You and another person are sunbathing on the beach near a lifeguard station. The other person chooses a spot that is the same distance from the shoreline but 11 feet closer to the station than you. The angles of elevation from you and the other person to the top of the lifeguard station are 36 degrees and 46 degrees, respectively. Estimate the height of the lifeguard station to the nearest tenth of a foot.

Answer:

y = -118 and x = 7

Step-by-step explanation:

I've attached a picture with my work.

Detailed steps on solving equations with variables y and x, including simplification and solving for the unknowns.

Solving the equation 64−(3y+8y+y)÷40=37:

Solving the equation 8,000÷(28x+4)−15 = 25:

48 and 81 basically you just have to multiply

Answer:

144 cubic inches

Step-by-step explanation:

We are given a diagram of a pyramid with length = 8 inches, height = 9 inches and width = 6 inches.

We are to find the volume of this pyramid.

We know that the formula of volume of a pyramid is given by:

[tex] \frac { l \times w \times h } { 3 } [/tex]

Substituting the given values in the above formula to get:

Volume of pyramid = [tex] \frac { 8 \times 6 \times 9 } { 3 } [/tex] [tex]=\frac{432}{3}[/tex] = 144 cubic inches

Answer:

y=3(x-1)^2-12

Step-by-step explanation:

Answer:

12000 m³

Step-by-step explanation:

The volume (V) of a pyramid is calculated using the formula

V = [tex]\frac{1}{3}[/tex] × area of base × height, hence

V = [tex]\frac{1}{3}[/tex] × 900 × 40 = 300 × 40 = 12000 m³

Answer:

12000 no problem

Step-by-step explanation:

since triangles are similar

4/x = 7x/7

=》 4/x = x

=》x^2 = 4

=》 x = 2

for right triangles a^2 = b^2+c^2

DF^2 = 7^2+2^2 = 53

=》 DF = 7.28

perimeter of DEF = 7 +2+7.28 = 16.28

Answer:

46x^2 + 73x + 15

Step-by-step explanation:

Expand both equations

Wall = (6x + 7)(8x + 5) = 48x^2 + 56x + 30x + 35 = 48x^2 + 86x + 35

Mural = (x + 4)(2x + 5) = 2x^2 + 5x + 8x + 20 = 2x^2 + 13x + 20

Minus them.

Wall - Mural =

(48x^2 + 86x + 35) - (2x^2 + 13x + 20)

(48x^2 - 2x^2) + (86x - 13x) + (35 - 20)

46x^2 + 73x + 15

Answer:

46x^2 + 73x + 15

Step-by-step explanation:

Expand both equations

Wall = (6x + 7)(8x + 5) = 48x^2 + 56x + 30x + 35 = 48x^2 + 86x + 35

Mural = (x + 4)(2x + 5) = 2x^2 + 5x + 8x + 20 = 2x^2 + 13x + 20

Minus them.

Wall - Mural =

(48x^2 + 86x + 35) - (2x^2 + 13x + 20)

(48x^2 - 2x^2) + (86x - 13x) + (35 - 20)

46x^2 + 73x + 15

Answer:

(x - 15)(x + 3)

Step-by-step explanation:

Factors of 45 include 5 and 9, 3 and 15, 1 and 45, and so on.

Note that 3*15 =+45; this is not what we wanted.  Thus, try (-3)*15 = -45.

Do -3 and 15 combine to yield -12?  No.  Thus drop (-3)(15) and try (3)(-15).

Do 3 and -15 combine to yield -12?  YES

Therefore, the factored form of x² - 12x - 45 is (x - 15)(x + 3).

A decameter is the longest, as it has a length equal to 10 meters.

Hope this helps!

Answer:

Decameter

Step-by-step explanation:

A decameter = 10 meter

millimeter = 0.001 meter

meter = meter

centimeter = 0.01 meter

Best regars

Answer:

Answer:

X=2

Step-by-step explanation:

Answer:

[tex]3^{3}[/tex] = 27.

Step-by-step explanation:

3 to the third power ( [tex]3^{3}[/tex] ) is the same as :

3 x 3 x 3 which would equal :

3 x 3 = 9 x 3 = 27.

Hope this helps,

Davinia.

27

3 times.3 times 3

9 times 3

27

Answer:

64 inches

Step-by-step explanation:

12 x 3ft (1yard)=36in

Answer:

Step-by-step explanation:

The sqrt of 1/64 is 1/8, or 0.125.

1/4 is equivalent to 0.25.

0.2 repeating is 0.222222222222 ...

Least:  0.125

Middle:  0.25

Greatest:  0.222222222222 ...

The numbers from least to greatest are: square root of 1/64 (0.125), 0.2 repeating (0.222...), and 1/4 (0.25).

This problem requires an understanding of fractions and square roots to order the numbers correctly. Firstly, you have to calculate the square root of 1/64. The square root of 1/64 is 1/8 or 0.125. Then, let's consider the other numbers: 1/4 which is equal to 0.25, and 0.2 repeating which is actually equivalent to 0.222 continuing. Now we can order them from least to greatest: 1/8 (0.125), 0.2 repeating (0.222...), and 1/4 (0.25).

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Answer:

The answer in the procedure

Step-by-step explanation:

we know that

[tex]sin(A + B) = sin A cos B + cos A sin B[/tex]

In this problem we have

[tex]sin(x + \pi)=sin (x)cos(\pi) + cos(x)sin(\pi)[/tex]

Remember that

[tex]sin(\pi) = 0[/tex]

[tex]cos(\pi) = -1[/tex]

substitute

[tex]sin(x + \pi) = sin(x)(-1) + cos(x)(0)[/tex]

[tex]sin(x + \pi) = -sin(x)[/tex]

Final answer:

To prove that sin (x + π) = -sin x, the trigonometric identity for the sine of a sum is used, and by considering the specific values for cos π and sin π, the identity simplifies to the required expression.

Explanation:

To show that sin (x + π) = -sin x, we can use the trigonometric identity for the sine of a sum:

sin (α + β) = sin α cos β + cos α sin β

Applying this identity to sin (x + π):

sin (x + π) = sin x cos π + cos x sin π

Since cos π = -1 and sin π = 0, we substitute these values:

sin (x + π) = sin x (−1) + cos x (0)

sin (x + π) = −sin x + 0

Hence, sin (x + π) = −sin x, demonstrating the original statement.

Answer:

Dividend- The number that is divided is called the dividend

Divisor- a number that divides a integer ( It is the number that is divided by the Dividend)

Quotient- is the result when dividing.

Remainder-  is the amount that is left over after dividing

Step-by-step explanation:

Example

36 ÷ 6 = 6

36 is the Dividend

6 is the Divisor

6 is the Quotient

No remainder

Hopes this helps!

The number that is in the millions place is 3

The value of each digit in a number is known as the place value. The correct option is C, 3.

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

The million in a digit is represented by the sixth digit from the right in a number. Therefore, In the number 3,657,892, the digit that is in the millions of places is 3.

Learn more about the Place Value:

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Answer:

$5.40

Step-by-step explanation:

To find the increase we need to consider our variables.

Current Rate = $4.50

Increase Percentage = 20% or 0.20

Now we can find the new rate by multiplying the Current Rate to the Increase Percentage and add it to the Current Rate again.

Total Price w/ Increase = ($4.50 x 0.20) + $4.50

Total Price w/ Increase = $0.90 + $4.50

Total Price w/ Increase = $5.40

Answer:

Step-by-step explanation:

"the greatest value of n is 8" is signified by n ≤ 8.

This is a set, and also an inequality.

Answer:

59062.50

Step-by-step explanation:

Is means equals

9450 = 16% of a number

9450 = .16 N

divide by .16

9450/.16 = .16N/.16

59062.50 = N

The number is 59062.50

We want 100% of the number which is all of it

59062.50

Answer: I think 1 or 2

Answer:

4: 3 and 2

5: 1 and 4

7 is the answer

Area =length *breadth

Area =length *length

Area=49=x *x

[tex]49 = {x}^{2} \\ \sqrt{49} = x \\ x = 7[/tex]

your answer is 15 centimeters

Answer:

3X(5+7)

Step-by-step explanation:

Because correctly is of this way:

3X(5+7)

and not so:

(3X5) + 7

Best regards

➷ You have written it the incorrect way.

Following the rules of PEMDAS, the multiplication would be carried out before the addition. This is not what is wanted

The question would want 3 times the SUM of 5 and 7.

To make sure you get the correct answer, you would have to write the expression slightly different

The correct way would be:

3(5 + 7)

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

[tex]4,151.25\ m^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the trapezoidal prism (swimming pool) is equal to

[tex]V=BL[/tex]

where

B is the area of the trapezoidal base

L is the length (distance between the two trapezoidal faces)

Find the area B

[tex]B=\frac{1}{2}(4+8)(30.75)=184.5\ m^{2}[/tex]

[tex]L=22.5\ m[/tex]

Find the volume

[tex]V=184.5(22.5)=4,151.25\ m^{3}[/tex]

52 divided by 4 then you’ll get 13

Answer:

center:(4,-2)

Radius: 3 units

Step-by-step explanation:

The standard equation of a circle is given as [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius of the circle.

The given equation is [tex](x-4)^2+(y+2)^2=9[/tex].

We compare to the standard equation of the circle to get;

[tex]x-h=x-4[/tex]

[tex]\Rightarrow -h=-4[/tex]

[tex]\Rightarrow h=4[/tex]

and

[tex]y-k=y+2[/tex]

[tex]\Rightarrow -k=2[/tex]

[tex]\Rightarrow k=-2[/tex]

Hence the center of the circle is (4,-2).

Also, we have [tex]r^2=9[/tex]

Therefore [tex]r=\sqrt{9}[/tex]

[tex]r=3[/tex] units.

Answer:

Center at (4,-2); radius: 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

$300-$125=$175

Answer:

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point

We have the points (-7, 2) and (-8, -9). Substitute:

[tex]m=\dfrac{-9-2}{-8-(-7)}=\dfrac{-11}{-1}=11[/tex]

[tex]y-2=11(x-(-7))\\\\y-2=11(x+7)[/tex]

Convert to the standard form:

[tex]y-2=11(x+7)[/tex]           use the distributive property a(b + c) = ab + ac

[tex]y-2=11x+77[/tex]            add 2 to both sides

[tex]y=11x+79[/tex]           subtract 11x from both sides

[tex]-11x+y=79[/tex]        change the signs

[tex]11x-y=-79[/tex]