Drag the correct number of pieces to show how to find the area of the shaded figure in
two different ways. Pieces can be rotated to fit.

The product of the two binomials is (y + 1)(y - 5)

Step-by-step explanation:

To write a polynomial as a product of two binomials

∵ The polynomial is (y - 5) - y(5 - y)

- Multiply y by the bracket (5 - y)

∵ y(5 - y) = y(5) - y(y)

∴ y(5 - y) = 5y - y²

- Substitute 5(5 - y) by (5y - y²)

∴ (y - 5) - y(5 - y) = (y - 5) - (5y - y²)

- Multiply (-) by the bracket (5y - y²)

∵ (-)(5y) = -5y

∵ (-)(-y²) = y²

∴ (y - 5) - y(5 - y) = y - 5 - 5y + y²

- Add the like terms

∴ (y - 5) - y(5 - y) = -4y - 5 + y²

- Arrange the terms from greatest power of y

∴ (y - 5) - y(5 - y) = y² - 4y - 5

Now let us factorize y² - 4y - 5 into two factors

∵ y² = y × y

∵ -5 = -5 × 1

- Multiply y by 1 and y by -5, then add the product the sum

   must be equal the middle term of the polynomial above

∵ y(1) + y(-5) = y - 5y = -4y ⇒ as the middle term

- Now write the two bracts

∴ y² - 4y - 5 = (y + 1)(y - 5)

The product of the two binomials is (y + 1)(y - 5)

Learn more:

You can learn more about the polynomials in brainly.com/question/12700460

#LearnwithBrainly

Answer:

it's dilation by 2 because the purple one is 2x bigger

Answer:

The value of 'x' is 7 that will make make L║M.

Step-by-step explanation:

Given,

Line segment L and line segment M are cut by a transversal line.

We can name it as 't' transversal line and also the given angle measures as ∠1 and ∠2.

So, ∠1 = [tex]7x+9[/tex]

∠2 = [tex]8x+2[/tex]

We have to find the value of 'x'.

Solution,

Since L and M are two line segment which is cut by another line segment 't'.

For L║M, the measure of ∠1 and ∠2 must be equal according to corresponding angle property.

"When the measure of a pair of same side corresponding angle is equal, then the line segments are parallel".

[tex]\therefore \angle1=\angle2[/tex]

On substituting the values, we get;

[tex]7x+9=8x+2[/tex]

Combining the like terms, we get;

[tex]8x-7x=9-2\\\\x=7[/tex]

Now we will find out the measure of  ∠1 and ∠2.

[tex]\angle1=7x+9=7\times7+9=49+9 =58[/tex]

[tex]\angle2=8x+2=8\times7+2=56+2=58[/tex]

Hence The value of 'x' is 7 that will make make L║M.

Answer:

Step-by-step explanation:

Let, the three islands A, B and C has a, b and c houses respectively.

According to the question, a + b = 15; a + c = 17; b + c = 12; a + b + c = 22.

Adding [ a + b = 15; a + c = 17]-these two, we get, [tex]a + (a + b + c) = 15 + 17 = 32\\a + 22 = 32\\a = 10[/tex].

Now, [tex]a + b = 15\\10 + b = 15\\b = 5[/tex].

[tex]a + c = 17\\10 + c = 17\\c = 7[/tex].

[tex]\frac{1}{6}[/tex] or 0.167 pounds more butter was used than sugar

Solution:

Given that, Desmond's Desserts made a batch of fresh scones with 2/3 of a pound of butter and 1/2 of a  pound of sugar

To find: Amount of butter used than sugar

From given information,

[tex]\text{Butter used} = \frac{2}{3} \text{ pound }[/tex]

[tex]\text{Sugar used } = \frac{1}{2} \text{ pound }[/tex]

To find how much butter is used than sugar, find the difference between them

[tex]Difference = Butter\ used - Sugar\ used[/tex]

[tex]Difference = \frac{2}{3} - \frac{1}{2}\\\\Difference = \frac{2 \times 2-1 \times 3}{3 \times 2}\\\\Difference =\frac{4-3}{6}\\\\Difference =\frac{1}{6} = 0.167\\\\[/tex]

Thus [tex]\frac{1}{6}[/tex] or 0.167 pounds more butter was used than sugar

Answer: She isn't correct.

Step-by-step explanation: The BODMAS rule must be strictly followed and as such gives different answers to the two expressions.

(12-3)*2 basically gives:

9*2 (Dealing with the bracket first)

18.

While 12-(3*2) while dealing with the bracket first will give:

12-6; which would eventually give

6.

(1)  [tex]1\frac{7}{8}[/tex] pounds of soil   (2) [tex]\frac{35}{2}[/tex]   (3)  33

Solution:

(1) Number of pots = 5

Quantity of soil each pot can hold = [tex]\frac{3}{8}[/tex] pounds

Quantity of soil need to fill all the pots = [tex]5\times \frac{3}{8}[/tex]

                                                               = [tex]\frac{15}{8}[/tex] pounds

                                                               = [tex]1\frac{7}{8}[/tex] pounds

Therefore, [tex]1\frac{7}{8}[/tex] pounds of soil need to fill all of the pots.

(2) To find the product of [tex]4\frac{2}{3}[/tex] and [tex]3\frac{3}{4}[/tex].

Let us first convert the mixed fraction into improper fraction.

[tex]4\frac{2}{3}\times3\frac{3}{4}=\frac{(4\times3)+2}{3}\times\frac{(3\times4)+3}{4}[/tex]

             [tex]=\frac{14}{3}\times\frac{15}{4}[/tex]

             [tex]=\frac{210}{12}[/tex]

This can be simplified. Divide both numerator and denominator by 6.

             [tex]=\frac{35}{2}[/tex]

[tex]4\frac{2}{3}\times3\frac{3}{4}=\frac{35}{2}[/tex]

(3) To evaluate the expression 12x + 6 for [tex]x=2\frac{1}{4}[/tex].

Let us first convert the mixed fraction into improper fraction.

[tex]x=\frac{(2\times4)+1}{4}=\frac{9}{4}[/tex]

[tex]12x+6=12(\frac{9}{4})+6[/tex]

            [tex]=(\frac{108}{4})+6[/tex]

            [tex]=27+6[/tex]

12x + 6 = 33

Answer:14

Step-by-step explanation:

figure out 5x20,, which gives you 100 points

use trial and error is my method :)

if he answered 10 correct, he would get 50 points and lose 10. this gives 40 points. its an error

we now know its between 11 right and 19 right

we continue to do this till we get it right

14 x 5 = 68. - 4 makes 64.

Sammy answered 14 questions correctly on his test, as determined by setting up and solving the equation 5x - (20 - x) = 64, where x represents the number of correct answers.

Sammy is taking a test where each correct question awards him 5 points and each incorrect one deducts a point. With 20 questions in total and a score of 64, we can set up an equation to find out how many questions he answered correctly. Let x represent the number of correct answers. Then, the number of incorrect answers would be 20-x. The scoring system gives us the following equation:

5x - (20 - x) = 64

By solving this equation, we can find out how many questions Sammy answered correctly:

Combine like terms: 5x - 20 + x = 64

Simplify: 6x - 20 = 64

Add 20 to both sides: 6x = 84

Divide both sides by 6: x = 14

Thus, Sammy answered 14 questions correctly on his test.

Answer:653.8

Step-by-step explanation:

467 /5=93.4 miles in five hours.   93.4 *7 =653.8

Answer:

yes

Step-by-step explanation:

Answer:

$320

Step-by-step explanation:

To find the answer to this you would need to multiply the price by 2 so that you may find out what double the half of price would be, so in theory you and doing the reciprocal.

5/20=x/36

1/4=x/36

x=9

9 minutes.

Final answer:

To determine the time Bob spends running, a proportion is set up based on the original 5:20 running to dribbling ratio. Solving this proportion shows that Bob runs for 9 minutes when he spends 36 minutes dribbling.

Explanation:

Bob's practice ratio for running and dribbling is 5 minutes running to 20 minutes dribbling. To find how many minutes Bob spends running when he practices dribbling for 36 minutes, we set up a proportion using the original ratio. The proportion is:

5 minutes running / 20 minutes dribbling = x minutes running / 36 minutes dribbling

To solve for x, we cross-multiply:

(5 minutes running) × (36 minutes dribbling) = (x minutes running) × (20 minutes dribbling)

This gives us:

180 = 20x

Now divide both sides by 20 to solve for x:

x = 180 / 20

x = 9 minutes

Thus, Bob spends 9 minutes running when he practices dribbling for 36 minutes.

Answer:

c&d

Step-by-step explanation:

because they are connected

Answer:

2y-4x

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

y=2x-5

Putting the value of y in 2y-4x

2(2x-5)-4x

4x-10-4x

0-10

-10

Answer:

(1, - 2 )

Step-by-step explanation:

Given the 2 equations

10x + 6y = - 2 → (1)

2x + 6y = - 10 → (2)

Multiplying (2) by - 1 and adding to (1) will eliminate the y- term

- 2x - 6y = 10 → (3)

Add (1) and (3) term by term

(10x - 2x) + (6y - 6y) = (- 2 + 10), that is

8x = 8 ( divide both sides by 8 )

x = 1

Substitute x = 1 into either of the 2 equations.

Substituting x = 1 into (1)

10(1) + 6y = - 2

10 + 6y = - 2 ( subtract 10 from both sides )

6y = - 12 ( divide both sides by 6 )

y = - 2

Solution is (1, - 2 )

Answer:

7^2*5^2

Step-by-step explanation:

The equation contains two 7's and two 5's. 7 squared and 5 squared can be written like this, so the answer is 7^2*5^2

Answer:

Can of Coke

Step-by-step explanation:

Calculate how much money each ounce of drink costs, or the money per ounce ($/oz).

Coke:

$/oz = $1 ÷ 12oz = $0.083333/oz

Pepsi:

$/oz = $1.35 ÷ 16oz = $0.084375/oz

Coke < Pepsi

0.083333 < 0.084375

The calculations show that you would pay more money for one ounce of Pepsi than for one ounce of Coke. Coke costs less than Pepsi.

Therefore the can of Coke is the best buy.

Final answer:

After calculating the cost per ounce for both the Coke and Pepsi, the 12 ounce can of Coke at $1.00 is the better buy as it costs approximately $0.0833 per ounce compared to the 16 ounce bottle of Pepsi at $1.35, which costs approximately $0.0844 per ounce.

Explanation:

To determine whether the can of Coke or the bottle of Pepsi is the better buy, we will calculate the cost per ounce for each.

For the 12 ounce can of Coke priced at $1.00, the cost per ounce is calculated as follows:

Divide the total cost by the number of ounces: $1.00 \/ 12 ounces.

This results in approximately $0.0833 per ounce for the Coke.

For the 16 ounce bottle of Pepsi priced at $1.35, the cost per ounce is calculated in a similar manner:

Divide the total cost by the number of ounces: $1.35 \/ 16 ounces.

You get approximately $0.0844 per ounce for the Pepsi.

Comparing the two, the cost per ounce of Coke is cheaper than the cost per ounce of Pepsi. Thus, the can of Coke is the best buy.

The expression that represents the points of Smith Elementary School scored is x - 30

Step-by-step explanation:

Let us revise some words that means operations in mathematics

∵ Smith Elementary School scored 30 less points in their

   track meet than Jones Elementary School

- That means the score of Smith Elementary School is less than

   the score of Jones Elementary School by 30

∵ Jones Elementary School scored x points

- Subtract 30 from x to find the score of Smith Elementary School

∴ Smith Elementary School scored = x - 30

The expression that represents the points of Smith Elementary School scored is x - 30

Learn more:

You can learn more about the expressions in brainly.com/question/13087541

#LearnwithBrainly

Answer:

x-30

Step-by-step explanation:

We know that Jones Elementary has x points. If Smith Elementary has 30 less points then we should subtract 30 from x to get x-30.

Answer:

x = -6

=b=6=

Step-by-step explanation:

Answer:

Step-by-step explanation:

Incomplete question!

Answer:

a) [tex]\log 52[/tex]

b) [tex]\log_57[/tex]

Step-by-step explanation:

Use logarithm properties:

[tex]\log_ab+\log_ac=\log_a(b\cdot c)\\ \\\log_ab-\log_ac=\log_a\dfrac{b}{c}[/tex]

Then

a) [tex]\log 13+\log 4=\log 13\cdot 4=\log 52[/tex]

b) [tex]\log_514-\log _52=\log _5\dfrac{14}{2}=\log _57[/tex]

Answer:

6/7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(7-1)/(5-(-2))

m=6/(5+2)

m=6/7

Answer:

The slope is [tex]m=\frac{6}{7}[/tex]

Step-by-step explanation:

Step-by-step explanation:

[tex](x,\ y)\\\\x\in\text{Domain}\\\\y\in\text{Range}\\\\(6,\ 1),\ (-1,\ -8),\ (3,\ 5),\ (9,\ 1)\\\\\text{Domain}=\{-1,\ 3,\ 6,\ 9\}\\\text{Range}=\{-8,\ 1,\ 5\}\\\\\text{This relation is a function because each x is assigned one value of y.}[/tex]

Answer:

Yes, this relation is a function.

Step-by-step explanation:

Take the first element from each ordered pair to obtain the domain:

(6, -1, 3, 9).  Since the inputs are all unique (no duplication), the relation is a function.

Answer:the mean score would decrease more than the median score

Step-by-step explanation:

i did the quiz

Adding a score of 0 would decrease the mean more than the median, with the new mean being 100 and the new median 120.

Adding a score of 0 to the data set of game scores will impact both the mean and the median of the distribution. However, the way each measure of central tendency is affected will be different.

For the mean, which is the arithmetic average, adding a score of 0 will bring the average down. To find the new mean, you would add 0 to the sum of the existing scores and divide by the new total number of scores. Since 0 is lower than any of the existing scores (100, 120, 130, and 150), the mean will decrease.

The initial mean is 125, which is the sum of all the scores (500) divided by the number of scores (4).

Calculating the new mean after including the score of 0, we get (500 + 0) / (4 + 1) = 500 / 5 = 100. This shows the mean would decrease as a result of the 0 score.

As for the median, if we incorporate the score of 0 into the data set, it will become the new lowest score. With an odd number of scores (5), the median will be the middle value.

The scores in order would be 0, 100, 120, 130, and 150. So the new median would be 120. The median is less influenced by extreme values, especially when they are an outlier like the 0 in this case.

Therefore, the correct answer is that the mean score would decrease more than the median score when adding a 0 to the data set.

Answer:

Part 1) x=5

Part 2) x=2

Step-by-step explanation:

The question is solve for x

Part 1) we have

[tex]x+3x=x+x+10[/tex]

Combine like terms both sides

[tex]4x=2x+10[/tex]

subtract 2x both sides

[tex]4x-2x=10\\2x=10[/tex]

divide by 2 both sides

[tex]x=5[/tex]

Part 2) we have

[tex]2x+3+3x=x+11[/tex]

Combine like terms left side

[tex]5x+3=x+11[/tex]

subtract x both sides

[tex]5x+3-x=11\\4x+3=11[/tex]

subtract 3 both sides

[tex]4x=11-3\\4x=8[/tex]

divide by 4 both sides

[tex]x=2[/tex]

The tenth value is 15

Solution:

Given that, data set has 9 values

The mean of the set is 5

Number of values = 9 and mean = 5

The mean is given by formula:

[tex]mean = \frac{\text{Sum of terms}}{\text{Number of terms}}[/tex]

[tex]5 = \frac{\text{Sum of 9 terms}}{9}\\\\sum\ of\ 9\ terms = 5 \times 9 = 45[/tex]

When a tenth value is added, the mean becomes 6

Let the tenth value be "x"

New mean is given as:

[tex]6 = \frac{\text{sum of 9 terms} + x}{10}\\\\sum\ of\ 9\ terms + x = 60[/tex]

The tenth value is given as:

sum of 9 terms + x = 60

45 + x = 60

x = 60 - 45

x = 15

Thus the tenth value is 15

Answer:

  [tex]y^4\sqrt{39y}[/tex]

Step-by-step explanation:

[tex]\displaystyle\sqrt{39y^9}=\sqrt{39y(y^4)^2}=y^4\sqrt{39y}[/tex]

To simplify √(39y¹¹), rewrite y¹¹ as (y²)·(y²)·(y²) and take out the perfect square. The simplified expression is 3y√(39y).

To simplify the expression √(39y¹¹), we need to remove the perfect square from inside the square root. Since y is raised to the power of 9 and is positive, it is a perfect square. We can rewrite y¹¹ as (y²)·(y²)·(y²).

Therefore, √(39y¹¹) = √(39(y²)·(y²)·(y²)) = √(39)·(y²)√(y²)√(y²) = √(39)·y²·y²·y² = √(39)·y¹ = 3y√(39y).

https://brainly.com/question/35515383

#SPJ2

Answer:

Interest rate tend to be lower in weak economy than in strong economy to encourage people to borrow money to invest in businesses, the lower the interest rate, the more willing people are to borrow money to make big purchases and this will make economic growth tend to be faster.

Moreso a weak economy tends to have low inflation, so interest rates drop to match.

Answer:

y=3/2x + 1

•••••••••••••