Suppose a plumber charges $80 for a house call and $60 for each hour it takes him to complete the repair. Write an equation in slope-intercept form to represent this situation.

Answer:

I believe the answer is 0.7813

Step-by-step explanation:

Find the difference between 400 and 200, as they are first and second terms. This is going to be 0.5 since it is being divided.

The formula is: a∨n=a∨1(r)^(n-1)

n= the number of the sequence you are looking for

r=0.5

a∨1=400

a∨2=200

400(0.5)^(10-1)

Answer:

y = 12

Step-by-step explanation:

To solve this equation... The function is basically:

y = 3x - 15

So by substituting in x=9:

y = 27 - 15 = 12.

y = 12

Hope this helps.

Answer:

y = 12

Step-by-step explanation:

f(x) = y, so to find y, we jut need to substitute 9 for all the x-values in the equation:

f(9) = 3(9) - 15

Simplify:

f(9) = 27 - 15

f(9) = 12

Since f(x) = y

y = 12 when x is 9

Hope this helped!

Answer:

x ≤ 3

Step-by-step explanation:

[tex]\dfrac{1}{2}-\dfrac{1}{4}x \geq -\dfrac{1}{4}[/tex]

Subtract 1/2 from both sides:

[tex]\implies \dfrac{1}{2}-\dfrac{1}{4}x-\dfrac{1}{2} \geq -\dfrac{1}{4}-\dfrac{1}{2}[/tex]

[tex]\implies -\dfrac{1}{4}x \geq -\dfrac{3}{4}[/tex]

Multiply both sides by 4:

[tex]\implies -\dfrac{1}{4}x \cdot 4 \geq -\dfrac{3}{4} \cdot 4[/tex]

[tex]\implies -x \geq -3[/tex]

Divide both sides by -1 (remembering to flip the sign):

[tex]\implies \dfrac{-x}{-1} \geq \dfrac{-3}{-1}[/tex]

[tex]\implies x \leq 3[/tex]

Answer:

2250

Step-by-step explanation:

In this problem, you do 9000/4 because he earns $4 commissions, and that will give you 2250.

Answer:

Step-by-step explanation:

The deck is divided into 4 different kinds of cards

Each kind of card has a 2

So there are 4 twos in a standard deck of cards.

Answer:

Answer:

Ray

Step-by-step explanation:

Ray is correct . Have a nice day :)

Answer:

-3

Step-by-step explanation:

5•-3=-15

4•-3=-12

-15+3=-12

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

[tex]1351+780\sqrt{3}[/tex]

Decimal Form:

2701.99962990

Thus, 2,701 is your answer

Answer:

The answer is simply 26,25/3 which gives that each book costed 8,75 dollars assuming of course that all books have the same price.

root*324=18

441=21

529=23

hope it helps

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Answer:

23/5

Step-by-step explanation:

* means multiply

4 3/5

5 * 4 = 20

20 + 3 = 23

23/5

Answer:

[tex]\frac{23}{5}[/tex]

Step-by-step explanation:

The type of fraction we are dealing with is called a mixed fraction

In order to convert this fraction into a fraction greater than 1, we will have to convert it into an improper fraction

So we keep the denominator

Multiply the whole number by the denominator and add that to the numerator

Answer:

Step-by-step explanation:

Remark

You want the 60th term of the arithmetic (?) sequence given.

Formula

L = a + (n - 1)*d

Givens

L = ?

a =  8

d = 8

n = 60

Solution

L = 8 + (60 - 1)*8

L = 8 + 60*8 - 8

L = 480

Answer

The 60th term is 480

Answer:

Step by step explanation :

As we know

[tex]\:\bf\boxed{an\:=\:a\:+\:(n\:-\:1)\:d}[/tex]

where,

an = the nth term in the sequence

n = the term

d = common difference

a = first term of the AP.

Here,

an = a60

n = 60

d = 16 - 8 = 8

a = 8

Now,

[tex]\:\mathsf{a60\:=\:8\:+\:(60\:-\:1)(8)}[/tex]

=> [tex]\:\mathsf{a60\:=\:8\:+\:(59)(8)}[/tex]

=> [tex]\:\mathsf{a60\:=\:8\:+\:472}[/tex]

=> [tex]\:\bf{a60\:=\:480}[/tex]

Therefore the 60th term of the AP is 480.

Answer:

T' = (-8, 8)

U' = (2, 8)

V' = (-8, 7)

Step-by-step explanation:

reflection over x axis means we change the sign of the y coordinate and nothing else

T = (-8, -8)

y coordinate = -8, change the sign to get 8

T' is thus (-8, 8)

U = (2, -8)

y coordinate = -8, y' = 8

U' = (2, 8)

V = (-8, -7)

y' = 7

V' = (-8, 7)

Answer:

B

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

where:

Given:

[tex]\implies \sf PMT=\dfrac{195000(0.066)(1+0.066)^{360}}{(1+0.066)^{360-1}}[/tex]

Answer:

9

Step-by-step explanation:

The least number of packages she should buy is 9 because 9 x 6 is 54 so she would have 4 extra ducks but she would still have enough for the carnival game

Answer:

5x - 2

Step-by-step explanation:

if x is your number its 5 lots of your number - 2

Answer:

x + y = 4.5

Step-by-step explanation:

x + y = 1.5 + 3 = 4.5

Answer:

x=29°

Step-by-step explanation:

angle measure of circular arc=180-122=58°

x=1/2×58=29°

Answer:

2nd option

Step-by-step explanation:

the graph has a minimum value of - 6  ( U ) not a maximum

Answer:

2nd option

Step-by-step explanation:

Answer:

250

Step-by-step explanation:

Bulb box and carton both are of cuboidal shape.

For bulb box the dimensions are:

For Carton the dimensions are:

To find the number of bulbs packed in the carton, divide the [tex]V_{Carton}[/tex] by [tex] V_{Bulb\: box}[/tex]

So, 250 bulbs will be packed in one carton.

A. Line

D. Segment

E. Ray

Math dimensions include length, width, and height (in that order). The dimension that an object occupies is dependent on how many different measurements, aka dimensions, an object has.

0th Dimension

The first dimension is actually the zeroth dimension. This dimension includes objects that do not have any measurements. A point does not have a length because it only occupies one spot on a plane.

The 0th dimension includes:

1st Dimension

The next dimension, the 1st dimension, has only length. This means the object can travel across the x-axis, but it can only go in one direction.

The 1st dimension includes:

2nd Dimension

For this question, the last dimension is the 2nd dimension. The 2nd dimension has both length and width. This means that the object occupies both the x and y-axis.

The 2nd dimension includes:

3rd Dimension

The 3rd dimension is not included in the question or the answer choices but is still important. The 3rd dimension has length, width, and height. This occupies the x, y, and z-axis and cannot be graphed on a regular geometric plane. The 3rd dimension is graphed in a geometric space.

The 3rd dimension includes:

Step-by-step explanation:

length × width = 24

2×length + 2×width = 22

length + width = 11

length = 11 - width

this we use in the first equation again :

(11 - width) × width = 24

11×width - width² = 24

width² - 11×width + 24 = 0

the general solution to an quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = 1

b = -11

c = 24

and so we get

width = (11 ± sqrt((-11)² - 4×1×24))/2×1) =

= (11 ± sqrt(11² - 96))/2 = (11 ± sqrt(121-96))/2 =

= (11 ± sqrt(25))/2 = (11 ± 5)/2

width1 = (11 + 5)/2 = 16/2 = 8 cm

width2 = (11 - 5)/2 = 6/2 = 3 cm

and teenaged to this is then

length1 = 11 - width1 = 11 - 8 = 3 cm

length2 = 11 - width2 = 11 - 3 = 8 cm

so, it is clear. one dimension has to be 8 cm, and the other one 3 cm. it does not matter which is which.

Using the Factor Theorem, it is found that the correct option regarding the complex zeros of f(x) is given by:

D The function has one real zero and two nonreal zeros.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the function is given by:

f(x) = x³ - 3x² + 16x + 48.

Using a calculator, the roots are given by:

[tex]x_1 = -1.89767, x_2 = 2.44884 + 4.39288i, x_3 = 2.44884 - 4.39288i[/tex]

The first root is real, while the second and third are complex(nonreal), hence option D is correct.

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The unknown sides of the right angle triangle using trigonometric ratios are as follows;

PR = 13.2 units

RQ = 17.6 units

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sides of the triangle can be found using trigonometric ratios.

Therefore,

sin 37° = opposite / hypotenuse

sin 37° = PR / 22

cross multiply

PR = 22 sin 37

PR = 22 × 0.60181502315

PR = 13.2399305093

PR = 13.2 units

cos 37 = adjacent / hypotenuse

cos 37 = RQ / 22

RQ = 22 cos 37

RQ = 17.569981221

RQ = 17.6 units

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Problem 4

The template of [tex]y = a*b^x[/tex] becomes [tex]y = 10800*0.975^x[/tex] to represent the exponential function.

We want to know when the population reaches half of 10800, so we want to know when the population is 10800/2 = 5400

Plug in y = 5400 and solve for x.

[tex]y = 10800*0.975^x\\\\5400 = 10800*0.975^x\\\\0.975^x = 5400/10800\\\\0.975^x = 0.5\\\\\log(0.975^x) = \log(0.5)\\\\x\log(0.975) = \log(0.5)\\\\x = \log(0.5)/\log(0.975)\\\\x \approx 27.377851\\\\x \approx 28\\\\[/tex]

I rounded up to the nearest whole number because x = 27 leads to y = 5452, which is not 5400 or smaller.

Luckily, x = 28 leads to y = 5315 which gets over the hurdle of being 5400 or smaller.

Add 28 years onto the starting year 2002 and we get to 2002+28 = 2030

The population reaches half of its original amount in the year 2030.

============================================================

Problem 5

If the car loses 12% of its value each year, then it keeps the remaining 88%

Plug those values into [tex]y = a*b^x[/tex].

We find the equation is [tex]y = 28750*0.88^x[/tex] where,

Replace y with 10,000 and solve for x.

[tex]y = 28750*0.88^x\\\\10000 = 28750*0.88^x\\\\0.88^x = 10000/28750\\\\0.88^x \approx 0.347826\\\\\log(0.88^x) \approx \log(0.347826)\\\\x\log(0.88) \approx \log(0.347826)\\\\x \approx \log(0.347826)/\log(0.88)\\\\x \approx 8.261168\\\\x \approx 9\\\\[/tex]

Like in the previous problem, we round up so we clear the hurdle.

Adding 9 years onto 2012 gets us to 2012+9 = 2021

Answer:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given:

As the population is decreasing by 2.5% each year, the population will be 100% - 2.5% = 97.5% of the previous year. Therefore, the base is 0.975.

Final equation:  [tex]\large \text{$ y=10800(0.975)^x $}[/tex]

Half of population:  10800 ÷ 2 = 5400

[tex]\large \begin{aligned}y & =5400\\\implies 10800(0.975)^x & =5400\\(0.975)^x & = \dfrac{5400}{10800}\\(0.975)^x & = 0.5\\\ln (0.975)^x & = \ln 0.5\\x \ln 0.975 & = \ln 0.5\\x & = \dfrac{\ln 0.5}{\ln 0.975}\\x & = 27.377785123\end{aligned}[/tex]

2002 + 27.37785... = 2029.37785...

Therefore, the population will reach half during 2029 (by 2030).

Given:

As the value is decreasing by 12% each year, the value will be 100% - 12% = 88% of the previous year. Therefore, the base is 0.88.

Final equation:  [tex]\large \text {$ y=28750(0.88)^x $}[/tex]

Find when the car is worth $10,000:

[tex]\large \begin{aligned}y & = 10000\\\implies 28750(0.88)^x & = 10000\\(0.88)^x & = \frac{10000}{28750}\\(0.88)^x & = \frac{8}{23}\\\ln (0.88)^x & =\ln \left(\frac{8}{23}\right)\\x \ln (0.88) & =\ln \left(\frac{8}{23}\right)\\x & =\dfrac{\ln \left(\frac{8}{23}\right)}{\ln (0.88)}\\x & = 8.26116578\end{aligned}[/tex]

2012 + 8.26116578.. = 2020.26116578..

Therefore, the value of the car will reach $10,000 during 2020 (by 2021).

Answer:

65,520

Step-by-step explanation:

12x13x20x21=64,520

Answer:

x= 27.71281 = 16√3

y= 13.85641 = 8√3

Step-by-step explanation:

hope it helps :)

Answer:

∠ B = 85°

Step-by-step explanation:

the inscribed angle B is half the measure of its intercepted arc AC , then

∠ B = [tex]\frac{1}{2}[/tex] × 170° = 85°

Answer:

the table of the function is below

Step-by-step explanation:

The volume of the rectangular prism is 180 ft³, From the net of the prism, A = 10 feet, B = 4 feet, C = 6 feet and D = 3 feet.

An equation is an expression that shows the relationship between two or more numbers and variables.

The volume of the rectangular prism = length * width * height = 10 * 6 * 3 = 180 ft³

From the net of the prism, A = 10 feet, B = 4 feet, C = 6 feet and D = 3 feet.

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