Answer:
The number of pencils that needs to be placed at the other 1 inch end to get a balance again is approximately 3 pencils
Step-by-step explanation:
The given parameters are;
The length of the ruler used as a seesaw = 12 inch
The location where the pencil is placed = Under the 4 inch mark
The location where the weight is placed to balance the seesaw = The 2 inch mark
Therefore, the pencil at the 4 inch mark is fulcrum
The location where a pencil is placed on the ruler = The 12 inch end
The number of pencils, x, that needs to be placed at the other 1 inch end to get a balance again is given as follows;
The distance of the pencil at the 12 inch end from the fulcrum = 12 inches - 4 inches = 8 inches
The distance of the pencils placed at the 1 inch end from the fulcrum = 4 inches - 1 inch = 3 inches
Therefore at balance point, (equilibrium) the anticlockwise moment = The clockwise moment, which gives;
The mass of 1 pencil × 8 inches = x × The mass of 1 pencil × 3 inches
x = (The mass of 1 pencil × 8 inches)/(3 inches × The mass of x × 1 pencil)
x = 8/3 = 2.[tex]\overline 6[/tex] ≈ 3 pencils
The number of pencils that needs to be placed at the other 1 inch end to get a balance again = x ≈ 3 pencils.
please help and show work
Answer:
see explanation
Step-by-step explanation:
(3)
The opposite sides of a parallelogram are congruent, so
6x = 3x + 15 ( subtract 3x from both sides )
3x = 15 ( divide both sides by 3 )
x = 5
and
2y - 10 = y + 5 ( subtract 5 from both sides )
y - 10 = 5 ( add 10 to both sides )
y = 15
Then x = 5 and y = 15
-------------------------------------------------------------------------
(4)
The diagonals of a parallelogram bisect each other, thus
y = 4x - 6 → (1)
9x - 25 = 2y → (2)
Substitute y = 4x - 6 into (2)
9x - 25 = 2(4x - 6)
9x - 25 = 8x - 12 ( subtract 8x from both sides )
x - 25 = - 12 ( add 25 to both sides )
x = 13
Substitute x = 13 into (1)
y = 4(13) - 6 = 52 - 6 = 46
Then x = 13 and y = 46
Solve the triangle.
B = 36°, a = 41, c = 20
choices:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
b ≈ 45.3, C ≈ 25.5, A ≈ 118.5
b ≈ 45.3, C ≈ 29.5, A ≈ 114.5
b ≈ 27.5, C ≈ 25.5, A ≈ 118.5
The triangle solve for B = 36°, a = 41, c = 20 is:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
TriangleTo solve the triangle, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and angles A, B, and C opposite those sides,
c² = a² + b² - 2ab cos(C)
We can use this formula to find the length of the missing side b:
b² = a² + c² - 2ac cos(B)
b² = 41² + 20² - 2(41)(20) cos(36°)
b² ≈ 1074.12
b ≈ 32.8
Now that we have found the length of side b, we can use the Law of Sines to find the measures of angles A and C:
sin(A) / a = sin(B) / b
sin(A) / 41 = sin(36°) / 32.8
sin(A) ≈ 0.274
A ≈ 16.5°
We know that the angles in a triangle add up to 180°, so C = 180° - A - B ≈ 127.5°.
The closest choice to these values is:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
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please help and show work if you can
Answer:
25. a = 60
26. a = 17
Step-by-step explanation:
In these two problems we are going to use a property of parallelograms that says: opposite angles have equal measure
so we have
25.
[tex]6a+10=130\\\\6a=130-10\\\\6a=120\\\\a=60[/tex]
and for 26 we have
[tex]4a-4=2a+30\\\\4a=2a+30+4\\\\4a=2a+34\\\\4a-2a=34\\\\2a=34\\\\a=17[/tex]
solve for x enter the number that belongs in the green box
(you will have to right-click on the image and open it in a new tab to be able to see it)
Answer:
fwufuhwwhfwfweofwefwef
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(6x+20)
105
(7-10)
Answer:
x=5
Step-by-step explanation:
Angles in a triangle adds up to 180 degrees
so 105 + (6x+20) + (7x-10) = 180
simplify
115+13x=180
subtract 115 to each side
13x=65
divide by 13
x=5
check work
105 + (6(5) + 20) + (7(5) -10)
105 + (30 +20) +(35 - 10)
105 + 50 + 25 = 180
What is the quotient? ?
-22
O
O
11
11
50
O
22.
Answer:
Didn't get it!
write correctly please!
Beth has had her car for a while and knows that it gets pretty good gas mileage On a recent business trip she used 16.25 gallons of gas and drove 471 miles. To the nearest tenth of a mile, what was her gas mileage? OA) 29 0 mpg OB) 30 0 mpg OC) 28.5 mpg OD) 270 mpg
Answer:
A) 29.0 mpg
you divide 471 by 16.25
Mikah is proving the base angles of this triangle are congruent.
In isosceles triangle QRS, RT is the angle bisector of ∠QRS. Mikah begins the proof by stating ∠1≅∠2. What is a valid reason for this statement?
A. Definition of Angle Bisector
B. Reflexive Property of Congruence
C. Symmetric Property of Congruence
D. Corresponding angles are congruent.
Answer:
its B
Step-by-step explanation:
can someone 10points!!!!
Answer:
it would be 19/15k
Step-by-step explanation:
Answer:
Hi! I think it's 15/8t and 19/15k
What is (4-4) k I need help
Answer:
zero
Step-by-step explanation:
Find the slope of the line that passes through the points (-2, 6) and (9, -5).
Answer:
slope = -1
Step-by-step explanation:
Use the slope formula [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] to find the slope. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point, and the [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point. So, we'll use the points given in the question, (-2,6) and (9, -5). Substitute -2 for [tex]x_1[/tex], 6 for [tex]y_1[/tex], 9 for [tex]x_2[/tex], and -5 for [tex]y_2[/tex]. Then, solve:
[tex]\frac{(-5)-(6)}{(9)-(-2)} \\= \frac{-5-6}{9+2} \\= \frac{-11}{11} \\= -1\\[/tex]
Therefore, the slope is -1.
The slope of the line that passes through the points (-2, 6) and (9, -5) is -1.
A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
Given the coordinates of the two points on the graph is (-2, 6) and (9, -5). Therefore, the slope of the line that passes through this point is,
Slope = [6 - (-5)] / [-2 - 9]
Slope = (11) / (-11)
Slope = -1
Hence, the slope of the line will be -1.
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Help please & thanks!
Answer:
D
Step-by-step explanation:
Just add all the number together.
1.12 unit test
Enter an inequality that represents the graph in the box.
Answer:
45
Step-by-step explanation:
it is blah blah this is the best you multiply by 5 add 40 subtract 5 and add 5 again
What number is 40% of 160?
Try to explain
Answer: 64
Step-by-step explanation:
40% of 160
40/100 x 160
6400/100
64
Did I explain this well?
Answer: 64
Step-by-step explanation: So you would start off with the ratio of 40:100 other known as in fraction form 40/100 and you know of means to multiply so you grab the numbers 160 and 40 and mulitiply those digits together and you get 6400. This is where the 100 comes to place and you divide the 6400 by 100 and you get 64.
triangle ABC has perimeter 22cm
AB= 8cm
BC= 5cm
by calculation deduce whether triangle ABC is right-angled triangle
9514 1404 393
Answer:
not a right triangle
Step-by-step explanation:
The perimeter is 22, so we have ...
AB +BC +CA = 22
8 + 5 + CA = 22
CA = 22 -13 = 9
If this is a right triangle, the sum of the squares of the short sides will be equal to the square of the long side.
AB² +BC² = 8² +5² = 64 +25 = 89
This is not the same as ...
CA² = 9² = 81
The triangle is not a right triangle.
_____
Additional comment
If you're familiar with a few Pythagorean triples, you know that a couple involving a side length 5 are (3, 4, 5) and (5, 12, 13). That is, (5, 8, 9) is NOT a Pythagorean triple, so you know immediately that those side lengths do not form a right triangle. (No calculation is necessary.)
Do it please..............h
Answer:
False
Step-by-step explanation:
-x^2+x is the same as x-x^2.
Only difference is the way it's written.
After swimming 55 feet below the surface of the water, a
fish swims up 30 feet. Use a number line to help you create
an equation that shows the new location of the fish in
relation to the water's surface.
-80 -70 -60 -50 40 -30 -20 -10 0
10
Interpret the sum in the context of the problem.
Answer:
c.
Step-by-step explanation:
when the fish swam down 55, you moved 55 to the left of zero. then when he swam 30 up, you take that 55 and move it 30 towards to the right. since -55 is greater than 30, your answer is still negative. -55+30=-25.
Answer:
C
Step-by-step explanation:
please help!
"a line intercepts the point (3, -4) and has a slope of 17. what is the slope-intercept equation for this line?"
then it has the partially filled out equation:
y=17x+__
Answer:
-55 = b
Step-by-step explanation:
If you fill in the x and the y with the equation you have below, you would get:
-4 = 17(3)+b
Multiply 17 and 3
-4 = 51 + b
-55 = b
Answer:
y=17x-55
Step-by-step explanation:
4 = 17(3)+b
-4 = 51 + b Subtract 51 both sides
-55 = b
Hope this helps :)
My friend needs help plz answer
Answer:
Order the data from least to greatest.
Find the median.
Calculate the median of both the lower and upper half of the data.
Ask me if you need more help!
Step-by-step explanation:
Answer:
31.5
Step-by-step explanation:
plot the x- intercept and y- intercept. then write the intercepts as ordered pairs
Answer:
x-intercept = 4
y-intercept = -1
As ordered pairs they would be ( 4, 0) and ( 0, -1)
Step-by-step explanation:
The line goes through 4 on the x line and goes through -1 on the y line.
As an ordered pair you just put the numbers in their x and y spots being ( x, y )
With 4 being on the X and -1 being on the Y it would make them ( 4, 0) and
( 0, -1).
Find the distance between a and b
i need help please answer for me ... Logan drove from New Orleans to Nashville to visit friends. Logan drove the speed limit which was 60 miles/hour. If Logan's driving time for the trip was 9 hours, how many miles did Logan drive?
Which statement is not true?
Answer:
C
Step-by-step explanation:
There can be multiple solutions when two lines intersect.
PLEASE HELP ME dhdjdbjfjf
Answer:
Option A
Step-by-step explanation:
Since X,Y and Z are on the same line, The gradient is the same so far as the point chosen are on the same line.
Faye borrowed $9600 at 8% per anum compound interest.
(a) Calculate the interest on the loan for the first year.
At the end of the last year,she repaid $4368.
(b) How much did she still owe at the beginning of the year?
(c)Calculate the interest on the remaining balance for the second year.
Answer:
(a) $768
Step-by-step explanation:
Faye borrowed $9600 at 8% interest compounded per annum.
Solution for question (a):
Amount accumulated is given by;
A = P(1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]
Where A is the amount, P is the pricipal, r is the rate, n is the number of times in a year, and t is the number of years.
So the amount after one year was;
A = 9600(1 + [tex]\frac{8}{1 * 100}[/tex][tex])^{1 * 1}[/tex] = 9600 × 1.08 = 10368
Interest = Amount - Principal = $10368 - $9600 = $768
a. The interest on the loan for the first year is $768.
b. The amount she still owe at the beginning of the year is $6,000.
c. The interest on the remaining balance for the second year is $480.
a. Interest on loan:
Interest on loan=$9600 × 8%
Interest on loan=$768
b. Amount owed
Amount owed=$9,600+$768-$4368
Amount owed=$6,000
c. Interest on remaining balance :
Interest on remaining balance=$6,000×8%
Interest on remaining balance=$480
Inconclusion the interest is $768, amount owe is $6,000 and Interest on remaining balance is $480.
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For each situation, write an expression answering the question. The expression should only
use multiplication,
a. A person's salary is $2,500 per month. She receives a 10% raise. What is her new salary,
in dollars per month?
b. A test had 40 questions. A student answered 85% of the questions correctly. How many
questions did the student answer correctly?
C. A telephone cost $250. The sales tax is 7.5%. What was the cost of the telephone
including sales tax?
Answer:
The expressions for each statement are as follows:
a: 2500+(0.10*2500)
b: 40 * 0.85
c: 250 + (0.075*250)
Step-by-step explanation:
Part a:
Given
Salary = $2500
Percentage of raise = 10%
The new salary will be:
[tex]= 2500+ (10\%\ of\ 2500)\\=2500 + (0.10*2500)\\=2500+250\\=\$ 2750[/tex]
Part b:
Given
Total questions = 40
Percentage of correct answers = 85%
The required expression for correct answers is:
[tex]= 85\%\ of\ 40\\= 0.85*40\\=34[/tex]
Part c:
Given
Price of phone = $250
Percentage of sales tax = 7.5%
The required expression is:
[tex]Cost\ with\ sales\ tax = 250 + (7.5\%\ of\ 250) \\= 250 + (0.075*250)\\=250+18.75\\=268.75[/tex]
Hence,
The expressions for each statement are as follows:
a: 2500+(0.10*2500)
b: 40 * 0.85
c: 250 + (0.075*250)
Select the correct answer.
The function fx) = 2x + 3x + 5, when evaluated, gives a value of 19. What is the function's input value?
OA 1
OB-1
О с 2
OD. -2
OE-3
The input value that gives an output of 19 is not listed in the answer choices. None of the options are correct.
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
We can start by setting up the equation:
2x² + 3x + 5 = 19
Subtracting 19 from both sides:
2x² + 3x - 14 = 0
(2x - 7)(x + 2) = 0
Using the zero product property, we can solve for x:
2x - 7 = 0 or x + 2 = 0
2x = 7 or x = -2
x = 7/2 or x = -2
Therefore, the input value could be either 7/2 or -2.
The answer choices do not include 7/2, but we can check both input values to see which one gives an output of 19:
f(7/2) = 2(7/2)^²+ 3(7/2) + 5 = 19.25
f(-2) = 2(-2)² + 3(-2) + 5 = 3
Thus, the input value that gives an output of 19 is not listed in the answer choices.
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the diameter of each circular hole in a paint palette is 42 milliliters m Use 3.14 as an approximation
Answer:
Hmm your answer would be (19)
Step-by-step explanation
Im not 100% sure but good luck
complete the addition equation that represents the associative property
Which expressions are in their simplest form? Check all that apply.
Answer:
The first one is the only one in simplest form.
Answer: this is answerrrr
A C Dpeace