As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable? What one-variable equation is she left with after adding?

5x + 6y = 18
2x – 3y = 12

Factor:________
Equation:________x=_________

Answer:

look at picture shown.

Answer:

4 cm

Step-by-step explanation:

Perimeter of a parallelogram is 2b+2h=30 where b is base and h is height.

if AD is 3cm more than twice AB, then it's 3+2x where x is length of AB.

Input this into the perimeter equation: 2(3+2x)+2(x)=30

Simplify to get 6+6x=30

x=24/6=4

Answer is 4 cm.

Final answer:

The length of AB in the parallelogram is 4 cm after solving the algebraic equation for the given perimeter.

Explanation:

The student is asking us to find the length of AB in a parallelogram ABCD where the perimeter is given as 30 cm, and side AD is 3 cm more than twice the length of AB. We can use algebra to determine the length of AB in a few steps.

Let's denote AB as 'x'. Since opposite sides of a parallelogram are equal, AD and BC will equal '2x + 3' while CD will also equal 'x'. The formula for the perimeter (P) of a parallelogram is P = 2(AB + BC), so substituting our known values and solving for 'x' will give us the length of AB.

Putting it all together:

Therefore, the length of AB is 4 cm.

Answer:whole numbers

Step-by-step explanation:

Answer:

Find below the calculations of the two areas, each with two methods. The results are:

                     [tex]Area=5000\sqrt{3}units^2[/tex]

                     [tex]Area=14,530m^2[/tex]

Explanation:

A) Method 1

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

           [tex]Area=side_1\times side_2\times sin(\alpha)[/tex]

Where, [tex]\alpha[/tex] is the measure of the included angle.

1. Upper triangle:

          [tex]side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2[/tex]

2. Lower triangle:

         [tex]side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2[/tex]

B) Method 2

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

            [tex]Area=(1/2)\times base\times height[/tex]

Use it for both triangles.

3. Upper triangle:

The trigonometric ratio that you can use is:

                    [tex]sine(\alpha)=opposite\text{ }leg/hypotenuse[/tex]

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

         [tex]sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units[/tex]

[tex]Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2[/tex]

3. Lower triangle:

         [tex]sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2[/tex]

[tex]Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2[/tex]

Answer:

-6

Step-by-step explanation:

12, 10, 8, 6, 4, 2, 0, -2, -4, -6

Subtracting two each time

Answer:

-6

Step-by-step explanation:

It subtracts 2 each time in the sequence.

The first term is 12.

You subtract 2 ten times to get to the tenth number in this sequence. 10*2 = 20. 12-20 = -6

Answer:

umm give me more examples

Step-by-step explanation:

Answer:

x=8+a

Step-by-step explanation:

sum of a and 8

x=a+8

when they say the sum of you add an equal sign

and when they said of a and 8 it means that whatever the sum is its equal to a+8

since the sum wasn't mentioned the sum will be known as a variable

lets put x as the variable

The diameter of the #12 wire is approximately 0.08081 inches.

Calculating the diameter involves converting the measurement in mils to inches, since an inch is 1000 mils. Once we have the diameter in inches, we can round the answer to five decimal places, as instructed.

So, after performing the necessary calculations, the diameter of the #12 wire with a measurement of 80.81 mils is approximately 0.08081 inches.

A mil is a unit equal to one thousandth of an inch (0.001 inch). To convert mils to inches, we divide the mil measurement by 1000. So, 80.81 mils is equal to

80.81 / 1000 = 0.08081 inches.

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Final answer:

The diameter of the #12 wire in inches is 0.08081 inches, after converting 80.81 mils using the mil to inch conversion factor. The resistance of a wire changes with its gauge; a wire of one gauge number lower would have about 20% less resistance compared to the next higher gauge for the same length.

Explanation:

To convert the diameter of a #12 wire from mils to inches, you need to understand that one mil is equivalent to 0.001 inches. The stated diameter of the #12 wire is 80.81 mils.

By multiplying the value in mils by the conversion factor, we can find the diameter in inches:

80.81 mils × 0.001 inches/mil = 0.08081 inches.

Therefore, the diameter of #12 wire in inches is 0.08081 inches, rounded to five decimal places.

Discussing the resistance and resistivity of copper wire, it's known that resistance is proportional to the length of the wire and inversely proportional to the cross-sectional area.

Gauge sizes have a standardized series of diameters which differ by about 20% from one gauge to the next, which means that a wire with one gauge number lower (higher in diameter) would have approximately 20% less resistance than one of the next higher gauge (smaller in diameter) for the same length of wire.

Answer:

4 [tex]\frac{8}{9}[/tex]

Step-by-step explanation:

2 [tex]\frac{1}{5}[/tex] × 2 [tex]\frac{2}{9}[/tex]

[tex]\frac{11}{5}[/tex] × [tex]\frac{20}{9}[/tex] = [tex]\frac{220}{45}[/tex] = 4 [tex]\frac{8}{9}[/tex]

Answer:

I think it's B. (-1,3)

Step-by-step explanation:

The solution is the point the two lines intersect each other.

The answer is (-1,3)

Answer:

The needle palm tree is growing faster.

Step-by-step explanation:

The rate of growth of needle palm tree = 4.35 cm / day

The rate of growth of cabbage palm tree = 1.26 cm /day

From the given data we can clearly see ,

                 4.35  > 1.26

So the needle palm tree is growing faster.

2x + 3y + 4 = 15

2(1) + 3(3) + 4 = 15

2 + 9 + 4 = 15

11 + 4 = 15

15 = 15

x = 1 and y = 3

Hope this helps! ;)

Answer: The correct answer choice is D.

Step-by-step explanation: I will show all the work done for each answer choice so it is more clear.

First Answer Choice's Work:

2(6) + 3(3) + 4

12 + 9 + 4

12 + 9

21

21 + 4

25.

Second Answer Choice's Work:

2(3) + 3(5) + 4

6 + 15 + 4

21 + 4

25.

Third Answer Choice's Work:

2(6) + 3(4) + 4

12 + 12 + 4

24

24 + 4

28.

Fourth Answer Choice's Work:

2(1) + 3(3) + 4

2 + 9 + 4

11

11 + 4

15.

Therefore, the correct answer choice is D.

Answer:

4.07 is greater

Answer:

4.07

Step-by-step explanation:

Answer:

nth term, [tex]T_n=1(2)^n^-^1[/tex]

10th term, [tex]T_1_0=512[/tex]

Step-by-step explanation:

From the question;

We are required to write the formula of getting nth term and find the 10th term of the sequence;

[tex]T_n=a_1r^n^-^1[/tex]

Therefore, in this case;

nth term will be given by;

[tex]T_n=1(2)^n^-^1[/tex], where n is the term in the sequence;

Therefore;

To get the 10th term of the sequence;

[tex]T_1_0=1(2)^1^0^-^1[/tex]

[tex]T_1_0=1(2)^9[/tex]

[tex]T_1_0=512[/tex]

Therefore, the tenth term of the sequence is 512

Answer:

x=2, y=-2. (2, -2).

Step-by-step explanation:

y=x-4

y=4x-10

x-4=4x-10

x-4x-4=-10

-3x-4=-10

-3x=-10+4

-3x=-6

3x=6

x=6/3

x=2

y=2-4=-2

Answer:

240 miles

Step-by-step explanation:

The actual distance between two towns, which are separated by 6 inches on a map with a scale of 1 inch to 40 miles, is 240 miles.

The subject of this question is Mathematics, specifically focusing on understanding how map scales work. In this case, the map scale is 1 inch equals 40 miles. This means, for every inch on the map, it represents 40 miles in actual distance.

To find out the real distance between two towns that are separated by 6 inches on the map, you multiply the map scale distance (40 miles) by the number of inches (6).

Which is, 6 inches x 40 miles = 240 miles.

So, the actual distance between the two towns is 240 miles.

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Answer:

5

Step-by-step explanation:

The time taken to stuff and seal 63 envelopes by both Tom and Jerry will be 6 minutes.

Given the Parameters :

Combined rate :

Time taken if they work together :

Therefore, the time taken of they both worked together will be 6 minutes

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Answer:

The sales tax rate is 5%

Given:

Sales price = 5.00

Total amount paid = 5.25

Sales tax value = Total amount paid - sales price

                         = $5.25 - $5.00 

Sales tax value = $0.25

Sales tax rate = Sales tax / Sales price

                       = 0.25/5 

Sales tax rate  = 0.05 or 5%

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Thanks to taskmasters.

Step-by-step explanation:

Manuela works at least 22 hours in a week.

Step-by-step explanation:

Given,

Per hour salary of Manuela = $15

Amount deducted = $125

Amount received = $205

Let,

x be the number of hours per week.

Per hour salary * Number of weeks - Amount deducted ≥ Amount received

[tex]15x-125\geq 205\\15x\geq 205+125\\15x\geq 330[/tex]

Dividing both sides by 15

[tex]\frac{15x}{15}\geq \frac{330}{15}\\x\geq 22[/tex]

Manuela works at least 22 hours in a week.

Keywords: inequality, division

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Answer:

6 gallons

Step-by-step explanation:

23.00-6.50=16.50

16.50/2.75=6

Answer:

6000

Step-by-step explanation:

if you do 200+800=1000 and the if you do 4000+1000=5000+1000=6000

The inequality that represents the amount raised in the second hour of the charity auction is x ≤ 6000.

To represent the amount raised in the second hour of the charity auction, let's use the variable x. According to the information given, the amount raised in the first hour is $4800, which is at most $1200 more than the amount raised in the second hour. This can be represented as the inequality:

x ≤ 4800 + 1200

Simplifying the inequality, we have:

x ≤ 6000

Therefore, the inequality that represents the amount raised in the second hour is x ≤ 6000.

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Answer:

Not equivalent

Step-by-step explanation:

Let,

3(x-2) + 5 = 3x + 1

By Multiplying

3x - 6 + 5 = 3x + 1

3x - 1 = 3x + 1

So, the expressions are not equal

Answer:

314 square feet

Step-by-step explanation:

we know that

The area that will be covered by the spray of the quarter-circle sprinkler head, is equal to the area of a quarter circle with radius of 20 feet

so

The area of a quarter circle is

[tex]A=\frac{1}{4}\pi r^{2}[/tex]

we have

[tex]r=20\ ft[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]A=\frac{1}{4}(3.14)(20)^{2}=314\ ft^2[/tex]

The area covered by the quarter-circle sprinkler head to the nearest square foot is 314 square feet.

To find the area covered by the quarter-circle sprinkler head, we need to calculate the area of a quarter circle with a radius of 20 feet. The formula for the area of a circle is [tex]\( A = \pi r^2 \), where \( r \)[/tex] is the radius. Since we are dealing with a quarter circle, we will take [tex]\( \frac{1}{4} \)[/tex] of the full circle's area.

Given that the radius [tex]\( r \)[/tex] is 20 feet, the area of the full circle would be:

[tex]\[ A_{\text{full circle}} = \pi \times (20 \text{ feet})^2 \] \[ A_{\text{full circle}} = \pi \times 400 \text{ square feet} \] \[ A_{\text{full circle}} = 400\pi \text{ square feet} \][/tex]

Now, to find the area of the quarter circle, we divide the full circle's area by 4:

[tex]\[ A_{\text{quarter circle}} = \frac{1}{4} \times 400\pi \text{ square feet} \] \[ A_{\text{quarter circle}} = 100\pi \text{ square feet} \][/tex]

Using the value of [tex]\( \pi \)[/tex] as approximately 3.14159, we get:

[tex]\[ A_{\text{quarter circle}} \approx 100 \times 3.14159 \text{ square feet} \] \[ A_{\text{quarter circle}} \approx 314.159 \text{ square feet} \][/tex]

Rounding to the nearest square foot, the area covered by the quarter-circle sprinkler head is 314 square feet.

Answer:

x>-2

Step-by-step explanation:

13+x>11

x>11-13

x>-2

Answer:

-7

Step-by-step explanation:

Hope it helped!

The perimeter of second plot is 180 feet

Solution:

Given that,

The second parking lot is being designed so that its perimeter is 3/4 of perimeter of the first parking lot

Perimeter = 2(length + width)

From given figure in question,

length = 40 feet

width = 80 feet

Therefore,

Perimeter = 2(40 + 80)

Perimeter = 2(120) = 240

Thus, we got,

Perimeter of first parking plot = 240 feet

Also, given that,

[tex]\text{Perimeter of second plot }= \frac{3}{4} \times \text{Perimeter of first parking plot}\\\\\text{Perimeter of second plot }= \frac{3}{4} \times 240\\\\\text{Perimeter of second plot }= 180[/tex]

Thus perimeter of second plot is 180 feet

To find the perimeter of the second parking lot, you multiply the perimeter of the first parking lot by 3/4. For example, if the first parking lot has a perimeter of 100 meters, the second would be 75 meters.

The problem revolves around the concept of perimeter, specifically of a rectangle. The perimeter of a rectangle is given by the formula 2*(length + width). Now, according to the question, the perimeter of the second parking lot is three-quarters (3/4) that of the first. So, if we denote the perimeter of the first parking lot as 'P', then the perimeter of the second parking lot would be (3/4)*P.

For instance, if the perimeter of the first parking lot is 100 meters, then the perimeter of the second parking lot would be (3/4)*100 = 75 meters. Hence, the second parking lot's perimeter is determined by the first parking lot's perimeter, reduced by a quarter.

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Answer:

4x² - 20x + 26

Step-by-step explanation:

To evaluate g(f(x)), substitute x = f(x) into g(x), that is

g(2x - 5 )

= (2x - 5)² + 1 ← expand factor using FOIL

= 4x² - 20x + 25 + 1

= 4x² - 20x + 26

Answer:

[tex]x = -1[/tex]

Step-by-step explanation:

To do the last question using the quadratic formula, you first need the equation in standard form.

ax² + bx + c = 0.

To convert 2(x - 2)(x + 1) = x² - 4x - 5 into standard form, simplify by expanding and collecting like terms. Then, have the equation equate to "0" by moving everything to one side.

2(x - 2)(x + 1) = x² - 4x - 5        Expand brackets first using FOIL

2(x² + x - 2x - 2) = x² - 4x - 5        Collect like terms in brackets (x - 2x = -x)

2(x² - x - 2) = x² - 4x - 5        Distribute, multiply bracket numbers by "2"

2x² - 2x - 4 = x² - 4x - 5        Now make the equation equal 0

2x² - 2x - 4 - x² = x² - 4x - 5 - x²        Subtract x² from both sides

x² - 2x - 4 = -4x - 5        "x²" eliminated from the right side. Simplify left side.

x² - 2x - 4 + 4x = -4x - 5 + 4x        Add 4x to both sides.

x² + 2x - 4 = -5        "4x" eliminated from right side. Simplify left side.

x² + 2x - 4 + 5 = -5 + 5        Add 5 to both sides to eliminate it on the right.

x² + 2x + 1 = 0               Simplified left side.

This is now in standard form. State the "a", "b" and "c" values based on the standard form variables.

a = 1; b = 2; c = 1

Substitute into the quadratic formula

[tex]x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex]      (Please ignore the Â, it's a formatting error)

[tex]x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}[/tex]   Simplify the square root

[tex]x = \frac{-2±\sqrt{0} }{2}[/tex]     The square root of 0 is 0.

[tex]x = \frac{-2}{2}[/tex]      The numerator can only be -2. Simplify the fraction

[tex]x = -1[/tex]         Only one answer for "x".

Whenever the square root equals "0", there will only be one answer for "x".

Answer:

lenght= 60 inches

width = 18 inches

Step-by-step explanation:

parameter = 2(L+B)

let lenght be x

width be y

so

x = 3y+6

let's put this in formula

156 = 2( x+y )

156 = 2( 3y+6 + y )

156 = 2 ( 4y + 6 )

156/2 = 4y + 6

78 = 4y + 6

4y = 78-6

4y = 72

y = 72/4

y = 18

so width is 18 inches

and lenght is 3*18+6 = 60 inches

The width of the rectangle is 18 inches, and the length is 54 inches.

Let's denote the width of the rectangle as 'w'. According to the problem, the length of the rectangle can be expressed as 3w + 6. The problem also states that the perimeter of the rectangle is 156 inches. Remember that the formula for the perimeter of a rectangle is 2(length + width). Given that the length is expressed as 3w + 6 and the width as w, we can plug these values into the perimeter formula: 2(3w + 6 + w) = 156. Simplifying, we get 8w + 12 = 156. Isolating w, we have w = 18 inches. We also need to find the length, which is  3w + 6 = 54 inches. This gives us a width of 18 inches and a length of 54 inches.

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