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3 years ago

(I WILL RATE BRAINIEST)

Mathematics

1 answer:

Umnica [9.8K]3 years ago

7 0

Answer:

(a)

Shortest Side of the trapezoid =6 yds

Longest Side =8 yds

(b)42 Square Yards

Step-by-step explanation:

Part A

In the Trapezoid, Width =6 yd

Since the shortest side of the playground and its width have the same dimension, then:

Shortest Side of the trapezoid =6 yd

Longest Side =6+1+1=8 yd

Part B

Area of the Playground

In the trapezoid

a=6 yd, b=8 yd, h=Width=6 yd

Area of a trapezoid $=\frac{1}{2}(a+b)h$

$Therefore: Area=\frac{1}{2}(6+8)*6\\=14*3\\=42$ Square Yards$

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How many and what type of solutions does the equation have?

Natali [406]

Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0

As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ = 9 + 72
Δ = 81

Δ>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √81)/2*2 = (3-9)/4 = -6/4 = -3/2

So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2

A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.

3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.

So 2k^2 = 9 + 3k have two rational solutions (Option B).

Hope this Helps! :)

7 0

3 years ago

Read 2 more answers

Which of the following appear in the diagram below? Check all that apply. X Z. W O A. _XYZ B. ZYXZ C. w D. YX

iren2701 [21]

Answer:

A, C, and D.

Step-by-step explanation:

<XYZ appears in the diagram as the vertex angle Y, has two sides, YW and YX that intersect at point Y to form <XYZ.

Thus, <XYZ, line segments YW and YX all appear in the diagram given.

<YXZ does not appear because there's no vertex angle labelled X.

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3 years ago

Convert the repeating decimal to a fraction

lilavasa [31]

17. 2/3
18. 1 1/9
20.9 1/11
21. 2 909/100 (closest i could get)
Hope I helped and hope you had a good day!

6 0

3 years ago

An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The r

aleksandrvk [35]

To solve the question, we will be using a Venn Diagram. Let's list down what's given first:

855 drank alcohol

657 smoked cigarettes

192 used illegal drugs

418 both drank alcohol and smoked cigarettes

109 drank alcohol and used illegal drugs

116 smoked cigarettes and used illegal drugs

88 engaged in all three

and 251 engaged in none of these

We will draw a Venn Diagram with 3 circles, one for each vice. Then we will start with the intersection of all three and the area outside of the circles (for those who do not engage in vices).

Because we know how many engaged in all 3 vices, we can deduct that number from those who belong to the intersection of 2 vices since they have already been counted in that too.

418 - 88 = 330 drank and smoked, but not used drugs

109 - 88 = 21 drank and used drugs, but not smoked

116 - 88 = 28 smoked and used drugs but not drank

Then, we subtract the numbers in each circle from the total for each vice.

855 - (330 + 88 + 21) = 416 drank only

657 - (330 + 88 + 28) = 211 smoked only

192 - (88 + 21 + 28) = 55 used drugs only

To find the total number of surveyed students, we just need to add all the numbers in the Venn Diagram.

416 + 330 + 88 + 21 + 211 + 28 + 55 + 251 = 1,400

Therefore, there were 1,400 students who were surveyed.

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1 year ago

Bella wants to know how tall the oak tree in her back yard is, so she picks

melamori03 [73]

Answer:

B = 62.9ft

Step-by-step explanation:

The distance where she is from the oak tree is 75ft,

The angle of elevation the stone makes with the top of the oak tree is 40°

The height of the tree is x ft

See attached document for better illustration

Using SOHCAHTOA,

Tanθ = opposite/ adjacent

θ = 40°

Opposite = x ft

Adjacent = 75ft

Tan40 = x / 75

X = 75 × tan40

X = 75 × 0.8390

X = 62.92ft

The height of the oak tree is 62.9ft

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3 years ago