reduce to simplest form
6/3+(- 1/6)​

The width of the rug is 9 feet.

Step-by-step explanation:

Perimeter of rug = 42 feet

Lengths are same in square and rectangle shapes; therefore;

Length of rug = 12 feet

Width of rug = w

Perimeter = Length + Length + Width + Width

Perimeter = [tex]12+12+w+w[/tex]

[tex]42=24+2w\\42-24=2w\\18=2w\\2w=18[/tex]

Dividing both sides by 2

[tex]\frac{2w}{2}=\frac{18}{2}\\w=9[/tex]

The width of the rug is 9 feet.

Keywords: perimeter, division

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Answer:

c. Either a minimum or a maximum

Step-by-step explanation:

considering that a parabola can grow or decrease from its vertex we can note that in the case of a parabola with the branches down the vertex will always be a maximum, and in the case of a parabola with the branches up it will always be a minimum.

Answer:

A=60

Step-by-step explanation:

Answer:

[tex]Leading\ candidates\ votes\approx 18784\ votes[/tex]

Step-by-step explanation:

Percentage:[tex]x\%\ of\ y=\frac{x}{100}\times y[/tex]

[tex]Total\ votes=24082\\\\Leading\ candidates\ votes=78\%\ of\ total\ votes\\\\Leading\ candidates\ votes=\frac{78}{100}\times 24082\\\\Leading\ candidates\ votes=0.78\times 24082\\\\Leading\ candidates\ votes=18783.96\\\\Leading\ candidates\ votes\approx 18784\ votes[/tex]

The coordinates of x-intercepts of the graph of y = (x - 3)(x + 2) are (3 , 0) and (-2 , 0) ⇒ 4th answer

Step-by-step explanation:

The x-intercepts of a quadratic function is the values of x when y equal to zero

If y = (x - a)(x + b), then to find x-intercepts do that:

∵ The equation of the graph is y = (x - 3)(x + 2)

- To find the x-intercepts equate y by 0

∴ (x - 3)(x + 2) = 0

- Equate each bracket by 0

∵ x - 3 = 0

- Add x to both sides

∴ x = 3

∵ x + 2 = 0

- Subtract 2 from both sides

∴ x = -2

∴ The graph intersects the x-axis at points (3 , 0) and (-2 , 0)

The coordinates of x-intercepts of the graph of y = (x - 3)(x + 2) are (3 , 0) and (-2 , 0)

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Answer:

17

Step-by-step explanation:

Answer:

you want to divide 2¾ by ¼to find how many pieces leah cut.

hope this helps.

Step-by-step explanation:

Answer:

square root of 89

Step-by-step explanation:

squ^re r00t 0f 89 !s 9

Answer:

[tex]0.08[/tex]

Step-by-step explanation:

Given : 8%

To find the decimal value of the percentage number

Remove the percentage symbol with 100 in the denominator

gives            

              [tex]\frac{8}{100}\\[/tex]

Now taking the numerator to the decimal place equal to the number of zeros in the denominator or simply divide denominator with numerator.

Gives =   [tex]0.08[/tex]

So, the decimal equivalent of the given value is  [tex]0.08[/tex]

0.08

Step-by-step explanation:

8% can be written as 8/100 in the fractional form.

now when we will divide anything by 100, we will count the 0s in 100. here 2 zeros are there.

so we will put the decimal point before two digit. in numerator we already have 8.

we need another digit, so we put 0 then the decimal point.

that means 0.08

In geometry is defined as the equality between the two line segments are said to be congruent when they have the same length.

Given that, if EF=FG, then F is the midpoint of EG.

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

Congruent line segments are 1-dimensional geometrical figures having equal measures. The word "congruent" with respect to congruent lines in geometry is defined as the equality between the two line segments. Two lines are said to be congruent when they have the same length.

Here, F is the midpoint of EG it bisects the line EG, which is EF=FG

Therefore, in geometry is defined as the equality between the two line segments are said to be congruent when they have the same length.

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Answer:

1

Step-by-step explanation:

use PEMDAS=

2+6=12

12x2=24

48/24=2

2-1= 1

Answer:

2

Step-by-step explanation:

first you do things that are in perrinthes so that would be 2+6 is 8  times 2 because there is another perrinthes so thats 16 then divide 48 by 16 so then you get 3 minus 1 is 2( yeah im bad at spelling)

Answer:

30.4

Step-by-step explanation:

30.4-8.4=22

Answer:

(I) using the equation y=3x+1 at x=2 the length of Line DO is y=3(2)+1

Therefore y=7

(II) the coordinates At x=-3

Y=3(-3)+1=-8

Hence from (I) above also the coordinates are (7,-8)

Step-by-step explanation:

Step 1 :you declare variables

Step 2: you solve the equation at both points on the graph

Answer:

Explanation:

(i) When the car has only 80 m to stop, show that [tex]3v^2+20v-1600<0.[/tex]

The distance, [tex]d[/tex] [tex]m[/tex], it takes for a car moving at a speed of [tex]v[/tex] [tex]m/s[/tex]  to stop completely is given by [tex]d=0.15v^2+v[/tex]

The car must stop before the 80 m, so the distance to stop is less than 80 m:

                       [tex]d<80[/tex]

                      [tex]0.15v^2+v<80[/tex]

             [tex]20\times 0.15v^2+20\times v<20\times 80\\\\3v^2+20v<1600[/tex]

            [tex]3v^2+20v-1600<0[/tex]

Which is the expression you wanted to prove.

(ii) Solve the inequality in part (i) to find the maximum speed of the car.​

To solve the inequality you need to factor the left side:

         [tex]3v^2+80v-60v-1600<0[/tex]

         [tex]3v^2-60v+80v-1600<0[/tex]

         [tex](3v^2-60v)+(80v-1600)<0[/tex]

        [tex]3v(v-20)+80(v-20)<0[/tex]

          [tex](v-20)(3v+80)<0[/tex]

There are two possible solutions: 1) the first factor is positive and the second negative, and 2) the first factor is negative and the second positive.

1. First tentative solution

              [tex]v-20>0\\\\v>20\\\\3v+80<0\\\\3v<-80\\\\ v<-80/3\\\\v<-26.26[/tex]

The speed cannot be greater than 20m/s and less than - 26.26 m/s at the same tine, thus, there are not solutions for this assumption.

2. Second tentative solution

              [tex]v-20<0\\\\v<20\\\\3v+80>0\\\\3v>-80\\\\ v>-80/3\\\\v>-26.26[/tex]

You are looking for an upper bound, thus the solution is that the speed is less than 20m/s.

Option D:

Right triangle

Solution:

Let us first define obtuse, acute right triangle and supplementary.

Obtuse angled triangle:

If any one of the angle in the triangle is more than 90°, then the triangle is an obtuse angled triangle.

Acute angled triangle:

If all the angles of the triangle are less than 90°, then the triangle is an acute angled triangle.

Right angled triangle:

If any one of the angle in the triangle is exactly 90°, then the triangle is a right angled triangle.

Supplementary:

If sum of the angles is 180°, then the angles are supplementary angles.

But this is not a kind of triangle.

In given triangle one of the angle is 90°.

Therefore, this is a kind of right triangle.

Option D is the correct answer.

Answer:

You may need to plot them.

Step-by-step explanation:

Looks like your confused, if there is a line plot plot it there. Hope this helps! If it doesn't, phone a friend!

Answer: it would be 47.9 if you rounded to nearest tenth

Step-by-step explanation: Add all numbers together then divide by how many numbers are there

Answer:

∴ΔGHJ ≅ΔLMK

∴ΔABC≅ΔPQR

Step-by-step explanation:

5.

GH= 3.6 , HJ=2.84 and GJ=2.24

LK= 9 ,KM= 5.6 and LM = 7.1

[tex]\frac{LK}{GH} =\frac{KM}{GJ} =\frac{LM}{HJ}[/tex]

[tex]\frac{9}{3.6} =\frac{5.6}{2.24} =\frac{7.1}{2.84} =2.5[/tex]

Therefore ΔGHJ and ΔLMK satisfy SSS rule(side-side-side)

∴ΔGHJ ≅ΔLMK

6.

ΔABC

Since AB=AC this equivalent to the two angels of the triangle  are equal

Then

∠CAB+∠CBA=180°-34°

⇔∠CAB=73°     [∵∠CAB=∠CBA]

Similarly for ΔPQR ∴ ∠RPQ=∠RQP=73°

Therefore ΔABC and ΔPQR satisfy AAA rule(angle-angle-angle)

∴ΔABC≅ΔPQR

Answer:

actually the right answer is A

Step-by-step explanation:

if you solve it you get x=36 but remember that x is the amount of water that you need to evaporate so if you want to check it just subtract it from 90 and the salt will be 25%

To find the amount of rope needed for the new garage, calculate the perimeter of the planned structure. If the new garage is similar to the current one, maintaining the same width to length ratio (5:4), and the width is increasing to 30 feet, the length will be 24 feet. The total rope required is the perimeter, which is 108 feet.

To calculate the amount of rope needed for the new garage with a width of 30 feet, we must find the length of the rectangle that represents the area to be roped off for the concrete pour. If the garage maintains the same shape, which is similar to the current one, we can assume that the length will increase in the same ratio as the width.

The current dimensions are 25 feet wide by 20 feet long, which gives a width to length ratio of 25:20 or 5:4. If we increase the width to 30 feet, maintaining the same ratio, the length should be 24 feet (as 30:24 or 5:4). So the perimeter of the new rectangular area will be twice the width plus twice the length (2 x width + 2 x length = 2 x 30 ft + 2 x 24 ft = 60 ft + 48 ft = 108 ft). Therefore, you will need 108 feet of rope to stake out the perimeter of the new garage.

Final answer:

To find the amount of rope needed for the new garage, calculate the perimeter of the new garage by summing all the sides of the rectangle. The perimeter of the current garage can be used as a reference point. The result is 100 feet of rope needed.

Explanation:

To find the amount of rope you will need, you need to calculate the perimeter of the new garage. The perimeter is the sum of all the sides of a rectangle.

The current garage has a width of 25 feet and a length of 20 feet, so its perimeter is 2(25) + 2(20) = 90 feet.

The new garage will have a width of 30 feet, so its perimeter will be 2(30) + 2(20) = 100 feet.

Therefore, you will need 100 feet of rope to stake and rope off where the concrete will be poured for the new garage.

Step-by-step explanation:

We have,

3014 divided by 63

To find, the remainder of 3014 divided by 63 = ?

3014 divided by 63

∴ [tex]\dfrac{3014}{63}[/tex]

= 63 × 47 + 53

We know that,

Dividend = Quotient ×  Divisor + Remainder

∴ Remainder = 53

Thus, when 3014 divided by 63, the remainder is 53.

Answer:

-78 + 55 = -23

Step-by-step explanation:

Answer:

Step-by-step explanation:

-78+55 = -23

Answer:

7 months

Step-by-step explanation:

equation:

75+65x

75+65(6)=465 <495

75+65(7)=530>495

Ben will need to make deposits for at least 7 months to have enough money to buy the TV.

To determine the minimum number of months Ben will need to make deposits until he has enough money to buy the TV, we can set up an equation.

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Answer:

  see below for one possibility

Step-by-step explanation:

Many methods are taught for doing long division. You may find it most convenient to use the one taught in your class. One method is shown in the attachment below.

Generally, the first step is to adjust the decimal points so the divisor is an integer. Here, that means multiplying both numbers by 100, so the problem becomes 1517.76/248. This makes it easy to keep the decimal point of the quotient in the right place.

If you're using the method illustrated below, you find the smallest portion of the dividend that is a multiple of the divisor between 1 and 9. Multiply the divisor by that quotient digit and subtract the result from the dividend. Repeat as often as necessary to get the desired result. When the remainder is zero, as here, there is no point to continuing, as the remaining quotient digits are zero.

The quotient digit described in the previous paragraph is aligned with the least significant digit of the dividend that you're working with. If that is not adjacent to the previous quotient digit, use zero as a place-holder. The second attachment shows an example.

When the dividend is the same as one you have seen before, it means the digits of the quotient will repeat. The third attachment shows an example of this.

_____

For the problem shown here, you know that 15/2.5 is a number between 1 and 10, so you can ignore the decimal points and place the decimal point in the quotient so its value is between 1 and 10. This is the way it is done when the tool used for division is a slide rule, not a modern scientific calculator. (When using a slide rule, the powers of ten need to be managed manually.)

Answer:40z

Step-by-step explanation: i got this answer by using the distributive property. So when I distribute 5 to 8 you just basically multiply the two and add the variable on the end

Answer:

The expression for the width of the rectangle is [tex]9x^{5}y^{5}[/tex].

Step-by-step explanation:

The formula to compute the area of a rectangle is,

[tex]Area=length\times width[/tex]

Given:

Area = [tex]45x^{8}y^{9}\ square\ yards[/tex]

Length = [tex]5x^{3}y^{4}\ yards[/tex]

Determine the expression for the width of the rectangle as follows:

[tex]Area=length\times width\\45x^{8}y^{9}=(5x^{3}y^{4})\times width\\width = \frac{45x^{8}y^{9}}{5x^{3}y^{4}} \\=\frac{45}{5}\times [x^{8-3}]\times [y^{9-4}]\\ =9x^{5}y^{5}[/tex]

Thus, the width is [tex]9x^{5}y^{5}[/tex].

Step-by-step explanation:

x : y = 5 : 6

[tex] \therefore[/tex]let x = 5k & y = 6k

We need to find: 5x-2y:6x+2y

[tex] \therefore \: \frac{5x - 2y}{6x + 2y} \\ \\ = \frac{5 \times 5k - 2 \times 6k}{6 \times 5k + 2 \times 6k} \\ \\ = \frac{25k - 12 k}{30k + 12k} \\ \\ = \frac{13 k}{42k} \\ \\ =\frac{13 }{42} \\ \\ = 13 : 42 \\ \\ \purple{ \boxed{\therefore \: (5x - 2y) :({6x + 2y}) = 13 : 42}}[/tex]

So we know that 1 inch on the map = 5 inches.

So if Brady's house is 23 inches away from Flagstaff on the map:

23 * 5 = 115.

So 115 inches is the actual distance...

Wait. His house is 9 feet away from Flagstaff? That's cool.

Answer:4

Step-by-step explanation:

You only multiple the top or in this case 4 so 4x5= 20/5 simplified would be 20 divided by 5=4

Answer:

4

Step-by-step explanation:

Because all you need to do is multiply-5 times 4 equals 20/5 and 20 divided by 5 equals 4.