Solve the literal equation |ax+b|=c for x.

A

reducing one side by 2 is expressed as (x - 2) ← length

increasing the other side by 2 is expressed as (x + 2 ) ← width

the area of new patio = (10 - 2 )(10 + 2) 8 × 12 = 96 ft²

Answer: A. lw = (x + 2)(x – 2); 96 square feet

Step-by-step explanation:

Given: Stephon has a square brick patio. He wants to reduce the width by 2 feet and increase the length by 2 feet.

Let x be the side-length of the patio, then

The length of the patio after change = x+2

The width of the patio  after change = x-2

Then the area of the patio is given by :-

[tex]A=lw\\\Rightarrow\ A=(x+2)(x-2)[/tex]

If the original patio measures 10 feet by 10 feet.

Then the area of the patio= [tex](10+2)(10-2)=(12)(8)=96[/tex] square feet.

Hence, A is the right answer.

These are three equations and three answers.

Answers:

Explanation:

Equation A: 20 - 4x = 12 - x + 8 - 3x

The objective is clearing the unknown, which is to isolate it in one side of the equation.

These are the steps and properties that you need to use:

1.  Combine like terms on right side:

20 - 4x  = 20 - 4x

2. Use addition property of equality (add 4x on each side).

20 = 20 ↔ identity

Conclusion: you have gotten a condition that is always true, no matter the value of x, which means that the equation has infinite solutions and it is an identity.

Equation B: 5x + 4x - 3  =  24 + 8x (note that I placed the equal sign as it was missing)

1.  Combine like terms on each side:

9x - 3 = 24 + 8x

2. Subtraction property and addition propertiy of equality (subtract 8x and add + 3 on both sides)

x = 27 ↔ solution (neither contradiction nor identity)

Conclusion: the solution is x = 27.

Equation C: 5x + 6 = 2x + 6 + 3x - 15 (note that I placed the equal signs as it was missing)

1. Comitne like terms on the right side:

5x + 6 = 5x - 9

2. Subtraction property of equality (subtract 5x from each side)

6 = - 9 ↔ contradiction

Conclusion: the equation does not have a solution since the final equality is always false (a condradiction or absurd).

For your information, when the variable (x) dissapears and fhe final equality is always true (for example 0 = 0, or 20 = 20), the equation is an identity.

A) 20-4x=12-x+8-3x

Bring all x values at one side and all numerical values to the other side of the equal sign and solve. Also, do not forget to change the sign when you change the side.

-4x + x + 3x = -20 + 12 + 8

-4x + 4x = -20 + 20

0 =0 No solution

B) 5x+4x-3+24+8x

this expression can only be simplified to 17x + 21 and not solved because there is no equal sign here

C) 5x +6+2x+6+3x-15

this expression can only be simplified to 10x - 3 and not solved because there is no equal sign here

Also, neither of these is an identity or contraction.

Answer:

1a. 42 liters

1b. 345 miles

2a. 10 h 20 min 41.4 sec

2b. 361.6 km

5a. $8

5b. 444.5 km

5c. 46 h 13 min 20.9 sec

5d. $160

Step-by-step explanation:

Each of these problems expresses a proportion and asks you to find a missing value. You are given, for example, value 1 and related value 1. You are asked to find value 2 that corresponds to related value 2.

Solving the Proportion

Expressed as a proportion, this looks like ...

... (value 1)/(related value 1) = (value 2)/(related value 2)

If you multiply both sides of this equation by related value 2, you can find value 2.

... (related value 2)/(related value 1)×(value 1) = value 2

Another way to think about it

I like to think of the related values as making a fraction. If the related value 2 is larger than related value 1, the fraction is greater than 1 and the value 2 will be larger than value 1. (This realization can serve as a check on your answer.)

1a. related value 2 = 168 km. This is the value for which you want to find value 2, the number of liters of gasoline. related value 1 has the same units as related value 2 (km), and value 1 has the same units as value 2 (liters).

Then the fraction of interest is (168 km)/(468 km), and it multiplies 117 L. The result is ...

... (168/468)×(117 L) = 42 L

1b. (10 h)/(4 h)×(138 mi) = 345 mi

2a. (180 mi)/(261 mi)×(15 h) ≈ 10.3448 h

2b. (4 h)/(5 h)×(452 km) = 362.6 km

You may have noticed that I keep the units with the numbers. When the same units are in the numerator and denominator, they cancel—the way any common factors cancel. The remaining units will be the units of the answer. This practice of keeping units with numbers can help ensure you're using the right numbers for the right purpose. If the units don't work out, your math has an error.

5a. (2 lb)/(50 lb)×$200 = $8

5b. (7 h)/(6 h)×381 km = 444.5 km

5c. (459 km)/(427 km)×(43 h) ≈ 46.2225 h

5d. (20 kg)/(11 kg)×$88 = $160

You can see that this line passe through the points (-4,-2) and (4,3).

The slope of the line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is

[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]

Thus, the slope is

[tex]\dfrac{3-(-2)}{4-(-4)}=\dfrac{5}{8}.[/tex]

Then the equation of the line is

[tex]y-3=\dfrac{5}{8}(x-4),\\\\y=\dfrac{5}{8}x+\dfrac{1}{2}.[/tex]

Answer: correct choice is C.

Answer,

C. 1650

Explanation,

495/6 = 82.5

82.5 x 20 = 1650

Hope this helps :-)

we are given that the English Aplhabet has 26 letters. we let g represent the number of letters in the Greek alphabet. From the statement given, English alphabet which is 26 = 20 + 1/4 *g. The expression which is similar to this is in option A. 1/4g + 20 = 26.

Answer:

  C.  -20

Step by step explanation:

It appears you want the value of the expression -5² +8|-1| +(-3).

The order of operations tells us that the first step is to evaluate expressions in parentheses. Here, the absolute value symbols effectively serve as parentheses, so we start there.

|-1| signifies the absolute value of -1, its magnitude, or positive value. That simplifies to 1. So, your expression is ...

  -5² +8·1 -3

The next step is to evaluate the term with an exponent: -5² = -(5·5) = -25.

  = -25 +8·1 -3

Now, we perform the multiplication:

  = -25 +8 -3

And finally, the addition/subtraction

  = -17 -3

  = -20

__

Additional comment

The expression you show in the problem statement looks like the first term is negative fifty-two. That is very different from negative five squared. An exponent is indicated using a caret (^), as -5^2, or using a superscript font, as -5². Please be careful to use appropriate math symbols where exponents are involved.

Answer:

Option D [tex]BC=63\ in[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

[tex]\frac{DC}{ML}=\frac{BC}{KL}[/tex]

substitute the given values and solve for BC

[tex]\frac{56}{8}=\frac{BC}{9}[/tex]

[tex]BC=56(9)/8\\BC=63\ in[/tex]

Let's evaluate the quantity within the parentheses.  (11 - 3^2) becomes (2).  Then we have:

(72 divided by 2) / 3, or 36/3, or 12.

C

given 1 /( 3 + √2 )

then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

the conjugate of 3 + √2 is 3 - √2

1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )

= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7

The fraction [tex]\frac{1}{3+\sqrt{2}}[/tex] can be written as [tex]\frac{3-\sqrt 2}{7}[/tex]. Option C is correct.

Fraction simplification is a method of fraction reduction that entails making a fraction as simple as possible.

This is accomplished by dividing the numerator and denominator by the biggest integer that divides both integers exactly.

Given fraction;

[tex]\frac{1}{3+\sqrt{2}}[/tex]

Multiplying the numerator and denominator by the conjugate of the denominator will rationalize the denominator;

The conjugate of the denominator (3 + √2) is 3 - √2;

Apply the rationalization of fraction;

[tex]\frac{1}{3+\sqrt{2}} \\\ \frac{1}{3+\sqrt{2}} \times \frac{3-\sqrt2}{3-\sqrt 2} \\\\ \frac{3-\sqrt 2}{9-2} \\\\\ \frac{3-\sqrt 2}{7}[/tex]

Hence option C is correct.

To learn more about fraction simplification, refer to https://brainly.com/question/11479469.

#SPJ2

After the 15% discount, Maria pays 85% of the cost. That cost is the sum of the fixed cost and the variable (per visit) cost.

... (updated cost) = 0.85×($150 +$30×a)

... (updated cost) = 127.50 +25.50a . . . . in dollars

Quite often, the CD will earn more interest—even if you have to pay a penalty for early withdrawal.

_____

For example, my local credit union offers 0.10% interest on passbook savings and 1.46% interest on a 4-year CD. One of my local banks offers 0.01% interest on passbook savings, and 0.60% on a 4-year CD.

A CD (Certificate of Deposit) generally offers a higher interest rate than a passbook savings account, which may lead to a greater return on investment. But it has a drawback where money cannot be withdrawn without penalty until a set time period ends.

The primary advantage of a CD (Certificate of Deposit) over a passbook savings account is typically a higher interest rate. A CD is a type of timed deposit, meaning that the money is typically put in the bank for a fixed amount of time. During this time, the interest rate is usually higher than that of a typical savings account, allowing for a greater return on the initial investment. Unlike a passbook savings account, however, you cannot withdraw money from a CD without penalty until the time period ends, which in this case is four years. This is an important consideration for Beth and Mark.

https://brainly.com/question/34489138

#SPJ2

After the 10% discount on marked price (P), the selling price is ...

... P×(100% -10%) = 0.90P

After a markup off 35% on cost, the value is

... $70×(100% +35%) = 1.35×$70 = $94.50

The retailer wants these two values to be equal:

... 0.90P = $94.50

... P = $94.50/0.90 = $105.00 . . . . . divide by the coefficient of P

The marked price should be $105.00.

To make a 35% profit on the cost, the retailer should mark the sunglasses at a price of $85.05.

To determine the price at which the retailer should mark the sunglasses, we need to calculate the original price and then apply the discount. First, let's find the 35% profit on the cost, which is $70. 35% of $70 is 0.35 * 70 = $24.50.

To make a profit of $24.50, the original price should be $70 + $24.50 = $94.50. To sell the sunglasses at a 10% discount, the marked price will be 90% of $94.50. 90% of $94.50 is 0.90 * 94.50 = $85.05.

Therefore, the retailer should mark the sunglasses at a price of $85.05.

https://brainly.com/question/35711616

#SPJ2

Remark

Answer: The second one. The second step removes the brackets on the right. It uses the distributive property which puts back the common factor that was taken out of the two terms 6x and 24. Quite often the distributive property is useful when presenting a problem to be solved.

The associative property is more of an order thing and that is very useful sometimes as well what it says is that if you have three numbers a + b + c the order which you combine things does not matter.

For example 3 + 4 + 5 could be combined as 3 + 4 = 7;  7 + 5 = 12 or 3 + 5 = 8, 8 + 4 = 12.  

The associative property is useful when adding fractions.

To know which of the following expressions are polynomials, let us look at the definition of a polynomial:

Polynomial is derived from poly- (which means "many") and -nomial (meaning "term"), so it says "many terms".

For an instance: [tex]2x^2y+2y^2[/tex] is a polynomial, but [tex]4xy^2[/tex] is not a polynomial because it contains single term only.

We must keep in mind that in polynomial it can have variables, constants, and exponents but it can never have division by a variable.

Now lets, look at the

[tex]30y^2[/tex] since it has got one term it can not be a polynomial.

[tex]30y^2+x[/tex]: it has got more than one term therefore, it is a polynomial.

[tex]30y^2x[/tex]: again it has got just one term so it is not a polynomial.

[tex]30y^2+x^{12}[/tex]: Since it has got more than one term, so again it is a polynomial.

The correct polynomial expressions are 30y²+x and 30y². Option A and D is the correct answer.

Polynomials are expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and exponentiation.

30y²+x: This expression is a polynomial because it consists of a constant term (30), a variable term (y²) raised to a non-negative integer exponent, and an additional variable term (x).

30y²: This expression is a polynomial because it consists of a constant term (30) and a variable term (y²) raised to a non-negative integer exponent.

These expressions are considered polynomials because they consist of variables, constants, and non-negative integer exponents, and they involve the appropriate mathematical operations of addition and multiplication.

Learn more about Polynomial here:

https://brainly.com/question/1496352

#SPJ6

The complete question is, "Which expressions are polynomials? Select each correct answer.

a.  30y²+x

b. 30y²+x (¹/²)

c. (30y²) ÷ x

d. 30y²"

The term sin(x+[7pi/4]) can be rewritten in terms of sin(x) and cos(x) using the formula for sine of the sum of two angles. Given A = x and B = 7pi/4, the equation can be simplified to sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2).

To rewrite the term sin(x+[7pi/4]) in terms of sin(x) and cos(x), we can use the formula for sine of the sum of two angles. The formula is given by:

sin(A + B) = sinAcosB + cosAsinB

Substituting our given values into this formula, where A = x and B = 7pi/4, we get:

sin(x + [7pi/4]) = sin(x)cos(7pi/4) + cos(x)sin(7pi/4)

Note that cos(7pi/4) = √2/2 and sin(7pi/4) = -√2/2. Therefore:

sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2)

https://brainly.com/question/37065283

#SPJ3

The number of k-element subsets of a set of n elements is given by

... C(n, k) = n!/(k!(n-k)!)

a) C(100, 99) = 100!/(99!×1!) = 100

b) C(100, 98) = 100!/(98!×2!) = 100*99/2 = 4950

c) C(100, 2) = 100!/(2!×98!) = 4950 . . . . same as  (b)

Answer: 40,000,000

Population: 400,000,000

40X1010

Step-by-step explanation:

I have memorized facts about fractions like these, so can tell you ...

[tex]\dfrac{5}{9}=0.5\overline{5}\\\\-\dfrac{3}{8}=-3\times 0.125=-0.375\\\\-\dfrac{3}{11}=-0.27\overline{27}[/tex]

_____

A fraction with 9 as a denominator is a repeating 1-digit decimal with the decimal digit being the numerator of the fraction.

A fraction with 11 as a denominator is a repeating 2-digit decimal with the two digits being 9 times the numerator of the fraction.

1/8 = 0.125, so any multiple of 1/8 is that multiple of 0.125.

To convert 5/9 - 3/8 - 3/11 into a decimal, you find a common denominator (792), subtract the numerators, resulting in -73/792, and then divide the numerator by the denominator to find the decimal, which is -0.0922.

The problem is asking us to write the rational number 5/9 - 3/8 - 3/11 as a decimal. To do this, we need to first subtract these fractions and then convert the result into a decimal.

https://brainly.com/question/35123994

#SPJ3

The multiples for 6 : 6, 12, 18, 24, 30,36, 42, 48

The multiples for 8 : 8, 16, 24, 32, 40, 48, 56, 64

Hope this helps

Answer:125a6

-64q12

-c^30d^9f^18g^3

Step-by-step explanation:

Got it right on edgy

Answer:

See the attached

Step-by-step explanation:

An exponential function has the variable in the exponent.

Answer:

Exponential functions: [tex]f(x)=8e^x[/tex],[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex]

Non-exponential functions: [tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex]

Step-by-step explanation:

The general form of an exponential function is

[tex]f(x)=ab^x[/tex]

where, a is initial value and b is growth factor.

It means the variable term i.e., x must be the exponent . In other words we can say that the variable term must be in the power of constant terms.

We need to check whether the given function is an exponential function or not.

The given function is

[tex]f(x)=8e^x[/tex]

It is an exponential function with initial value 8 and growth factor e≈2.718.

Similarly,

[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex] are exponential functions.

[tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex] are non-exponential functions.

To convert the density of the textbook to slug/in³, we first convert the density from g/cm³ to kg/m³ and then use the given conversion factors to convert it to slug/in³.

To convert the density of the textbook to slug/in³, we need to use the given conversion factors: 1 slug = 14.59 kg and 1 in = 2.54 cm. First, we need to convert the density from g/cm³ to kg/m³ by dividing by 1000. Then, we can convert from kg/m³ to slug/in³ using the given conversion factors. Let's calculate:

Given density = 3 g/cm³

Step 1: Convert g/cm³ to kg/m³

Density in kg/m³ = 3 g/cm³ / 1000 = 0.003 kg/m³

Step 2: Convert kg/m³ to slug/in³

Density in slug/in³ = 0.003 kg/m³ × (1 slug / 14.59 kg) × (1 in³ / (2.54 cm)³)

Performing the calculations gives us the density of the textbook in slug/in³.

https://brainly.com/question/33833616

#SPJ2

The value of F(8) is 64.

Given that,

Based on the above information, the calculation is as follows:

[tex]F(8) = 8 \times 8[/tex]

= 64

learn more: https://brainly.com/question/13496810?referrer=searchResults

x = [tex]\frac{y}{c}[/tex] - b

divide both sides by c

x + b = [tex]\frac{y}{c}[/tex] ( subtract b from both sides )

x = [tex]\frac{y}{c}[/tex] - b

The equation solved for x is x = y/c - b.

Two or more expressions with an equal sign are defined as an equation.

The given equation is y = c(x + b).

y = c(x + b)

y/c = x + b

y/c - b = x

Or, x = y/c - b

Hence, the equation solved for x is x = y/c - b.

To learn more about equations, click here:

brainly.com/question/10413253

#SPJ2

109.93 lbs

since the quantities vary directly, then

w(moon) = kw(earth ) ← ( k is the constant of variation )

to find k use the given condition

k = w( moon ) / w( earth ) = [tex]\frac{25.66}{150.94}[/tex]

given w(earth) = 218.24

w(moon) = [tex]\frac{25.66(218.24)}{150.94}[/tex] = 109.93