The ages of three friends are consecutive integers. If the sum of the three
friends' ages is 45, which equation below can be used to determine the age, x,
of the youngest friend?

The correct mathematical expression for eight times the difference of 4 and a number is 8(4 - n), where 'n' is the variable representing the number.

The expression that represents eight times the difference of 4 and a number can be written as 8(4 - n), where 'n' represents the number in question. In this expression, '4 - n' is the difference between 4 and the number, and by multiplying this difference by eight, we are following the order of operations where the subtraction within the parentheses is performed first before the multiplication.

Answer:

[tex]x=\frac{d+c}{b-a}[/tex]

Step-by-step explanation:

The question is

Solve for x

we have

[tex]bx-c=ax+d[/tex]

Solve for x

That means ----> isolate the variable x

Group terms

[tex]bx-ax=d+c[/tex]

Factor x left side

[tex]x(b-a)=d+c[/tex]

Divide by (b-a) both sides

[tex]x=\frac{d+c}{b-a}[/tex]

The amount at end of 1 year is $ 109.2025

Solution:

Given that,

Principal = $ 100

Rate of interest = 9 % compounded semiannually

Number of years = 1

The formula for total amount using compounded semiannually is:

[tex]A=p\left(1+\frac{r}{n}\right)^{n t}[/tex]

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Here, [tex]r = 9 \% = \frac{9}{100} = 0.09[/tex]

Here, n = 2 since interest is compounded semiannually

Substituting the values in formula,

[tex]A=100\left(1+\frac{0.09}{2}\right)^{2 \times 1}[/tex]

[tex]\begin{aligned}&A=100(1+0.045)^{2}\\\\&A=100(1.045)^{2}\\\\&A=100 \times 1.092025=109.2025\end{aligned}[/tex]

Thus the amount at end of 1 year is $ 109.2025

50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

Step-by-step explanation:

Given,

Weight of small box of paper = 50 pounds

Weight of large box of paper = 80 pounds

Total weight of boxes = 1750 pounds

Let,

x represent the number of small boxes of papers.

y represent the number of large boxes of papers.

According to given statement;

50x+80y=1750

y = x+4  

50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

Keywords: linear equation, addition

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The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:

50x+80y=1750

y = x+4 ,

where x represent the number of small boxes of paper and y represent the number of large boxes of paper.

We have:

Weight of small box of paper = 50 pounds

Weight of large box of paper = 80 pounds

Total weight of boxes = 1750 pounds

Let us consider that  the number of small boxes of papers be x.

The number of large boxes of papers be y.

 Then, according to question

50x+80y=1750

y = x+4  

Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.

where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.

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Answer:

y = -2/3 x + 1/3

Step-by-step explanation:

Use the slope-intercept linear formula: y = mx + b

x and y represent point on the line

m is the slope

b is the y-intercept

The equation of the line requires "m" and "b". We already have "m".

Substitute point (-4, 3) and slope -2/3 into the formula. x=-4; y=3; m=-2/3. Find b by isolating the variable.

y = mx + b

3 = (-2/3)(-4) + b   Simplify

3 = 8/3 + b     Subtract 8/3 from both sides

b = 1/3

Put b = 1/3 into the formula.

y = -2/3 x + 1/3

Answer:

6.39

Step-by-step explanation:

6.39

Answer:

6.39

Step-by-step explanation:

When dividing by 10 you can always just move the decimal place once to the left.

Glad I was able to help!!

The answer is implicit

Answer:

Implicit Differentiation is necessary in order to find derivatives of curves that do not represent a function because the functions cannot be simplified to a simple function. Using dy/dx and implicit differentiation can be used to find the derivative with respect to one variable and determine the affect each variable has on one another and calculate the rate of change of the variables over time. Differentiating both x and y in Implicit Differentiation makes it so that complex functions are much easier and instead of solving for one variable, differentiating one variable to the other is an easier method. My implicit function is 2y^2-x^2+x^3y=2. First Derivative= -3yx^2+2x/4y+x^3 Second Derivative= 3yx^4-4y^3-24y^2x+8y/(4y+x^3)^2 Third Derivative = 6y(-x^6+28yx^3+4y^2x^2-8x^2-16y)/(4y+x^3)^3

Answer:

a=0.41

Step-by-step explanation:

7(a-10)=13-202a+3

7a-70=13+3-202a

7a-(-202a)-70=16

7a+202a=16+70

209a=86

a=86/209

a=0.41

To solve the equation 7(a - 10) = 13 - 202a + 3, begin by simplifying both sides of the equation and combining like terms. Then isolate the variable 'a' to one side and the constant terms to the other. Finally, divide both sides by the coefficient of 'a' to solve for 'a'.

To solve the equation 7(a - 10) = 13 - 202a + 3, you can start by simplifying both sides of the equation. Expand the terms on the left side by distributing the 7 to the terms inside the parentheses. Combine like terms on both sides of the equation. Then, isolate the variable by moving all the terms with 'a' to one side of the equation and all the constant terms to the other side. Finally, divide both sides of the equation by the coefficient of 'a' to solve for 'a'.

Step-by-step solution:

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Answer:

2

Step-by-step explanation:

Answer:

5 more of the sum would be + 5 to the final answer you are adding

Step-by-step explanation:

Answer:

the answer would be 85

Step-by-step explanation:

because they are added by an increasing value of 5 so 60 plus 25 would be 85

Answer:

B.

Step-by-step explanation:

'At least 35 years old'  can be written as ≥ 35 ( greater than or equal to 35)  so its graph B.

Note there is a filled circle on the 35 meaning the 35 years is included in the range.

Answer:

f(x) = x³ + x² - 5x + 3

Step-by-step explanation:

The cubic polynomial has zeros at 1, 1, - 3.

Therefore, x = 1, 1, - 3 are the roots of the polynomial and hence, (x - 1), (x - 1) and (x + 3) will be factors of the cubic polynomial.

Hence, we can write the polynomial as a function of x as

f(x) = (x - 1)(x - 1)(x + 3)

⇒ f(x) = (x² - 2x + 1)(x + 3)

⇒ f(x) = x³ - 2x² + 3x² + x - 6x + 3

⇒ f(x) = x³ + x² - 5x + 3

So, this is the cubic polynomial function in standard form. (Answer)

Answer:

7/10

Step-by-step explanation:

3/10+2/5=3/10+4/10=7/10

Step-by-step explanation:

You first find the LCM and multiply both fractions by it. Over here the LCM is 10.

(10 (3/10) + 10 (2/5))/10

(3+4)/10

7/10

Answer:

[tex]\sqrt{-5}=i\sqrt{5}[/tex]

[tex]\sqrt{-25}=5i[/tex]

Step-by-step explanation:

i is an imaginary unit, this means

[tex]i^2=-1[/tex]

Rewrite -5 as [tex]5\cdot (-1)=5\cdot i^2,[/tex]

then

[tex]\sqrt{-5}=\sqrt{5i^2}=\sqrt{5}\cdot \sqrt{i^2}=\sqrt{5}\cdot i=i\sqrt{5}[/tex]

Rewrite -25 as [tex]-25=25\cdot (-1)=25\cdot i^2,[/tex]

then

[tex]\sqrt{-25}=\sqrt{25\cdot i^2}=\sqrt{25}\cdot \sqrt{i^2}=5\cdot i=5i[/tex]

Answer:

801-792

Step-by-step explanation:

I got my answer by picking out a big number first (801) and subtracting it by another big number (701) to get an answer less than 100.

To form a subtraction equation with two three-digit numbers having different hundreds digits and a difference of less than 100, choose numbers where the hundreds digits are one number apart and the tens and ones digits are close, such as 756 - 657 = 99.

To write a subtraction equation that involves two three-digit numbers with different hundreds digits and a difference of less than 100, we need to select numbers where the hundreds digit is only 1 apart and the tens and ones digits are close. For example, the numbers 654 and 756. Subtracting these gives us:

756 - 654 = 102

We notice the result is slightly over 100. Therefore, we can adjust the tens or ones digits to reduce the difference. If we change 654 to 657, then:

756 - 657 = 99

In this case, we achieved a result that is less than 100. It's important to note that, in subtraction, we change the sign of the subtracted number before operating the addition as per standard arithmetic rules.

Answer:

Option D. x=-2.5

Step-by-step explanation:

we have

[tex]-2x-3=3^x+2[/tex]

I can divide the expression above in a system of two equations

[tex]y=-2x-3[/tex] ----> equation A

[tex]y=3^x+2[/tex] ----> equation B

Solve by graphing

The solution is equal to the x-coordinate of the intersection point both graphs

using a graphing tool

The intersection point is ( -2.5,2.1)

see the attached figure

therefore

The solution is x=-2.5

Answer:

D) -2.5

Step-by-step explanation:

Answer: -5 1/2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

y = 2x² - 8x + 9

The coefficient of the x² term must be 1, so factor out 2 from 2x² - 8x

y = 2(x² - 4x) + 9

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² - 4x

y = 2(x² + (- 2)x + 4 - 4) + 9

   = 2(x - 2)² - 8 + 9

   = 2(x - 2)² + 1 → C

The given quadratic equation y = 2x^2 - 8x + 9 can be rewritten into vertex form by completing the square, resulting in y = 2(x - 2)^2 + 5.

The given equation y = 2x2 - 8x + 9 can be rewritten in vertex form by completing the square for the -8x term. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h,k) is the vertex of the parabola.

First, we need to divide the coefficient of the x term, which is -8, by 2 to get -4. Then, we square this result to get 16.

This should be inserted into the equation to complete the square, however, we must also take it out again in order to not change the equation. The new equation will be y = 2(x2 - 4x + 16) - 2*16 + 9 = 2(x - 2)2 + 5.

The correct answer then is B. y = 2(x - 2)2 + 5

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Answer:

[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]

Step-by-step explanation:

Given:

Shape is of Trapezoid

Height = 14xy² cm

Length 1 = 3x² cm ( one Parallel side)

Length 2 = 7x² cm ( other Parallel side)

To Find:

Area of Trapezoid = ?

Solution:

We know that

[tex]\textrm{Area of Trapezoid }= 0.5(length\ 1+length\ 2)Height[/tex]

substituting the given values we get

[tex]\textrm{Area of Trapezoid }= 0.5\times(3x^{2}+7x^{2})\times 14xy^{2}[/tex]

[tex]\textrm{Area of Trapezoid }= (10x^{2})7xy^{2}[/tex]..((x^{a}x^{b}=x^{(a+b)})

[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]

Answer:

[tex]A(x)=7x^2-2x+10[/tex]

Step-by-step explanation:

Long Division

The polynomial long division implies the sequential division of each term of the dividend polynomial by the terms of the divisor polynomial. The procedure is a well-know sequence of steps from which there are two outputs: the quotient and the remainder.

We have two mathematical models, one for the total number of visitors who went to a theme park:

[tex]F(x)=126x^3+279x^2+90x+450[/tex]

The other for the number of shows played at the theme park in the same period

[tex]G(x)=18x+45[/tex]

Where x is the number of days since October 1. We are required to find the expression for the average number of visitors per show. It comes by dividing F(x) by G(x). We must perform a long division as shown  below.

The average number of visitors per show is

[tex]A(x)=7x^2-2x+10[/tex]

For example, day 5

[tex]A(5)=7\ 5^2-2(5)+10=175[/tex]

There were 175 visitors per show (on average)

Answer:

-11

Step-by-step explanation:

Because -2+(-9)=-2-9=-11.

Answer:

6 × 35

2×3×5×7

6 × 15

2×3×3×5

So your least common multiple is 2

Answer: 2

Step-by-step explanation:

Answer:

6 × 35

2×3×5×7

6 × 15

2×3×3×5

So your least common multiple is 2

Answer:

A. 0

Step-by-step explanation:

Because there is no correlation between any of the points.

Answer:

There is No Solution for the equation.

Step-by-step explanation:

Given:

[tex]-2x+9-3x=-5x+3[/tex]

We need to find number of solutions for above equation.

Now Solving the equation we get;

[tex]-5x+9=-5x+3[/tex]

Now adding both side by 5x we get;

[tex]-5x+9+5x=-5x+3+5x\\\\9=3[/tex]

Which can't be true.

Hence There is No Solution for the equation.

Answer:

1/6 of one minute, 10 seconds.

Step-by-step explanation:

8/48=1/6

Answer:

Amount of juice left over is 1.5 cups.

Step-by-step explanation:

Given:

Amount of juices Grace has = 6 cups

Number of friends = 8

She divides the juice equally among her friends.

Now we will first find Amount of juice each friend will have.

Amount of juice each friend will get can be calculated by dividing Amount of juices with total number of friends.

Framing in equation form we get;

Amount of juice each friend will have = [tex]\frac{6}{8}= \frac{3}{4}\ cups \ \ \ OR \ \ \ \ 0.75\ cups[/tex]

Number of friends who do not drink = 2

Amount of juice left will be equal to Number of friends who do not drink multiplied by Amount of juice each friend will have.

Framing in equation form we get;

Amount of juice left = [tex]2\times \frac{3}{4} = \frac{3}{2} \ cups \ \ \ \ OR \ \ \ \ 1.5\ cups[/tex]

Hence Amount of juice left over is 1.5 cups.

Answer:

The volume of the box is [tex]V=(4x^3+16x^2+15x)\ in^3[/tex]

Step-by-step explanation:

we know that

The volume of the box is equal to

[tex]V=LWH[/tex]

where

L is the length of the box in inches

W is the width of the box in inches

H is the height of the box in inches

we have

[tex]L=(2x+5)\ in\\W=(2x+3)\ in\\H=x\ in[/tex]

substitute in the formula

[tex]V=(2x+5)(2x+3)x[/tex]

[tex]V=(4x^2+6x+10x+15)(x)[/tex]

[tex]V=(4x^2+16x+15)(x)[/tex]

[tex]V=(4x^3+16x^2+15x)\ in^3[/tex]

For this case we must find the value of "x" that meets the following equation:

[tex]\frac {4} {3} = x + \frac {10} {15}[/tex]

We subtract [tex]\frac {10} {15}[/tex] on both sides of the equation:

[tex]\frac {4} {3} - \frac {10} {15} = x\\\frac {15 * 4-3 * 10} {3 * 15} = x\\\frac {60-30} {45} = x\\- \frac {30} {45} = x[/tex]

We simplify:

[tex]x =\frac {6} {9}=\frac{2}{3}[/tex]

Finally, [tex]x =\frac {2} {3}[/tex]

Answer:

[tex]x =\frac {2} {3}[/tex]