The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of y when x = 5?
Enter your answer in the box.

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:

Part 1:

Jose's Banquet Hall: 50g+100

Palace of Aaron: 45g+200

Part 2:

20 guests

Step-by-step explanation:

Part 1:

$50 per guest plus $100 fee

50g+100

$45 per guest plus $200 fee

45+200

Part 2:

$50(20)+$100=$1100

$45(20)+$200=$1100

Answer:

II. [tex]\displaystyle 20\:wedding\:guests[/tex]

I. [tex]\displaystyle 100 + 50g = 200 + 45g[/tex]

Step-by-step explanation:

100 + 50g = 200 + 45g

- 200 - 50g - 200 - 50g

___________________

[tex]\displaystyle \frac{-100}{-5} = \frac{-5g}{-5} \\ \\ 20 = g[/tex]

So, at twenty wedding guests, the cost will balance for both venues.

I am joyous to assist you anytime.

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

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.

Keywords: Percentage, subtraction

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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:

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:

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: collision zone

Step-by-step explanation:As a result of this collision, the sedimentary rocks which were settled in the large-scale depression in the Earth's crust called Tethys were folded and formed the Himalayas.

C collision zone

The Himalayas are the world's highest mountains, straddling the Indian and Eurasian plates. The Himalayas were formed by a collision zone.

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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:

The equation of line whose x-intercept is 5 and whose y-intercept is 3

is given as    5 y + 3x = 15.

Step-by-step explanation:

Here, the given x - intercept  = 5.

⇒ The point on the given equation is (x,0)  = (5,0)

And, the y- intercept is given as 3

⇒ The point on the given equation  is (0,y)  = (0,3)

So, the two points given on the equation of line is A(5,0) and B(0,3)

Now, the slope of the line equation [tex]m = \frac{y_2 - y_2}{x_2-x_1}[/tex]

So, here the slope of line AB  is [tex]m = \frac{3- 0}{0-5}  = -\frac{3}{5}[/tex]

Now by POINT SLOPE FORMULA:

The equation of a line with point (x0,y0) and slope m is given as:

(y- y0) = m (x-x0)

⇒The equation of line AB is given as

[tex]( y - 0) =  -\frac{3}{5} (x -5)\\\implies 5 y = -3x + 15\\\implies 5 y + 3x = 15[/tex]

Hence, the equation of line AB is given as 5 y + 3x = 15.

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)

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:

D) 2

Step-by-step explanation:

5x + 7 [tex]\leq[/tex] 8x -3 +2x

5x + 7 [tex]\leq[/tex] 10x - 3

7 + 3 [tex]\leq[/tex] 10x - 5x

10 [tex]\leq[/tex] 5x

2[tex]\leq[/tex] x

x[tex]\geq[/tex]2

Answer:

hnjmmm

Step-by-step explanation:

m,,\

l;'

Answer:

x = 2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given that y varies inversely as the square of x then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = yx² = 2 × 4² = 2 × 16 = 32

y = [tex]\frac{32}{x^2}[/tex] ← equation of variation

When y = [tex]\frac{4}{5}[/tex], then

[tex]\frac{4}{5}[/tex] = [tex]\frac{32}{x^2}[/tex] ( cross- multiply )

4x² = 160 ( divide both sides by 4 )

x² = 40 ( take the square root of both sides )

x = [tex]\sqrt{40}[/tex] = [tex]\sqrt{4(10)}[/tex] = 2[tex]\sqrt{10}[/tex]

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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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

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:

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

First find x and y.

Solve system of equations by elimination.

  3x-y=3

+(-x+y=3)

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

2x=6

x=3

Now plug in x into one of the equations to find y.

-3+y=3

y=6

xy=3x6=18

Final answer:

The product of xy, given the system of equations 3x - y = 3 and -x + y = 3, is 18. This is found by first solving for x and y using the elimination method and then multiplying the obtained values.

Explanation:

To find the product of xy, we need to solve the system of equations given by 3x - y = 3 and -x + y = 3. Here we'll use the elimination method. Adding both equations together, we eliminate y:

3x - y + (-x + y) = 3 + 3

Which simplifies to:

2x = 6

Dividing both sides by 2, we get:

x = 3

To find y, we substitute x back into one of the original equations, for example, the second equation -x + y = 3:

-(3) + y = 3

-3 + y = 3

Adding 3 to both sides gives us:

y = 6

Now we can find the product of xy:

xy = 3 * 6

xy = 18

Therefore, the product of xy is 18.

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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Answer:

46% × 2.3 =

(46 ÷ 100) × 2.3 =

(46 × 2.3) ÷ 100 =

105.8 ÷ 100 =

1.058 ≈

1.06;

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]

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:

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:

first proof should be cpctc, second proof is the triangle sum theorem

Answer:

One pair of sunglasses is $70

Step-by-step explanation:

Answer:

A) The second day

B) 9/16 inches

Step-by-step explanation:

A) Elsa reached farther on the second day because -1/16 > -5/8

B) To calculate this we must first put both fractions above the same denominator. We can then subtract the smaller one from the bigger one:

-1/16 - (-10/16) = 9/16

Elsa reached 9/16 inches farther on the second day then she did on the first.

Final answer:

Elsa reached farther on the second day than the third day during her flexibility tests. She reached 9/16 inches farther on the second day compared to the third day.

Explanation:

Elsa is taking physical fitness tests in her strength training class where she tracks her progress by comparing her flexibility results to the baseline (first day). A negative value indicates she did not reach as far as the baseline.

A. On the second day, Elsa's flexibility test result was recorded as - 1/16 inches, and on the third day, it was -5/8 inches. Since -1/16 is greater than -5/8 (closer to zero), it means Elsa reached farther on the second day than the third day.

B. To find out by how much Elsa reached farther on the second day compared to the third day, we calculate the difference between the two measurements: (-1/16) - (-5/8) = 5/8 - 1/16. We must find a common denominator to subtract these fractions, which is 16. So we have (10/16) - (1/16) = 9/16 inches. Therefore, Elsa reached 9/16 inches farther on the second day compared to the third day.

Answer:

165150 is the sum of the multiples of 3 between 100 and 1000.

Step-by-step explanation:

We need to find the sum of multiples of 3 between 100 and 1000.

First we will find the Total number of multiples of 3 between 100 and 1000.

Let a be the first multiple and l be the last multiple of 3

100 is not the multiple of 3.

101 is not the multiple of 3.

102 is the multiple of 3.

Hence first term a = 102

Similarly.

1000 is not a multiple of 3

999 is a multiple of 3

hence last term l = 999

Also d is the common difference.

hence d = 3.

Now by using Arithmetic progression formula we get;

[tex]T_n(l) =a+(n-1)d\\ 999=102+(n-1)3\\999-102=(n-1)3\\897=(n-1)3\\\frac{897}{3}=n-1\\\\n-1=299\\n=299+1\\n=300[/tex]

Hence there are 300 multiples of 3 between 100 and 1000

Now n=300, a=102, l = 999

Hence to find the sum of all the multiples we use the Sum of n terms in AP  formula;

Sum of n term [tex]S_n= \frac{n}{2}(a+l)[/tex]

[tex]S_{300}= \frac{300}{2}(102+999)\\\\S_{300}= 150(102+999)\\S_{300}= 150\times 1101\\S_{300}= 165150[/tex]

Hence,165150 is the sum of the multiples of 3 between 100 and 1000.