The area of a square garden is 98m squared. How long is the diagonal?

98 small cups of lemonade and 57 large cups of lemonade were sold by Harold.

Step-by-step explanation:

Given,

Cost of small cup of lemonade = $1.25

Cost of large cup of lemonade = $2.50

Total cups sold = 155

Total worth of cups = $265

Let,

x be the number of small cups sold

y be the number of large cups sold

According to given statement;

x+y=155      Eqn 1

1.25x+2.50y=265   Eqn 2

Multiplying Eqn 1 by 1.25

[tex]1.25(x+y=155)\\1.25x+1.25y=193.75\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](1.25x+2.50y)-(1.25x+1.25y)=265-193.75\\1.25x+2.50y-1.25x-1.25y=71.25\\1.25y=71.25[/tex]

Dividing both sides by 1.25

[tex]\frac{1.25y}{1.25}=\frac{71.25}{1.25}\\y=57[/tex]

Putting y=57 in Eqn 1

[tex]x+57=155\\x=155-57\\x=98[/tex]

98 small cups of lemonade and 57 large cups of lemonade were sold by Harold.

Keywords: linear equation, elimination method

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Answer:

x = 4

Step-by-step explanation:

from the given expression, factorise to have;

x (x - 4) = 0

Thus, X = 0 or x - 4 = 0

x - 4 = 0

x = 4

Thus, x = 0 or x = 4

Therefore the positive solution to the quadratic function is 4.

Answer:

61.375

Step-by-step explanation:

Given : [tex]\frac{491}{8}[/tex]

The fraction is not dividing by a common number in numerator and denominator to simplify, So dividing the numerator directly by 8.

Gives   [tex]\frac{491}{8}= 61.375[/tex]

So, 61.375 is the answer of the above problem.

To divide 4/5 by 1/4, multiply by the reciprocal of the second fraction to get 16/5, which converts to the mixed number 3 1/5.

To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. In the case of 4/5 divided by 1/4, you would flip 1/4 to get its reciprocal, which is 4/1, and then multiply it by 4/5.

Step-by-step:

Therefore, 4/5 divided by 1/4 as a mixed number is 3 1/5.

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Answer:

2

Step-by-step explanation:

If you do 249/89 you will get 2.79775280899

so 89 goes into 249 2 times equally

Answer:  2

Step-by-step explanation:

If you do 249/89 you will get 2.79775280899

so 89 goes into 249 2 times equally

(-2x + 5) + (5x + 3) = 5

3x + 8 = 5

3x = -3

x = -1

(Combine Like Terms)

(−2x+5x)+(5+3)=5 ----> 3x+8=5

Subtract 8 from both sides.

3x + 8 − 8 = 5 − 8 -------> 3x = − 3

Divide both sides by 3.

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

x = −1

Answer:

The surface area of the triangular prism is [tex]145.3[/tex]  [tex]ft^2[/tex]

Step-by-step explanation:

Step 1:  Finding the two area of two triangles

Area of the triangle  =  [tex]\frac{1}{2} (base \times height})[/tex]

Area of the triangle  = [tex]\frac{1}{2} (9.8\times 5.33})[/tex]

Area of the triangle  = 26.117

Area of 2 triangles  =  [tex]52.234[/tex]

Step 2: Finding the area of the side rectangles

Area of the rectangle  = [tex]length \times breadth[/tex]

Area of the rectangle  1 = [tex]6.2 \times 3.8[/tex]  = 23.56 [tex]ft^2[/tex]

Area of the rectangle  2  = [tex]8.5 \times 3.8[/tex] = 32.3 [tex]ft^2[/tex]

Area of the rectangle  3  = [tex]9.8 \times 3.8[/tex] = 37.24 [tex]ft^2[/tex]

Step 3: surface area of the triangular prism.

Surface area of the triangular prism =  52.234 + 23.56 + 32.3 + 37.24

Surface area of the triangular prism = 145.334 [tex]ft^2[/tex]

Answer:

B. 145.3 ft2

Step-by-step explanations:

Answer:

24.708

Step-by-step explanation:

Divide the perimeter by 4 to get the length of a side:

112/4= 28

Now solve for x:

X + 4 = 28

Subtract 4 from both sides:

X = 24

Answer:

[tex]\large \boxed{\$70.02}[/tex]

Step-by-step explanation:

The compound interest formula is

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

Data:

P = 300

r = 2.12 % = 0.0212

t = 10 yr

n = 1 calculation per year

1. Accrued amount:  

A = 300(1+ 0.0212)¹⁰

  = 300 × 1.0212¹⁰

  = 300 × 1.233 41

  = 370.02

2. Interest

I = A - P = 370.02 - 300.00 = 70.02

[tex]\text{The interest is $\large \boxed{\mathbf{\$70.02}}$}[/tex]

Final answer:

Using the compound interest formula, investing $300 at an annual interest rate of 2.12% compounded annually for 10 years will result in approximately $70.37 in interest, totaling $370.37.

Explanation:

A bank offers 2.12% interest compounded annually for investing money in a savings account, and you open an account with $300. How much money in interest will you earn if you leave it for 10 years?

To calculate the amount of money you will have after 10 years, including interest, you can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:

Plugging these values into the formula gives us: [tex]A = $300(1 + 0.0212/1)^{(1*10)[/tex] = [tex]$300(1 + 0.0212)^{10[/tex] = [tex]$300(1.0212)^{10.[/tex]

Calculating this, we get A = $300(1.234567), which equals approximately $370.37. Therefore, the total interest earned over 10 years is approximately $70.37.

Answer:

y = [tex]\frac{1}{2}[/tex] x - 2

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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 5) and (x₂, y₂ ) = (- 4, - 4)

m = [tex]\frac{-4+5}{-4+6}[/tex] = [tex]\frac{1}{2}[/tex], thus

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 6, - 5), then

- 5 = - 3 + c ⇒ c = - 5 + 3 = - 2

y = [tex]\frac{1}{2}[/tex] x - 2 ← equation of line

To find the equation of the line through (-6, -5) and (-4, -4), calculate the slope and then apply the point-slope form to yield the line equation y = 1/2x - 2.

The question is about finding the equation of the line that passes through two given points, (-6, -5) and (-4, -4). To do this, we first need to find the slope of the line (m) using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the points, we get m = (-4 + 5) / (-4 + 6) = 1 / 2. Next, we use the point-slope form of a linear equation, y - y1 = m(x - x1), to find the equation. Using point (-6, -5) and the slope 1/2, the equation becomes y + 5 = 1/2(x + 6). Finally, simplifying, we get y = 1/2x - 2 as the completed equation of the line.

Answer:

147.27 degrees.

Step-by-step explanation:

All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the angles, we know that the sum of all the angles is 1620 degrees (from above)... And there are eleven angles... So, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

The solution is, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

here, we have,

we know that,

All sides are the same length (congruent) and all interior angles are the same size (congruent).

To find the measure of the angles, we know that the sum of all the angles is 1620 degrees (from above)...

And there are eleven angles...

So, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

Hence, The solution is, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

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How many cups in a batch of batter??

Answer:

16 corn muffins made.

Step-by-step explanation:

Since there is 8 cups of cornmeal, and corn muffins need 1/2 cornmeal per batch. We need to divide.

Equation: 8 divided by 1/2 = M

Then in order to divide fractions. We have to use the kcf.(Keep, change, flip)

8 is 8,(Keep) division turns into multiplication(change) and then 1/2 is 2/1 (flip).

Then multiply 8 x 2.(Since 2/1 is 2)

Your answer is 16!

Answer:

12 km

Step-by-step explanation:

m = b + 8

p = 3b - 1

p = m + 15

p = m + 15....and m = b + 8....so we  are gonna sub

p = b + 8 + 15

p = b + 23

b + 23 = 3b - 1

23 + 1 = 3b - b

24 = 2b

24/2 = b

b = 12 <==== Bill ran 12 km

m = b + 8

m = 12 + 8

m = 20 km....this is what mike ran

p = m + 15

p = 20 + 15

p = 35 km....this is what pete ran

Bill ran a distance of 12 kilometers. This was determined through algebraic calculations, taking into account the given information about the distances run by Mike, Pete, and the relationships between their distances.

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Answer:

The milligrams of vitamin C in a serving of orange juice is 96 and the milligrams of vitamin C in a serving of pineapple juice is 25

Step-by-step explanation:

Let

x ----> the milligrams of vitamin C in a serving of orange juice

y ----> the milligrams of vitamin C in a serving of pineapple juice

we know that

Servings of two juices contain a total of 121 mg of vitamin C

so

[tex]x+y=121[/tex] -----> equation A

A one-cup serving of orange juice contains 4 mg less than four times the amount of vitamin C as a one cup serving of pineapple juice

so

[tex]x=4y-4[/tex] ----> equation B

substitute equation B in equation A

[tex]4y-4+y=121[/tex]

solve for y

[tex]5y=121+4\\5y=125\\y=25\ mg[/tex]

Find the value of x

[tex]x=4(25)-4=96\ mg[/tex]

therefore

The milligrams of vitamin C in a serving of orange juice is 96 and the milligrams of vitamin C in a serving of pineapple juice is 25

Answer:

6 13 15 18 22

Step-by-step explanation:

absolute value just makes it positive unless it is a negative absolute value-|n|

Answer:

-6b+21

Step-by-step explanation:

Answer:

Question 1  10 / 10 points

A summary of selected ledger accounts appear below for S. Ball for the current calendar year.

Answer questions 1 through 4 based on this information.

1. What was the total amount of withdrawals for the year?  

$6000

Question 2

2.What was the net income?

$4250

Question 3

3.What was the total revenue?

$17,000

4.What were the total expenses?

$12.750

5.

__2__  

Unearned Revenue

__5__  

Brandon Jones, Capital

__1__  

Cash

__3__  

Equipment

__4__  

Mortgage

1.  

Current Assets

2.  

Current Liabilities

3.  

Fixed Assets

4.  

Long-term Liability

5.  

Equity

Question 6  

At the end of the closing process, Income Summary will hold a balance.

Question options:

b) False

Step-by-step explanation:

I just took this quiz and got a 100%

The total amount of withdrawals for the year is $7,250.

The total amount of withdrawals for the year can be found by adding up the amounts in the S. Ball Withdrawals ledger account. Looking at the provided information, we can see that the withdrawals were as follows: $2,000 on 10/31, $4,250 on 12/31, and $1,000 on 12/22. Adding these amounts together, the total amount of withdrawals for the year is $7,250.

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Answer:

-19/20

Step-by-step explanation:

[tex]2 \frac{3}{8} \div - 2 \frac{1}{2} [/tex]

[tex] \frac{19}{8} \div - \frac{5}{2} [/tex]

Keep Change Flip

[tex] \frac{19}{8} \times - \frac{2}{5} [/tex]

[tex] - \frac{38}{40} = - \frac{19}{20} [/tex]

Angle measures are ∠M = 90° and ∠L = 24°

Step-by-step explanation:

Tangents create right angles at the point of contact with a circle.

So ∠M = 90°

⇒ ∠L = 180° - (∠M + ∠N) = 180° - (90° + 66°)

         = 180° - 156° = 24°

Answer:

m= 90 degrees and L= 24 degrees

Step-by-step explanation:

4r + 5 = 3 is not an algebraic expression because expressions are basically equations but WITHOUT answers. In this equation, 3 is shown as the answer, which makes it an equation, not an expression.

Hope this helps! Please correct me if I'm wrong! :D

4r + 5 = 3 is not an algebraic expression because it contains an equals sign making it an equation rather than an algebraic expression. Algebraic expressions are mathematical phrases lacking an equals sign.

The equation 4r + 5 = 3 is not an algebraic expression because it is, in fact, an equation. The distinction between these two lies in the presence of the equals sign (=).

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators (like +, -, ×, ÷), but it does not have an equals sign. For example, 4r + 5 is an algebraic expression. However, when there is an equals sign present, as is the case in 4r + 5 = 3, the resulting mathematical phrase is an equation, which is a statement that two algebraic expressions are equal.

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Answer:

A

Step-by-step explanation:

Final answer:

Wen Ti travels 9.2π feet in one complete spin on the outer edge of the carousel, which has a radius of 4.6ft. The correct option is A.

Explanation:

The question asks how far Wen Ti travels in one spin of the carousel, if she is on the outer edge with a radius of 4.6ft. To find this distance, we use the formula for the circumference of a circle, which is C = 2πr, where r is the radius of the circle. Plugging in the given radius of 4.6ft, we find that Wen Ti travels 2π(4.6) = 9.2π feet in one spin of the carousel.

Answer:

the answer missing length is 7.6 and yes i rounded it to the nearest tenth.

Step-by-step explanation:

Answer:

The Graph below have the same shape.Equation of the red graph

Step-by-step explanation:

The graph is shifted up 1 unit. That's equivalent to adding 1 to all points:

In other words:

G(x) = F(x) + 1

Plugging in F(x) = 3 - x^4:

G(x) = 3 - x^4 + 1

G(x) = 4 - x^4

Answer:

A. G(x) = 4 - x^4

Answer:

[tex]Guests\ attending\ the\ party\ first\ time=12[/tex]

Step-by-step explanation:

[tex]Total\ guests=48\\\\Guests\ attended\ the\ party\ last\ year=\frac{6}{8}\ of\ total\ guests\\\\Guests\ attended\ the\ party\ last\ year=\frac{6}{8}\ of\ 48\\\\Guests\ attended\ the\ party\ last\ year=\frac{6}{8}\times 48\\\\Guests\ attended\ the\ party\ last\ year=6\times 6\\\\Guests\ attended\ the\ party\ last\ year=36\\\\Guests\ attending\ the\ party\ first\ time=Total\ guests-Guests\ attended\ the\ party\ last\ year\\\\Guests\ attending\ the\ party\ first\ time=48-36\\\\[/tex]

[tex]Guests\ attending\ the\ party\ first\ time=12[/tex]

The amount of mark-up is $4.25

Step-by-step explanation:

To find the mark-up cost of each  dog collar, increase $1.19 by 356 %

Lets take that 100% = $1.19

So the 356% =?

Perform cross-product as;

(356*1.19)/100 = $4.25

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Answer:

4.25

Step-by-step explanation:

I did the quiz