A 22inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one inch more than four times the length of the first piece. Find the length of the pieces

Answer:

[tex]FJ=39\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]

we have

[tex]FE=HF+EH=26+14=40\ units[/tex]

[tex]FH=HF=26\ units[/tex]

[tex]FG=60\ units[/tex]

substitute the given values

[tex]\frac{40}{26}=\frac{60}{FJ}[/tex]

[tex]FJ=26(60)/40\\FJ=39\ units[/tex]

Answer:

The answer is 39!!

Step-by-step explanation:

Answer:

its 2/9

Step-by-step explanation:

I remember this from a long time ago but any number repeating that is less than nine is just put over 9, but as it goes up you put it over 99 and so on.

Answer: [tex]a=\frac{b(zd-c)}{d}[/tex]

Step-by-step explanation:

Having the following equation given in the exercise:

[tex]z=\frac{a}{b}+\frac{c}{d}[/tex]

You can solve for "a" following this procedure:

1. You can apply the Subtraction property of equality and subtract [tex]\frac{c}{d}[/tex] from both sides of the equation:

[tex]z-(\frac{c}{d})=\frac{a}{b}+\frac{c}{d}-(\frac{c}{d})\\\\z-\frac{c}{d}=\frac{a}{b}[/tex]

2. Now you must subtract the terms on the left side of the equation. Notice that the Least Common Denominator is "d". Then:

[tex]\frac{zd-c}{d}=\frac{a}{b}[/tex]

3. Finally, you can apply the Multiplication property of equality and multiply both sides of the equation by "b". So, you get:

[tex](b)(\frac{zd-c}{d})=(\frac{a}{b})(b)\\\\a=\frac{b(zd-c)}{d}[/tex]

You can add 1350 additional watts without overloading the circuit.

Step-by-step explanation:

Given,

Circuit overloads at 2400 watts

Electricity used by heater = 1050 watts

Let,

x be the number of additional watts.

Electricity used by heater + Additional watts ≤ Circuit's capacity

[tex]1050+x\leq 2400[/tex]

Subtracting 1050 from both sides

[tex]1050-1050+x\leq 2400\\x\leq 1350[/tex]

You can add 1350 additional watts without overloading the circuit.

Keywords: inequality, subtraction

Learn more about subtraction at:

#LearnwithBrainly

If a circuit can handle up to 2400 watts, and a heater using 1050 watts is already plugged in, an additional 1350 watts of electrical devices can be plugged in without overloading the circuit.

The subject at hand is related to electrical power and circuits. In electrical circuits, overloading occurs when more electrical power is drawn than the circuit can safely handle. This limit in your scenario is represented as 2400 watts of electricity. If a portable heater using 1050 watts of electricity is already plugged into the circuit, you subtract the wattage of the heater from the maximum wattage to find out how much more you can add without overloading the circuit.

So, we calculate 2400 watts (total wattage that the circuit can handle) - 1050 watts (wattage used by the heater) = 1350 watts. Therefore, you can plug in additional items up to 1350 watts without overloading the circuit.

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To find how much each friend get's we can put this into a ratio or fraction. 4/6 is the fraction of apples to friends. This can be simplified;

4/6 = 2/3 (Each person gets 2/3 of an apple)

Best of Luck!

Answer:

175

Step-by-step explanation:

The circle has to = 360 degrees. 360-10=350

350/2=175

The x is halfway that's why you divide by 2.

Answer:

length iof opposite sides are equal

Step-by-step explanation:

Final answer:

To prove ABCD is a parallelogram, we showed that the given pairs of opposite sides are parallel and the slopes of opposite sides are equal, confirming the definition of a parallelogram.

Explanation:

To complete the proof that ABCD is a parallelogram, we must show that both pairs of opposite sides are parallel and that the lengths of opposite sides are equal or that the slopes of opposite sides are equal. Since it's given that BC is parallel to AD and CD is parallel to AB, the condition for parallel sides is satisfied. To fulfill the second condition, we calculate the slopes of the sides.

The slope of BC is calculated using the coordinates of B(-3,4) and C(2,2):

Slope of BC = (4 - 2) / (-3 - 2) = 2 / -5

The slope of AD, using the coordinates A(-2,-2) and D(3, -4), is:

Slope of AD = (-4 - (-2)) / (3 - (-2)) = (-2) / 5

Because the slopes of BC and AD are negative reciprocals, BC and AD are parallel. A similar calculation can be made for AB and CD, using their corresponding coordinates, to confirm that their slopes are equal. Thus, because both pairs of opposite sides are parallel, ABCD is a parallelogram.

Step-by-step explanation:

Transforming the coordinates from (x, y) to (y, x) leaves the triangle unchanged.

Step-by-step explanation:

When the coordinates are being transformed from (x, y) to (y, x) such that A(1,3) B(-3,4) C(-4,2) are transformed to A(3,1) B(4,-3) C(-4,2), the nature of the triangle remains the same. In other words, it doesn't turn either way. The reason is because the coordinates are the points of intersection between x and y so whichever axis (x or y axes) is plotted first does not transform the given shape.

Answer:

7

Step-by-step explanation:

Answer:

53 1/3 km/h

Step-by-step explanation:

The car is going at 80km in 1.5 hours, so if you divide that value you get 26 2/3 km for every half hour, now you would want to multiply this times 2 to find the value for every hour, so then this would give you the answer 53 and 1/3 kilometers per hour.

Marco has ( d + 14.55 ) $

Step-by-step explanation:

Marco's mom gave him d dollars for his allowance one week.

Allowance of one week = d $

He also earned $ 1 4 . 5 5 for his newspaper route that week.

Earning of Marco by selling newspaper route that week = 14.55 $

Total earning = Allowance of one week + Earning of Marco by selling newspaper route that week

Total earning = ( d + 14.55 ) $

So Marco has ( d + 14.55 ) $

Answer:

Step-by-step explanation:

Answer:

11/10

Step-by-step explanation:

Answer:

x = -2

x+3y = 4

This is the substitution method. You need to plug the -2 in x's place to get y.

-2+ 3y = 4

3y = 4+2

3y = 6

y= 6/3

y= 2

Answer:

Debra needs to buy 32 bottles of a quarter of fertilizer, that will cost her $ 473.28 to fertilize her garden of 1,008 square feet or 112 square yards of area.

Correct statement and question:

Debra’s rectangular vegetable garden measures 9 1/3 yards by 12 yards. A bottle of fertilizer cost $14.79. If Debra needs to mix 1/8 cup of fertilizer with water for each square foot of her garden, how many cups of fertilizer did she need? How can you persevere in solving this problem? And what's the answer?

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's review the information given to us to answer the question properly:

Length of the garden = 12 yards

Width of the garden = 9 1/3 = 9.33 yards

Cost of a bottle of fertilizer = $ 14.79

Ratio of fertilizer : water for the garden = 1/8 cup for each square foot

2. How many cups of fertilizer did she need?

For answering the question, we need to know the area of the garden and convert it to square feet, this way:

Area = Length of the garden * width of the garden

Area = 12 * 9.33 = 111.96 square yards, that we will round to 112

Let's recall that 1 square yard = 9 square feet

Area = 112 * 9 = 1,008 square feet

Now, we can calculate the cups of fertilizer needed:

Cups of fertilizer = 1,008/8 = 126

Finally, for calculating how many bottles of fertilizer does Debra need to buy, let's assume that each bottle has a quart because that information wasn't given to us.

Let's recall that 1 cup = 1/4 quart

126 cups = 32 quarts ⇒ 32 bottles

Cost of 32 bottles of fertilizer = 32 * 14.79

Cost of fertilizer = $ 473.28

The subject of this question is Mathematics.

The subject of this question is Mathematics because it involves measuring the dimensions of a rectangular vegetable garden.

Answer:

The pair of equations which has (2,12) as its solution is,

equation B and equation C.

Step-by-step explanation:

According to the question,

equation of line A is [tex]\frac {y - 16}{x + 6} = \frac {16 + 4}{-6 - 9}[/tex]

                            or, [tex]\frac {y - 16}{x + 6} = \frac {-4}{3}[/tex]

                            or, [tex] 3y - 48 = -4x - 24[/tex]

                            or, 3y + 4x = 24 ------------------(1)

Now, the point (2, 12) doesn't satisfy (1). Hence, (2,12) is not a solution for the line A.

Equation of line B is, [tex]\frac {y - 20}{x + 2} = \frac {20 - 0}{-2 - 8}[/tex]

                              or, [tex]\frac {y - 20}{x + 2} = -2[/tex]

                              or, [tex] y - 20 = -2x  - 4[/tex]

                              or, y + 2x = 16  -----------------------------(2)

The point (2,12) is satisfied by (2). Hence, (2, 12) is a solution for line B.

Equation of line C is, [tex]\frac {y + 6}{x + 7} = \frac {20 + 6}{6 + 7}[/tex]

                              or, [tex]\frac {y + 6}{x + 7} = 2[/tex]

                              or, y + 6 = 2x + 14

                              or. y - 2x = 8 -----------------------------------(3)

The point (2, 12) is satisfied by (3). Hence, (2 , 12) is a solution for the line C.

Equation of line D is, [tex]\frac {y - 20}{x - 7} =\frac {20 + 7}{7 - 0}[/tex]

                               or, [tex]\frac {y - 20}{x - 7} = \frac {27}{7}[/tex]

                               or, 7y - 140 = 27x - 189

                               or, 7y  - 27x = -49----------------------------------------(4)

The point (2, 12) is not satisfied by (4). hence, (2, 12) is not a solution of the line D

Hence, the pair of equations which has (2,12) as its solution is,

equation B and equation C.

Answer:

63.1∅∅

Step-by-step explanation:

Answer:

63.1

Step-by-step explanation:

If you are rounding anything, look at the number before. If its 5 or above, move the next number up. If its 4 or below, just keep the number the same. In this case the number is .094. The 4 is irrelevant because we are rounding in the tenths not the hundreths. So we look at the next one. Its a 9 there for round it up so you have 63.1

Question:

One dollar is worth 3 1/2 kruneros. What is the value of 43 3/4 kruneros?

Answer:

The value of [tex]43\frac{3}{4}[/tex] kruneros is 12.5 dollars

Solution:

Given that,

Dollar is worth three and 3 1/2 kruneros

Which means,

[tex]1 \text{ dollar } = 3\frac{1}{2} \text{ kruneros }\\\\1 \text{ dollar } = 3.5 \text{ kruneros }[/tex]

We have to find the value of [tex]43\frac{3}{4}[/tex] kruneros

Let us convert the mixed fractions to improper fractions

Multiply the whole number part by the fraction's denominator.

Add that to the numerator.

Then write the result on top of the denominator.

[tex]43\frac{3}{4} = \frac{43 \times 4 + 3}{4} = \frac{175}{4} = 43.75[/tex]

So we have to find the value of 43.75 kruneros

Let "x" be the value of 43.75 kruneros

Then,

1 dollar = 3.5 kruneros

x dollar = 43.75 kruneros

This forms a proportion and we can solve the sum by cross multiply

[tex]1 \times 43.75 = x \times 3.5\\\\x = \frac{43.75}{3.5}\\\\x = 12.5[/tex]

Thus value of [tex]43\frac{3}{4}[/tex] kruneros is 12.5 dollars

Answer:

I put it into a calculator and got this: 7/125

Step-by-step explanation:

It is equal to 8 x 7 x 1 / 100 x 1 / 10

And multiplying something by 1 doesn't change it. So we can get rid of that:

8 x 7 / 100 / 10

8 x 7 is 56, so we can simplify it to

56 / 100 / 10

56 / 100 is 0.56, and 0.56 / 10 is 0.056. So the final answer is 0.056.

Answer:

  16/15

Step-by-step explanation:

  [tex]\dfrac{-3}{5}\cdot\dfrac{2}{-9}\cdot 8=\dfrac{3\cdot 2\cdot 8}{5\cdot 9}=\dfrac{2\cdot 8}{5\cdot 3}=\dfrac{16}{15}[/tex]

The two minus signs cancel, so the result is positive.

The value of area after 12 years is 1409 square kilometer

Solution:

Given that,

A certain forest covers an area of 2300 square kilometer

Suppose that each year this area decreases by 4%

To find: Area after 12 years

This is decreasing function

The decrease function is given as:

[tex]y = A(1-r)^t[/tex]

Where,

y is the value after t years

A = initial amount

r = decreasing rate in decimal

t is the number of years

Here in this sum,

A = 2300

t = 12 years

[tex]r = 4 \% = \frac{4}{100} = 0.04[/tex]

Substituting the values in formula,

[tex]y = 2300(1-0.04)^{12}\\\\y = 2300(0.96)^{12}\\\\y = 2300 \times 0.612709\\\\y = 1409.23 \approx 1409[/tex]

Thus value of area after 12 years is 1409 square kilometer

Answer:

8,14

Step-by-step explanation:

Let one number = x

Other number = 22-x

x - (22-x) = 6

x - 22 +x =6

2x = 6 + 22

2x = 28

x = 28/2

x = 14

Other number = 22 - 14 =8

Answer:

the answer is b

Step-by-step explanation:

trust me im looking at the answer rn

Answer:

B

Step-by-step explanation: A.P.E.X

Answer:

1 Quarter + 1 Nickel , 3 Dimes , 30 Pennies , 15 Pennies + 1 Nickel + 1 Dime ,    10 Pennies +  2 Nickels + 1 Dime ...

Step-by-step explanation:

1 Dollar = 100 cents

30% of 100 = 30 cents

There are many different ways to make 30 cents with certain coin combinations.

Using the different available coins, a combination of 3 different coins can be combined to give a total value of 30 cents.

30% of a dollar = (30/100) = $0.30 = 30 cents

1 Quarter + 1 Nickel , 5 Pennies = 25 + 5 + 5 = 30 cents

1 dime + 2 Nickels + 10 Pennies = 10 + 10 + 10 = 30 cents

3 Nickels + 1 dime + 5 Pennies = 15 + 10 + 5 = 30 cents

Therefore, the listed are 3 possible combinations of obtaining 30 cents.

Learn more : https://brainly.com/question/17225268

Answer:it is function and it is 25

Step-by-step explanation:it is 25 in the y inputs because every time the x input increases by one the y input increases by 25

it is a function because each one of the “x” imputes has there own “y” input and if they all have there own that makes it a function. but it there were 2 “y” inputs pointing to one “x” input that would make it a non function

Answer:

the measure of xy is 9

Answer:

The coordinates of the Pizza Hut is (6,-11)

Step-by-step explanation:

Gym is equidistant and collinear from Target and Pizza Hut.

T (-17, 17) :  [tex](x_1,y_1)[/tex]

G (-5.5, 3) : (x,y)

P : [tex](x_2,y_2)[/tex]

Mid point formula ; (x,y) is on mid point on line formed by joining points [tex](x_1,y_1)[/tex]and [tex](x_2,y_2)[/tex]

m = 1, n = 1

[tex]x=\frac{x_1+x_2}{2}[/tex]

[tex]-5.5=\frac{-17+x_2}{2}[/tex]

[tex]-11=-17+x_2[/tex]

[tex]x_2=17-11 = 6[/tex]

[tex]y=\frac{y_1+y_2}{2}[/tex]

[tex]3=\frac{17+y_2}{2}[/tex]

[tex]6=17+y_2[/tex]

[tex]y_2=-17+6 = -11[/tex]

The coordinates of the Pizza Hut is (6,-11)

To find the coordinates of Pizza Hut, use the midpoint formula with the given coordinates of You Fit Gym and Target.

To find the coordinates of Pizza Hut, we can use the fact that You Fit Gym is equidistant and collinear from Target and Pizza Hut. Since Target is located at (-17, 17) and You Fit Gym is at (-5.5, 3), we can use the midpoint formula to find the coordinates of the Pizza Hut. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are [(x1 + x2)/2, (y1 + y2)/2].

Using this formula, we can find the coordinates of the Pizza Hut:

x-coordinate: (-17 + (-5.5))/2 = -11.25

y-coordinate: (17 + 3)/2 = 10

Therefore, the coordinates of the Pizza Hut are (-11.25, 10).

Answer:

28,224

Step-by-step explanation:

use photomath it will help u with math problems.

Answer:28224

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) r = 10/2 = 5 feet

Area of floor =πr² =3.14*5*5 = 78.5 feet²

B) h = 3 foot

Volume of cylinder = πr²h = 3.14*5*5*3 = 235.5 cubic feet

Volume of hemisphere =2/3πr³= 2*3.14*5*5*5/3=261.67 cubic feet

Volume of space inside the observatory = 497.17 cubic feet

Answer:

y = 14

Step-by-step explanation:

The triangle in the figure is an isoceles triangle meaning the two sides of the triangle are equal. This I know because of that short lines on line AC and CB of the triangle.

Now, the base angles of an isoceles triangle are equal and applying this theorem to this problem, we have:

50 = 2x

solving for x,

x = 25

Now the sum of angles in a triangle is 180 degrees

=> 50 + 50 + 5y + 10 = 180

5y = 180 - 110

5y = 70

y = 14

Answer: The Answer would be 18.6 cups.

Step-by-step explanation: Kinda dont know how to explain it lol