PLEASE HELP I WILL REWARD BRAINLY. PLEASE ONLY ANSWER IF YOU KNOW HOW TO SOLVE THIS PROBLEM. PLEASE INCLUDE INSIGHTFUL EXPLAINATION AND THOUGHT PROCESS: A woman and her two children are playing on a seesaw. This seesaw has seats that can move to different distances from the fulcrum. Riders can also add seats to the seesaw. The woman weighs 145lb, her son weighs 95lb, her daughter weighs 70lb, each seat weighs 5 pounds. Question: The woman is on the left side of the seesaw, 60 inches from the fulcrum. The daughter and son both get on the right side. The son sits 60 inches from the fulcrum. Where should the daughter sit to balance the seesaw. Please explain your process and give correct answer.
Answers
Answer:
40 inches
Step-by-step explanation:
Left side of seesaw:Woman + sit = 145 lb + 5 lb = 150 lb
Distance from the fulcrum to the left side = 60 in
Moment of the force on the left side:
150*60 = 9000 Right side of seesaw:Son + sit = 95 lb + 5 lb = 100 lb
Distance from the fulcrum to the son's seat = 60 in
Moment of the force:
100 * 60 = 6000Daughter + sit = 70 lb + 5 lb = 75 lb
Distance from the fulcrum to the daughter's seat = x
Moment of the force:
75 * xSince left and right sides are balanced, moments should be equal on both sides.
This is shown as:
75x+6000= 900075x= 3000x= 3000/75x= 40So, the daughter should sit at 40 in distance from the fulcrum.
Answer:
[tex]\large \boxed{\text{40 in from the fulcrum}}[/tex]
Step-by-step explanation:
An object is in rotational equilibrium when the net torque applied to it is zero.
For example, if a seesaw is not rotating, you know the torque on each side is balanced.
The counterclockwise torque of the woman equals the sum of the clockwise torques of her son and daughter.
The formula for torque τ is
τ = Fr,
where
F = the turning force and
r = the distance from the fulcrum
Thus, we can write
[tex]F_{\text{w}}r_{\text{w}} = F_{\text{s}}r_{\text{s}} + F_{\text{d}}r_{\text{d}}[/tex]
Data:
Each person has a 5 lb seat, so they are exerting 5 lb in addition to their weight.
Fw = 150 lb; rw = 60 in
Fₛ = 100 lb; rₛ = 60 in
Fd = 75 lb; rd = ?
Calculation:
[tex]\begin{array}{rcl}F_{\text{w}}r_{\text{w}} &=& F_{\text{s}}r_{\text{s}} + F_{\text{d}}r_{\text{d}}\\\text{150 lb $\times$ 60 in} & = & \text{100 lb $\times$ 60 in} + \text{75 lb} \times r_{\text{d}} \\\text{9000 in} & = & \text{6000 in}+ 75 r_{\text{d}}\\\text{3000 in} & = &75 r_{\text{d}}\\ r_{\text{d}} & = & \dfrac{\text{3000 in}}{75}\\\\& = & \textbf{40 in}\\\end{array}\\\text{The daughter should sit $\large \boxed{\textbf{40 in from the fulcrum}}$}[/tex]
Check:
[tex]\begin{array}{rcl}150 \times 60 &=& 100 \times 60 + 40 \times 75\\9000 & = & 6000 + 3000\\9000 & = & 9000\\\end{array}[/tex]
It checks.
Related Questions
Wendy's mother recorded how many donuts she has eaten over the past few months. Jelly-filled donuts 6 maple donuts 53 glazed donuts 11 powdered sugar donuts 5 What is the experimental probability that the next donut Wendy eats will be a powdered sugar donut? Write your answer as a fraction or whole number. P(powdered sugar donut) =
Answers
Answer:
[tex]P(\text{Powdered sugar donut})=\dfrac{1}{15}[/tex] .
Step-by-step explanation:
It is given that Wendy's mother recorded how many donuts she has eaten over the past few months.
Jelly-filled donuts = 6
Maple donuts = 53
Glazed donuts = 11
Powdered sugar donuts = 5
Now,
Total number of donuts = 6 + 53 + 11 + 5 = 75
We need to find the experimental probability that the next donut Wendy eats will be a powdered sugar donut.
[tex]P(\text{Powdered sugar donut})=\dfrac{\text{Powdered sugar donuts}}{\text{Total number of donuts}}[/tex]
[tex]P(\text{Powdered sugar donut})=\dfrac{5}{75}[/tex]
[tex]P(\text{Powdered sugar donut})=\dfrac{1}{15}[/tex]
Therefore, [tex]P(\text{Powdered sugar donut})=\dfrac{1}{15}[/tex].
6 For every 3 girls in Mr Hegarty's class there are 5 boys. What is the ratio of girls to boys in the class? Give your answer in its simplest form.
Answers
We cannot simplify this further because 3 and 5 have no factors in common, other than 1. So we just leave it as is.
PLS HELPPPPP!!!!!!!!!!!!!!!!!!!! 15 POINTS
The graph for the equation y = negative 2 x + 1 is shown below. On a coordinate plane, a line with negative slope goes through (0, 1) and (1, negative 1). If another equation is graphed so that the system has no solution, which equation could that be?
Options:
y = negative 2 (x minus one-half)
y = negative one-half (4 x + 2)
y = negative x + 1
y = negative one-half x + 2
Answers
Answer:
y = negative 2 (x minus one-half)
Step-by-step explanation:
The equation of a line is given as:
y = mx + c, where m is the slope and c is the intercept on the y axis.
The equation of a line going through (0, 1) and (1, - 1) is calculated using:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ y-1=\frac{-1-1}{1-0}(x-0)\\ y-1=-2x\\y=-2x+1[/tex]
The solution of two lines is at their point of intersection. The equation of the line that would not have any solution with y = -2x + 1 would be a line that is parallel to y = -2x + 1. Since the two lines would be parallel to each other, their would be no intersection and therefore no solution.
Two lines are said to be parallel to each other if they have the same slope. The slope of y = -2x + 1 is gotten by comparing with y = mx + c, therefore the slope m = -2. From the options the only line with a slope m = -2 is y = -2(x -1/2). Therefore y = -2(x -1/2) is parallel to y = -2x + 1 and would have no solution
Answer:
b
Step-by-step explanation:
i did test
(38x+61y)-(3x-11y) simplify this expression
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
35x + 72y
▹ Step-by-Step Explanation
(38x + 61y) - (3x - 11y)
38x + 61y - (3x - 11y)
38x + 61 y - 3x + 11y
35x + 61y + 11y
35x + 72y
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
If the point (8. 6) is the result of the composition T3,30 RO,-180º, what are the coordinates of the point prior to the
composition?
A. (-11, -9)
B. (-8, -3)
C. (-8,6)
D. (-5, -3)
Answers
Answer:
The correct answer is A. [tex](-11, -9)[/tex].
Step-by-step explanation:
Given that the point is (8,6)
Let this point be A(8,6).
The composition is T3,30 RO,-180º
First translate the point by 3,3.
Let this point becomes A'.
A' is formed by translation of point A by 3,3
i.e.
x coordinate of A' = x coordinate of A + 3 and
y coordinate of A' = y coordinate of A + 3
So, A' (8+3, 6+3)
So, A'(11,9)
Now, a rotation of -180º is applied to point A'.
Let it becomes A''.
By a rotation of -180º, the coordinate gets changed by 2 quadrants.
A is in 1st quadrant because both x and y coordinates are positive.
A'' will be in 3rd quadrant where both x and y coordinates are negative.
Please refer to the attached image for the graphical representation of A, A' and A''.
So, the answer will be option A. [tex](-11, -9)[/tex].
A model village is built to scale. It has a scale of 1 : 23. A road has a real-life length of 1.61 km. What is the length of the road in the model village in m?
Answers
Answer:
We need to find how much more or less the ratio becomes
1.61 / 23 = 0.07
we multiply 0.07 with 1 to make the ratio even and get your answer
1 x 0.07 = 0.07 on the map
Hope this helps
Step-by-step explanation:
Suppose that the distribution of lifetimes of females in France is not symmetric. According to Chebyshev's Theorem, at least approximately what percentage of these lifetimes are within k=3.8 standard deviations of the mean?
Answers
Answer:
93.7% of the lifetimes are within 3.8 standard deviations of the mean
Step-by-step explanation:
Generally Chebyshev's Theorem, can be mathematically represented as
[tex]1 - \frac{1}{k^2}[/tex]%
The percentage of these lifetimes that are within k=3.8 standard deviations of the mean is mathematically evaluated using Chebyshev's Theorem as follows
[tex]1 - \frac{1}{k^2}[/tex]% [tex]= (1 - \frac{1}{3.8^2} )[/tex]% = [tex]= 93.07[/tex]%
So from the above calculation we see that 93.7% of the lifetimes are within 3.8 standard deviations of the mean
Which set represents the range of the function shown? {(−1, 5), (2, 8), (5, 3), (13, −4)}
Answers
Answer:
the range are all the value of y :{5,8,3,-4}
Step-by-step explanation:
the range are all the value of y :{5,8,3,-4}
Answer:
{−4, 3, 5, 8}
Step-by-step explanation:
i just took the test
EXTRA POINTS >> Which of the following graphs shows all the possible values for a number that is more than 8? Number line with closed circle on 8 and shading to the left. Number line with closed circle on 8 and shading to the right. Number line with open circle on 8 and shading to the left. Number line with open circle on 8 and shading to the right. Ignore the shaded option
Answers
The correct answer is D, you are right.
Answer:
The answer is D.
Step-by-step explanation:
Combine like terms -5.55-8.55c+4.35c
Answers
5.55/4.2= 1.32142857
All of the following expressions simplify to 3, except _____.
-6 + 9
1 - (-2)
-9 ÷ (-3)
-5 - 2
Answers
Answer:
-5 - 2
Step-by-step explanation:
Solve each of the following
A is -6 + 9 which equals 3
B is 1 - (-2) which simplifies into 1 + 2 which equals 3
C is -9 / -3. the negatives cancel leaving 9/3 which is 3
D is -5 - 2 which simplifies into -5 + -2 which equals -7
Because
-6+9=3
1-(-2)=3
-9/(-3)=3
-5-2=-7
ONE MORE well maybe 3 more LOLLL ok can u answer this dont look it up pls!!!!!!!!!! :/ thank you sm
Answers
Answer:
Hey there!
Your answer would be 1/3 (12) hours.
Since it can fill 1/12 of the tank in 1/3 hour, then in 12 1/3 hr's, the tank would be filled.
Hope this helps :)
Answer:
1/3 * 12
4 hours
Step-by-step explanation:
We can use ratios to solve
1/12 tank 1 tank
---------------- = ----------------
1/3 hour x hours
Using cross products
1/12 x = 1/3 *1
Multiply each side by 12
12 * 1/12 x = 1/3 * 12
x = 4
4 hours
please help me with this one.
Answers
Answer:
2x^2 -x +1 = 0
Step-by-step explanation:
For roots α and β, the original equation can be factored as ...
f(x) = 2(x -α)(x -β)
If we add 1 to each of those roots, the factors become ...
g(x) = 2(x -(α+1))(x -(β+1))
This can be rearranged to be ...
g(x) = 2((x -1) -α)((x -1) -β)
That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.
2(x -1)² +3(x -1) +2 = 0
2x^2 -x +1 = 0
An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c Consider the trinomial x2 + 10x + 16. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?
Answers
Answer:
The pair of numbers that has a product of ac and a sum of b = (+2, +8)
The factored form of the trinomial = (x+2) (x+8)
Step-by-step explanation:
ax² + bx + c = 0
This is in the form of a trinomial algebraic expression
Given trinomial: = ax² + 10x + 16
Where a = 1, b= 10, c= 16
To find the pair of numbers that has a product of ac and a sum of b, we would solve the equation.
Using factorisation method:
ac = a×c = 1×16 = 16
Let's find the factors of 16 whose sum gives +10 and product gives +16
Factors of 16 = 1, 2, 8, 16
+2 + +8 = +10
+2 × +8 = +16
The factors are +2 and +8
The pair of numbers that has a product of ac and a sum of b = (+2, +8)
x² + 10x + 16 = x + 2x + 8x + 16
x² + 10x + 16 = x(x+2) + 8(x+2)
= (x+2) (x+8)
The factored form of the trinomial = (x+2) (x+8)
Answer:
(x+2) (x+8)
Step-by-step explanation:
Rita purchased two loaves of wheat bread. Each loaf was $1.89. How much
money did Rita spend in all? Do not include $ in your answer.
Answers
Answer: 3.78
Step-by-step explanation:
Because she bought 2 $1.89 loaves, she spent 2 * 1.89, or 3.78 dollars.
Hope it helps <3
Answer:
3.87Step-by-step explanation:
This is because you have to multiply the number of 1.89 by 2. This is equal to 3.87.
Given:
Price of one bread = 1.89
Unknown:
Total money used = ?
So,
1.89 * 2 = 3.87
or
1.89 + 1.89 = 3.87
Total money used is 3.87.Hope this helped,
Kavitha
Pleas answer in two minutes now
Answers
Answer:
I believe the answer is C.
I NEED HELP PLEASE, THANKS! :)
Find the solutions of each equation on the interval [0, 2π). Show work.
Answers
Answer: 0π
Step-by-step explanation:
[tex]sin\bigg(\dfrac{3\pi}{2}+x\bigg)+sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-2\\\\\\2sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-2\\\\\\sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-1\\\\\\\dfrac{3\pi}{2}+x\bigg=sin^{-1}(-1)\\\\\\\dfrac{3\pi}{2}+x=\dfrac{3\pi}{2}\\\\\\\large\boxed{x=0}[/tex]
In an orchard the ratio of apple trees to pear trees is 2 : 5, and the ratio of pear trees to peach trees is 3 : 4. Work out the ratio of apple trees to pear trees to peach trees.
Answers
Answer:
5/8
Step-by-step explanation:
apple trees to pear trees=5/2 to peach trees=(5/2)/4=5/8
34 POINTS see attached
Answers
Answer:
Step-by-step explanation:
-2x + 3 = 0
-2x = -3
x = 3/2
-x^2 + 2x + 3 = (-3/2)^2 + 2 × 3/2 + 3
= 9/4 + 3 + 3
= 9/4 + 6
= 33/4
Hope this helps
plz mark as brainliest!!!!!!
Answer:
33/4 or as a mixed number8 1/4Step-by-step explanation:
-2x + 3 = 0
-2x = -3
x = 3/2
-x^2 + 2x + 3 = (-3/2)^2 + 2 × 3/2 + 3
= 9/4 + 3 + 3
= 9/4 + 6
= 33/4
or 8 1/4 as a mixed number
Do it in two minutes right now
Answers
Answer:
Step-by-step explanation:
Answer:
so the coordinates of C are (12,29)
Step-by-step explanation:
as we know that CD is a line segment and M is its mid-point in order to find the coordinates of C we will use mid-point formula
[tex]M(x,y)=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
putting the values of known coordinates
[tex](15,-6.5)=(\frac{x1+18}{2},\frac{y1+(-16)}{2})[/tex]
comparing the coordinates separately
[tex]15=\frac{x1+18}{2}[/tex] and [tex]-6.5=\frac{y1-16}{2}[/tex]
15×2=x1+18 and -6.5×2=y1-16
30=x1+18 and 13=y1-16
30-18=x1 and 13+16=y1
12=x1 and 29=y1
so the coordinates of C are (12,29)
in order to check the values put it back in the mid-point formula to find the coordinates of M
I HOPE THIS WILL HELP YOU :)
Choose the inverse of y=x^2-10
Answers
Answer:
x = 5 + sqrt(y+25), for x>=5
x = 5 - sqrt(y+25), for x<=5
Step-by-step explanation:
y = x^2 - 10x + 25 - 25
y = (x-5)^2 - 25
y+25 = (x-5)^2
x-5 = +/-sqrt(y+25)
And you get TWO inverses:
x = 5 + sqrt(y+25), for x>=5
x = 5 - sqrt(y+25), for x<=5
Which shows one way to determine the factors of 4x3 + x2 - 8x - 2 by grouping?
Answers
Answer:
(4x+1)(x²-2)
Step-by-step explanation:
one way to determine the factors of 4x^3 + x^2 - 8x - 2 by grouping:
x²(4x+1)-2(4x+1)
(4x+1)(x²-2)
Answer:
(x^2-2)(4x+1)
Step-by-step explanation:
4x^3 + x^2 - 8x - 2
Group:
(4x^3 + x^2)+( - 8x - 2)
Factor out as much as possible: (The GCF)
x^2(4x+1)-2(4x+1)
Regroup:
(x^2-2)(4x+1)
Which solid has a greater volume?
A. Figure A has a greater volume.
75
B. Figure B has a greater volume.
C. They are equal.
D. It cannot be determined.
SUBMIT
Answers
Answer:
C
Step-by-step explanation:
A = [tex]\pi[/tex]r^2 h/3
A= 235.62
B = [tex]\pi[/tex]r^2 h
B = 235.62
They are equal
Could these triangles be congruent?
B
E
O yes,
O yes, if AB - DE
s, if BC = 7
O yes, if AB EF
O no, because the hypotenuses must have different
lengths
A
7
С
D
7
F
Answers
Answer:
yes, if AB ≅ DE
Step-by-step explanation:
Triangles are said to be congruent if they have the same sides and the same angles.
The following measures are used to determine if triangles are congruent:
1) Angle-side-angle: If two angles and a side of a triangle is equal to two angles and corresponding side of another triangle, then they are congruent.
2) Side-side-side: If all three sides of a triangle is equal to three sides of another triangle, then the two triangles are congruent.
3) Side angle side: If two sides and an included angle of a triangle is equal to the two sides and corresponding angle of another triangle, then they are congruent.
4) Hypotenuse - leg: If the hypotenuse and one leg of a triangle is equal to the hypotenuse and leg of another triangle then they are congruent.
From the triangles DEF and ABC, already, they already have one equal triangle that is ∠F = ∠B and an equal side i.e DF = AC.
To satisfy congruence, two sides and an angle have to be equal, therefore if AB = DE then the two triangles would be congruent
Answer:
D). no, because the hypotenuses must have different lengths
Step-by-step explanation:
I just did the assignment on Edge and it's 100% correct.
Hope this helps!! Also heart and rate if you found this answer helpful!! :)
What is the slope of y= x+ 5
Answers
Answer: slope is 1
y- intercept =5
x-0,1
y- 5,6
Step-by-step explanation:
This equation is written in y = mx + b form where the m represents
the slope of the line and the b represents the y-intercept.
The equation y = x + 5 can be thought of as [tex]y = \frac{1x}{1} + 5[/tex].
So we can see that our slope is 1.
The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 2 and x = 5. (10 points) Graph of 2 to the power of x plus 1
Answers
Then, we use the following formula:
(f(b)-f(a))/(b-a),
where b and a are the largest and smallest x values respectively.
Finally, we plug our values in:
(11-5)/(5-2)=6/3=2
In fact, the average rate of change of any linear function is just the coefficient of the x term. Hope this helped!
what number must you add to complete the square? x^2-7
Answers
Answer:
12.25
Step-by-step explanation:
To find the c value in the equation, we need to divide b by two and then square it.
b= -7 and -7/2 is 3.5
Then we square 3.5 and we get 12.25
Answer:
(x+0)^2-7
Step-by-step explanation:
x^2-7 to complete the square use the formula (b/2)^2 in order to create a new term.
ax^2+bx+c in this case b=0
(x+0)^2-7
hope it works
Simplify √5x/x √ 20 answer choices
a.1/2
b.√x/2x
c.√x/2
Answers
Answer:
a
Step-by-step explanation:
Explain how you setup your excel worksheet. Make sure to address any formula used by showing an example but avoid using cell references (B5, A3, G12, etc.) What final course percentage (to 1 decimal) did you calculate? What letter grade in the course did this student earn?
Answers
Answer:
Step-by-step explanation:
to set a spreadsheet on excel, you start with the category labels on the top row, then you go down in columns. Then you enter the scores that you want for each category . after you are done with entering the scores, you found the average percent of each category by dividing the total amount of scores by the number of score in one cell . For Example, the total score was 1530 and there was 20 , you got 76.5%. you continue this for each category. Then multiplied it by the category weights. Finishing it off, I added each categories’ answers up and got my final grade of 76.5%. The letter grade this student got was a C.(google spread sheet)
A family of two adults and three children went to a water park. Admission to the water park costs $18 per person. Nora used the expression 2 (18) + 3 (18) to model the total cost for the family, and Alex used the expression 5 (18). Which property of operations makes both of their expressions correct? associative property commutative property distributive property identity property
Answers
Answer: distributive property
Step-by-step explanation:
[tex]5(18)=2(18)+3(18)[/tex]
[tex]18(2+3) = 2* 18+ 3*18[/tex]
[tex]18*5 = 2* 18+ 3*18[/tex]
Answer: Distributive Property
Step-by-step explanation: