If it takes John 10 hours to paint the fence, how long will it take John and his 2 friends to do the job if they work at the same rate? If it takes John 10 hours to paint the fence, how long will it take John and his 2 friends to do the job if they work at the same rate?

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{Lyle's cabin}}{(\stackrel{x_1}{-27}~,~\stackrel{y_1}{23})}\qquad \stackrel{\textit{dining hall}}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6-(-27)]^2+[3-23]^2}\implies d=\sqrt{(-6+27)^2+(3-23)^2} \\\\\\ d=\sqrt{21^2+(-20)^2}\implies d=\sqrt{841}\implies d=29[/tex]

The shortest distance from Lyle's cabin to the dining hall is 29 meters.

To calculate the shortest distance between Lyle's cabin and the dining hall, we can use the distance formula for two points in a coordinate plane. The distance formula is:

d = √[(x2 - x1)² + (y2 - y1)²]

Given:

Lyle's cabin coordinates: (-27, 23)

Dining hall coordinates: (-6, 3)

We use the following steps:

Calculate the difference in the x-coordinates: -6 - (-27) = -6 + 27 = 21

Calculate the difference in the y-coordinates: 3 - 23 = -20

Square these differences: 21² = 441 and (-20)² = 400

Add the squares: 441 + 400 = 841

Take the square root of the sum: √841 = 29

Thus, the shortest distance from Lyle's cabin to the dining hall is 29 meters.

With the height of the rectangular box, the baton can fit diagonally in the box.

The length of the baton that Kylie needs to pack = 38 inches

The width of the rectangular box = 13 inches

The length of the rectangular box = 35 inches

The height of the rectangular box = 13 inches

Comparing the dimensions:

The baton is 38 inches long and longer than the length and width of the box.

The height of the box is 13 inches, making the box greater than the length of the baton diagonally.

Thus, the baton will fit in the box diagonally.

972pi mm^3 as height is 12 mm radius is half of 18 mm ie 9mm

therefore volume=pi(r^2)h

ie 972pi mm ^3

Answer: [tex]972\pi\text{ mm}^3[/tex]

Step-by-step explanation:

We know that the volume of a cylinder is given by :-

[tex]\text{Volume}=\pi r^2 h[/tex], where r is radius and h is height of the cylinder.

Given: Diameter of cylinder = 18 mm

Then , radius of cylinder = [tex]\dfrac{18}{2}=9\ mm[/tex]

Height of cylinder = 12 mm

Then the volume of cylinder will be :-

[tex]\text{Volume}=\pi (9)^2 (12)\\\\\Rightarrow\text{Volume}=972\pi\text{ mm}^3[/tex]

Hence, the volume of the given cylinder = [tex]972\pi\text{ mm}^3[/tex]

Answer:

The dimensions of rectangle are 230 in by 59 in

Step-by-step explanation:

The question in English is

What are the dimensions of a rectangle with a perimeter equal to 578 inches, if its length is 6 inches less than 4 times its width?

Let

x-----> the length of rectangle

y----> the width of rectangle

we know that

The perimeter of rectangle is equal to

P=2(x+y)

P=578 in

so

578=2(x+y)

289=x+y -----> equation A

x=4y-6 -----> equation B

substitute equation B in equation A

289=(4y-6)+y

5y=295

y=59 in

Find the value of x

x=4y-6 -----> x=4(59)-6=230 in

therefore

The dimensions of rectangle are

230 in by  59 in

Answer:

Fourth answer choice:  y = x + 3

Step-by-step explanation:

Note that sides a and s are perpendicular to side r.  Both sides a and s have positive slopes, so we can immediately eliminate answer choices 1 and 2.

If we extend side s up and to the left, it intersects the y-axis at (0, 3).  Thus, the y-intercept is +3 and the desired equation is:

y = x + 3

Answer:

The answer is D

Step-by-step explanation:

Answer:

A or B

Step-by-step explanation:

Answer:

Should be B, No because her debt-to-income ratio is lower than 36 percent.

Step-by-step explanation:

For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.

So:

We look for the factors of 18 and 36:

18: 1,2,3,6,9,18

36: 1, 2,3,4, 6,9,18 ...

Thus, the GFC of both numbers is 18.

Then, the GFC of[tex]18x ^ 2[/tex] and [tex]36x[/tex] is:

[tex]18x[/tex]

Answer:

[tex]18x[/tex]

Final answer:

The Greatest Common Factor of 18x² and 36x is 18x, which is the product of shared prime factors to the lowest powers and includes the variable x.

Explanation:

Finding the Greatest Common Factor (GCF)

To find the Greatest Common Factor of 18x² and 36x, we need to break down each term into its prime factors and include the variable parts:

The GCF is the product of the lowest powers of common factors in both terms. Hence, the GCF of 18x² and 36x is 18x, which consists of 2 × 3 × 3 × x (or 2 × 3² × x).

Answer:

1

Step-by-step explanation:

Slopes of perpendicular lines are opposite reciprocal of one another i.e.

slope m1, of given line l1 = -1/slope m2, of its perpendicular line l2

slope m2, of its perpendicular line l2 = -1/slope m1, of given line l1

m2= -1/m1

Finding m1 from the given graph

m1= y2-y1/x2-x1

    = -2-1/2+1

    = -3/3

    = -1

m2= -1/-1

     = 1 !

½ = v; multiply the divisor to remove the variable from the denominator.

I assume the 38º measurement refers to the measure of arc BE. Then

[tex]37^\circ=\dfrac{m\widehat{AJ}-38^\circ}2\implies m\widehat{AJ}=112^\circ[/tex]

and so

[tex]32^\circ=\dfrac{112^\circ-m\widehat{FH}}2\implies m\widehat{FH}=\boxed{48^\circ}[/tex]

(I think the theorem I used here is called "angle of intersecting secants")

Answer:

Painting USA is the most cost effective company.

Step-by-step explanation:

Painting USA company charges:

$75.00 to evaluate the house

Plus, $25.00 per hour of labor.

Total number of hours taken to paint the house is 25 hrs

Total cost here = $75.00 + $25.00(25) = $700.00

Upscale Home Painting company charges:

$0.00 to evaluate the house

$40.00 per hour of labor.

Total number of hours taken to paint the house is 25 hrs

Total cost here = $0.00 + $40.00(25) = $1000.00

So Painting USA is the most cost effective company since it charges $700.00 which is less that Upscale Home Painting company's painting charges of $1000.00.

Answer:

Painting USA

Step-by-step explanation:

They will charge 700

Answer:

you spent 3 hours bagging groceries.

Step-by-step explanation:

you can use a calculator and do 11 times 3 plus 15.

Final answer:

To find out how many hours were spent bagging groceries when making $48 in total, solve the given equation with the respective earnings from shoveling and bagging.

Explanation:

The question: During the Winter, you charged people $15 for shoveling snow and $11 for every hour bagging groceries. If you made $48 one day, how many hours did you spend bagging groceries?

Step-by-step explanation:

Let's denote the hours spent bagging groceries as x.

Write the equation: $15 (for shoveling) + $11x (for bagging) = $48.

Solve the equation to find x: $15 + $11x = $48, $11x = $33, x = 3 hours.

When solving integer inequalities, isolate the variable on one side just like an equation. If the inequality involves a negative number, remember to flip the sign.

Since the exercise isn't specifically provided, I will walk you through a general process of solving integer inequalities.

First, treat the inequality similar to an equation. You'll need to isolate the variable (usually represented by 'x') on one side of the inequality.

Example 1: Let's say your inequality is x + 3 < 7. You can subtract 3 from both sides to isolate 'x', giving you x < 4.

Example 2: For an inequality like 5x > 30, you'd divide both sides by 5. This gives you x > 6. In both examples, the solution sets are all the integers less than 4 and greater than 6, respectively.

Remember that if you multiply or divide by a negative number, the inequality sign will flip.

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Answer:

'm guessing you mean with parallels and a transversal. If this is the case, then find he angle that is either

a; supplementary (creating a flat angle, 180 degrees) or

b; complimentary (creating a 90 degree angle)

Step-by-step explanation:

subtract the supplementary/complimentary angle from either 180 or 90 and the difference is your answer. Hope I helped!

* * * * *

More likely the question is concerned with the interior angles of a polygon. If the polygon is irregular then there is no simple answer. An interior angle can have any value.

However, if it is a regular polygon then the question can be answered. The sum of all the exterior angles is 360 degrees - irrespective of the number of sides (or vertices). Suppose the polygon has n sides/vertices.

Then, since it is regular, each exterior angle is 360/n. Therefore, each interior angle is 180-360/n degrees.

The sum of interior angles of a polygon can be found using the formula (n-2) x 180 degrees.

To find the measures of the interior angles of a polygon, you must first consider the type of polygon you're dealing with. For a triangle, the sum of the interior angles is always 180 degrees. If you're working with another type of polygon, such as a quadrilateral, the sum of the interior angles is greater, and there's a simple formula to follow: (n-2)  imes 180 degrees, where n represents the number of sides of the polygon. This means that for a quadrilateral, with four sides, the sum of the interior angles would be (4-2) * 180 degrees, which equals 360 degrees.

When it comes to alternate interior angles, these are pairs of angles found on the inside of two lines that are cut by a transversal. If the lines are parallel, the alternate interior angles are equal in measure. For example, if you have two parallel lines cut by a transversal forming angle a and angle f, then a and f would be alternate interior angles and thus, would have the same measure.

The sum of the exterior angles in any polygon is 360 degrees, regardless of the number of sides. When finding the measure of an exterior angle, knowing the measure of its corresponding interior angle can be helpful because the interior and exterior angles form a linear pair (adding up to 180 degrees). Therefore, if the interior angle is 150 degrees, the exterior angle would be 180 degrees - 150 degrees, which equals 30 degrees.

Answer:

right-most fourth graph

Step-by-step explanation:

Given:

f(x)= -x+4    for 0≤x<3

i.e. from x=0 till x=3 the graph is linear line

then

f(x) = 5        for x≥3

i.e. at x=3 and onward graph is a straight line with y-axis point of 5 !

Answer:

Step-by-step explanation:

The given piecewise function is

[tex]f(x)=\left \{ {{-x+4 \ ; \ 0\leq x<3} \atop {5 \ ; \ x\geq3 }} \right.[/tex]

Notice that the domain of the function specifies that, from zero to three, the function represents a decreasing (because the variable is negative) straight line. When the function is defined from 3 to infinite, the function is a constant of 5.

So, the right graph must shows first a decreasing line, where the initial point is solid and the final point is empty, as the fourth fraph (from left to right), then it must show a horizontal line with an initial point solid.

Therefore, the fourth graph, from left to right, is the correct answer.

Answer:

x = -2; x = -3

Step-by-step explanation:

(-x - 3)(x + 2) = 0

(-x - 3) = 0

x = -3

(x + 2) = 0

x = -2

The prime factorization of a number is the set of prime numbers that can be multiplied together to give you that number. Therefore, two different numbers cannot have the same prime factorization, because if you multiply the same set of numbers together, you must get the same answer. For example, 2 × 3 × 5 will always give you 30.

Therefore, the answer will be no.

Answer:

Option 2: 14.06 minutes

Step-by-step explanation:

For the first scenario, we will convert the minutes into hours first to get all the quantities in same unit

So,

15 minutes = 1/4 hours = 0.25 hours

Speed = 7.5 miles per hour

Now using the speed, distance and time formula

Speed = distance/time

[tex]Speed = \frac{distance}{time}[/tex]

[tex]7.5 = \frac{distance}{0.25}[/tex]

[tex]7.5 * 0.25 = Distance[/tex]

Distance = 1.875 miles

So the distance for 1st day is 1.875 miles.

For next day

Speed = 8 miles per hour

Distance = 1.875

So,

[tex]speed = \frac{distance}{time}[/tex]

[tex]8 = \frac{1.875}{time}[/tex]

[tex]time = \frac{1.875}{8}[/tex]

[tex]time = 0.234375 hours[/tex]

Converting the hours into minutes will give

0.234375 * 60 min =  14.0625 minutes

Rounding off to two decimals = 14.06 min

So 2nd option is correct..

8-6z=26

8-8-6z=26-8

-6z=18

divide by -6 for -6z and 18

-6z/-6=18/-6

z=-3

Check answer by using substitution method

8-6(-3)=26

8+18= 26

26=26

Answer is z=-3

Answer:

answer - 3

Step-by-step explanation:

8 - 6z = 26                    Subtract 8 from both sides.

8-8 - 6z = 26 - 8

- 6z = 18                         Divide by - 6

-6z/-6 = 18/-6                 Do the division. Note: you must leave the letter with 1 in front of it.

z = - 3

Answer:

Step-by-step explanation:

ac + cb = ab

- A translation to 3 units left and 2 units up = E

- A translation to 2 units right and 3 units down = O

- A sequence of reflections across the x- and y-axes, in any order = A

- A translation to 3 units down and 3 units left = W

- Ouma

Translating 3 units left and 2 units right gives E(5,6), F(1, 12), G(9, 14) and H (11, 8)

Translating 2 units right and 3 units down gives O(10, 1), P(6, 7), Q(14, 9) and R(16, 7)

Reflecting across the x and y axis gives A(-8, -4), B(-4, -10), C(-12, -12) and D(-14, -10)

Translating 3 units down and 3 units left gives W(5, 1), X(1, 7), Y(9, 9) and Z(11, 7)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Quadrilateral JKLM has vertices J(8,4), K(4,10), L(12,12) and M (14,10) .

1) Translating 3 units left and 2 units right gives E(5,6), F(1, 12), G(9, 14) and H (11, 8)

2) Translating 2 units right and 3 units down gives O(10, 1), P(6, 7), Q(14, 9) and R(16, 7)

3) Reflecting across the x and y axis gives A(-8, -4), B(-4, -10), C(-12, -12) and D(-14, -10)

4) Translating 3 units down and 3 units left gives W(5, 1), X(1, 7), Y(9, 9) and Z(11, 7)

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Answer:

The ordered pair that represent the other zero is [tex](4,0)[/tex]

Step-by-step explanation:

we know that

The zeros or x-intercepts of the quadratic function, represent the value of x when the value of y is equal to zero

In this problem to find the other zero equate (x-4) to zero and solve for x

[tex](x-4)=0[/tex]

[tex]x=4[/tex]

therefore

The ordered pair that represent the other zero is [tex](4,0)[/tex]

Answer:

The experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).

Step-by-step explanation:

Theoretical probability of number 3 on a die:

Total no. of possibilities = 6

Probability of getting a 3 on a die each time it is rolled = 1/6

= 0.16667

= 17%

Experimental probability of number 3 on a die:

Total no. of rounds = 4

Rolls each round = 20

no. of 3s in round 1 = 6

no. of 3s in round 2 = 6

no. of 3s in round 3 = 5

no. of 3s in round 4 = 7

Total rolls = 20*4 = 80

no. of times 3 comes up = 6+6+5+7 = 24

Experimental probability of getting a 3 on a die

each time it is rolled = no. of 3s/total rolls

= 24/80

= 0.3

= 30%

Difference = 30% - 17% = 13%

Experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).

Answer:

The experimental probability of rolling a 3 is  30 %, which is approximately  13 % more than its theoretical probability.

Step-by-step explanation:

PLATO

Answer:

Option C.

Step-by-step explanation:

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side

therefore

In this problem

HF=HG

Answer:

18.=400%

Step-by-step explanation:

80/20 we get 4 then we multiple 4 ×100 we get 400 and we check the answer 400% ×20 =80

Answer:

m=7

Step-by-step explanation:

1 blue jar = 21 marbles

1 blue jar = 3 red jars

Therefor

21 marbles= 3 red jars

(Now let m=1 red jar)

21= 3m

(Then sine we have 3m dived both sides by 3 to isolate the m)

21/3= 3m/3

7=m

There are 7 marbles in a red jar if there are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

There are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.

Let m be the number of marbles in the red jar​

From the problem, we can make a linear equation in one variable:

3m = 21

m = 7

Thus, there are 7 marbles in a red jar if there are 21 marbles in a blue jar. The blue jars have 3 times as many marbles as a red jar.

Learn more about the linear equation here:

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Answer:

9 months

Step-by-step explanation:

Answer: 6 months

Step-by-step explanation: you take the initial membership fee of $49.50 and add it to the monthly for the first fee so it would be $67 and subtract that from the $172 he has. then divide the left over which is 105 and 17.50 you get 6

A polygon is a plane figure with at least three straight sides and angles, and typically five or more. In other words, a polygon is a 2 dimensional shape with straight sides. No curves!

A quarter of a circle has a curve on one side, and is therefore not a polygon.

Answer: She will be there 8 years.

Step-by-step explanation:

Step-by-step explanation:

Volume of a cylinder is the area of the circular cross section times the height:

V = πr²h

Answer:

V=(3.14)r^2×h

Step-by-step explanation:

(3.14)= pie

r^2= radius to the second power

h=height of cylinder