What is the slope of a line perpendicular to a line with the equation y = 5x - 2 ?

Answer:

[tex]\frac{40}{19}\text{ or }2\frac{2}{19}[/tex] cases per hour.

Step-by-step explanation:

We are told that Jerry hears 5 cases every [tex]2\frac{3}{8}[/tex] hours.

To find the number of cases that Jerry hears per hour let us divide 5 by [tex]2\frac{3}{8}[/tex].

[tex]\text{Jerry hears cases per hour}=5\div 2\frac{3}{8}[/tex]

Let us convert our mixed fraction into improper fraction.

[tex]\text{Jerry hears cases per hour}=5\div \frac{19}{8}[/tex]

Since dividing a number by a fraction is same as multiplying the number by the reciprocal of the fraction.

[tex]\text{Jerry hears cases per hour}=5\times \frac{8}{19}[/tex]

[tex]\text{Jerry hears cases per hour}=\frac{40}{19}[/tex]

[tex]\text{Jerry hears cases per hour}=2\frac{2}{19}[/tex]

Therefore, Jerry hears [tex]\frac{40}{19}\text{ or }2\frac{2}{19}[/tex] cases per hour.

Answer:

Center (1,3) and radius 6

Step-by-step explanation:

We must complete the square to find the center and radius of the circle.

First make sure the x and y squared terms have 1 as their coefficients. We also make sure x and y terms together.

[tex]x^2-2x+y^2-6y=26[/tex]

We now create space between the x and y terms with parenthesis.

[tex](x^2-2x)+(y^2-6y)=26[/tex]

We complete the square by taking the middle terms -2x and the -6y - divide each and square them.

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

[tex]\frac{-6}{2} =(-3)^{2} =9[/tex]

We add the squares to both sides.

[tex](x^2-2x+1)+(y^2-6y+9)=26+1+9[/tex]

Simplify.

[tex](x^2-2x+1)+(y^2-6y+9)=36[/tex]

And write the quadratics in factored form.

[tex](x-1)^{2} +(y-3)^{2} =36[/tex]

The center is (h,k) or (1,3). The radius is the square root of 36 which is 6.

Answer:

The required domain is [tex]x\ne -1[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{1-x}{x}[/tex]

We need the inverse of this function.

We first of all have to let [tex]y=f(x)[/tex].

This implies that,

[tex]y=\frac{1-x}{x}[/tex]

Next, we interchange [tex]x[/tex] and [tex]y[/tex] to obtain,

[tex]x=\frac{1-y}{y}[/tex]

We make y the subject to get,

[tex]xy=1-y[/tex]

[tex]xy+y=1[/tex]

[tex](x+1)y=1[/tex]

[tex]y=\frac{1}{1+x}[/tex]

The inverse function is

[tex]f^{-1}(x)=\frac{1}{1+x}[/tex]

The domain of this function is

[tex]x+1\ne 0[/tex]

[tex]\Rightarrow x\ne -1[/tex]

The correct answer is D

Answer:

C.p(v)=5000/v

Step-by-step explanation:

Got it right on the test.

The equation that can be used to find the pressure of the gas when the volume is changed is P(v) = 500/v

Given:

p(v) = pressure of a gas

v = volume of the gas

P(v) varies inversely with v

let

k = constant of proportionality

The equation:

P(v) = k/v

If P(v) = 25 kg/cm² and v = 200cm²

Therefore,

P(v) = k/v

25 = k / 200

25 × 200 = k

k = 5,000

substitute the value of k into the equation

So,

P(v) = 500/v

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B) 87 feet

The mnemonic SOH CAH TOA reminds you the relationship between angle, adjacent, and opposite sides is ...

... Tan = Opposite/Adjacent

In this geometry, the side adjacent to the angle is marked 150 ft, and the side opposite the angle is the height we want to find. This means ...

... tan(30°) = height/(150 ft)

Multiplying by 150 ft, we get ...

... height = (150 ft)·tan(30°) ≈ 87 ft

Answer:

C.) 1/169

Step-by-step explanation:

There are 4 jacks in a deck of 52 cards

The probability the first card is a jack

4/52 = 1/ 13

Since we replace the card

The probability the second card is a jack

4/52 = 1/ 13

To get the probability that we get a jack then a jack, we multiply the probabilities

1/13 * 1/13 = 1/169

Answer:

25 miles

Step-by-step explanation:

[tex]\frac{6}{40} :\frac{3.75}{y} \\y=25[/tex]

Answer: In the question, 3.75 miles is equal to 6 kilometers (that's rounding in a real life situation. It would actually be about 3.72... but who cares?! :)). So, if you divide 3.75/6... you get 0.625. Now, you multiply 40 by 0.625. After so, you get 25. 40 kilometers is equal to 25 miles!

Answer:

4000

Step-by-step explanation:

Davila can job 400 feet in 8 min

Answer:

[tex]x>-3[/tex]

Step-by-step explanation:

To solve equations, we use inverse operations. Normally, we use PEMDAS to simplify an equation. To solve it, we use the inverse of each in this order SADMEP. Solving an inequality is the same except for step. When dividing by a negative, the sign of the inequality changes.

We have [tex]5x+7>2(x-1)\\5x+7>2x-2[/tex] in simplified form. We begin by subtracting or adding constants across the equal sign. Then doing the same with the variable terms. We finish by dividing by the coefficient of the variable term.

[tex]5x+7>2x-2\\5x+7-7>2x-2-7\\5x>2x-9\\5x-2x>2x-2x-9\\3x>-9\\x>-3[/tex]

To graph, we draw a number line, draw an open circle at -3.

Since it is not equal to, we do not fill it in. We leave it open. We also draw an arrow to the right of -3

Answer:

-99

Step-by-step explanation:

Given :

Arithmetic sequence : 15 , 9 ,3 , -3 , ........

To Find : 20th term .

Solution :

Formula of nth term in Arithmetic mean : [tex]a_{n} = a+(n-1)*d[/tex]  ---(A)

where

a = first term of sequence

n = term position

d = common difference

[tex]a_{n}[/tex] = the term you want to find

Thus in the given sequence:

a = 15 ( first term )

n = 20 th term ( given )

d = 9-15 = 3-9 = -6(common difference)

Putting values in (A)

⇒[tex]a_{20} = 15+(20-1)*(-6)[/tex]

[tex]a_{20} = 15-114[/tex]

[tex]a_{20} = -99[/tex]

Hence the 20th term is -99 i.e. option 1

Answer:

3746148

Step-by-step explanation:

i know you probably just want the answer but hear me out it is just simple math and can be resolved with a quick search. Find or search 1.8% of 3,381,000 and multiply it times the years progressed.

60858 x 6 = 3746148

Final answer:

Using the exponential growth formula, the approximate population of Henderson City in the year 2000 is calculated to be around 3,769,706 if the annual growth rate remains constant at 1.8%.

Explanation:

To calculate the approximate population of Henderson City in the year 2000, we can use the formula for exponential growth. The formula is
[tex]A = P(1 + r)^t[/tex]

where A is the amount of the final population, P is the initial population, r is the growth rate expressed as a decimal, and t is the time in years. In this case:

So the equation becomes:

A =[tex]3,381,000(1 + 0.018)^6[/tex]

Calculating this gives us the approximate population, A:

A ≈[tex]3,381,000(1.018)^6[/tex]

A ≈ 3,381,000(1.1155)

A ≈ 3,769,706

Therefore, the approximate population of Henderson City in the year 2000 would be 3,769,706 residents if the growth rate remains constant at 1.8%.

Answer:

see explanation

Step-by-step explanation:

For words per minute divide 228 by 4

words per minute = [tex]\frac{228}{4}[/tex] ( = 57 )

Final answer:

To find the number of words Carlos types per minute, set up an equation and solve for 'x'.

Explanation:

To find the number of words Carlos types per minute, we can set up an equation using the given information. Let's assume that the number of words Carlos types in 1 minute is 'x.' We know that Carlos can type 228 words in 4 minutes. So, the equation would be:

228 words in 4 minutes = x words in 1 minute

To solve this equation, we can cross-multiply and divide:

(228 words) x (1 minute) = (4 minutes) x (x words)

Simplifying further:

x = (228 words) / (4 minutes)

Therefore, the equation that represents the number of words Carlos types per minute is:

x = 228 / 4

Ava must work 43.5 more hours in order to save the rest of the money

Money is any item that generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. In math, it can be defined as the medium of exchange such as notes, coins, and demand deposits, to pay for commodities and services.

If you're self-employed, it's unwise  to work more than 40 hours a week on a regular basis because, you'll get a burst of productivity, the extra hours have diminished returns over time and within any time period.

Ava is saving for A new computer that cost 1218 she has already saved half of the money

[tex]\frac{1218 }{2} = 609[/tex]  $, hence  she has already saved half of the money ($609), so  she needs $609

Ava earns $14 per hour

Hence [tex]\frac{609}{14} = 43.5[/tex] hours

Ava must work 43.5 more hours in order to save the rest of the money

Hope it helps!

Grade:  5

Subject:  math

Chapter:  hours

Keywords:  hours, money, saved, order, Ava

Answer:

The answer is BD is the bisector angle

Answer:

The even functions are options 2, 3, and 5

Step-by-step explanation:

Please, see the attached file.

Thanks.

Answer:

Options B, C and E are even functions.

Step-by-step explanation:

If f(x) = f(-x) then function is called to be even.

A). f(x) = ∛8x

f(-x) = ∛8(-x) = (∛8)(∛(-x) = 2∛(-x)

Therefore f(x) ≠ f(-x)

So function is not an even function.

B). [tex]f(x)=log_{9}x^{6}[/tex]

[tex]f(-x)=log_{9}(-x)^{6}[/tex]

[tex]=log_{9}(x)^{6}[/tex]

f(x) = f(-x)

So this function is even.

C). [tex]f(x)=\frac{1}{x^{8}+7x^{7}}[/tex]

[tex]f(-x)=\frac{1}{(-x)^{8}+7(-x)^{6}}[/tex]

            = [tex]\frac{1}{x^{8}+7x^{6}}[/tex]

f(x) = f(-x)

Therefore given function is even.

D). f(x) = [tex]e^{x^{8}-x }[/tex]

[tex]f(-x)=e^{(-x)^{8}-(-x)}=e^{x^{8}+x}[/tex]

Therefore f(x) ≠ f(-x)

So the given function is not even.

E). f(x) = |8x| - 3

f(-x) = |8(-x)| - 3

      = |8x| - 3

f(x) = f(-x)

Therefore, function is even.

F). [tex]f(-x)= -9(-x)^{10}+5(-x)^{4}-12(-x)[/tex]

[tex]f(-x)= -9(x)^{10}+5(x)^{4}+12(x)[/tex]

f(x) ≠ f(-x)

Therefore the given function is not an even function.

Options B, C and E are even functions.

Answer:

9.6667

Step-by-step explanation:

3t=29

Divide each side by 3

3t/3 = 29/3

t = 29/3

Three goes into 29  nine times  (3*9 = 27 ) with 2 left over

t =  9 2/3

We know 1/3 = .3 repeating

so 2/3  = .6 repeating

t = 9 .6 repeating

Answer: 3.0650

Step-by-step explanation:

K-12

Answer:

(1, 3)

(-1, 3)

Step-by-step explanation:

h(x) = 3x^2

Let x =1

h(1) = 3 * (1)^2

    = 3(1)

    = 3

So if the input is 1 the output is 3

h(-1) = 3 * (-1)^2

     = 3 *1

If the input is -1 the output is 3

Answer:(1,3) and (-1,3)

Step-by-step explanation:

Answer:

∠DBC = 40°

Step-by-step explanation:

We are given a figure where we know that the angle m∠1 = 65°, m∠2 = 60° and m∠6 = 85°. With the help of these given measures of the angles, we are to find the measure of the angle m∠DBC.

Since the sum of angles in a triangle is equal to 180 degrees, so:

∠1 + ∠2 + ∠3 = 180

∠3 = 180 - (65 + 60)

∠3 = 55°

Also ∠6 and ∠B are alternate interior angles so if ∠6 = 85° then ∠B is also = 85°.

Now that we know ∠3 and ∠B, we can find ∠DBC:

∠DBC = 180 - (85 + 55)

∠DBC = 40°

Answer:40

Step-by-step explanation:

See angle 1 = 65°

Angle 2 = 60°

We know in a triangle all angle count 180°

So angle 3 = 55°

Now in a straight line all angle count 180°

So angle DBC + angle 3 + remaining angle along the line m will count 180°

Now angle 6 and remaining angle along the line m will be equal as 'm' ?and 'b' are parallel lines and t is intersecting them so it subtend equal angles.

Angle 6 = 85° so remaining angle along the line m is also 85°

We know angle DBC + angle 3 + rem. angle = 180°

Or 55° + 85° + angle DBC = 180°

Therefore, angle DBC = 40°

Hope it helps!!!

Answer:

10.3 units

Step-by-step explanation:

From the given graph, we can see the coordinates of the points B (-2, 4) and D (3, -5).

To use the Pythagorean Theorem, we must have a right angled triangle. So we can select a point X (3, 4) to calculate the distance between B and D using the Pythagoras Theorem.

BX = 5, XD = 9

BD = [tex]\sqrt{BX^2+XD^2}[/tex]

BD = [tex]\sqrt{(5)^2+(9)^2} =\sqrt{106} =10.29[/tex]

Therefore, the points B and D are 10.3 units apart.

Answer:

Standard form: [tex]\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]

This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]

Step-by-step explanation:

Consider expression [tex]x^2+y^2-9x+10y+15=0.[/tex]

First, form perfect squares:

[tex](x^2-9x)+(y^2+10y)+15=0,\\ \\\left(x^2-9x+\dfrac{81}{4}\right)-\dfrac{81}{4}+(y^2+10y+25)-25+15=0,\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=10+\dfrac{81}{4},\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]

This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]

Answer:

Correct choice is B

Step-by-step explanation:

All three functions are increasing when x is increasing. You can find values of each function when x is "enough large". For example, at x=100,

1. linear function: [tex]y=10\cdot 100=1,000.[/tex]

2. exponential function: [tex]y=5^{100}\approx 0.8\cdot 10^{70}.[/tex]

3. quadratic function: [tex]y=4\cdot 100^2+5\cdot 100=40,500.[/tex]

As you can see,  when x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.

Also you can use graphical method to get from the attached diagrams result. When x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.

Correct choice is B.

8.

   Statement                                           Reason

1. A'F is perpendicular bisector of JK    1. Given

2. JA ≅ KA                                               2. Dfinition of perp bisector

3. ∠JAF and ∠KAF are right angles      3. Dfinition of perp bisector

4. A'F ≅ A'F                                              4. Reflexive Property

5. ΔJFA ≅ ΔKFA                                      5. SAS Theorem

6.

(ANGLE): It is given that ∠AMD ≅ ∠EDM

(SIDE): MD ≅ MD by the Reflexive Property

Which angle would satisfy AAS?   ∠MAD ≅ ∠ DEM

NOTE: If you chose the other angle, it would satisfy ASA

Answer: (d-21) represent in this context

The number of days the book is late

Step-by-step explanation:

The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Camilla borrows a book from the library for d days.

The library charges a late fee 0.10 dollars per day that the book is late.

If Camilla returns the book more than 21 days after she borrowed it.

Then the expression will be 0.10d.

The total amount is given as

Total amount = 0.10 d

Total amount = 0.10 x 21

Total amount = $2.1

More about the Algebra link is given below.

https://brainly.com/question/953809

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Answer:

3 Dollars

Step-by-step explanation:

$4+.50cents=4.50

6 quarters is $1.50

4.50-1.50=3 dollars

So, I got this question for my Imagine Math, and here is what I got;

4+0.50−1.50.

Why; I got this because 4+0.50 is 4.50 and then 4.50-1.50 is 3.

Hopes this helps.

Answer:

6 baskets were filled and 12 tomatoes were left

Step-by-step explanation:

Just do 612/100= 6

Answer: 691

Step-by-step explanation:

There are 3 different ways to find the remainder.  I am not sure which method you are supposed to use, so I will solve using all 3 methods.

Long Division:

         10x³ + 24x² + 77x + 230

x - 3 ) 10x⁴ -  6x³  + 5x²   - x  +  1

      - (10x⁴ - 30x³)   ↓       ↓      ↓

                   24x³ + 5x²     ↓      ↓

               - (24x³ - 72x²)   ↓      ↓

                              77x²  - x       ↓

                         -  (77x² - 231x)  ↓

                                        230x + 1

                                     - (230x - 690)

                                                    691 ← remainder

Synthetic Division:

x - 3 = 0   ⇒  x = 3

3  |  10     -6        5       -1        1

   |   ↓      30     72    231    690

      10      24     77    230   691 ← remainder

Remainder Theorem:

f(x) = 10x⁴ - 6x³ + 5x²  - x  +  1

f(3) = 10(3)⁴ - 6(3)³ + 5(3)² - (3)  +  1

     =  810   - 162    + 45    -  3  +  1

     = 691

Answer: Second, third, fifth and sixth options are correct.

Step-by-step explanation:

Since we have given that

[tex]\frac{3}{4}+m=\frac{-7}{4}[/tex]

Now, we will solve it for the value of m :

[tex]\frac{3}{4}+m=\frac{-7}{4}\\\\m=\frac{-7}{4}-\frac{3}{4}\\\\m=\frac{-7-3}{4}\\\\m=\frac{-10}{4}[/tex]

Hence, the value of m is

[tex]\frac{-10}{4}[/tex]

and we can also apply m=[tex]\frac{-5}{2}[/tex]

if [tex]\frac{-5}{4}+m=\frac{-15}{4}\\\\m=\frac{-15}{4}+\frac{5}{4}\\\\m=\frac{-10}{4}\\\\m=\frac{-5}{2}[/tex]

And

[tex]m+2=-0.5\\\\m=-0.5-2\\\\m=-2.5\\\\m=\frac{-5}{2}[/tex]

Therefore, Second, third, fifth and sixth options are correct.

Answer: D. (6, 9)

Step-by-step explanation:

Midpoint is the "average" of the x's and y's:

Given: (5, 13) and (7, 5)

Midpoint: [tex](\dfrac{5+7}{2},\dfrac{13+5}{2})[/tex]

             = [tex](\dfrac{12}{2},\dfrac{18}{2})[/tex]

              = (6, 9)

Answer: (6, 9)

Step-by-step explanation:

Final answer:

To set up a profitable computer repair business, assuming $50 for parts per repair and a service fee of $150, the weekly expenses equation is y = 50x + 500, and income equation is y = 150x, where x is the number of repairs.

Explanation:

When starting a computer repair business with estimated expenses of $500 per week, it's crucial to set average costs for replacement parts and fees for services to ensure profitability. Let's assume an average cost of $50 for parts per computer repaired and a service fee of $150 per repair. If x represents the number of computers you repair each week, your total weekly expenses for parts would be 50x plus the fixed expenses of $500, resulting in a total expense equation of y = 50x + 500. Your total weekly income can be modeled by the equation y = 150x, with each repair contributing $150 to the income.

To break even or make a profit, the total income must exceed total expenses, leading to an analysis based on the number of repairs done weekly. This practical application of linear equations in a business setting helps in budgeting, pricing strategies, and understanding economic principles behind running a service-based business. Monitoring these variables is key to achieving sustainability.