Write the equation of the horizontal line given m = 0 that passes through the point (3,-2).

ANSWER

[tex]x=\sqrt{3}-1[/tex] or [tex]x=-\sqrt{3}-1[/tex]

EXPLANATION

To complete the square for [tex]x^2+2x-2=0[/tex].

We rewrite the equation to get

[tex]x^2+2x=2[/tex].

We now add [tex](1)^2[/tex] to both sides to get

[tex]x^2+2x+1^2=2+1^2[/tex].

The expression on the Left Hand Side of the equation is a perfect square.

So our equation becomes

[tex](x+1)^2=2+1[/tex]

This gives us,

[tex](x+1)^2=3[/tex]

We take square root of both sides to obtain,

[tex]x+1=\pm \sqrt{3}[/tex]

[tex]x=-1\pm \sqrt{3}[/tex]

We split the [tex]\pm[/tex] to obtain,

[tex]x=\sqrt{3}-1[/tex]

or

[tex]x=-\sqrt{3}-1[/tex]

Answer:

x = √3 - 1 and x = -√3 - 1

Step-by-step explanation:

x^2  +2x - 2 = 0

To solve this equation, keep the variables on one side and constants on the other

x^2 + 2x = 2

Now to complete the square, divide the coefficient of x by 2:

2x ---> coefficient of x is 2

so 2/2 = 1

Now add the square of 1 to both the sides of the equation:

x^2 + 2x + (1)^2 = 2 + (1)^2

which makes it

(x + 1)^2 = 3

To solve it, take square root of both sides which gives

x = √3 - 1 and x = -√3 - 1

C: an employ is paid $12 for each hour worked

Step 1 : (5x-4)/2 = 2x-1                     [Given]

Step 2 : ((5x-4)/2) × 2 = 2 × (2x-1)                 [Multiplicative Property of Equality i.e. by multiplying both sides of the equation by same number]

Step 3 : (5x-4) = 4x-2                     [By Distributive Property]

Step 4 : 5x - 4 + 4 = 4x - 2 + 4                     [By addition property of equality i.e.  by adding both sides of the equation by same number]

⇒ 5x = 4x + 2

Step 5 : 5x - 4x = 4x + 2 - 4x                      [By subtraction property of equality i.e.  by subtracting both sides of the equation by same number]

⇒ x = 2

Answer:

Step 1 : (5x-4)/2 = 2x-1                                {Given}

__________________________________________________________

Step 2 : ((5x-4)/2) × 2 = 2 × (2x-1)               {Multiplicative Property}  

__________________________________________________________

Step 3 : (5x-4) = 4x-2                                   {Distributive Property}

__________________________________________________________

Step 4 : 5x - 4 + 4 = 4x - 2 + 4                     {Addition property}

 5x = 4x + 2

__________________________________________________________

Step 5 : 5x - 4x = 4x + 2 - 4x                     {Subtraction property}    

x = 2

Answer:

x=2

Step-by-step explanation:

To solve this, you must isolate x. To do this, divide both sides by 425 because that is what x is being multiplied by (and dividing is its opposite). Then, you get the answer, x=2.

The nearest thousandth is 1.298. You get this because you don't round the 3 up, it is too small. If it was 5 or higher, then you would round up. Is this helpful? I hope it is.

The given decimal number rounded to the nearest thousandth is 1.298.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

The given decimal number is 1.2983.

To the nearest thousandth:

In the place ten thousandth, number 3 is there

Here, 1.298

Therefore, the given decimal number rounded to the nearest thousandth is 1.298.

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It would be 4(12 + 6). The answer to this is 7.

Hope that helps :)

1. Express the ratio in three different ways (grey and white)

-[tex]\frac{2}{5}[/tex]

-[tex]2[/tex] to [tex]5[/tex]

-[tex]2:5[/tex]

2.  *(Integer)*       *(Opposite)*         *(Absolute Value)*                                                                        

         3                        -3                               3

       -4                         4                                4

        8                       -8                                 8

3. Write an expression to represent:

- "A number n divided by 6" = [tex]\frac{n}{6}[/tex] or [tex]n[/tex]÷[tex]6[/tex]

4. Solve. Show your work.

- [tex]27.9+212.5=240.4[/tex]

- [tex]175.5-12.7=162.8[/tex]

5. Shade the blocks

- [tex]975[/tex]÷[tex]6=162.5[/tex]

- [tex]478[/tex]·[tex]38=18,164[/tex]

1. 4 shirt for 32.00

- Rate: [tex]x[/tex]·[tex]32[/tex]        This rule only happens if there are 4 shirts.

- Unit Rate: [tex]\frac{32}{4}=8[/tex]      It cost $8 for every shirt is bought

2. Write every form from illustration.

- Fraction: [tex]\frac{30}{100}=\frac{3}{10}[/tex]

- Decimal: [tex]0.3[/tex]

- Ratio: [tex]30:100[/tex] or [tex]3:10[/tex]

- Percentage: [tex]30[/tex]%

3. What is 50% of 80?

- Your answer is correct

4. Ken grew [tex]\frac{4}{5}[/tex] of an inch last year. Sang grew [tex]\frac{3}{8}[/tex] of an inch. Who grew more and by how much?

- Your answer is correct

5. Complete the table and then graph the coordinates.

- Attachment for this question

Answer:

In 5 weeks they will have the same amount.

Step-by-step explanation:

1. You have that Tyronne has $60, she gets $5 each week and also gets an additional $10 each week. She saves her money. Therefore, you can write the following expression:

[tex]60+5x+10x\\60+15x[/tex]

Where [tex]x[/tex] is the number of weeks.

2. Her sister has $135, she gets $5 each week and also gets an additional $10 each week, but she spends this money. Therefore:

[tex]135+5x+10x-5x-10x\\135[/tex]

3. If this amounts of money will be equal, you have:

[tex]60+15x=135\\15x=75\\x=5[/tex]

4. Therefore, in 5 weeks they will have the same amount.

[tex]a=\dfrac{2d}{t^2}\ \ \ \ \ |\text{solve for t} \\ \\\\\dfrac{2d}{t^2}=\dfrac{a}{1}\ \ \ \ \ |\text{cross multiply}\\\\at^2=2d\ \ \ \ \ |:a\\\\t^2=\dfrac{2d}{a}\to t=\sqrt{\dfrac{2d}{a}}\\\\\text{We have}\\ \\a=2\dfrac{m}{s^2},\ d=10m\\\\\text{substitute}\\\\t=\sqrt{\dfrac{2\cdot10m}{2\frac{m}{s^2}}}=\sqrt{10m\cdot\dfrac{s^2}{m}}=\sqrt{10s^2}=\sqrt{10}\ s\\\\Answer:\ C.\ \sqrt{10}\ seconds[/tex]

To solve this we must isolate x which involves having the variables on one side and the numbers on the other.

First add 2m to both sides

3m+7/2=-2m+5/2

5m+7/2=5/2

Then we subtract 7/2 from both sides

5m+7/2=5/2

5m=-1

Finally we divide both sides by 5

5m/5=-1/5

Our final answer is -1/5

So the answer is B

Hope this helps!

Determine the slope - down 1, right 3. This is -1/3.

Determine the y-intercept. Up 3 from the origin.

Use this information to form an equation:

[tex]y = -1/3x + 3[/tex]

Answer:

I would say you lifeGuarding

Step-by-step explanation:

Answer:

Its lifegaurding doing the quiz rn

Step-by-step explanation:

Remark

The general formula is fraction * solid food = amount

Total amount = 1/2 * 3 oz + 3/4 * 3 oz + 1/3 * 2 oz

Total amount = 3/2 oz + (9/4) oz + 2/3 oz

The lowest common denominator of  2 4 and 3 = 12

Total amount = 3*6/2*6 + 9*3/4*3 + 2*4/3*4

Total amount = 18/12 + 27/12 + 8/12

Total amount = 53/12 = 4 5/12 <<< Answer oz of food.

4.42 oz of food <<<< Answer

Final answer:

The domain of the function f(x)=5ˣ-3+1 is all real numbers (-∞, +∞), and the range is all real numbers greater than -2 (-2, +∞).

Explanation:

For the given function f(x) = 5ˣ - 3 + 1, the domain and range can be determined by understanding the behavior of the function's formula. The domain refers to all possible x-values that can be input into the function, and the range refers to all possible y-values that the function can output.

The domain of any exponential function like 5ˣ is all real numbers because you can raise 5 to any power, whether it's positive, negative, or zero. Therefore, the domain of f(x) is (-∞, +∞).

To find the range of the function, we look at the output values. Since exponential functions grow without bound as x increases and approach zero as x decreases (but never actually reaches zero), 5^x will do the same. When we subtract 3 and then add 1, we're simply moving the graph down by 2 units. Thus, where the original function 5ˣ would never be less than 0, after the transformation, the function will never be less than -2. So, the range of f(x) is (-2, +∞).

75+65w≥635

This is the inequality because you already saved 75 so you just add it to the amount you save after a certain amount of weeks. It needs to be more than 635 for the the trip.

So firstly, factor out the GCF, or greatest common factor. To find the GCF, list the factors of every term and the greatest one they all share is their GCF. In this case, the GCF is "a":

[tex]a(a^2+4a+4)[/tex]

Next, we are going to apply the square of binomials rule in this situation, which is [tex](x+y)(x+y)=x^2+2xy+y^2[/tex] In this case:

[tex]a^2+4a+4=(a+2)(a+2)\\\\a(a+2)(a+2)[/tex]

Your final answer is [tex]a(a+2)(a+2)[/tex]

Answer:

Step-by-step explanation:

9 *10= 90 feet

90+ 46= 136 square feet

[tex]-\frac{10}{27}[/tex]  hope this helps :)

For this case we have:

The division given by:

102 ÷ 3 = 34

To verify its result we use multiplication as a reverse operation, that is:

We multiply the quotient by the divisor and its result must be the dividend.

So:

[tex](34) (3) = 102\\[/tex]

Answer:

Multiplication, [tex](34) (3) = 102[/tex]

most likely it would be less than

I would say that the answer that best describes the distributive property is "a property of the real numbers that states that the order in which numbers are added or multiplied does not change the value". Distributive property says that when you have a(b+c), you can add b and c together and then multiply by a or multiply b and c by a separately and then add them together after. It does not matter what order you choose to add and multiply in.

I hope this helps :)

The number of full servings of bibimbap can you make is dividing the total cups of rice by cups of rice per serving.

You can make 6 whole servings remainder 1 cup of rice

Given:

Total cups of rice = 5 cups

Cups of rice per servings = 4/5 cup

Number of servings of bibimbap can you make = Total cups of rice ÷ Cups of rice per servings

= 5 cups ÷ 4/5 cup

= 5 × 5/4

= (5 × 5) / 4

= 25 /4

= 6 whole servings remainder 1 cup of rice

Therefore, you can make 6 whole servings remainder 1 cup of rice

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Here we are given the formula for compound interest as :

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Here

A= Amount

P=Principal

r=rate of interest

n=number of times interest is compounded per year

t=time(years)

So we are given

P= $400

r=4% or 0.04

t= 11 years

n= 12

Plugging these values in the formula for compound interest we have,

[tex]A=400(1+\frac{0.04}{12})^{12*11}[/tex]

A= $620.6286

Amount = $620.6

Answer: The final amount after 11 years will be $620.6 .

To find the value of $400 invested at 4% interest compounded monthly for 11 years, use the compound interest formula A(t) = P(1 + r/n)^(nt) and solve for A(t). After calculations, the amount comes to approximately $660.44 when rounded to the nearest cent.

To calculate the future value of $400 invested at 4% interest compounded monthly over 11 years, we can use the compound interest formula provided: A(t) = P(1 + r/n)^(nt). In this formula, P represents the principal amount ($400), r is the annual interest rate (0.04), n is the number of times interest is compounded per year (12 for monthly compounding), t is the number of years the money is invested (11 years), and A(t) is the amount of money accumulated after t years, including interest.

Using the formula:

The calculation is as follows:

A(t) = $400(1 + 0.003333...)¹³²

A(t) = $400(1.003333...)¹³²

A(t) = $400(1.6511)

A(t) = $660.44

After rounding to the nearest cent, $400 invested at 4% interest compounded monthly for 11 years would be worth approximately $660.44.

The product of the functions f(x) and g(x), (f • g)(x), is found by multiplying the two functions together. The resulting function is 2x^3 + 5x^2 - x - 6.

The question is asking for the product of functions f(x) and g(x), denoted as (f • g)(x). To find (f • g)(x), we simply have to multiply function f(x), which is 2x^2 + x - 3, and function g(x), which is x + 2, together.

Let's do it: (2x^2 + x - 3) * (x + 2). Multiplying these two functions out, we get: 2x^3 + 4x^2 + x^2 + 2x - 3x - 6. Simplifying these, we arrive at 2x^3 + 5x^2 - x - 6.

So, (f • g)(x) = 2x^3 + 5x^2 - x - 6.

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To travel 2600 miles in a hybrid car with a fuel efficiency of 45 mpg, it would require approximately 57.78 gallons of gas.

To calculate the amount of gas needed for a hybrid car to travel 2600 miles with a fuel efficiency of 45 miles per gallon (mpg), you can use the formula:

So, it would take approximately 57.78 gallons of gas to travel across the country in a hybrid car with a fuel efficiency of 45 mpg.

Equals to 54...

Hope this helps....