The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and length of this rectangle?

Answer:

(-4+(-6))+(6i-2i)

(-10+4i)

Answer:

-10+4i = -2(5-2i)

Step-by-step explanation:

(-4+6i) + (-6-2i)

Collecting like terms

(-4-6) + (6i-2i)

-10+4i

-2(5-2i)

Final answer:

Nancy bought 177 long sleeve shirts and 354 short sleeve shirts for her business by solving a system of linear equations based on the provided constraints that she bought a total of 531 shirts and twice as many short sleeve shirts as long sleeve shirts.

Explanation:

The student's question involves solving a system of linear equations to find out how many of each type of shirt Nancy bought for her business. Following the given relationships between long sleeve shirts (x) and short sleeve shirts (y), we understand that Nancy bought a total of 531 shirts and that she bought twice as many short sleeve shirts as long sleeve shirts. The two equations that can represent this scenario are:

Equation 1: x + y = 531

Equation 2: y = 2x

To solve this system, we substitute Equation 2 into Equation 1 to get:

x + 2x = 531

Which simplifies to:

3x = 531

Dividing both sides by 3, we find that:

x = 531 / 3 = 177

Using the value of x to find y from Equation 2, we get:

y = 2 * 177 = 35

Therefore, Nancy bought 177 long sleeve shirts and 354 short sleeve shirts.

Answer:

i multiplied them together and the result is 19740 but in decimal it would be 19740.0

Final answer:

To simplify 15 × 1316, you multiply to get 19740, which is rounded to 19700 when limited to three significant figures.

Explanation:

To simplify the expression 15 × 1316 in decimal form, you need to perform basic multiplication. Multiplying 15 times 1316 gives you a result of 19740.

However, to express this answer in terms of significant figures, specifically limiting to three significant figures, you would round this number to 19700, as the number 740 does not contribute to the first three significant digits.

$ 2772 is paid in state income tax

Solution:

Given that, Tina lives in a state that charges her 4.5% state income tax on her federal taxable income

Federal taxable income = $61,600

To find: Amount paid by Tina in state income tax

Tax rate = 4.5 %

Which means, 4.5 % of $61,600 is paid as tax

[tex]Tax\ Rate = 4.5 \% \text{ of } 61600[/tex]

Here, "of" means multiplication or product

[tex]Tax\ Rate = 4.5 \% \times 61600\\\\Tax\ Rate = \frac{4.5}{100} \times 61600\\\\Tax\ Rate = 0.045 \times 61600\\\\Tax\ Rate = 2772[/tex]

Thus $ 2772 is paid in state income tax

4.5% of 61,600

0.045(61,600) = 2772

Your score in the game is 305 points.

Step-by-step explanation:

Given,

Expression used for score = p + 3b

p = game points

b = triple bonus points

Game points earned by you = p = 245 games point

Triple bonus points = b = 20

Putting these values in given expression

Total points = [tex]245+3*20[/tex]

Total points = [tex]245+60[/tex]

Total points = 305 points

Your score in the game is 305 points.

Keywords: addition, expression

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Answer:

d

Step-by-step explanation:

since since the scale factor is 3 angle ab abyou multiply 6 * 3 to get 18

The length of the Side EF is 18.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

Given that  corresponding sides are AB and EF, and EF is a side of the larger (second) triangle.

scale factor 3 means each length of the second is 3 times as long as the first.

Therefore, the length of the side EF when the length of side AB is 6 units is,

EF = 3 x AB

     = 3 x 6 units

     = 18 units.

Therefore, Side EF is 18.

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Answer:

37750

Step-by-step explanation:

Answer:

D. Less than $100,831

Step-by-step explanation:

There is an equation for calculating monthly payment:

x = p • r • (1+r)^n / (1+r)^n - 1

It may seem a bit complicated, but let's explain it step by step:

- p is the amount of loan, in this case $155,000

- r is monthly interest rate, in this case (4.4/12) / 100, which is 0.00367

- n is the number of months for paying back, or in this case 20 • 12 = 240

Now that we know all the values, all that's left is to plug them in and solve it on the calculator:

x = 155,000 • 0.00367 • (1.00367^240) / (1.00367^240) - 1

x = $972.27

So, the monthly payment is around $972.3. We now multiply it by the number of months to get total payment:

$973.3 • 240 = $233,352

So, the total amount, loan plus interest, is 233,352 dollars.

To only find amount of interest, we simply subtract loan from total amount:

$233,352 - $155,000 = $78,352

Answer: 0.3125

Step-by-step explanation:

Convert the fraction to a decimal by dividing the numerator by the denominator.

Elmer's bank contained coins totaling $1.37, calculated by summing the value of each type of coin separately.

To find the total value of the coins in Elmer's bank, we need to calculate the value of each type of coin separately and then sum them up. The value of coins is counted based on their denomination, with pennies being worth 1 cent, nickels 5 cents, dimes 10 cents, and quarters 25 cents.

Adding these amounts gives us a total value of 17 + 20 + 50 + 50 = 137 cents. Therefore, the value of the coins in Elmer's bank is $1.37.

The value of the coins in Elmer's bank is $2.17.

17 pennies = $0.17

4 nickels = $0.20

5 dimes = $0.50

2 quarters = $0.50

Adding these amounts together: $0.17 + $0.20 + $0.50 + $0.50 = $2.17.

Answer:

Step-by-step explanation:

y = mx + b

slope(m) = 1/9

y int (b) = 8.....or (0,8)

y = 1/9x + 8.....this is ur equation

ur x intercept is : (can be found by subbing in 0 for y

0 = 1/9x + 8

-1/9x = 8

x = 8 * -9

x = - 72....or (-72,0)

The equation of line is y = ( 1/9 )x + 8

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is given by

The slope of the line m = 1/9

So , Slope m = 1/9

The point on the line is given by P = P ( 0 , 8 )

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = ( 1/9 ) ( x - 0 )

y - 8 = ( 1/9 ) x

On simplifying the equation , we get

Adding 8 on both sides of the equation , we get

y = ( 1/9 )x + 8

Therefore , the value of A is y = ( 1/9 )x + 8

Hence , The equation of line is y = ( 1/9 )x + 8

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Answer:

The height is 6 units.

The radius is 8 units.

The volume is 128 Pi cubic units

Step-by-step explanation:

The height is 6 units.

Use Pythagorean Theorem to find the radius.

6² + x² = 10²

36 + x² = 100

-36           -36

x² = 64

x = 8

V = πr²h/3

V = π(8)²6/3

V = π(64)2

V = 128π

Answer:

6,8,128

Step-by-step explanation:

Answer:

Step-by-step explanation:30x-18

Answer: 141

Step-by-step explanation:

23 1/2 *6=141

Answer:

30240

Step-by-step explanation:

There are two primary ways to approach this problem - the logical and the mathematical.

The logical way is very simple:

Since you know that there are 5 digits and each must be different, start with the first digit and work your way up.

The first digit can be any of 10 digits (0–9).

However, the second digit can be any of only 9 digits as 1 digit has already been used and cannot be repeated.

Similarly, applying the same logic, there are only 8 options for the third digit, 7 for the fourth digit, and 6 for the fifth and final digit.

Now, multiply all these numbers together to get the total number of configurations like so:

10⋅9⋅8⋅7⋅6=30240

The more mathematically inclined way requires the use of a special formula. Since in this particular scenario, the order of the numbers matter, we can use the Permutation Formula:

P(n,r)=n!(n−r)!

where n is the number of numbers in the set and r

is the subset.

Since there are 10 digits to choose from, we can assume that n=10

.

Similarly, since there are 5 numbers that need to be chosen out of the ten, we can assume that r=5

.

Now, plug these values into the formula and solve:

=10!(10−5)!

=10!5!

=10⋅9⋅8⋅7⋅6

=30240

Answer: 7cm

Step-by-step explanation:

Answer: the answer is 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

5(3m + n) = 15m + 5n

Final answer:

The expression equivalent to 5(3m + n) is found by applying the distributive property, resulting in 15m + 5n, where the 5 is multiplied by each term inside the parentheses.

Explanation:

The expression 5(3m + n) is an example of the distributive property in algebra. To find an expression equivalent to this, we need to distribute the 5 across the terms inside the parentheses. This means we multiply 5 by each term inside the parentheses.

Putting these two results together, the equivalent expression is 15m + 5n. This is a straightforward application of the distributive property, which is a fundamental concept in algebra.

Answer:

1.85 %

Explanation:

APR refers to the "Annual Percentage Rate." This refers to the rate that is being charged to the borrower on a yearly basis.

It is very easy to get the monthly percentage rate once you know the APR. All you have to do is to divide the APR by the total number of months.

In the situation above, we just have to divide the APR of 22.2% by 12 (number of months on one year).

Answer:

Answer:

The True statements are:

The sphere has a diameter of 32 in.

The radius’s length is one-half the length of the diameter.

The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.

Step-by-step explanation:

      This is false because a radius is half of a diameter. Half of      the given diameter of 8 in is 4 in whereas the radius in the question is 16 in.

        This is false because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.

This is True because a radius is half of a diameter. Half of the given diameter of 32 in is 16 in and  the radius in the question is also 16 in.

This is True because a radius is half of a diameter

This is True because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.

It is the radius’s length that is one-half the length of the diameter

Use the basic kinematic equation of

Final velocity = initial velocity + acceleration * time (shown in image)

simply plug the numbers in to get

Velocity(final) = 0 + -9.80 m/s^2 * 1.55 s

to give us

-15.19 m/s for our final velocity

Answer:

7.50*35=262.50

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

Answer:

x = 12

Add 6 to both sides, simplify then subtract x from both sides

Question:

Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each did she sell

Answer:

The number of small cups of lemonades  is 98

The number of Large cups of lemonades is 57

Step-by-step explanation:

Given:

Cost of small lemonade  cups = $1.25

Cost of large Lemonade cups =  $2.50

Total number of lemonade cups  = 155 cups

The total cost for which the lemonade is sold =  $265

To Find:

Number of each types of lemonade sold = ?

Solution:

Let the number of small cups of lemonade sold be x

the number of large cups of lemonade sold be y

Then according to the question,

x+y = 155-----------------------------(1)

Then the amount earned by  selling small and large lemonade cups is $265

Then

1.25x+2.50y = 265------------------(2)

From (1)

y = 155-x----------------------------------(3)

Substituting (3) in (2), we get

1.25x+ (155-x)2.50 = 265

1.25 + (387.5 -2.50x) =265

-1.25x + 387.5 = 265

-1.25x= 265 -387.5

-1.25x =  -122.5

[tex]x = \frac{-122.5}{-1.25}[/tex]

x= 98--------------------------------(4)

Substituting (4) in (3)

y = 155-98

y =57

Solving e²ˣ + 3eˣ- 18 = 0 involves substituting y = ex to transform it into a quadratic equation. Solving this quadratic equation yields a valid solution, y = 3, leading to x = ln(3). Therefore, the solution is x = ln(3).

To solve the equation e²ˣ + 3eˣ- 18, we perform a substitution to convert it into a quadratic form.

Let y =eˣ. Then the equation becomes:

This gives us two solutions for y:

Since y = eˣ, and eˣ must be positive:

Finally, solve for x:

Therefore, the solution to the equation e²ˣ + 3eˣ- 18 = 0  is x = ln(3).

The correct equation of the new line parallel to y = 3x + 2 and passing through (1, 6) is y = 3x + 3.

To find the equation of the line that is parallel to the given line y = 3x + 2 and passes through the point (1, 6), we first need to acknowledge that parallel lines have the same slope.

Therefore, the slope of the new line will also be 3. We can use the point-slope form of the equation y - y1 = m(x - x1) to find the equation. Substituting the given point into the equation, we get y - 6 = 3(x - 1).

Simplifying the equation, we find y = 3x + 3. So, the equation of the line that is parallel to the original line and passes through the given point is y = 3x + 3.

Answer:

115

Step-by-step explanation:

a + s = 345

s = 2a

a + 2a = 345

3a = 345

a = 345/3

a = 115 <===== adult tickets

s = 2a

s = 2(115)

s = 230......student tickets

Answer:

yes

Step-by-step explanation

because it is an algebraic expression. 3a + a are called like terms because they both contain the same letter. To simplify an expression we collect together like terms. You can only add or subtract when the letters are the same.