graph the system below and write it solutions(2x + y = -4(y= -1/2x + 2

After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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Answer:

Runner A is running at 9 mph while runner B is running at 4 mph

Step-by-step explanation:

From online values, 4 laps make 1 mile.

We are told Runner A has made 18 laps in the time it took Runner B to make 8 laps.

This means that runner A has run in mile; 18/4 = 4.5 miles

While runner B has run in miles; 8/4 = 2 miles

Runner A is running 5 mph faster than Runner B, thus speed of runner A is;

V_b + 5 while speed of runner B is V_b.

We know that; time = distance/speed

Thus;

t_a = 4.5/(V_b + 5)

t_b = 2/V_b

Since the times are equal from the question, then;

4.5/(V_b + 5) = 2/V_b

Cross multiply to get;

4.5V_b = 2(V_b + 5)

4.5V_b = 2V_b + 10

4.5V_b - 2V_b = 10

2.5V_b = 10

V_b = 10/2.5

V_b = 4 mph

Since V_a = V_b + 5

Thus, V_a = 4 + 5 = 9 mph

Runner A is running at 9 mph while runner B is running at 4 mph

c) representing data with a histogram is an example of data organization

Answer:

No.

Step-by-step explanation:

Because the equation has an exponent, it is quadratic, and not linear.

Answer:1

Step-by-step explanation:

Answer:

Step-by-step explanation:

So there are two types of variables we need to focus on, the first is the dependent variable, the second is the independent variable ( which is the one in question).  You asked about it in relation to mathematics, although even across the board, in science they both really mean the same thing. Here's an example, say you are taking a test, and the rubric for grading the test is 5 points (p) for every question (q) answered correctly. So given that information you can conclude that (p) is equal to 5 x the amount of questions you got right (p = 5q). The amount of points in this equation relies on how many questions you get right, you can't logically say that question (q) is equal to 5 points (p), because the questions don't depend on the points, the points depend on the amount of questions you get right. So that means since the points (p) depend on the # of questions you answered correctly, it is the dependent variable, there for by process of elimination you're independent variable is (q) since they don't rely on the points, the points rely on the questions. It all boils down to how well you can recognize this, and how complicated your question is, but hopefully this provided some insight.

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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Answer:

7. n (Division sign) -5+1<7 = n<11   8. n (division sign) 3-2>-12= n>11      9. -2 x n-6>-18= n>-10

Step-by-step explanation:

I think this is right

Answer:

Step-by-step explanation:

You want to identify the x-intercepts on the graph.

An "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.

The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...

  (-2, 0) and (3, 0)

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The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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Answer:

(14)78.54

(15)55.42

(16)

Step-by-step explanation:

The cost of each funnel cake from the obtained equation is $6.975.

Given that, a group of 4 friends went to the fair. They each ordered a funnel cake and shared a large pack of candy that costed $6.50.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the cost of each cake be x.

They paid a total of $34.50.

Now, 4x+6.50=34.40

⇒ 4x = 34.40-6.50

⇒ 4x = 27.90

⇒ x = 27.90/4

⇒ x = $6.975

Therefore, the cost of each funnel cake from the obtained equation is $6.975.

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Answer:

Yes

Step-by-step explanation:

8/6 simplified is 4/3

20/15 simplified is 4/3

Choose me as smartest

Answer:

a) 1/15 or 0.067 km/s

b) 2.5/30 or 0.083 km/s

Step-by-step explanation: To calculate the speed, you would need to find the slope of the distance vs. time graph. To do this, simply divide the change in distance over the change in time. For example, for the first 15 minutes, it would be 1 divided by 15 since Jo's change in distance was 1 km and the change in time was 15 minutes.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so the speed in this case will be the rate of change or namely the slope, hmm to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below for both intervals

\(\stackrel{ \textit{first 15 minutes} }{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{1})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{0}}} \implies \cfrac{ 1 }{ 15 } \implies \cfrac{1}{15} ~~ \cfrac{km}{min}\qquad 0.0\overline{66}~km/m \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{last 30 minutes} }{(\stackrel{x_1}{30}~,~\stackrel{y_1}{1.5})\qquad (\stackrel{x_2}{60}~,~\stackrel{y_2}{4})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{1.5}}}{\underset{\textit{\large run}} {\underset{x_2}{60}-\underset{x_1}{30}}} \implies \cfrac{ 2.5 }{ 30 } \implies - \cfrac{1}{12} ~~ \cfrac{km}{min}\qquad 0.8\overline{33}~km/m\)

The selling price of the item at 10% marlkup is $55

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Selling price = Cost To Store * (1 + Markup)

substitute the known values in the above equation, so, we have the following representation

Selling price = 50 * (1 + 10%)

Evaluate

Selling price = 55

Hence the selling price of the item is $55

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The translation of point A to point B is done by translation vector (- 3, - 6).

In this problem we find the a point that is part of a rectangle and that must be translated by means of a rigid transformation formula, that is, a translation formula that does not alter the features of the rectangle. We need to determine the translation vector by means of the following formula:

T(x, y) = B(x, y)  - A(x, y)

Where:

If we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:

T(x, y) = (3, 3) - (6, 9)

T(x, y) = (- 3, - 6)

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Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

The yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

The function f(x) = 1,000 * 1.02^t represents the amount in Karl's savings account over t years. The number 1.02 is the growth factor, which is equal to (1 + r), where r is the yearly interest rate.

To find the yearly interest rate, we need to solve the equation:

1.02 = 1 + r

Subtracting 1 from both sides of the equation:

0.02 = r

Therefore, the yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

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The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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Answer:

Y = 3x - 6

Step-by-step explanation:

- 3y = -9x + 18

divide by -3

y = 3x - 6

The number of points gained overall by Julia playing the game is 30 point

From the question, we have the following parameters that can be used in our computation:

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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The quadratic function in standard form is f(x) = x² - 4x - 12.

The coefficients of the quadratic function in standard form is calculated as follows;

The quadratic function is in the form of;

f(x) = ax² + bx + c

when x = -4, f(x) = -12

16a - 4b + c = -12

when x = -3, f(x) = -15

9a - 3b + c = -15

when x = -2, f(x) = -16

4a - 2b + c = -16

when x = -1, f(x) = -15

1a - 1b + c = -15

when x = 0, f(x) = -12

0a + 0b + c = -12

c = -12

Simplifying the equations, the value of a and b is calculated as;

16a - 4b + c = -12

9a - 3b + c = -15

4a - 2b + c = -16

a - b + c = -15

16a - 4b = 0

9a - 3b = -3

4a - 2b = -4

a - b = -3

16a = 4b

a = b/4

Substituting this expression for a into the last equation, we get:

b/4 - b = -3

b - 4b = -12

-3b = -12

b = 4

a = b/4

a = 4/4

a = 1

Therefore, the quadratic function in standard form is:

f(x) = x² - 4x - 12

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The value of secant XY is 37.5 units.

The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

VZ * VW = VX * VY

30 * 45 = 22.5 * VY

22.5VY = 1350

VY = 1350/22.5

VY = 60 units

Since VY = VX + XY. We have:

60 = 22.5 + XY

XY = 60 - 22.5

XY = 37.5 units

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\(p(t)=1650e^{0.11t}\implies \stackrel{p(t)}{2479}=1650e^{0.11t}\implies \cfrac{2479}{1650}=e^{0.11t} \\\\\\ \log_e\left( \cfrac{2479}{1650} \right)=\log_e\left( e^{0.11t} \right)\implies \log_e\left( \cfrac{2479}{1650} \right)=0.11t \\\\\\ \ln\left( \cfrac{2479}{1650} \right)=0.11t\implies \cfrac{ ~~ \ln\left( \frac{2479}{1650} \right) ~~ }{0.11}=t\implies 3.7\approx t\)

at that moment, the population will reach 2479, and right after that, it'll exceed it.

No

Since ratios are simply proportions, they may be represented in multiple ways as long as the relationship remains equal.

Simplifying Ratios

There are 2 ways to check if these ratios are equivalent. The first is to simplify both ratios and see if they match each other. Firstly, find the greatest common factor (GCF) between the 2 numbers.

Then, divide each ratio by its GCF

Since 7:10 is not equal to 3:5, we know that these ratios are not equal. It is important to note that this method only works when both ratios have been completely simplified.

Find the Relationship as a Decimal

Another to see if 2 ratios are equivalent is to see if their relationships are equal as decimals. To find the relationship of a ratio as a decimal, simply divide the 2 numbers within a ratio.

Clearly, the ratios do not have equal relationships. Thus, the ratios are also not equivalent.

The first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3

From the question, we have the following parameters that can be used in our computation:

The sequence is generated by using gn = 2(gn-1)

Such that g1 = 1/3 and n is a whole number greater than 1.

Using the above as a guide, we have the following:

The sequence means that we multiply the current term by 2 to get the next term

So, we have the following representations

a(2) = 2 * 1/3 = 2/3

a(3) = 2 * 2/3 = 4/3

a(4) = 2 * 4/3 = 8/3

a(5) = 2 * 8/3 = 16/3

Hence, the first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3

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