Given: x + y = 15.



Which of the following are ordered pairs of this equation?
{(-3, 14),(0, 15),(3, 16)}
{(16, -3),(15, 0),(14, 3)}
{(-3, 16),(0, 15),(3, 14)}

The right answer is Option B.

Step-by-step explanation:

No. of baseball cards = 35

Increase = 20%

Number of increased cards = 20% of 35

[tex]Increased\ cards = \frac{20}{100}*35\\Increased\ cards=\frac{700}{100}\\Increased\ cards=7[/tex]

Total cards = 35+7 = 42

No. of cards sold = 8

Cards left = Total cards - No. of cards sold

[tex]Cards\ left=42-8\\Cards\ left=34[/tex]

The right answer is Option B.

Keywords: Addition, subtraction

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Answer:

x=-5, y=-5. (-5, -5).

Step-by-step explanation:

-x-5y=30

10x+5y=-75

-----------------

9x=-45

x=-45/9

x=-5

-(-5)-5y=30

5-5y=30

5y=5-30

5y=-25

y=-25/5

y=-5

The solution is x = 6

Step-by-step explanation:

Let us revise some rules of the exponents

∵ [tex]9^{(x+15)}=3^{7x}[/tex]

∵ 9 = 3 × 3

∴ 9 = 3²

- Substitute 9 by 3² in the equation above

∴ [tex](3^{2})^{(x+15)}=3^{7x}[/tex]

- Use the second rule above for the left hand side

∵ [tex](3^{2})^{(x+15)}=3^{2(x+15)}[/tex]

∴ [tex](3^{2})^{(x+15)}=3^{2x+30}[/tex]

∴ [tex]3^{2x+30}=3^{7x}[/tex]

- By using the first rule above

∴ 2x + 30 = 7x

- Subtract 2x from both sides

∴ 30 = 5x

- Divide both sides by 5

∴ 6 = x

The solution is x = 6

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Answer:

(x − 6i) (x + 6i)

Step-by-step explanation:

Using real numbers, x² + 36 is already simplified.

Using imaginary numbers:

x² + 36

x² − 36i²

(x − 6i) (x + 6i)

The right answer is Option D.

Step-by-step explanation:

Given,

Food and Drinks = $200

Game tokens = $100

Other = $60

Total amount = 200+100+60 = 360

Deposit = 10%

Deposit amount = 10% of total amount

[tex]Deposit\ amount=\frac{10}{100}*360\\Deposit\ amount=\frac{3600}{100}\\Deposit\ amount= \$36[/tex]

Amount left to be paid = Total amount - deposit amount

Amount left to be paid = [tex]360-36=\$324[/tex]

$324 is still owed for Molly's party.

The right answer is Option D.

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The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]

Step-by-step explanation:

Given

Length of box = l = ab

Width of box = w = a+5b

Height of box = h = 2b^2

The volume of a box is given by:

[tex]V = Length*Width*Height\\V = l*w*h[/tex]

Putting the values

[tex]V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4[/tex]

Hence,

The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]

Keywords: Volume, Polynomials

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Answer:

k=5

Step-by-step explanation:

7

k

−

12

=

13

+

2

k

Move all terms containing

k

to the left side of the equation.

Answer:

The sum of the age of pupils is 81

Step-by-step explanation:

Let sum of age of 18pupils = x

Average ages = 4.5

Average = total/no. of pupil

4.5 = x/18

x = 81

Answer:

The sum of the age of pupils is 81

Answer:

y-4=4(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

m=4

y-4=4(x-(-1))

y-4=4(x+1)

Answer: equation = y=4x+8

Step-by-step explanation:

y=mx+b

4=4(-1)+b

b=8

equation = y=4x+8

Answer:

[tex]f(x) = -2x^2 + 7x + 9[/tex]

Step-by-step explanation:

[tex]f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 <=> 2a + b  = 3\\f(3) = 9a + 3b + 9 = 12 <=> 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9[/tex]

To find a quadratic function, substitute each given coordinate into the equation and solve the resulting system of equations.

To find a quadratic function, we need to use the form y = ax^2 + bx + c. From the given set of values, we can substitute each coordinate (x, y) into the equation to get three different equations. So:

Now we have a system of equations that we can solve simultaneously. Solving the second and third equations using any appropriate method, we find that a = -1 and b = 5.

Therefore, the quadratic function that includes the given set of values is y = -x^2 + 5x + 9.

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Answer:

B.9

Step-by-step explanation:

9*1=9

Answer:

[tex]a_{n}[/tex] = 2n - 3

Step-by-step explanation:

Note the difference in consecutive terms is constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2

This indicates that the terms are an arithmetic sequence with

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 2, thus

[tex]a_{n}[/tex] = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

Answer:

The average rate of change = -10

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Step-by-step explanation:

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function [tex]f(x) =-x^2 + 20x + 100[/tex] models the crops in pounds per acre over x years.

The average rate of change can be calculated using formula

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

In your case,

[tex]a=10\\ \\b=20,[/tex]

then

[tex]f(a)=-10^2+20\cdot 10+100=-100+200+100=200\\ \\f(b)=-20^2+20\cdot 20+100=-400+400+100=100[/tex]

and the average rate of change is

[tex]\dfrac{100-200}{20-10}=\dfrac{-100}{10}=-10[/tex]

This means the crop yield decreased by 10 pounds per acre (negative rate of change) from year 10 to year 20.

Answer:

'The crop yield decreased by 10 pounds per acre from year 10 to year 20.'

Step-by-step explanation:

i got it right on the test =)

Answer:

[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 6 and r = 30 ÷ 6 = 5, thus

[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]

Answer:

6-pack for 3.12

Step-by-step explanation:

Find unit price

2.24/4=0.56

3.00/3=1

4.24/8=0.53

3.12/6=0.52

Answer:

101/3 or 33 2/3

Step-by-step explanation:

7 2/15=107/15

9 13/15=138/15

107/15+52/3+138/15

107/15+138/15+52/3

245/15+52/3

245/15+260/15

505/15

simplify,

101/3

Answer:

One pair of sunglasses is $70

Step-by-step explanation:

The equation of the line in standard form is 3x - 5y = 26

Step-by-step explanation:

Let us revise the forms of the linear equation

∵ The line passes through point (2 , -4)

∵ The slope of the line is [tex]\frac{3}{5}[/tex]

- Let us using the point-slope form and then change it to the

  standard form

∵ [tex]x_{1}[/tex] = 2 and [tex]y_{1}[/tex] = -4

∵ m = [tex]\frac{3}{5}[/tex]

- Substitute these values in the form of the equation below

∵ [tex]y-y_{1}=m(x-x_{1})[/tex]

∴ [tex]y-(-4)=\frac{3}{5}(x - 2)[/tex]

∴ [tex]y+4=\frac{3}{5}(x - 2)[/tex]

Let us change it to standard form

- Multiply each side my 5 to cancel the denominator in the

   right hand side

∴ 5(y) + 5(4) = 3(x - 2)

- Simplify the two sides

∴ 5y + 20 = 3x - 6

- Add 6 to both sides

∴ 5y + 26 = 3x

- Subtract 5y from both sides

∴ 26 = 3x - 5y

- Switch the two sides

∴ 3x - 5y = 26

The equation of the line in standard form is 3x - 5y = 26

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Answer:

46% × 2.3 =

(46 ÷ 100) × 2.3 =

(46 × 2.3) ÷ 100 =

105.8 ÷ 100 =

1.058 ≈

1.06;

Answer:

5

Step-by-step explanation:

take 0.5 divided by 5 and it gives you your next number on the chart:)

Answer:  5

Step-by-step explanation:

The growth factor of the exponential function is the ratio of the two consecutive terms (y-values).

i.e. Growth factor = [tex]b=\dfrac{y(x_2)}{y(x_1)}[/tex]

As per given , we have table

x         y

-2     0.004

-1       0.02

0       0.1

1        0.5

Then, for [tex]x_1=-2[/tex] and [tex]x_2=-1[/tex] the growth factor of the exponential function represented by the table would be :

[tex]b=\dfrac{y(-1)}{y(-2)}=\dfrac{0.02}{0.004} =5[/tex]

Hence, the growth factor of the exponential function represented by the table is 5 .

Answer:

yes.

Step-by-step explanation:

because I did the work and 10 times 3 equals 30 and 4 plus 6 times 3 equals 30.

Answer:

Yes because L.H.S = R.H.S

Step-by-step explanation:

4 + 6 = 10

(4 + 6) X 3

=> 10 X 3

=> 30

Answer:

x=65/14

Step-by-step explanation:

(x-10)/(x-4)=50/-6

-50/6=-25/3

(x-10)/(x-4)=-25/3

x-10=-25/3(x-4)

x-10=-25/3x+100/3

x-(-25/3x)=100/3+10

x+25/3x=130/3

28/3x=130/3

x=(130/3)/(28/3)

x=(130/3)(3/28)

x=130/28

x=65/14

Answer:

7 and 8 would work

Step-by-step explanation:

just insert them as w and they have to be greater than 20. I hope this helps.

Answer:

7 and 8

Step-by-step explanation:

Solving the inequality

5w - 10 > 20 ( add 10 to both sides )

5w > 30 ( divide both sides by 5 )

w > 6

The only values from the solution set greater than 6 are

7 and 8

Answer:

Step-by-step explanation:

$3.55 ÷ 5 = .71 each peach

To find out how much Tomas paid for each fruit, we set up the equation m = $3.55 / 5, which when solved gives m = $0.71. This means that Tomas paid $0.71 for each peach.

To find out how much Tomas paid for each peach, you can set up an equation. Because Tomas buys 5 peaches for $3.55 in total, you can express this as a simple division. To solve the equation, divide $3.55 (total cost) by 5 (total number of peaches).

So, the equation would be m = $3.55 / 5.

Solving this equation gives: m = $0.71. Therefore, Tomas paid $0.71 for each peach.

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Answer:

1260 words

Step-by-step explanation:

if you divide 840 by 2.4 you would get 350 then multiply by 3.6

With the same rate the number of words typed in 3.6 hour is 1260.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a typewriter types 840 words in 2.4 hours.

Now, number of words typed in 1 hour is

840/2.4

= 350

Now, the number of words typed in 3.6 hour is

350×3.6

= 1260

Therefore, with the same rate the number of words typed in 3.6 hour is 1260.

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Answer:

The age of the pottery bowl to the nearest year is 15606 years.

Step-by-step explanation:

Let the initial amount of C-14 in the bowl i.e. [tex]N_{0} = 100[/tex] and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.

Therefore, from the given equation we can write  

[tex]21 = 100 e^{- 0.0001t}[/tex] {Since, k is give to be 0.0001}

⇒ [tex]0.21 = e^{- 0.0001t}[/tex]

Now, taking ln on both sides we get

ln 0.21 = - 0.0001t (ln e) {Since, [tex]\ln a^{b} = b \ln a[/tex]}

⇒ - 1.560647 = - 0.0001t  {We have ln e = 1}

⇒ t = 15606.47 years ≈ 15606 years  

Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)

Answer:

Step-by-step explanation:

Put the values of a = -46 and b = 34 to the expression a + b:

-46 + 34        use the commutative property a + b = b + a

= 34 + (-46) = 34 - 46 = -12

The question is asking to evaluate the expression a + b, with a being -46 and b being 34. Evaluating the expression, we substitute the given values in to get -12. Therefore, the correct answer is A: -12.

In algebra, when a question asks us to evaluate an expression, that simply means we need to substitute the given values into the equation and perform the operations to simplify it. In this problem, the expression is a + b, and the values given are a = -46 and b = 34.

To evaluate this, we substitute the given values in: (-46) + 34. When you add -46 and 34 together, you get a result of -12. Therefore, the correct answer is A: -12.

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Step-by-step explanation:

You have the equation of a line in the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

Convert the given equation to the slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept (0, b)

[tex]y+1=\dfrac{1}{3}(x-3)[/tex]         use the distributive property

[tex]y+1=\dfrac{1}{3}x-1[/tex]          subtract 1 from both sides

[tex]y=\dfrac{1}{3}x-2[/tex]

We only need two points to draw the line.

Choose two different x values. Put them in the line equation and calculate the y values:

for x = 0:

[tex]y=\dfrac{1}{3}(0)-2=0-2=-2\to(0,\ -2)[/tex]

for x = 3:

[tex]y=\dfrac{1}{3}(3)-2=1-2=-1\to(3,\ -1)[/tex]