Answer:
50(5-3x)
Step-by-step explanation:
250=2*5^3
150=2*3*5^2
GCF=2*5^2=50
250/50=5
150/50=3
50(5-3x)
Find the area of the shaded portion.
6
120
Answer:
A = 36√3 - 12π
Step-by-step explanation:
Make 2 identical 30-60-90 triangles out of the "wedge"
For each 30-60-90 triangle:
Since the short leg is 6 the long leg is 6√3
short leg is the base and long leg is the height
a = (1/2)bh
a = (1/2)(6)(6√3)
a = 3(6√3)
a = 18√3
Since there are 2 triangles
a = 36√3
--------------------------------
Then subtract off the area of the 120º sector
a = (120/360)πr^2
a = (1/3)π(6^2)
a = (1/3)π(36)
a = 12π
Shaded area
a = 36√3 - 12π
Step-by-step explanation:
we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).
since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.
basically, the area of a triangle is
1/2 × b×c × sin(A)
A being the angle between the 2 sides b and c. for any 2 sides of the triangle.
one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.
we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.
remember, the sum of all angles in a triangle is 180 degrees.
so, via the law of sines we can then calculate all sides :
a/sin(A) = b/sin(B) = c/sin(C)
with the angles being opposite of the sides.
6/sin(30) = baseline/sin(90)
6/0.5 = baseline/1
12 = baseline
top side² + 6² = 12²
top side² = 12² - 6² = 144 - 36 = 108
top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)
we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.
the area of the 2 triangles is then
6×sqrt(3)×6×sin(90) = 36×sqrt(3)
and the circle segment to be deducted is
pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12
so, the complete answer is
A = 36×sqrt(3) - 12×pi
Write an equation of a line
that passes through the
points
(-6,0) and (0,-24).
Answer:
y= -4x-24
Step-by-step explanation:
change in y/change in x = 0- -24/-6-0 = 24/-6 = -4
gradient is -4
then you put a set of coradinates into the formular y-y=m(x-x)
y - 0= -4 (x+6)
y-0=-4x-24
y=-4x-24
Answer:
4x +y = -24
Step-by-step explanation:
The given points are the x- and y-intercepts. It is convenient to write the equation in intercept form:
x/a +y/b = 1 . . . . . . x-intercept 'a', y-intercept 'b'
x/-6 +y/-24 = 1 . . . . . equation in intercept form
4x +y = -24 . . . . . . . equation in standard form (multiply by -24)
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than −1.66.
Using the normal distribution, there is a 0.9515 = 95.15% probability of a bone density test score greater than −1.66.
The graph is given by option B.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean of the distribution. From the z-score table, the p-value associated with the z-score is found, representing the percentile of the measure X.In the context of this problem, the mean and the standard deviation of the scores are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
The probability of a bone density test score greater than −1.66 is one subtracted by the p-value of Z when X = -1.66, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (-1.66 - 0)/1
Z = -1.66
Z = -1.66 has a p-value of 0.0485.
1 - 0.0485 = 0.9515, which is the probability.
The graph of the probability is given at the end of the answer, and in the context of this problem, is given by option B.
More can be learned about the normal distribution at https://brainly.com/question/4079902
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Find the value of f(-3)f(−3).
Write the exponential function for the values in the table below.
Answer:
f(x) = [tex]8^{x}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{512} = 8\\\sqrt[4]{4096} = 8\\\sqrt[5]{32768} = 8[/tex]
which means 8 to the power of 3 will give you 512, to the fourth power will give you 4096.
So the exponential function is f(x) = [tex]8^{x}[/tex]
Simplify the expression
8h+(−7.3d)−14+5d−3.7h.
group of 3 people is going on a boat tour. If each boat holds 3 people, how many will boats will the group need?
Answer:
1
Step-by-step explanation:
there are 3 people and 1 boat holds three people
does anyone know how to view what answers you got correct on a post test for plato/ edmentum? please give detailed instructions
Answer:
Step-by-step explanation:
For Plato just press the + button to add an introduction or whatever.
Write 1.42 as a mixed number in simplest form.
1.42=
The decimal is repeating
Answer:
71/50
Step-by-step explanation:
a football team won 80% of the 150 games in a season. Wright the percent proportion that will help you solve the problem in that point
A jar contains n nickels and d dimes. There are 20 coins in the jar, and the total value of the coins is $1.50. How many nickels and how many dimes are in the jar?
The jar contains ___nickels and ___ dimes.
10 nickels = $0.50
10 dimes = $1.00
So- 10 nickels + 10 dimes = $1.50
50 POINTS
Consider this equation: 2/3x - 9 - 2x+2=1
Which is an equivalent equation after combining like terms?
O 8/3x - 11 = 1
O -4/3x - 7 = 1
O 8/3x - 7 = 1
O -4/3x - 11 = 1
Answer:
-4/3x-7=1
Step-by-step explanation:
just combine like terms
Solve each inequality
-5y-2<8
Answer:
y > -2
Step-by-step explanation:
-5y-2<8
= -5y<8+2
= -5y<10
= y > 10/-5
∴ y > -2
Note: Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.
A youth group went on trip to EXPO Dubai Travelling in two Vans. The number of people in each van and the total cost of admission are shown in the table. Find the adult price and student price of admission
Answer:
Refer to the attachment
Soo :
2a + 3b = 325
2a + 7b = 505 -
-4b = -180
4b = 180
b = 45
[tex] \: [/tex]
2a + 3b = 325
2a + 3(45) = 325
2a + 135 = 325
2a = 325 - 135
2a = 190
a = 95
Which of the following is not a subset of {1, 2, 3}?
{0}
{1, 2, 3}
Ø
Answer:
{0}
Step-by-step explanation:
{0} is not because 0 is not an element of set {1, 2, 3}
The null set is a subset of every set, so Ø is.
A set is a subset of itself.
(04.04)
Which graph represents a linear function? (4 points)
Group of answer choices
A coordinate plane is shown with a line passing through the x-axis at negative 2 and the y-axis at negative 6.
A coordinate plane is shown with a curved line that starts in the bottom left area of the graph, passing through the point -1 comma -5, curving to pass through the y-axis at 2.5, then curving up again to pass through the point 1 comma 5
A coordinate plane is shown with a parabola graphed in an upward U shape. The bottom of the parabola touches the y-axis at -10 and curves upward on both sides
A coordinate plane is shown with a wavy line that sits on the x-axis and moves across the graph in even up and down waves.
A linear function is one of the most simplest form of functions. As the name "linear" indicates, a linear function is simply a line, more precisely a straight line.
So it is in the form of f(x) = ax + b.
Lets now check the possible answers : (second answer :) "a curved line", not correct.
(third answer:) "a parabola", this is not a straight line, so not correct.
(fourth answer:) "a wavy line", not a straight line, so not correct.
The only correct answer is the first one : a line passing through the x axis at negative 2 and the y axis at negative 6.
Pls help me solve this
Answer:
F. Yes, by the SAS Congruence Theorem
Explanation:
In △ABC and △EDC:
BC = CD (given)AC = CE (given)∠ACB = ∠ECD (vertically opposite angles)Hence, by the SAS Congruence Theorem, which states two triangles, with two sides and one angle equal, as congruent.
△ABC ≅ △EDC
The price of Stock A at 9 AM was $12.73. Since then, the price has been increasing at the rate of $0.06 per hour. At noon, the price of Stock B was 13.48. It begins to decrease at the rate of $0.14 per hour. If the stocks continue to increase and decrease at the same rates, in how many hours will the prices of the stocks be the same?
Answer:
Let the hours when they equalize=h, then we have:
12.25 + .13h=13 - .09h
.13h + .09h=13 - 12.25
.22h=.75 divide both sides by .22
h=.75/.22
h=3 9/22, hours, when they will equalize.
The stock prices will be the same in 3.4 hours.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
At 9 a.m., the price of Stock A was $12.73. Since then, the price has risen at a pace of $0.06 per hour. Stock B was trading at 13.48 at midday. It starts to fall at a pace of $0.14 each hour.
Let's assume the hours would be h when to equalize,
As per the given question, we can write the equation as:
12.25 + 0.13h = 13 - 0.09h
Rearrange the terms of h in the above equation,
0.13h + 0.09h = 13 - 12.25
Combine the likewise terms in the above equation,
0.22h = 0.75
Divide both sides by 0.22
h = 0.75/0.22
h = 3.4
Thus, the stock prices will be the same in 3.4 hours.
Learn more about the equation here:
brainly.com/question/13947055
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Do you know what the variables could be
Answer:
5, 7, and 12
Step-by-step explanation:
First we can make and equation
x + z + y = 24
we can plug in the numbers you gave us giving us
y = x + z
z = y - x
x = (y - 2) ÷ 2
Once, were done we get that x = 5 ≈ smallest number
z = 7 ≈ second largest number
y = 12 ≈ largest number
What are the roots of the equation?
X^2(6x - 11) (7x– 8) = 0
Answer:
0, 11/6 , 8/7
Step-by-step explanation:
Answer:
[tex]0, \frac{11}6, \frac87[/tex]
Step-by-step explanation:
Good thing it's already written as a product, which spares us the most complicated (and boring) part.
We know that a product is zero if it's 0 any of the factors.
From the first one [tex]x^2=0 \rightarrow x=0[/tex]
from the second factor [tex]6x-11=0 \rightarrow x=\frac{11}6[/tex]
and finally, for the third one, [tex]7x-8 =0 \rightarrow x = \frac87[/tex]
[tex]at a school of 1050 pupils exactly 4% are absent on a particular day.how many are present.[/tex]
at a school of 1050 pupils exactly 4% are absent on a particular day.how many are present.
What is 4 percent of $128.72 ?
Answer:
124.72
Step-by-step explanation:
Answer:
Step-by-step explanation:
4% of 128.72 = 0.04 * 128.72
= 5.1488
Use angle relationships to complete the top equation. Then, solve for x and find the measure of both angles.
9514 1404 393
Answer:
7x +40x = 204x +30 = 110°3x +10 = 70°Step-by-step explanation:
The marked angles are supplementary, so you have ...
(4x +30) +(3x +10) = 180
7x +40 = 180
__
Subtracting 40 gives ...
7x = 140
x = 140/7 . . . . . divide by the coefficient of x
x = 20
__
Then the angle measures are ...
4x +30 = 4·20 +30 = 110°
3x +10 = 3·20 +10 = 70°
During vacation, Dave and his brother, Scott,rode their bikes form their family's rental house to a pond to go fishing. Although they left the rental house together, Dave arrived at the pond a few minutes before Scott. This weekend, they plan to ride a nearby mountain trial and turn back after an hour if they can't complete it. Who will likely ride farther along the mountain trial?
Answer:
Im soooooo hungry ughhh
Step-by-step explanation:
Hi
Solve this equation, show all your work:
6(x+1)=-2(3x+9)
Answer:
x=-2
Step-by-step explanation:
6(x+1)=-2(3x+9)
Distribute the 6.
6x+6=-2(3x+9)
Distribute the -2.
6x+6=-6x-18
Move the variable to the left-hand side and change the sign.
6x+6+6x=-18
Collect like terms
12x=-18-6
Calculate the difference.
12x=-24
Divide both sides by 12.
x=-2
Hope this helps :)
Five players are given $10 each and asked to contribute any portion of it to a group account. They are also told that the total collection will be doubled and distributed equally among each of them. In this case, the players are likely to contribute __________.
Answer:
nothing
Step-by-step explanation:
Slope - Part 1
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest
form in the box
Please hurry!!
Answer:
-1
Step-by-step explanation:
We can use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
Using the points on the line (-2,0) and (0,-2)
m = ( -2-0)/(0- -2)
= (-2-0)/(0+2)
-2/2
-1
A ski resort is building two parallel straight ski slopes for children. One of them has a gradient of 1/3. The other ski slope will pass through points (2,-3) and (s,-5). Find the value of s
Answer: s= -8
Step-by-step explanation:
The gradient of the ski slope can ge used as the slope (literally) of a line equation:
y = mx + b,
where m is the slope and b the y-intercept (the value of y when x = 0).
The first slope would be y = -(1/3)x + b.
The slope is (-1/3) since the ski run is headed downhill. The second ski slope is assumed to have the same gradient ("two parallel straight ski slopes").
y' = -(1/3)x' + b
We may assume that b is the same for both slopes - they start and end at the same point.
We can find b by using the given point (2,-3):
y' = -(1/3)x' + b
-3 = -(1/3)(2) + b
-3 = -(2/3) + b [Add -(2/3) to both sides: (-3 + 2/3 = -9/3 + 2/3 = -7/3]
-7/3 = b
b = -(7/3)
The second ski slope, y', thus has the equation
y' = (1/3)x' -(7/3)
We want the value of s in (s, -5).
y' = (1/3)x' -(7/3)
-5 = (1/3)s -(7/3)
(1/3)s = -5 +(7/3) [-15/3 + 7/3 = -8/3]
(1/3)s = -(8/3) [Multiply both dies by 3]
s = -(24/3)
s = -8
school x and school y play each other in a competition
school x has eight more than school y
school x has three times as many points as school y.
how many points does each school have ?
Answer:
x=12 y=4
Step-by-step explanation:
x=y+8
x=3y
x=y+8 times 3
3x=3y+24
x=3y
3x=3y+24 - x=3y
2x=24
x=24
24-8=4
4 times 3 =12
the perimeter of a rectangle is 20cm. if the breadth of the rectangle is 2cm what is it's area
Answer:
perimeter =20cmbreadth=2cmlength=?we know that
perimeter =2*(l+b)
20=2*(l+2)
20=2l+4
2l=20-4
2l=16
l=16/2
l=8