Using the graph, determine the value of the slope.
What is the slope?

Answer:

Step-by-step explanation:

[tex]n+1=4(n-8)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\n+1=(4)(n)+(4)(-8)\\\\n+1=4n-32\qquad\text{subtract 1 from both sides}\\\\n+1-1=4n-32-1\\\\n=4n-33\qquad\text{subtract}\ 4n\ \text{From both sides}\\\\n-4n=4n-4n-33\\\\-3n=-33\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3n}{-3}=\dfrac{-33}{-3}\\\\n=11[/tex]

Final answer:

To find the length of the altitude of an equilateral triangle with a perimeter of 36 inches, divide the perimeter by 3 to get the side length, then calculate the altitude using the formula for a 30-60-90 right triangle, resulting in an altitude length of 6\(\sqrt{3}\) inches.

Explanation:

To solve for the length of the altitude of an equilateral triangle with a perimeter of 36 inches, we first need to determine the length of one side of the triangle. Since an equilateral triangle has all sides of equal length, we divide the perimeter by 3 to find the length of one side:

Side length = Perimeter ÷ 3 = 36 inches ÷ 3 = 12 inches

Now, let's draw the equilateral triangle and an altitude. An altitude in an equilateral triangle splits the triangle into two 30-60-90 right triangles. In such a right triangle, the length of the altitude (which is the same as the longer leg) is \(\sqrt{3}/2\) times the length of the shorter leg (which is the side of the original equilateral triangle).

Hence, the altitude (h) can be calculated as:

Altitude (h) = Side length × (\(\sqrt{3}/2\)) = 12 inches × (\(\sqrt{3}/2\)) = 6\(\sqrt{3}\) inches

Therefore, the length of the altitude is 6\(\sqrt{3}\) inches.

Answer:

C. 560

Step-by-step explanation:

50% is one half, so there is another half of 280. 280*2=560

Answer:

C

Step-by-step explanation:

Answer:

The surface area of Rectangular prism is [tex]358 \ cm^2[/tex].

Step-by-step explanation:

Given:

Length of the rectangular prism = 7 cm

Width of the rectangular prism = 5 cm

Height of the rectangular prism = 12 cm

we need to find the surface area of rectangular prism.

Solution:

the surface area of rectangular prism is equal to 2 times sum of length times width and width times height and length times height.

framing in equation form we get;

the surface area of rectangular prism = [tex]2(l\times w+w\times h+h\times l)[/tex]

the surface area of rectangular prism = [tex]2(7\times5+5\times12+12\times7) = 2(35+60+84) = 2\times179 = 358\ cm^2[/tex]

Hence The surface area of Rectangular prism is [tex]358 \ cm^2[/tex].

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Explanation:

Using a calculator,

3/8 = 0.375

The decimal stops and does not go on forever. So it is terminating.

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One way to be able to tell that it terminates is to look at the denominator 8, which factors to 2*2*2 or 2^3. The prime factor 2 indicates that the decimal will terminate. The rule is that if the denominator is factored into 2's or 5's only, then the decimal will terminate.

Examples:

1/5 = 0.2,   4/10 = 0.4,   5/8 = 0.625

Some non-examples would be

1/3 = 0.333333...

5/6 = 0.83333....

2/7 = 0.285714...

Each denominator of these non-terminating fractions do not have solely 2's or 5's as part of the factorizations.

Answer:

fraction > -18/5

dec> -3.6

Step-by-step explanation:

Answer:

-212.5

Step-by-step explanation:

-212.5 x 0.4 = -85

Final answer:

The student's question regarding dividing -85 by 0.4 results in -212.5. You divide the absolute values first and then apply the negative sign because dividing a negative by a positive yields a negative result.

Explanation:

The student is asking how to divide a negative number by a positive decimal number. Specifically, the question is about dividing -85 by 0.4. To perform this division, we'll divide the absolute values and then apply the negative sign to the result. The steps are as follows:

The division of a negative number by a positive number results in a negative outcome. Hence, -85 divided by 0.4 equals -212.5.

Try to leave a screenshot of the answers if you can please! Here's the graph for that function :D

The price will increase 8024 dollars.

The price of next model will be $67,024.

Step-by-step explanation:

Given,

Cost of current model = $59,000

Increase in new model = 13.6% of cost of current model

Amount of increase = [tex]\frac{13.6}{100}*59000[/tex]

Amount of increase = 0.136 * 59000

Amount of increase = $8024

The price will increase 8024 dollars.

Cost of next model = Cost of current model + Amount of increase

Cost of next model = 59000 + 8024 = $67,024

The price of next model will be $67,024.

Keywords: addition, division

Learn more about division at:

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Answer:

[tex]y-8=-5(x-7)[/tex]

Step-by-step explanation:

we know that

The equation of the line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-5\\(x1,y1)=(7,8)[/tex]

substitute

[tex]y-8=-5(x-7)[/tex]

y = -x - 1 is the equation of the line that passes through (2,-3) and is perpendicular to y = x - 5

Solution:

Given that we have to write the equation of the line that passes through (2,-3) and is perpendicular to y = x - 5

The equation of line in slope intercept form is given as:

y = mx + c ------ eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Given equation of line is:

y = x - 5

On comparing the above equation with eqn 1,

m = 1

We know that,

Product of slope of line and slope of line perpendicular to given line is equal to -1

Therefore,

[tex]1 \times \text{ slope of line perpendicular to given line } = -1\\[/tex]

Slope of line perpendicular to given line = -1

Now we have to find the equation of line with slope -1 and passing through (2, -3)

Substitute m = -1 and (x, y) = (2, -3) in eqn 1

-3 = -1(2) + c

-3 = -2 + c

c = -3 + 2

c = -1

Substitute m = -1 and c = - 1 in eqn 1

y = -x - 1

Thus the equation of line is found

Answer: Answer is 40%

Step-by-step explanation: The total number of players in the game is 30 (that is boys and girls added together becomes 18 + 12= 30) altogether which is a hundred percent. The percentage of girls playing the game is calculated as;

12/30 × 100%

=2/5 × 100%

=200/5

=40%

Answer:

x=14

y=10

Step-by-step explanation:

The median divide the data‘s set into two parts with the same frequency = 50%

then we must have 2+5+x+12+17 = 50 ⇔ 36+x=50 then x =50-36=14

also 20+y+9+7+4=50 ⇔ y=10

Answer:

50-6=14

Step-by-step explanation:

just do the math and then you will find the answer

In this question, you're trying to transform the equation into slope intercept form.

Slope intercept form equation:

y = mx + b

In this case, you would need to get the "y" variable by itself.

To do so, you would subtract -2x from both sides:

2x + y = 2

y = -2x + 2

Answer:

y = -2x + 2

The equation of the line 2x + y = 2 in slope-intercept form is y = -2x + 2.

The equation of a line is expressed as;

y = mx + b

Given the equation of the line in the question:

2x + y = 2

To convert the equation 2x + y = 2 into slope-intercept form (y = mx + b), where "m" represents the slope and "b" is the y-intercept, follow these steps:

First, Isolate "y" on one side of the equation by moving the term with "x" to the other side.

2x + y = 2

Subtract 2x from both sides:

2x - 2x + y = 2 - 2x

y = 2 - 2x

Rearrange:

y = -2x + 2

Therefore, the slope-intercept form is y = -2x + 2.

Learn more about equation of line here: brainly.com/question/2564656

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Answer:

x<6

Step-by-step explanation:

4x-13<11

4x<11+13

4x<24

x<24/4

x<6

Answer:

Step-by-step explanation:

so he needs at least 35 and he already knows 18...

k + 18 > = 35 (thats a greater then or equal sign)

k > = 35 - 18

k > = 17

so he would have to learn at least 17 more

Answer:

k + 18 > = 35 (thats a greater then or equal sign)

k > = 35 - 18

k > = 17

so he would have to learn at least 17 more

Final answer:

To find the two numbers whose sum is 38 and difference is 16, we set up and solve a system of equations, which reveals the numbers to be 27 and 11.

Explanation:

The question involves finding two numbers when their sum and difference are known. To solve it, we can set up a system of equations based on the information provided. Suppose the two numbers we are trying to find are X and Y. According to the question, the sum of the two numbers is 38, and their difference is 16. Therefore, we can write the following equations:

Equation 1: X + Y = 38

Equation 2: X - Y = 16

To find the values of X and Y, we can add these two equations to eliminate Y. This gives us 2X = 54, which simplifies to X = 27. Substituting the value of X back into Equation 1, we find that Y = 11. Thus, the two numbers are 27 and 11.

The 3 angles when added together make a straight line which is 180 degrees. To find x subtract the 2 known angles from 180.

The answer would be x = 180 - (67 + 52)

Answer:

Step-by-step explanation:

Perimeter = 2(l + w)

Perimeter = 464inches

Length l = 100inches

: 464 = 2(100 + w)

Dividing be 2

464/2 = 100 + w

232 = 100 + w

Collecting like terms

232 - 100 = w

132 = w

It is 132 inches long

903 kg of potatoes will be delivered to stores in Bronx

Solution:

Given that, lamar has 1354.5 Kilograms of potatoes to deliver equally to 18 stores

12 of the stores are Bronx

Number of stores in Bronx = 12

From given,

Kilograms of potatoe = 1354.5 kg

Total number of stores = 18

Let us first find the kilograms of potato delivered to 1 store

[tex]\text{kg of potato to 1 store } = \frac{\text{Total kg of potato}}{\text{ total number of stores}}[/tex]

Substituting the values we get,

[tex]\text{kg of potato to 1 store } = \frac{1354.5}{18} = 75.25[/tex]

Thus 75.25 kg potato is delivered to 1 store

How many kilograms of potatoes will be delivered to stores in Bronx

Number of stores in bronx is 12, so multiply 75.25 by 12

[tex]\rightarrow 12 \times 75.25 = 903[/tex]

Thus 903 kg of potatoes will be delivered to stores in Bronx

Answer:

Step-by-step explanation:

Tom and Dipak share $114 in the ratio 7:5

Total amount shared = $114

Ratio of Tom to Dipak = 7:5

Total ratio = 7+5 = 12

Dipak got = 5/12 × $114 = $ 47.5

Good morning ☕️

Answer:

Step-by-step explanation:

Let our number be “ xy ”

the tens digit is four less than the units digit means y-4=x

Seven times the tens digit plus five times the units digit is equal to 56 means

7x+5y=56

now we have to solve the system:

y-4=x  (1)

7x+5y=56  (2)

(1) ⇒ y=4+x

Then we substitute y by 4+x into the second equation like this:

7x+5(x+4)=56

⇔ 7x+5(x+4)=56

⇔ 12x+20=56

⇔ x = 3

now using equation (1) we get : y=3+4 = 7

:)

Step-by-step explanation:

9.

Given that, the measure of [tex]\angle A[/tex] is [tex]45^\circ[/tex]. The measure of [tex]\angle B[/tex]is [tex]b^\circ[/tex]. The measure of[tex]\angle C[/tex] is [tex]3b^\circ[/tex] .

We know that the sum of all angles of triangle is [tex]180^\circ[/tex].

Therefore

[tex]45^\circ + b^\circ +3b^\circ =180^\circ[/tex]

⇔[tex]4b^\circ[/tex] = [tex]135^\circ[/tex]

10.

Given that , the measure of [tex]\angle X[/tex] and [tex]\angle Y[/tex]are same [tex]x^\circ[/tex]. The angle of [tex]\angle Z[/tex] is twice the measure of [tex]\angle Y[/tex].

∴[tex]\angle X[/tex]+[tex]\angle Y[/tex]+[tex]\angle Z[/tex]=[tex]180^\circ[/tex]

⇔[tex]x^\circ[/tex]+[tex]x^\circ[/tex]+2[tex]x^\circ[/tex]=[tex]180^\circ[/tex]

⇔4[tex]x^\circ[/tex]= [tex]180^\circ[/tex]

Bisecting diagonals

Two pair of opposite parallel sides

Two pair of opposite equal angles

Solution:

Let us first define the properties of parallelogram.

Now, let us define the properties of square.

From these properties, we can conclude that  every square can always be classified as a parallelogram if

Bisecting diagonals

Two pair of opposite parallel sides

Two pair of opposite equal angles

Answer:

The Amount paid by dealers is $20464.75    

Step-by-step explanation:

Given as :

The base price of car = $23,800

The option cost of car stereo = x = $365

The option cost of car wheels and paint = y = $900

Total option cost = $365 + $900

The charges of destination = $640

The Amount paid by dealer = 82% of total base price + 75% of total option cost

Let The Amount paid by dealers = $A

Now, According to question

The Amount paid by dealers =  82% of total base price + 75% of total option cost

i.e A = [tex]\dfrac{82}{100}[/tex] × total base price +  [tex]\dfrac{75}{100}[/tex] × total option cost

Or, A = [tex]\dfrac{82}{100}[/tex] × total base price +  [tex]\dfrac{75}{100}[/tex] × (x + y)

Or, A = [tex]\dfrac{82}{100}[/tex] × $23,800 +  [tex]\dfrac{75}{100}[/tex] × ($365 + $900)

Or, A = [tex]\dfrac{82}{100}[/tex] × $23,800 +  [tex]\dfrac{75}{100}[/tex] × $1265

Or, A = 82 × $238 +  75 × 12.65

Or, A = $19,516 + $948.75

Or, A = $20464.75

So, The Amount paid by dealers = A = $20464.75

Hence, The Amount paid by dealers is $20464.75       Answer

Answer:A

Step-by-step explanation: