Ruby ate 1/3 of a pizza, and Angie ate 1/5 of the pizza. How much of the pizza did they eat in all?

This is an isosceles triangle. Therefore |AC| = |BC|.

2x = 3x - 5     |subtract 3x from both sides

-x = -5       |change the signs

The way I did this was made everything decimals so .75/.25 and it equals 3

The two fractions with the common denominator will be 6/ 15 and 4 / 15.

The fraction is defined as the division of the whole part into an equal number of parts.

The two fractions are 2 / 5 and 4 / 15 will be converted into the same common denominator as;-

For fraction 2 / 5 multiply it by 3 in both the numerator and the denominator.

= ( 2  x 3 ) / ( 5  x  3 )

= ( 6 / 15 )

Therefore two fractions with the common denominator will be 6/ 15 and 4 / 15.

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Ruben has 6 new books for his collection. This increases his collection by 12%

Let x be the number of books Ruben has before 6 new books added

x + 12% of x = x+6

x + 0.12x = x+6

1.12 x = x+6

Subtract x on both sides

0.12x = 6

Divide by 0.12

x = 50

6 new books are added for his collection

So 50 + 6 = 56

He have 56 books now.

x = the number of hours

write an equation of the problem: 8x + 20 = 52

subtract 20 from each side: 8x = 32

divide each side by 8: x = 4

she rented the bike for 4 hours.

The expression evaluates to -4 when x equals 4.

To evaluate the expression –0.4(3x – 2) + for [tex]\( x = 4 \)[/tex], follow these steps:

1. Substitute the value of [tex]\( x \)[/tex] into the expression.

2. Perform the arithmetic operations according to the order of operations (PEMDAS/BODMAS).

Here's the step-by-step calculation:

Given expression: [tex]\(-0.4(3x - 2) +\)[/tex]

Substitute [tex]\( x = 4 \)[/tex]:

[tex]\(-0.4(3(4) - 2) +\)[/tex]

Now, simplify inside the parentheses first:

[tex]\(-0.4(12 - 2) +\)[/tex]

[tex]\(-0.4(10) +\)[/tex]

Next, multiply [tex]\(-0.4\)[/tex] by [tex]\( 10 \)[/tex]:

[tex]\(-4 +\)[/tex]

Finally, there's no more to compute since there's no other term. So the result is:

[tex]\(-4\)[/tex]

Therefore, the value of the expression [tex]\(-0.4(3x - 2)\)[/tex] when [tex]\( x = 4 \)[/tex] is [tex]\( -4 \)[/tex].

Checking Account

it should be that

The account which is not the example of the type of savings vehicle is Checking Account. Thus option 3rd is correct.

The three kinds of the saving account are regular deposit, money market, and Certificate of Deposits. There is a difference in all the three types in terms of the accessibility and amount of interest.

The Checking account is the account which carries the day to day transactions of the money. It ensures the easy access to the money. Many of the people generally uses the debit card or the checks to make the purchases.  Thus option 3rd is correct.

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12.8 * 1.35 =17.28

Therefore Marissa spent $17.28 on potatoes.

Hey there!!

Slope-intercept form :

y = mx + b

m is the slope and b is the y-intercept.

Given equation :

x - 2y = 12

We will have to isolate the y.

... x - 2y = 12

... -2y = x - 12

... y = ( x - 12 ) / -2

... y = x / - 2 + 6

Hence, the slope is -1/2

Hope my answer helps!

Final answer:

Using the information that Ram is twice as old as Sheeta and that five years ago his age was three times the age of Sheeta, we solve the equation 2S - 5 = 3(S - 5) to find that Sheeta's current age is 10 years old.

Explanation:

The question involves creating equations based on the given information to solve for Sheeta's age. Let's denote Sheeta's age as 'S' and Ram's age as '2S' since Ram is twice as old as Sheeta. According to the second statement, five years ago Ram's age was three times Sheeta's age at that time. Therefore, we can write the equation as 2S - 5 = 3(S - 5).

Solving the equation step-by-step:

This simplifies to -S = -10

Hence, Sheeta's current age is 10 years old.

The three consecutive numbers that can be equal to 24 are 7,8,9

7+8+9=24

Answer:

37 mph

Step-by-step explanation:

if he starts at 0 then goes to 20 then add another 35 which gives you 55mph then he slows down you decrease 11 which is 44 then decrease again 7 gives you 37mph

Answer:

37 mph

Step-by-step explanation:

if he starts at 0 then goes to 20 then add another 35 which gives you 55mph then he slows down you decrease 11 which is 44 then decrease again 7 gives you 37mph

Answer:

Correct option is:

a. 6,000 ft²

Step-by-step explanation:

A pavement is 20 ft wide and 100 yd long

1 yd= 3 ft

100 yd = 300 ft

we have to find the area of pavement

Area= Length × Width

       = 300 ft × 20 ft

       = 6000 ft²

Hence, Correct option is:

a. 6,000 ft²

-2x^6 That is pertty short :)

Answer:

Density of the material is 5 grams per cubic centimeter.

Step-by-step explanation:

The answer is required to be given in grams per cubic centimeter.

So we should first convert the values to match the units.

Mass is given as 2500 grams so we don't need to change the units.

Volume is given in cubic centimeters. So we don't need to change the units.

Density      = [ Mass of the material / Volume of the Solvent]

                  =2500 grams / 500 cubic centimeters

                  =5 grams per cubic centimeter

Substitute y = x - 4 to the first equation:

-3x + 4(x - 4) = -20     use disrtibutive property

-3x + (4)(x) + (4)(-4) = -20

-3x + 4x - 16 = -20     add 16 to both sides

x = -4

Substitute the value of x yo the equation y = x - 4:

y = -4 - 4 = -8

22+5d=-8x7d=56d+ -8x-4=32

22+5d=-56d+32

22+32=54 and -56d+5d=-51d

The answer would be 51d+54

Remark

The steps are the same usually. Remove the brackets and collect like terms on each side of the equal sign.

Solution

22+5d = -8(7d - 4)          Remove the brackets.

22+5d = -56d + 32        Notice the sign change on 32. 2 minus quantities = a plus when multiplied.  Add 56d to both sides.

22 + 5d + 56d = - 56d + 56d + 32

22 + 61d = 32                  Subtract 22 from both sides.

61d = 32 - 22

61d = 10                            Divide by 51

d = 10/61

d = 0.1639  Answer

Check

LHS

22 + 5*0.1639 = 22.8197

RHS

-8(7*0.1639 - 4)

-8(1.1473 - 4)

-8(-2.8527)

22.8216    

The difference is a rounding error.

[tex]-12\leq3x-15\leq9\qquad|+15\\\\3\leq3x\leq24\qquad|:3\\\\1\leq x\leq8[/tex]

given -2(x + 1) = 5x + 4 - x ( distribute left side )

-2x - 2 = 4x + 4 ( simplifying both sides )

subtract 4x from both sides

- 6x - 2 = 4 ( add 2 to both sides )

- 6x = 6 ( variable by itself on left side )

divide both sides by - 6

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

as a check, substitute x = - 1 into the equation and if both sides are equal then it is the solution.

left side = - 2(-1 + 1 ) = - 2 × 0 = 0

right side = (5 × - 1) + 4 - (- 1) - 5 + 4 + 1 = 0

hence x = - 1 is the solution

Move the decimal until its below 10 and greater than 1:

Mercury: 3.5 x 10^7

Earth: 9.2 x 10^7

Neptune: 2.7 x 10^9

hope this helps :)

[tex]\frac{3}{4}q[/tex] - 7 = 8

     +7   +7

[tex]\frac{3}{4}q[/tex] = 15

[tex]4(\frac{3}{4}q)[/tex] = 4(15)

3q = 60

[tex]\frac{3q}{3} = \frac{60}{3}[/tex]

q = 20

Answer: q = 20

All you have to do is add 25+ 27= 52

This type of relationship is exponential decay

The answer is choice C

On the left side we have something in the form a*b+a*c+a*d

On the right side we have something in the form a*(b+c+d)

All together, we have a*b+a*c+a*d = a*(b+c+d), where the letters a,b,c,d are to be replaced with the proper values (0.5, 0.5, 0.3, and 0.2 in that exact order).

The idea of distribution is to multiply the outer value 0.5 by each of the values inside the parenthesis (0.5, 0.3, and 0.2) and add up the products.

Equation C and D that is (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) and 0+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005) ​applies the distributive property correctly as defined "multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together".

The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive property of binary operations. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication. In order to quickly solve expressions, a number is distributed among the numbers in the brackets. When using the distributive property of multiplication, for instance, to resolve the expression 4(2 + 4), we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.

The distributive property states,

A × (B + C) = AB + AC

for equation C

(0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​

for equation D,

50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005)

According to the definition of the distributive property, which states that "multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together," Equations C and D, which are correctly applied that is (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​and 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005).

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Remark

The slope intercept graph needs a table like the one provided by the graph shown below.

A sample calculation would look like this

y = (2/3)x - 2  Let x = 6 (which is not plotted on the graph).

y = 2/3 * 6 - 2   The 3 will divide into the 6 two times

y = 4 - 2

y = 2

So you would plot this as (6,2)