Let f(x)=3x+5 and g(x) =x^2 find g(x)/f(x) and state its domain

Answer:

(1,7)

Step-by-step explanation:

You are given the system of two equations

[tex]\left\{\begin{array}{l}x-y=-6\\5x+3y=24\end{array}\right..[/tex]

Each equation represents straight line in the diagram. The point of intersection between these two lines represents the solution of the system of two equations. From the diagram  the best approximation of the solution of the system rounded to the nearest whole number is (1,7).

Or you can solve this system algebraically. Express x from the first equation

[tex]x=y-6[/tex]

and substitute it into the second equation:

[tex]5(y-6)+3y=24,\\ \\5y-30+3y=24,\\ \\8y=54,\\ \\y=\dfrac{54}{8}=\dfrac{27}{4}=6.75\approx 7.[/tex]

Then

[tex]x=6.75-6=0.75\approx 1.[/tex]

Answer:

a. 19 degrees

Step-by-step explanation:

The angles of a triangle add up to 180 degrees.

This triangle is a right triangle, so it has a 90 degree angle.

The three angles are 90, 71, and x

90+71+x = 180

Combine like terms.

161+x=180

Subtract 161 from each side

161-161 +x =180-161

x =19

Answer:

Hence final answer is [tex]-\frac{1}{216}[/tex].

Step-by-step explanation:

Expression is not typed in proper format but as per given instruction "evaluate the exponent", I think it is:

[tex]\left(-6\right)^{-3}[/tex]

So let's simplify that:

[tex]\left(-6\right)^{-3}[/tex]

Apply formula x^-m=1/x^m

[tex]=\frac{1}{\left(-6\right)^{+3}}[/tex]

[tex]=\frac{1}{\left(-6\right)^3}[/tex]

[tex]=\frac{1}{\left(-6\right)\left(-6\right)\left(-6\right)}[/tex]

[tex]=\frac{1}{-216}[/tex]

[tex]=-\frac{1}{216}[/tex]

Hence final answer is [tex]-\frac{1}{216}[/tex].

Answer: It becomes 120% of original dough.

Step-by-step explanation:

Since we have given that

Jay is letting her bread dough rise,

After 3 hours, her bread dough is [tex]1\frac{1}{5}=\frac{6}{5}[/tex] of its original size.

We need to find the percent of its original size is Jay's bread dough.

So, Percentage will be

[tex]\frac{6}{5}\times 100\\\\=6\times 20\\\\=120\%[/tex]

So, it becomes 120% of original dough.

The population increase in the town is linear, and with a constant increase of 611 people per year, the population is projected to be 4855 in five years.

The population of a town described is increasing at a constant rate, therefore, this represents linear growth. Each year, the population increases by a fixed number, in this case, 611. This contrasts to exponential growth, where the population would increase by a fixed percentage.

To calculate the population in five years, we multiply the rate of increase (611) by the number of years (5) and add the starting population. So, 611*5 = 3055. Adding the current population of 1800 gives us 4855.

Therefore, the population of the town in five years will be 4855, given the linear growth rate holds steady.

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Answer:

Uranium-234 is an isotope of uranium. In natural uranium and in uranium ore, U-234 occurs as an indirect decay product of uranium-238, but it makes up only 0.0055% (55 parts per million) of the raw uranium because its half-life of just 245,500 years is only about 1/18,000 as long as that of U-238.

Step-by-step explanation:

Answer: D) [tex]m+l=18\\\\1.25 m+0.75 l=19[/tex]

Step-by-step explanation:

Let 'm' represents the number of Mylar balloons  and 'l' represents the number of latex balloons.

Given : Mylar balloons cost $1.25 each l, and latex balloons cost $0.75 each.

i.e. cost of m Mylar balloons in dollars = 1.25 m

i.e. cost of l Latex balloons in dollars = 0.75 l

Then, the equations can be used to find the number of each type of balloon in a bunch of 18 balloons that costs $19 will be :-

[tex]m+l=18\\\\1.25 m+0.75 l=19[/tex]

Hence, the correct answer is Option D.[tex]m+l=18\\\\1.25 m+0.75 l=19[/tex]

The equations which can be used from the options given are :

(m + l) = 18

($1.25l + $0.75m) = $19

Cost per mylar balloon, m = $1.25

Cost per latex balloon, l = $0.75

Number of balloons in bunch = 18

Cost of bunch = $19

The cost can be expressed as :

(unit cost of each Ballon × number of each Ballon in a bunch) = total cost of bunch

($1.25l + $0.75m) = $19

Since the total Number of balloons in bunch = 18

And only mylar and latex balloons are present in the bunch ;

Then ;

(Number of mylar+number of latex) balloons = 18

(m + l) = 18

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Answer:

Option D is correct.

[tex]\frac{4}{5}[/tex] is the ratio form a proportion with [tex]\frac{16}{20}[/tex]

Step-by-step explanation:

Proportion states that the two fraction or ratios are equal.

i.e, [tex]\frac{a}{b} = \frac{c}{d}[/tex]

Given the ratio [tex]\frac{16}{20}[/tex]

To find the proportion of this ratio forms.

[tex]\frac{16}{20}[/tex]

Divide top and bottom by 4 , we have;

[tex]\frac{\frac{16}{4} }{\frac{20}{4} }[/tex]

Simplify:

[tex]\frac{4}{5}[/tex]

therefore, a ratio form a proportion with [tex]\frac{16}{20}[/tex] is, [tex]\frac{4}{5}[/tex]

Option D, 4/5 forms a proportion with 16:20.

To determine which ratio forms a proportion with 16:20, we must find a ratio equivalent to 16:20.

We start by simplifying 16:20. Both 16 and 20 can be divided by their greatest common divisor, which is 4:

16 ÷ 4 = 4

20 ÷ 4 = 5

This gives us the simplified ratio of 4:5. Now, we need to check which of the given options matches 4:5.

4/10: When simplified, 4:10 becomes 2:5, which is not equal to 4:5.

32/50: When simplified, 32:50 becomes 16:25, which is not equal to 4:5.

8/12: When simplified, 8:12 becomes 2:3, which is not equal to 4:5.

4/5: This ratio is already simplified and equal to 4:5.

Therefore, the ratio 4:5 forms a proportion with 16:20.

Correct Question

Which ratio forms a proportion with 16:20 ?      

A. 4/10    

B.  32/50  

C.  8/12    

D. 4/5

Answer:

the price is 6.75

Step-by-step explanation:

you deduct 25 from 16 what gives you 12.00

then deduct 25 from 12that gives you 9

then deduct 25 from 9 gives you 6.75

Answer:

24 photos per day

Step-by-step explanation:

Set up a chart.

x      y

1       24

2       48

3       72

4       96

5       120

6        144

The change between y is =24

The change in x is +1

change in y

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

change in x

24

----     =

1

24 photos per day

Answer:

1. -9       2. 160

3. 3.9

Step-by-step explanation:

I dd the assignment

The equation in standard form that represents the relationship between Fahrenheit (F) and Celsius (C) is 5F + (5/9)(F - 32) = 39.

In order to represent the relationship between Fahrenheit (F) and Celsius (C) in standard form, we can use the conversion formula:

C = (5/9)(F - 32)

Given the equation 5F + C = 39, we can substitute the value of C from the conversion formula into the equation:

5F + (5/9)(F - 32) = 39

Simplifying the equation further:

45F + 5(F - 32) = 351

45F + 5F - 160 = 351

Combine like terms:

50F - 160 = 351

Add 160 to both sides:

50F = 511

Divide both sides by 50:

F = 10.22

Therefore, the equation in standard form that represents the relationship between F (degrees Fahrenheit) and C (degrees Celsius) is 5F + (5/9)(F - 32) = 39.

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The complete question is here:

The table shows temperatures below freezing measured in different units. Complete the equation in standard form to represent the relationship between F, a temperature measured in degrees Fahrenheit, and C, a temperature measured in degrees Celsius. 5F + C =  39°F = °C rounded to the nearest tenth of a degree

Freezing Temperatures (°)

Column A. F

1. -13

2. -4

3. 5

4. 14

5. 23

Column B. C

A. -25

B. -20

C. -15

D. -10

E. -5

Answer: 7 and 8

Step-by-step explanation:

Let x represent the first number, then x + 1 is the other number.

(x)² + (x + 1)² = 113

x²  +  x² + 2x + 1 = 113    expanded (x + 1)²

2x² + 2x + 1 = 113          added like terms

2x² + 2x - 112 = 0        subtracted 113 from both sides

x² + x - 56 = 0           divided both sides by 2

(x + 8) (x - 7) = 0        factored polynomial

x + 8 = 0   x - 7 = 0    applied zero product property

x = -8     x = 7            solved for x

  ↓

not valid since the restriction is that x > 0 (a positive number)

So, x = 7     and     x + 1 = (7) + 1   = 8

Answer:

20,000

Step-by-step explanation:

We can create a proportion to find the total budget. A proportion is an equation where two ratios are set equal to each other. We create two fractions using the budget and percents.

[tex]\frac{13}{100} =\frac{2600}{x}[/tex]

We begin solving by cross multiplying numerator to denominator of each fraction.

[tex]13(x)=100(2600)\\13x=260000\\\frac{13x}{13}=\frac{260000}{13}  \\20,000=x[/tex]

Answer:

the company's total budget is 20,000

Step-by-step explanation:

A company spends 13% of its month budget on rent which total $2600

Let x be the month budget on rent

13% of the month budget is 2600

13% can be written as 13/100

[tex]\frac{13}{100} \cdot x=2600[/tex]

Now we solve for x

multiply both sides by 100

[tex]13x= 260000[/tex]

divide both sides by 13

x=20000

So, the company's total budget is 20,000

Answer:

The equation is q + 10 = 20

The solution is q = 10

Step-by-step explanation:

"sum" means an addition.

"sum of q and 10" means "q + 10".

"is" means "="

That means you have the equation

q + 10 = 20

To solve the equation, subtract 10 from both sides.

q + 10 - 10 = 20 - 10

q = 10

Answer:

The equation is q + 10 = 20

The solution is q = 10

Answer:

q+10 = 20

Solving for q,

q=10

Step-by-step explanation:

Sum means addition and is means equals

q+10 = 20

We can solve for q by subtracting 10 from each side

q+10-10 = 20-10

q=10

Answer:

The answer is y=20

Step-by-step explanation:

If you take a look at the attached picture you will notice that angles B and C are congruent, so that means they both are 25 degrees.

Next, add angles B and C together to get 50.

Then you take that 50 and add it to 70 in angle A's equation, and you will get 120.

Next, plug 120 into angle A's equation where the 70 was and you will have the equation 3y+120=180. (180 is there because that is what all the interior angles equal together.)

Next, slove the equation.

And theres your answer, I hope I helped. Put any questions in the comments.

The value of y in the isosceles triangle is 20. This was determined by making use of the angles sum property of a triangle and the specific properties of an isosceles triangle.

The subject of this question is geometry, specifically the properties of an isosceles triangle and the inner angles. An isosceles triangle is a triangle with at least two equal sides - in this case, sides AB and AC. Because it is an isosceles triangle, angles B and C are equal. Therefore, we know that the value of angle C in degrees is also 25 (5x = 25).

According to the angles sum property of a triangle, the sum of the inner angles of a triangle is always 180 degrees. Therefore, we have the equality: (3y + 70) + 25 + 25 = 180. If we subtract 70 from both sides, we have 3y = 180 - 120, which simplifies to 3y = 60. To solve for y, we divide both sides by 3. Concluding, y = 60/3 = 20.

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The point-slope form:

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

We have m = 4/5 and the point (7, -9). Substitute:

[tex]y-(-9)=\dfrac{4}{5}(x-7)\\\\\boxed{y+9=\dfrac{4}{5}(x-7)}[/tex]

Equation of the line is a way of representation of the line in a algebraic from with point which form the line in the coordinate system and the slope. Thus the equation of the line passing through the point (7,-9) having the slope 4/5 is,

[tex](y-7)=\dfrac{4}{5} (x+9)[/tex]

Hence, the option 2 is the correct option.

The line passes through the point (7,-9).

The slope of the line is 4/5.

Equation of the line is a way of representation of the line in a algebraic from with point which form the line in the coordinate system and the slope.

The standard form of the equation of the line can be given as,

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

Here m is the slope of the line.

Thus, the equation of the line passes through (7,-9) having the slope 4/5 can be given as,

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

Put the values,

[tex](y-7)=\dfrac{4}{5} (x-(-9))[/tex]

[tex](y-7)=\dfrac{4}{5} (x+9)[/tex]

Thus the equation of the line passing through the point (7,-9) having the slope 4/5 is,

[tex](y-7)=\dfrac{4}{5} (x+9)[/tex]

Thus the option 2 is the correct option.

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Answer:

see explanation

Step-by-step explanation:

the n th term of an arithmetic sequence is

[tex]t_{n}[/tex] = [tex]t_{1}[/tex] + (n - 1)d

given [tex]t_{1}[/tex] = 3 and [tex]t_{2}[/tex] = 10, then

[tex]t_{2}[/tex] = 3 + d = 10 ⇒ d = 10 - 3 = 7

[tex]t_{n}[/tex] = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2[tex]t_{1}[/tex] + (n - 1)d ]

                        = [tex]\frac{n}{2}[/tex][(2 × 3) + 7(n - 1) ]

                        = [tex]\frac{n}{2}[/tex](6 + 7n - 7 )

                        = [tex]\frac{n}{2}[/tex](7n - 1)

                        = [tex]\frac{7}{2}[/tex] n² - [tex]\frac{1}{2}[/tex] n

Answer:

5/16

Step-by-step explanation:

We need to change the mixed number to an improper fraction to find the reciprocal

3 1/5 = (5*3+1)/5 = 16/5

The reciprocal of 16/5 is found by flipping the fraction

5/16

Answer:

5/16

Step-by-step explanation:

To find the reciprocal you have to make the fraction a mixed number by multiplying the denominator by the whole number then adding the numerator, in this case it would give you 16/5. Since the reciprocal is the number that you multiply to get one, if you switch the denominator and the numerator, you get 5/16.

You can check your work by multiplying the numbers together, if it equals one, your reciprocal is correct, if not, then you may have to do it again.

Answer:

-3 degrees per hour

Step-by-step explanation:

Temperature was [tex]0[/tex] degrees and it fell to [tex]-6\frac{3}{5}=-\frac{33}{5}[/tex] in [tex]2\frac{1}{5}=\frac{11}{5}[/tex] hours.

To get temperature change per hour, we divide the change by total number of hours. So:

So temperature changer per hour:

[tex]\frac{-\frac{33}{5}}{\frac{11}{5}}\\=-\frac{33}{5}*\frac{5}{11}\\=-\frac{33}{11}\\=-3[/tex] degrees per hour.

Answer:

The temperature change per hour was -3 degrees per hour.

Step-by-step explanation:

We know that the temperature fell from [tex]0[/tex] degrees to [tex]-6\frac{3}{5}[/tex] degrees in a time period of [tex]2\frac{1}{5}[/tex] hours.

So to find the rate of change of the temperature, we will divide the change in temperature by the number of hours.

For that, we will change the mixed number into improper fractions and then solve:

[tex]-6\frac{3}{5}=-\frac{33}{5}degrees[/tex]

[tex]2\frac{1}{5}=\frac{11}{5} hours[/tex]

Temperature change per hour = [tex]\frac{-\frac{33}{5}}{\frac{11}{5}} = \frac{33}{5}*-\frac{5}{11}=-3[/tex]

Therefore, the temperature change per hour was -3 degrees per hour.

Answer:

Step-by-step explanation:

3-4i

The complex number is represented by the point graphed on the complex plane is 3-4i. Therefore, option C is the correct answer.

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.

Since the point (a, b) can be written in the form a + bi, where 'a' is the measurement along X-axis and 'b' is the measurement along Y-axis, so the point (3, -4) an be written in the following form:

(3, -4) = 3 + (-4)i = 3-4i.

Therefore, option C is the correct answer.

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Answer,

= 4

Explanation,

So, basicly they want you to put the numbers (1/5) & (15) in place of the letters (c) & (d). Let's do that,

5 * 1/5 + 1/5 * 15

So, now that we have replaced the letters with numbers we simply simplify,

5 * 1/5 = 1

1/5 * 15 = 3

3 + 1 = 4

Hope this helps :-)

Answer:

Correct choice is C

Step-by-step explanation:

Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Thus, if a, b and c are triangles sides, then

[tex]a+b>c,\\ \\a+c>b,\\ \\b+c>a.[/tex]

A. Consider lengths a=5, b=10 and c=4. Since

[tex]a+c=5+4=9<10=b,[/tex]

these side lengths couldn't create triangle.

B. Consider lengths a=5, b=7 and c=13. Since

[tex]a+b=5+7=12<13=c,[/tex]

these side lengths couldn't create triangle.

C. Consider lengths a=7, b=9 and c=3. Since

[tex]a+b=7+9=16>3=c,\\ \\a+c=7+3=10>9=b,\\ \\b+c=9+3=12>7=a.[/tex]

These side lengths could form a triangle.

D. Consider lengths a=10, b=4 and c=5. Since

[tex]b+c=4+5=9<10=a,[/tex]

these side lengths couldn't create triangle.

Answer:

C?

Step-by-step explanation:

x = number of months

7*x = 7 times the number of months

7*x = total cost if you ignore the $100 fee

7x+100 = total cost with the fee of $100 included

y = total cost

y = 7x+100

Final Answer: y = 7x+100

note: the slope is 7 and the y intercept is 100

The simplified expression of the expression (0.07b³m + 7) ÷ (15bm⁻¹) is (0.07b³m + 7) ÷ (15bm⁻¹)

To simplify the expression, we have

The GCD of the numerator and denominator is 1.

So, the simplified expression is:

(0.07b³m + 7) ÷ (15bm⁻¹) = (0.07b³m + 7) ÷ (15bm⁻¹)

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Answer:

y=6/5x+13

Step-by-step explanation:

6y=-5x+16

Divide by 6

y=-5/6x + 8/3

Slope: 6/5 (opposite reciprocal)

7=-5(6/5)+b

7=-6+b

b=13

Answer:

see explanation

Step-by-step explanation:

MP = HP - HM = 22 - 10 = 12

MN = [tex]\frac{1}{2}[/tex] MP = 6 = NP

RN = RP + PN = 5 + 6 = 11

HN = HM + MN = 10 + 6 = 16

Answer:

22.5 calories per oz.

Step-by-step explanation:

Simplify. Find the amount for 1 oz. Divide 450 with 20

450/20 = 22.5

22.5 calories per oz.

~

Answer:

Shade in the first three rectangles

Step-by-step explanation:

1/4 of 12 is 3. So u fill in three

Answer:

3 boxes

Step-by-step explanation:

you would divide 12 by 4 and get 3 so shade in 3 boxes