Glven: 3x - 2 = 2(x + 1)Prove: x=4REASONSTATEMENT1. 3x - 2 = 2(x + 1)30.2. 3x - 2 = 2x + 231.3. X-2= 232.4. x= 433.Word Bank:A. Distributive PropE. Transitive PropC. Substituion PropD. Subtraction PropB. GivenF. Addition Prop

ANSWER

1058 grams

EXPLANATION

Each day she eats 46 grams of protein. In 23 days of training, she will eat 23 times that amount,

Hence, in 23 days she will eat 1058 g of protein.

Let's find the vertex for the following equation:

y = x² - 2x - 3

As you can see, we found graphically that (1, -4) is the vertex for this equation.

Now, let's find the intercept form, as follows:

x-intercept:

0 = -1² -2 * - 1 - 3

0 = 1 + 2 - 3

Then, (-1, 0)

0 = 3² - 2 * 3 - 3

0 = 9 - 6 - 3

Then (3, 0)

y-intercept:

yy

Answer:

===========================

Use arc length formula:

Substitute the values and calculate:

The matching answer choice is C.

Answer: x=4

Step-by-step explanation:

1. 3x+5 = 8x-16+1

2. 3x+5 = 8x-15

3. 3x+20 = 8x

4. 20 = 5x

5. x = 4

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

A square is a quadrilateral in geometry that has four equal sides and four right angles (90-degree angles). It is a unique kind of both a rhombus and a rectangle. A square is made up of four equal-length sides, two equal-length diagonals, and right-angle diagonal cuts. A square's area and perimeter can be calculated by multiplying one of its sides by itself (squared), and one of its sides by four, respectively. Because of their symmetry and regularity, squares are frequently employed in mathematics and building.

given

By multiplying the first lawn's length by its breadth, one may determine its area: 56 square metres is the size of the first lawn, which is 8 metres by 7 metres.

The second lawn's breadth is six times that of the first lawn's, so:

The second lawn's width is equal to 6 × 7 metres, or 42 metres.

The second lawn is the same length as the first one, so:

The second lawn is 8 metres long.

The second lawn's area is calculated by multiplying its length by its width:

The second lawn is 336 square metres in size (8 metres by 42 metres).

The first and second lawns' combined areas make up the overall area of the two lawns:

Total area equals the sum of the first and second lawns.

56 square metres + 336 square metres make up the total area.

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

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[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]

[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]

how much will it be in interest alone?

well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned

[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]

He took 3 1/4 hours to clean the bathroom and then he took 1/8 hours to clean the kitchen.

First, we can convert the mixed number 3 1/4 into a fraction:

3 1/4 = 3/1 + 1/4 = 13/4

Now, we can sum both times:

13/4 + 1/8 = ((13*8)+(4*1)) / (4*8) = (104 +4)/ 32 = 108/32 = 27/8

Finally, we need to convert the total of hours 27/8 as a mixed number:

If 27/8 = 3.375

We take the whole number and then convert the decimal remaining into a fraction:

3 - whole number

0.375* (1000/1000) = 3/8

Hence, the mixed number for the total time that Ali spent cleaning both rooms is 3 3/8

The most appropriate choice for square root will be[tex]\sqrt{19}[/tex] lies between 4 and 5

What is square root of a number?

A number's square root is a value that, when multiplied by itself, yields the original number. The opposite way to square a number is to find its square root. Squares and square roots are therefore related ideas. Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. When multiplied by itself, the positive number represents the square of the original number. The original number is obtained by taking the square root of a square of a real integer. For instance, the square of 3 is 9, the square root of 9 is 9, and 9 squared equals 3. Finding the square root of 9 is simple because it is a perfect square.

[tex]\sqrt{p} = p^{\frac{1}{2}}[/tex]

[tex]\sqrt{19} = 4.36\\[/tex]

4.36 lies between 4 and 5

[tex]\sqrt{19}[/tex] lies between 4 and 5

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Answer:

Volume = 2268 ft³

1814.4 bushels of corn

Explanation:

The volume of the corn crib can be calculated as:

Volume = Length x Width x Height

Then, the volume is equal to:

Volume = 21 ft x 9 ft x 12 ft

Volume = 2268 ft³

Finally, to know the number of bushels of corn that can be stored, we need to divide the volume of the corn crib by the volume of each bushel of corn. So:

Therefore, the volume of the corn crib is 2268 ft³ and it can store 1814.4 bushels of corn.

To find f(7) substitute x by 7 in the function

The constant of proportionality is A. 9.

The constant of proportionality is simply used to show that the numbers given have a constant value.

From the information, the Busy Bee store bottles fresh jars of honey at a constant rate. In 2 hours, it bottles 18 jars. The constant will be:

= Number of jars / Number of hours

= 18/2

= 9

In 6 hours, it bottles 54 jars of honey. The constant will be:

= 54 / 6

= 9

Therefore, the constant is 9.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

A(t) = 800e^(-0.86t)

Step 02:

Rate of change

t1 = 0

A(t) = 800e^(-0.86t)

A(t) = 800e^(-0.86*0)

A(0) = 800

t2 = 5

A(t) = 800e^(-0.86t)

A(t) = 800e^(-0.86*5)

A (t) = 800e^(-4.3)

A(5) = 10.85

Step 03:

The values for the composition of the functions are:

(f o g)(x) = 9x² + 5

(g o f)(x) = 3x² + 15

To evaluate the composition of a function, the first thing to do is to evaluate the inner function, then use the output as an input to evaluate the outer function of the composition.

Given the following functions:

f(x) = x² + 5

g(x) = 3x

We are required to find (f o g)(x) and (g o f)(x).

To find (f o g)(x), replace g(x) for x in the outer function f(x):

(f o g)(x) = (3x)² + 5

(f o g)(x) = 9x² + 5

To find (g o f)(x), replace f(x) for x in the outer function g(x):

(g o f)(x) = 3(x² + 5)

(g o f)(x) = 3x² + 15

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Given

Wholesale price for a pair of shoes = $3.50.

Wholesale price by 60%.

Find

price of the pair of shoes in the department store

Explanation

Price in deparrtmental store is 60% more than wholesale

so ,

Final Answer

Therefore , the price of the pair of shoes in the department store is $5.60.

To simplify the expression above, simply combine similar terms.

The similar terms in the expression above are 8c and -3c as well as 6 and -2.

Let's combine the pairs of similar terms.

So, 8c - 3c = 5c and 6 - 2 = 4. Hence, the answer is:

The answer is 5c + 4. (Option A)

Solution

We are given the expression

The image below shows the definition of a polynomial and some examples as well

Thus, given

Here;

Degree = 0

Leading coefficient = 3

Answer:

Progressive Era

Step-by-step explanation:

When Tanvir applies the distributive property to the left-hand side of the equation, 1/3(3q+15)=101, the equation that shows the correct application is equation 4: q+5=101.

The distributive property applies basic mathematical operations, especially in equations.

This property is that when a value is multiplied or divided by a number to a set that will be added or subtracted, the result is the same, notwithstanding if the operation is done before the addition or subtraction.

1/3(3q+15) = 101

(3q/3+15/3) = 101

= q + 5 = 101

q = 96

Check of Distributive Property:

1/3(3q+15) = 101

1/3(3 x 96+15) = 101

= 1 x 96 + 5 = 101

= 96 + 5 = 101

= 101 = 101

Or: 1/3(3q+15) = 101

1/3(3 x 96+15) = 101

= 1/3(288 + 15) = 101

= 1/3(303) = 101

= 101 = 101

Thus, the equation that correctly applies the distributive property is equation 4: q+5=101.

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Given:

There are given the equation:

Explanation:

To find the factor of the given equation, first, we need to take a common variable from the given equation:

Then,

Final answer:

Hence, the factor of the given equation is shown below:

Answer:

Step-by-step explanation:

The domain and range of a linear function is always real numbers (T or F)

It is True. This is because of a couple of reasons.

    1.) You cannot divide by 0.

     2. A negative number cannot have its square root taken.

The range is determined by the domain in a linear function, and thus it must always consist of real numbers.

The fabric  has a cost per yard of $6 per yard

From the question, the given parameters are:

Yards of fabric = 2 1/2 yards

Cost of the fabric = $15

The cost per yard of the fabric is then calculated as

Cost per yard = Cost of the fabric/Yards of fabric

Substitute the known values in the above equation

So, we have

Cost per yard = 15/(2 1/2)

Evaluate the quotient

So, we have

Cost per yard = 6

Hence, the cost per yard is $6 per yard

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We know that Mary is x years old.

The age in 10 years will be x plus 10, as follows:

And the age she had two years ago was:

An example of this could be: imagine that Mary is 10 years now. In ten years, she will have:

10 + 10 = 20 years ( we add 10 to the original number). Likewise, 2 years ago, she had 10-2 = 8 years.

Therefore, the answers are two equations:

The z - score of the normal deviation will be 0.8.

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

A normal distribution has the mean = 62

Standard deviation = 20

Since, The formula for the z - score will be;

z = (x - μ) / σ

Where, σ is the standard deviation and  μ is the mean of normal distribution.

Substitute all the values in above equation, we get;

z = (x - μ) / σ

z = (46 - 62) / 20

z = - 16 / 20

z = - 0.8

Therefore,

The z - score of the normal deviation will be 0.8.

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Explanation

Step 1

Aya sold printed T-shirts for $7.50 each at a carnival. She earned

$187.50.

then

let x represents the number of T-shirts Aya sold.so, if she made $187.5 and the cost per T-shirt is $7.50

therefore, for part A , the answer is

Step 2

What is the number of T-shirts Aya sold at the carnival?

to figure out this,we need to solve for x

it means she sold 25 T-shirts at the carnival

I hope this helps you

Given:

• Degree of polynomial = 3

• Zeros of the polynomial: 2, 3 - 2i

Let's find the polynomial.

Since the polynomail is of degree 3, it's highest exponent will be 3.

Equate the zeros to zero:

x = 2

Subtract 2 from both sides:

x - 2 = 2 - 2

x - 2 = 0

x = (3 - 2i)

Since this root is a complex conjugate, we have the other complex root: (3 + 2i)

Hence, we have:

(x - (3 - 2i)) and (x - (3 + 2i)).

Therefore, to write the function, we have:

Now, simplify the expression:

Solving further:

Combine like terms:

ANSWER:

Answer:

There are 126 months in 10 years and 6 months.

Explanation:

In a year there are 12 months.

Then, to know how many months are in 10 years, we multiply by 10:

Now we add the additional 6 months:

The answer is 126.

Remember that the volume of a rectangular pyramid is given by the expression:

Where:

• a ,and ,b ,are the lenght of the sides of the rcetangle (base)

• h, is the height of the pyramid

Using this, and the data given, we'll get that:

The volume of the pyramid is 665 cubic feet

So,

We're going to multiply:

Multiplying numerators and denominators together, we obtain:

Now, to simplify, what we're going to do is to reduce the fraction dividing by a common number. Let's begin dividing by 2:

As you can see, we can't divide by a common number more times, so, the simplified fraction is 5/36.

Given:

It is given that you roll a die 96 times.

Required:

We have to find the expectation of landing on 3 or 4.

Explanation:

If you roll a die then there are 6 possibilities (1-6) and the possibility of landing on 3 or 4 is 2.

Then the probability of landing on 3 or 4 is

If you roll the die 96 times then the probability of landing 3 or 4 is

Final answer:

Hence the final answer is:

You could expect it to land on 3 or 4 is