Carmen sold 70 homemade lollipops. The price of each lollipop was $0.35. No sales tax was charged. Of the lollipops sold, 5/7 were grape. How much money did Carmen earn from the sale of the grape lollipops

This equation cannot be factorised, at least not easily. It would require decimals and that's not worth the time. Instead you can use the quadratic formula to solve for x, which works for any quadratic equation:

[tex]\frac{-b + or - \sqrt{b^{2} - 4ac} }{2a}[/tex]

a being the x^2 coefficient

b the x coefficient

and c the constant

here a = 21

b = -55

c = -14

let's solve this one:

You can simply input this into a calculator to find the answer, or you can work it out mentally.

= 2.852740993

Now, since this is a quadratic we need to possible values of x. So we just redo the same formula, but this time with a negative square root:

[tex]\frac{-(-55) - \sqrt{(-55)^{2} - 4(21)(-14)} }{2(21)}[/tex]

= -0.2336933736

You can round these answers however you like, but I would recommend doing to either 3 significant figures, either 2 or 3 decimal places.

Answer:

[tex]\displaystyle [7x - 2][3x - 7][/tex]

Step-by-step explanation:

Find two quantities that when summed to 55, they also multiply to 294. Those will be 6 and 49. The TINIER quantity gets the plus sign because the B-value is −55, therefore 49 gets the minus sign, leaving 6 with the plus sign. In extension, sinse we have a leading coefficient greater than one, we need to take extra procedures. Here is how it is done:

[tex]\displaystyle 21x^2 - 55x + 14 \\ \\ [21x^2 + 6x] - [49x + 14] \\ 3x[7x - 2] - 7[7x - 2] \\ \\ \boxed{[7x - 2][3x - 7]}[/tex]

I am joyous to assist you at any time.

**For all you moderatours out there, this user made a typographical errour with the symbol of the C-value. It was supposed to be 14, not −14. BELIEVE ME.

Answer: s = 12 degrees

Step-by-step explanation:

We know that the sum of angles in a triangle is 180 degrees.

So we can set up an equation to find s given that:

7s + 4s + s + 36 = 180

Combine like terms:

12s + 36 = 180

Subtract 36 from both sides:

12s = 144

Divide both sides by 12:

s = 12

It would be A.15ft

Step-by-step explanation:

Answer:

- 12

Step-by-step explanation:

2x14= 28

28-9=19

19-17=2

2- -14= - 12

Answer:

no real solutions

Step-by-step explanation:

x² + 6x + 12 = 0

the general solution :

x = (-b ±sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 6

c = 12

the discriminate is (b² - 4ac).

so,

x = (-6 ± sqrt(6² - 4×1×12))/(2×1)

the discriminate is

6² - 4×12 = 36 - 48 = -12

this is negative, so via the square root of a negative number we get 2 complex (imaginary) solutions.

Answer:

Imagine an example to make it easier. . . I guess.

Step-by-step explanation:

For example:

Molly had 1 cookie.

Leo had 2 cookies.

Leo stole Molly's cookie.

How many cookies does Leo have now?

He has 3 cookies now.

Hope I helped :D

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Answer:

Some equations are easy to solve in your head. If the numbers are easy to work with, you just have to figure out what question you need to answer. For example, to solve x + 8 = 12, you have to determine what number can be added to 8 in order to have a sum of 12. In this case, x must be equal to 4.

Other equations, however, are much harder to solve using mental math. Equations that have lots of negative numbers, large numbers, fractions, or decimals can be difficult to solve in your head. That's why there is a system, called an algorithm, for solving these equations.

An algorithm is just a step-by-step process for solving problems. The algorithm for solving equations is based on a very important property called the property of equality, which says that whatever is done to one side of the equation must also be done to the other side.

The algorithm for solving equations has four steps:

Locate the variable.

Determine what operation is being done to the variable.

Do the inverse operation on both sides of the equation.

Check your solution using substitution.

Remember that the goal of solving an equation is to determine what value of the variable will make the sentence true. This means you need to find what the variable is equal to. That's why the first step, although it may seem easy, is so important. You need to start by locating the variable in the equation. Take a look at Ondi's equation from above:

n - 1.4 = 3.7

In this case, the variable is n, and it's on the left side of the equation. That was easy! Now for the second step. Remember that the goal is to figure out what the variable is equal to when it's by itself. So in the second step, you have to identify what is being done to the variable in the equation. If you look at the equation above, you can see that 1.4 is being subtracted from n. The second step is complete!

The third step is when you actually start working with the equation. You're going to do the opposite of what is already being done to the variable. For example, if a number is added, you're going to subtract. If a number is subtracted, you're going to add. This will help you get the variable by itself on one side of the equation. Then you'll know what the variable is equal to!

In the equation, 1.4 is being subtracted from n. So you're going to do the opposite and add 1.4. Remember that the property of equality says that if you do something to one side of the equation, you must do it to the other side as well. Take a look:

n - 1.4 + 1.4 = 3.7 + 1.4

Can you see what is going to happen on the left side of the equation? Subtracting 1.4 and adding 1.4 cancel each other out, leaving you with just n. That's because subtraction and addition are inverse operations, which means they undo each other.

So the left side of the equation simplifies to the variable n. What will happen on the right side? The constants 3.7 and 1.4 will combine to give you 5.1.

n = 5.1

The fourth and final step of the algorithm is to check the solution using substitution. Substitute the value of 5.1 in for n in the original equation to see if the sentence is true:

n - 1.4 = 3.7

5.1 - 1.4 = 3.7

3.7 = 3.7

Yes! This statement is true, so the solution is correct!

Step-by-step explanation:

Hope this helped you!

Answer: 81%

Step-by-step explanation:

From the question, we are informed that a student received the following test scores: 71%, 89%, 72%,

84% and 83% in 5 tests and the student wants to maintain an average of 80%.

The lowest score/grade they can receive on the next test to maintain at least an 80% average first thus:

First, to make it easy we can remove the percent sign. Then we multiply 80 by 6 since we're calculating for 6 tests scores. This will be:

= 80 × 6

= 480

We then add all the 5 test scores. This will be:

= 71 + 89 + 72 + 84 + 83

= 399

We then subtract the values gotten. This will be:

= 480 - 399

= 81

This means the student must get at least 81%

Answer:

y=2x+1

Step-by-step explanation:

Y intercept is 1 and slope is 2/1

Answer:

The width is 8 meters.

Step-by-step explanation:

30-6=24

24/3=8

width=8 meters

The answer is 2.25, or 2 1/4

Well if Marco is spending 17.25 on 3 bags we know that six bags will just be double the 17.25 or 17.25 times two. This means that for six bags Marco will be spending $34.50 to feed his cat.

Step-by-step explanation:

let the first number be x

let the second number be y

½ of the first number= ½x

Double the second; 2*y=2y

the sum... that is ½x+2y=14

The equation that could represent this description will be (1/2)x + 2y = 14.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

Diego then says, If we take half of the first number (x) and double the second (y), the sum is 14. Then the equation is given below.

(1/2)x + 2y = 14

The equation that could represent this description will be (1/2)x + 2y = 14.

More about the conversion of sentences into equation link is given below.

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Answer:

They are congruent, the side lengths are the same. All that happened was a translation.

Step-by-step explanation:

For a figure to be congruent, it has to be the same size and shape. The size didn't change, just the position.

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Answer:

13

Step-by-step explanation:

6x2=12+13=25-15=10+3=13

Answer:

y= 2/3x -1

Step-by-step explanation:

Answer:

If the rational number is ab then, te reciprocal is ba

Step-by-step explanation:

Suppose that rational number is ab

Then, the reciprocal of that number is ba

First find slope (m):

[tex]\sf \bold{slope-formula: {\frac{y2-y1}{x2-x1} }}[/tex]

[tex]\rightarrow \sf \dfrac{9-3}{-14-7}[/tex]

[tex]\rightarrow \sf \dfrac{6}{-21}[/tex]

[tex]\rightarrow \sf -\dfrac{2}{7}[/tex]

equation:

y - y₁ = m ( x - x₁ )

[tex]\rightarrow \sf y - 3 = -\dfrac{2}{7} ( x - 7)[/tex]

[tex]\rightarrow \sf y = -\dfrac{2}{7} x +2 +3[/tex]

[tex]\rightarrow \sf y = -\dfrac{2}{7} x +5[/tex]

Answer:

A = $129,659.95

Step-by-step explanation:

the equation used for compound is  A = Pe^rt, where p= principle, r=rate(interest) e=2.71828, and t=time. first convert the rate into a decimal, then plug in the numbers into the equation.

A = 81,200.00(2.71828)^(0.036)(13)

expression: 20 - n

numbers of balloons left = total balloons - popped balloons

numbers of balloons left = 20 - n

Answer:

20 - n balloons remained

Explanation:

Finding how much balloons remained:

20 - n balloons remained.

Answer:

61.875

length 3

width 2.5

hight 8.25

Answer:

this is hard-

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I know my reflections =D

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Answer:

c

Step-by-step explanation:

Answer:

2 inches

Step-by-step explanation:

first figure is 6x12, so the length is half the width, so side g is 2 cause 1 is half of 2

Answer:

g = 2 inches

Answer: Total surface area of cuboid = 312 sq m

Step-by-step explanation:

Let the length of the cuboid be " X "

Then the breadth of it will be X/4

and the hight of it will be X × 2/3

So the volume will be

= L × B × H

= X × X ÷4 × X× 2÷3

2 X ^ 3

= --------------

12

X^3

= ------------- = 288

6

X^3 = 288 × 6 =1,728

X = cuberoot 1,728

= 12

Length 12

Breadth 12÷4 = 3

Hight 12 × 2 ÷3 = 8

Total surface area of cuboid

= 2 LB +2 BH +2 LH

= 2× 12× 3 + 2× 3 × 8 + 2× 12 × 8

= 312 sq m

Given that triangles RAM and PQR are similar triangles, therefore, the measure of PR is: 16 cm.

The sides of triangles that are similar to each other have proportional measures.

Given:

Thus:

AM/QP = RM/PR

Substitute

18/12 = 24/PR

PR = (24 × 12)/18

PR = 16 cm

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The height of the building at which 39 ft long ladder was hold is 23.6 ft or 24 ft.

What is Pythagoras theorem?

Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples.

Here, length of ladder (Hypotenuse) is 39 ft

         distance from building (base) is 31 ft.

By Pythagoras Theorem,

[tex]Hypotenuse^{2} = perpendicular^2 + Base^2[/tex]

[tex]39^2 = P^2 + 31^2[/tex]

[tex]P^2 = 39^2 - 31^2[/tex]

[tex]P^2 = (39+31)(39-31)[/tex]

[tex]P^2 = 70 X 8[/tex]

[tex]P = \sqrt{560}[/tex]

P = 23.6 ft ≈ 24 ft.

Thus, the height of the building at which 39 ft long ladder was hold is 23.6 ft or 24 ft.

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The selection of the 5-digit number illustrates arrangements

There are 1875 different numbers greater than 50000

The digits of the 5 digit numbers are given as:

3 4 6 7 9

For the number to be greater than 50000, the first digit must be 6, 7 or 9 i.e. 3 numbers.

The other four digits can be any of the 5 numbers.

So, the count of numbers greater than 50000 is:

Count = 3 * 5 * 5 * 5 * 5

Count = 1875

Hence, there are 1875 different numbers greater than 50000

Read more about arrangements at:

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