You need 35 black tiles and 28 white tiles to tile a patio. How many
tiles will you need in all? Use the Distributive Property to help you
find the sum.

Answer:

no

Step-by-step explanation:

a natural number has to be a whole number

Each of Tasha's friends receives one-quarter (¼) of the whole snack after she eats half and divides the remainder equally between them.

To determine what portion of the whole snack each of Tasha's two best friends gets, let's first understand the portions.

Tasha eats half of the snack, leaving the other half to be shared equally between her two friends.

Since there are two friends, the remaining half is divided into two equal parts.

Mathematically, when the remaining half (½) of the snack is divided equally among two people, this half is further divided by 2, which is the same as multiplying by ½ (since dividing by a number is the same as multiplying by its reciprocal).

So, the calculation would be ½ (remaining portion) × ½ (each friend's share) = ¼.

Therefore, each of Tasha's friends gets one-quarter (¼) of the whole snack.

We can visualize this through a drawing not included here, but imagine a circle (representing the snack) divided into 4 equal parts. Tasha eats 2 parts (half), and each friend gets 1 part (one-quarter).

The portion of the whole snack each friend gets is 1/4

What portion of the whole snack does each friend get?

From the question, we have the following parameters that can be used in our computation:

Proportion eaten = 1/2

Proportion to friends = 1/2

There are  2 friends

So, the portion of the whole snack each friend gets is

Each friend = 1/2 ÷ 2

Rewrite as

Each friend = 1/2 * 1/2

Evaluate

Each friend = 1/4

Hence, the portion of the whole snack each friend gets is 1/4

7(x - 2) = 5(x + 4)

Multiply the first bracket by 7

(7)(x)=7x

(7)(-2)=-14

Multiply the second bracket by 5

(5)(x)=5x

(5)(4)=20

7x-14=5x+20

Move 5x to the other side. Sign changes from -5x to +5x.

7x-5x-14=5x-5x+20

7x-5x-14=20

2x-14=20

2x-14+14=20+14

2x=34

Divide both sides by 2

2x/2=34/2

Answer: x=17

Answer:

7(x-2)=5(x+4)

7x-14=5x+20

7x-5x=20+14

2x=34

x=17

Answer:

The number 24 is called the dividend ('that which is to be divided'). The number 8 is called the divisor ('that which divides'). The number 3 is called the quotient, (from the Latin quotiens meaning 'how many times'). Division without remainder can be visualized as skip-counting.

Answer:

x = 8

Step-by-step explanation:

First distribute the -2 to (x - 4), -2 × x is -2x and -2 × -4 is 8. The equation should now look like this, -2x + 8 = -8. Then subtract the positive 8 from both sides, giving you, -2x = -16. Then divide both sides by -2 and you should get 8 as your answer.

Answer: x=8

Step-by-step explanation:

-2(x-4)=-8

divide both sides

x-4=4

move constant to the right

x=4+4

add the number

x=8

I hope it helped!

Answer:

672,800

Step-by-step explanation:

672,800 672800

Answer:

Step-by-step explanation:

[tex]\dfrac{y}{x}=a\to y=ax\\\\\text{We have}\ x=1,\ y=0.5.\\\\\text{Substitute:}\\\\a=\dfrac{0.5}{1}=0.5\\\\\text{Therefore}\ y=0.5x[/tex]

Answer:

y = 0.5x

Step-by-step explanation:

x = 1; y = 0.5; 0,5 is [tex]\frac{1}{2}[/tex] of 1

1 * 0.5 would equal 0.5

So, y = 0.5x

Hope this helps :)

Step-by-step explanation:

(3 × 10) × 8 = 3 × (10 × 8)

It's an Associative Property of addition:

(a + b) + c = a + (b + c)

Check it:

Left side: (3 × 10) × 8 = 30 × 8 = 240

Right side: 3 × (10 × 8) = 3 × 80 = 240

CORRECT

Answer:

The rocket will take 6.49 seconds to fall back to the ground

Step-by-step explanation:

* Lets explain how to solve the problem

- A rock is thrown upward from the top of  a 25 foot tower with an initial

 upward  velocity of 100 ft/sec

- That means at t = 0 the height of the rock is 25 feet above the ground

- A function of time can  be modeled by the equation:

 h(t) =  - 16t² + 100t + 25, where h is the height of the rocket from the

 ground at time t

∵ h(t) = -16t² + 100t + 25

- The height of the rocket is 25 feet above the ground when it

  is thrown up

∴ h(t) = 25 at t = 0 ⇒ initial position of the rocket

- The height of the rocket when hits the ground is zero

∴ h(t) = 0 when the rocket hits the ground ⇒ final position of it

- We need to find the time that the rocket takes to fall back to

 the ground

∵ h(t) = 0

∵ h(t) = -16t² + 100t + 25

∴ -16t² + 100t + 25 = 0

- Lets solve it to find the value of t

∵ -16t² + 100t + 25 = 0

- Multiply both sides by -1 to make the coefficient of t² positive

∴ 16t² - 100t - 25 = 0

- Use your calculator to find the values of t

∴ t = 6.49 sec and t = -0.24 sec

∵ We will reject the value of t = -0.24, because time can not be

   negative value

∴ The rocket will take 6.49 seconds to fall back to the ground

Answer:

5/8

Step-by-step explanation:

0.625

625/1000

125/200

25/40

5/8

Answer:

there are many possible answers, but some samples are 625/1000, 125/200, 25/40, and 5/8.

Step-by-step explanation:

I just turned the decimal into a fraction using a simple method where, say, if the decimal went to the thousandths place value, like this one does, we put the decimal over 1000. If the number goes to the hundredths place, we put it over 100, etc. Then I simplified it a few times (by dividing both the numerator and denominator by 5) to get some more equivalent fractions (although you could multiply upwards and get fractions like 3125/5000 which would still be equivalent because I multiplied both the numerator and denominator, though that's besides the point) and ended up with the fully simplified fraction of 5/8.

Hope this helps! :3

Answer: S+8

Step-by-step explanation:

The score increased by 8

Let S represent the score

Increased means additional

Hence the equation is

S+8

Algebraic expression:

S = Score

S+8

Increased means add 8. Then, add 8 to the score which is "S" S would be the more common variable in which you will use here.

Answer:

y = (8/5)x + 15

Step-by-step explanation:

First change the equation to standard form (y=mx+b)

5x + 8y = 16

8y = 16 - 5x

y = - (5/8)x + (16/8)

y = - (5/8)x + 2

Perpendicular Lines have the inverse opposite sign of slope

[For example: inverse opposite sign of 2 is - (1/2)]

Original equation slope (m) : - (5/8)

2nd Equation (m) : 8/5

After finding the slope, plug in the slope and points the standard form equation (y=mx+b)

Point: (-5,7)     x : -5     y : 7

Slope (m) : 8/5

y = m x + b

7 = (8/5) (-5) + b

'b' is the y-intercept and the last thing to solve for the equation

7 = - 8 + b

15 = b

Now, put the slope (m) and y-intercept (b) back into the equation

y = (8/5)x + 15

Move 5 units left and 4 units up

Final answer:

To plot the point (-5, 4) from the origin, move 5 units to the left and 4 units up in a standard Cartesian coordinate system.

Explanation:

To plot the point (-5, 4) starting from the origin in a standard Cartesian coordinate system, you would need to move 5 units left and 4 units up. This is because the x-coordinate is negative, indicating a movement to the left of the origin, and the y-coordinate is positive, indicating a movement above the origin.

The correct steps are as follows:

This method adheres to the standard convention that in an xy-coordinate system, right and up are positive directions, while left and down are negative.

[tex]\huge\boxed{\text{1. False}}[/tex]

Integers are the numbers in the set [tex]{..., -3, -2, -1, 0, 1, 2, 3, ...}[/tex]. This means that you can add two opposite integers to get [tex]0[/tex].

For example, [tex]-3+3=0[/tex].

[tex]\huge\boxed{\text{2. True}}[/tex]

When you add a negative number to another negative number, the only thing that can happen is that the result goes down.

For example, [tex](-3)+(-2)\ =\ -3-2\ =\ -5[/tex].

[tex]\huge\boxed{\text{3. 6}}[/tex]

Let's write this as an equation, where [tex]x[/tex] represents the unknown value. [tex]-6+x=0[/tex]

We need to isolate the variable by adding [tex]6[/tex] on both sides of the equation. [tex]x=\boxed{6}[/tex]

Answer:

1) false example -1+1=0

2) true

3) 6

Final answer:

Upon examining the prices of the three cars and calculating the potential original price before rounding, we find that all three cars could have a maximum price change of £49 when rounded to the nearest £100. Therefore, all cars have the same greatest potential change in price.

Explanation:

To determine which car's price changes by the greatest amount when rounded to the nearest £100, we need to consider the possible original prices before rounding. The original price could be up to £49 above or £50 below the rounded price, as values are rounded up when they reach the halfway point (£50).

Car A

Price: £12,380. Possible price range before rounding: £12,350 to £12,429.

Car B

Price: £16,760. Possible price range before rounding: £16,750 to £16,809.

Car C

Price: £14,580. Possible price range before rounding: £14,550 to £14,629.

Now, we must calculate the maximum changes in price. The greatest amount of change occurs when the original price is at the extreme end of the range.

With each car having a possible maximum change of £49, it means that all cars could potentially have the same greatest amount of change.

The total cost Abe needs to pay is the cost of one loaf, which is $2.50. Hence, the correct answer is $2.50.

Let's solve this question step by step:
Step 1: We know Abe has a coupon that allows him to buy one loaf and get the second free.
Step 2: The cost of a single loaf of bread is given as $2.50.
Step 3: As per the coupon, if Abe buys two loaves of bread, he is only required to pay for one. This means he needs to pay for one loaf only.
Step 4: Therefore, the total cost Abe needs to pay is the cost of one loaf, which is $2.50.
Hence, the correct answer is $2.50.

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Answer:

(4, 0 )

Step-by-step explanation:

A translation of 1 unit left, subtract 1 from the original x- coordinate

A translation of 2 units down, subtract 2 from the original y- coordinate

The rule is (x, y ) → (x - 1, y - 2 ), thus

(5, 2 ) → (5 - 1, 2 - 2 ) → (4, 0 )

The image point of (5,2) after a translation left 1 unit and down 2 units is (4, 0).

To find the image point of (5,2) after a translation left 1 unit and down 2 units, we need to subtract 1 from the x-coordinate and subtract 2 from the y-coordinate.

The translated image point would be (5-1, 2-2) = (4, 0).

So, the image point of (5,2) after the translation left 1 unit and down 2 units is (4, 0).

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Answer:

The value of x is [tex](+/-)\sqrt{6}[/tex]

Step-by-step explanation:

The question in English is

Find the value of x so that the distance between the given points is 2V5 units.

(2x - 1,2) and (1 + x,x + 4)

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

[tex]d=\sqrt{(x+4-2)^{2}+(1+x-2x+1)^{2}}[/tex]

[tex]d=\sqrt{(x+2)^{2}+(-x+2)^{2}}[/tex]

[tex]d=\sqrt{x^2+4x+4+x^2-4x+4}[/tex]

[tex]d=\sqrt{2x^2+8}[/tex]

Remember that

[tex]d=2\sqrt{5}\ units[/tex]

substitute

[tex]2\sqrt{5}=\sqrt{2x^2+8}[/tex]

squared both sides

[tex]20=2x^2+8\\\\2x^{2}=12\\\\x^{2}=6\\\\x=(+/-)\sqrt{6}[/tex]

therefore

The value of x is [tex](+/-)\sqrt{6}[/tex]

Answer:

The given equation not represent a proportional relationship

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have

[tex]y=\frac{2}{5}x-4[/tex]

This line not passes through the origin

Verify

For x=0

[tex]y=\frac{2}{5}(0)-4=-4[/tex]

therefore

The given equation not represent a proportional relationship

Answer:

16 pizza's

Step-by-step explanation:

you multiple 8 x 2 which is 16

Answer:

n=68

Step by step explanation:

When a number n is increased by two means n+2 so we can put parenthesis around it

(n+2)/5 = 14  

now we solve for the equation (for the variable n)

First multiply both sides by 5 to isolate the parenthesis on the left side by itself

(n+2) = 14*5

then we can simply isolate n by itself by subtracting both sides by 2

n = 70 -2 = 68

n = 68

To find the value of n when [tex]\frac{(n + 2) }{5}[/tex]  = 14,  resulting in n = 68.

The question asks to define an equation based on a described operation with a given result, and then solve it to find the value of n. The operation described is increasing a number n by two, then dividing the result by five to get a quotient of 14.

To translate this into an equation, you would set up the following equation:

[tex]\frac{(n + 2) }{5}[/tex] = 14

To find the value of n, you would first multiply both sides by 5 to isolate n on one side:

n + 2 = 70

Then, subtract 2 from both sides to solve for n:

n = 68

Therefore, the value of n is 68. This solves the equation and provides the value that n must be for the operation to result in a quotient of 14.

Answer:

[tex]\frac{x^2}{9}[/tex] - 4x + 36

Step-by-step explanation:

([tex]\frac{x}{3}[/tex] - 6)² = ([tex]\frac{x}{3}[/tex] - 6)([tex]\frac{x}{3}[/tex] - 6)

Each term in the second factor is multiplied by each term in the firs t factor, that is

[tex]\frac{x}{3}[/tex]([tex]\frac{x}{3}[/tex] - 6) - 6([tex]\frac{x}{3}[/tex] - 6)

Distribute both parenthesis

= [tex]\frac{x^2}{9}[/tex] - 2x - 2x + 36 ← collect like terms

= [tex]\frac{x^2}{9}[/tex] - 4x + 36

Answer: The smaller number is 30, the larger is 38

Step-by-step explanation:

x + (x - 8) = 68

2x - 8 = 68

2x = 60

x = 30

Answer:

The answer would be 'D'.

Step-by-step explanation:

An expression does NOT have an equal sign while a formula does. A variable is some letter symbol that you are solving for, but a constant would be a number such as 2 or 4 that could be added, multiplied, subtracted, or divided in an equation. 

I hope this helps!

Answer:

Step-by-step explanation:

a formula

Answer:

If you solved this, it wouldn't have a remainder. First you would solve the numbers in the parenthesis, (15 - 3), which is 12. Now it should look like, 12 ÷ 12 + 1. Next you divide 12 by 12 and that equals 1. And all you need to do now is add 1 + 1, which is 2. So your answer will be 2.

Answer:

2

Step-by-step explanation:

To be able to solve this equation, you would use PEMDAS. This stands for the order of operations, and which order you would do them in.  P stands for parenthesis, E stands for exponents, M stands for multiplication, D stands for division, A stands for addition, and S stands for subtraction. Using this order, you would solve what is inside the parentheses first. So, 15-3 is 12. Once this piece is solved, you would have 12÷12+1. Then, since you don't have any exponents or multiplication, you would skip to division. 12 ÷ 12 is 1. So then your equation would be: 1+1. 1+1 is equal to 2. So your answer is 2! There is not remainder in the solution of this problem.

Answer:

[tex]5811 \frac{1}{1} [/tex]

Step-by-step explanation:

You could do this.

I am joyous to assist you anytime.

The simplified equation from the given 3x + 9 + 4x + x = _x + _ is 8x + 9 = _x + _. This equation cannot be solved further without the values for the variables represented by the underscores.

The first step to solving the equation is to simplify it. Your original equation is 3x + 9 + 4x + x = _x + _. When we simplify the left side of the equation by combining like terms we get 8x + 9 = _x + _. However, the variables in the blanks on the right side of equation are unknown, so we can't solve it fully. But now you have a simpler equation to work with, and if you receive any additional information, you can substitute those values into your simplified equation.

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Answer:

29/1000

Step-by-step explanation:

Answer:

29/1,000

Step-by-step explanation: it says thousands so u put thousand at the bottom then you put 29 on top

Answer:

If x-2 is a factor of p(x) = x^{4} - 3 x^{2} + 2 x - 8 ,then p(x)  = 0

Solution:

According to factor theorem of polynomials,  

x-a is a factor of polynomial p(x), if and only p(a)=0

Step 1:

Since x-2 is factor of p(x),

x - 2 = 0

x = 2

Step 2:

[tex]p(x) = x^{4} - 3 x^{2} + 2 x - 8 ------ (equation 1)[/tex]

By substituting x = 2 in equation 1,

[tex]p(x) = 2^{4} - 3(2)^{2} + 2(2) - 8[/tex]

p(x) = 16 - 3(4 ) + 4 -8

p(x) = 16 - 12 - 4

p(x) = 16 - 16

p(x) = 0

Since x - 2 is a factor of p(x)  , we get p(x)=0

Answer:

4(a-2)+a=4a-2 No solution

Step-by-step explanation:

This  would never be true. Try plugging in a as 1.

4(1-2)+1 isn't equal to 4(1)-2.