Which of the following is the equation of a line in slope-intercept form for a line with slope =1/4 and y-intercept at (0,-1)?
A. y=-1/4x - 1/4
B. y= 1/4x - 1
C. y= 1/4x +1
D. y=4x - 1

Answer:

1. The capacity of the water tank = 240 litres

2. So it will take 180 litres to fill it three quarters full.

Step-by-step explanation:

Dimensions of a water tank:

1 Meter=100 CM

Length (l) = 100 cm,

wide (w) = 40 cm,

Depth (h)= 60 cm,

Volume of the tank (V)

LWH

100 cm × 40 cm × 60 cm

240,000 cm³

The capacity of the water tank = 240,000 cm³ / 240 litres

(240,000*3)/4 = 180,000 cm3

So it will take 180 litres to fill it three quarters full.

Answer:

C

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 9) and (x₂, y₂ ) = (12, 20)

m = [tex]\frac{20-9}{12-4}[/tex] = [tex]\frac{11}{8}[/tex] → C

Answer: He should have used 13 instead of 13i

Step-by-step explanation:

Answer:

He should have used 13 instead of 13i

Step-by-step explanation:

Answer:

B (3,6)

Step-by-step explanation:

y = x + 3

then we will use this y to substitute the other y

4x + y = 18

4x + (x +3) = 18

4x + x + 3 = 18

5x = 18 - 3

5x = 15

x = 15/5 = 3

then we can find the value of y

y = x + 3 = 3 + 3 = 6

so the (x,y) is (3,6)

Answer:

x = 52 Degrees

Step-by-step explanation:

Welp, here I go again

According to the Exterior Angle theorem Angle R + Angle S = Angle PQS

So simplified that'd be (90 + 34) = x + 72

124 = x + 72

x = 124 - 72

x = 52 Degrees

Because if you divide 1/4 by 3/8 you get 2/3.

Answer:

I think the answer would be 79200 feet as 1 miles = 5280 feet

traductor de español

¡Hola! La siguiente descripción dice que el hogar de Caleb para su escuela es de 15 millas. La pregunta pregunta cuántos pies hay en 15 millas

Respuesta: 79.200.

Razonamiento: El razonamiento para esto es que 1 milla es 5280 pies. Cuando descubras que puedes multiplicar esto por 15 obtendrás 79200

Prueba: 5280

        x 15

___________

         79200

__________________________________

English Translator

Hello! the following description says that Caleb's house to his school is 15 miles. The question asks how many feet are in 15 miles

Answer: 79200

Reasoning: The reasoning to this is that 1 mile is 5280 feet. When you find out that you can multiply this by 15 you would get 79200

Proof: 5280

        x      15

___________

         79200

Answer:

$12.00

Step-by-step explanation:

a product that normally costs $20 with a 40 percent discount will cost you $12.00, and you saved $8.00.

Answer:

a. 4

b. 10

Step-by-step explanation:

A. If the math department buys 60 textbooks, which are $89 each, we need to multiply 60 by $89 to get the amount that the textbooks will cost. This gives us $5340. Since the math department has $7200 to spend, we subtract 5340 from 7200. This gives us $1860 that the math department has left to spend on laptops.  Since the laptops cost $395 each, and we have $1860 to spend, we divide 1860 by 395 to figure out how many laptops they can buy. This is 4.7. Since you can't buy 0.7 of a laptop, they can only buy 4 laptops. The final answer is 4.

B. The math department has $7200 to spend and buys 35 textbooks, which are $89 each. Multiply 35 by 89. This is $3115. Subtract this from $7200 to see how much the department has left to spend. The math department now has only $4085 to spend on laptops, which are $395 each. Divide 4085 by 395. This gives us 10.3. We can't buy 0.3 of a laptop, so they can only buy 10 laptops. The answer is 10.

Answer:

A:$7200-$5340

=$1860

They can buy 4 laptops which will cost $1580 and leave you with $280

B: 35 textbooks will cost $3115, which will leave us with $4085, so we can get 10 laptops

Step-by-step explanation:

Answer:

it is D c= 180 + 50h + 20p

Step-by-step explanation:

c is the total cost and the boat is 180 but for additional hour it would be +$50

now the first four passenger is free but if another person comes on then it would be +$20 hope this help

The linear equation which describes the total cost of the rental is           c = 180 + 50h + 20p

The correct option is an option (D)

"It is an equation in which the highest power of the variable is always 1."

For given example,

The boat rental has a flat fee of $180 for up to three hours.

Fixed rental cost = 180                       ...............(1)

The boat rental has $50 per hour for each additional hour.

Let, h is each additional hour (over 3)

So, the rental cost for each additional hour = 50h               .............(2)

The first four passengers are included in this cost, but $20 is charged for each additional passenger.

Here, p is each additional passenger (over 4)

So, the rental cost for each additional passenger = 20p         ..................(3)

From (1), (2) and (3),

the required linear equation would be,

c = 180 + 50h + 20p

Therefore, the linear equation which describes the total cost of the rental is c = 180 + 50h + 20p

The correct option is an option (D).

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The total number of books that we had in out bookcase when we were 11 years old was 2,187 books.

Suppose the initial term of a geometric sequence is [tex]a[/tex]

and the term by which we multiply the previous term to get the next term is [tex]r[/tex]

Then the sequence would look like

[tex]a, ar, ar^2, ar^3, \cdots[/tex]

(till the terms to which it is defined)

Thus, the nth term of such sequence would be

[tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).

Lets suppose its initial term is  [tex]a[/tex] , multiplication factor is  [tex]r[/tex]

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

For this case the initial number of books (2) is multiplied by 3 each year.

So we got:

a = 2,

r = 3

Since a = 2 was for age 5, and  if we take age 5 at 1st position, then age 11 is at the 7th position.

The number of books we read at each age is a geometric sequence with initial term 2 and multiplication factor 3.

The sum of its term(which would make it geometric series) will give the total number of books we will have.

Since age 11 is at 7th position, so n = 7

Thus, the total number of books we had in the bookcase when we were 11 years old is:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}\\\\S_7 = \dfrac{2((3)^7-1)}{3-1} = 2187[/tex]

We could've derived it without formula as:

Their sum is 2187.

Thus, the number of books that we had in out bookcase when we were 11 years old was 2187 books.

Learn more about sum of terms of geometric sequence here:

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Answer:

Step-by-step explanation:

The third, fifth and sixth expressions (from the top) are NOT polynomials, and the reason in each case is that the expression has one or more negative powers of x in it.

Since both fractions have the same denominator, divide the numerators:

15/3 = 5

There are 5 servings.

Answer:

1200$

Step-by-step explanation:

(840/(100-30))*100

(840/70)*100

12*100

1200

Answer:

This is a bad argument because when talking about negative numbers, the closer the numbers are to 0, the bigger they are. -4 is closer to 0 than -5, so -4 is the bigger number.

Step-by-step explanation:

Answer:

-5 is not larger than -4.

Step-by-step explanation:

Think of a number line. The absolute value of -5 is 5, meaning -5 is 5 away from 0 to the left. On the other hand, -4's absolute value is 4, meaning -4 is 4 away from 0 to the left. In the money scenario, owing $5 is a bigger debt because the absolute value is larger, not the number itself. Hope this helps!!

Answer:

See picture attached

Step-by-step explanation:

The missing question is:

Draw the graph of the growth function by plotting its G-intercept and another point.

Given the function:

G(x) = 2 + 7x

its G-intercept is found when variable x is equal to zero.

G(0) = 2 + 7(0) = 2

Then, the G-intercept is point (0, 2)

To graph a line, two points are needed. Replacing x = 1 into the equation, we get:

G(1) = 2 + 7(1) = 9

So, point (1, 9) is on the line. The graph of the function is the line that passes through these two points, as can be seen in the picture attached.

Answer:

n = 7

Step-by-step explanation:

n = (-1) x (-7)

Simplify:

When two minus signs appear in the product of two numbers, you can cancel them out.

Therefore:

n = (1) x (7) = 7

Hope this helps!

:)

Answer:

c

Step-by-step explanation:

Answer:

A - ( 2, - 4 )

Step-by-step explanation:

M, N , O is reflected at the points (-2,2) - O (-5,3) - M (-2,4) - N, and the triangle MNO is rotated 180 degrees around the origin , Down once because the triangle is being rotated around the origin and then right which would be the answer A. Hope this Helps : )

Answer:

i really dont know

Step-by-step explanation:

this is confusing

Answer:

dont get mad  if I got it wrong but I think its C

Answer:

1) 0.21

Step-by-step explanation:

This is because there are 4 bananas out of all 19 fruits. 4/19 is equal to 0.21052631578.

Answer: 3.66 cm

Step-by-step explanation: Given a rectangular casing BCDE with segment DE = 3 cm and segment BE = 3.5 cm.

The area A of a rectangle is length multiply by width.

Where length L = 3.5 cm and

width W = 3 cm

Area A = 3.5 × 3 = 10.5 cm^2

The pipe that will fit the fiber optic line is in cylindrical shape. Where area of a cylinder = πr^2.

But area A = 10.5. Substitute the values for the area of the cylinder

10.5 = πr^2

10.5 = 3.143 × r^2

Make r^2 the subject of formula

r^2 = 10.5/3.143

r = sqrt ( 3.34225 )

r = 1.828

Diameter = 2 × radius

Diameter = 2 × 1.829

Diameter = 3.656 cm

Therefore, the smallest diameter of pipe that will fit the fiber optic line is 3.66 cm approximately.

Answer:

4.24 cm

Step-by-step explanation:

pythagorean theorem

a^2+b^2=C^2

3^2+3^2=18

square root of 18 =4.24

hope this helped :)

Answer:

44.4

Step-by-step explanation:

right on edge

Answer:

2 y^2 - 9

Step-by-step explanation:

(-3y^2 − 8) − (-5y^2 + 1)

Distribute the negative sign

(-3y^2 − 8) + 5y^2 - 1

Combine like terms

-3y^2 + 5y^2 - 1 − 8

2 y^2 - 9

Answer:

The answer to (-3y² - 8) - (-5y² + 1) is 2y² - 9

Step-by-step explanation:

[tex](-3y^2-8)-(-5y^2+1)[/tex]

Since there is a minus sign in front of the second parentheses, then the terms within that parentheses will be changed to their opposite signs.

[tex]-3y^2-8+5y^2-1[/tex]

Combine like terms.

[tex]2y^2-9[/tex]

Answer:

The first graph

Step-by-step explanation:

I think it is the first one because I remember doing this. If this is wrong please forgive me. Have a wonderful day!

First graph shows the function f(x) and g(x).

" Graph is representation of the coordinates on the coordinate plane along x-axis and y-axis."

According to the question,

Given function,

[tex]f(x) = x^{5} -3x^{2} +5x\\\\g(x) = f(-x+4)[/tex]

Plot the given functions on the graph we get,

Compare the drawn graph with the given graph.

First graph is same as graph drawn for the function f(x) and g(x).

Hence, we conclude that  first graph shows the function f(x) and g(x).

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The first two values were calculated, but the 0.4 one is wrong.

2/5% would result to 0.4% which is converted to 0.004 so it's wrong.

40/100 would be reduced to 2/5.

2/5 would result to 0.4.

0.4 means 40%.

If the question intentionally gives 2/5%, then you have to compute it all the way back.

2/5% to 0.4% to 0.004 to 4/1000

I have no clue what part is given but you can get the idea where this is going.

The second one depends on the value in question one.

So Good luck!

Step-by-step explanation:

D. In a column two-way relative frequency table, each column totals 100%.

Answer:

Step-by-step explanation:

Find  the maximum value of

C = 3x -2y  Objective function

subject to the following constraints.

Constraints

x ≥ 0

y ≥ 0                

2x + y ≤ 10  vertex 1 : when x=0 then y=10  (0,10)

3x + 2y ≤ 18 vertex 2 : y=0, then x=6          ( 6,0)

two equations together to determine vertex 3 :

3x+2y = 18

2x+y = 10

x=2, y= 6

The feasible region determined by the constraints is

shown. The three vertices are (0, 10),  and (6, 0), (0,9)

and (2,6)

First evaluate C = 3x -2 y at each of the vertices.

At (0, 10): C = 3(0) - 2(10) = -17

At (6, 0): C = 3(6) - 2(0) = 18

At ( 2,6) : C = 3(2) -2(6) = -6

At (0,9) : C = 3(0)-2(9)= -18

the maximum value occur on 18 when x=9 and y=0

Given the objective function is [tex]C=3x-2y[/tex] and the contraints as follows:

[tex]x\geq 0\\ y\geq 0\\ 2x+y\leq 10\\ 3x+2y\leq 18[/tex]

       Substitute 0 for [tex]x[/tex] in [tex]2x+y=10[/tex].

        [tex]2(0)+y=10\\ y=10[/tex]

      So, the intersecting point is [tex](0,10)[/tex].

       Substitute 0 for [tex]y[/tex] in [tex]2x+y=10[/tex].

        [tex]2x+0=10\\ 2x=10\\ x=5[/tex]

      So, the intersecting point is [tex](5,0)[/tex].

       Substitute 0 for [tex]x[/tex] in [tex]3x+2y=18[/tex].

        [tex]3(0)+2y=18\\ 2y=18\\ y=9[/tex]

      So, the intersecting point is [tex](0,9)[/tex].

       Substitute 0 for [tex]y[/tex] in [tex]3x+2y=18[/tex].

        [tex]3x+2(0)=18\\ 3x=18\\ x=6[/tex]

      So, the intersecting point is [tex](6,0)[/tex].

        Add [tex]-2[/tex] times [tex]2x+y=10[/tex] to [tex]3x+2y=18[/tex].

        [tex]-2(2x+y)+3x+2y=-2(10)+18\\ -4x-2y+3x+2y=-20+18\\ -x=-2\\ x=2[/tex]

       Substitute [tex]x=2[/tex] in [tex]2x+y=10[/tex]:

        [tex]2(2)+y=10\\ 4+y=10\\y=6[/tex]

      So, the intersecting point is [tex](2,6)[/tex].

Corner points:

          The corner points are the boundary points of the bounded region of   the given constraints.

The bounded region of the given constraints is shown below.

Evaluate the objective function [tex]C=3x-2y[/tex]at these boundary points:

At [tex](0,0)[/tex]:

[tex]C=3(0)-2(0)\\C=0[/tex]

At [tex](5,0)[/tex]:

[tex]C=3(5)-2(0)\\C=15[/tex]

At[tex](0,9)[/tex]:

[tex]C=3(0)-2(9)\\C=-18[/tex]

At[tex](2,6)[/tex]:

[tex]C=3(2)-2(6)\\C=6-12\\C=-6[/tex]

From the above calculated values, one can notice that the maximum value of [tex]C[/tex] is 15 and it is obtained at [tex](5,0)[/tex].

Hence, the maximum value of [tex]C[/tex] is 15 occurs at the corner point [tex](5,0)[/tex].

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