Find the values of the variables and the measure of the angles.

Gavin worked 7 hours on his tutoring job and 3 hours on his landscaping job

A system of equations is a group of two or more equations with the same variables. A solution to a system of equations is the values of the variables that make all of the equations in the system true. A solution to a system is also an intersection point of the graphs of the equations in the system.

Let;

We need to write system of equations to solve this problem.

14x + 13y = 137 ...eq(i)

x + y = 10 ...eq(ii)

Solving equation (i) and (ii),

x = 7 and y = 3

He worked 7 hours tutoring and 3 hours landscaping

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Answer:

Step-by-step explanation:

By determining the value of y when x=1, we'll find the constant of proportionality.

[tex]\sf y=0.5[/tex]

when, x = 1

The constant of proportionality:-

[tex]\sf \cfrac{y}{x},\:is\:\cfrac{0.5}{1}\: or \: 0.5[/tex]

Therefore, your answer is 0.5 .

________________________

Hope this helps!

Have a great day!

Answer: 50 mph

Step-by-step explanation:

Answer: A 550g box for $10.89

Step-by-step explanation:

Represent each option as grams per dollar

225g / $5.77 = 38.99g / $1.00

550g / $10.89 = 50.51g / $1.00

725g / $16.89 = 42.92g / $1.00

The second option gives the most grams per dollar

The number of trips that can be taken based on the money than they have is 27 trips.

The amount that each person has is illustrated below:

Carlos = $120

Roxana = $200

Claudia = $180..

In order to travel around Ambato, $18 is needed. Therefore, the trips that can be taken will be:

= Total amount / Value for each trip

= ($120 + $200 + $180) / 18

= 500 / 18

= 27

There'll be 27 trips.

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Answer:

3/19

Step-by-step explanation:

No. of people who ordered the small lemon yogurt divided by total no. of people

= 9/57

= 3/19

The number of times that 3.08 × 10^8 is greater than 4.4 ×× 10^6 as a scientific notation is 0.7 × 10^2.

Scientific notation simply means the way of expressing numbers that are too big or too small.

In this case, the numbers that are given are 3.08 × 10^8 and 4.4 ×× 10^6

Then we have to divide them to know the number of times that it's greater. This will be:

= (3.08 × 10^8) / (4.4 × 10^6)

= 0.7 × 10^2

This illustrates scientific notation.

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The total length of the wood attached together is 31.89 centimetres

Size of the wood found by Camille = 15.65 centimetres

Size of the wood found by her friend = 16.24 centimetres

The act of determining an object's length in some standard or non-standard units is known as a length measurement. In our daily lives, the ability to measure length is crucial.

Let's say Mathew is shopping with a friend when he notices a lovely picture frame that can be displayed in his parent's bedroom. But how would he go about telling them how long the frame was? If he knows the length of a particular unit, such as 3 feet, he can do that.

The total length of the wood = 15.65 + 16.24 = 31.89 centimeter

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The value of x when he equation given is solved is x = 4/27.

To solve for x in an equation, we have to apply all necessary properties of equality to will enable us isolate x to one side of the equation. The value of x is the solution to the equation that will make the equation a true statement.

Given the equation:

4(4/4x) + 5 = 32

Subtract 5 from both sides

4(4/4x) + 5 - 5 = 32 - 5 [subtraction property of equality]

4(4/4x) = 27

4/x = 27

Cross multiply

4 = 27(x)

4 = 27x

Divide both sides by 27 [division property of equality]

4/27 = 27x/27

4/27 = x

x = 4/27

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Answer:

6.75

Step-by-step explanation:

I've had this question before. You solve like this:

4/4 = 1 so x.

so 4 times x is 4x. You then subtract 5 from each side.

4x+5-5=32-5

4x=27 Divide both sides by 4 to get

x=27/4 which as a decimal is 6.75.

Answer:

21

Step-by-step explanation:

175 x 3 = 525. Divide that by 25 and you get 21.

If a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal, then, he/she is incorrect as 3.8¯ can be represented as a fraction which is (35/9).

As per the question statement, a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal.

We are required to determine if the claim is correct or incorrect, and if the claim is correct, then we will have to justify our answer, while if it is incorrect, we will have to determine the fraction that is equal to 3.8¯.

To solve this question, let us first try to convert our concerned decimal 3.8¯ into its equivalent fraction.

Now, 3.8¯ = 3.888...

Let us assume a random variable "x" such that, 3.8¯ = x = 3.888...

Then, 10x = (10 * 3.888...) = 38.888...

Now, [(10x - x) = {(38.888...) - (3.888...)}]

Or, (9x = 35)

Or, x = (35/9)

That is, the non-terminating decimal 3.8¯ can be converted to a fraction which is equal to (35/9).
Hence, the student's claim that that 3.8¯ is an irrational number because it is a non-terminating decimal is incorrect.

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The result of the equation 4 x + 2 + x = x – 19 is - 5.25.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables.

Given equation -

4 x + 2 + x = x – 19

Simplify the equation

5x + 2 = x - 19

5x - x = -19 - 2

4x = -21

x = -21 / 4

x = -5.25

Hence, -5.25 is the answer to the equation 4 x + 2 + x = x - 19.

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Solving an inequality, it is found that the interval over which the function y = 2x + 1 is positive is given by:

(-1/2, ∞).

To verify if the function is positive or negative, we have to look at the graph of the function relative to the x-axis, as follows:

In the context of this problem, the function is given by:

y = 2x + 1.

We want to find when the function is positive, hence we have to solve this following inequality:

y > 0

2x + 1 > 0

2x > -1

x > -1/2.

Hence the interval is:

(-1/2, ∞).

The problem asks for the interval in which the function is positive.

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

Step 01:

time = 98.4 minutes

rate = 8.2 minutes per mile = 8.2 minutes / mile

distance = ?

Step 02:

distance = 12 miles

The answer is:

Jasmine ran 12 miles.

The least common denominator (LCD) of the fractions 3/10 and 2/15  is 30.

Given fractions:

3/10 and 2/15

First the least common multiple for denominators (10,15) is 30.

Calculations to rewrite the original inputs to equivalent fractions with LCD:

3/10 = 3/10 * 3/3 = 9/30

2/15 = 2/15 * 2/2 = 4/30

Therefore the least common denominator (LCD) of the fractions 3/10 and 2/15  is 30.

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Answer:

3.2

Step-by-step explanation:

Any number raised to the zero power is one. 3.2 x 1 = 3.2

74.5645 miles is 120 kilometers per hour.

Divide the speed of the vehicle by 1.609 to get an approximation.

Therefore, 120 kilometers per hour = 120/1.609

=74.5645 miles per hour

74.5645 miles is 120 kilometers per hour.

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The rectangular playing field's perimeter is 290 yards. The field's length is 5 yards less than its width. The playing field's measurements length and width will be 70 and 75.

Given that,

In Hadleyville, a brand-new community wellness complex is being constructed. The rectangular playing field's perimeter is 290 yards. The field's length is 5 yards less than its width.

We have to find what are the playing field's measurements.

Take the width as x.

Length is x-5.

Perimeter of the rectangle is 2l+2w

290=2l+2w

290=2(x-5)+2x

290=2x-10+2x

290=4x-10

4x=290+10

4x=300

x=300/4

x=75

The length will be x-5=75-5=70

The width will be x=75

Therefore, the playing field's measurements length and width will be 70 and 75.

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Answer:

158.4

Step-by-step explanation:

32% multiple 495

=158.4

Answer:

y = x - 5

Point Slope form: y + 8 = 1 (x + 3)

Step-by-step explanation:

(-3,-8) and (-7,-12)

(x₁, y₁)         (x₂, y₂)

        y₂ - y₁        -12 - (-8)         -12 + 8         -4

m = ------------ = --------------- = -------------- = -------- = 1

        x₂ - x₁          -7 - (-3)          -7 + 3          -4

y - y₁ = m(x - x₁)

y - (-8) = 1(x - (-3))

y + 8 = x + 3

   -8         -8

---------------------

y = x - 5

I hope this helps!

lilkyky67, this is the solution:

Let's recall that the angles in the image are consecutive interior angles and they add up to 180 degrees.

Therefore,

12x - 29 + 4x + 1 = 180

16x - 28 = 180

Adding 28 at both sides:

16x - 28 + 28 = 180 + 28

16x = 208

Dividing by 16 at both sides:

16x/16 = 208/16

x = 13

Now, we can find out the measures of the two angles, as follows:

First angle:

12x - 29 = 12 * 13 - 29

156 - 29 = 127

Second angle:

Using the given description < NOP is found to be 46 degrees

given data]

< OPQ = ( 9x - 19 ) degrees

< PNO = ( 2x + 5 ) degrees

< NOP = ( 3x + 16 ) degrees

From the figure described

let < NPO = y

< PNO + < NOP + y = 180 degrees ( sum of angles of triangle )

< OPQ + y = 180 degrees ( linear pair theorem )

Hence we equate both

< PNO + < NOP + y = < OPQ + y

< PNO + < NOP  = < OPQ + y - y

< PNO + < NOP  = < OPQ

( 2x + 5 ) + ( 3x + 16 ) =  ( 9x - 19 )

2x + 3x + 5 + 16 = 9x - 19

5x + 21 = 9x - 19

21 + 19 = 9x - 5x

40 = 4x

x = 40 / 4

x = 10

< NOP = ( 3x + 16 ) degrees

< NOP = ( 3 * 10 + 16 ) degrees

< NOP = ( 30 + 16 ) degrees

< NOP = 46 degrees

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Step 1: write out the formula

The simple interest on the loan can be calculated using the formula:

where p is the principal, in our case, it is the loan = $51000

r is the rate = 10%

t is the time = 1 year

Step2: substitute the values into the equation.

Our next step is to put the values of p, r, and t into the equation so that

Therefore, the simple interest on the loan is $5, 100

Through the given equation the simplification of (4x-6)-(5x+1) is = -x -7.

An illustration of distributive property:

When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you wish to multiply 5 by the product of 10 plus 3. When two terms are similar, we often sum the two amounts before multiplying by 5. However, the property states that you should first multiply each addend by 5.

The expression provided is:

(4x-6)-(5x+1)

Using the distributive property, expand the brackets to get:

4x-6- 5x-1

Organize the terms to get,

4x- 5x -1 -6

combine similar phrases to simplify to obtain;

-x -7

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7.13 x 6 = 42.78

7 x 6 = 42

0.1 x 6 = 0.6

0.03 x 6 = 0.18

12 + 0.6 + 0.18 = 42.78

Answer:

An equivalent function to the given function is;

Explanation:

Given the function;

we want to find an equivalent function to the given function;

Applying the rules of exponent;

Therefore, An equivalent function to the given function is;

Expression is a combination of numbers, operators and variables. the value of the expression −51 − 17 − (−37) is -31.

Expression is a combination of numbers, operators and variables.

The given expression is minus fifty one minus seventeen minus of minus thirty seven.

−51 − 17 − (−37)

We have to use BODMAS rule to solve this expression

-51-17+37

Now add  minus fifty one and minus seventeen

We get minus 68

-68+37

Now subtract 37 from 68 and put minus sign in the answer.

We get answer as minus thirty one.

-31

Hence option C is correct. the value of the expression −51 − 17 − (−37) is -31.

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The expression that is equivalent to [tex]\frac{5^{-10}}{5^{4}5^{0}}[/tex] is 1/5¹⁴

Expression:

An expression is a mathematical statement that does not contain an equal sign. It cannot be solved for unless the value of the variable is given.

Given,

Here we have the expression [tex]\frac{5^{-10}}{5^{4}5^{0}}[/tex]

Now we need to find the equivalent expression for this one.

In order to find the equivalent expression first we have to simplify the given expression.

For that we have to use the exponent rule,

1) Product of powers rule

When we multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

2) Quotient of powers rule

When we dividing two bases with same value, keep the base the same, and then subtract the exponent values.

3) Negative exponent rule.

While we have the negative exponent then we have to convert them into fraction.

Based on the rule 1, we have simplify the denominator as,

[tex]\frac{5^{-10}}{5^{4}5^{0}}=\frac{5^{-10}}{5^{4+0}}\\\\= > \frac{5^{-10}}{5^{4}}[/tex]

Now we have to apply the rule (2), then we get,

=> 5⁻¹⁰⁻⁴

=> 5⁻¹⁴

Finally, we have to apply the thirds rule,

=> 1/5¹⁴

Therefore, the equivalent expression is  1/5¹⁴.

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Answer:

limit = 1

Step-by-step explanation: