Mathematics College

A patio is to be made in the shape of an isosceles triangle as shown.

(a) Why would the calculation A= 1/2 (22) (16) not result in the correct area of the triangle?
(b) Determine the area of the patio to the nearest square foot.
(c) If the patio is to be covered by stone that costs $12.25 per square foot, what will be the total cost of covering the patio with stone?

Answers

Answer 1

9514 1404 393

Answer:

(a) 22 is not the correct value of h

(b) 164 ft²

Step-by-step explanation:

(a) Apparently, the formula ...

A = 1/2bh

was used. We recognize the base of the triangle is 16 feet, so apparently the formula was used with h=22.

22 is the side length, not the perpendicular distance from the base to the opposite vertex.

The computed value is not the area because 22 is not the height.

(b) Given three side lengths, an appropriate formula is Heron's formula:

s = (a+b+c)/2 and A = √(s(s-a)(s-b)(s-c))

Here, we have ...

s = (22 +22 +16)/2 = 30 and A = √(30(8)(8)(14) = 16√105 ≈ 163.95

The area is about 164 square feet.

(164 ft²)($12.25/ft²) = $2009

Related Questions

Thirty-five percent of adult Americans are regular voters. A random sample of 250 adults in a medium-size college town were surveyed, and it was found that 110 were regular voters. Estimate the true proportion of regular voters with 90% confidence and comment on your results.

Answers

Answer:

Hence the true proportion is (0.388, 0.492).

Step-by-step explanation:

Given n=250,

[tex]p= 110/250 =0.44[/tex]

[tex]a=0.1, |Z(0.05)|=1.645[/tex] (check standard normal table)

So 90% CI is

[tex]p ± Z*√[p*(1-p)/n]\\0.44 ± 1.645*sqrt(0.44*(1-0.44)/250)\\ ( 0.388, 0.492)[/tex]

I need the answer find the value of x

Answers

Answer:

1. x = 126

angle POS = 33

2. x = 31

angle MOL = 118

Step-by-step explanation:

for question one, 147 degrees equals x + 21

so x = 126

147 plus 147 equals 294

360-294 equals 66

66/2 equals angle POS

angle POS = 33

for question 2, 62 degrees equals 2x

62 divided by 2 is 31

x = 31

62 + 62 = 124

360-124 = 236

236/2 = 118

angle MOL = 118

Answer:76

Step-by-step explanation:

Write the following series in sigma notation. 8+18+28+38

Answers

Answer:

[tex]\Sigma\left {n} \atop {1}} \right. (5n^2+3n)[/tex]

Step-by-step explanation:

Given the series 8 + 18 + 28 + 38

First, we need to find the sum of the nth term of the sequence as shown

Sn = n/2[2a+(n-1)d]

n is the number of terms

a is the first term = 8

d is the common difference = 18-8 = 28-18 = 10

Substitute

Sn = n/2 [2(8)+(n-1)*10]

Sn = n/2 [16+10n-10]

Sn = n/2[10n+6]

Sn = 2n/2(5n+3)

Sn = n(5n+3)

Sn = 5n²+3n

In Sigma form;

[tex]\Sigma\left {n} \atop {1}} \right. (5n^2+3n)[/tex]

Rhombus ABCD has a diagonal BD¯¯¯¯¯. m∠ADB=(5x+10)° m∠CDB=(4x+19)° What is the m∠ADC ? Enter your answer in the box º

30 POINTS PLEASE HELP ASAP

Answers

Answer:

110°

Step-by-step explanation:

5x+10=4x+19

5x-4x =19-10

x = 9

m L ADB = 5(9)+10=45+10=55°

so m L ADC = 2×55° = 110°

Samuel made a list of his test scores: 88, 100, 92, 80, 85, 94, and 90. What is the lowest test score he can get on his next test to have mean score of 90?

Answers

Answer:

he needs to get a 91 to have a mean score of 90

Step-by-step explanation:

add up all the known scores to get 629

let 's' = lowest test score

(629 + s) ÷ 8 = 90 [we divide by 8 because there are 7 known and 1 unknown score)

cross-multiply to get:

629 + s = 720

s = 720-629

s = 91

Trigonometry please help

Answers

Answer:

7.5

Step-by-step explanation:

[tex]x = 10 \tan \: 37 \degree \\ \\ \therefore \: x = 7.535540501 \\ \\ \therefore \: x \approx 7.5[/tex]

Answer:

x = 7.5

Step-by-step explanation:

tan = opp/adj

tan 37 = x/10

multiply both sides by 10

10 * tan37 = x

x = 7.535540501027942

Rounded

x = 7.5

Divide.

5,743 ÷ 9

Enter your answer by filling in the boxes.

R

Answers

Answer:

638.11

Step-by-step explanation:

In a study of 792 randomly selected medical malpractice lawsuits, it was found that 508 of them were dropped or dismissed. Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.

Answers

Answer:

H0:p=0.5

H1:p>0.5

Sample proportion=492/792=0.6276

Test statistic:

z=(0.6276-0.5)/sqrt(0.5*(1-0.5)/784)

z=7.14

p-value=P(z>7.14)=0

Step-by-step explanation:

Alguien puede ayudarme?

Answers

Answer:

I don’t understand you language

Step-by-step explanation:

Make it in English

The hypotenuse of a right triangle Measures 17 cm and one of its legs measures 8 cm. find the measure of the other leg if necessary round to the nearest 10th

Answers

8^2+b^2=17^2
64+b^2=289
b^2=289-64
b^2=225
b=15
the measure of the other leg is 15 cm

2x+ 4y =16 -2x- 3y = -6 solve this system of equations using the elimination method

Answers

[tex] \large{ \boxed{ \boxed{ \tt{☂ \: OUR \: FINAL \: ANSWER : \underline{ \tt {x = - 12 \: and \: y = 10}}}}}✓}[/tex]

See the attached picture! Let me know if you have any questions regarding my answer! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

[tex] \small \sf \: x = - 12 \: \: and \: y = 10[/tex]

Step-by-step explanation:

2x + 4y = 16.

-2x - 3y = -6

Add both equation ;

[tex] \small \sf \: \: \: \: \: 2x + 4y = 16 \\ + \small \sf \: \: \underline{ -2x - 3y = -6 }\\ \small \sf \: \: \: \: \: \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \blue{y = 10}} [/tex]

Therefore , y = 10

Substitute the value of y in the first equation

2x + 4 = 16

2 x + 4 × (10) = 16

2x + 40 = 16

subtract 40 from both side

2x + 40 - 40 = 16 - 40

2x = - 24

divide each side by 2

2x/ 2 = - 24 / 2

x = - 12

Somebody help I’m stuck :(

Answers

Answer:

I got x1 =0 x2=220

Step-by-step explanation:

y=- 00.1x (x-220)

-0.01x (x-220)=0

- 1/100 x(x-220)=0

x (x-220)=0

x=0

x-220=0

Answer x=0 and x=220

Name two grouping symbols.

Answers

Answer:

parentheses ( ), brackets [ ], and braces { }—are used to group numbers or variables (letters

Step-by-step explanation:

I put three for if u need hope this helps:)

Parentheses & brackets

how do u graph s ≤ 60 - (3 ÷ 1/15)

Answers

Answer:

s≤15

Step-by-step explanation:

since its a ≤ you will need to fill in the circle..

Which of the following best shows the distributive property?
1. 2(2 - 3) = 2(-1)
2. 2(2 - 3) = 2(2) - 2(3)
3. 2 - 3 = (-3) + 2
4. 2 + (2 - 3) = (2 - 2) + 3

Answers

The answer is 2 because distributive property means that you can multiply with the numbers inside of the parentheses and still get the same answer

Answer:

number 2

Step-by-step explanation:

2x2=4

2x-3=-6

4-6=-2

2x2=4

-2x3=-6

4-6=-2

Plzzz answer I don’t have a lot of time

Answers

Answer:

p=35

Step-by-step explanation:

2p+5+3p =180 degree (being linear pair)

5p+5=180

5p=180-5

p=175/5

p=35

A linear pair is a pair of adjacent angles formed when two lines intersect.

Convert the given base ten numeral into a numeral in base eight.

Answers

Answer:

714 i think??

Step-by-step explanation:

Pls help I’m not good at this
A=-2
B=-1
C=0
D=3

Answers

Answer:

d is the correct answer this qestion

Can someone help me please

Answers

Answer:

Step-by-step explanation:

Answer: It has to be A

Step-by-step explanation: It's the only statement that makes sense.

Find the product of (x + 3) (x - 18)

Answers

Answer:

x^2-15x-54

Step-by-step explanation:

(x+3)(x-18) Multiply them all

x^2-18x+3x-54

ans=x^2-15x-54

What is the volume of the rectangular prism?
3 cm
8 cm
2 cm
cm3

Answers

Answer:

48 cm^3

Step-by-step explanation:

Since there is no image, I’m just going to assume that these three measurement are the length, width, and height of the rectangular prism:

The formula for the volume of a rectangular prism is length x width x height.

Use formula with given dimensions:

3 x 8 x 2 = 48

Volume is measured in cubic centimeters

(cm in this case)

Therefore, the volume of the rectangular prism is 48 cm^3

Hope this helps!

What is the slope of the line graphed below?
(-2,2)
(3, 1)

Answers

Answer:

hey. your questions is not complete. pls add an attachment of the graph to your question

Answer:

[tex]-\frac{1}{5}[/tex]

Step-by-step explanation:

To find the slope, the formula is [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{1-2}{3-(-2)}=-\frac{1}{5}[/tex]

Hope this helps

In triangle ABC, the size of the B is 4 times the size of angle A, and the size of angle C is 14 cel less than 5 times the size of the.

The size of angle a is ____
The size of angle b is____
The size of angle c is________

Answers

Answer:

[tex]A = 19.4[/tex]

[tex]B = 77.6[/tex]

[tex]C =83[/tex]

Step-by-step explanation:

Given

By interpreting each line, we have:

[tex]B = 4A[/tex]

[tex]C = 5A -14[/tex]

Required

Solve for A, B and C

In a triangle,

[tex]A + B + C = 180[/tex]

Substitute expressions for B and C

[tex]A + 4A + 5A - 14 = 180[/tex]

[tex]A + 4A + 5A = 180+14[/tex]

[tex]10A = 194[/tex]

Solve for A

[tex]A = 194/10[/tex]

[tex]A = 19.4[/tex]

[tex]B = 4A[/tex]

[tex]B = 4 * 19.4[/tex]

[tex]B = 77.6[/tex]

[tex]C = 5A -14[/tex]

[tex]C =5 * 19.4 - 14[/tex]

[tex]C =83[/tex]

Write the formula for the area of a trapezoid

Answers

Answer:

Step-by-step explanation:

A=(a+b)/2 x h.

Find the area of the figure shown

Answers

Answer:

Step-by-step explanation:

Find the area under the standard normal curve between z=0.45 and z=1.13

Answers

Step-by-step explanation:

the answer is in the above image

Find the measure of each angle.

Answers

Answer:

Step-by-step explanation:

23/pi is 23.00 pi=3.14 23-3.14= 19.86-86=19+4= 23pi/4

The_____ is the result of the sum of the numbers being divided by how many numbers are in set.

Answers

Answer:

Mean

Step-by-step explanation:

Mean

less precisely called the average

Ralph Chase plans to sell a piece of property for $155000. He wants the money to be paid off in two ways - a short-term note at 9% interest and a
long-term note at 7% interest. Find the amount of each note if the total annual interest paid is $12550.

Answers

Answer:

7% = 70.000

9% = 85,000

Step-by-step explanation:

Two equations can be derived from this question

x + y = 155,000 equation 1

0.09x + 0.07y = 12,550 equation 2

where y = amount invested in 7% note

x = amount invested in 9% note

multiply equation 1 by 0.09

0.09x + 0.09y = 13,950 equation 3

subtract equation 2 from 3

0.02y = 1400

y = 70,000

substitute for y in equation 1

70,000 + x -= 155,000

x = 155,000 - 70,000

x = 85,000

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp

Answers

Answer:

4. 52sq.ft

5.25sq.ft

Step-by-step explanation:

In attachment

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