A traveler pulls a suitcase, as shown in the figure.

The force acting on the handle is 30 N at an angle of θ = 40°. How much work is done if the traveler moves 120 meters? Round to the nearest whole number.

2,314 Nm
2,758 Nm
3,085 Nm
4,156 Nm

&

A cart weighing 180 pounds rests on an incline at an angle of 35°. What is the required force to keep the cart at rest? Round to the thousandths place.

77.073 pounds
103.244 pounds
147.447 pounds
162.665 pounds

Step-by-step explanation:

The slope formula from 2 points is:

m=(y2-y1)/(x2-x1)

So input the numbers:

m = (6 - -2) / (5 - 2)

Solve within parenthesis:

m = (8) / (3)

Then divide!
8/3 = 2 2/3

the slope of the line is 2 and 2/3

The perimeter of the picnic area is 107 yards

A triangular picnic area has the side lengths of 45, 31 and 31 yards; To the nearest yard, what amount of fencing is needed to surround the perimeter of the picnic area? 95 yards 107 yards 160 yards 190 yards

From the complete question, we have:

Shape: Triangle

Side lengths = 45 yards, 31 yards, 31 yards

The perimeter is the sum of the side lengths.

So, we have:

Perimeter = 45 + 31 + 31

Evaluate

Perimeter = 107

Hence, the perimeter of the picnic area is 107 yards

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Answer:B

Step-by-step explanation:

107 Yards

Answer:

0.0308.

Step-by-step explanation:

There are 11 months out of the year which have a 29th day except for a leap year when all 12 have it.

Required probability = number of '29th' days in 4 years / total days in 4 years

= (3*11 + 12) / (3*365 + 366)

=  45/1461

= 0.0308.

The number of balloons on each package will be 15

From the information, Jason is a party planner. In 124 packages, he has a total of 1,860 balloons and each package has the same number.

Therefore, the number of balloons on each package will be:

= 1860 / 124

= 15

When a plane has to travel 2,800 miles at an average speed of 560 miles per hour. The number of hours used will be:

= 2800/560

= 5

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The median of the number recorded in the question is 51.5 feet. This is obtained by dividing the sum of two numbers that occur centrally in half.

The central value in a list ordered from smallest to largest is the median of a set of values.

The formula for the Inter-quartile range is given as:

IQR = Q₃- Q₁ (that is Median of the Upper Half Less the Median of the lower half)

Step 1 - First, let's arrange the numbers sequentially

→  40, 40, 47, 49, 50, 53, 55, 57, 63, 76

Step 2 - Determine the upper and lower halves and their median

If the Lower half is  40, 40, 47, 49, 50, then it's median is 47

If the Upper half is   53, 55, 57, 63, 76, then its median is 57.

Hence:

IQR = 57 - 47

= 10 feet.

No, the friends didn't perform better in the second round because the was a significant drop in the median and the IQR. The median dropped from 51.5 to 47 and the IQR from 10 to 6.

It can be concluded that the distance in the second set of data is less variable when juxtaposed with those form the first set.

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If Circle K has a radius of 8 inches. The figure that is closest to the length of FA is: 14.8.

MAC=1/2×360°=180°

mΔAFC=1/2×180°=90°

Circumference angle theorem

AK=8

AC=2

AK=16

Pythagorean theorem

FA²+FC²=AC²

Substitution

FA²+6²=16²

FA²+36=256

FA²=√220

FA=14.8

Therefore the figure that is closest to the length of FA is: 14.8.

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Answer:

36.32 m

Step-by-step explanation:

perimeter = 2(l+b) = 2(10.5 + 7.66)

=2(18.16)= 36.32 m

Answer:

Irrational

Step-by-step explanation:

If the number goes on and on it’s irrational

Hope this helps! ;-)

Answer:

It is not rational because the square root of 3 is not a fraction nor a repeating decimal.

Answer:

True

Step-by-step explanation:

Straight angles are straight lines which equal 180 degrees

Answer:

true it is equals 180 for that angle

Answer:

This is incorrect because 1 meter is 100 centimeters. But then when you keep going and when you get to 4 meters, you would get 400.

For example:

1 meter - 100 centimeters

2 meters - 200 centimeters

3 meters - 300 centimeters

4 meters - 400 centimeters

Hope this helps!

Answer:(x-4)^2+(y+2)^2=121

Step-by-step explanation:

eqaution of circle is this

(x-h)^2+(y-k)^2=r^2

(x-4)^2+(y--2)^2=r^2

and 2 negatives make positive

(x-4)^2+(y+2)^2=r^2
and r^2=121

(x-4)^2+(y+2)^2=121

Answer:

f(3) = 2

Step-by-step explanation:

Remark

The formula starts out as

f(x)= 2x - 4        

So what is telling you is that were ever you see a variable on the right, it can from the x on the left.

If you change the variable on the left, you must also do it on the right.

f(3) = 2*3 -4

f(3) = 6-4

f(3) = 2

Answer:

I think its 4.9

Step-by-step explanation:

i used a calculator

Answer:

6+33/9 ≈ 9.67

Step-by-step explanation:

first you have to divide 33 by 9 getting roughly 3.67

once you have that u add 6

roughly giving you 9.67

Answer:

No solution or Undefine

Step-by-step explanation:

Answer:

C. y = -9x - 8

Step-by-step explanation:

Setting up the equation:

eight LESS (so minus sign before the 8) THAN (so 8 is being subtracted from the -9x) negative (-) nine TIMES (multiplication) a number, (variable) x.

We want to get the variable y alone, so this can be written as y = -9x - 8

Answer:

put x= 2 and y = 1

and see this inequality will holds

Answer:

all you have to do is plug points into the equation m=(x1-x2)/(y1-y2) to find the slope. then choose one of the points to plug into the equation y-y1=m(x-x1).

Step-by-step explanation:

use the formulae for each question.

Answer:

Step-by-step explanation:

a straight line equals 180°. so if one side is 117°, the other side would have to add up to 180.

180-117=63

And you can kind on figure out what is the same as the other angles. Hope his helps

The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units

An equation is an expression that shows the relationship between two or more numbers and variables.

Let p and q represent the length of the diagonals.

Hence:

[tex]p=\sqrt{9^2+6^2+2(9)(6)cos(34)}=14.371\ units\\\\q=\sqrt{9^2+6^2-2(9)(6)cos(34)}=5.241\ units[/tex]

The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units

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Answer:

Jace did not make a mistake, because the answers are the same. Jace just did the problem in a unique way.

The additive inverse of the complex number -12 + 4i is 12 - 4i

The complex number is given as:

-12 + 4i

The additive inverse of a complex number a + bi is -a - bi

This means that the additive inverse of -12 + 4i is 12 - 4i

Hence, the additive inverse of the complex number -12 + 4i is 12 - 4i

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Answer:

It's C

Step-by-step explanation:

Answer:

The answer choices are garbled.

Step-by-step explanation:

(18 pints)/(8 bottles) = (9/4) pint/bottle

2 and 1/4 pints per bottle

Answer:

Step-by-step explanation:

88 / 184 ≈ 0.48

96 / 184 ≈ 0.52

104 / 166 ≈ 0.63

62 / 166 ≈ 0.37

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \: 5(z + 4) + 5(2 - z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (5 \cdot z) + (5\cdot4) + (5\cdot2) - (5\cdot z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5z + 20 + 10 - 5z[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5z - 5z+ 20 + 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: 30[/tex]

So, the equivalent expression is 30

Answer:

30

Step-by-step explanation:

Let us divide the whole expression by 5. Then we must multiply the whole expression by 5 to obtain the same value as before.

Thus, we get the following expression:

[tex]\implies\huge\text{[}\dfrac{5(z+4)+5(2-z)}{5}\huge\text{]} \times 5[/tex]

[tex]\implies\huge\text{[}\dfrac{(z+4)+(2-z)}{1}\huge\text{]} \times 5[/tex]

Now, open the inner-most parentheses as the expression inside the inner-most parentheses, cannot be simplified further.

[tex]\implies\huge\text{[}\dfrac{z+4+2-z}{1}\huge\text{]} \times 5[/tex]

It should be noted that any number being subtracted from the same number is equivalent to 0. Therefore, we get the following expression:

[tex]\implies\huge\text{[}\dfrac{4+2}{1}\huge\text{]} \times 5[/tex]

Simplify the expression inside the long brackets.

[tex]\implies\huge\text{[}\dfrac{6}{1}\huge\text{]} \times 5[/tex]

Now, we can open the long brackets and simplify the product of 6/1 and 5.

[tex]\implies\huge\text{[}\dfrac{6}{1}\huge\text{]} \times 5 = \dfrac{6 \times 5}{1} = \dfrac{30}{1} = 30[/tex]

Therefore, the simplified expression is 30.

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[tex]\text{Arc length,}\\\\s = r \theta \\\\~~=12\cdot \left(30 \times \dfrac{\pi}{180} \right)\\\\~~=12\cdot \dfrac{\pi}6\\\\~~=2\pi[/tex]

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=59\\ \theta =40 \end{cases}\implies 59=\cfrac{(40)\pi r^2}{360}\implies 59(360)=40\pi r^2 \\\\\\ \cfrac{59(360)}{40\pi }=r^2\implies \cfrac{531}{\pi }=r^2\implies \sqrt{\cfrac{531}{\pi }}=r\implies 13\approx r[/tex]