Sandy has built a triangular pool and wants to
add a rectangular deck around it as shown in the
figure. How many square feet of wood does Sandy
need for the deck?

The distance will remain constant. Then the time taken by Adam with an average speed of 60 miles per hour is 9 hours.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

[tex]\rm Speed = \dfrac{Distance}{Time}\\\\\\[/tex]

The formula can be written as

Distance = Speed × Time

The time it takes Adam to drive to Disney World varies inversely with his average rate of speed.

If it takes Adam 10.8 hours at an average speed of 50 miles per hour.

If the average speed is 60 miles per hour, then the time taken will be

The distance will remain constant.

S₂ × T₂ = S₁ × T₁

60 × T₂ = 50 × 10.8

        T₂ = 9 Hours

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Answer:

$200

Step-by-step explanation:

$700

-$500

$200

Therefore Alex needs to save $200 more to get the $700

Answer:

dy = -3

dx

equation of normal=

y=1/3x+1

Step-by-step explanation:

dy/dx=10x-3

=10(0)-3

= -3

equation of normal:

grad=1/3

y-1 =1/3

x-0

3y-3=x

y= 1/3x+1

[tex]\underline{\textbf{First part:}} \\\\\text{Given that,}\\\\~~~~~~y= 5x^2-3x+6\\\\\\\implies \dfrac{dy}{dx} = \dfrac{dy}{dx} (5x^2 -3x +6)\\ \\\\~~~~~~~~~~~=5\dfrac{d}{dx} x^2-3\dfrac{d}{dx} x + \dfrac{d}{dx} (6)\\\\\\~~~~~~~~~~~=5\cdot 2x-3+0\\\\\\~~~~~~~~~~~=10x-3\\\\\text{At (0,1)}\\\\\dfrac{dy}{dx} = 10(0) -3 \\\\~~~~~=0-3\\\\~~~~~=-3[/tex]

[tex]\underline{\textbf{Second part:}}\\\\[/tex]

[tex]\text{Equation of normal,}\\\\~~~~~~y-y_1 = -\dfrac{1}{\tfrac{dy}{dx}} (x-x_1)\\\\\\\implies y - 1 = -\dfrac 1{-3 }(x-0)\\\\\\\implies y-1 = \dfrac 13 x\\\\\\\implies y= \dfrac 13 x +1[/tex]

Answer:

cot(t) = 56/33

Step-by-step explanation:

cot(t) = 56/33, because cot = adj/opp simple as that..

Answer:

Below.

Step-by-step explanation:

f(x)=3x^2-6x-45/x^2-5x

= 3x^2-6x-45 / (x(x - 5))

The denominator is zero when x - 0 and x = 5.

So there will be a vertical asymptote  at x = 0 and a hole at x = 5.

If we do the division  we get f(x)  = 3  remainder 9x - 45

so there will also be a horizontal asymptote where x = 3.

Answer:

Hole at (3, 4.8)

Asymptotes at x = 0 and y = 3

Step-by-step explanation:

[tex]f(x)=\dfrac{3x^2-6x-45}{x^2-5x}[/tex]

Factor the numerator:

[tex]\implies 3x^2-6x-45[/tex]

[tex]\implies 3(x^2-2x-15)[/tex]

[tex]\implies 3(x^2+3x-5x-15)[/tex]

[tex]\implies 3(x(x+3)-5(x+3))[/tex]

[tex]\implies 3(x-5)(x+3)[/tex]

Factor the denominator:

[tex]\implies x^2-5x[/tex]

[tex]\implies x(x-5)[/tex]

Factored form of function:

[tex]\implies f(x)=\dfrac{3(x-5)(x+3)}{x(x-5)}[/tex]

Discontinuity: a point at which the function is not continuous.

Holes

After factoring the rational function, if there is a common factor in both the numerator and denominator, there will be a hole at that point (x-value):

[tex]\implies (x-5)=0 \implies x=5[/tex]

Factor out the common factor from the function and input the found value of x into the new function to find the y-value of the hole:

[tex]\implies f(x)=\dfrac{3(x+3)}{x}[/tex]

[tex]\implies f(5)=\dfrac{3(5+3)}{5}=4.8[/tex]

Therefore, there is a hole at (5, 4.8)

Asymptotes

To find the vertical asymptotes, set the denominator of the new (factored) function to zero and solve:

⇒ Vertical Asymptote at x = 0

As the degrees of the leading terms of the numerator and denominator are equal (both x²), the horizontal asymptote is equal to the ratio of the leading coefficients.

⇒ Horizontal Asymptote at y = 3

Answer:

$9.60

Step-by-step explanation:

$1.92 = per dozen

60 = how many dozens?

12 = one dozen.

60/12 = 5

5 dozens in 60 popiscles

If we know that we have 5 dozens and it costs $1.92 per dozen, we can just multipty those two numbers.

1.92*5=9.60

So, the cost of 60 popsiciales is $9.60!

The sides of the shaded triangle do not form a Pythagorean triple, therefore, it is not a right triangle.

A triangle is a right triangle if the square of its longest side equals the sum of the square of the other two smaller sides, based on the Pythagorean Theorem.

Using the Pythagorean Theorem, find the lengths of the legs of the shaded triangle, and find out the sum of their squares equals the length of the longest side.

First leg of the shaded triangle = √(8² + 6²) = 10

Second leg of the shaded triangle = √(8² + 9²) = 12

The third side (longest side) of the shaded triangle is 9 + 6 = 15.

15² = 10² + 12²

225 = 244 (not true)

Therefore, the shaded triangle is not a right triangle.

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Answer:

Side length of square (inches): 1 ,2, 4, 7

Perimeter of square (inches). : 4, 8, 16, 28

Step-by-step explanation:

Ratio is 1:4 (S:P).

So:

#:8, #=2. This is because 2/8 and 1/4 both = 0.25.

#:16, #=4. 4/16=0.25

7:#, #=28. 4x7=28, 7/28=0.25

Hope that helps

Answer:

y=[tex]-\frac{1}{6}[/tex]x-2

Step-by-step explanation:

by using this website

its a graphing calculator

desmos. com/calculator

Answer:

C. 32%

Step-by-step explanation:

The percent 17 is of 25.

17 of 25 can be written as:

17/25

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

17/25 * 100/100

= (17 * 100/25) * 1/100 = 68/100

Therefore, the answer is 68%

If Sara made 68% of her free shows, that means she didn't make 32% of her free throws (100 - 68 = 32).

Answer:

3(x+4)=36

You would multiply 3 times x and 4

3x+12=36

Subtract 12 from both sides

3x=24

x=8

Step-by-step explanation:

       [tex]\rule{289}{2}[/tex]

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

          how to solve [tex]\textsc{3(x+4)=36}[/tex]

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

First of all, multiply the number before the parentheses by the expression inside the parentheses:-

[tex]\bigstar\sc{3\times x\times4}[/tex]

Which equals

[tex]\bigstar\textsc{3x+12}[/tex]

So the equation is:-

[tex]\square[/tex] [tex]\textsc{3x+12=36}[/tex]              Subtract 12 on both sides:-

[tex]\textit{3x=24}[/tex]                     Next, divide by 3 on both sides:-

[tex]\textit{x=8}\Huge\checkmark[/tex]

[tex]\smile\rule{300}{2}\smile[/tex]

Answer:

y=3x+8

Step-by-step explanation:

Formula is L(x)=f(a)+f(a)(x-a)

This is for linearization

Answer:

$1.51 is in the account after 10 years.

Step-by-step explanation:

Step 1: Identify the Type of Problem

We can see that this is a compound interest problem due to the phrase "earns 1.15% interested compounded" in the problem.

The formula for compound interest is as follows:

[tex]A=P(1+\frac{r}{n})^{n*t}[/tex] where:

Step 2: Identify what we Know

Now that we have the formula we'll be working with, let's see what we know. From the problem, we can see:

Step 3: "Plug and Chug"

Now, all we have to do is substitute the above values into our formula. Doing so, we get:

[tex]A=1.35*(1+\frac{0.0115}{2})^{2*10} \\= \bf \$1.51[/tex]

(Note: Since the answer is an amount of money, I have rounded to the hundreths place.)

Hope this helps!

To learn more about compound interest, check out the following question:

Answer: 'X' = 24 degrees

Step-by-step explanation:

5 times 'X' = 120 degrees (because the formula is base times height divided by 2).

120 divided by 5 = 'X'

                            = 24

'X' = 24 degrees

Answer:

I think c sorry if wrong

Step-by-step explanation:

have a good day

Mean, median, and mode of the given data is 8.4, 7, and 6 respectively.

A central tendency is a central or typical value for a probability distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode.

Here, Given data

   x                             f                     xf

  5                             1                       5

  6                             4                      24

  7                             3                       21

  8                             2                       16

  10                           2                        20

  13                            2                        26

   14                           1                         14

Mean = ∑xf/∑f

         = 126/15    

         = 8.4

Median = 7

Mode = 6

Thus, Mean, median, and mode of the given data is 8.4, 7, and 6 respectively.

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Answer:

V=20.17

Step-by-step explanation:

V=πr²h

=π1.3²×3.8

=20.17

Answer:

[tex]\cos(\theta - x)=\dfrac{33}{65}[/tex]

Step-by-step explanation:

Given:

[tex]\sin\theta=\dfrac{4}{5}\implies \cos \theta=\dfrac{3}{5}[/tex]

[tex]\cos x=-\dfrac{5}{13}\implies \sin x=\dfrac{12}{13}[/tex]

Using the trig identity:

[tex]\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B[/tex]

[tex]\begin{aligned}\implies \cos(\theta - x) &=\cos \theta \cos x + \sin \theta \sin x\\\\&=\dfrac{3}{5} \cdot -\dfrac{5}{13} + \dfrac{4}{5} \cdot \dfrac{12}{13}\\\\&=-\dfrac{15}{65} + \dfrac{48}{65}\\\\&=\dfrac{33}{65}\end{aligned}[/tex]

sinø=4/5

so

And

cosx=-5/13

so

cos(ø-x)

Answer:

1/3

Step-by-step explanation:

When two lines are perpendicular, it means the lines intersect at a right angle and have opposite reciprocal slopes.The slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees.

To figure out d we need to use the formula:

- 1 / m

Plug in:

- 1 / - 1/3

Solve:

1/3

[tex]~~~~~~m_c \times m_d = -1\\\\\implies -\dfrac 13 \times m_d=-1\\\\\implies m_d = 3\\\\\text{The slope of line d is 3.}[/tex]

It should be greater not lesser

Answer:

Correlation analysis is used to quantify the degree to which two variables are related.

Step-by-step explanation:

In research, correlation analysis is a statistical approach for calculating and measuring the strength of a linear relationship between two variables. Simply defined, correlation analysis determines how much one variable changes as a result of the change in the other. A high correlation indicates a strong association between two variables, whereas a low correlation indicates a weak relationship.

Answer:

Answer:

124.84

Step-by-step explanation:

A = ah + bh + ch + 1 /2×√( ﹣a^4 ﹣ b^4 ﹣ c^4+ 2(ab)² + 2(ac)² + 2(bc)² ) =4×7+5×7+6×7+ 1 /2×√(-4^4 - 5^4 - 6^4 + 2(4×5)² + 2(4×6)² + 2(5×6)² )

≈ 124.84313

Step-by-step explanation:

Answer:

I think the total is 628.20$

Step-by-step explanation:

15*12=180

180*2.99=538.2

180*.5=90

90+538.2=628.2

Hope this helped :)

Answer:

DD

Step-by-step explanation:

If you distribute the 2 you get 12.2x + 14 so D

Answer:

using quadratic equation formula

-b±/b²‐4ac all over 2a

Answer:

C = 101

Step-by-step explanation:

A triangle has 180 degrees, so just minus 28 and 51 by that and you get 101... it's pretty simple