Write the equation of the line that passes through the given points (0,-3) and (-15,-5)

Answer:

$2,225.54

Step-by-step explanation:

Principal, p = $1000

interest rate r = 16% 0r 0.16

years of deposit, t = 5

Finding ending balance below

Since interest compounded continuously,

Substitute the following values

p = $1000, e = exponent, r = 0.16 and t = 5

B = 1000e^((0.16)(5))

=1000e^(0.8)

=1000 X 2.2255409284924676

=2,225.5409284924676

Which B is approximately $2,225.54

Ending balance =$2,225.54

Assuming the amount of  $1,000 was invested at an interest rate of 16%, compounded continuously, for a period of five years, what the ending balance will be is: $2,225.54

p represent Principal = $1000

r represent Interest rate= 16% or 0.16

t represent=5 years  

Now let determine the ending balance

Ending balance= $1000e^(0.16)(5)

Ending balance=$1000e^(0.8)

Ending balance=$1000 X 2.2255409284924

Ending balance=$2,225.5409284924

Ending balance=$2,225.54 (Approximately)

Inconclusion if  the amount of  $1,000 was invested at an interest rate of 16%, compounded continuously, for a period of five years, what the ending balance will be is: $2,225.54

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The police cruiser travels a total distance of 275.0 meters. It covers 137.5 meters during acceleration and the same distance during deceleration (in the opposite direction), summing up to 275.0 meters in total.

Calculating the distance covered during acceleration:

The equation for distance covered with constant acceleration is given by:

[tex]\[ s = ut + \frac{1}{2}at^2 \][/tex]

Where:

[tex]\( u \)[/tex] = Initial velocity

[tex]\( a \)[/tex] = Acceleration

[tex]\( t \)[/tex] = Time

Given:

Initial velocity [tex](\( u \))[/tex] = 20.0 m/s

Acceleration[tex](\( a \))[/tex] = 3.0 m/s²

Time[tex](\( t \))[/tex]= 5.0 seconds

Let's find the distance covered during acceleration using the above formula:

[tex]\[ s = ut + \frac{1}{2}at^2 \][/tex]

[tex]\[ s = (20.0 \, \text{m/s} \times 5.0 \, \text{s}) + \frac{1}{2} \times 3.0 \, \text{m/s}^2 \times (5.0 \, \text{s})^2 \][/tex]

[tex]\[ s = (100.0 \, \text{m}) + \frac{1}{2} \times 3.0 \, \text{m/s}^2 \times 25.0 \, \text{s}^2 \][/tex]

[tex]\[ s = 100.0 \, \text{m} + 37.5 \, \text{m} \][/tex]

[tex]\[ s = 137.5 \, \text{m} \][/tex]

Therefore, the distance covered during acceleration is 137.5 meters.

Calculating the distance covered during deceleration (slowing to a stop):

The cruiser starts at a speed of 20.0 m/s and decelerates uniformly until it comes to a stop. The distance covered during deceleration will be the same as the distance covered during acceleration but in the opposite direction.

So, the distance covered during deceleration = 137.5 meters (in the opposite direction).

Total distance traveled:

The total distance traveled by the cruiser during acceleration and then deceleration is the sum of these distances (taking the magnitudes):

Total distance = Distance during acceleration + Distance during deceleration

Total distance = 137.5 m + 137.5 m

Total distance = 275.0 meters

Therefore, the entire distance covered by the cruiser in the entire time is 275.0 meters.

Answer:

x- intercept (- 8, 0), y- intercept (0, 8)

Step-by-step explanation:

To find the y- intercept, let x = 0 in the equation and solve for y

y = 0 + 8 = 8 ⇒ (0, 8 ) ← y- intercept

To find the x- intercept, let y = 0 in the equation and solve for x

x + 8 = 0 ( subtract 8 from both sides )

x = - 8 ⇒ (- 8, 0 ) ← x- intercept

X-intercept is (-8,0) and y-intercept is (0,8). the correct option is A.

The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x)

At y-axis, we've got x = 0, so putting it will give us the y-intercept.

Thus, y-intercept of y = f(x) is y = f(0)

We are given that;

Function y=x+8

Now,

The equation of the graph is y = x + 8. To find the x-intercept, we set y = 0 and solve for x.

0 = x + 8

x = -8

Therefore, the x-intercept is (-8, 0).

To find the y-intercept, we set x = 0 and solve for y.

y = 0 + 8

y = 8

Therefore, X-intercept will be (-8,0) and y-intercept will be (0,8).

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Answer:

Step-by-step explanation:

[tex]1\ L=1,000\ mL\Rightarrow1\ mL=\dfrac{1}{1,000}\ L=0.001\ L\\\\0.743\ mL=0.743\cdot0.001\ L=0.000743\ L[/tex]

Answer:

12 feet

Step-by-step explanation:

Perimeter=all 4 sides added up

So perimeter=14+14+w+w, if w is width

52=28+2w

24=2w

w=12

Answer:

Step-by-step explanation:

Answer:

(x + 1)(x + 8)

Step-by-step explanation:

Given

x² + 9x + 8

Consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 9)

The factors are + 1 and + 8, since

1 × 8 = 8 and 1 + 8 = 9, thus

x² + 9x + 8 = (x + 1)(x + 8)

The larger number is 66 and the smaller number is 14.

Step-by-step explanation:

Let,

The larger number = x

The smaller number = y

According to given statement;

x-y=52     Eqn 1

5y = x+4   Eqn 2

From Eqn 2

x = 5y-4    Eqn 3

Putting value of x from Eqn 3 in Eqn 1

[tex]5y-4-y=52\\4y=52+4\\4y=56[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{56}{4}\\y=14[/tex]

Putting y=14 in Eqn 3

[tex]x=5(14)-4\\x=70-4\\x=66[/tex]

The larger number is 66 and the smaller number is 14.

Keywords: linear equation, substitution method

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I assume you mean (x^2+8)/(x-5)?

If so, we have:

(8^2+8)/(8-5)

(64+8)/3

72/3

24

So the value is 24 when x=8

Hope this helped!

Answer:

b)  Complement of spinning any number less than 3 is Spinning 3 or 4.

Step-by-step explanation:

COMPLIMENT of any Set A  is the set of all the elements which are in the  sample space but NOT IN SET A.

Here, Event E  = Spinning a spinner with 4 parts and getting a number less than 3.

Here, Sample Space = {1,2,3,4}

Also, as outcomes is LESS THAN 3, ⇒   E  = {1 ,2}  

Now, Compliment E  = Sample Space - { Elements in set E}

                                    = {1,2,3,4} -  {1 ,2}

or, E'  = { 3,4}

Hence,  complement of spinning any number less than 3 is Spinning 3 or 4.

Answer:

Spinning a 3 or 4

Step-by-step explanation:

The numbers that are less than 3 on the spinner, are 1 and 2. Therefore, the complement or opposite of that are all the numbers other than 1 and 2. So the answer is 3 and 4.

43,604

Subtract 5398 from 49002

Answer:

Step-by-step explanation:

49,002 is greater than -5,398

When x dissapears we have a false equation:

-4 = 5, so the equation does not have solutions, which means that Evelyn is incorrect.

The equation has infinite solutions?

Let's simplify the equation:

3(x - 3) + 5 = 3x + 1 + 4

distributing the left side.

3x - 9 + 5 = 3x + 1 + 4

3x - 4 = 3x + 5

If you subtract 3x in both we will get:

3x - 4 - 3x = 3x + 5 - 3x

-4 = 5

This is false, and x disappeared, so there is no value of x that makes this equation true, meaning that the equation does not have a solution.

Answer:

A- 170$

Step-by-step explanation:

The approximate six month premium is $170.

A linear equation is an equation in which there is one variable that is raised to the power of 1. An example is x + 2

In order to determine the six month premium, substitute for d and b in the given equation:

P = 2 x 1.02 x $500 = $1020

Monthly premium = $1020 / 6 = $170

Here is the complete question:

Jerome uses the formula, P = 2DB, to find his approximate six-month premium when his driver risk factor, D, is 1.02 and the basic six-month premium is $500.What will his monthly premium be?

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Answer:

You cant Simplify it an further

Answer:

0.1676

Step-by-step explanation:

Answer:

$12.79

Step-by-step explanation:

$45 - $18.63 = $26.37

$26.37 - ($.47 x 2) = $26.37 - $.94 = $25.43

$25.43 - $12.64 = $12.79

Step-by-step explanation:

We know that

[tex]tan\theta =\frac{altitude}{base}[/tex]

Using this for the triangles

For the small triangle

[tex]tan \theta =\frac{6\frac{1}{2} }{9}[/tex]

[tex]\Leftrightarrow tan \theta =\frac{\frac{13}{2} }{9}[/tex]

[tex]\Leftrightarrow tan \theta =\frac{13} {18}[/tex]

Again for the bigger triangle

[tex]tan \theta =\frac{h}{31\frac{1}{2} }[/tex]

[tex]\Leftrightarrow tan \theta =\frac{h}{\frac{63}{2} }[/tex]

[tex]\Leftrightarrow tan \theta =\frac{2h}{63}[/tex]

Therefore

[tex]\frac{2h}{63} =\frac{13}{18}[/tex]

[tex]\Leftrightarrow h=\frac{13 \times 63}{18 \times 2}[/tex]

[tex]\Leftrightarrow h=\frac{819}{36}[/tex]

[tex]\Leftrightarrow h = 22.75[/tex] ft

Therefore h = 22.75 ft

Answer:

PR=8; ST=5

Step-by-step explanation:

Find PR:

PQ=PR

8=2x

x=4

PR=2x=2(4)=8

Find ST:

TU=ST

2z+3=5z

3=3z

z=1

ST=5z=5(1)=5

If Brittany is starting at the origin and the destination is (6,3), Brittany should move 6 units to the right then 3 units up. This is location where she should plot the point.

Brittany graphs the plot (6,3), she should move 6 units to the right then 3 units up.

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used.

How to solve?

If Brittany is starting at the origin and the destination is (6,3), Brittany should move 6 units to the right and then 3 units up. This is a location where she should plot the point.

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Answer: If it is on a coordinate plane, (-1,-4) would be in quadrant 3. (1,4) would be in quadrant one.

Step-by-step explanation:

quadrant 1 is both positive numbers (both the x and the y axis).

quadrant 2 is when the x axis is negative and the y axis is positive.

quadrant 3 is when both the x and y axis is negative

quadrant 4 is when the x axis is positive and the y axis is negative.

Answer:

=0.4

Step-by-step explanation:

1/3= 0.33

5/6=0.83

Then: 0.33/0.83 = 0.4

You can also do 6/15 which results from (1*6)=6 and (3*5)=15

2 bottles divided by 6 people = 2/6 which equals 1/3.

Answer:

12.28

Step-by-step explanation:

[tex]\sqrt{14}-\sqrt{3} )(\sqrt{12}+\sqrt{7})[/tex]

Multiplying [tex]\sqrt{14} and\sqrt{3}[/tex] individually to the values inside the brackets to find the product of the equation.

[tex]\sqrt{14}\sqrt{12}+\sqrt{14}\sqrt{7}-\sqrt{3}\sqrt{12} -\sqrt{3} \sqrt{7}[/tex]

[tex]\sqrt{168} +\sqrt{98} -\sqrt{36}- \sqrt{21}\\2\sqrt{42}+7\sqrt{2}-6-\sqrt{21}\\ 12.96 +9.90 -6 -4.58\\12.28[/tex]

The product of the above values is 12.28

Answer:

2√42 + 7√2 - √21 - 6

Step-by-step explanation:

(√14-√3)(√12+√7)

First let us expand the expression by doing the following:

√14(√12+√7) -√3(√12+√7)

√168 + √98 - √36 - √21

√(4x42) + √(49x2) - 6 - √21

2√42 + 7√2 - √21 - 6

Answer:

139

Step-by-step explanation:

Substract 41 from 180 assuming line LN is a straight line. the angles are supplementary

Answer:

ur numbers are 2 and -5

Step-by-step explanation:

7x + 3y = -1

x + y = -3......x = -3 - y

7(-3 - y) + 3y = -1

-21 - 7y + 3y = -1

-7y + 3y = - 1 + 21

-4y = 20

y = -20/4

y = -5 <====

x = -3 - y

x = -3 - (-5)

x = -3 + 5

x = 2 <====

Answer: The numbers are 2 and -5

Step-by-step explanation:

7x+3y=-1  ...(equation 1)

x+y=-3    ...(equation 2)

x+y=-3

Broken down, we have x=-3-y

Substitute x=-3-y into equation 1

Then we have 7(-3-y) +3y=-1

Which is -21-7y+3y=-1

which is -21-4y=-1

-4y=-1+21=20

y=-20/4=-5

y=-5

Substitute y=-5 into equation 1  

x+y=-3

x-5=-3

x=-3+5=2

x=2

Answer:

First Problem:  $50.15

Second Problem:  $20,468

Step-by-step explanation:

First Problem:  If the original price is $41.00 and the discount is $6.15

41.00 - 6.15 = $34.85 is the discounted price

34.85 / 41.00 = 0.85 -> this shows the amount that you pay from the original price

So if the other product costs $59.00 you just do 59.00 * 0.85 = $50.15

This shows that %85 of the original cost is what you pay.

Second Problem:  So, the first amount sold is 160 tickets and the price for each ticket is $59.50.

160 * $59.50 = $9,520 for the afternoon batch

If they sold %15 more in the evening that means that they sold 160 tickets plus another %15 of the 160.

160 * 1.15 = 184 tickets sold in the evening

184 * $59.50 = $10,948 for the evening batch

So they sold a total of $9,520 + $10,948 = $20,468

Answer:

44)  $50.15

45) $20,468

Step-by-step explanation:

44)  $ off sweater = 6.15

41.00 - 6.15 = 34.85

6.15 ÷ 41.00 = 0.15 = 15% discount

$59.00 - 15%

$50.15

45)

Afternoon = 160 tickets

Evening = 15% more = 160 + 15% = 184 tickets

160 + 184 = 344 tickets total

344 * $59.50 = $20,468

Hope this helps :)

Answer:

B. 119.32

Step-by-step explanation:

Use C = πd as the formula, which is 3.14x38=119.32

Answer:

B) [tex]119.32[/tex] [tex]cm[/tex]

Step-by-step explanation:

Circumference of a circle is the total length of its boundaries that it makes to complete 360°

Circumference of a circle = [tex]2\pi r[/tex]

Given:

             [tex]r=19 cm\\\pi =3.14[/tex]

Putting the given values in the formula of circumference of the circle

               = [tex]2*3.14*19[/tex]

               = [tex]119.32[/tex] [tex]cm[/tex]

On putting the value of radius and [tex]\pi[/tex] in the formula the circumference of the circle is ≈[tex]119.32[/tex] [tex]cm[/tex]

Answer:

4

Step-by-step explanation:

Factor of 8n = 2x2x2n

Factor of 12m = 2x2x3m

GCF = 2x2 = 4

Answer:

x=10

Step-by-step explanation:

First combine like terms:

14x + 40 = 180

Second subtract 40 from both sides:

14x = 140

Third divide both sides by 14:

x = 10

The answer to your question is 4x^2 - 16

Hope this helped

Answer:

Step-by-step explanation: (2x + 4) x (2x - 4)

2x + 4 = 6x

2x - 4 = 4 - 2x = 2x

6x X 2x = 12x