A park has a triangular sandbox. Todd wants to create a smaller sandbox at his backyard having the same angles as the park sandbox.


What is the perimeter in feet of Todd’s sandbox?

Complementary angles have sum 90°

\(\\ \sf\longmapsto 2x+10=90\)

\(\\ \sf\longmapsto 2x=90-10\)

\(\\ \sf\longmapsto 2x=80\)

\(\\ \sf\longmapsto x=40\)

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

The book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

The straight-line method is a common method of calculating depreciation for fixed assets. It assumes that the asset will lose an equal amount of value each year over its useful life. To calculate depreciation using the straight-line method, you subtract the asset's estimated salvage value from its original cost to determine the total amount that needs to be depreciated. Then, divide that amount by the estimated number of years the asset will be in use to find the annual depreciation expense. The formula for straight-line depreciation is:

Annual depreciation expense = (Original cost - Salvage value) / Estimated useful life

The annual depreciation expense for the equipment is:

Depreciation expense = (cost - residual value) / useful life

Depreciation expense = ($212,000 - $14,000) / 15

Depreciation expense = $12,533.33 per year

The total depreciation expense for the first five years is:

Total depreciation expense = Depreciation expense x number of years

Total depreciation expense = $12,533.33 x 5

Total depreciation expense = $62,666.65

To find the book value at the end of the fifth year, we subtract the total depreciation expense from the original cost:

Book value = Cost - Total depreciation expense

Book value = $212,000 - $62,666.65

Book value = $149,333.35

Therefore, the book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

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Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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Answer:

y=6x+31

Step-by-step explanation:

Since we are given a point and a slope, we can use the slope-intercept formula.

\(y-y_{1} =m(x-x_{1})\)

where (x1,y1) is a point on the line and m is the slope.

The point given is (-6,-5) and the slope is 6.

x1= -6

y1= -5

m=6

\(y--5=6(x--6)\)

A negative number subtracted from another number, or two negative signs, becomes a positive.

\(y+5=6(x+6)\)

We want to find the equation of the line, which is y=mx+b (m is the slope and b is the y-intercept). Therefore, we must get y by itself on one side of the equation.

First, distribute the 6. Multiply each term inside the parentheses by 6.

\(y+5=(6*x)+(6*6)\)

\(y+5=6x+36\)

Subtract 5 from both sides, because it is being added on to y.

\(y+5-5=6x+36-5\)

\(y=6x+36-5\)

\(y=6x+31\)

The equation of the line is y=6x+31

Answer:

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote  

         = 0.408 X 1600

         = 652.8    

Step-by-step explanation:  

Step(i):-

Given sample size 'n' = 1600

95% confidence interval of the margin error is determined by

                      \(M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }\)

Level of significance = 0.05

Z₀.₀₅ = 1.96

Given Margin of error = 2% = 0.02

       \(M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }\)

       \(0.02 = \frac{1.96 X S.D}{\sqrt{1600} }\)

      0.02 X √1600 = 1.96 X S.D

       \(S.D = \frac{0.02X\sqrt{1600} }{1.96} = 0.408\)

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote  

         = 0.408 X 1600

         = 652.8  

Using the z-distribution, it is found that you would have to poll 2401 students.

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so \(z = 1.96\).

There is no prior estimate, hence \(\pi = 0.5\) is used.

The sample size is n for which M = 0.02, hence:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.02 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.02\sqrt{n} = 1.96(0.5)\)

\(\sqrt{n} = \left(\frac{1.96(0.5)}{0.02}\right)\)

\((\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.02}\right)^2\)

\(n = 2401\)

You would have to poll 2401 students.

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If Whitney collected 9 bags of clothes, the number of bags that Akira collected is 3.

We know that Akira collected 1/3 as many clothes as Whitney did, so if Whitney collected W clotes, the number of clothes that Akira collected is given by the expression:

(1/3)*W

If Whitney collected 9 bags, then: W = 9

And the expression becomes:

(1/3)*9 = 9/3 = 3

Akira collected 3 bags.

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Answer:

800

Step-by-step explanation:

By definition, the diagonals of a square bisect each other, so these diagonals are perpendicular, which means that they form a Right angle (90 degrees) when they intersect. The diagonals of a square have equal length.

In this case, you in order for the parallelogram to be a square:

Then, you can solve for the variable "x":

Therefore, the answer is:

Answer:

\(7/4\)

Solution:

\(\frac{7}{9} /\frac{4}{9}\)

Reciprocal.

\(7/9(9/4)\)

Multiply.

\(\frac{63}{36}\)

Simplify

\(\frac{7}{4}\)

Answer:

Ye

Step-by-step explanation:

A

Answer:

A) y=9x

B) y=45 when x=5

Step-by-step explanation:

Part A

\(y=kx\\-27=k(-3)\\-27=-3k\\9=k\\y=9x\)

Part B

\(y=9(5)\\y=45\)

Answer:

Discrete

Discrete data represent items that can be counted; they take on possible values that can be listed out. The list of possible values may be fixed (also called finite); or it may go from 0, 1, 2, on to infinity (making it countably infinite).

Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

Answer:

D

Step-by-step explanation:

Associative Property of Multiplication is a(bc) = (ab)c

d is the only one that follows the rule

Answer:

True

Step-by-step explanation:

The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4\(\neq\)9, 1\(\neq\)9, 8\(\neq\)9, and 7\(\neq\)9 then 9 is not an element of this set and the statement is true.

The proportions of progeny of each phenotype produced for this cross is 50% Gl in first crossing and 50% Lg in second crossing.

Gl/gl x GL/gl You've discovered a new plant species in which green fruit colour (g) is recessive to yellow fruit colour (G), and long fruit shapeのis recessive to round fruit shape (L) Reset Help

0% 3% 6% 12% 22% 44% 53% 1. yellow, round The genes for fruit colour and shape are located on the same chromosome and are 12 mu apart 2 yellow, long 4. green, long

After realising it, the crossings are

Gl * Gl

GG, Gl, Gl, ll

gl * gl

gg, Lg, Lg, LL

Therefore, the proportions of progeny of each phenotype produced for this cross is 50% Gl in first crossing and 50% Lg in second crossing.0% 3% 6% 12% 22% 44% 53% 1. yellow, round The genes for fruit colour and shape are located on the same chromosome and are 12 mu apart 2 yellow, long 4. green, long

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easy claps!!

Answer: 30=2x+4 and there are 17 girls in the class.

Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.

It's BASIC prealgebra so you should probably practice bit more with linear equations!

The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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\(\text{L.H.S}\\\\=\dfrac{\sin A \tan A}{1- \cos A}\\\\\\=\dfrac{\sin A \cdot \tfrac{\sin A}{\cos A} }{ 1- \cos A}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\tan A = \dfrac{\sin A }{\cos A}\right]\\\\\\=\dfrac{\tfrac{\sin^2 A}{ \cos A}}{1- \cos A}\\\\\\=\dfrac{\sin^2 A}{\cos A(1-\cos A)}\\\\\\=\dfrac{1-\cos^2 A}{\cos A( 1- \cos A)}~~~~~~~~~~~~~~~~~~~~~~~~;[\sin^2 A + \cos^2 A = 1]\\\\\\\)

\(=\dfrac{(1+ \cos A)(1 - \cos A)}{\cos A(1 - \cos A)}\\\\\\=\dfrac{1+ \cos A}{ \cos A}\\\\\\=\dfrac{1}{\cos A} + \dfrac{\cos A}{ \cos A}\\\\\\=\sec A + 1 \\\\\\=1+ \sec A\\\\\\=\text{R.H.S}\\\\\text{Proved.}\)

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1:

Answer:

87°

Step-by-step explanation:

      Angle bisector is a ray that divides an  angle into two congruent angles.

∠LKR = ∠LKJ ÷ 2

        = 174° ÷ 2

        = 87°

The constant of proportionality is a value that determines how much will y change each time x increases or decreases one unit.

If you look at the formula, the constant of proportionality is always the number multiplying x, so:

y= 5x

The constant k=5

Answer:

Area = 502 sq ft

perimeter = 166 ft

Step-by-step explanation:

How to find the area:

To find the area of a composite figure, you need to find the area of each shape. First, we see there's two triangles, so we can easily calculate it without multiplying them by 1/2 because there's two which makes a rectangle. So 22 x 9 = 198 sq feet. Next, we find the area of the rectangle at the bottom, so multiply 38 x 8 and you get 304. Now add them up, to get 198 + 304 = 502

How to find the perimeter:

To find the perimeter, we must add up the side lengths EXCLUDING the two 9 feet lengths where the triangle and rectangle's sides meet. So it would be 24 + 22 + 20 + 22 + 24 + 8 + 38 + 8 and you'll get 166.

Hope this helps!

Answer:

Step-by-step explanation:

C

The midpoint is 26.

Midpoint in this scenario = mean

(23+29)/2 = 26

Answer:

-6

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

i cant really see answer D but i belive its C

Answer:

look below

Step-by-step explanation:

(7.25 * 2) + 5.50 + (3 * 1.80) + 4.85

Lets combine

(7.25 * 2) + (3 * 1.8) + 10.35

7.25 * 2 is 14.50

3 * 1.8 is 5.4

14.50 + 5.4 + 10.35

is $30.25 before tip

(Tip should be 6.05 minimum, 20% of 30.25 is 6.05)

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Answer:

B) 5

Step-by-step explanation:

a(x)=1/9(90-x)

x=45

1/9(90-45)

1/9(45)

5

Hope this helps plz hit the crown :D

Answer:

The value of h(45) ⇨ 5  | B Choice.

Step-by-step explanation:

\(h(x)=\frac{1}{9}(90-x)\)

⟺ Find the value of h(45), substitute x = 45 in h(x)

\(h(45) = \frac{1}{9}(90-45)\\h(45)=\frac{1}{9}(45)\\h(45)=5\)

Thus, the answer is 5.

The remainder and factor of the given algebraic expression \(\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}\) is \((5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)\) and \(0\)

As per the given question, we are supposed to find out the factor and remainder of the given algebraic expression \(\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}\) using remainder theorem concept.

Before solving this, we need to know the concept of remainder theorem.

According to which "When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem."

Hence using the same concept we can conclude that the factors are \((5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)\) and remainder is \(0\)

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