a nice skill to have when you're learning about the water cycle or rock formations, or the moving of the tectonic plates (and other natural disasters). It's also a very important skill to have when you want to start traveling.

Slope of the given data is 579.88

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.

Here, given data;

            x₁ = 2009                   y₁ = 12078 burger

            x₂ = 2017                    y₂ = 16717 burger

Now, Slope = (y₂ - y₁)/(x₂ - x₁)

         Slope = (16717 - 12078) / (2017 - 2009)

         Slope = 4639 / 8

         Slope = 579.88

Thus, Slope of the given data is 579.88

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Answer:

AB : y=1/5x+12

CB : y=-3x+10

CD : y=1/2x-1

DA : y=-2x+1

Answer:

29/7

Step-by-step explanation:

4 1/7 = 4 + 1/7

4 = 28/7

then:

4 1/7 = 28/7 + 1/7 = (28+1) / 7

= 29/7

Answer:

n^2 -10n + 24

Step-by-step explanation:

Given expression:

(n-6)(n-4)

Solution:

Apply distributive property,then simplifying using PEMDAS,we obtain

Hence,n^2 -10n -24 is the answer.

Answer:

-9

Step-by-step explanation:

-|1-2|2+7

-|-1|9

-9×1

-9

Answer:

[tex]52\sqrt{3} ft^{2}[/tex]

Step-by-step explanation:

Please refer to the attached picture.

First we will find the area of rectangle BCDE.

Area of Rectangle = Length x Breadth = DE x CD

= 11 x [tex]4\sqrt{3}[/tex]

[tex]=44\sqrt{3} ft^{2}[/tex]

Next we will find Area of Triangle ABE.

Area of Triangle = 0.5 x Base x Height

[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]

Area of Trapezoid = Area of Rectangle + Area of Triangle

[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]

Answer:

A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height and b₁ , b₂ the parallel bases

here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)

   = 2[tex]\sqrt{3}[/tex] × 26

   = 52[tex]\sqrt{3}[/tex] ft²

   ≈ 90.1 ft² ( to the nearest tenth )

Answer:

7.1%

Step-by-step explanation:

Those that did not complete the race either gave up or were disqualified. This means that 18 + 3 = 22 people did not complete the race. The percentage is 22/310 × 100% = 7.1%

Answer:

50 ml

Step-by-step explanation:

50 ml

Answer:

6

Step-by-step explanation:

the blue factors are all the factors 12 and 18 have in common.

Step-by-step explanation:

hope you can understand

The value of the integral over limit is 20,  the average is 1.73

The signed area is shown in the graph attached.

A function is a mathematical statement used to find a relation between two variable.

To Evaluate the definite integral between

f(x) = 5 if 4≤x ≤9

f(x) = -1 if 9≤x≤14

[tex]\rm \int_{4}^{14}f(x) dx = \int_{4}^{9} 5 dx +\int_{9}^{14} (-1)dx\\\\\int_{4}^{14}f(x) dx = (5x)^{9}_{4} -(x)^{14}_{9}\\\\\int_{4}^{14}f(x) dx = 5*(9-4) - (14-9)\\\\\int_{4}^{14}f(x) dx = 20[/tex]

The average value of the interval is

= (5+5+5+5+5-1-1-1-1-1-1)/ 11 = 1.73

Therefore the average is 1.73.

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Answer:

G. 0.45

Step-by-step explanation:

To find expected value, you simply multiply the value of each outcome (the numbers in the left column) by its probability

(the numbers in the right column) and then add them all together.

0(0.7) + 1(0.2) + 2(0.05) + 3(0.05)

0 + 0.2 + 0.1 + 0.15 = 0.3 + 0.15 = 0.45

The expected value is 0.45. Thus, the correct option is G.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The expected value is calculated as,

E(x) = 0 x 0.70 + 1 x 0.20 + 2 x 0.05 + 3 x 0.05

E(x) = 0 + 0.20 + 0.10 + 0.15

E(x) = 0.45

Thus, the correct option is G.

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The domain of the graph is [-3, 2) and the range is (-4, 5]

From the given graph, we have the following highlights:

Open circles are represented with () while closed circles are represented with []

Hence, the domain of the graph is [-3, 2) and the range is (-4, 5]

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Answer:

20

Step-by-step explanation:

Answer:

20$ For the Roses

Step-by-step explanation:

Think about it like this. For each daisy (1$), the price is double for roses (2$).

Brad has a limit of 33$. And he bought 3 more daisies than roses.

If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.

(10 Daisies = 10$) + (10 Roses = 20$) = 30$

30$ + (3 Daisies = 3$) = 33$

Answer:

at least 450 minutes

Step-by-step explanation:

Find an expression for the cost of each plan as a function of the number of minutes. Set the expressions equal to each other, and solve for the number of minutes.

Let x = number of minutes.

First plan:

cost (in dollars) = 0.21x

Second plan:

cost (in dollars) = 0.11x + 44.95

Set the expressions equal:

0.21x = 0.11x + 44.95

Subtract 0.11x from both sides.

0.1x = 44.95

Divide both sides by 0.1

x = 44.95/0.1

x = 449.5

Since you cannot have a fraction of a minute, the answer is 450 minutes.

Answer:

the answer is c

Step-by-step explanation:

Answer:

15 cm

Step-by-step explanation:

The length of the shorter pole can be found by forming and subsequently solving 2 equations.

Start by defining the variables that are going to be used in the working.

Let the original length of the shorter pole be a cm and that of the longer pole be b cm.

'Product' refers to the multiplication operation.

ab= 285 -----(1)

On the other hand, 'sum' refers to the addition operation.

Length of shorter pole after cutting= a -2

Length of longer pole after cutting= b -2

(a -2) +(b-2)= 30

a +b -4= 30

Adding 4 to both sides:

a +b= 30 +4

a +b= 34 -----(2)

From (2):

a= 34 -b -----(3)

Let's solve by substitution:

Substitute (3) into (1):

b(34 -b)= 285

Expand:

34b -b²= 285

b² -34b +285= 0

Factorise:

(b -15)(b -19)= 0

b -15= 0       or       b -19= 0

b= 15            or             b= 19

Substitute into (1):

a(15)= 285       or       a(19)= 285

a= 285 ÷15      or             a= 285 ÷19

a= 19                or             a= 15

Since a <b, a= 15 and b= 19.

Thus, the length of the shorter pole is 15 cm.

Answer:

( 2, -1)

Step-by-step explanation:

(X1 + X2)/2 , (Y1 + Y2)/2

(6-2)/2 , (3-5)/2

4/2 , -2/2

2 , -1

Answer:

(2, -1)

Step-by-step explanation:

(x1, y1)=(6, 3)

(x2, y2)=(-2, -5)

[(6+(-2))/2, (3+(-5))/2]

=(4/2, -2/2)

=(2, -1)

Answer:

170

Step-by-step explanation:

[tex]x+40=210\\x=170[/tex]

If a number, x, is increased by 40 (+40) and is now equal to 210 (=210), then the number, x, is equal to 170.

Both Amy and Laura increased their gas mileage in the first two weeks.

Option B is the correct answer.

The missing graph is attached with the answer.

A graph is a statistical way of showing data , it is used to show relation between the points.

A graph is useful in understanding the nature of a function.

From the data given in the question

The statements that can be concluded is , Option B

Both Amy and Laura increased their gas mileage in the first two weeks.

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In solving minimum and maximum problems, result we are looking for would be the constant, k.

When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.

An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.

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Using the z-distribution, the sample size that will produce the widest confidence interval is given by:

D. 36.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.

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Answer:

[tex] - 3 \frac{5}{7} x - 2\ \frac{1}{2} [/tex]

[tex] \frac{ - 26}{7} - \frac{5}{2} [/tex]

LCM of 7 and 2 is 14

Multiplying (-26/7) with 1/2 (to make the denominator 14) and -5/2 with 1/7

[tex] \frac{ - 26}{7} \times \frac{1}{2} - \frac{5}{2} \times \frac{1}{7} [/tex]

[tex] \frac{ - 26}{14} - \frac{5}{14} [/tex]

[tex] \frac{ - 26 - 5}{14} [/tex]

[tex] - \frac{31}{14} [/tex]

Answer:

11

Step-by-step explanation:

i don't know

Answer:

No

Step-by-step explanation:

The graph and the table do not show the same function as none of the y values on the graph correspond to the y values on the table.