Rebecca took a total of 12 quizzes over the course of 3 weeks. How many weeks of school will Rebecca have to attend this quarter before she will have taken a total of 24 quizzes? Assume the relationship is directly proportional.

Answer:

12cm and 16cm

Step-by-step explanation:

The hypotenuse of the right angle triangle  = 20cm

 let the other two sides be x and y;

 The difference;

                x  = y - 4

Problem:

Find x and y;

Solution:

According to the pythagoras theorem;

    x² + y² = 20²  ------ i

       x² + y² = 400 ----- i

and  x - y = 4 ---- ii

So;   x = 4 + y

Now input the value into equation (i);

  (y + 4)² + y² = 400

   (y+4)(y+4) + y² = 400

    y² + y² + 4y + 4y + 16 = 400

    2y² + 8y + 16 = 400

    2y² + 8y + 16 -400 = 0

   2y² + 8y - 384 = 0;

      y² + 4y - 192 = 0

Factorize the equation;

  y² + 16y - 12y - 192 = 0

  y(y + 16) - 12(y + 16) = 0

  (y-12)(y + 16) = 0

     y -12 = 0 or y+ 16 = 0

     y = 12 or -16

It is not realistic for the length of a body to be a negative value, so y= 12;

   since;

    x - y = 4,

    x = 4 + 12

    x = 16

Answer:

14

Step-by-step explanation:

42-28

Answer:

first you subtract 2 from both sides

-6x>18

then you divide

-6 by 18 which is -3 and since you divided with a decimal that flips your sign so your answer is X<-3

Answer:

x<-3

Step-by-step explanation:

First, write the equation and subtract 2 on both sides.

-6x+2>20

     -2  -2

-6x>18

Divide both sides by -6.

-6x>18

/-6  /-6

x<-3

(Remember, we have to flip the sign when multiplying or diving by a negative.)

Hope this helps! Have an amazing day C:

Answer:

20% x $95 = .20 x $95 = $19.

Step-by-step explanation:

Answer:

276

Step-by-step explanation:

The minus reverses the negative too a positive then you subtract

Answer:

Guang reports a higher density of 4.5 × 10⁷ bacteria/m²

Step-by-step explanation:

Since Guang reports a density of 4500 bacteria per square centimeter and Orion reports a density of 50 bacteria per square millimeter, we convert both densities into bacteria per square meter to compare their values.

So, for Guang 4500 bacteria/cm² = 4500 bacteria/cm² × 10⁴ cm²/1 m² = 4500 × 10⁴ bacteria/m² = 4.5 × 10⁷ bacteria/m²

For Orion 50 bacteria/cm² = 50 bacteria/cm² × 10⁴ cm²/1 m² = 50 × 10⁴ bacteria/m² = 5 × 10⁵ bacteria/m²

Since 4.5 × 10⁷ bacteria/m² > 5 × 10⁵ bacteria/m², Guang reports a higher density of 4.5 × 10⁷ bacteria/m²

Answer:

B.) orion reports a higher desity than guang

Step-by-step explanation:

We found that Guang's reported density is 45 bacteria/ millimeter^2, while orion's reported density is 50 bacteria/ millimeter^2.

Answer:

Hi there!

Your answer is:

x-9y +41

Step-by-step explanation:

4x-5x+7-9y+2x+34

COMBINE LIKE TERMS!

First, X

4x-5x+2x

-1x+2x

x

x+7-9y+34

Next, whole numbers

7+34

41

x-9y +41

Answer:

product A on machine 1 would make 27 units (rounded down) 81 dollars profit.

product A on machine 2 would make 25 units (rounded down) 75 dollars profit.

product b on machine 1 would make 15 units (rounded down) 75 dollars profit.

product b on machine 2 would make 16 units (rounded down) 80 dollars profit.

Step-by-step explanation:

a1 refers to product a on machine 1

a2 refers to product a on machine 2

same rule applies for product b 1 and 2

Answer:

La cantidad de pasajeros que quedan en el avión serán [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Sabes que en el primer aeropuerto se bajan la mitad de los pasajeros, es decir que se bajan [tex]\frac{1}{2}[/tex] pasajeros, y en la segunda parada llegando a destino se bajan [tex]\frac{1}{3}[/tex] pasajeros. Entonces, la cantidad de pasajeros que se bajan en ambas paradas es la suma de la cantidad de pasajeros que se bajaron entre el primer y segundo aeropuerto:

[tex]\frac{1}{2}+\frac{1}{3}[/tex]

Lo primero que debes hacer es hayar un denominador común entre el 2 y el 3. Para eso, hallas el mínimo común múltiplo entre ambos, en este caso 6.

Luego debes multiplicar cada numerador por el número que hayas multiplicado el denominador. Para ello, dividis este mínimo común múltiplo entre el denominador inicial, y este resultado se multiplica por el numerador de esa fracción. De esta manera se obtiene:

[tex]\frac{1}{2}+\frac{1}{3}=\frac{3}{6} +\frac{2}{6}[/tex]

Finalmente se suman los numeradores y se obtiene:

[tex]\frac{1}{2}+\frac{1}{3}=\frac{5}{6}[/tex]

Considerando que 1 es un entero que representa la cantidad de total de pasajeros, para calcular la cantidad de pasajeros que quedan en el avión se realiza la sustracción:

[tex]1-\frac{5}{6}[/tex]

Resolviendo de manera similar a la suma, se obtiene:

[tex]1-\frac{5}{6}=\frac{6}{6} -\frac{5}{6}[/tex]

[tex]1-\frac{5}{6}=\frac{1}{6}[/tex]

Entonces la cantidad de pasajeros que quedan en el avión serán [tex]\frac{1}{6}[/tex]

Answer:

boom ganag

Step-by-step explanation:

Answer:

4 hours after summer leaves she will have passes zoe

Step-by-step explanation:

Answer:

C is not in scientific notation

Step-by-step explanation:

Answer:

c's not

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Answer:

well the answer is (2,-5)

Step-by-step explanation:

The answer is (2,-5) is because on a graph none of the other Coordinates Match (-3,-5).

Answer:

Step-by-step explanation:

From the given information:

Social security taxes can be calculated as:

$128,400 - $128,120

= $280

Also, we know that the current monthly salary = $13, 400

So, social security tax is withheld by $280

This implies that:

Social security taxes = 280 × 0.062

= $17.36

The medical care taxes will now be:

= $13,400 × 1.45%

= $194.30

Using the percentage method to calculate the federal income tax; we have:

Use the tax bracket from 2017, marginal tax rate = 28%

∴

federal income tax = $13400 × 0.028

federal income tax = $3752

Answer:

The cost will be $1662.136  

The total square ft of carpeting will be 231.1122ft^2    

Step-by-step explanation:

For the bedrooms,  the dimension from the image is shown as(see attahced)

Bedroom #2= 10"8' x10"4'

Bedroom #3= 10"8' x11"4'

let us convert all dimension to feet and solve for the area of the bedrooms

Bedroom #2= 10"8' x10"4'

Bedroom #2=10.67x10.33feet

Area of Bedroom #2= 110.2211ft^2

Bedroom #3 = 10"8' x11"4'

Bedroom #3 =10.67x11.33feet

Area of Bedroom #3= 120.8911ft^2

The total area of both rooms is

Total area=110.2211+120.8911

Total area=231.1122ft^2

now the cost of one square floor s $8.99

hence the cost of 231.1122ft^2 will be

Cost of carpet = 231.1122*8.99

Cost of carpet = $2,077.67

Given that, because you are a contractor, you will receive 20% off

therefore it will cost

= (20/100)*2,077.67

=0.2*2,077.67

=$415.534

The cost will now be  $2,077.67-$415.534

= $1662.136

The difference between a theorem and a conjecture :-

Theorem :- Something which is true and can be proved .

I am giving a very simple example here .

Angle sum theorem :- sum of all angles in a triangle will be equal to 180° .

This is a theorem because every interior angle of a triangle will add up to 180° . It cannot change .

So , something that is definitely true and can be proved is a theorem .

Conjecture :- Something that is supposed to be true , but still hasn't been proved to be true .

Example :-

1a = 10

2a = 20

3a = 30

With this you can guess that 4a must be equal to 40 , but it can't be proved without using algebra .

Therefore , something which is likely to be true is a conjecture ( in maths ) .

Joy makes 6.5 litres soup correct to the nearest 0.5 litres. She serves the soup in 280ml portions correct to the nearest 10ml. 22 people order this soup. Does joy definitely has enough soup to serve the 22 people.

Answer:

Yes, Joy definitely does has enough soup

Step-by-step explanation:

From the question, we know,

Joy make 6.5 litres of soup

Serves it in 280ml portions

Step 1

We convert the portions to liters

1 ml = 0.001 litre

280 ml

= 280ml × 0.001 litre/1 ml

= 0.28litre

Step 2

We divide 6.5 liters by 0.28 to find out how many people can be served

= 6.5 ÷ 0.28

= 23.2142857143 people

We can see that 6.5 liters soup can serve 23 people approximately.

Therefore, Yes, Joy definitely does has enough soup to serve 22 people

Answer:

Cost: $11.50, $13, $14.50, $16, $17.50

Step-by-step explanation:

the pizza's 10 + 1.50x

its always 10 plus the price of the toppings

(x is the amount of toppings)

Answer:

b = 2

Step-by-step explanation:

3b + 2(b - 3) = 4

--distributive property-- 2(b - 3) = 2b - 6

3b + 2b - 6 = 4

(add like terms)

5b - 6 = 4

(add 6 to both sides)

5b = 10

(divide both sides by 5 to get b alone)

b = 2

Answer: 432 ft^2

Step-by-step explanation:

See attached picture

Answer:

c≥5

Step-by-step explanation:

hope that helps :)

Answer:

x = -4

Step-by-step explanation:

x-5 = -9

Add 5 to each side

x-5+5 = -9+5

x = -4

Answer:

A. x = -4

Step-by-step explanation:

x - 5 = -9 (plus 5 on each side to get rid on 5 on the left side) so -9 + 5

x = -4

Answer:

Step-by-step explanation:

2x + 1 + 7x= -8

~2x + 7x = 9x

9x + 1 = -8

move 1 to the other side

9x = -1 -8

9x = -9

divide

X = -1

Answer:

Step-by-step explanation:

Simplifying

2x + -1 = 7x + -8

Reorder the terms:

-1 + 2x = 7x + -8

Reorder the terms:

-1 + 2x = -8 + 7x

Solving

-1 + 2x = -8 + 7x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7x' to each side of the equation.

-1 + 2x + -7x = -8 + 7x + -7x

Combine like terms: 2x + -7x = -5x

-1 + -5x = -8 + 7x + -7x

Combine like terms: 7x + -7x = 0

-1 + -5x = -8 + 0

-1 + -5x = -8

Add '1' to each side of the equation.

-1 + 1 + -5x = -8 + 1

Combine like terms: -1 + 1 = 0

0 + -5x = -8 + 1

-5x = -8 + 1

Combine like terms: -8 + 1 = -7

-5x = -7

Divide each side by '-5'.

x = 1.4

Simplifying

x = 1.4

Answer:

#1. 115

#2. 16.36

#3. 16.36

#4. 1.49

Step-by-step explanation:

#1. 180 - 65 = 115

#2. 180 ÷ 11 = 16.36

#3. 16.36

#4. 1.49

Hope this helped!

Pls Brainliest! It would mean a lot ;)!

Answer:

22 blueberry pies and 19 apple pies.

Step-by-step explanation:

This can be solved using a system of equations. Your equation for amount of pies sold is x + y = 41, with x representing apple pies and y representing blueberry pies, and 41 being the total amount of pies sold. The other equation is for the amount of dollars earned from selling the pies, which is:

12x + 14y = 536     $12 per apple pie, $14 per blueberry pie, and a total of $536.

Let's first solve for x. The new equation would be x = 41 - y. Now, we plug this equation into the second equation.

12(41 - y) + 14y = 536    Here we substituted x for the equation we made.

429 - 12y +14y = 536

-12y +14y = 44   Here we moved the 429 to the other side by subtracting it from the left and right.

2y = 44

y = 22. Now we know that there was a total of 22 blueberry pies sold. Now we plug 22 pies back into the very first equation to find x, the amount of apple pies.

x + 22 = 41

x = 19. Now we know there was a total of 19 apple pies sold.

Hope this helps!

Answer: 80 sq. ft

Step-by-step explanation:

Company A’s charges can be represented by the equation: 10m + 250

Company B’s charges can be represented by the equation: 12m + 90

To find when the square feet got which they have the same amount, I will set them equal to each other and solve for it.

10m+250=12m+90

-10m -10m

250=2m+90

-90 -90

160=2m divide both side by 2

80=m

For 80 square feet, both companies charge the same amount.