A bus travels 36 miles in 45 minutes. enter the total numbet of miles the bus travels in 60 minuted at this rate.

Answers

Answer 1

Answer: A rate is a special ratio in which the two terms are in different units. A rate is a little bit different than the ratio, it is a special ratio. For this case, the rate would have units of miles per minutes. We calculate as follows:

rate = 36 miles / 45 min = 0.8 miles per min
distance traveled = 0.8 miles per min ( 60 min ) = 48 miles

Hope this answers the question. Have a nice day.

Answer 2

Answer:

0.8 miles per minute

0.8miles/minutes/60 minutes =45 minutes

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Factor the expression 5x^3 - x^2 + 5x - 1

Answers

Hello,

5x^3-x^3+5x-1=x²(5x-1)+(5x-1)=(5x-1)(x²+1)=(5x-1)(x-i)(x+i)

$5 x^(3) - x^(2) + 5x - 1$

Group like terms
$( 5x^(2) - x^(2) ) + (5x - 1)$

Find the common factor of each term and simplify
$x^(2) (5x - 1) + 1 (5x - 1)$
$( x^(2) + 1) (5x - 1)$

Additional :-
Find the roots of each of the terms:
(i) $( x^(2) + 1)$
- using the quadratic equation ( $x = \frac{-b (+ or -) \sqrt{ b^(2) - 4ac } }{2a}$ )
- $\frac{-0 + \sqrt{0^(2 - 4(1)(1)) } }{2}$ OR $\frac{-0 - \sqrt{0^(2 - 4(1)(1)) } }{2}$
- Since the discriminant is negative ( $√(-4)$ ) [a negative number cannot be rooted] then this equation has no real roots (imaginary roots)

(ii) $5x - 1$
- Simply Solve for x
5x - 1 = 0
5x = 1
x = $(1)/(5)$

Thus the only solution this has or the only root this expression has is $(1)/(5)$ OR 0.2

Hi, can anyone graph y=15x+75?

Answers

Answer:

Graph

Step-by-step explanation:

The simplest way to graph a linear equation is to make an x, y chart.

Plug in values for x ( 3 values for x works ), then find the y values and graph the cordinates.

Another way to graph the above line is to identify the slope and the y-intercept. Because the function is in slope-intercept form, we can readily see both ( slope intercept form is y= mx + b where m= slope and b= y-intercept )! So b= 75 and m= 15. So to graph the y-intercept, it is ( 0, b ) and just count the slope from that point!

Final answer:

To graph the equation y = 15x + 75, start by plotting the y-intercept (0,75). Then move 15 units up and 1 to the right from the intercept. Connect the points to create the graph.

Explanation:

To graph the equation y = 15x + 75, you need to recognize it as the linear equation in slope-intercept form, y = mx + b. In this equation, m (slope) is 15 and b (y-intercept) is 75.

Start by plotting the y-intercept which is at the point (0, 75) on the y-axis. Then, from that initial point, use the slope or 'rise over run,' to find the next points. Given the slope is 15 (or 15/1), you will go up 15 units and right 1 unit from the intercept to plot your next point. Continue this process until you have enough points to produce a straight line.

By connecting these plotted points, you create the graph of y = 15x + 75.

Learn more about Graphing Linear Equations

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Write the equation of the line that passes through (3, 4) and (2, −1) in slope-intercept form.

Answers

m = (-1 - 4) /(2-3) = -5/-1 = 5

slope = 5

passing (3, 4)

y = mx + b

4 = 5(3) + b

4 = 15 + b

4 -15 = b

-11 = b or b = -11

answer:

equation

y = 5x - 11

Calculate ten minus four point three five

Answers

the answer is five point six five, 5.65

Final answer:

To calculate ten minus four point three five, you subtract 4.35 from 10. The result of this calculation is 5.65.

Explanation:

To calculate ten minus four point three five, you simply subtract 4.35 from 10. This is a basic math operation, and can be solved on a calculator or by hand. If you are performing the operation by hand, you align the numbers vertically by their decimal points and subtract normally, remembering to carry over any values from the right of the decimal point:

10.00
- 4.35
----------
5.65

So, ten minus four point three five equals 5.65.

Learn more about Subtraction here:

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The length of a rectangle is 10 feet more than the width. The area of the rectangle is 96 square feet. Find the dimensions of the rectangle. Solve algebraically.

Answers

Answer: The dimensions of the rectangle are 6ft and 16ft.

Step-by-step explanation:

Let the width of the rectangle be y

Let the length of the rectangle be y+10

Area= 96ft

Since area of a rectangle is length multiplied by width

y(y+10) = 96

y^2 +10y =96

y^2 +10y -96= 0

Solving algebraically,

y^2 +16y - 6y - 96= 0

y(y+16) - 6(y+16)= 0

(y-6)(y+16)= 0

y-6= 0

y =6ft

Recall that the width was denoted as y. That means the width is 6ft.

Since length is y+10= 6+10 = 16ft

Length is 16ft, width is 6ft.

Answer:

Dimensions of the rectangle = 16 by 6

Step-by-step explanation:

Let the length and breadth represent L and B

Hence L= B+10=------eqn 1

LB = 96 -----eqn2

From eqn1 L=B+10, it's substituted into eqn2

B(B+10)=96

B²+10B-96=0

It's now solved quadratically

B²+16B-6B-96

B(B+16)-6(B+16)=0

(B-6)(B+16)=0

B=6 and -16

Hence B=6 ft since it's the positive value

L= 96/B = 96/6 = 16 ft

Dimensions of the rectangle = 16 by 6

Dwayne is selling hamburgers and cheeseburgers. He has 100 burger buns. Each hamburger sells for $3, and each cheeseburger sells for $3.50. Which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80? h + c ≤ 80 3h + 3.5c ≤ 100 h + c ≤ 80 3h + 3.5c ≥ 100 h + c ≤ 100 3h + 3.5c ≤ 80 h + c ≤ 100 3h + 3.5c ≥ 80

Answers

Given:
hamburger = h ; sells for 3
cheeseburger = c ; sells for 3.50
100 burger buns

h + c = 100

3h + 3.5c > 80 last option.

Answer:

Its D

Step-by-step explanation:

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