given f(x)= -3/4x-6 and its domain: (-8, 0, 4) what is the range of the function?

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

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:

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:

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

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:

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:

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:

[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:

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:

One pair of sunglasses is $70

Step-by-step explanation:

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:

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:

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

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:

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:

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:

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:

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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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:

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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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:

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:

$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:

[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 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:

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:

46% × 2.3 =

(46 ÷ 100) × 2.3 =

(46 × 2.3) ÷ 100 =

105.8 ÷ 100 =

1.058 ≈

1.06;

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:

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