a certain rectangle has an area of x^2+7x+12. Factor the trinomial to find the length and width of the rectangle. (Please show the steps for working this out)

Answer:

45/28

Step-by-step explanation:

Convert them to mixed fractions

(2 * 4 + 1) / 4 ÷ (1 * 5 + 2) / 5

8 + 1 / 4 ÷ 5 + 2 / 5

9/4 ÷ 7/5

Flip the second fraction and flip the sign - to multiply.

9/4 × 5/7

9 × 5 = 45

4 × 7 = 28

45/28

This could be left as a fraction or converted to a number:

1.60714285714

Answer:

The Answer is 1 17/28

Step-by-step explanation:

1) turn the mixed fraction into a regular fraction

2 1/4 divided by 1 2/5 = 9/4 divided by 7/5

2) Then Multiply

9/4 X 7/5= 45/28 (Straight across)

3) Simplify 45/28

Give you 1 17/28

Hopes this helps!

Answer:

(0,-1)

Step-by-step explanation:

The solution to the system of linear equation is (0, -1)

To solve for the system of linear equations, we can use substitution method;

y = -2x - 1 ...eq(i)

y = -x - 1 ...eq(ii)

Equate both equations

-x - 1 = -2x - 1

-x = -2x

This shows it can not be solved by any other means except graphically.

To solve this equation graphically, we can plug in the equations and then find the point of intersection;

Kindly find the attached graph below

The solution to the system of equation is (0,-1)

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Answer:

1/4

Step-by-step explanation:

Divide the top and the bottom by 2 to get the simplest form.

2 / 2 = 1

8 / 2 = 4

2/8 = 1/4

Answer:

A. 8kg

Step-by-step explanation:

You don't really need any solution but if

1000 paperclips = 1 kg, then

8000 paperclips = 8kg

Final answer:

To determine the mass of 8,000 paperclips in kilograms, divide 8,000 by 1,000, since 1,000 paperclips weigh 1 kilogram. The result is 8 kilograms, making option A the correct answer.

Explanation:

The question concerns the mass of paperclips in grams and kilograms, which are units of mass in the metric system. To find out how many kilograms 8,000 paperclips would weigh, we need to use the given conversion that 1,000 paperclips have a mass of 1 kilogram. Here's the step-by-step calculation:

Since 1,000 paperclips weigh 1 kilogram, we can find out how many groups of 1,000 paperclips there are in 8,000 paperclips by dividing 8,000 by 1,000.

8,000 paperclips ÷ 1,000 paperclips/kg = 8 kg

Therefore, 8,000 paperclips have a mass of 8 kilograms.

The correct answer to the question is A. 8 kg.

Answer:

(1;-2)

Step-by-step explanation:

x=-2y-3

2(2y+3)=-6y-9-5

10y=-20

y=-2

x=4-3=1

Answer:

b

Step-by-step explanation: 62-18 is 44 and 44 is greater than 18

Answer:

B) p ≤ 44 is your ANSWER

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

anything over 9 that is not 9 is a repeating decimal

Answer:

True

Step-by-step explanation:

7/9 = 0.777777777778

Answer:

8

Step-by-step explanation:

The question is basically "Find the radius of the circle that has a circumference of 16π"

The formula for circumference of a circle is given as  [tex]C=2\pi r[/tex]

Where

C is the circumference

r is the radius

Plugging in 16π into C and solving for r gives us the radius. Shown below:

[tex]C=2\pi r\\16\pi = 2\pi r\\r=\frac{16\pi}{2\pi}\\r=8[/tex]

the radius is 8

Answer:

Step-by-step explanation:

Yes the math is correct. But the A part asks for the interest. The interest is 795.96 and that is what her account is worth. She thinks the interest is 3795.96, but it's not. She's added the bare principle in a second time.

Account amount = 3795.96

Interest = 795.96

Answer:

Step-by-step explanation:

(4/3)*[tex]\pi[/tex]*r^3

V = 113,04

Best regards

Answer:

-200

Step-by-step explanation:

400 - 600 = -200

Answer:

-200

Step-by-step explanation:

600-400=-200

Among the given options, statement D, which says 'For every man who likes running, 7 men like playing golf,' is the correct statement based on the numbers provided.

In order to determine which statement is correct, we would need to relate the numbers given in the question. So let's take a look.

With this comparison, we can conclude that the correct statement is D. For every man who likes running, 7 men like playing golf.

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The correct statement is option B: for every woman who likes running, 3 women like playing golf.

In order to determine which statement is correct, we would need to relate the numbers given in the question. To determine which statement is correct, we need to compare the ratio of women who like running to women who like playing golf.

There are 18 women who like running and 6 women who like playing golf.

Therefore, the correct statement is option B, which states that for every woman who likes running, 3 women like playing golf.

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The surface area of the cylinder is 326.56 square inches.

For the surface area (SA) of a cylinder, you can use the formula:

SA = 2π[tex]r^2[/tex]+ 2πrh

where:

Given that the height (h) is 9 inches and the base radius (r) is 4 inches, you can substitute these values into the formula:

SA = 2 × 3.14 × [tex](4)^2[/tex]+ 2 × 3.14 × 4 × 9

SA = 2 × 3.14 × 16 + 2 × 3.14 × 36

SA = 100.48 + 226.08

SA = 326.56

Therefore, the surface area of the cylinder is

326.56 square inches.

Answer:

y = 2

Step-by-step explanation:

(1) x  + 2y = 9

(2) x  -   y = 3

Subtract (2) from (1)

3y = 6

 y = 2

The y-coordinate is y = 2.

The graphs of the two equations intersect at (5, 2).

Answer:

6

Step-by-step explanation:

Minus both from each other;

x=2y=9

x-y=3

x cancels, 2y-y= y; 9-3=6

Therefore; y=6

Answer:

Step-by-step explanation:

Mean: 8 + 7 + 8.5 + 6.5 + 5 + 11 + 15 + 8 + 8 + 7 + 7.5 + 6.5 + 8 + 14 + 12 = 132 / 15 = 8.8

Median: You have to arrange the numbers first in ascending order.

5, 6.5, 6.5, 7, 7, 7.5, 8, 8, 8, 8, 8.5, 11, 12, 14, 15

The median is 8 because that is the middle value/number.

Mean Absolute Deviation:

Get the average/mean (1), find the deviation (2) to get MAD (3).

Step #1 Mean = 8.8

Step #2 To get the deviation, you subtract the mean from the values given.

8 - 8.8 = -0.8

7 - 8.8 = -1.8

8.5 - 8.8 = -0.3

6.5 - 8.8 = -2.3

5 - 8.8 = -3.8

11 - 8.8 = 2.2

15 - 8.8 = 6.2

8 - 8.8 = -0.8

8 - 8.8 = -0.8

7 - 8.8 = -1.8

7.5 - 8.8 = -1.3

6.5 - 8.8 = -2.3

8 - 8.8 = -0.8

14 - 8.8 = 5.2

12 - 8.8 = 3.2

Step #3 Get the summation from step #2, and get its average. Disregard the negative signs.

0.8 + 1.8 + 0.3 + 2.3 + 3.8 + 2.2 + 6.2 + 0.8 + 0.8 + 1.8 + 1.3 + 2.3 + 0.8 + 5.2 + 3.2 = 33.6 / 15 = 2.24 is the Mean Asolute Deviation

Median Absolute Deviation:

Get the median (1) and subtract it from the values (2). Get the median of the new values (3)

Step #1 Median = 8

Step #2

8 - 8 = 0

7 - 8 = -1

8.5 - 8 = 0.5

6.5 - 8 = -1.5

5 - 8 = -3

11 - 8 = 3

15 - 8 = 7

8 - 8 = 0

8 - 8 = 0

7 - 8 = -1

7.5 - 8 = -0.5

6.5 - 8 = -1.5

8 - 8 = 0

14 - 8 = 6

12 - 8 = 4

Step #3 Arrange the numbers in ascending order.

-3, -1.5, -1.5, -1, -1, -0.5, 0, 0, 0, 0, 0.5, 3, 4, 6, 7

The Median Absolute Deviation is 0 since it is the middle value/number.

It is important that you calculate this by yourself in case I did some careless mistakes.

Answer:

Step-by-step explanation:

12,347/10

=1,234.7

So 1/10th of the income would be

$1,234.7

One tenth of an income of $12,347, calculated by dividing by 10, gives the result $1,234.7. Dividing by 10 is a common mathematical method for finding a tenth of a value.

To calculate one tenth of an income of 12,347 you need to divide 12,347 by 10. This will give you the value of 1,234.7. This method is often used in mathematics to calculate percentages, fractions, or a portion of a given value.

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(0,4) because its the coordinates where the lines intersect

Answer:

C) (-3,3)

Step-by-step explanation:

The solution set is the region of intersection of the blue shaded region and the red shaded region.

We plot the given points, and the only one that falls within the solution set is  (-3,3).

Answer: C. (3,-2) (-6,-9) (-6,9) (-9,6) (9,6)

The coordinates of B with the information missing about the different transformations of ABC will be (3,-2) (-6,-9) (-6,9) (-9,6) (9,6).

It should be noted that coordinates simply mean a set of values that simply show an exact position.

In this case, the coordinates of B with the information missing about the different transformations of ABC will be (3,-2) (-6,-9) (-6,9) (-9,6) (9,6). This is important to determine the position of the points.

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Answer:

the answer is 90 degrees

Step-by-step explanation:

angle PT=18

180-39-23-28=90

Answer:

Step-by-step explanation:

90

Answer:

c) 6(5m2+2m+3)

Step-by-step explanation:

Given expression = 30m2 + 12m + 18

The simplified form can be calculated by taking GCF

The GCF of 30m2, 12m and 18 is = 6

Therefore, the expression becomes

(6*5m2 + 6*2m + 6*3)

=> 6(5m2+2m+3) so option c is correct

x+14=23/-14

x=9

9+14=23

9 because 14+9 equals 23

Number of calories in 8 ounces of orange juice = 100

Number of calories in 1 ounce of juice = [tex]\frac{100}{8}[/tex]

Number of calories in 4 ounces of juice = [tex]\frac{100}{8}*4=50[/tex] calories

Number of calories in 8 ounces of pineapple juice = 140

Number of calories in 1 ounce of juice = [tex]\frac{140}{8}[/tex]

Number of calories in 4 ounces of pineapple juice =

[tex]\frac{140}{8}*4=70[/tex] calories

Now the mixture has 50+70 = 120 calories in 8 ounce.

So, 1 ounce of mixture has = [tex]\frac{120}{8}= 15[/tex] calories.

To find the number of calories in Tia's juice mixture, we set up an equation based on the given information. Solving the equation, we find that there are 4 calories in each fluid ounce of Tia's juice mixture.

To find the number of calories in Tia's juice mixture, we can set up an equation based on the information provided. Let's say x represents the number of calories in each fluid ounce of orange juice, and y represents the number of calories in each fluid ounce of pineapple juice. Since Tia mixed 4 fluid ounces of each juice, the total number of calories in the mixture would be 4x + 4y. We know that there are 100 calories in 8 fluid ounces of orange juice and 140 calories in 8 fluid ounces of pineapple juice. We can set up the equation:

100 calories = (8/4)x

140 calories = (8/4)y

Simplifying the equations, we have:

25x = 100

35y = 140

Solving for x and y, we find:

x = 4

y = 4

Therefore, there are 4 calories in each fluid ounce of Tia's juice mixture.

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Keira spends approximately $119.12 on food.

To find the fraction of Keira's total spending on petrol, we need to determine the total amount she spent on all items and then calculate the fraction spent on petrol.

Total amount spent on all items (T): We'll use algebra to find the total amount Keira spent.

Fraction spent on other items and clothes: Given Keira spends 1/9 of the money on other items and 1/5 of the money on clothes, we'll find the combined fraction spent on other items and clothes.

Fraction spent on petrol: Subtract the fraction spent on other items and clothes from 1 to find the fraction spent on petrol.

Amount spent on food: Subtract the amounts spent on petrol, other items, and clothes from the total amount to find the amount spent on food.

Total amount spent on all items (T): Let T represent the total amount spent.

Fraction spent on other items and clothes:

[tex]\[ \frac{1}{9} + \frac{1}{5} = \frac{5}{45} + \frac{9}{45} = \frac{14}{45} \][/tex]

Fraction spent on petrol:

[tex]\[ 1 - \frac{14}{45} = \frac{31}{45} \][/tex]

Amount spent on food:

  [tex]\[ \text{Amount spent on food} = T - (45 + \frac{1}{9} \times T + \frac{1}{5} \times T) \] \[ \text{Amount spent on food} = T - (45 + \frac{14}{45} \times T) \] \[ \text{Amount spent on food} = \frac{31}{45} \times T \][/tex]

Now, to find the value of T, we solve the equation:

[tex]\[ \frac{31}{45} \times T = 45 + \frac{14}{45} \times T \]\[ \frac{31}{45} \times T - \frac{14}{45} \times T = 45 \]\[ \frac{17}{45} \times T = 45 \]\[ T = \frac{45 \times 45}{17} \]\[ T \approx 119.12 \][/tex]

So, Keira spends approximately $119.12 on food.

The complete question is:

Keira goes shopping at a supermarket. the pie chart below shows information about the money she spends on petrol, clothes, food and other items. what fraction does she spend on petrol? if keira spends $45 on petrol, 1 9 of the money on other items and 1 5 of the money on clothes. how much money does she spend on food? $

1. Answer:  [tex]\bold{\dfrac{188}{3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{y_4-y_1}{x_4-x_1}=\dfrac{128-316}{4-1}=\large \boxed{-\dfrac{188}{3}}\\\\\\\text{The negative sign represents "decrease".}[/tex]

2. The parent graph is y = | x |

a)  Shifted down 3 units

b) vertex = (0, -3)

c) Equation: y = | x | - 3

3. The parent graph is y = x²

a) Shifted right 1 and down 1 unit

b) vertex = (1, -1)

c) Equation: y = (x - 1)² - 1

Her biweekly paycheck is 38358.26

As we know that there are 52.14 weeks in a year

So weekly paycheck will be 1000000 / 52.14 = 19179.13

Since she gets biweekly check so we multiply it with 2

19179.13 * 2 = 38358.26

Her biweekly paycheck is 38358.26

Step-by-step explanation:

This is a simple angle problem, and what we need to do is subtract 73-44. This is because if we subtract the angles we already have, we will get the angle that we are trying to solve. The answer would be 29.

Percentage increase is 30% increase.

The value of the percentage increase would be 30 percent.

Used the concept of the percentage that states,

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.

Given that,

The price of a toy usually costing £50 is increased to £65.

Hence, the increased price is,

£65 - £50 = £15

So, the percentage increase would be,

[tex]P = \dfrac{\£15}{\£50} \times 100\%[/tex]

[tex]P = \dfrac{1500}{50}\%[/tex]

[tex]P = 30\%[/tex]

Therefore, the percentage increase is 30%.

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Answer: 1 and 3/5

Step-by-step explanation: The common denominator is 10. So, in order for everything to have a denominator of 10, we need to multiply a few things.

4 x 2 = 8

5 x 2 = 10

1 x 5 = 5

2 x 5 = 10

With that out of the way, we can finally move on to figure out the answer.

8/10 + 3/10 + 5/10 = 16/10. The question asks to write as a mixed number, if necessary. And it is. So:

10 goes into 16 once, with 6 left over, so 1 and 6/10. the fraction can be reduced, so we do that. Because 2 goes into 6 (3 times), and 2 goes into 10 (5 times), that leaves us with a final answer of 1 and 3/5.

Final answer:

To add 4/5, 3/10, and 1/2, first find a common denominator, which is 10. Convert the fractions to 8/10, 3/10, and 5/10, add them to get 16/10, which simplifies to 1 6/10, and then further simplify to the mixed number 1 3/5.

Explanation:

To add the fractions 4/5, 3/10, and 1/2, we need a common denominator. The least common multiple of the denominators 5, 10, and 2 is 10. Thus, we convert each fraction to an equivalent fraction with a denominator of 10. The converted fractions are 8/10, 3/10, and 5/10.

Next, we add the numerators: 8 + 3 + 5 = 16. The sum of the fractions is 16/10, which simplifies to 1 6/10 by dividing 16 by 10. Finally, we can simplify the fraction 6/10 to 3/5 because both the numerator and the denominator can be divided by 2. Therefore, our final answer is 1 3/5.

Answer:

5) a) complementary

6) b) supplementary

7) c) vertical angles

Step-by-step explanation:

5)

The sum of the complementary angles = 90 degrees

According to the graph, both angles add up to 90 degrees

Answer: a) complementary

6)

Straight angle is equal 180 degrees

The sum of the supplementary angles = 180 degrees

Answer: b) supplementary

7)

Vertical Angles are the angles opposite each other when two lines cross. The vertical angles are congruent.

Answer: c) vertical angles

Answer:

5. a) complementary; 6. b) supplementary; 7. c) vertical angles

Step-by-step explanation:

Question 5

The sum of the two angles is 90°.

The angles are complementary.

Question 6

x° + 62° = 180°

The angles are supplementary angles.

Question 7

The angles are opposite each other where the two lines cross.

∴ They are vertical angles.

Note: "Vertical" in this context doesn't mean "up-and-down." It means the angles share the same vertex (corner point).