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3 years ago

The equation of the line which passes through the point (0,5) and has a gradient of 4 is

Mathematics

1 answer:

const2013 [10]3 years ago

6 0

Answer:

y = 4x + 5

Step-by-step explanation:

slope = m = 4

y-intercept = b = 5

y = mx + b

y = 4x + 5

You might be interested in

Which expression represents the phrase 17 less than three times a number

Mila [183]

This is an algebra expression. What we do is write it down in simplest form.

1. Write down equation

= 17 - 3 x n

= 3 x n + (-17)

I hope this answer helped. Have a great day everyone!

8 0

3 years ago

A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.35 per square foot, the

denpristay [2]

Answer:

Length = 2 ft

Width = 2 ft

Height = 5 ft

Step-by-step explanation:

Let the square base of the box has one side = x ft

Therefore, area of the base = x² ft²

Cost of the material to prepare the base = $0.35 per square feet

Cost to prepare the base = $0.35x²

Let the height of the box = y ft

Then the volume of the box = x²y ft³ = 20

$y=\frac{20}{x^{3} }$ -----(1)

Cost of the material for the sides = $0.10 per square feet

Area of the sides = 4xy

Cost to prepare the sides of the box = $0.10 × 4xy

= $0.40xy

Cost of the material to prepare the top = $0.15 per square feet

Cost to prepare the top = $0.15x²

Total cost of the box = 0.35x² + 0.40xy + 0.15x²

From equation (1),

Total cost $C=0.35x^{2}+(0.40x)\times \frac{20}{x^{2} }+0.15x^{2}$

$C=0.35x^{2}+\frac{8}{x}+0.15x^{2}$

$C=0.5x^{2}+\frac{8}{x}$

Now we take the derivative of C with respect to x and equate it to zero,

$C'=0.5(2x)-\frac{8}{x^{2}}$ = 0

$x-\frac{8}{x^{2}}=0$

$x=\frac{8}{x^{2} }$

$x^{3}=8$

x = 2 ft.

From equation (1),

$(2)^{2}y=20$

4y = 20

y = 5 ft

Therefore, Length and width of the box should be 2 ft and height of the box should be 5 ft for the minimum cost to construct the rectangular box.

8 0

3 years ago

Homework help...Last question: Estimate the product of 15.217 × 9.54. Round each number to the nearest whole number.

neonofarm [45]

I rounded it to 150.

You could round 15.217 down to 15 and 9.54 up to 10 and then multiply 15 x 10 = 150. But you could also multiply 15.217 x 9.54 to get 145.17018 and round that up to 150 because any number that ends with 5 or higher rounds up.

7 0

3 years ago

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. which expression represents the pro

schepotkina [342]

The probability expression is $\frac{^{6}C_2}{^{20}C_2}$

<h3>How to determine the probability expression?</h3>

The given parameters are

Sophomore = 6
Freshmen = 14

The total number of people is

n = 20

2 of the 20 people are to be selected.

So, the number of selection is

$n = ^nC_r$

This gives

$n = ^{20}C_2$

The expression that represents both students being sophomore is

$n = ^{6}C_2$ --- i.e. 2 students selected from 6

The probability is then represented as:

$\frac{^{6}C_2}{^{20}C_2}$

Hence, the probability expression is $\frac{^{6}C_2}{^{20}C_2}$