Literal Equations

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The solution of the given equation is x = 12. The solution is the value, that satisfies the given equation.

Given equation is 5(x - 1) + 3x = 7(x + 1)

On simplifying the equation, we get

5(x - 1) + 3x = 7(x + 1) ⇒ 5x - 5 + 3x = 7x + 7

⇒ 8x - 5 = 7x + 7

⇒ 8x - 7x = 7 + 5

⇒ x = 12

Therefore, the solution for the given equation is x = 12.

Here, the power or the degree of the variable x is 1 in the given equation. Thus, it has only one solution.

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The statement 5 less than three times a number x is expressed as an expression to 3x - 5

An algebraic expression can be described as an expression made up of coefficients, terms, factors, variables and constants.These expressions are also composed of some mathematical and arithmetic operations.

They include;

Addition

Division

Multiplication

Subtraction

Parentheses

Bracket, etc

From the information given, we have that; The number is x. The number is 5 times lesser than three times the value of xThis can be represented as; 3x - 5

Hence, the expression represented is 3x - 5

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By using the concept of function, it can be seen that the given graph represents a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values on the x axis represents the domain and the values on the y axis represents the Range.

From the graph it can be seen that

Every point of the domain maps to unique point on the range.

So this is a function

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Factorization is the reverse process of expansion of mathematical expression to simple terms. The factorized term is: [tex]\frac{x + 14}{6}[/tex]

Factorization is a procedure in which a given number of terms of a mathematical expression is reduced by collecting common terms. It involves reducing a given mathematical expression to a simple form of terms.

Given that:

[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] ÷ [tex]\frac{x - 2 }{x^{2} }[/tex]

[tex]\frac{x^{2}+ 12x - 28}{6x^{2} }[/tex] x [tex]\frac{x^{2} }{x -2}[/tex]

[tex]\frac{x^{2} + 12x - 28}{6(x - 2)}[/tex]

Factorizing the numerator, we have;

[tex]x^{2} + 12x - 28[/tex] = (x - 2) (x + 14)

So that,

[tex]\frac{(x- 2) (x + 14)}{6(x - 2)}[/tex]

[tex]\frac{(x + 14)}{6}[/tex]

Thus the factorized form of the given question is [tex]\frac{1}{6}[/tex](x - 14).  

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For the expression -34 < x < 10, interval notation, builder notation and graphical solution is shown below.

A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.

The given expression is -34 < x < 10

The interval notation of the expression -34 < x < 10 is given as,

x ∈ (-34, 10)

The builder notation of the expression -34 < x < 10 can be given as,

{x |  -34 < x < 10}

The graphical solution of the expression -34 < x < 10 is given below.

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If the ratio of the measure of the three sides of the triangle is 9:7:5 and the perimeter is 191.1 inches, then the three sides of the triangle are 81.9 inches, 63.7 inches and 45.5 inches

The ratio of the measure of the three sides of a triangle = 9 : 7 : 5

Then three sides of the triangles = 9x, 7x and 5x

Where x is the constant

The  perimeter of the triangle = 191.1

The perimeter of the triangle is the sum of the three sides of the triangle

Then the equation will be

9x + 7x + 5x = 191.1

21x = 191.1

x = 191.1 / 21

x = 9.1

The first side = 9x

= 9 × 9.1

= 81.9 inches

The second side = 7x

= 7 × 9.1

= 63.7 inches

The third side = 5x

= 5 × 9.1

= 45.5 inches

Therefore, the measure of the sides of the triangle is 81.9 inches, 63.7 inches and 45.5 inches

I have solved the question in general, as the given question is incomplete

The complete question is:

The ratio of the measures of the three sides of a triangle is 9:7:5. Its perimeter is 191.1 inches. Find the measure of each side.

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The ratio of the mass of Earth to the mass of Jupiter is equal to 3.14*10⁻³, thus option B is correct.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Given, the mass of Earth = 5.97*10²⁴ kg

Also, mass of Jupiter = 1.90*10²⁷ kg

Hence, ratio of mass of Earth to Jupiter is calculated by dividing mass of Earth upon the mass of Jupiter.

Ratio = (5.97*10²⁴/1.90*10²⁷ )

= 3.14*10²⁴⁻²⁷

= 3.14*10⁻³

Thus, the ratio of the mass of Earth to the mass of Jupiter is equal to 3.14*10⁻³, thus option B is correct.

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The dates the survey was conducted are not crucial to the findings, so the researcher is not required to report them. It is "false" to say that.

This information is thorough data that was acquired from the a target audience regarding a particular subject to perform research.

Thus, it is "false" to say that the dates the survey was conducted are not crucial to the findings, so the researcher is not required to report them.

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The solution of the given system of equation is (6, 12). So the option c is correct.

In the given question, Carissa works as a babysitter during her summer vacation.

She gets paid one rate for daytime hours and a higher rate for nighttime hours.

One week, she worked 12 daytime hours and 4 nighttime hours and earned $120.

The next week, she earned $60 for a total of 4 daytime hours and 3 nighttime hours.

Let x represent the hourly daytime rate and y represent her hourly nighttime rate.

The system of equations is

12 x + 4 y = 120……………(1)

4 x + 3 y = 60……………(2)

We have to find the solution to the system of equations.

To find the solution for the system of equation we solve the given equation using elimination method.

Multiply equation by 3 on both sides, we get;

12x + 9y = 180

Subtract equation 3 and 1

12x+9y-(12x+4y)=180-120

12x+9y-12x-4y=60

5y=60

Divide by 5 on both side, we get;

y=12

Now putting the value of y in equation 2

4x+3×12=60

4x+36=60

Subtract 36 on both side, we get

4x=24

Divide by 4 on both side, we get

x=6

Hence, the solution of the given system of equation is (6, 12). So the option c is correct.

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Answer:  (6, 12)

Step-by-step explanation: did edge test

Answer:

84%

Step-by-step explanation:

21/25=?/100  ==> decimal value is dividing a number by 100

100 * 21/25=100 * ?/100  ==> percent value is multiplying a decimal by 100

2100/25 = ? ==> solve for ?

? = 84%

Answer:

21 is 84% of 25

please mark brilliant

Answer:

Step-by-step explanation:

A: If she were to travel 1 block every minute it would take 24 minutes because there are 24 blocks but if she were to travel two blocks every minute it would take 12 minutes because 24/2 is 12.

B: 1=24, 2=12, 3=8, 4=6, 6=4, 8=3, 10=2 4/10, 12=2, and 24=1

C: The speed causes the time to change because the faster she goes the quicker she will get there.

D: No, because the time it takes her constantly changes with there being no constant rate.

If another freight train leaves an hour later from the same station and also heads east at 25 mph. The second freight train catches up with the first one by 11:12 pm.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

The relative speed for the given condition is,

=25 mph - 20mph

=5 mph

Relative distance = relative speed × time

Relative distance = 5 mph × 1 hour

Relative distance = 5 miles

The time will the second freight train catch up with the first one is obtained as,

Distance = speed × time

5 miles = 25 mph × t

t = 5 / 25

t=0.2 hour

1 hour = 60 minute

0.2 hour = 60 × 0.2

0.2 hour = 12 minute

=10:00 + 60:00 +12:00

=11:12

Thus, if another freight train leaves an hour later from the same station and also heads east at 25 mph. The second freight train catches up with the first one by 11:12 pm.

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The value of x in the linear inequality 5/8x - 1 ≥ 9 is x ≥ 16

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.

An inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).

In the problem given;

5/8x - 1 ≥ 9

Solving for x in the inequality;

x ≥ 16 which can be represented using an interval notation as [16, ∞)

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The answer to this Question is (5^7)*(x^7/5), the question is based on exponents laws

What are exponent laws?

These are some basic laws in maths that helps us to simplify the complicated expressions easily

Solution:

Here we can first distribute the power 7 to both 5 and 5th root of x by exponent laws

we get 5^7 * 5th root(x)^7

now we know nth root(x) = x ^1/n

we will do the same as

we get 5^7 * x^7/5 which is our required answer and there many more properties of exponents that we study in higher classes

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The value of x is 69°.

What is a quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined.

Given that ABCD is a quadrilateral.

The diagonal AC divides the quadrilateral into 2 triangles △ABC and △ACD.

The length of sides AC and CB of the △ABC is same. Thus △ABC is isosceles triangle. Therefore ∠BAC = ∠ABC = x°.

Similarly, the length of sides AC and CD of the △ADC is same. Thus △ADC is isosceles triangle. Therefore ∠CAD = ∠CDA = 66°

Given that ∠DCB = 90°.

∠A = ∠CAD + ∠BAC = 66° + x°

The sum of all interior angle of a quadrilateral is 360°.

Therefore,

∠A + ∠B + ∠C + ∠D = 360°

66° + x° + x° + 90° + 66° = 360°

Add to the like terms:

222 + 2x = 360

Subtract 222 from both sides:

2x = 138

x = 69

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Answer:

The answer is 81.85%

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean.

The z score is given by:

z = x - μ/σ

where,

For x = 88

z = 88 - 116/14

z = (-2)

For x = 130

z = 130 - 116/14

z = (1)

Thus,

P(88 < x < 130) = P(-2 < z < 1)

= P(z < 1) - P(z < -2)

= 0.8413 - 0.0228 = 81.85%

Thus, 81.85% of the population would be between 88 and 130.

Yes, Gabby is correct. Lake city is warmer at 8F  than Ellenville.

Temperature is defined as the sum of the kinetic energies of all the atoms or molecules in a substance. The kinetic energy of a substance's constituent particles varies. A distribution can be used to depict the particles' kinetic energy at any particular moment.

Temperature is measured in Fahrenheit, Celsius and Kelvin.

As minus sign with the temperature depicts cold and hot and it have to do nothing with the calculation. The correct way is 14-6 = 8f. So Gabby is correct. We will not consider minus sign with six in calculations.

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Answer:

Step-by-step explanation:

4.2430

Answer:

x≤−10

Step-by-step explanation:

x−(−11)≤1

Step 1: Simplify both sides of the inequality.

x+11≤1

Step 2: Subtract 11 from both sides.

x+11−11≤1−11

x≤−10

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Answer:

C

Step-by-step explanation:

If you draw multiple vertical lines through each graph, C is the only graph that touches the line once. Which means it passes the vertical line test.

Answer:

see explanation

Step-by-step explanation:

By the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0

if (r - 4) is a factor then substituting r = 4 into the polynomial should result in it having a value of zero, that is

6[tex]r^{4}[/tex] - 17r³ - 46r² + 77r - 20 ( substitute r = 4 )

= 6[tex](4)^{4}[/tex] - 17(4)³ - 46(4)² + 77(4) - 20

= 6(256) - 17(64) - 46(16) + 308 - 20

= 1536 - 1088 - 736 + 288

= 0

Then (r - 4) is a factor of the polynomial

Answer:

4

Step-by-step explanation:

Constant of proportionality is the same as slope in the context of a linear function, which is defined as Δy / Δx. We can find this by taking two points and finding the difference in their x- and y-coordinates.

I'll use (1, 4) and (2, 8).

[tex]\textrm{slope}=\dfrac{8-4}{2-1} = \dfrac{4}{1} = 4[/tex]

The lengths of the three sides are 14 feet, 19 feet and 23 feet respectively.

The formula for determining the perimeter of a triangle is expressed as;

Perimeter = a + b + c

Where; a, b and c are the length of the sides

From the information given, we have that;

56 = 2z- 5 + 5 + z + z

collect like terms

56 = 4z

Make 'z' the subject of formula

z = 56/4

z = 14

Shortest side, z = 14 feet

Second side, y = 5 + z = 19 feet

Third side, x = 2z - 5 = 2(14) - 5 = 23 feet

Hence, the values are 14 feet, 19 feet and 23 feet respectively.

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109 dollars in her savings account is greater than  -21 dollars in her checking account, that is 109 > -21.  When comparing values that may not be equal that is, when one value is bigger or less than another inequalities are utilised.

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Answer:

[tex]\sf 0.19\overline{2} \quad Repea\:\!ting[/tex]

[tex]\sf 0.\overline{314} \quad Repea\:\!ting[/tex]

0.5353...   Repeating

0.7777  Non-repeating

Step-by-step explanation:

A repeating decimal is a decimal number with a digit (or group of digits) that repeats forever.

There are three ways to show a repeating decimal:

[tex]\sf 0.19\overline{2}[/tex]

This is a repeating decimal as the line over the "2" means that this digit repeats forever.

[tex]\sf 0.\overline{314}[/tex]

This is a repeating decimal as the line over the "314" means the group of digits 314 repeats forever, e.g. 0.314314314...

0.5353...

This is a repeating decimal as there are two duplicates of the repeating block of digits "53" followed by an ellipsis.

0.7777

This is non-repeating decimal as there are no dots or lines above any of the digits, nor an ellipsis after the repeating digits.

Answer:2 to 4 pounds per

Step-by-step explanation:

since we know that PQ and PR are twin sides, well, the angle they each make at the base are also twin angles, Check the picture below.

The fish's position with respect to the water's surface at 4:00 p.m. is 3/4.

What is a fraction?

Any number of equal parts is represented by a fraction, which also means a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Here, we have

Based on the given conditions, formulate: 3 1/4 - 2 1/2

Remove the parentheses: 3 + 1/4 - 2 - 1/2

Reorder and combine like terms: (3-2)+1/4 - 1/2

Calculate the sum or difference: 1+ 1/4 - 1/2

Expand the fraction to get the least common denominator: 4/(1×4) + 1/4 - 2/(2×2)

Calculate the product or quotient: 4+1/4 - 2/(2×2)

Calculate the product or quotient: 4 + 1/4 - 2/4

Write the numerators over the common denominator: 4 + 1 -2/4

Calculate the sum or difference: 5 - 2/4

Calculate the sum or difference: 3/4

Hence, the fish's position with respect to the water's surface at 4:00 p.m. is 3/4.

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Answer: 60

Step-by-step explanation:

3 / 100 * x = 15

3x = 1500 multiply both sides by 100

x = 500

500x0.12 = 60

The 12 percentage of the number is A = 60

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let's call the number we're looking for N

We can set up an equation based on the information given:

0.03N = 15

To solve for N, we can divide both sides by 0.03:

N = 15 / 0.03

N = 500

So the number we're looking for is 500

Now , the percentage value is = 12 %

And , we can find 12% of that number by multiplying it by 0.12:

A = 0.12 x 500 = 60

Hence , 12% of the number is 60.

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