Jean and Jericho who are playing in the school grounds decided to sit on a
seesaw. Jean, who is heavier, tends to raise Jericho on the other end of the seesaw.
They tried to position themselves in order to balance the weight of each other.

Questions: Underline the correct answer.

1. This situation illustrates (direct, inverse) variation.
2. The two quantities that must vary in this situation are (weight and
distance from the center, height and weight).
3. The heavier the kid, the (closer, farther) he/she should be at the
center to balance the seesaw?
4. When Jean moves farther from the center, Jericho tends to go (up,
down).
5. If Jericho moves closer to the center, Jean tends to go (up, down).

Answer:

x = 21 and both sides are 53 units long

Step-by-step explanation:

They are congruent, so they are equal, so

3x-10=x+32 then solve for x

2x=42

x=21

then plug x into each side to get its length

3x-10=3(21)-10=53

x+32=21+32=53

You would expect them to be the same since they are congruent

Answer:

[tex]A=\frac{1}{2}h(b_{1}+b_{2} ) | *2\\2A=h(b_{1}+b_{2} ) | : (b_{1}+b_{2} )\\\frac{2A}{(b_{1}+b_{2} )} = h[/tex]

I hope it's good.

Take care !

Answer:

The equation of a line in the slope-intercept form is:

y = 5x - 18

The slope-intercept form of the line equation

where

   m is the slope

   b is the y-intercept

In our case, we are given

   m = 5

   Point (4, 2)

now substituting m = 5 and (4, 2) in the slope-intercept form of the line equation to determine the y-intercept

y = mx + b

2 = 5(4) + b

20 + b = 2

subtract 20 from both side

20 + b - 20 = 2 - 20

b = -18

now substituting b = -18 and m = 5 in the slope-intercept form of the line equation

y = mx + b

y = 5x + (-18)

y = 5x - 18

Therefore, the equation of a line in the slope-intercept form is:

y = 5x - 18

Pls mark me as brainliest thank you

Answer:

Step-by-step explanation:

m = 4

y = mx +c

y= 4x + c

Plugin x = 3 and y= 4 in the above equation

4 = 4*3 + c

4 = 12 +c

4 - 12 = c

c = -8

Equation of the line :

y = 4x - 8

Answer:

5/6

Step-by-step explanation:

3 hours= 2 1/2 miles

1 hour= 2 1/2 divided by 3

It would take him 5/6 of an hour

Hop this helps!

Answer:

y - 7 = 6(x - 2)

Step-by-step explanation:

1. Since we're given one point and the slope of a line, we can use the point slope form: [tex]y-y_1=m(x-x_1)[/tex]

2. (Plugging in values)

Therefore, one equation of the line is y - 7 = 6(x - 2).

Answer:4.84

Step-by-step explanation:

Answer: Check attached :) Right on ED22

Step-by-step explanation:

Greg and George bought shoes at a local store. Greg bought one dress shoe and 4 sneakers and spent less than $400.

George bought one dress shoe and 6 sneakers and spent more than $400.

Inequality signs < and > denote less than and greater than respectively.

To solve the above inequalities in order to find x and y prices, a pair of solutions will be the result since linear inequalities with two variables will have a range of solutions

In other words, to find x and y for the inequalities we find a point (x,y) that satisfies the inequality.

Example: if the price of a dress shoe is $80 and the price of a sneaker is $60, it satisfies the system of inequalities for Greg and George since their shoe expenses stay below and above $400 respectively.

We could then say that the point (80,60) is one of the solutions to the inequalities.

We could graph the inequalities in order to find points on the graph that satisfy the inequalities. To graph the inequality we make the equation a linear equation x+4y=400 and plot a straight line in accordance to the inequality. All points above the line satisfy George's inequality and vice versa.

Read more here: https://brainly.com/question/14399777

Answer:

4 ounces each

Step-by-step explanation:

16 ounces = 1 pound

16x2=32

32/8=4

Answer:

-53

Step-by-step explanation:

(x+2)

x^4 =       -2^4 = 16

15x^3 =     15* (-2)^3 = -120

6x^2 =       6(-2^2) = 24

12x =        12*(-2) = -24

substitute into equation:

x^4 + 15x^3 + 6x^2 - 12x + 3 = 16+ (-120) + 24 - (-24) + 3 = -53

Given Polynomial is x^4 +15x^3 +6x^2 - 12x +3

Divisor = x+2

We know that

Remainder Theorem:

Let P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial,If P(x) is divided by (x-a) then remainder is P(a).

So, P(x) is divided by (x+2) then the remainder is P(-2).

P(-2) =

⇛(-2)^4+15(-2)^3+6(-2)^2-12(-6)+3

⇛ 16+15(-8)+6(4)+72+3

⇛16-120+24+72+3

⇛ 67-120

⇛ -53

P(-2) = -53

Answer:- The remainder is -53.

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The remainder obtained when x^4 + 3x^2 - 2x + 2 is divided by (x + b) is the square of the remainder obtained when x^2 – 3 is divided by (x + b...

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[tex]\red{\bold{Answer:}}[/tex]

The Inverse variation of the total stopping distance and the force of the pavement to determine the speed the car travelling.

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#CarryOnLearning

(≡^∇^≡)

Answer:

Osmosis is the diffusion of water to an area of high water concentration to an area of low water concentration.

Step-by-step explanation:

Answer:

the spontaneous passage or diffusion of water or other solvents through a semipermeable membrane

Step-by-step explanation:

a process by which molecules of a solvent tend to pass through a semipermeable membrane from a less concentrated solution into a more concentrated one, thus equalizing the concentrations on each side of the membrane.

Answer:

Khaled made 16 baskets.

Step-by-step explanation:

3 12

-- = ---

4 x

12 / 3 = 4

4 x 4 = 16

x = 16

Answer:

x=16

Step-by-step explanation:

Heres the work below

Hope this Helps

Answer:

25 seconds

Step-by-step explanation:

Two methods:

1)  Calculate Tyana's speed in m/sec:  4m/5sec = 0.8 m/sec.  Now find the number of seconds, x, needed to travel 20 meters:

 x*(0.8 m/sec) = 20 m

x = 20 m/(0.8 m/sec)

x = 25 seconds

2)  Do a proportion.  If Tyana can swim 4 meters in 5 sec, then she can do 8 meters in 10 seconds.  That also then means 16 meters in 20 seconds.  Another 5 seconds adds another 4 meters, for a total of  20 meters in 25 seconds.

Answer:

Since there is a right angle, this is a right-angled triangle and we can solve for x using Pythagoras Theorem that goes [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse (longest side of the triangle).

In this case, x would be the c.

Substitute in values of a and b:

[tex]10^2+10^2=c^2[/tex]

[tex]c^2=200[/tex]

[tex]c=\sqrt{200}[/tex]

[tex]c=10\sqrt{2}[/tex] (Option A)

Answer: D.25

Step-by-step explanation:

Since they gave you P(10) You'll have to substitue 10 wherever you see the variable 10.

2(10)+5

 2(10)=20

20+5+25

Answer:

25

Step-by-step explanation:

Since they're asking you to find the value of p(10) when t is 10, you would substitute t out for 10 in the function and then solve.

p(10)=2(10)+5

p(10)=20+5

p(10)=25

Answer:

I think the answer to the question is 3/10?

Answer:

B.   4

Step-by-step explanation:

[tex] \dfrac{\sqrt{32}}{\sqrt{2}} = [/tex]

[tex] = \dfrac{\sqrt{16 \times 2}}{\sqrt{2}} [/tex]

[tex] = \dfrac{\sqrt{16} \times \sqrt{2}}{\sqrt{2}} [/tex]

[tex] = \dfrac{4\sqrt{2}}{\sqrt{2}} [/tex]

[tex] = 4[/tex]

184 people

groups of 13

How many vans needed to take the people to the hotel.

[tex] \frac{184}{13} [/tex]

[tex] = 14.1538461538[/tex]

[tex]nearest \: whole \: number = 14[/tex]

therefore, they'll need 14 vans to take the people to the hotel.

answer= option B

Answer:

l = 104/3

w = 40/3

Step-by-step explanation:

l = 2*w + 8

P = 2(l + w) = 96

48 = l + w

2w + 8 + w = 48

3w = 40

w = 40/3

l = 2*40/3 + 8

= 80/3 + 8

= 80 + 24  / 3

= 104/3

Answer:

Yes, 30 would be your outlier.

Step-by-step explanation:

The rest of the numbers are closer and 30 is far away from the rest.

Answer:

I believe it is d

Step-by-step explanation:

it is the only option where every combination of two sides is larger than the third

Answer:

d

Step-by-step explanation:

if you add up 2 sides it is larger than the third, which is what we are looking for :))

Answer:

$350,000

Step-by-step explanation:

lets say the original price is x, then 378000=1.08x, divide by 1.08 to get 350000

Answer: [tex]y=\frac{2}{3}x+1\frac{1}{3}[/tex]

Step-by-step explanation:

take 2 points and use slope formula to find slope

[tex]\frac{4-2}{4-1}[/tex][tex]=\frac{2}{3}[/tex]

take the slope and a point on the graph and use point slope formula to get equation in point slope intercept form

[tex]y-2=\frac{2}{3}( x-1)[/tex]

[tex]y-2=\frac{2}{3}x-\frac{2}{3}[/tex]

[tex]y=\frac{2}{3}x-\frac{2}{3} + 2[/tex]

[tex]y=\frac{2}{3}x+1\frac{1}{3}[/tex]

Answer:

14) Not a function 15) Function 16) Function

Step-by-step explanation:

The vertical line test is when you draw a line on the graph to see if it passes the function. The rule is that you can only have one intersection per line

for number 14, if you draw a line, it intersects the function twice each time

for 15, no matter what kind of vertical line you draw, each line will only intersect the function once and the same for 16 (except 16 is more of a linear function)

Answer:

Well a function can’t be on the same one as each other so thats why the vertical line test is used.

For number 14 if you’d draw a vertical line, you’d see there would be 2 answers So that can’t be a function.

For number 15, if you draw a vertical line, none of the given have 2 questions so number 15 is a function.

Whilst in number 16 if you’d draw a vertical line, there wouldn’t be anything that have 2 answers of that overlap. So it is a function

Answer:

6.4

Step-by-step explanation:

5+7+7+5+7+7+6+7+7 = 58

There are 9 numbers

58 ÷ 9 = 6.444444

To the tenth = 6.4

The absolute measurement specifies the magnitude of the difference

which may be positive or negative.

The completed table is presented as follows;

[tex]\begin{tabular}{|l|c|c|c|}&\textbf{Apple}&\textbf{Grapefruit}&\textbf{Watermelon}\\\textbf{Keiko's measurement}&15 cm&24 cm& \underline{81 cm}\\\textbf{Actual measurement}&\underline{10 cm}&30 cm&90 cm\\\textbf{Absolute difference}&5 cm&\underline{6 cm}&9 cm\\\textbf{Percent error}&\underline{50\%}&\underline{20\%}&\underline{10\%}\end{array}\right][/tex]

Reasons:

The formulas for the inputs in the table are;

Absolute difference = Keiko's measurement - Actual measurement

The difference between Keiko's measurement and the actual measurement can be positive or negative while the absolute difference is always positive

[tex]\displaystyle Percent \ error = \mathbf{\frac{Keiko's \ measurement - Actual \ measurement}{Actual \ measurement} \times 100}[/tex]

Therefore;

[tex]\displaystyle Percent \ error = \frac{ \mathbf{Absolute \ difference}}{Actual \ measurement} \times 100[/tex]

Which gives for Apple;

The actual measurement for Apple = 15 cm - 5 cm = 10 cm

[tex]\displaystyle Percent \ error \ for \ Apple = \frac{5 \, cm}{10 \, cm} \times 100 = \mathbf{50\%}[/tex]

Grapefruit column of the table;

Absolute difference for Grapefruit = |24 cm - 30 cm| = |-6 cm| = 6 cm

The absolute difference for Grapefruit = 6 cm

[tex]\displaystyle Percent \ error \ for \ Grapefruit = \mathbf{\frac{6 \, cm}{30 \, cm} \times 100} = 20\%[/tex]

Percent error for Grapefruit = 20%

Watermelon column of the table;

Keiko's measurement = Absolute difference + Actual measurement

Using the given options, we have, 90 - 9 = 81

Therefore, the difference = -9, while the absolute difference = 9

Keiko's measurement for Watermelon = 90 cm - 9 cm = 81 cm

[tex]\displaystyle Percent \ error \ for \ Grapefruit= \frac{9 \, cm}{90 \, cm} \times 100 = 10\%[/tex]

The completed table is as follows;

[tex]\begin{tabular}{|l|c|c|c|}&\textbf{Apple}&\textbf{Grapefruit}&\textbf{Watermelon}\\\textbf{Keiko's measurement}&15 cm&24 cm& \underline{81 cm}\\\textbf{Actual measurement}&\underline{10 cm}&30 cm&90 cm\\\textbf{Absolute difference}&5 cm&\underline{6 cm}&9 cm\\\textbf{Percent error}&\underline{50\%}&\underline{20\%}&\underline{10\%}\end{array}\right][/tex]

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Answer:2 1/2

Step-by-step explanation: