Gwen borrows $300 from her parents to buy a bike. She agrees to pay them back plus 3% simple interest over one year. Write an equation to represent the total amount Gwen will owe her parents. What is the total amount of money Gwen will owe her parents?

GCF of 38 and 48

First find the prime factorization of 38 and 48.

38=2*19

48=2*2*2*2*3

The two number share the factor 2 and only 2. The GCF = 2.

Final answer:

The greatest common factor (GCF) of the number 38 is technically 38 itself. However, in the context of two or more numbers, it's the largest factor they share in common. For the single number 38, its factors are 1, 2, 19, and 38.

Explanation:

Finding the Greatest Common Factor (GCF) of 38

The greatest common factor of a number is the largest number that divides it, other than the number itself. Since 38 is a composite number and not a prime number, its factors are 1 and 38. The number 38 can also be divided evenly by 2 and 19, because 38 = 2 × 19. So, the factors of 38 are 1, 2, 19, and 38 itself. However, when we refer to the greatest common factor, it is usually in the context of finding the GCF between two or more numbers. For the single number 38, the GCF can be considered as the largest factor, which is 38 itself. But typically, the term 'greatest common factor' is more relevant when comparing it with another number to see the largest factor they have in common.

Answer:

6xy+x

Step-by-step explanation:

4xy+2xy=6xy

you do NOT ad the x since it is not xy

so the answer is 6xy+x

a. (3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. No, it is not possible to have more than one (x,y) pair that is solution to both equations

Step-by-step explanation:

a. Decide whether each neither of the equations,

i (3,4)

ii. (4,2.5)

ill. (5,5)

iv. (3,2)

To decide whether each point is solution to equations or not we will put the point in the equations

Equations are:

Equation 1: 6x + 4y = 34

Equation 2: 5x – 2y = 15

i (3,4)

Putting in Equation 1:

[tex]6(3) + 4(4) = 34\\18+16=34\\34=34\\[/tex]

Putting in Equation 2:

[tex]5(3) - 2(4) = 15\\15-8 = 15\\7\neq 15[/tex]

ii. (4,2.5)

Putting in Equation 1:

[tex]6(4) + 4(2.5) = 34\\24+10=34\\34=34\\[/tex]

Putting in Equation 2:

[tex]5(4) - 2(2.5) = 15\\20-5 = 15\\15=15[/tex]

ill. (5,5)

[tex]6(5) + 4(5) = 34\\30+20=34\\50\neq 34[/tex]

Putting in Equation 2:

[tex]5(5) - 2(5) = 15\\25-10 = 15\\15=15[/tex]

iv. (3,2)

[tex]6(3) + 4(2) = 34\\18+8=34\\26\neq 34[/tex]

Putting in Equation 2:

[tex]5(3) - 2(2) = 15\\15-4 = 15\\11\neq 15[/tex]

Hence,

(3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. Is it possible to have more than one (x, y) pair that is a solution to both

equations?

The simultaneous linear equations' solution is the point on which the lines intersect. Two lines can intersect only on one point. So a linear system cannot have more than one point as a solution

So,

a. (3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. No, it is not possible to have more than one (x,y) pair that is solution to both equations

Keywords: Linear equations, Ordered pairs

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The pair (3, 4) is a solution to both equations. The pairs (4,2.5), (5,5), and (3,2) are not solutions for either equation. There can be multiple solutions to simultaneous equations if the equations represent identical lines.

The subject of these equations involves the concept of simultaneous equations. We substitute the (x, y) pairs into both equations to determine whether they are solutions or not.

In simultaneous equations, it's possible to have more than one solution if the equations represent identical lines, otherwise there is usually a unique solution.

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Answer:

f(1/2)=6

Step-by-step explanation:

f(x)=3^2x+1

f(1/2)=3^(2*1/2)+1

f(1/2)=3^(1)+3

f(1/2)=3+3

f(1/2)=6

Answer:

f(1/2)=9

Step-by-step explanation:

f(1/2)=3^2(1/2)+1

f(1/2)=3^1+1

f(1/2)=3^2

f(1/2)=9

Answer:

y=2

Step-by-step explanation:

-1+8y=23-4y

-1+12y=23

12y=24

y=2

Answer:

THE FISRT GRAPH FOR THE QUESTION IS THE CORRECT ANSWER

Answer:

answer A or the first option

Step-by-step explanation:

Well, the main rules for negative numbers are that a negative combined with a negative always makes a positive. This rule applies almost everywhere, except subtraction. So, the rule also applies in division. So no matter what, if you divide a negative number with a negative number, the answer should always be positive.

The expression "negative 0.3 divided by negative 0.05" or -0.3/-0.05 has a positive quotient.

What is Quotient ?

Quotient is defined as the value resulting from dividing two numbers. When dividing two signed numbers (positive or negative), divide their absolute values and follow these rules:

(+) divided by (+) equals (+)

(-) divided by (-) equals (+)

(+) divided by (-) equals (-)

(-) divided by (+) equals (-)

To have a positive quotient, both the numerator and the denominator should have the same signs, either both (+) or both (-).

negative 0.3 divided by negative 0.05 :

-0.3/-0.05 = -/- = +

Therefore, The expression "negative 0.3 divided by negative 0.05" or -0.3/-0.05 has a positive quotient.

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Explanation:

Recall that the slope is equal to the rise/run.

Rise = change in y = change in distance

Run = change in x = change in time

If we have a horizontal line, then there is no change in y. The rise would be 0 here. The run can be anything you want. Let's just call it x

Slope = rise/run = 0/x = 0

Therefore, all horizontal lines have a slope of 0.

The slope of a distance time graph represents the velocity because

velocity = (change in distance)/(change in time) = rise/run = slope

for example, a velocity of 10 meters per second represents a change of 10 meters over 1 second. The rise here woud be 10 meters and the run would be 1 second.

Answer:

1/5

Step-by-step explanation:

First, put the equation into slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept.

5y=x+10, then divide both sides by 5;

y=1/5x+2

The slope is m, and m=1/5.

Answer: Any number between 25 and 35 excluding both endpoints

(ie the number cannot be 25, the number cannot be 35)

One possible answer is 27 but there are infinitely many other choices

=======================================

Explanation:

The notation p ^ q in a logic math class setting means "p and q". Basically its a way of saying "both p and q are the case of some event happening". More specifically, it means that we have some number that is greater than 25 AND it is also less than 35.

If x is that number then p translates to x > 25. Statement q translates to x < 35

Flip both sides of x > 25 to get 25 < x.

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

So we have 25 < x  and x < 35. Those two combine to 25 < x < 35

Therefore x is some number between 25 and 35, where we leave out both endpoints. You can pick any number from this interval.

Answer:

(18 miles/inch)(14 inches) = 252 miles

The distance between Nashville and Memphis is 252 miles.

Using the map scale of 1 inch to 18 miles, the distance between Nashville and Memphis, given as 14 inches apart on the map, is calculated to be 252 miles.

The question involves calculating the actual distance between two cities using a map scale. In order to find the distance between Nashville and Memphis, we'll use the scale given on the map to convert inches into miles.

The map scale is 1 inch:18 miles. Since the cities are 14 inches apart on the map, we can set up a simple multiplication to find the distance:

Therefore, the actual distance between Nashville and Memphis is 252 miles.

Answer:

see the explanation

Step-by-step explanation:

we have that

The scale factor is

[tex]1\frac{1}{2}=1.5[/tex]

we know that

To find the length of the segment CZ, multiply the segment CR by the scale factor

so

[tex]CZ=CR(1.5)[/tex]

substitute

[tex]CZ=4(1.5)=6\ units[/tex]

therefore

Roy's diagram is not correct, because on the graph, Roy draws the length of the CZ segment equal to 10 units instead of 6 units.

Roy is using a scale factor equal to 2.5 instead of 1.5.

Answer:

No solutions for x

Step-by-step explanation:

X+15=x

15=0

Which is obviously not true.

Answer:

35/9

Step-by-step explanation:

5/3*7/3

=35/9

Answer:

26/45 or about 58% of the log is left

Step-by-step explanation:

could be wrong though

Answer:

three fourth mile=[tex]\frac{3}{4} mile[/tex]

Step-by-step explanation:

Given

⇒

[tex]\text{Distance from house to store}=\frac{1}{3} \times \text{Distance from house to friends house}\\ \text{Distance from house to friends house}= 3\times \frac{1}{4}\\ \text{Distance from house to friends house}=\frac{3}{4}[/tex]

Distance from her house to friends house  [tex]\frac{3}{4}[/tex] miles

Answer:  x = -20

================================

Explanation:

The expression 18+x is the same as x+18. This is because we can add two numbers in any order to get the same result. Example: 2+3 = 3+2 = 5.

Whats happening to the x is we add on 18. To isolate x, we undo this operation to subtract 18 from both sides.

Keep in mind that subtracting a negative from a negative will have us add the positive versions of the number, and the final result is ultimately negative. So that's why -2-18 = -20. You can think of it as 2+18 = 20 and you make the 20 negative.

Here's how the steps look like

--------

18 + x = -2

x + 18 = -2

x + 18 - 18 = -2 - 18 ... subtracting 18 from both sides

x + 0 = -20

x = -20

Leon needs to use 1/3 cup of olive oil for the amount of 1 teaspoon of cinnamon to maintain the same proportion as the original recipe.

Leon originally had a recipe that called for 2 teaspoons of cinnamon and 2/3 cup of olive oil. He now wants to adjust the recipe because he only has 1 teaspoon of cinnamon. To keep the proportions the same, he needs to halve the amount of the other ingredients as well.

Therefore, if 2 teaspoons of cinnamon requires 2/3 cup of olive oil, then 1 teaspoon of cinnamon will require half of 2/3 cup of olive oil, which is 1/3 cup of olive oil.

Step-by-Step Calculation

Answer:

25 revolutions

Step-by-step explanation:

step 1

Find the circumference of the road roller

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=77\ cm[/tex]

Convert to meters

[tex]r=77\ cm=77/100=0.77\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14)(0.77)[/tex]

[tex]C=4.8356\ m[/tex]

step 2

Calculate the number of revolutions that the roller will take to cover an area of 96.8 meter square

Remember that

The circumference of complete circle subtends one revolution

The circumference multiplied by the wide of road roller is equal to the area cover for the roller in one revolution

[tex]wide=80\ cm[/tex] ----> [tex]wide=0.80\ m[/tex]

[tex]4.8356(0.80)=3.86848\ m^2[/tex]

so

using proportion

Find out the number of revolutions for an area of 96.8 meter square

[tex]\frac{3.86848}{1}\ \frac{m^2}{rev}=\frac{96.8}{x}\ \frac{m^2}{rev} \\\\x=96.8/3.86848\\\\x=25\ rev[/tex]

Answer:

Model a community, 77% of which is houses, by placing orange houses on 77 of the 100 squares in the grid.

Step-by-step explanation:

Answer:

OPTION C - Distributive Property

Step-by-step explanation:

Given: [tex]$ \frac{6x + 9}{3} $[/tex]

This is equal to: [tex]$ \frac{6x}{3} + \frac{9}{3} $[/tex]

⇒ [tex]$ 2x + 3 $[/tex]

Here, [tex]$ 3 $[/tex] is distributed over each term. Hence, distributive property is used.

Answer:

C. Distributive property

Step-by-step explanation:

From the question,

      [tex]\frac{6x+ 9}{3}[/tex] =  [tex]\frac{6x}{3} + \frac{9}{3}[/tex]     (distributive property of the denominator)

             = 2x + 3

The denominator in the question is distributive over the two terms in the numerator.

Answer:

She scored 1200 in all ten games

Answer:

1,200 points

Step-by-step explanation:

  120 points each game

×   10 games                  

   1, 200 points

Answer: No

Step-by-step explanation:

I can’t think of one but if you have a pegboard there is a formula called Pick’s Formula

Answer:

[tex]\displaystyle 45[/tex]

Step-by-step explanation:

[tex]\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45[/tex]

Extended Information on the Complex Number System

[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\:[Any\:multiple\:of\:four][/tex]

I am joyous to assist you anytime.

Step-by-step explanation:

If x is the number of t-shirts, and y is the number of sweatshirts:

10x + 15y ≥ 500

x + y ≤ 50

y ≥ x/2

And since x and y can't be negative:

x ≥ 0

y ≥ 0

Graph:

desmos.com/calculator/mw6dsei6jm

The boundaries of the feasible region are:

(0, 50), (0, 33.3), (28.6, 14.3), and (33.3, 16.7)

Since x and y must be integers, any non-integer solutions are not viable.

The maximum profit will be when the most product is sold.  Since sweatshirts are more profitable, we want to sell as much of that as we can.  

So they should sell 0 t-shirts and 50 sweatshirts for a maximum profit of $750.

Answer:

y=-2x+7

Step-by-step explanation:

Memorize the formula y=mx+b where m=slope and b=y-intercept.

y=-2x+b passes through the point (1, 5)

5=-2(1)+b

5=-2+b

b=5-(-2)=5+2=7

So the y-intercept in this case is 7.

y=-2x+7

Answer:

588 should be the answer :)

Answer:

300

Step-by-step explanation:

Solve for x.

x+(2/5*x)=420

x=300

Answer:

a=-1

Step-by-step explanation:

2a-3=-5

2a=-5+3

2a=-2

a=-2/2

a=-1

The expression after performing the indicated operation written as trinomial is:

[tex]x^2+5x-8[/tex]

Step-by-step explanation:

Given

(x + 4)(x - 2) + 3x

We have to multiply (x + 4)(x - 2) and then add 3x to it

So,

[tex](x + 4)(x - 2) + 3x\\=[x(x-2)+4(x-2)]+3x\\= (x^2-2x+4x-8)+3x\\=x^2+2x-8+3x[/tex]

Combining alike terms

[tex]=x^2+2x+3x-8\\=x^2+5x-8[/tex]

The expression after performing the indicated operation written as trinomial is:

[tex]x^2+5x-8[/tex]

Keywords: Polynomials, Expressions

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Final answer:

To express (x + 4)(x - 2) + 3x as a trinomial, expand the product, combine like terms, and then add the additional term which results in the trinomial x² + 5x - 8.

Explanation:

To perform the indicated operations and express as a trinomial, we need to expand the binomial product and combine like terms with the additional term.

First, we expand the product: (x + 4)(x - 2) = x² - 2x + 4x - 8

Next, we combine the terms within the product: x² + (4x - 2x) - 8 = x² + 2x - 8

Now, we add the additional term: (x² + 2x - 8) + 3x

Lastly, we combine like terms: x² + (2x + 3x) - 8 = x² + 5x - 8

Answer:

We need to use the compound interest formula where the future amount is determined by

A = P(1 + r/n)nt

A = future or present amount = 5,000,000

P = initial amount invested = 8,000

r = interest rate as a decimal (to be determined)

n = # times compounded in a year = 1

t = # years = 200

5000000 = 8000(1+r/1)1(200)= 8000(1+r)200

(1+r)200 = 5,000,000/8,000

(1+r)200 = 625

1+r = 200√625

1 + r = 6251/200

r = 6251/200 - 1 = 0.0327

r ≅ 3.27%

Step-by-step explanation:

3.27% is interest rate compounded annually would this growth occur.

What exactly does "interest rate" mean?

The formula is -

A = P(1 + r/n)nt

given,

A = 5,000,000

P = 8,000

r = ?

n =  1

t =  200

put all the value in formula

5000000 = 8000(1+r/1)1(200)

5000000 = 8000(1+r)200

(1+r)200 = 5,000,000/8,000

(1+r)200 = 625

(1+r) = 200√625

(1 + r) = 6251/200

r = 6251/200 - 1

r = 0.0327

nearest points of r

r ≅ 3.27%

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1. There was 20% error.

2. There was 5.33% error.

Step-by-step explanation:

1. Jerri estimated that 30 people would attend the dinner event, but only 25 people attended.

Exact value = 25

Approx value = 30

Percent error = [tex]\frac{|approx-exact|}{exact}*100[/tex]

Percent error = [tex]\frac{|30-25|}{25}*100 = \frac{|5|}{25}*100[/tex]

Percent error = [tex]\frac{500}{25} = 20\%[/tex]

There was 20% error.

2. Gene estimated the length of the fence to be 150 feet, but the actual measurement was 142.

Exact value = 142 feet

Approx value = 150 feet

Percent error = [tex]\frac{|150-142|}{150}*100 = \frac{|8|}{150}*100[/tex]

Percent error = [tex]\frac{800}{150} = 5.33\%[/tex]

There was 5.33% error.

Keywords: Error, percentage

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