Landon was taking a math test. He finished 1/2 of the test in 3/5 of an hour. How much of the test will he have done in one hour if he keeps the same pace?

Answer:

Domain f(x) = R - {1}

As it is a rational expression, the denominator cannot be zero.

Now the function holds all real values except 1 for which the denominator will become zero which is undefined.

Therefore the domain will be all real numbers except 1.

The system of linear inequalities which is represented by the  graph is:

        y>x-2 and    y<x+1

The first inequality--

It is a dotted line which passes through (-1,0) and (0,1) and the shaded region is below the line.

first we find the equation of line:

The equation of a line passing through (a,b) and (c,d) is given by:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Hence,

(a,b)=(-1,0) and (c,d)=(0,1)

Hence, the equation of line is:

[tex]y-0=\dfrac{1-0}{0-(-1)}\times (x-(-1))\\\\i.e.\\\\y=\dfrac{1}{1}\times (x+1)\\\\i.e.\\\\y=x+1[/tex]

Also, the inequality is strict since the line is dotted.

Hence, the inequality is given by: y<x+1

The second inequality --

is a dotted line which passes through (0,-2) and (2,0)

and the shaded region is above the line.

The equation of line is given by:

  y=x-2

and the inequality is strict.

Hence, the inequality is given by:

        y>x-2

Answer:

1+i

Step-by-step explanation:

The explicit formula for the compound interest geometric tell us: If P1 is invested at an interest rate of i per year, compounded annually, the future value Pn at the end of the nth year is:

[tex]Pn=P1(1+i)^{(n-1)}[/tex]

For example if you have $10 at 5% at an interest rate of 5% per year.

Then if you want to know the amount of money at the end of the 2, 3 and 4 year, you have:

n=1 year P1=10

n=2 year

[tex]P2=10(1+(5/100))[/tex]

[tex]P2=10(1+(5/100))^{(2-1)}[/tex]

[tex]P2=10(1+(5/100))^{(1)}[/tex]=10,5

n=3 year

[tex]P3=10(1+(5/100))*(1+(5/100))[/tex]

[tex]P3=10(1+(5/100))^{(3-1)}[/tex]

[tex]P3=10(1+(5/100))^{(2)}[/tex]=11.025

n=4 year

[tex]P4=10(1+(5/100))*(1+(5/100))*(1+(5/100)) [/tex]

[tex]P4=10(1+(5/100))^{(4-1)}[/tex]

[tex]P4=10(1+(5/100))^{(3)}[/tex]= 11.57625

Final answer:

The dealer's cost for the car is $15,851.65 and the sticker price is $20,636.

Explanation:

To find the sticker price and dealer's cost for the car, we need to calculate the prices of the base price, options, and destination charges.

First, calculate the dealer's cost for the base price by multiplying 85% of the base price: $18,649 x 0.85 = $15,851.65.

Next, calculate the dealer's cost for the options by multiplying 70% of each option cost and summing them up: $453 x 0.70 + $612 x 0.70 + $386 x 0.70 + $290 x 0.70 = $845.20.

Finally, calculate the sticker price by adding the base price, options, and destination charges: $18,649 + $453 + $612 + $386 + $290 + $246 = $20,636.

Therefore, the dealer's cost is $15,851.65 and the sticker price is $20,636.

To convert 25/38 to a percentage, divide 25 by 38, multiply by 100, and round to the nearest tenth, resulting in 65.8%.

To convert 25/38 to a percentage, you divide 25 by 38 and then multiply the result by 100.

The calculation would look like this:

Divide 25 by 38: 25 ÷ 38 = 0.6578947368

Multiply the result by 100 to get the percentage: 0.6578947368 × 100 = 65.78947368%

Round the result to the nearest tenth of a percent: 65.8%

Therefore, 25/38 as a percentage rounded to the nearest tenth of a percent is 65.8%.

Final answer:

To express 25/38 as a percentage, divide 25 by 38 and then multiply the result by 100. The answer is approximately 65.8%.

Explanation:

To express 25/38 as a percentage, you can divide 25 by 38 and then multiply the result by 100.

25 ÷ 38 ≈ 0.6578947368421053

0.6578947368421053 × 100 ≈ 65.8

Therefore, 25/38 as a percentage, rounded to the nearest tenth of a percent, is approximately 65.8%.

Hello There!

intersecting lines and lines that have the same equation.

Answer:

intersecting lines and lines

Step-by-step explanation:

Answer:

[tex]\frac{81}{3}[/tex]

Step-by-step explanation:

Given the direct variation equation

y = kx ← k is the constant of proportionality

then for

y = [tex]\frac{81}{3}[/tex] x

k = [tex]\frac{81}{3}[/tex]

Answer:

Unless there is more to the question than c = 2 because 30 /5 = 6 and if c is 3 than 3 = 6 so simplify if needed.

Answer:

c = 18

Step-by-step explanation:

Rewrite c / 3 equals 30 / 5 as:

 c       30

----- = -----

  3       5

Reduce 30/5 to 6/1:

 c        6

----- = -----

  3       1

Cross multiplying, we get 1c = 18, or c = 18.

Answer:

The constant term is the area of weight room.

Step-by-step explanation:

A rectangular gym has an area of [tex]4x^2[/tex]  square feet

The school decides to add a new  weight room.

The total area of the gym and the weight room is [tex](4x^2+480)[/tex] ft^2.

Here, 480 is the area of the weight room because [tex]4x^2[/tex] is the area of gym and the total area will be addition of both the areas.

Hence, the constant term is the area of weight room.

The area of the weight room is 480 square ft and the constant term 480 represents the area of the weight room.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

The area of the rectangular gym = 4x² square ft

The total area of the gym and the weight room = (4x² + 480) square ft

Let A be the area of the weight room:

Total area = area of gym + area of weight room

4x² + 480 = 4x² + A

A = 480 square ft

Thus, the area of the weight room is 480 square ft and the constant term represents the area of the weight room.

Learn more about the rectangle here:

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The graph is attached.

To find the graph that shows the solution to the system of linear inequalities below, we need to find the axis intercepts and consider the given conditions for both inequalities.

So, solving we have:

First inequality: Blue line and area.

[tex]y\leq -3x+2[/tex]

Finding the x-axis intercept, making "y" equal to 0.

[tex]y=-3x+2[/tex]

[tex]0=-3x+2\\\\3x=2\\\\x=\frac{2}{3}=0.66[/tex]

So, the x-axis intercept is located at the point (0.66,0)

Finding the y-axis intercept, making "x" equal to 0.

[tex]y=-3x+2[/tex]

[tex]y=-3*0+2=2[/tex]

So, the y-axis intercept is located at the point (0,2)

Also, we can see that since the coefficient of the linear term is negative (-3) the line is decreasing (line with negative slope).

Now, that we already know the axis intercepts, we need to remember that the inequality is given by the following expression:

[tex]y\leq -3x+2[/tex]

The less or equal inequality symbol means that the solution region of the inequality is under the function.

Second inequality: Red line and area.

[tex]y>2x-3[/tex]

Finding the x-axis intercept, making "y" equal to 0.

[tex]y=2x-3+2[/tex]

[tex]0=2x-3\\\\2x=3\\\\x=\frac{3}{2}=1.5[/tex]

So, the x-axis intercept is located at the point (1.5,0)

Finding the y-axis intercept, making "x" equal to 0.

[tex]y=2x-3[/tex]

[tex]y=2*0-3=-3[/tex]

So, the y-axis intercept is located at the point (0,-3).

Also, we can see that since the coefficient of the linear term is positive (-3) the line is increasing (line with positive slope).

Now, that we already know the axis intercepts, we need to remember that the inequality is given by the following expression:

[tex]y>2x-3[/tex]

The greater inequality symbol means that the solution region of the inequality is above the function.

Hence, since we have a system of linear inequalities, the solution to the whole system is located between the solution region of the given inequalities.

The graph is attached, the solution to the system of linear inequalities is represented by the shaded area (light purple area).

Have a nice day!

The solution to the inequality is attached. It is the side that is dark green as shown in the graph.

Inequality

Inequality is an expression used to show the non equal comparison of two or more numbers and variables.

Given the inequalities:

y < -3x + 2   (1)

y > 2x - 3    (2)

Plotting the graph using the online geogebra tool.

The solution to the inequality is attached. It is the side that is dark green as shown in the graph.

Find out more on inequality at: https://brainly.com/question/24372553

Answer:

6 since 8(3/4)=6

Step-by-step explanation:

(x^8)^(3/4)

=x^(8*3/4) by one of the law of exponents

=x^(8/4 *3)

=x^(2 *3)

=x^6

Answer:

True

Step-by-step explanation:

we know that

A circle can be circumscribed about any regular polygon

A circumscribed circle surrounds a regular polygon, touching every vertex

Answer:

Hi there!

A way to remember how to do each way is: Soh Cah Toa

Sin- opposite over hypotenuse Cos- Adjacent over hypotenuse Tan- opposite over adjacent.

Hypotenuse is the longest the side of the triangle

and the adjacent side is the side laying near the symbol theta.  

Answer:

16

Explanation:

Area of Triangle = 1/2(B*H)

Height - 4

Base - 8

8 * 4 = 32

32 / 2 = 16

Answer:

$3400 after one year

$17400 after the 36 months

Step-by-step explanation:

3000+400*1=3400

3000+400*36=17400

After a year, $7,800 will have been spent on the car. The final cost of the car will be $16,800.

i) To find out how much money will have been spent after a year, we need to substitute the value of M with 12 (since there are 12 months in a year) in the formula S = 3000 + 400M. Therefore, S = 3000 + 400 × 12 = $7,800.

ii) The final cost of the car can be found by substituting the value of M with 36 (since there are 36 months of payments) in the same formula. Therefore, S = 3000 + 400 ×36 = $16,800.

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the slope intercept form is y=mx+b

since the line intersects at (0,3) b= 3

since the slope is 0 m= 0

so the equation would be y=0x+3 or y=3

Answer:

y=3

Step-by-step explanation:

Hi there!

We are given that a line contains the point (0, 3), and has the slope 0

We want to find the equation of this line, in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

The y intercept is the point that intersects the y axis; at this point, the value of x is 0

The point (0, 3) we were given is actually the y intercept of this line (the value of x at this point is 0!)

We can therefore, plug it into the formula.

We can just plug in the y value as b into the equation.

Here's the equation so far:

y=mx+3

Now we need to find m.

As the the slope of the line is 0, it means that if we plug 0 in as m, then we can find the equation of the line.

So substitute 0 as m

y=0x+3

This can also be written as y=3

Hope this helps!

See more on finding the equation of the line from a slope and a point here (n.b. the answer is written in a different format, but the logic is still the same): https://brainly.com/question/14358313

Answer:

6x³ - 4x² + 4x

Step-by-step explanation:

The additive inverse is the value added to make the expression equal to zero.

Given

- 6x³ + 4x² - 4x , then the additive inverse is

- ( - 6x³ + 4x² - 4x)

= 6x³ - 4x² + 4x

The additive inverse of the polynomial is 6x³ - 4x² + 4x.

Given: Polynomial

-6x³ + 4x² - 4x

Additive inverse of the polynomial is the polynomial when added to the original polynomial gives the sum zero.

Let, the additive inverse of the given polynomial be P.

⇒ P + -6x³ + 4x² - 4x = 0

⇒ P = 6x³ - 4x² + 4x

Therefore, the additive inverse of the given polynomial is 6x³ - 4x² + 4x.

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Answer:

75 cm^2

Step-by-step explanation:

We have the lengths of two corresponding sides. The scale factor from the large triangle to the small triangle is 16/64 = 1/4. Each side of the smaller triangle is 1/4 times the length of the corresponding side of the large triangle.

For the areas, the scale factor is the square of the scale factor of the lengths. Area scale factor = 1/4^2 = 1/16.

The area of the small triangle is 1/16 the area of the large triangle.

area of small triangle = (area of large triangle) * (area scale factor)

area of small triangle = 1200 cm^2 * 1/6 = 1200 cm^2/16

area of small triangle = (1200 cm^2)/16 = 75 cm^2

Answer:

I would say 75cm^2.

Final answer:

The system of equations y = 1/4x + 2 and 3y = -3/4x - 6 represents two distinct parallel lines with the same slope but different y-intercepts, thus the system has no solution.

Explanation:

To find the solution to the system of equations y = 1/4x + 2 and 3y = -3/4x - 6, we need to check if they have a common solution, indicating the point where they intersect, or if they are parallel, which would mean they have no solution, or if they are the same line, which would translate into infinitely many solutions.

First, simplify the second equation by dividing every term by 3, which gives y = -1/4x - 2. Now we can see that the coefficients of x and the constant terms in both equations are multiples of one another but with opposite signs, which means the lines are parallel and have the same slope but different y-intercepts. Therefore, these two equations represent two distinct parallel lines that never intersect.

The correct answer is that there is no solution to this system of equations because the lines are parallel and will never meet.

If

[tex]S=1+2+\cdots+(n-1)+n[/tex]

then it's also true that

[tex]S=n+(n-1)+\cdots+2+1[/tex]

so that

[tex]2S=(1+n)+(2+(n-1))+\cdots+((n-1)+2)+(n+1)=n(n+1)\implies S=\dfrac{n(n+1)}2[/tex]

For any integer [tex]n[/tex], [tex]n(n+1)[/tex] is even. We have [tex]5\mid S[/tex] if either [tex]5\mid n[/tex] or [tex]5\mid(n+1)[/tex]. This means [tex]n[/tex] must satisfy either [tex]n\equiv0\pmod5[/tex] or [tex]n\equiv4\pmod5[/tex], in which case we have a general solution of

[tex]n=5k[/tex]

or

[tex]n=5k-1[/tex]

where [tex]k[/tex] is any integer.

Answer:

A and D on edge

just took the assessment

Answer:

a and d

Step-by-step explanation:

Answer:

(-3, -4)

Step-by-step explanation:

The parabola shown here opens up.  The vertex is the lowest point of this graph.  The coordinates of the vertex are (-3, -4).  

Answer:

(-3, -4)

Step-by-step explanation:

your welcome

Answer:

2/3

Step-by-step explanation:

-5/12 ÷ -5/8

Copy dot flip

-5/12 * -8/5

The 5's cancel

-8/-12

Divide the top and bottom by -4

2/3

Answer:

2/3

Step-by-step explanation:

-5/12 divided by -5/8

To solve this you need to change the division sign to a multiplication sign.Then find the reciprocal of the second fraction. It should look like this.

-5/12*-8/5

Then you multiply straight across

5*8=40

5*12=60

40/60

This can be simplified to 2/3

Answer:

-20 + 48i

Step-by-step explanation:

(4 +6i)^2 (Perfect square)

= (4)^2 + 2(4)(6i) + (6i)^2

= 16 + 48i + 36i^2

= 16 + 48i - 36    (i^2 = -1)

= -20 + 48i

Answer:

[tex]-20+48 \text{i}[/tex]

Step-by-step explanation:

Note that

[tex](4+6i)^2=4^2+2\cdot(4\cdot6i)+(6\cdot i)^2=16+48i+36i^2=16+48i-36\\\\=(36-13)+48i=-20+48i[/tex]

and we are done.

I believe the answer is 286 since the equation is 250(1.07) t

this tells me that 250= original size and 1.07= growth of the bacteria and t for time or hour in this case

250x(1.07) 2

267.5x(1.07)

286.225 = 286

Answer:

75

Step-by-step explanation:

Mode means the number that occurs the most. There can be more than 1 mode also no mode at all.

Looking at the number set closely, we see that "75" occurs twice and every number occurs once. Hence 75 is the mode.

Hello There!

The "MODE" is the numbers that occur most often in a set of numbers.

In this scenario, 75 would be the mode because it occurs twice, No other numbers in this data set repeat except 75.

Answer:  8 yds³ 22ft³ 1712 in³

Step-by-step explanation:

9 yds³ + 113 in³ - (4 ft³ + 129 in³)

Understand that you need to "borrow" 1 yd³ and convert it into ft³ and then "borrow" 1 ft³ and convert it into in³

Conversions:

[tex]1 yd^3\times \bigg(\dfrac{3ft}{1yd}\bigg)^3=\large\boxed{27ft^3}\\\\\\1ft\times\bigg(\dfrac{12in}{1ft}\bigg)^3=\large\boxed{1728in^3}[/tex]

The given equation:

   9 yds³ +  0 ft³    + 113 in³          

                - 4 ft³   - 129 in³

Borrow 1 yd³ to create 27 ft³:

= 8 yds³  + 27 ft³ + 113 in³

               -   4 ft³  - 129 in³

Borrow 1 ft³ to create 1728 in³:

= 8 yds³  + 26 ft³ + 1841 in³

               -   4 ft³  -  129 in³

= 8 yds³  + 22 ft³ + 1712 in³

Final answer:

Strategic voting leads to the Pepsi candidate winning the election for Soft Drink commissioner, despite the strong preference for Coca-Cola among the voting population.

Explanation:

The Pepsi candidate wins in a landslide in the election for Soft Drink commissioner, despite there being a strong preference for Coca-Cola among the voting population because of the concept of strategic voting. Strategic voting occurs when voters strategically choose a candidate who they believe has a better chance of winning, rather than their preferred choice. In this scenario, it is possible that the supporters of the Coca-Cola party split their votes among the four candidates, while the supporters of the Pepsi candidate remained united, resulting in the Pepsi candidate winning by a large margin.

Answer:

[2, -10]

Step-by-step explanation:

Simply plug in 2⃣ for every "x" you see, evaluate, then you will arrive at your answer.

Answer:

y = [tex]\frac{1}{4}[/tex] x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{4}[/tex] x - 1 ← is in this form

with slope m = [tex]\frac{1}{4}[/tex]

• Parallel lines have equal slopes, thus

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (8, 5) into the partial equation

5 = 2 + c ⇒ c = 5 - 2 = 3

y = [tex]\frac{1}{4}[/tex] x + 3 ← equation of parallel line