Austin and Dale earn money by painting fences over the summer. Working alone, Austin takes 3 hours longer than Dale to paint a fence. Working together, the two of them can paint a fence in 2 hours. How many hours would it take each of them working alone?

Answer:

x = 4, y = 6

Step-by-step explanation:

Consider the triangle BEC.

∠BEC=112 (vertically opposite angles)

∠EBC=∠ECB (BEC is an isosceles triangle)

All the angles in a triangle add up to 180, so:

∠BEC+∠EBC+∠ECB=180

112+(7x+6)+(7x+6)=180

14x=180-112-6-6

x=56/14=4

Consider the triangle CED

∠CED=68 (lies on a straight line with 112, angles on a straight line add up to 180)

∠EDC=∠ECD (CED is an isosceles triangle)

All the angles in a triangle add up to 180, so:

∠CED+∠EDC+∠ECD=180

68+(9y+2)+(9y+2)=180

18y=180-68-2-2

y=108/y=6

The value of x and y for quadrilateral ABCD is at x = 4 and y = 6. Option A is correct.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Given quadrilateral ABCD,

Consider the ΔBEC.

∠BEC = 112 (vertically opposite angles)

∠EBC=∠ECB

ΔBEC is an isosceles triangle because BE = EC.

the sum of angles of a triangle is 180°,

∠BEC + ∠EBC + ∠ECB = 180°

112 + (7x + 6) + (7x + 6) = 180°

14x = 180 - 112 - 6 - 6

x = 56/14

x = 4

Consider the ΔCED

∠CED = 68

lies on a straight line with 112°, and angles on a straight line add up to 180°.

∠EDC = ∠ECD

ΔCED is an isosceles triangle because DE = CE.

the sum of the angles of a triangle is 180°

∠CED + ∠EDC + ∠ECD = 180°

68 + (9y + 2) + (9y + 2) = 180°

18y = 180 - 68 - 2 - 2

y=108/18

y = 6

Hence values of x = 4 and y = 6.

Learn more about quadrilaterals

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Answer:

red=-1/4 blue= 4/1

Step-by-step explanation:

rise/run

Answer:

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

0.0268 = 2.68% probability that the sample average is greater than $229,500

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Single house:

The mean appraised value of a house in this subdivision for all houses is $228,000, with a standard deviation of $8,500, which means that [tex]\mu = 228, \sigma = 8.5[/tex]

Sample:

Sample of 120, so, by the central limit theorem, [tex]n = 120, s = \frac{8.5}{\sqrt{120}} = 0.7759[/tex]

What is the probability that the sample average is greater than $229,500?

This is 1 subtracted by the pvalue of Z when X = 229.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{229.5 - 228}{0.7759}[/tex]

[tex]Z = 1.93[/tex]

[tex]Z = 1.93[/tex] has a pvalue of 0.9732

1 - 0.9732 = 0.0268

0.0268 = 2.68% probability that the sample average is greater than $229,500

Answer: x=1/3

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

3x−1<0

Step 2: Add 1 to both sides.

3x−1+1<0+1

3x<1

Step 3: Divide both sides by 3.

3x/3 <1/3

x/1/3

Answer:

3x²+6x+10 is your answer

Step-by-step explanation:

(x^2+6x-5)+(2x^2+15)

open bracket

x²+6x-5+2x²+15

add or subtract common

3x²+6x+10

Answer:

4 5/12 feet tall

Step-by-step explanation:

Find the LCM first. The LCM is the lowest common multiple between the two denominators. The LCM in this problem is 12, so you multiply each fraction until the denominators equal 12

4 3/4 -> 4 9/12

1/3 -> 4/12

Now it's much easier to solve. 4 9/12 - 4/12 = 4 5/12 feet tall

Answer:

Equivalent to a), b), and d). It is NOT equivalent to c).

Step-by-step explanation:

6m + 12 is also equivalent to a) 3(2m+4) because when you distribute, it's 6m + 12. It is also equivalent to b) 3m + 8 + 4 + 3m because if you add them together, you get 6m + 12. It is not equivalent to c) but is do d) 4m + 2(m + 6) cause you use the distributive property then add. I hope this helped and please mark brainliest!

Step-by-step explanation:

<CEB and < BED are adjacent angles then

The common side to the two angles is

EB

Answer:

If you really meant that the number of dogs is 12 greater than 3 times the number of cats then:

3 cats

Step-by-step explanation:

21= number of dogs

c = number of cats

21 = 12 + (3c)

3c = 9

c = 3

Answer:

114

Step-by-step explanation:

add the areas of all 6 faces

the formula is A= 2(l*w)+2(l*h)+2(h*w)

A=2(8*3)+2(8*3)+2(3*3)=114

answer: 114yd^2

Answer:

It can't be a kite. A kite has 2 pairs of equal sides.

Step-by-step explanation:

Answer:

3,480

Step-by-step explanation:

After 4 years she had to repay 3,480, i did this one before and got it right hope it helped have a nice day!

[tex]\color{plum}\tt\bold{(b) \: \$3480 }[/tex]

Money Maria borrowed = $3000

Percentage of simple interest per annum = 4%

Time she took to repay the money she borrowed = 4 years

We know that :

[tex]\color{hotpink}\tt \: Simple \: interest = \color{plum}\frac{principal \times rate \times time}{100} [/tex]

In this case :

Principal = $3000

Rate = 4%

Time = 4 years

Which means. the simple interest :

[tex] = \tt \frac{3000 \times 4 \times 4}{100} [/tex]

[tex] = \tt \frac{48000}{100} [/tex]

[tex]\color{plum} =\tt\$ 480[/tex]

Thus, the interest she has to pay = $480

We know that :

[tex]\color{hotpink}\tt \: Amount \color{plum}= principal + interest[/tex]

Then, the Amount Maria has to pay :

[tex] =\tt 3000 + 480[/tex]

[tex]\color{plum} =\tt \$3480[/tex]

Thus, the amount Maria has to repay after 4 years = $3480

Therefore, the correct option is (b) $3480

Answer:

Height = 7m

Step-by-step explanation:

Hope that helps!

Answer:

7m

Step-by-step explanation:

Answer:

y = -1 , x = 4

Step-by-step explanation:

(4x - 5y = 11) x8

(8x - 5y = 27) x4

32x - 40y = 88

- - -

32x - 20y = 108

[0. 20y = -20] divide both by 20

y = -1

8x - 5y = 27

8x - 5(-1) = 27

8x = 27 + 5

8x = 32 ( divide both by 8)

x = 4

Answer:

3.6 repeating or 3 and 2/3

Step-by-step explanation:

I did the work on a calculator.

Answer:

f be it is right

Step-by-step explanation:

okay that is it

Answer:

a line segment.

Step-by-step explanation:

a line segment

A ray can intersect a circle at points on the circumference. Option D is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
A ray can intersect a circle at a maximum of two points,
The line which intersects the circle at two points is called the secant to the circle, and the line that intersects the circle at one point is called the tangent two the circle.

Thus, a ray can intersect a circle at points on the circumference. Option D is correct.

Learn more about circle here:

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Step-by-step explanation:

bla bla bla.....................

Answer:

Tha mean is 23 which means there is no answer:)

14, 26, 24, 28: still 23

22, 16, 18, 36:STILL 23

22, 28, 20, 22: 23

21, 19, 27, 25: STILL 23

Answer:

the answer is B

Step-by-step explanation: each number on a c and d is 7-5 away from 23 but b has 36 which is 13 away from 23 and in all is the farthest plz mark brainlest

Answer:

A. 25 km

Step-by-step explanation:

1 hour = 60 minutes

30 minutes is a half of an hour, therefore

50 / 2 = 25

Answer:

a, 25km

Step-by-step explanation:

i dont need brainliest but thx

im jamming to rick astley right now its so fun

Answer:

interest is $105

total is $455

Step-by-step explanation:

350 * .03 = 10.5

10.5*10 = 105

interest is 105

350 +105 = 455

Interest earned: $105

The balance of the account: $455

(I just need one more brainliest then I get the rank ACE)

Answer: 4

Step-by-step explanation:

(Can someone please answer my math question)

Answer:

5

Step-by-step explanation:

Answer:

907.5

Step-by-step explanation:

Formula to find the area of a circle: πr²

πr² = 3.14 x 17²

     = 3.14 x 289

     = 907.46

     ≈ 907.5

Hope this helps :)

Answer:

2x² + 3x/2 - 9

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

= x/2 - 3 + 2x² + x - 6

= 2x² + x/2 + x -3 -6

= 2x² + 3x/2 - 9