Solve x^2=2x+3 by factoring

Juan and raj cut up a banana to put on cereal. juan puts 1/7 of the banana on his bowl of cereal, and raj puts 2/5 ​ of the banana on his bowl of cereal.

what fraction of the banana did juan and raj put on their cereal altogether?

a. 2/35 banana

b. 3/12 banana

c. 3/7 banana

d. 19/35 banana

Juan and Raj altogether put 19/35 banana

Given that, Juan and Raj cut up a banana to put on cereal

[tex]fraction\ of\ banana\ put\ by\ Juan = \frac{1}{7}\\\\fraction\ of\ banana\ put\ by\ Raj = \frac{2}{5}[/tex]

We have to find the fraction of banana put by Juan and Raj altogether

This means, we have to add both the fractions

[tex]fraction\ of\ banana\ put\ altogether = fraction\ of\ banana\ put\ by\ Juan + fraction\ of\ banana\ put\ by\ Raj[/tex]

[tex]fraction\ of\ banana\ put\ altogether = \frac{1}{7} + \frac{2}{5}\\\\\text{Cross multiply to simplify }\\\\fraction\ of\ banana\ put\ altogether = \frac{1 \times 5 + 2 \times 7}{7 \times 5}\\\\fraction\ of\ banana\ put\ altogether = \frac{5+14}{35}\\\\fraction\ of\ banana\ put\ altogether = \frac{19}{35}[/tex]

Thus they put [tex]\frac{19}{35}[/tex] of banana by Juan and Raj altogether

The equation of the line that is parallel to given line is 12x + 3y = -1

Solution:

Given that, the line that is parallel to y = –4x + 3 and has a y-intercept of -1/3

Given equation of line is:

y = -4x + 3

Let us first find the slope of line

The equation of line in slope intercept form is given as:

y = mx + c ------- eqn 1

Where, "m" is the slope and "c" is the y intercept

On comparing the above slope intercept form with given equation of line, we get m = -4

Thus the slope of line with equation y = -4x + 3 is -4

We have to find the slope of line that is parallel to above line

We know that slopes of parallel lines are equal

Therefore, slope of line passing parallel to given line is -4

Now find the equation of line

[tex]\text{Substitute } m = -4 \text{ and } c = \frac{-1}{3} \text{ in eqn 1 }[/tex]

[tex]y = -4x -\frac{1}{3}\\\\3y = -12x -1\\\\12x + 3y = -1[/tex]

Thus the equation of line is found

Answer:

$2.26

Step-by-step explanation:

6 ice cream cones means the price is 6 time as much as on cone so divide by 6.

$14.58                       total

   /6                           number of cones

$2.43                        cost of a single cone

now, we remove the $0.17 tax

$2.43

-$ .17

$2.26

Answer:

226 cent

Step-by-step explanation:

Let x represent the price of a single cone

   6×(x+17) = 1458

⇔ x+17 = 1458/6 =1 458÷6 = 243

⇔ x = 243 - 17 = 226

Step-by-step explanation:

A bag of calories=1,596

calories in each serving of corn chips=?

1,596/12=133

"133 calories are present in each serving of corn chips."

Each serving of corn chips contains 133 calories.

To find the number of calories in each serving of corn chips, we need to divide the total number of calories in the bag by the number of servings.

Calories per serving= Number of servings/Total calories in the bag

​Calories per serving= 12servings/1,596calories= 133

In conclusion each serving of the corn chips contributes 133 calories to the overall caloric content of the bag.

This calculation allows you to find the caloric content per serving, providing a helpful metric for individuals managing their calorie intake.

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2y + 4 is the expression for twice a number y increased by 4

Solution:

Given statement is:

Twice a number y increased by 4

Let us convert the given statement into algebraic expression

Let the number be "y"

In the given statement,

Twice a number means "y" is multiplied by 2

"Twice a number" is translated as 2y

Also,

"Increased by" means added, Which means 2y is added to 4

Therefore,

Twice a number y increased by 4 is translated as 2y + 4

Thus the final equation becomes: 2y + 4

Answer:

132 ft squared

Step-by-step explanation:

One way is to divide the shape into a rectangle and a triangle, by drawing a vertical line.

This gives a rectangle that is 9 by 11, so has area 99.

The triangle has a base of 11 and height of 15 - 9 = 6.

So the area of the triangle = 1/2 x b x h = 1/2 x 11 x 6 = 33

So the total area is 99 + 33 = 132.

Answer:

x = 6

y = 0

Explanation:

−2x+y=−12;3y−2x=−12

Rewrite equations:

−2x+y=−12;−2x+3y=−12

Solve −2x+y=−12 for y

−2x+y=−12

−2x+y+2x=−12+2x(Add 2x to both sides)

y=2x−12

Substitute 2x−12 for y in −2x+3y=−12

−2x+3y=−12

−2x+3(2x−12)=−12

4x−36=−12 (Simplify both sides of the equation)

4x−36+36=−12+36 (Add 36 to both sides)

4x=24

Divide both sides by 4

4x / 4 = 24 / 4

x = 6

Substitute 6 for x in y=2x−12

y=2x−12

y=(2)(6)−12

y=0 (Simplify both sides of the equation)

Measure of one of the vertical angle is 156°

Solution:

The measure of angles given are (x + 104)° and 3x°.

The given angles are vertical in order.

If two lines meet at a point, then the angle formed in vertical positions are equal.

That is vertically opposite angles are equal.

⇒ 3x° = (x + 104)°

⇒ 3x° = x° + 104°

Subtract x° on both sides of the equation to equal the expression,

⇒ 3x° – x° = x° + 104° – x°

⇒ 2x° – x° = 104°

⇒ 2x° = 104°

Divide both sides of the expression by 2, we get

⇒ x° = 52°

Substitute x° = 52° in one of the vertical angle.

3x° = 3 × 52° = 156° (or)

x° + 104° = 52°+ 104° = 156°

Hence the measure of one of the vertical angle is 156°.

Answer:

Divide −56

by −8

and the answer will be 7

Step-by-step explanation:

Answer:

65% remains in the barrel

:)

Answer:

65%

Step-by-step explanation:

Answer:

None of the answers are correct, because 12/15=4/5, it's equivalent to 12 divided by 15.

Step-by-step explanation:

Answer:

Slope= -3/4

Step-by-step explanation:

Answer:

There are 8 more girls than boys.

Step-by-step explanation:

First, find how many girls and boys are in the class. Add the two parts of the ratio together, 3 and 5 to get 8. Then divide 32 by 8 to get 4. Since the total number of students in the class is 4 times the ratio of boys to girls, multiply both sides of the ratio by 4. You then get 12 boys : 20 girls. You can check this by adding 12 + 20 to get 32. Next, subtract the number of girls from the boys. 20 - 12 = 8. Therefore, there are 8 more girls than boys.

Therefore there are 8 girls more than boys

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Answer:

x= 40°

Step-by-step explanation:

Please see attached picture for full solution.

Key concepts:

- Corresponding angles are equal to each other

- The sum of the angles in a triangle add up to 180°

Step-by-step explanation:

Check out the pic, if it doesn't help you can ask me whichever part you don’t understand

Answer:

- 12

Step-by-step explanation:

The rate of change is measured by the slope m of the data

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 2) and (x₂, y₁ ) = (5, - 26) ← 2 ordered pairs from the table

m = [tex]\frac{-26+2}{5-3}[/tex] = [tex]\frac{-24}{2}[/tex] = - 12

Rate of change = - 12

Answer:

I believe the answer to this question is: X=5.

Answer:

1 1/2 hours

Step-by-step explanation:

divide 3/2 and whatever you got is your answer

Answer:

15

Step-by-step explanation:

Answer: -8z-40

Step-by-step explanation:

-4(2z+6) = -8z-24

-8z-24-12=-8z-36

-8z-36=4 (you have to move 4 to the other side of the equal sign so 4 becomes -4)

-8z-40

Answer:

z= - 5

Step-by-step explanation:

−4(2z+6)−12=4

Step 1: Simplify both sides of the equation.

−4(2z+6)−12=4(Distribute)

−8z+−24+−12=4

(−8z)+(−24+−12)=4(Combine Like Terms)

−8z−36=4

Step 2: Add 36 to both sides.

−8z−36=4

−8z=40

Step 3: Divide both sides by -8.

−8z=40

z=−5

I hope that this will help

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}}\implies \cfrac{-1+2}{3+4}\implies \cfrac{1}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{\cfrac{1}{7}}[x-\stackrel{x_1}{(-4)}]\implies y+2=\cfrac{1}{7}(x+4) \\\\\\ y+2=\cfrac{1}{7}x+\cfrac{4}{7}\implies y=\cfrac{1}{7}x+\cfrac{4}{7}-2\implies y=\cfrac{1}{7}x-\cfrac{10}{7}[/tex]

Answer:

14a + 70 + 84b

Step-by-step explanation:

Each term in the parenthesis is multiplied by 14, that is

= (14 × a) + (14 × 5) + (14 × 6b)

= 14a + 70 + 84b

The velocity of plane is 379 kilometer per hour

Solution:

Given that, plane was traveling from Florida to Canada

It flew 5 hours and went 1895 km

To find: Velcoity

The velocity can be found by dividing the distance traveled by time taken

[tex]velocity = \frac{distance}{time}[/tex]

Here in this sum,

distance = 1895 km

time = 5 hours

Substituting the values in formula,

[tex]velocity = \frac{1895}{5}\\\\velocity = 379[/tex]

Thus velocity of plane is 379 kilometer per hour

Answer:

Step-by-step explanation:

Because 4 to the power of -3 divided by 4 to the power of -1 switched (Like when there is a negative exponent you move the number or variable to the other side of the fraction) and scince both have a negative number you switch both. and 1-3 is -2 so you switch it to the bottem and put a 1 at the top.

                                         ^^Hope this helps!

The expressions equivalent to 4^-3 / 4^-1 are 1/4^2 and (4^-1)^-3.

In the subject of mathematics, the given expression is 4^-3 / 4^-1. To simplify this expression, you need to understand two rules of exponents:

Applying these two rules, 4^-3 / 4^-1 = 4^-3 * 4^1 = 4^(1 - 3) = 1/4^2.

Another way to simplify the expression is to use the rules of exponents to rewrite each part independently. 4^-3 = 1/4^3 and 4^-1 = 1/4. Therefore, 4^-3 / 4^-1 = (1/4^3) / (1/4) = 4, which is equivalent to (4^-1)^-3.

Therefore, the equivalent expressions are (B) 1/4^2 and (D) (4^-1)^-3.

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Answer:

To find out the length of AB you are trying to figure out how long it is

If B is at 45, and A is at 16

You need to figure out how far it is from 16 to 45

In order to do this the easiest way, you would go 45-16

45-16=29

AB=29

Hope this helps ;)

Answer:

first C then B

Step-by-step explanation:

The distance Raphael needs to travel goes down by time. Therefore the y-value (the amount of distance) will go down as the x-value (the amount of time) will go up. So C.

The speed of the rollercoaster is increasing as time goes by. Therefor the y-value (the speed) will go up and the x-value (the amount of time) will also go up. So B.

Time is almost always moving forward so you can almost always assume x will go up.