What could be the next statement that Ivan makes his proof?

Answer:

y = -2x+11

Step-by-step explanation:

If we have a slope and a line, we can use the slope intercept form of a line

y-y1 = m(x-x1)

where (x1,y1) is the point and m is the slope.

Substitute in what we know

y-5 = -2 (x-3)

We want it in slope intercept form which is y = mx+b

Distribute the -2

y-5 = -2x+6

Add 5 to each side

y-5+5 = -2x +11

ANSWER:

y = -2x + 8

ABOUT POINT SLOPE FORM:

ABOUT SLOPE INTERCEPT FORM:

y - Y1 = m (x - X1)

y - 5 = -2 (x - 3)

y - 5 = -2x + 3

 + 5           + 5

y = -2x + 8 --- IN SLOPE INTERCEPT FORM

Hope this helps you!!! :)

Answer:

3 and 4

Step-by-step explanation:

21/7 = x/1

x = 21/7*1 = 3

16/4 = y/1

y = 16/4*1 = 4

Answer:

p = 10t - 100

Step-by-step explanation:

Perform the indicated multiplication:  p = 10t - 100.

The equivalent form of the algebraic equation p = 5(2t - 20) is p = 10t - 100, which is a simplified linear representation of the original equation.

The student is looking for an equivalent form of the algebraic equation p = 5(2t - 20). By distributing the 5, we obtain p = 10t - 100. This is now a simplified linear equation representing the same rule as the original equation. It's also similar to manipulating a quadratic equation to find the value of t, as shown in the other examples provided. However, this linear equation doesn't require solving for t; rather, we're simply rewriting it in a more straightforward format.

Answer:

2y

Step-by-step explanation:

Simplifying

21x + -42y = 0

Solving

21x + -42y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '42y' to each side of the equation.

21x + -42y + 42y = 0 + 42y

Combine like terms: -42y + 42y = 0

21x + 0 = 0 + 42y

21x = 0 + 42y

Remove the zero:

21x = 42y

Divide each side by '21'.

x = 2y

Simplifying

x = 2y

Answer:The answer is 7 hours here is how I solved it. If it's out of 500 pieces and you've already done 325 then lets minus that so we only have to deal with the left over pieces. So 500- 325 which will give you 175 from there let's divide it by 25 to see how many hours it will take. Once you divide you will get 7 you can double check by doing 7 times 25 then add that to 325 to get 500 pieces.

Step-by-step explanation:

Answer: The number of ballots increases by 3: 3x3=9, 9x3=27, 27x3=81...

After 10 cuts, there will be 59,049 ballots.

(7) is the same problem with different numbers as (4) in another question you posted: https://brainly.com/question/11799042

(8) is not correct. [tex]\mathbf u\cdot\mathbf v=(12)(-15)+(4)(-5)=-200[/tex]

(9) is not correct. The direction of the vector [tex]\langle3,4\rangle[/tex] is [tex]\theta[/tex] where

[tex]\tan\theta=\dfrac34\implies\theta=\tan^{-1}\dfrac34[/tex]

so the applied force is the vector

[tex]\mathbf F=\langle14\cos\theta,14\sin\theta\rangle=\langle11.2,8.4\rangle[/tex]

(if you're not sure how to compute the (co)sine of the inverse-tangent expression, note that a tangent of 3/4 corresponds to a right triangle with hypotenuse 5)

The object is moved 7 ft in the same direction as [tex]\mathbf F[/tex], so that its displacement is given by the vector

[tex]\mathbf d=\langle7\cos\theta,7\sin\theta\rangle=\langle5.6,4.2\rangle[/tex]

Then the work done on the object is the dot product of these two vectors,

[tex]W=\mathbf F\cdot\mathbf d=(11.2)(5.6)+(8.4)(4.2)=98\approx97[/tex]

(the discrepancy here might be coming from finding a numerical value for [tex]\theta[/tex])

(10) is correct. We can find a unit vector pointing in the direction of any vector [tex]\mathbf v[/tex] by dividing [tex]\mathbf v[/tex] by its magnitude:

[tex]\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\frac23\,\mathbf i-\frac12\,\mathbf j}{\sqrt{\left(\frac23\right)^2+\left(-\frac12\right)^2}}=\dfrac45\,\mathbf i-\dfrac35\,\mathbf j[/tex]

Answer:

7.0

Step-by-step explanation:

If we had the number 7.1  the 1 is the tenth digit. .

So 7 to the nearest tenth is written 7.0.

Answer:

7.5 is exactly halfway between 7 and 8. Therefore, 7.5 rounds to 8.

Step-by-step explanation:

To round to the nearest tenth using a number line, look at the tenth place value closest to the number you are rounding.

Answer:

x = 16/5

Step-by-step explanation:

(x-2)= -1/4(x-8)

Multiply each side by -4 to clear the fraction

-4 (x-2) = -4*-1/4 (x-8)

Distribute

-4x+8 = x-8

Add 4x to each side

-4x+4x+8 = x+4x-8

8 = 5x-8

Add 8 to each side

8+8 = 5x-8+8

16 = 5x

Divide each side by 5

16/5 = 5x/5

16/5 =x

Answer: h = -4

Step-by-step explanation:

-9h-6+12h+40=22

-9h+12h=22+6-40 "collect all unknown values in a side and collect numbers in other side "

"Don't forget to Change signs"

3h= -12

3h/3 = -12/3 "dividing by 3 in both sides"

h= -4

[tex]-9h-6+12h+40=22\qquad\text{combine like terms}\\\\(-9h+12h)+(-6+40)=22\\\\3h+34=22\qquad\text{subtract 34 from both sides}\\\\3h=-12\qquad\text{divide both sides by 3}\\\\\boxed{h=-4}[/tex]

Answers are attached in the pictures. Solutions are in RED.

Answer:

12. 7.5

13. 0.224

14. 193.5

15. 2/3

16.  5/7

17. -10

18. 2:1

19. 16

20. 150

21. 46,200

22. 4

23. 18

24. 5.29

25. 7.07

26. 19.80

27. 15.87

28. 9.80

29. 6.71

30. 1.26

Step-by-step explanation:

12. 5/8 = x/12

  8x = 60

   x = 7.5

13. x/1.11 = 1/5

  5x = 1.12

   x = 0.224

14. 6x /27 = 43

      6x = 1161

         x = 193.5

15. x+2)/3 = 8/9

   9x + 18 = 24

   9x = 6

  x = 2/3

16. (3x -5)/4 = -5/7

     21x - 35 = -20

     21x = 15

     x = 5/7

17. (x-2)/4 = (x+4)/2

    2x - 4 = 4x + 16

    -2x = 20

     x = -10

18.  9 grams of fat.

      6 grams are saturated.

     9-6 = 3 grams are cheese.

  ratio of saturated to cheese = 6:3

                                                   = 2:1

19. goats to sheep = 4:7

     7/11 x = 28

     x = 28 × 11/7

     x = 44

   goats = 44-28 = 16

20. 280:4 = 10,500:x

   280/4 = 10,500/x

  280x = 42000

     x = 150

21. 42:2 = x:2200

   42/2 = x/2200

   92,400 = 2x

    x = 46,200

22. √(2×8) = √16 = 4

23. √(9×36) = √324 = 18

24. √(4×7) = √28 = 5.29

25. √(5×10) = √50 = 7.07

26. √(28×14) = √392 = 19.80

27. √(7×36) = √252 = 15.87

28. √(8×12) = √96  = 9.80

29. √(3×15) = √45 = 6.71

30. √4/5 × 2) = √8/5 = 1.26

Answer:

Option D. [tex]\frac{24}{7}[/tex].

Step-by-step explanation:

In any right angle triangle tangent of an angle is the ratio of opposite side and adjacent side.

tan x =[tex]\frac{\text{Opposite side (24)}}{\text{Adjacent side (7)}}[/tex]

        = [tex]\frac{24}{7}[/tex]

therefore, Option D. [tex]\frac{24}{7}[/tex] is the answer.

Answer:

A

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the given condition x = 24 and y = 360

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{360}{24}[/tex] = 15

Hence y = 15x is the equation → A

Answer: A

Step-by-step explanation:

Answer:

He would make $4391.92

The constant of proportionality is 14.6

Step-by-step explanation:

If Daniel works 213 hours and makes $1820.00

(I assume that is a typo and he made 1820. not 18.20)

How much does he make per hour

$1820/213 = $8.54 per hour

Now if he works 514 hours

514 * 8.54/hour = $4391.92

y = kx, where k is the constant of proportionality

a = 14.6h,

The constant of proportionality is 14.6

Answer: a - add 3 to both sides

Step-by-step explanation: you want to have the variable with the number all to itself to solve for x, so you have to add 3 to both sides to get 3/4x=-15. then divide by 3/4 to both sides and you will get a final answer.

Answer: The volume of a block of ice is 9 meters

You have to LxWxH

Answer:

one box of crackers costs $0.70

Step-by-step explanation:

Let $x be the price of 1 container of yogurt and $y be the price of 1 box of crackers.

1. Man can buy 4 containers of yogurt and 3 boxes of crackers for $9.55. 4 containers of yogurt cost $4x and 3 boxes of crackers cost $3y. In total,

[tex]3x+4y=9.55.[/tex]

2. Man can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. 2 containers of yogurt cost $2x and 2 boxes of crackers cost $2y. In total,

[tex]2x+2y=5.90.[/tex]

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}3x+4y=9.55\\2x+2y=5.90\end{array}\right.[/tex]

Multiply the second equation by 2 and subtract it from the first equation:

[tex]3x+4y-2(2x+2y)=9.55-5.90\cdot 2,\\ \\3x+4y-4x-4y=9.55-11.80,\\ \\-x=-2.25,\\ \\x=\$2.25.[/tex]

Then

[tex]2\cdot 2.25+2y=5.90,\\ \\2y=5.90-4.50,\\ \\2y=1.40,\\ \\y=\$0.70[/tex]

By setting up a system of equations and using elimination, we find that one box of crackers costs $2.25.

To solve the cost of one box of crackers, we need to set up two equations based on the information given:

We use 'y' to represent the cost of one container of yogurt and 'c' for the cost of one box of crackers. To find the value of 'c', we can use substitution or elimination.

Let's eliminate 'y' by multiplying the second equation by 2, which gives us 4y + 4c = $11.80. Subtracting the first equation from this, we get:

c = $11.80 - $9.55

c = $2.25

So, one box of crackers costs $2.25.

Answer: a=2 b=5 c=-7

parabola equation is y = 2x^2+5x-7 = 0

Step-by-step explanation:

Substitute (x,y) into y = a x^2 + b x + c

(2,11)      11 = 4a + 2b + c

(-1,-10)  -10 = a - b + c

(-4,5)      5 = 16a -4b + c

Solve the linear system in a, b, c

Det[{{4,2,1},{1,-1,1},{16,-4,1}}] = 54

Det[{{11,2,1},{-10,-1,1},{5,-4,1}}] = 108

Det[{{4,11,1},{1,-10,1},{16,5,1}}] = 270

Det[{{4,2,11},{1,-1,-10},{16,-4,5}}] = -378

a = 108/54 = 2

b = 270/54 = 5

c = -378/54 = -7

parabola equation is y = f(x) = 2x^2+5x-7

f(2) = 8+10-7 = 11 ✔

f(-1) = 2-5-7 = -10 ✔

f(-4) = 32-20-7 = 5 ✔

Answer:

13 y^2 - 9 x y + 3 x^2

Step-by-step explanation:

Simplify the following:

6 x^2 - 7 x y + 8 y^2 - (x^2 - 3 x y - y^2) - (2 x^2 + 5 x y - 4 y^2)

-(x^2 - 3 x y - y^2) = -x^2 + 3 x y + y^2:

6 x^2 - 7 x y + 8 y^2 + -x^2 + 3 x y + y^2 - (2 x^2 + 5 x y - 4 y^2)

-(2 x^2 + 5 x y - 4 y^2) = -2 x^2 - 5 x y + 4 y^2:

6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 + -2 x^2 - 5 x y + 4 y^2

Grouping like terms, 6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 - 2 x^2 - 5 x y + 4 y^2 = (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2):

(8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

8 y^2 + y^2 + 4 y^2 = 13 y^2:

13 y^2 + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

x y (-7) + x y 3 + x y (-5) = -9 x y:

13 y^2 + -9 x y + (6 x^2 - x^2 - 2 x^2)

6 x^2 - x^2 - 2 x^2 = 3 x^2:

Answer:  13 y^2 - 9 x y + 3 x^2

Answer:

D

Step-by-step explanation:

use the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8.9}{10.9}[/tex], hence

x = [tex]sin^{-1}[/tex]( [tex]\frac{8.9}{10.9}[/tex] ) → D

Answer:

D

Step-by-step explanation:

Answer:

She need 72 index cards.

Step-by-step explanation:

Ms. James has a 6 square foot bulletin board and a 12 square food bulletin board and she wants to cover both boards with index cards without gaps or overlaps.

Each index card has an area of [tex]\dfrac{1}{4}[/tex] square foot.

Dividing the area of each board with the area of the index card will yield the the number of cards she needs to cover up completely.

Let us assume T₁ and T₂ are the number of cards she needs to cover 6 square feet food bulletin board and 12 square feet food bulletin board respectively. So

[tex]T_1=\dfrac{6}{\frac{1}{4}}=24,\\\\T_2=\dfrac{12}{\frac{1}{4}}=48[/tex]

Therefore, in total she need 24+48=72 index cards.

Answer:

D

Step-by-step explanation:

Answer: We can say that (a/b)^2 is a rational number

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

Proof:

Rational means the number is a ratio of two whole numbers

If 'a' is rational, then a = p/q for some whole numbers p,q (eg: p = 2, q = 3 so p/q = 2/3)

The same applies for b, which I'll let b = r/s, with r & s being whole numbers.

To avoid division by zero, I'm going to make p,q,r,s nonzero which leads to 'a' and 'b' being nonzero.

Now let's divide 'a' over b to get

a/b = (p/q) divided by (r/s)

a/b = (p/q) * (s/r)  .... flip the second fraction; multiply

a/b = (ps)/(qr)

The new numerator is p*s which is a whole number (because the product of two whole numbers is also a whole number). The same goes for q*r in the denominator. So a/b is rational if both 'a' and 'b' are rational together.

We can extend this to (a/b)^2 as well

(a/b)^2 = [ (ps)/(qr) ] ^2

(a/b)^2 = [ (ps)^2 ]/[ (qr)^2 ]

(a/b)^2 = (p^2*s^2)/(q^2*r^2)

p is a whole number, and so is p^2. Same for s and s^2. Overall, the final numerator p^2*s^2 is also a whole number. Similarly, q^2*r^2 is a whole number.

So we have yet another ratio of two whole numbers proving that (a/b)^2 is a rational number.

Simplify 2/3x to 2x/3

2x/3 = -20

Multiply both sides by 3

2x = -20 × 3

Simplify 20 × 3 to 60

2x = -60

Divide both sides by 2

x = -60/2

Simplify 60/2 to 30

x = -30

Answer: B) -30

Answer:

the answer to you question is -30

Step-by-step explanation:

what you have to do is take the fraction and multiply it by its reciprocal to get it away from the x and if you multiply on one side then you have to multiply on the other side also so you would multiply -20 by 3/2 the you would get the answer of -30

Hope this helps!!!:) can I get the Brainliest?

There is only one solution to this system of equations.  The solution is where the two equations meet, which in this system is (2, 1).

Answer:

One Solution

Step-by-step explanation:

GOT IT RIGHT ON EDGE 2020

Answer:

a = - 15 and b = - 9

Step-by-step explanation:

distribute the left side

- 15x² - 25x - 5b

For - 15x² - 25x - 5b = ax² - 25x + 45

Then the coefficients of like terms must be equal, hence

comparing coefficients of x² term ⇒ a = - 15

comparing constant term ⇒ - 5b = 45 ⇒ b = - 9

Answer: a = -15,   b = -9

Step-by-step explanation:

-5(3x² + 5x + b) = ax² - 25x + 45

-15x² - 25x - 5b = ax² - 25x + 45       distributed -5 on left side

Notice that the middle terms (-25x) are equal, so the the remaining terms will also be equal.

-15x² = ax²  ⇒  -15 = a

 -5b = 45   ⇒   b = -9

Answer:

C. The range of Liam's data set is 16

Step-by-step explanation:

Hello, my dear friend, I am sure the question you are intending should be corrected  (See below question), as well as the box plot should be uploaded (See attached the image of the box plot I uploaded for you).  

Q. The box plots show the data distributions for the number of laps two students run around a track each day. Which statement is true about the data?

Options:

A. The median of both data sets is 10.

B. The median of both data sets is 14.

C. The range of Liam’s data set is 16.

D. The range of Sumat’s data set is 17.

If this is the case, then the box plot shows the following data.

The median of Liam's data is 10, the range is (20-4) =16

The median of Sumat's data is 14, the range is (22-3) =19

The correct answer will therefore be:

C. The range of Liam's data set is 16  

Can you answer this:

The box plots show the data distributions for the number of laps two students run around a track each day.

Which statement is true about the data?

The difference between the medians of both data sets is 2.

The difference between the medians of both data sets is 4.

The difference between the ranges of both data sets is 2.

The difference between the ranges of both data sets is 4

check the picture below.

Final answer:

The radio station has 54,780 listeners now.

Explanation:

To find the number of listeners the radio station has now, we need to calculate the number of listeners it lost after changing its format. If the station lost 34% of its listeners, we can calculate the number of lost listeners by multiplying the original number of listeners by 0.34 (34%).

Lost Listeners = 83,000 * 0.34 = 28,220 listeners

To find the number of listeners the radio station has now, we subtract the lost listeners from the original number of listeners.

Number of Listeners Now = 83,000 - 28,220 = 54,780 listeners