Find the equation of the line parallel to y = 2x + 8 and passes through (4, - 6)

Answer:

The Amount invested at 7% interest is $12,855

The Amount invested at 6% interest = $1,102  

Step-by-step explanation:

Given as :

The Total money invested = $13,957

Let The money invested at 7% = [tex]p_1[/tex]  = $A

And The money invested at 6% = [tex]p_2[/tex] = $13957 - $A

Let The interest earn at 7% = [tex]I_1[/tex]

And The interest earn at 6% = [tex]I_2[/tex]

[tex]I_1[/tex] -  [tex]I_2[/tex] = $833.73

Let The time period = 1 year

Now, From Simple Interest method

Simple Interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]

Or,  [tex]I_1[/tex] = [tex]\dfrac{\textrm p_1\times \textrm 7\times \textrm 1}{100}[/tex]

Or,  [tex]I_1[/tex] = [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex]

And

[tex]I_2[/tex] = [tex]\dfrac{\textrm p_2\times \textrm 6\times \textrm 1}{100}[/tex]

Or,  [tex]I_2[/tex] = [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex]

∵  [tex]I_1[/tex] -  [tex]I_2[/tex] = $833.73

So, [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex] -  [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex] = $833.73

Or, 7 A - 6 (13,957 - A) = $833.73 × 100

Or, 7 A - $83,742 + 6 A = $83373

Or, 13 A = $83373 + $83742

Or, 13 A = $167,115

∴ A = [tex]\dfrac{167115}{13}[/tex]

i.e A = $12,855

So, The Amount invested at 7% interest = A = $12,855

And The Amount invested at 6% interest = ($13,957 - A) = $13,957 - $12,855

I.e The Amount invested at 6% interest = $1,102

Hence,The Amount invested at 7% interest is $12,855

And The Amount invested at 6% interest = $1,102   . Answer

Final answer:

The total amount invested and the difference in interest earned. Then, using algebraic techniques such as substitution or elimination, we solve for the amounts invested at 7% and at 6%.

Explanation:

To solve the problem of allocating investments at different interest rates, we can set up a system of equations. Let's designate x as the amount invested at 7% and y as the amount invested at 6%. Given the total investment is $13,957, our first equation will be:

x + y = 13,957 (1)

The interest from the amount invested at 7% exceeds the interest from the amount invested at 6% by $833.73. The second equation, reflecting the interest earned, will be:

0.07x - 0.06y = 833.73 (2)

y = 13,957 - x (3)

Now, substitute equation (3) into equation (2) and solve for x:

0.07x - 0.06(13,957 - x) = 833.73

Simplify and solve this equation to find the value of x.
Once we have the value for x, we can use equation (3) to find the corresponding value for y, giving us the amount invested at each interest rate.

Answer:

D.  120°

Step-by-step explanation:

Interior angles of a rhombus always add up to 360 degrees. Thus we can set up an equation:

g+g+2g+2g=360

Now let's combine all the like terms (g's).

6g=360

Now we divide both sides by six to isolate g.

g=60

We can now substitute g into angle B, to find its value.  

2g

2(60)

120

Thus, the measure of angle B is 120, or option D.

Answer:

0.3125

Step-by-step explanation:

Use definition of geometric probability:

[tex]P=\dfrac{\text{Desired Length}}{\text{Total Length}}[/tex]

In your case,

Total Length = 8 miles

Desired Length = 7 - 4.5 = 2.5 miles,

so the probability is

[tex]P=\dfrac{2.5}{8}=\dfrac{25}{80}=\dfrac{5}{16}=0.3125[/tex]

Final answer:

The probability of finding the lost cell phone by searching from mile 4.5 to mile 7 along an 8-mile path is 0.3125 or 31.25%.

Explanation:

The student's question deals with the probability of finding a lost cell phone on an 8-mile path by searching between the 4.5 and 7 mile markers.

To calculate this probability, we consider the length of the path where the phone could potentially be found (the search area) and the total length of the path.

The search area is from mile 4.5 to mile 7, which is 2.5 miles long. Since the phone could be anywhere along the 8-mile path, the probability of finding the phone is the length of the search area divided by the total path length:

Probability = Length of Search Area / Total Path Length = 2.5 miles / 8 miles = 0.3125 or 31.25%.

Answer:

Step-by-step explanation:

[tex]f(x)=2x^2+5x-3\\\\x-\text{intercept for}\ f(x)=0\\\\2x^2+5x-3=0\\\\2x^2+6x-x-3=0\\\\2x(x+3)-1(x+3)=0\\\\(x+3)(2x-1)=0\iff x+3=0\ \vee\ 2x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\\boxed{x=-3}\\\\2x-1=0\qquad\text{add 1 to both sides}\\2x=1\qquad\text{divide both sides by 2}\\\boxed{x=0.5}\\\\-3<0.5[/tex]

Answer:

[tex]z>6[/tex]

7z+5>47

Remove the 5:

[tex]7z+5-5>47-5\\7z>42[/tex]

Divide by 7 to get z by itself:

[tex]\frac{7z}{7} >\frac{42}{7} \\z>6[/tex]

hope this helps you mate

4x + 2 = -14

4x = -16

x = -4

4(-4) + 2 = -14

-16 + 2 = -14

-14 = -14

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well,I am not sure about the answer.

Final answer:

To simplify the expression 7(2 + 4) - 3(6) + 2(3 + 5), calculate within the parentheses, do the multiplications, and then the additions and subtractions to get the result, which is 40.

Explanation:

To simplify the numerical expression 7(2 + 4) - 3(6) + 2(3 + 5), you need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here's how you simplify the expression step by step:

First, calculate the expressions within the parentheses: (2 + 4) and (3 + 5).

Then, multiply each result by the number outside the parentheses.

Afterward, complete any multiplication or division from left to right.

Finally, perform the addition and subtraction from left to right.

Now let's apply these steps to the expression:

Calculate the expressions inside the parentheses: 2 + 4 = 6 and 3 + 5 = 8.

Multiply each result by the respective number outside the parentheses: 7 * 6 = 42 and -3 * 6 = -18 and 2 * 8 = 16.

Now rewrite the expression with these calculated values: 42 - 18 + 16.

Now it's just addition and subtraction: 42 - 18 = 24, and 24 + 16 = 40.

Therefore, the simplified expression is 40.

Answer:

-37

Step-by-step explanation:

-4(5)-17=-20-17=-37

Answer: r = 3

1st Step: Plug x in for 5

4(5)-17

Second Step: Multiply 4 and 5

20-17

Third Step: 20-17

20-17=3

So, the answer is 3 when r(5)

Hope this helps!

A) k=2 is the right answer

Step-by-step explanation:

The downward funtion transformation is defined as:

f(x) => f(x)-b where b is an integer.

Given

[tex]f(x) = (0.5)^x[/tex]

And

[tex]g(x) = (0.5)^x-k[/tex]

It is also given that g(x)  is obtained by shifting function f 2 units downward

We will apply the transformation to function f to find the value of k.

So,

Shifting f(x) 2 units downward

we will get

[tex]g(x) = (0.5)^x-2[/tex]

comparing with [tex]g(x) = (0.5)^x-k[/tex] we get that

k = 2

So,

A) k=2 is the right answer

Keywords: Functions, shifting

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Answer:

ok k does = 2 i got it right on the test

Step-by-step explanation:

:3

Answer:25%

It's spit into fourths so yeah

Step-by-step explanation:

Answer:  88 degrees

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

Explanation:

Sides AC and AB are tangents to the circle, so 90 degree angles form at points C and B.

Angle O = 92

Angle B = 90

Angle C = 90

Angle A = unknown

----------

The four interior angles of any convex quadrilateral always add to 360 degrees

(angle O) + (angle A) + (angle B) + (angle C) = 360

92 + A + 90 + 90 = 360

A + 272 = 360

A+272-272 = 360-272

A = 88

-----------

A shortcut is to subtract angle O from 180

angle A = 180 - (angle O)  = 180 - 92 = 88

we get the same answer

Answer:

∠2 = 78°

Step-by-step explanation:

Angle of a straight line is 180°.

So, that would mean ∠1 + ∠2 = 180°.

⇒ ∠2 = 180° - ∠1

⇒ ∠2 = 180° - 102°

⇒ ∠2 = 78°

Hence, the answer.

Answer:1st is 5 2nd is 15 last is 30

Step-by-step explanation:

1st = 5

2nd = 3 x 5 = 15

3rd = 15 x 2 = 30

5 + 15 + 30 = 50

The three numbers in question are 5, 15, and 30. This has been achieved by setting up and solving algebraic equations based on the given conditions.

To solve this problem, we should set up equations based on the information given. Let's define:
First number = x
Second number = 3x (since it is three times the first number)
Third number = 2 * 3x = 6x (since it is twice the second number)

According to the problem, the sum of these three numbers is 50. Therefore, we can write the equation as:
x + 3x + 6x = 50

Solve for x:
10x = 50
x = 50 / 10 = 5

So, the three numbers are:
First number = x = 5
Second number = 3x = 3 * 5 = 15
Third number = 6x = 6 * 5 = 30

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Answer:

Therefore,

[tex]y=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Given:

[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]

To Find:

x = ?

Solution:

[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]

Subtract 2 from both the side.

[tex]2-2+\dfrac{5}{6}\sqrt{6}=2-2+\sqrt{6}y[/tex]

Then we have

[tex]\dfrac{5}{6}\sqrt{6}=\sqrt{6}y[/tex]

Divide [tex]\sqrt{6} [/tex]on both the side

[tex]\dfrac{5}{6}\dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{\sqrt{6}}{\sqrt{6}}=y[/tex]

Then we have

[tex]\dfrac{5}{6}=y[/tex]

Therefore,

[tex]y=\dfrac{5}{6}[/tex]

Answer: x + 3y = 2

Step-by-step explanation:

Given:

y - 3 = 3 ( x + 1 )

y - 3 = 3x + 3

y = 3x + 3 + 3

y = 3x +6

comparing the equation with the formula for finding equation of line in slope - intercept form

y = mx + c , where m is the slope and c  is the y - intercept. This means that the slope of the line above is 3

Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if they are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1

Considering this rule , this means that the slope of the line we are to find = [tex]\frac{-1}{3}[/tex]

Using the formula : y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) to find the equation of the line , we have

y - (-1 ) = [tex]\frac{-1}{3}[/tex] ( x - 5 )

y + 1 = [tex]\frac{-1}{3}[/tex] ( x - 5 )

multiplying through by 3 , we have

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

Expanding , we have

3y + 3 = -x + 5

writing the equation in standard form , we have

3y + x = 5 - 3

Therefore :

x + 3y = 2

Answer:

36

Step-by-step explanation:

Here is the correct and complete question: The units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than twice the original number. What is the original number?

Lets assume the original number be"10y+x". (x is unit digit and y is 10th digit)

∴ if number is reversed then resulting number be "10x+y".

As given: x= 2y

        and [tex]10x+y= 2(10y+x)-9[/tex]

Now, solving the equation to get original number.

[tex]10x+y= 2(10y+x)-9[/tex]

Distributing 2 to 10y and x, then opening the parenthesis.

⇒ [tex]10x+y= 20y+2x-9[/tex]

subtracting by (2x+y) on both side.

⇒ [tex]8x= 19y-9[/tex]

subtituting the value of "x", which is equal to 2y.

∴ [tex]8\times 2y= 19y-9[/tex]

⇒ [tex]16y=19y-9[/tex]

subtracting both side by (16y-9)

⇒ [tex]3y= 9[/tex]

cross multiplying

We get, [tex]y= 3[/tex]

y=3

∵x= 2y

[tex]x=2\times 3= 6[/tex]

∴ x= 6

Therefore, the original number will be 36 as x is the unit number and y as tenth number.

Answer:

the smaller angle = 40

Step-by-step explanation:

Let x be the smaller angle.

Other angle = x + 10

x + x+ 10 = 90

2x  = 90 - 10

2x= 80

x = 80/2

x = 40

Answer:

40 degrees. A set of complementary angles make up 90 degrees. 90 - 40 is 50, which is 10 more than forty.

Answer:

Time taken by train in onward journey = 12 hours.

Step-by-step explanation:

Given:

Speed of train making a trip to a repair = 25 mph

Speed of train on return trip = 20 mph

Time taken for return trip = 15 hours

To find the time taken on the on wards trip.

Solution:

The distance traveled by the train on the trip and return trip is the same as the y are of same trips in opposite directions.

Distance can be calculated by using the data for the return trip.

Distance= [tex]Speed\times Time[/tex]

Distance= [tex]20\ mph\times 15\ h=300\ miles[/tex]

Speed of train for on ward trip = 25 mph

Time taken = [tex]\frac{Distance}{Speed}[/tex]

Time taken = [tex]\frac{300\ miles}{25\ mph}= 12\ h[/tex]

Thus, time taken by train in onward journey = 12 hours.

In the problem, one paper clip equals three matches, one pencil is greater than one paper clip, and twenty-two paper clips are greater than sixty-seven matches.

In this scenario, one paper clip is equivalent, or equal to, three matches. This is ascertained from the first sentence which states that each paper clip can be traded for three matches. Similarly, one pencil is greater than a single paper clip as it can be traded for six paper clips. This conclusion is drawn from the second sentence. Lastly, the value of twenty-two paper clips is greater than sixty-seven matches since one paper clip is equal to three matches, hence twenty-two paper clips would be worth sixty-six matches, but since we have sixty-seven matches, twenty-two paper clips are worth more.

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c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat

Given that a boat rental charges $7.50 for the first hour and $2 for each additional hour.

To find: Rule that gives the cost for x hours of renting a boat

Let "x" be the total hours of renting a boat

[tex]c = f + (v \times x - 1)[/tex]

"c" is the total cost for the boat rent

"f" is the fixed cost for boat rent for first hour

"v"  is the cost for each additional hours of rent

"x" is the total hours of renting a boat

In the expression we have used "x - 1" to represent the additional hour of boat rent after first hour

Here f = $ 7.50

v = $ 2

[tex]c = 7.50 + 2 \times x - 1\\\\c = 7.50 + 2(x - 1)[/tex]

Thus c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat

The cost for renting a boat for x hours can be found using the formula y = 7.50 + 2(x - 1), where y is the total cost and x is the number of hours.

Based on the given information, the boat rental company charges $7.50 for the first hour and then an additional $2 for each subsequent hour. Therefore, if x is the number of hours you rent the boat, the total cost would be calculated using the formula y = 7.50 + 2(x - 1). Here, y represents the total cost of renting the boat for x hours. The formula subtracts the one-hour charge included in the initial payment.

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Answer:

12% discount

Step-by-step explanation:

Answer:

y=1

x=1

Step-by-step explanation:

Answer:

The simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex].

Step-by-step explanation:

Given rational expression is  

[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]

Now to simplify the given rational expression:

[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]

[In the above expression 6 and 3 cancelled and the result is 2, (x-2) and (x-2) getting cancelled each other]

[tex]=\frac{2x(x+3)}{x+9}[/tex]

Now applying distributive property to the above expression

[tex]=\frac{2x^2+6x}{x+9}[/tex]

Therefore [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]

Therefore the  simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]

Answer:

The required image line is 3x + y = 8

Step-by-step explanation:

We have to find two points on the given straight line then find their reflection points over the x-axis and then finally the straight line passing through those two image points will give the required straight line.

Now, the given straight line is y = 3x - 8.

Now, two any points on this straight line are say (1,-5) and (2,-2).

So, the image of (1,-5) point reflecting over the x-axis will be (1,5) and the image of the point (2,-2) reflecting over the x-axis will be (2,2).

Therefore, the straight line passing through those two image points will have equation  

[tex]\frac{y - 5}{5 - 2} = \frac{x - 1}{1 - 2}[/tex]

⇒ y - 5 = 3(1 - x)

⇒ y - 5 = 3 - 3x

⇒ 3x + y = 8

Hence, the required image line is 3x + y = 8 (Answer)

Answer:

x=5.333

y=3

Step-by-step explanation:

given, y=5-2............(1)

1-3x+y=-12...............(2)

y=5-2=3

put y=3 in equ (2)

1-3x+3=-12

1+3+12=3x

3x=16

x=[tex]\frac{16}{3}[/tex]

x=5.333

hence, x=5.333

           y=3               answer

Answer:

Step-by-step explanation:

Let x represent the number of days , then

(1) The exponential function to represent the spread of Ben's social media spread implies :

f(x) = 2([tex]3^{x}[/tex])

(2) The exponential function that represent carter;s social media spread implies

f(x) = 10([tex]2^{3}[/tex]

(3) the graph of the three functions is attached below

color red graph represents  Ben's social media spread , the graph with color blue represents Carter;s social media spread and the graph with green color represents Amber's social media spread

(4) on the 3rd day

Amber will receive 192 shares .

The equation for the spread of his shares is

f(x) = 3([tex]4^{x}[/tex]

where x is the number of days , so we have

3([tex]4^{3}[/tex])

= 3 ( 64)

= 192 shares

Ben's shares on the 3rd day will be

f(x) = 2([tex]3^{x}[/tex] )

= 2([tex]3^{3}[/tex])

= 2 ( 27)

= 54

Therefore , Ben will have 54 shares on the third day

Carter's share on the third day

f(x) = 10 ( [tex]2^{x}[/tex] )

= 10 ([tex]2^{3}[/tex] )

= 10 (8)

= 80

Therefore , Carter will receive 80 shares on the 3rd day

Answer:

Step-by-step explanation:

y = -4/3x + 1

in y = mx + b form, the number in the b is the y intercept...so ur y intercept is

(0,1).....this is where ur line crosses the y axis

to find ur x axis, sub in 0 for y and solve for x

y = -4/3x + 1

0 = -4/3x + 1

4/3x = 1

x = 1 / (4/3)

x = 1 * 3/4

x = 3/4........and ur x intercept is (3/4,0)...this is where ur line crosses the x axis.

in y = mx + b form, the letter m represents ur slope....so ur slope is

-4/3.....that negative means ur line is descending.....so when we graph, we will start at the y int.

go ahead and plot ur intercepts.......(0,1) and (3/4,0)....now look at ur slope -4/3.....the numerator (either go up or down)....the denominator (go right)

if the numerator is negative....go down....if it was positive u would go up.

so start at (0,1).....slope is -4/3.....so go down 4 and to the right 3...plot that point......then go down 4 and to the right 3...plot that...ur gonna keep on going down 4 and to the right 3 as far as u need to...connect ur points and u have ur line

if it helps, ur line will be going through points (3,-3), (6,-7),(-3,5), (-6,9).....those are some whole number points.....its kinda hard to graph when ur intercepts dont fall on whole numbers

The graph of the function y = -4/3x + 1 is added as an attachment

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

y = -4/3x + 1

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations

The graph of the function is added as an attachment

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Answer:

A) quantitative data.

Step-by-step explanation:

'quantitative' derives from 'quantity', almost synonymous with a measure or measurement.

Answer:

[tex]m=-\frac{4}{3}[/tex]

Step-by-step explanation:

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

the point (13,-4) and (1,12)

substitute the values in the formula

[tex]m=\frac{12+4}{1-13}[/tex]

[tex]m=\frac{16}{-12}[/tex]

[tex]m=-\frac{16}{12}[/tex]

simplify

[tex]m=-\frac{4}{3}[/tex]

Answer:

-4/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(12-(-4))/(1-13)

m=(12+4)/-12

m=16/-12

simplify

m=-4/3