the hypotenuse longest side of similar triangles ABC and DFA both lie on line k, as shown below. Demonstrate whether the slope of line k is constant(same) between C and D. Use the leg length short sides of triangles ABC and DFA in your answer​

Answer:

[tex]5\frac{2}{3}[/tex] miles.

Step-by-step explanation:

Kevin recorded the distances he ran last week in the table attached to this question.

Now, the total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.

Hence, {x + (x + 9) + (x + 4)} = {2x + (4x - 2)}

⇒ 3x + 13 = 6x - 2

⇒ 9x = 15

⇒ [tex]x = \frac{15}{9} = \frac{5}{3}[/tex]  

Therefore, he ran on Wednesday = x + 4 = [tex]\frac{5}{3} + 4 = \frac{17}{3} = 5\frac{2}{3}[/tex] miles. (Answer)

Answer: 9 miles

Step-by-step explanation:

x + x + 9 + x +4 = 2x + 4x-2

Collecting like terms

x + x + x +9 + 4 = 2x + 4x -2

Collect like terms

3x +13 = 6x -2

3x - 6x = -2 -13

-3x = -15

Divide both side by -3

x = 5

Therefore ; total number he ran on Wednesday

x + 4

If x = 5

Therefore total number he ran on Wednesday = 5+4

= 9

Answer:

1640.

Step-by-step explanation:

1640 would be your best option. As you are much higher than average. 2060 would not be a better option as you are below average in this case.

Answer:2060

Step-by-step explanation: your closest to 2060

Answer:

The answer is 5 years ago.

Step-by-step explanation:

5 years ago the age of the mother was 5 times the daughter's age.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose the current age of the daughter is D while the mother is M.

As per the given, The daughter is 36 years younger than her mother.

D = M - 36

And , M = 50

D = 50 - 36 = 14

Let's say x year age the mother was 5 times the daughter's age.

(M - x) = 5(D - x)

(50 - x) = 5(14 - x)

50 - x = 70 - 5x

-x + 5x = 70 - 50

4x = 20

x = 5

Hence "5 years ago the age of the mother was 5 times the daughter's age".

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Using the cross product property on this proportion gives us the following equation:

20 (2x - 9) = 10 (9)

Use the distributive property and multiply

40x - 180 = 90

Add 180 to both sides

40x = 270

Divide 40 from both sides

x = 270/40

Simplify fraction

x = 27/4

This should be your answer. Let me know if you need any clarifications, thanks!

The cross product is a type of multiplication between vectors that results in a vector product. It has the distributive property and is anticommutative.

The cross product is a type of multiplication between vectors that results in a vector product. It is denoted by the symbol A x B and is also known as the vector product.

The cross product has the distributive property, which allows us to distribute a vector across the sum of two other vectors. For example, A x (B + C) = (A x B) + (A x C).

The cross product is anticommutative, meaning that the order in which we multiply two vectors matters. A x B = -B x A.

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Answer: 4, 6,7,10

Step-by-step explanation: since X is greater than 3, then X can assume all numbers great than 3.

Answer:

Step-by-step explanation:

x > 3 - we read: all numbers greater than number 3

Therefore:

#1: NOT, because -1 < 3 and -2 < 3

#2: NOT, because all numbers are less than 3

#3: NOT, because 3 is not greater than 3

#4: YES, because all numbers are greater than 3.

old: $16

new: $20

percent increase

-> formula: (new-old / old) x 100

(20-16 / 16) x 100

4/16 x 100

0.25 x 100

answer: 25% increase

According to the question,

Old selling price,

New selling price,

We know the formula,

→ [tex]Percent \ increase = \frac{New \ selling \ price- Old \ selling \ price}{Old \ selling \ price}\times 100[/tex]

By putting the values,

                               [tex]= \frac{20-16}{16}\times 100[/tex]

                               [tex]= \frac{4}{16}\times 100[/tex]

                               [tex]= 0.25\times 100[/tex]

                               [tex]= 25[/tex] (%)

Thus the above approach is appropriate.

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Answer:

9(5r+7s+7)

Step-by-step explanation:

Answer:

9(5r+7s+7)

Step-by-step explanation:

Rewrite 63 as 7*9

Rewrite 63 as 7*9

Rewrite 45 as 5*9

=5 * 9r+ 7 * 9s + 7 * 9

Factor out common term: 9

= 9(5r+7s+7)

Answer:

[tex]t_{n}  = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........

Step-by-step explanation:

Given the arithmetic sequence in recursive formula.

f(0) = 30 and f(n + 1) = f(n) + 7 ......... (1)

Therefore, putting n = 0 in equation (1) we get f(1) = f(0) + 7 = 30 + 7 = 37 {Since, f(0) is given to be 30}

Again, putting n = 1 in equation (1) we get f(2) = f(1) + 7 = 37 + 7 = 44

And, putting n = 2 in equation (1) we get f(3) = f(2) + 7 = 44 + 7 = 51

and so on.

Therefore, the arithmetic sequence is 30, 37, 44, 51, .......

Therefore, the linear equation of this sequence is given by [tex]t_{n}  = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........

(Answer)

Answer:

$2,480

Step-by-step explanation:

Let $x be next year tuition. Aiden will pay $2,400, that is 75% of $x.

$x - 100%

$2,400 - 75%

Write a proportion:

[tex]\dfrac{x}{2,400}=\dfrac{100}{75}\\ \\75x=2,400\cdot 100\\ \\75x=240,000\\ \\x=3,200[/tex]

Next year’s tuition will be $720 more than this year’s, then this year tuition is

[tex]\$3,200-\$720=\$2,480[/tex]

Answer:

3/4

Step-by-step explanation:

2/2=1

1-1/4=4/4-1/4=3/4

Answer:

3/4

Step-by-step explanation:

1. Cancel 2.

1 - 1/4.

2. Get the same dominators.

1 X 1/4 X 4/4

3. Simplify.

4/4 - 1/4.

4-1/4

3/4

Answer:

x = 65

Step-by-step explanation:

The triangle has 2 congruent sides and is therefore isosceles.

The base angles are congruent, both 25°

Subtract the sum of the base angles from 180° for vertex angle

vertex angle = 180° - (25 + 25)° = 180° - 50° = 130°

Hence x = 130° ÷ 2 = 65

Answer:

A

Step-by-step explanation:

3x+2y=15

-3x

2y=15-3x

divide by 2

y=-3/2x+7.5

Parallel Line = Same Slope

y=-3/2x+b

substitute (5,2)

2=-3/2(5)+b

2=-7.5+b

   +7.5

9.5=b

Final Equation: y=-3/2x+9.5

Lana needs to first convert the equation to slope-intercept form, and then use the parallel line's slope with the provided point in the point-slope formula to find her line's equation.

The correct option for Lana to find an equation for a line that passes through the point (5, 2) and is parallel to the given equation 3x + 2y = 15, is option A.

First, Lana needs to write the given equation in slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept. To do this, she needs to rearrange the equation by subtracting 3x from both sides and dividing by 2, which gives y = -1.5x + 7.5.

Parallel lines have the same slope, so the slope, m, of Lana's line is -1.5. Now, she uses the point-slope form of a linear equation which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. Substituting the point (5, 2) and slope -1.5 into this equation, Lana gets y - 2 = -1.5x + 7.5.

She rearranges this to get her final equation.

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Answer:

41.24 cm²

Step-by-step explanation:

Here is the complete question:  A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region?

Given: measurement of rectangle is [tex]3\ cm\times 3\ cm[/tex]

          Radius of circle is 4 cm.

We can find the area of shaded region by subtracting area of rectangle from area of circle.

First, lets find the area of rectangle

Formula; Area of rectangle= [tex]length\times width[/tex]

Area of rectangle= [tex]3\ cm\times 3\ cm= 9\ cm^{2}[/tex]

∴ Area of rectangle= 9 cm²

Now, finding the area of circle.

Formula: Area of circle= [tex]\pi r^{2}[/tex] (∵ r is radius)

Area of circle= [tex]3.14\times 4^{2} = 3.14\times 16[/tex]

∴ Area of circle= 50.24 cm²

Next solving to find area of shaded region.

Area of shared region= [tex]\textrm{Area of the circle} - \textrm{Area of the rectangle}[/tex]

Area of shaded region= [tex]50.24\ cm^{2} - 9\ cm^{2} = 41.24\ cm^{2}[/tex]

∴ Area of shaded region= 41.24 cm²

Sybil's profit for selling n watermelons is represented by the function P = 2n - 15, which is the result of subtracting her cost function from her revenue function.

The function that represents Sybil's profit, P, for selling n watermelons is found by calculating the difference between her revenue and her costs. The profit function, therefore, is the revenue function R = 6n minus the cost function C = 4n + 15. Executing the subtraction, we get:

P = R - C

P = 6n - (4n + 15)

P = 6n - 4n - 15

P = 2n - 15

This function represents the profit made on selling n watermelons.

Final answer:

The function representing Sybil's profit for selling n watermelons is P = 2n - 15.

Explanation:

Profit can be calculated by subtracting the total cost from the total revenue. In this case, the total revenue function is R = 6n and the total cost function is C = 4n + 15. To find the profit function, we subtract the total cost function from the total revenue function:

P = R - C

P = 6n - (4n + 15)

P = 2n - 15

Therefore, the function representing Sybil's profit for selling n watermelons is P = 2n - 15.

Answer:

3

Step-by-step explanation:

Answer:

Rock phosphate, insoluble phosphates in bone deposits, and dissolved phosphates available to plants

I believe that the answer is 7 because it is in the tens place.

Sorry misunderstood the Question the other user is correct

originally had a 2

Answer:

7 because it is in the 0.1 (1/10 or tenth) place of the number

Answer:

y=-3x+5

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-0)

y-5=-3(x)

y-5=-3x

y=-3x+5

Answer:

-1

Step-by-step explanation:

The answer is minus one. The third quadrant only has all negative numbers therefore the answer is -1. All the other answers in the selection is positive.

Answer:

A. -1

Step-by-step explanation:

In the third quadrant, the x-coordinate and the y-coordinate are negative.

The x-coordinate must be a negative number.

Answer: A. -1

Answer: 12 girls

Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's girls/boys.

Next, we set up our proportion. We know that at a movie there are 3 girls for every 8 boys so we have 3/8 and we are asked how many girls are at the movie if 32 boys are the movie so that's x/32.

Now we have the proportion 3/8 = x/32.

Notice that the 32 boys must go on the bottom of the second ratio because our unit ratio tells us that we put girls/boys.

Solving from here, we use the means-extremes property to get 3 times 32 to get 96 = 8 times x or 8x. So we have 96 = 8x.

Dividing both sides by 8, we find that 12 = x.

This means that 12 girls are at the movie when 32 boys are at the movie.

Answer:

As π/7 is in first quadrant and all trig functions are positive there,

so, cos pi/7 is positive.

Step-by-step explanation:

Please check the attached figure a.

As π/7 is in first quadrant and all trig functions are positive there,

so, cos pi/7 is positive.

Keywords: trigonometric function, cos π

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Answer:

Step-by-step explanation:

so 2/5 of 100 contain chocolate...

2/5 * 100 = 200/5 = 40 <== contain chocolate

Answer:

16

Step-by-step explanation:

So according to PEMDAS we need to do the work in the parentheses first. 2 plus 2 is 4 so we will put 4 in the parentheses to replace 2 plus 2. Now we will divide 8 by 2 which is 4. since 4 is right next to the parentheses, we need to multiply the 4 by the 4 in the parentheses. 4 times 4 is 16.

Good morning,

Answer:

if h= 2​  ⇒  18 - (2 + 6h) = 4.

Step-by-step explanation:

if h= 2​ Then 18 - (2 + 6h) = 18 -(2+6×2) = 18 - 14 = 4.

:)

Answer:

Question 1:

Draw a line that crosses the largest number of dots. Then use the line to check the best prediction of the number of baseballs that will be used if 275 pitches are thrown.

Question 2:

A). y = 1.2x - 6

Question 3:

J). y = [tex]\frac{9}{4}x - 81[/tex]

Question 4:

F). f(n) = -3n + 24 *Although it doesn't work when f(n) = 6 and n = 6*

Step-by-step explanation:

Question 2:

The line passes throught point (5, 0) and is parallel to the line whose equation is y = 1.2x + 3.8

For parallel lines, their values of slope is the same.

So our line, that passes through point (5, 0), also has a slope of 1.2

Taking another point (x, y) on our line;

Slope = change in y ÷ change in x

1.2 = [tex]\frac{y - 0}{x - 5}[/tex]

y = 1.2x - 1.2(5)

y = 1.2x - 6

Question 3:

The line passes x-axis at point (36, 0)

The line is perpendicular to another line whose equation is y = -[tex]\frac{4}{9}x[/tex] + 5

For perpendicular lines, the product of their slopes = -1

Let's say the slope of our unknown line is a ;

Given: The slope of our second line is -4/9

So,

a × -4/9 = -1

a = -1 × -9/4 = 9/4

Taking another point (x, y) on our unknown line;

Slope = change in y ÷ change in x

9/4 = [tex]\frac{y - 0}{x - 36}[/tex]

Cross-multiplying that you get;

y = [tex]\frac{9}{4}x - 81[/tex]

Question 4:

The function that model that situation is f(n) = -3n + 24 though it doesn't work when f(n) = 6 and n = 6

Answer (2 answers):

x = -2/5,  x = -14/5

Step-by-step explanation:

First step is to try and get the absolute value by itself on one side and everything else that's not inside the absolute value on the other side.

9|5x+8|=54

|5x+8| = 54/9

|5x+8| = 6

Remember how absolute values turn everything positive? For example

|-4|=4, but |4|=4 as well. So we must do the same to our problem by splitting up the absolute equation into two parts.

|5x+8| = 6     and     |-(5x+8)| = 6

now solve the first equation.

(Just remove the absolute value sign and solve it normally)

5x+8 = 6

5x = -2

x = -2/5

Now solve the other equation

-(5x+8) = 6

-5x - 8 = 6

-5x = 14

x = -14/5

Answer:

This number line

shows the numbers

between 95 and 101.

Step-by-step explanation:

96, 97, 98, 99, and 100 all fall between 95 and 101.

97, 98, 99, and 100 are all greater than 96, so option 2 is incorrect.

96 is less than 97, so option 3 is incorrect.

Answer:

24

Step-by-step explanation:

Answer:

first step divide 112 by 8 which is going to give you 14 per hours. second step 150 by 6 is going to give you 25 per hours

I'm assuming that you want to find the unit rate of both scenarios.

I'm going to assume that you meant 112 miles in 8 hours.

Divide to find the unit rate: 112 / 8 = 14 miles per hour.

150 miles in 6 gallons

Divide to find the unit rate: 150 / 6 = 25 miles per gallon.

Best of Luck!

Answer:

4[tex]\sqrt{450}[/tex] = 4[tex]\sqrt{25 * 18}[/tex]    

                                  = 4 × 5 [tex]\sqrt{18}[/tex]

                                  =  20 [tex]\sqrt{18}[/tex]

                                  = 20 [tex]\sqrt{9 * 2}[/tex]

                                  = 20 × 3 [tex]\sqrt{2}[/tex]

                                  = 60 [tex]\sqrt{2}[/tex]

-5 [tex]\sqrt{0.6}[/tex] =  -5 [tex]\sqrt{0.6}[/tex]

                                   =  -  [tex]\sqrt{25 * 0.6}[/tex]

                                   =  - [tex]\sqrt{25 * \frac{3}{5}[/tex]

                                   = - [tex]\sqrt{15}[/tex]

Steps Explanation: