Factorise. 5a² - 10a​

Answer:

Line 1 : y = -2x - 5

Line 2 : y = -3x + 3

Step-by-step explanation:

note the slope, and then note the y intercept

Answer:

y = - 2x - 5 and y = - 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = - 2, - 1) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line

m = [tex]\frac{-5-(-1)}{0-(-2)}[/tex] = [tex]\frac{x- 5+1}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

The line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = - 2x - 5 ← equation of line 1

Repeat with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 0) ← 2 points on line 2

m = [tex]\frac{0-3}{1-0}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

The line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - 3x + 3 ← equation of Line 2

Answer:

-9?????????????????????????

Step-by-step explanation:

Answer:

x-12

Step-by-step explanation:

let us say that the other number is n. then we have n+12=x or n=12-x

Answer:Answered 2 years ago. The total of the sum of the measures of any triangle has been proven to be 180 degrees. If the ratio of angle measure is 1:3:6.

Step-by-step explanation:

Answer:

1: 18 3: 54 6: 108

Step-by-step explanation:

A triangle has 180 degrees.

You need to add up all the ratios 1+3+6

Then divide that by 180----> 180/10=18

Then multiply all the ratios by but answer(18)

1*18=18

3*18=54

6*18=108

Answer:

The right answer is 32

Step-by-step explanation:

3/4 × 32 = 24

Answer:

18

Step-by-step explanation:

divide 24 by 4 which gives you 6. Multiply 6 by 3 which gives you 18 or (3÷4) × 24 = 18

Answer:

x=\frac{0.48+\sqrt{0.0768}}{0.0096},\:x=\frac{0.48-\sqrt{0.0768}}{0.0096}

Step-by-step explanation:

(x-50)^2 is x^2+2500-100x*.0048 is .0048x. 2500*0.0048 is 12, and -100*0.0048=-.48.

So, we have .0048x^2+12-.48x+6, which is

.0048x^2+18-.48x=10. USing the quadratic formula, we get

x=\frac{0.48+\sqrt{0.0768}}{0.0096},\:x=\frac{0.48-\sqrt{0.0768}}{0.0096}

(Enter into symbolab.com to see theanswer)

Answer:

600,000 cm²

Step-by-step explanation:

We know the conversion from meters to centimeters to be

1 m = 100 cm.

We need the conversion factor from square meters to square centimeters.

Start with

1 m = 100 cm

Square both sides.

(1 m)² = (100 cm)²

1 m² = 10,000 cm²

Now that we have the correct conversion factor from m² to cm², we can do the conversion of 60 m² into cm².

60 m² × (10,000 cm²)/(1 m²) = 600,000 cm²

Answer:

_16,-13,-9,0

Step-by-step explanation:

hope this helps u out!!

Answer:

Where's the question?

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

[tex]\frac{2}{15}[/tex] = 40

[tex]\frac{2}{15}[/tex] ÷ [tex]\frac{2}{1}[/tex] = [tex]\frac{1}{15}[/tex]

40 ÷ [tex]\frac{2}{1}[/tex] = 20

Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Step-by-step explanation: Hope it helps!!!!

Answer:

  a) b^3

  b) x^3

Step-by-step explanation:

It can be helpful to think of the exponent as specifying the number of times the base is a factor in the product. Of course, common factors in the numerator and denominator cancel.

  [tex]\dfrac{b^7}{b^4}=\dfrac{b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b}{b\cdot b\cdot b\cdot b}=b\cdot b\cdot b=b^{7-4}=\boxed{b^3}[/tex]

__

  [tex]\dfrac{x\cdot x^5}{x^2\cdot x}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=x\cdot x\cdot x=x^{6-3}=\boxed{x^3}[/tex]

Answer:

B and D

Step-by-step explanation

Answer:

D

Step-by-step explanation:

Answer:

11/20

Step-by-step explanation:

Answer:

$ 68 $ 58

Step-by-step explanation:

I'm not sure answer is $ 68 $ 58

Answer:

first one is -3/4a^3b^2

Step-by-step explanation:

i dont know the second one and i need help on that one too im sorry

The monomial of the functions are;

1. - 3/4 a³b²

2. - 0.1 aⁿ⁺¹

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

the expression are;

1. - 27/64 a⁹b⁶

2. - 0.001 a³n³ⁿ⁺³

Now,

Solve the expression as;

1. - 27/64 a⁹b⁶

Take cube root, we get;

∛- 27/64 a⁹b⁶ = ∛ - 3 × - 3 × - 3/4×4×4 a³a³a³ b²b²b²

                     = - 3/4 a³b²

And,  - 0.001 a³n³ⁿ⁺³

∛ - 0.001 a³n³ⁿ⁺³ = ∛-0.1×0.1×0.1 aⁿ⁺¹ aⁿ⁺¹ aⁿ⁺¹

                         = - 0.1 aⁿ⁺¹

Thus, The monomial of the functions are;

1. - 3/4 a³b²

2. - 0.1 aⁿ⁺¹

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Answer:

The surface area of the given triangular prism = 920 square cm.

In the given triangular prism

S1 = 25 cm

S2 = 25 cm

S3 = 14 cm = base

Height = 24 cm

length = 10 cm

Perimeter = S1 + S2+ S3

                 = 25+25+14

                 = 64 cm

Area of base =  length x base

                      = 10x14

                       = 140 square cm

Since we know that,

Surface area of triangular prism = (Perimeter × Length) + (2 × Base Area)

                                                     = (64x10) + 2x140

                                                     = 640 + 280

                                                     = 920 square cm

Hence,

The required surface area =  920 square cm.

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Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.

Given monthly income of Ron is $3,142.23

Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.

Total amount he contribute in 40 years paying 5.5% compounded monthly is given by

interest rate(r) = 0.055/12

time period = 40 years = 480 months

Principal amount = $314.223

Future value = [tex]P(\frac{(1+r)^{n}-1 }{r} )[/tex]

Substitute, we get,

= 3142.23 [tex].10(\frac{(1+\frac{0.055)^{12.40}-1) }{12} }{\frac{0.055}{12} }[/tex]

Thus, future value is $547074.681009.

After retirement his monthly income when he has $547074.681009 amount.

P = (A.i/2)/(1-(1+i/12)⁻ⁿ)

Putting values, we get,

P = (547074.68×0.55/12)/1-(1+0.055/12)⁻²⁴⁰

P = $3763.25

He will receive a monthly income of $3763.25.

But  given he will need a monthly income of $4,123 for 20 years, which is not met by Ron.

So, the amount he needs to supplement his monthly income when he retires by (4123-3763.25)= $359.74

Hence, Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

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Answer:

2nd option is correct

.........................

Answer:

1 1/9 ft^3

Step-by-step explanation:

5/3*1*2/3=10/9*1=10/9

10/9=1 1/9

Answer:

$31.92

Step-by-step explanation:

28.50 x .12 = 3.42

3.42 + 28.50 = $31.92

The total cost is thirty-one dollars and ninety-two cents, which includes a tip of three dollars and forty-two cents. Here’s one way to find these amounts.

Let’s set up a proportion. We can substitute the amounts we know into the proportion.  

Now, we cross multiply. Amount of tip times one hundred equals twenty-eight dollars and fifty cents times twelve.  

Then, we divide both sides of the equation by one hundred. The total cost is the food cost plus the amount of the tip. So, the total cost of the meal is thirty-one dollars and ninety-two cents.

Answer: y = -66x + 201

Step-by-step explanation:

Use rounding to get -6(0.2), and then multiply.

Use compatible numbers, such as -6(0.5), and then multiply.

Use front-end estimation to get -6(0.2), and then multiply.

Estimate -6.1(0.22)

Answer:

Use rounding to get -6(0.2), and then multiply.

Use front-end estimation to get -6(0.2), and then multiply.

Round the factors to the nearest whole number, and then multiply.

Step-by-step explanation:

Actual answer:

-6.1(0.22) = -1.342

Estimate answer:

-6 (.2) = 1.2

Answer:

A B D

Step-by-step explanation:

A family-wise inflation of error rate is the increase in the probability that one or more results of a numerous, independently (separately) conducted statistical analyses to become statistically significant, but these results can actually be attributed to random variation or measurement error.

In Statistics, a family-wise inflation of error rate is also referred to as family-wise error rate (FWER) and it can be defined as the probability of making at least one false conclusion or type I errors in numerous, separate statistical analyses or hypothesis tests.

Hence, a family-wise inflation of error rate increases the probability that one or more of the results among groups within an independent data set to be statistically significant, especially due to random variation or measurement error.

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Answer:

$243

Step-by-step explanation:

Answer:

0 us the answer for this question

Answer:

3.0233088 x 10 raise to power 7

Answer:

A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F

B) [tex]f(x)=-0.4x+88[/tex]

Step-by-step explanation:

A)

In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.

So we have:

x = minutes after the air conditioner started to cool the house

f(x) = temperature

Here we want to find what is the meaning of

[tex]f(30)=76[/tex]

Which implies that:

[tex]x=30[/tex], which means that 30 minutes have passed after the conditioner has started to cool the house

[tex]f(x)=76[/tex], which means that the temperature of the room at that time is 76°F

So, the interpretation of f(30) =76 is that:

"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"

B)

Here we want to write explicitly a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.

We know the following information:

- At time x = 0, the temperature inside the house is 88°F

- At time x = 30 min, the temperature inside the house is 76°F

We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:

[tex]f(x)=mx+q[/tex]

where

[tex]q[/tex] is the value of the temperature at x = 0, so q = 88

m is the rate of change of the temperature

The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:

[tex]m=\frac{76-88}{30-0} =-0.4[/tex]

which means that the temperature decreases by 0.4°F every minute. So, the function can be written as

[tex]f(x)=-0.4x+88[/tex]

Answer: y=-1/4x+4

Step-by-step explanation:

slope goes down 1, and right 4 so it's -1/4. Y-intercept is positive 4 so it will be +4