3x+3y=-x+5y which ordered pair is a solution of the equation

Answer:

75.

Step-by-step explanation:

The HCF is the highest common factor of two numbers - if these numbers are both divisible by 75 - this is their HCF.

Answer:

x=2            x=-2

Step-by-step explanation:

x² + 2x - 4 = 2x

Subtract 2x from each side

x² + 2x-2x - 4 = 2x-2x

x^2 -4 = 0

Factor

We know this is the difference of squares

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

Using the zero product property

x-2 =0      x+2 =0

x=2            x=-2

The correct answer is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.

Here's the step-by-step breakdown:

Parallelogram A B C D to A' B' C' D':

Reflection across the x-axis: This flips the parallelogram across the x-axis, resulting in A' B' C' D'.

Parallelogram A' B' C' D' to A" B" C" D":

Translation of negative 6 units x, 1 unit y: This shifts the parallelogram 6 units to the left and 1 unit upwards, resulting in A" B" C" D".

Therefore, the overall composition of transformations is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.

Answer:

-46

Step-by-step explanation:

We need to find the common difference of this arithmetic sequence:

[tex]\frac{-26-(-10)}{10-6} =\frac{-16}{4} =-4[/tex]

So, the common difference d = -4. We can now write the equation:

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_{15}=a_6+d(15-6)=-10-4(9)=-10-36=-46[/tex]

So, the 15th term is -46.

Hope this helps!

Step-by-step explanation:

the answer and explanation is in the picture

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Answer:

D: 32[tex]\sqrt{3}[/tex]

Step-by-step explanation:

8/3[tex]\sqrt{3}[/tex] * 1/2 * 4 = 16[tex]\sqrt{3}[/tex]/3

16[tex]\sqrt{3}[/tex]/3 * 6 = 32[tex]\sqrt{3}[/tex]

Answer:161700

Step-by-step explanation:

The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be 161700.

Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be

¹⁰⁰C₃ = (100!) / [(100 – 3)! × 3!]

¹⁰⁰C₃ = (100 × 99 × 98 × 97!) / (97! × 3 × 2)

¹⁰⁰C₃ = 50 × 33 × 98

¹⁰⁰C₃ = 161700

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In the given question one word is missing, the correct question is,

If the área of a right triangle is 6.22sq. In. And its base is 3.11 in. Write an equation that relates the área to the height, h, and the base. Solve the equation to determine the height.

The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.

Step-by-step explanation:

The given is,

               Area of right triangle, A = 6.22 square inches

               Its base is 3.11 inches

Step:1

               Formula for area of right angle triangle is,

                             [tex]A = \frac{1}{2} bh[/tex]......................................(1)

               Where, b - Base

                            h - Height

              Equation (1), that relates the área (A) to the height (h) and the base (b).

Step: 2

              From the given values,

                         Base, b = 3.11 inches

                         Area, A = 6.22 square inches

              Equation (1) becomes,

                             6.22 = [tex]\frac{1}{2} (3.11)(h)[/tex]

                      (6.22) (2) = (3.11) (h)

                            12.44 = (3.11) (h)

                                  [tex]h = \frac{12.44}{3.11}[/tex]

                                     = 4

                    Height, h = 4 inches

Result:

        The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.

The equation 4x^2 + 28x + 49 = 0 is already a perfect square trinomial, and when rewritten in completed square form, it is (x + 7/2)^2 = 0, resulting in the solution x = -7/2.

To rewrite the equation by completing the square for the given quadratic equation 4x^2 + 28x + 49 = 0, we must manipulate the equation so that the left side becomes a perfect square trinomial.

Steps to Complete the Square

Divide all terms by the coefficient of x^2, which is 4 in this case, to make the coefficient of the x^2 term equal to 1.

You now have x^2 + 7x + (49/4) = 0.

Find a number that, when added to x^2 + 7x, completes the square. This number is (b/2)
2, where b is the coefficient of x; thus, here it is (7/2)^2 = 49/4.

Since 49/4 is already present, it confirms that the equation is already a perfect square trinomial.

Therefore, you can rewrite the equation as (x + 7/2)^2 = 0.

Finally, solve for x by taking the square root on both sides of the equation and subtracting 7/2 from both sides to get x = -7/2.

The equation 4x^2 + 28x + 49 = 0 is rewritten in completed square form as (x + 7/2)^2 = 0, with the solution x = -7/2.

Answer:

I dont know... Never tried it.

Answer:

47

Step-by-step explanation:

not that difficult

Answer:

There are 18 rungs on the ladder.

Step-by-step explanation:

Given a firefighter who is standing on the middle of the ladder.

We have to find the number of rungs the ladder have.

Let the number of rungs be "2x" where "x" be the number of rungs from the middle of the ladder to the top of the ladder.

Rungs below the middle of the ladder is equal to rungs above the middle of the ladder.

According to the question:

Let the fire fighter be at "y" rungs this "y" will be the reference point.

⇒ Moved [tex]4[/tex] rungs from 'y' current position [tex]4[/tex] rungs above of 'y'.

⇒ Moved [tex]6[/tex] rungs down meaning that [tex](4-6)= -2[/tex] rung from 'y' below [tex]2[/tex] rung  downward from 'y'.

⇒ Moved [tex]7[/tex] rungs upward from here meaning [tex](-2+7) = 5[/tex] rung above 'y'.

Now,

⇒ Further the firefighter climbed [tex]4[/tex] rungs from here [tex](5+4) = 9[/tex] rungs above 'y' .

Finally the firefighter have climbed [tex]9[/tex] rungs from 'y' that is the middle of the ladder so there is equal rungs below of it.

Total rungs of the ladder = '2x' = 2(9) = 18 rungs.

Answer:

0.02

Step-by-step explanation:

Since 60​% of the​ factory's bikes come off assembly line B, Therefore:

The probability that the​ factory's bikes come off assembly line B = 60% = 0.6

Percentage line​ B's products pass inspection  = 93% = 0.93

Percentage line​ B's products that do not pass inspection = 1 - 0.93 = 0.07

The probability that the​ factory's bikes come off assembly line A = 1 - 0.6 = 0.4

Percentage line​ A's products pass inspection  = 95% = 0.95

Percentage line​ A's products that do not pass inspection = 1 - 0.95 = 0.05

Let D represent those that passes inspection and D' represent those that do not pass inspection.

P(A ∩  D') = P(A) × P(D'/A) = 0.4 × 0.05 = 0.02

P()bikes did not pass inspection and came off assembly line A) = P(A ∩  D') =  0.02

Final answer:

The probability that a bicycle failed inspection and came from assembly line A is 2%.

Explanation:

We're tasked with finding the probability that a bike did not pass inspection and came from assembly line A. First, we calculate the probability of a bike failing inspection from each line. Since 95% of line A's products pass, there is a 5% (100%-95%) chance a bike from line A fails inspection. For line B with a 93% pass rate, there's a 7% (100%-93%) chance of failure.

Next, we consider the distribution of production between lines A and B. 60% of bikes are from line B, so 40% are from line A. We then calculate the probability of a bike being from line A and failing inspection using the multiplication rule for independent events, which is P(A) times the probability of failure on line A.

P(Fail and from A) = P(A) * P(Fail | A) = 40% * 5% = 0.40 * 0.05 = 0.02 or 2%.

Therefore, the probability that a bike did not pass inspection and came from assembly line A is 2%.

Answer:

√36

Step-by-step explanation:

√(a·b) = √a·√b, so

√3·√12 = √(3·12) = √36 = 6

Answer:

√36

Step-by-step explanation:

√3*√12 = √36 = 6

This matches the second answer choice.

Answer:

A) middle: 32

Outside: 9

B) 25

C) 47

Step-by-step explanation:

71 = 14 + 25 + intersection

Intersection = 71 - 39 = 32

Outside: 80 - 71 = 9

Only french: 25

Spanish: 14 + 32 = 46

Answer:

  13.56

Step-by-step explanation:

Each batch makes a total of ...

  0.090 +0.300 +3 = 3.39 . . . liters

Then 4 batches makes ...

  4 × 3.39 L = 13.56 L

Kim made 13.56 liters of punch.

Final answer:

Kim made a total of 13.56 liters of fruit punch by making 4 batches, with each batch including a combination of strawberry, pineapple, and apple juices.

Explanation:

Kim made 4 batches of fruit punch, each containing 90 milliliters of strawberry juice, 300 milliliters of pineapple juice, and 3 liters of apple juice.

To find the total amount of fruit punch made, we first convert all quantities to liters and then sum them up. Since there are 1,000 milliliters in 1 liter, 90 milliliters is equal to 0.09 liters and 300 milliliters is equal to 0.3 liters.

For one batch, the total liters of juice is:

So for one batch, the total is 0.09 + 0.3 + 3 = 3.39 liters.

Since Kim made 4 batches, the total amount of fruit punch is:

4 batches × 3.39 liters per batch = 13.56 liters

Therefore, Kim made 13.56 liters of fruit punch in total.

To solve the problem we will first calculate the radius of the circle and substitute the value in the formula of the area of a circle.

Area of the circle [tex]=\pi r^2[/tex]

The area of the circle is 49π or 153.86 unit².

Radius,

[tex]\rm{ r = \dfrac{Diameter}{2} = \dfrac{d}{2}=\dfrac{14}{2} =7[/tex]

Thus, the radius of the circle is 7.

Area of the circle [tex]=\pi r^2[/tex]

                             [tex]=\pi\times (7)^2\\ = 49\pi[/tex]

Substituting the value of π = 3.14,

Area of the circle [tex]=49\pi\\ = 49 \times 3.14\\ = 153.86[/tex]

Hence, the area of the circle is 49π or 153.86 unit².

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The area of the circle is approximately 4.5m².

The formula to find the area of a circle is A = πr², where π is approximately 3.14 and r is the radius. In this case, we have a radius of 1.2m. Using a calculator with an eight-digit output, we can calculate A = 3.14 x (1.2m)² = 4.5238934m².

However, since the radius only has two significant figures, we need to limit the calculated quantity to two significant figures. So, the area of the circle is approximately 4.5m² (rounded to two significant figures).

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Answer:

Turn-0.9166666666666666

Degree-330.00000000081860208

Final answer:

11/12 of a full rotation equates to 330 degrees or approximately 2.91 radians.

Explanation:

11/12 of a full rotation in a mathematical context refers to completing 11 out of 12 equal parts of a circle. Since a circle has 360 degrees, we can calculate this portion of a rotation by finding 11/12 of 360 degrees, which is 330 degrees. In terms of radians, since a full rotation is 2π radians, the same portion in radians would be 11/12 of 2π radians, which is approximately 2.91 radians.

Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

when you subtract a negative, you are basically adding the number.

*2 negatives equal a positive*

24 (-  -) 6 = 30

combine negatives:

24 + 6 = 30

Answer:

8,000 bees

Step-by-step explanation:

Final answer:

Mr. Smith will need approximately 8,000 bees in his bee colony to produce 3.5 pounds of honey each week, based on the rate of 1,000 bees producing 1 ounce of honey per day.

Explanation:

Mr. Smith needs to calculate the number of bees required to produce 3.5 pounds of honey each week.

First, we need to convert pounds to ounces because the rate given is in ounces:

3.5 pounds = 3.5 * 16 ounces/pound = 56 ounces of honey per week.

Now, we use the given rate of honey production:

1,000 bees produce 1 ounce of honey per day.

Therefore, in one week (7 days), 1,000 bees will produce 7 ounces of honey.

To find out how many bees you need to produce 56 ounces, you divide the target ounces by the ounces produced by

1,000 bees per week:

56 ounces / 7 ounces per 1,000 bees = 8,000 bees.

So, Mr. Smith will need approximately 8,000 bees in his colony to produce 3.5 pounds of honey each week.

Answer:

8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts

Step-by-step explanation:

Lets form equations first.

->Peanuts cost $2.50 per pound, raisins cost $2.00 per pound,  granola costs $4.00 per pound

2.50p + 2.00r + 4.00g= 80 -->eq(1)

-> bought ingredients to make 30 pounds of trail mix

p+ r+ g= 30 -->eq(2)

->If you use twice as many pounds of peanuts as raisins

2r=p

eq(1)=> 2.50p + 2.00r + 4.00g= 80

2.5(2r) + 2r +4g =80

5r + 2r + 4g =80

7r + 4g =80

eq(2)=>

2r+ r+ g= 30

3r + g =30

-4(3r + g =30)

   7r + 4g =80

_______________

 -5r = -40

r= 40/5 =>8

For 'g':

3(8) + g =30

g= 6

For 'p':

2r=p

p=16

therefore, 8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts should be bought

The solution to the problem is to buy 20 pounds of peanuts, 4 pounds of raisins and 6 pounds of granola.

This problem requires the use of algebra. Let's denote the amount of peanuts as x, the amount of raisins as y and the amount of granola as z. We have certain constraints according to the problem that need to be satisfied. These are:

First, substitute x = 2y from the first equation into the other two equations. This gives you the new equations y + z = 10 and 9y + 4z = 80. Next, solve these simultaneous equations. The solutions are y = 4, z = 6. Substituting y into the first equation gives us x = 2*4 = 20. So, you should buy 20 pounds of peanuts, 4 pounds of raisins and 6 pounds of granola.

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Answer: 96 candles in 8 boxes

Step-by-step explanation:

There’s 12 candles in a box

Answer:

10 organisms.

Step-by-step explanation:

625 Square feet of lawn.

You would simply divide 6250 by 625 and you would get 10.

Feel free to let me know if you need more help! :)

Answer:

90

Step-by-step explanation:

If the original price of a bracelet was a

70%a = 63

70/100a = 63

a = 63 × 100/70

a = 90

The price before the decrease is 90 euros.

The amount of decrease is the original amount minus the final amount. For example if you are looking for the percent of decrease from 9 to 6, the original amount is 9 and the final amount is 6.

GIVEN

Based on the given conditions, write z= 63/(1-0.3)

Calculate the sum or difference = 63/0.7

Divide a fraction by multiplying its reciprocal:[tex]=63*10/7 =90[/tex]

Hence, The price before the decrease is 90 euros.

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6 ÷ 3 × 8 + 9

6÷3=2

2×8=16

16+9=25

Answer:

47 meters

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.

My answer:

Given

As we know, the formula to find the area of a parallelogram is:

A = the base* the height

=> the base in this question is:

= The area / the height

= 2150 / 25 = 86 meters

As we can see in the photo, x + 39 meters = the base

=> x =  the base  - 39 meters

= 86 meters - 39 meters  

= 47 meters

Answer:75 inches

Step-by-step explanation: 9+66=75

=75 inches

Answer:

75 inches

Step-by-step explanation:

66+9=75

The position of the light source(the focus) is at; (0, 3.516).

The distance from the position of light source to the deepest part of dish is; 3.516 ft.

We know that standard form of a parabola equation is;

x² = 4ay

Now, we are told the dish is 15 ft wide and the depth is 4ft.

This means that the edge of the parabolic cross section will have an x-coordinate of 15/2 = 7.5 ft

While the y-coordinate is the depth of 4ft.

Thus;

Since;

x² = 4ay

Plugging in 7.5 ft for x and 4 ft for y gives;

7.5² = 4a(4)

a = 7.5²/16

a = 3.516 ft

Thus, position of the light source which is the focus is; (0, 3.516)

And distance from the position of light source to the deepest part of dish = 3.516 ft.

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The position of the light source (the focus) in a satellite dish with a parabolic shape, with a 15 ft diameter opening and depth of 4 ft, is calculated using the formula for the focal length of a parabola. Plugging these values into the formula results in the finding that the focus is  14.0625 ft away from the base of the dish.

The parabola can be described by the equation y = x2/4f, where f is the distance of the focus from the vertex. In a practical situation, to determine the position of the light source (the focus) in a satellite dish, which has a parabolic shape, we need to know the dish's width and depth. Here, the dish is 15 ft wide at the opening (which is the diameter of the dish) and the depth is 4 ft.

So, we can use these dimensions to calculate the position of the focus. First, we need to recall that in a parabola, the focus lies at the point (0, p), where p is the focal length. The focal length (p) of a parabolic dish can be calculated using the formula p = D2/16h, where D is the diameter of the dish and h is the depth of the dish. In this case, D = 15 ft and h = 4 ft.

Putting these values in the formula, we get p = (152)/16(4) = 14.0625ft. Therefore, the light source (focus) is placed 14.0625 ft away from the base of the dish.

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Answer:

21

Step-by-step explanation:

0i s

If a 6-sided die is rolled then P(less than 6) is  [tex]\frac{5}{6}[/tex]    

Probability can be found by dividing the favourable cases by the total possible cases.

We know that if a die is rolled, the possible outcomes are {1,2,3,4,5,6}

To get the probability of getting a number which is less then 6 after the die is rolled, we can add the probabilities of each outcome.

∴ Probability of getting a number which is less then 6 = ( [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex])

                                                                          = [tex]\frac{5}{6}[/tex]            

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