if the measure of arc CDE=118 degrees and the measure of arc EF=62 degrees calculate measure of angle FGE

Answer: 450

Step-by-step explanation:

x is the original price.

40 percent times x = 180

or [tex]\frac{40}{100}[/tex] times x= 180

multiplying both sides by 100 and dividing by 40

x=180 times [tex]\frac{100}{40}[/tex]

now just do 180 times 100 divided by 40

which gives you 450

If my disposable income from a part-time job in 2019 was $17,000, and I repaid a loan of $560 at 15 percent interest, borrowed in 2018 from my income of 2019, then I will have $ available for spending in 2019.

As per the question statement, my disposable income from a part-time job in 2019 was $17,000, and I repaid a loan of $560 at 15 percent interest, borrowed in 2018 from it.

We are required to calculate the amount I will be left with, to spend in 2019.

To solve this question, first, let us calculate the amount we had to pay to close our loan of 2018, along with it's 1 year's interest.

Since the loan was repaid in a year, hence, it does not matter if the interest was simple or compound as the magnitude of simple and compound interest on the same principle and at same rate of interest for a year is equal.
Let us proceed with the consideration that the interest was compounded annually at the rate of 15% per annum.

As per the basic formula of Compound Interest,

[tex]A=[P*(1+\frac{R}{100})^n][/tex]

Where, A = Final Amount i.e., (Principle + Interest).

P = Principle on which Interest in compounded

R = Rate of Compound Interest per annum

n = Time period of interest .

Here, (P = $560), (R = 15%) and (n = 1).

Therefore, total amount to be repaid to close the loan in 2019

[tex]=[560*(1+\frac{15}{100})^1]\\\\=[560*(1+\frac{3}{20})]\\=[560*(\frac{20+3}{20})]\\ =(560*\frac{23}{20})\\ =(28*23)\\=644[/tex]

Hence, my left-over balance after paying $644 from my disposable income of $17,000 which I earned from a part time job in 2019, will be $(17000 - 644) = $16356.

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Answer:

$170.80

Step-by-step explanation:

Since it's $4.88 per yard, you could times that by 35, because she bought 35 yards of fencing.

Equation:

4.88(35)

   or

4.88x   x=35

I hope this helped! <3

The amount invested at each rate is $30,000 at 4%, and $2000 at 6%.

Given that;

Larry Mitchell invested part of his $32,000 advance at 4% annual simple interest and the rest at 6% annual simple interest.

If his total yearly interest from both accounts was $1,340.

To find;

The amount invested at each rate.

Let x is the amount at 4%, therefore the amount at 6% is 32000 - x.

The total interest is:

0.04x + 0.06(32000 - x) = 1320

0.04x - 0.06x + 1920 = 1320

0.02x = 1920 - 1320

0.02x = 600

x = 600/0.02

x = 30,000

The amount at 6% is:

$32,000 - $30,000 = $2000

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The amount of supply (in inventory) expense of the company during the year is $160

The amount of supplies at the start of the year = No supplies

Amount of supplies bought during the year = $200

The amount paid for the supply = $150

Amount of supplies left at the end of the year = $40

Required: The supply expense for the period

Solution:

Supply expense = Amount bought on credit - Amount remaining

Therefore;

Supply expense = $200 - $40 = $160

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9x+3y=18 and 5x+2y=10.75

where x is price of 1 cookie and

y is price of 1 brownie.

steps for writing  Systems of Linear Equations from Word Problems:

Savannah and Serenity were goes to the bakery for purchasing some cookies and brownies .

We have to write a system of linear equations for the given condition .

Let the cost of 1 cookie be  $x and

cost of 1 brownie be  $y

Savannah bought 9 cookies and 3 brownies at  $18

so, linear equation for this situation is

9x+3y=18

Serenity bought 5 cookies and2 brownies at  $10.75

so, linear equation for this situation is

5x+2y=10.75

Hence, System of equations for the given situation is

9x+3y=18 and

5x+2y=10.75

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The value of g(-4) is (-18)

A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given function:

g(x)=5x+2

So, the value of g(-4)

g(-4) = 5(-4) +2

g(-4) = -20+2

g(-4) = -18

Hence, the value of g(-4) is -18.

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Answer:

[tex]5z^2+3z[/tex]

Step-by-step explanation:

[tex]z\left(5z+3\right)=z\cdot \:5z+z\cdot \:3\\z\cdot \:5z+z\cdot \:3\\z \cdot 3 = 3(z)[/tex]

5z becomes squared

[tex]z\cdot \:5z\\= 5z^2[/tex]

z • z = z²

Remove parentheses

[tex]3(z)\\= 3z\\= 5z^2 + 3z[/tex]

Hope this helps.

According to the solving the explicit rule:

y = 52000 - 58000 * x

The explicit formula for an arithmetic sequence is a = a + (n - 1)d, and each term of the sequence may be computed without knowing the previous terms of the sequence. In general, the explicit formula is the nth term of an arithmetic, geometric, or harmonic sequence.

An implicit function is a function containing numerous variables, one of which is a function of the other set of variables. An explicit function is one in which the dependent variable may be clearly stated in terms of the independent variable.

Initial = 52000

Rate = 58000 each year

Determine the equation of the graph:

The equation can be used:

Amount = initial - rate * years

We used minus (-) because, the amount reduces as the student pays.

So,

y = amount

x = years

we have:

y = initial  - rate * x

putting the values we get:

y = 52000 - 58000 * x

According to the solving the explicit rule:

y = 52000 - 58000 * x

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An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

The expression 6 - 5 x 3 does not have the value 3.

6 - 5 x 3 = - 9

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

The math operation can be addition, subtraction, multiplication, or division.

We have,

-3( 4 - 5 )

= -3 x -1

[minus x minus = positive]

= 3

|-2| + 1 ( 3 - 2)

The modulus of any value is always positive.

= 2 + 1 x 1

= 2 + 1

= 3

-8 ÷ -4 + 1

Minus gets canceled after division.

= -8/-4 + 1

= 2 + 1

= 3

6 - 5. 3

= 6 - 15

= -9

Thus all the expressions have a value of 3 except the expression

6 - 5 x 3.

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Applying the inscribed angle theorem, the measures of the angles indicated are:

a. m<EDF = 53°

b. m<BCD = 92°

c. m<SWV = 37°

The inscribed angle theorem is a circle theorem that explains the relationship between the measure of an inscribed angle and the measure of the intercepted arc in a circle. It states that:

the measure of the inscribed angle = 1/2(the measure of intercepted arc).

Use the inscribed angle theorem to find the arc and angle measures indicated:

a. m<EDF = 1/2(106)

m<EDF = 53°

b. m<BCD = 180 - 88 (opposite angles in a cyclic quadrilateral have a sum of 180 degrees)

m<BCD = 92°

c. m<SWV = 1/2(74)

m<SWV = 37°

Therefore, applying the inscribed angle theorem, the measures of the angles indicated are:

a. m<EDF = 53°

b. m<BCD = 92°

c. m<SWV = 37°

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Answer:

X= 5, -9

Step-by-step explanation:

1. Move all terms not containing |x+2| to the right side of the equation.

3|x+2|=21

2. Divide each term in 3|x+2|=21 by 3 and simplify

|x+2|=7

3. Remove the absolute value term. This creates a ± on the right side of the equation because |x| = ±x

x+2= ±7

4. The complete solution is the result of both the positive and negative portions of the solution

x= 5, -9

-Rocketgamer360

f(x)=-4x+1

h(x)=19-3x

Using the concept of function we can solve the question

A function can be defined as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

f(-6) can be found out by substituting x=-6 in f(x)

  f(-6)=-4×(-6)+1

 f(-6)=24+1

 f(-6)=25

The question h(8)-f(-7) can be solved by first finding value of 8 in h(x)

h(8)=19-(3×8)

h(8)=19-24

h(8)=5

Now lets find f(-7)

f(-7)=-4×(-7)+1

f(-7)=28+1

f(-7)=29

Now we can find h(8)-f(-7) by substituting the values of h(8) and f(-7), which was found earlier

h(8)-f(-7)=5-29

h(8)-f(-7)=-24

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The correct question is " f(x)=-4x+1,h(x)=19-3x then find f(-6) and h(8)-f(-7)."

Answer:

Fraction-12/25     Decimal-0.48

Step-by-step explanation:

To divide fractions, we have the use the term, Keep, Change, Flip.

In this case, the two fractions are 2/5 and 5/6.

First, we Keep the 2/5.

Now, we Change the division sign by a multiplication sign.

So it would look like 2/5x5/6.

Now, for the final step, we Flip the second fraction.

Now, the question would look something like this.

2/5x6/5.

Now, we multiply.

2x6=12,  and 5x5=25.

The answer would be 12/25.

In decimal form, it would be 0.48.

Hope that helped!  :D

Answer:

Step-by-step explanation:

Simplification in steps:

The solution of the expression -2/5 x -1 1/4 is 1/2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

-2/5 x -1 1/4

Express the fractions as improper fraction

So, we have

-2/5 x -1 1/4 = -2/5 x -5/4

Evaluate the product

So, we have

-2/5 x -1 1/4 = 10/20

Divide the fraction

So, we have

-2/5 x -1 1/4 = 1/2

Hence, the solution of the expression -2/5 x -1 1/4 is 1/2

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a) The total dollar interest payments for the six months using the short-term financing interest rates is $377.73.

b.1) The total dollar interest payments for the six months using the long-term financing interest rate is $442.00.

b.2) If long-term financing at 12 percent had been utilized throughout the six months, the total-dollar interest payments would be larger than with the short-term financing plan by $64.27.

Month     Amount     Interest Rate         Interest       Long-Term

                              Annual   Month       Amount    Rate   Amount

January   $9,700     6%          0.50%     $48.50      1%     $97.00

February $3,700      7%          0.58%       21.46       1%       37.00

March     $4,700     10%          0.83%       39.01       1%       47.00

April       $9,700      13%          1.08%      104.76       1%      97.00

May      $10,700      12%          1.00%      107.00       1%    107.00

June      $5,700      12%          1.00%       57.00       1%      57.00

Total interest amount =                       $377.73            $442.00

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Carmen's Beauty Salon has estimated monthly financial requirements for the next six months as follows:

Month     Amount     Interest Rate

January   $9,700               6%

February $3,700                7%

March     $4,700               10%

April       $9,700                13%

May      $10,700                12%

June      $5,700                12%

a) Compute total dollar interest payments for the six months.

b.1) Compute the total dollar interest payments if the long-term financing at 12% had been used throughout the six months.

Answer:

The slope intercept of a line is given by y=mx+c, where:

m=slope, c=y-intercept.

Thus the slope-intercept form of our equation will be:

-6+2y≤42

adding 6 in both sides we get:

-6+6+2y≤42+6

2y≤6

dividing both sides by 2 we get:

(2y)/2≤6/2

y≤3

the answer is y≤3

Step-by-step explanation:

A set of positive integers is typically represented as Z+.
It implies all the integers are greater than 0.
When writing a set of positive integers it would look like {1, 2, 3, 4, 5, 6, 7, etc.}

Answer:

anything that is a whole number more than 0

Step-by-step explanation:

In Compound inequality the value of the x is 1/14 < x and 2/3≤ x.

According to the statement

We have to find that the value of the compound inequality.

So, For this purpose, we know that the

A compound inequality consists of two inequalities that are joined together by the word "and" or the word "or".

From the given information:

The equations are:

1/2x -4< 3 and 7≤ 3x +5

Now solve these equations then

1/2x -4< 3

1/2x < 3+4

1/2x < 7

1 < 14x

The value becomes 1/14 < x.

And then take second equation:

7≤ 3x +5

7-5 ≤ 3x

2≤ 3x

The value becomes 2/3≤ x.

So, In Compound inequality the value of the x is 1/14 < x and 2/3≤ x.

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The circles whose shaded area is equivalent to 2/6 of the total area are:

a. The circle which is labeled 1/3 shaded.

b. The circle which is labeled 4/12 shaded.

Given, a circle is 2/6 shaded.

Six equal halves of a circle are separated, two of which are darkened. The circle is marked as shaded by two-sixths.

= 2/6

which means that the fraction can be simplified furthermore.

= 1/3

which means for every 3 parts, one part is shaded.

Therefore, we need to find the circle which has the shaded area equivalent to 2/6 of the total area, that is for every 3 parts of the parts, there should be one part shaded.

a. A circle is divided into 3 equal parts with 1 parts shaded

The circle is labeled 1 third shaded.

= 1/3 which is equivalent to the area of the circle 2/6.

b. A circle is divided into 5 equal parts with 2 parts shaded.

The circle is labeled 2 fifths shaded.

= 2/5 which is not equivalent to 2/6.

c. A circle is divided into 10 equal parts with 4 parts shaded.

The circle is labeled 4 tenths shaded.

= 4/10

= 2/5 which is again not equivalent to 2/6.

d. A circle is divided into 12 equal parts with 4 parts shaded.

The circle is labeled 4 twelfths shaded.

= 4/12

after simplifying it furthermore, we get:

= 1/3 which is equivalent to the area of the circle 2/6.

hence we get the desired results.

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Answer:

Step-by-step explanation:

If you add you will get 9.90 but thats not what you want so you have to divide I think in order to get your answer.

Answer:

30.69

Step-by-step explanation:

9.3 x 3.30=30.69

The expression 3 as a quotient of two integers can be represented by the expression 6/2

Expressions are mathematical statements that are represented by variables, coefficients and operators

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The expression is given as

3

Next, we multiply 3 by 1

So, we have

3 = 3 x 1

Next, we express 1 as a fraction where the numerator and the denominator are the same e.g. 2/2, 3/3, 4/4...

So, we have

3 = 3 x 2/2

Evaluate the product of 3 and 2

So, we have

3 = 6/2

Hence, the expression 3 as a quotient of two integers can be represented by the expression 6/2

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The minute hand moves a full circle in 60 minutes (1 hour); so 360 degrees.

10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.

Since a clock is a circle and circles have 360 degrees, and there are 60 seconds in one minute, the answer can be derived by using the equation:

360°/60 minutes = 6° per minute

Edited to replace 60 seconds with 60 minutes in the formula.

Therefore,

Answer is 60 minutes the hand make 1/6 of a rotation.

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The product of positive number with itself found as 361/36.

For the stated question;

The given number is 3 1/6, which is in mixed fraction.

Write the number in proper fraction.

3 1/6 = 19/6

Squaring the number means, multiplying the number with itself.

(19/6)² = (19/6) × (19/6)

(19/6)² = 361/36

Thus, the product of positive number itself found as 361/36.

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Answer:

Midpoint: (-1,-5)

Step-by-step explanation:

Answer:

a. 250

b. 70

c. 3

Step-by-step explanation:

w = weeks

70 + 3w = 250

3w = 250 - 70

w = (250 - 70) / 3

Step-by-step explanation:

got u bro

airpods=250

her saving=70

30 per week=30x6=180

180+70=250

so she have 6 weeks till she buys the airpods pro

Given Expression

[tex]9v^2-1=-77[/tex]

Step-By-Step Process.

________________

1. Add 1 to both sides of the equation.

[tex]9v^2-1+1=-77+1[/tex]

________________

2. Simplify.

[tex]9v^2=-76[/tex]

________________

3. Divide both sides by 9.

[tex]\frac{9v^2}{9} =\frac{-76}{9}[/tex]

________________

4. Simplify.

[tex]v^2=-\frac{76}{9}[/tex]

For [tex]x^2=f(a)[/tex] the solutions are [tex]x=\sqrt{f(a),} - \sqrt{f(a)} \\[/tex].

[tex]v=\sqrt{-\frac{76}{9} }, v=-\sqrt{-\frac{76}{9} }[/tex]

_________________

[tex]\sqrt{-\frac{76}{9}}=\frac{2\sqrt{19} }{3}i[/tex]

[tex]-\sqrt{-\frac{76}{9} } =-\frac{2\sqrt{19} }{3}i[/tex]

_________________

Solution:

[tex]v=\frac{2\sqrt{19} }{3}i,v=-\frac{2\sqrt{19} }{3}i[/tex]

Hope this helps!