The first term of an arithmetic sequence is 4 and the tenth term is 67.
What is the common difference? Show your work or explain your answer.

The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.

Recall:

Given:

y = x + 5

2y - 2x = 10

The slope of y = x + 5 is 1.

Rewrite 2y - 2x = 10 in slope-intercept form to determine its slope.

2y - 2x = 10

2y = 2x + 10

y = x + 5

Thus, the slope of y = x + 5 (2y - 2x = 10) is also 1.

The equations representing the lines, y=x+5 and 2y-2x=10, have the same slope, therefore the lines are parallel.

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Answer:

the second

Step-by-step explanation:

Answer:

0.9 + n = 5.2

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

f(4)= -4(x+2)

f(4)= -4(6)

f(4)= -24

Answer:

F(x)=-4(x+2)

0=-4-8

4x=-8

X=-2

So,-2×2

-4

Step-by-step explanation:

Have a great day!

Answer:

About 35 or 34.27 if you round to the tenths spot.

Step-by-step explanation:

514 divided by 15 is 34.27 once rounded.

The motorcycle needs to travel 40 km, 0.42 gallons of fuel.

Given that,

A motorcycle can travel 60 miles per gallon.

We have to find,

How many gallons of fuel will the motorcycle need to travel 40 km?

According to the question,

The motorcycle travel 60 miles per gallon,

The motorcycle travels 40 km,

To convert it into kilometers 60 miles per gallon.

[tex]\rm 1 \ mile = 1.6\ k.m.\\\\60 \ miles \times 1.6 \ k.m. = 96 \ k.m.[/tex]

Therefore,

The gallons of fuel will the motorcycle need to travel 40 km is,

[tex]= \dfrac{96}{40}\\\\= 0.42[/tex]

Hence, The motorcycle needs to travel 40 km, 0.42 gallons of fuel.

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Answer:

Square roots are when you multiply the same number by itself like for example, the square root of 5 is 25, because 5*5=25

Step-by-step explanation:

The value of the root of 2√5 is approximately 2.116.

Here, we have,

To find the root of a number, you can use the concept of radicals.

The "root" refers to the inverse operation of raising a number to a power. For example, the square root (√) is the most common root, and it represents finding a number that, when squared, gives the original number.

To find the root of a number, such as the square root (√), you can use the following notation:

√(2 * √(5))

In this case, we have the square root of (2 times the square root of 5).

To simplify this expression further, we can break it down step by step:

Step 1: Simplify the square root of 5:

√(5) = 2.236 (approximately)

Step 2: Substitute the simplified value back into the original expression:

√(2 * 2.236)

Step 3: Simplify the expression:

√(4.472) = 2.116 (approximately)

Therefore, the root of 2√5 is approximately 2.116.

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Answer:

No it is not a factor of 56

Answer:

No

Step-by-step explanation:

6,12,18,24,30,36,42,48,54,60

Answer:

Step-by-step explanation:

You need to factorize each number in the set:

Common factors of both numbers are:

GCF(24, 32) = 8

Answer:

Rs. 14560

Hope you could get an idea from here.

Doubt clarification - use comment section.

In rectangle ABCD

[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]

[tex]\\ \sf{:}\longrightarrow Area=50(45)[/tex]

[tex]\\ \sf{:}\longrightarrow Area=2250m^2[/tex]

In rectangle PQRS

[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]

[tex]\\ \sf{:}\longrightarrow Area=48(43)[/tex]

[tex]\\ \sf{:}\longrightarrow Area=2064m^2[/tex]

Now

[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=Area_{(ABCD)}-Area_{(PQRS)}[/tex]

[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=2250-2064=186m^2[/tex]

Cost:-

[tex]\\ \sf{:}\longrightarrow 186(40)[/tex]

[tex]\\ \sf{:}\longrightarrow Rs 7440[/tex]

Answer:

67-63x

Step-by-step explanation:

Answer:

312.5 m

Step-by-step explanation:

let distance be d and velocity be v , then

d = kv² ← k is the constant of variation

To find k use the condition d = 112.5, v= 15

112.5 = k × 15² = 225k ( divide both sides by 225 )

0.5 = k

d = 0.5v² ← equation of variation

When v = 25 , then

d = 0.5 × 25² = 0.5 × 625 = 312.5 m

a. Ryan's rate of change is $15 per month;

Taylor's rate of change is $20 per month

b. Ryan's starting balance is $50;

Taylor's starting balance is $25.

Recall:

Ryan's Savings Plan Function:

s = 15m + 50

Thus, the starting value (starting balance) modelled by this function is $50

The slope/rate of change is $15 per month

Taylor's Savings Plan:

Given the table, the starting value will be the amount saved (initial value) at 0 number of months.

Using (0, 25) and (1, 45) find the rate of change:

In summary:

a. Ryan's rate of change is $15 per month;

Taylor's rate of change is $20 per month

b. Ryan's starting balance is $50;

Taylor's starting balance is $25.

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The equation showing the relationship between w and t is [tex]w = 4t[/tex]

From the table, we have the following points:

(0,0) and (1,4)

Start by calculating the slope (m)

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{4 -0}{1 -0}[/tex]

Simplify the numerator and the denominator

[tex]m = \frac{4}{1}[/tex]

Divide 4 by 1

[tex]m = 4[/tex]

The equation is then calculated as:

[tex]w = m(t - t_1) + w_1[/tex]

This gives

[tex]w = 4(t - 0) + 0[/tex]

Simplify

[tex]w = 4t[/tex]

Hence, the equation is [tex]w = 4t[/tex]

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Answer:

hi

Step-by-step explanation:

Answer:

She reads one page in 1.40

Answer:

23 Dimes and 8 Quarter.

Step-by-step explanation:

Important info:

31 Coins worth a total of $4.30

Note:

Dimes = .10

Quarters = .25

10 Dimes = 1.00

4 Quarter = 1.00

Question to Answer:

How many of each type of coin does she have?

Solution:

Lets get rid of the .30 cent in $4.30 so

.30 = 3 Dimes

Now $4.00,

4.00-1.00 of quarter

=

3.00 and 4 quarter..

Right now we have 3 Dimes and 4 Quarter = $1.30.

And that 7 Coins worth of $1.30.

3.00-2.00= 1.00 and 20 Dimes so now we have

23 Dimes and 4 Quarter.

And that add up to 27.

1.00-1.00 of Quarter = 4 Quarter.

so 31 worth a total of $4.30.

So that's 23 Dimes and 8 Quarter.

Check Work:

23 Dimes = $2.30 and 8 Quarter = $2.00

$2.30 + $2.00 = 4.30

Hence, The Correct Answer is 23 Dimes and 8 Quarter.

~[ RevyBreeze }~

Answer:

Step-by-step explanation:

Answer:

y=12x+3

Step-by-step explanation:

when parallel the slopes need to be the same but the y-intercept has to change

Answer: 9

Step-by-step explanation:

Answer:

9!

Step-by-step explanation:

Answer:

x=2

y=1

Step-by-step explanation:

9x+0=18

so it's x=2

6=4y=10

so y=1

Answer:

[tex]\frac{1}{4}[/tex] is larger than [tex]\frac{3}{14}[/tex]

[tex]\frac{1*14}{4*14}[/tex] = [tex]\frac{14}{56}[/tex]

[tex]\frac{3*4}{14*4}[/tex] = [tex]\frac{12}{56}[/tex]

i cant tell if it is [tex]\frac{1}{4}[/tex] or 2 [tex]\frac{1}{4}[/tex]

but if it is 2 [tex]\frac{1}{4}[/tex] that mean this is a mixed number

and [tex]\frac{3}{14}[/tex] is a proper fraction

Answer:

y = [tex]\frac{3}{3}[/tex]x - 5

y = 2x + 5

Step-by-step explanation:

In linear equations, both variables x and y must have the exponent of 1 (i.e. they cannot have a small number at the top-right). And they cannot be in the exponents (i.e. cannot be the small number at the top-right).

Answer:

The answer is C. (a + -a = 0 )

Step-by-step explanation:

"The additive inverse of a number a is the number that, when added to a, yields zero"

Step-by-step explanation:

A1

1 yard = 3 feet

1 foot = 12 inches

therefore,

100 yards = 100×3×12 inches = 3600 inches

A2

again, 1 yard = 3 feet

8 ft = 8/3 = 2.67 yards = 2 2/3 yards

A3

1 gallon = 8 pints

A4

1 liter = 1000 milliliters (remember, "mili" means 1/1000).

therefore,

2.2 liters = 2.2×1000 = 2200 milliliters

A5

again, 1 liter = 1000 milliliters

therefore

1 milliliter = 1/1000 liter

670 milliliters = 670 × 1/1000 liter = 670/1000 liter =

= 0.67 liter

B1

1 kg (kilogram) = 1000 grams ("kilo" means 1000).

we have 3 layers.

each layer weighs (cake plus icing)

1/2 kg + 100 g = 500 g + 100 g = 600 g

3 layers then weigh

3×600 g = 1800 g

the additional candle weighs 250 g.

so, the total is

1800 g + 250 g = 2050 g = 2.05 kg

B2

area is 110 m².

1 m = 100 cm ("centi" means 1/100).

and 1 m² is then 100×100 = 10000 cm².

so, the area in cm² is

110 × 10000 = 1,100,000 cm²

the top area of one brick = 10 × 20 = 200 cm²

so, we need

1,100,000 / 200 = 11,000 / 2 = 5500 bricks

Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school

Answer:

5 and 25

Step-by-step explanation:

let the son's age be x then the father's age is x + 20

In 5 years

son = x + 5 and father = x + 20 + 5 = x + 25

Then

x + 25 = 3(x + 5) ← father is three times as old as son

x + 25 = 3x + 15 ( subtract x from both sides )

25 = 2x + 15 ( subtract 15 from both sides )

10 = 2x ( divide both sides by 2 )

5 = x and x + 20 = 5 + 20 = 25

si=on is 5 and father is 25

Answer:

The son is 5 and the father is 25.

Step-by-step explanation:

We can do this using  Algebra.

Let the son be x years old.

Then the father's age is x + 20 years.

After 5 years the father's age is x + 25 and the son is x + 5 years.

So we can write the equation:

x + 25 = 3(x + 5)

x + 25 = 3x + 15

25 - 15 = 3x - x

10 = 2x

x = 5.

So the father's present age is 20 + 5 = 25 and the son is 5 years old.

Answer:

15

Step-by-step explanation:

Since, we need a number that if added to -14, it'll give a positive result. The first number is gonna be 15, . Because, it's the first number that can give a positive number if summed up with -14.