Does the placement of the slope triangles matter when finding the slope of a line? Explain your reasoning.


Choose the correct answer and justification.

Answer:

£8884.10625

Step-by-step explanation:

15% of £20,000:

20000x15/100=£3000

20000-3000=£17000

15% of £17000:

17000x15/100=£2550

17000-2550=£14450

15% of £14450:

14450x15/100=£2167.5

14450-2167.5=£12282.5

15% of £12282.5:

12282.5x15/100=£1842.375

12282.5-1842.375=£10440.125

15% of £10440.125:

10440.125x15/100=£1556.01875

10440.125-1556.01875=£8884.10625

Since the car loses 15% of it's value each year, it retains 85% of the value.

Value after 1 year = 85% of original value.

Value after 2 years = 85% of value after year 1

Value after 3 years = 85% of value after year 2

and so on...

We could calculate this year by year or we could do a single calculation to obtain the value.  We need to take 85% of the original value a total of 5 times, since we're wondering about the value in 5 years.

value after 5 years = 20000(0.85)(0.85)(0.85)(0.85)(0.85)

value after 5 years = 20000(0.85)^5

value after 5 years ≈ 8874.10625

So the value will be 8874.11 pounds in 5 years.

The percentage reduction in the cost of the coat is 20.58 %

As given,

Cost of coat =  $ 85  

Price in sale=  $ 67.50

Reduced price =$ 85  - $ 67.50= $ 17.5

Therefore to find the percentage reduction in the cost of the coat

% Reduction = (Reduced price / original price) x 100

= ( 17.5 / 85 ) x 100

= 20.58 %

Hence, the percentage reduction in the cost of the coat is 20.58 %

The percentage reduction formula is a mathematical tool that helps determine how much of a substance can be removed from a sample. This formula can be used to calculate the percentage of a substance that can be removed from a sample if the starting concentration and the ending concentration are known.

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Answer:

√78,9,10

Step-by-step explanation:

we know [tex]9^{2}[/tex] is 81

so √78 is less than √81(9) and 10 is obviously more than 9

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The expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .

Given:

The side length of the pillow is 2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches.

The length of ribbon :

= 4([tex]2x^{2} +1[/tex]) + 4(4x - 7)

= 4(2[tex]x^{2} +1[/tex]+4x - 7)

= 4([tex]2x^{2} +4x-6[/tex])

The length at x = 3.5 is,

= 4(2([tex]3.5^{2}[/tex])+4(3.5) - 6)

= 4(24.5+14-6)

= 4(24.5+8)

= 130 inches.

Therefore the expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .

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Answer:

Step-by-step explanation:2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What

expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?

The wage of 2001 in terms of wage in 2012 is option A $14.97

Given,

Mack's wages in 2001 = $7 per hour

Mack's wages in 2012 = $12 per hour

The CPI in 2001 = 94

The CPI in 2012 = 201

We have to fins the wage of 2001 in terms of wage in 2012;

CPI;- Consumer Price Index

The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.

Here,

The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year

= (201 / 94) x 7

= 14.97

That is,

The wage of 2001 in terms of wage in 2012 is option A $14.97

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The function f(x+3) in terms of x is 4x+14.

It is given that -

f(x) = 4x + 2

We have to find out f(x+3) in terms of x.

Now, f(x) = 4x + 2

=> f(x+3) = 4(x+3) + 2 [Substituting (x+3) in place of x]

=> f(x+3) = 4x + 12 + 2

=> f(x+3) = 4x + 14

Thus, the function f(x+3) in terms of x is 4x+14.

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The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.

Given that,

The system of inequality

y < x² + 2

y > x² - 6

We have to find the common point of the system of inequality.

We know that,

The graph is shown in the image.

Using the graphing technology,

A will be the first equation's vertex (0,2)

The parabola's outer region will be shaded and its boundary will be a dotted line because y is less than the value required by the quadratic equation.

In a similar way, the second equation's vertex, (0,-6), will be a dotted parabola with shaded inner portions.

The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.

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Answer: 4

Step-by-step explanation:

6 * 2/3 First simplify the expression.

Then you would get 2 * 2/1 = 2*2

The answer is 4

Answer:

None

Step-by-step explanation:

In order to solve an inequality you must isolate x on one side, so begin bringing the numbers from one side to another to make x the subject.

(numbers change their sign when brought to the other side)

5 > - 6 - 2x

5 + 6 > - 2x

11 ÷ - 2 > x

-5.5 < x (the sign switches when you divide or multiply by a negative number)

The solution is -5.5, which means none of the values provided are the solution.

Answer: the larger number is 59 and the smaller number is 17.

Step-by-step explanation:

Answer: D/ 6.

Step-by-step explanation: First, you have to do division to find out how many minutes = 1 nautical mile.

378 divided by 21= 18.

Then, you would do 108 divided by 18, to find out the answer; 6.

To double check your work, get the answer you got and multiply it by the minutes per mile which is 18.

18 x 6 = 108.

Therefore, it will be 6 nautical miles in 108 minutes.

Answer:

[tex]2Sb+3I_2=2SbI_3[/tex]

[tex]P_4+3O_2=2P_2O_3[/tex]  

[tex]2SO_3=2S+3O_2[/tex]  

[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]  

[tex]CH_4+2O_2=CO_2+2H_2O[/tex]

Step-by-step explanation:

Each side of the equations need to have the same number of each element.

Equation 1

Since there are 2 I on one side of equation 1, and 3 on the other side, I will do the following:

[tex]Sb+3I_2=2SbI_3[/tex]  

Now the number of Sb is unbalanced, so I balance it like so:

[tex]2Sb+3I_2=2SbI_3[/tex]

Equation 2

Using the same strategy, I focus on one element at a time. I can balance the P like this:

[tex]P_4+O_2=2P_2O_3[/tex]

Now, I can balance the O. There are 6 on the right, so if I put 3 on the left, there will be 6 there as well!

[tex]P_4+3O_2=2P_2O_3[/tex]  

Equation 3

Starting with O this time, I put 2 on the left and 3 on the right to bring them both to 6.

[tex]2SO_3=S+3O_2[/tex]  

Now there are 2S on the left and only 1 on the right, so I balance it:

[tex]2SO_3=2S+3O_2[/tex]  

Equation 4

Starting with O again, there are 3 on the left and 2 on the right.

[tex]2Fe_2O_3+C=Fe+3CO_2[/tex]

Now, the Fe are unbalanced as well. There are 4 on the left and 1 on the right:

[tex]2Fe_2O_3+C=4Fe+3CO_2[/tex]

Finally, balance the C, there is 1 on the left and 3 on the right.

[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]  

Equation 5

This one is pretty hard to read, so I will assume that the equation looks like this (please comment if this is incorrect)

[tex]CH_4+O_2=CO_2+H_2O[/tex]

Let's balance the H first:

[tex]CH_4+O_2=CO_2+2H_2O[/tex]

Now the O. There are 2 on the left and 4 on the right.

[tex]CH_4+2O_2=CO_2+2H_2O[/tex]

After changing the smaller exponent (-3) to the larger exponent (-1), its coefficient change to?l A. 0.23.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

From the information, it should be noted that the value was illustrated as:

= 2.3 × 10^-1

= 2.3 × 0.1

= 0.23

Therefore, the correct option is A.

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Answer:

x = 14   y = 37

Step-by-step explanation:

180 - (9x + 12) = 3x

180 - 9x - 12 = 3x

168 = 12x

x = 14

4y - 10 + 3(14) = 180

4y - 10 + 42 = 180

4y + 32 = 180

4y = 148

y = 37

Answer:

Step-by-step explanation:

Answer:

No, x=-5 is the answer

Step-by-step explanation:

Did this before, trust me

This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.

A)  1: proportion of gas-guzzlers manufactured by American firms.

p2: proportion of gas-guzzlers manufactured by international firms.

In this way, the boundary of interest is p1 - p2.

B) H_0: p_1-p_2=0

H_1: p_1-p_2\neq0

C) The following requirements must be satisfied: n (1 p) 10 and np 10.

American Guzzlers do not meet this requirement because np = 7.

D) If H0 is true, the test statistics are as follows: frac(hat p_1-hat p_2)-(p_1-p_2)surfactant p_1(1-hat p_1)n_1+frachat p_2(1-hat p_2)n_2sim N(0,1)

E) The p-value is calculated by multiplying p-value by P(z-3.75) = 0.

F) The 95% confidence interval is calculated as follows: p_1-p_2=hat p_1-hat p_2pm z_0.975sqrtfrachat p_1(1-hat p_1) n_1+frachat p_2(1-hat p_2) n_2 -0.0859 p_1-p_2 -0.0269

g. H0 should be rejected because the p-value is less than the 0.05 significance level.

There is enough evidence for us to reject H0. There is sufficient evidence to draw the conclusion that the proportion of Guzzlers in 2017 automobile models produced by American and international automakers differs.

Additionally, the 95% CI does not contain zero, does it?This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.

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Using the Side Angle Side Theorem, ∆KWL ≅ ∆ALW.

In the given question we have to

Prove: ∆KWL ≅ ∆ALW

Given: ∠KWL ≅ ∠WLK, ∠AWL ≅ ∠WLK

As given that

∠KWL ≅ ∠WLK

∠AWL ≅ ∠WLK

WL = WL (Diagonal)

Equal Parallel Sides

WK = AL

WA = KL

From Corresponding Angle Theorem

∠KWL=∠WLK and ∠AWL = ∠WLK

So ∠W=∠L

So from the Side Angle Side(SAS) Theorem

∆KWL ≅ ∆ALW.

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Answer:

61.2

Step-by-step explanation:

(36x2.9)-(24x1.8)

Unit conversion is the conversion of one unit to another unit with its standard conversion.

1 kg = 2.2 lb

The weight of the cat food in pounds is 33 lb.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 minute = 60 seconds

1 km = 1000 m

We have,

Number of bags of cat food = 3

Weight of each bag = 5 kg

1 kg = 2.2 lb ______(1)

Weight of 3 bag = 3 x 5 = 15 kg _______(2)

From (1) and (2) we get,

1 kg = 2.2 lb

Multiplying 15 on both sides.

15 x 1 kg = 15 x 2.2 lb

15 kg = 33 lb

Thus,

The weight of the cat food in pounds is 33 lb.

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Answer:

8

Step-by-step explanation:

You can solve this a few different ways.

Firstly I did 102 - 97 = 5

Then I took 5 and added 3 to it

5 + 3 ---> which gets us 8 as our final answer.

Hope I helped!

Have a great day!

Answer:

5

Step-by-step explanation:

to multiply fractions we multiply numerator with numerator and denominator with denominator

[tex]\frac{3}{36}x\frac{60}{1}[/tex]

[tex]\frac{3x60}{36x1}[/tex]

[tex]\frac{180}{36}[/tex]

5

Hopes this helps please mark brainliest

The median of the given data set is, 40.

What is median?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.

Let, a data set contains 5 numbers: 21, 32, x, 99, 40.

x is the unknown number.

The average is to be 50.

Since,

Average = Sum of numbers / total numbers

       50   = (21 + 32 + x + 99 + 40) / 5

   50 x 5 = 192 + x

      250  = 192 + x

           x = 250 - 192

           x = 58

Hence, the unknown number is 58.

Now to find the median,

Since median is the middle number of a data set.

So, write the numbers in ascending order.

21, 32, 40, 58, 99.

In this data set the middle number is, 40.

Therefore, the median is 40.

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A guitar manufacturer sells 532,475 warranties and has to honor 12% of them. The profit the manufacturer gains from the warranties is $66,772,365 (option b)

Profit is calculated as:

Profit = revenues - total cost

While,

Revenues = number of goods sold x price per unit

In the given problem,

Revenues = number of warranty sold x price per warranty

                 = 532,475 x 225

                 = 119,806,875

Cost of honored warranty = number of honored warranty x guitar cost

                                           = 12% x 532,475 x 830

                                           = 53,034,510

Hence,

profit from warranty = 119,806,875 - 53,034,510

                                  = 66,772,365

The profit from warranty is $66,772,365 (option b)

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Answer:

its b

Step-by-step explanation:

Expression which are equivalent to the given expression 3⁴ ×  3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.

As given in the question,

Given expression is equal to :

3⁴ ×  3ˣ

Using law of indices for multiplication we have ,

mᵃ × mᵇ = mᵃ⁺ᵇ

Here in the given expression m = 3 , a= 4 and b = x

Equivalent expression for the given expression is given by,

3⁴ ×  3ˣ

=  (3⁴⁺ˣ )

Also,

Now simplify the given expression we get,

 3⁴ ×  3ˣ

= ( 3 × 3 × 3 × 3) × 3ˣ

= 81 × 3ˣ

Therefore, expression which are equivalent to the given expression 3⁴ ×  3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.

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The weight of meteorite A is 207 tons and meteorite B is 23 tons.

Let the weight of B = w

Let the weight of A = 9 × w = 9w

Since the weight of meteorite A is 9 times the weight of meteorite B. If the sum of their weights is 230 tons. This will be illustrated as:

9w + w = 230

10w = 230

Divide

w = 230/10

w = 23

meteorite B = 23 tons

meteorite A will be:

= 9w

= 9 × 23

= 207 tons

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No, It will not be able to outbid your competitor if your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37.

A cost is the worth of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost. Any system for allocating expenses to a business component is known as costing. Costing is frequently used to establish expenses for customers, distribution channels, personnel, regions, goods, product lines, processes, subsidiaries, and whole businesses.

Given,

Your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37.

No, It will not be able to outbid your competitor.

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Answer:

Subtract 6 from both sides

Step-by-step explanation: