Answer:
10x^2 + 47.2x - 84.18
Step-by-step explanation:
You distribute both terms in the first set of parentheses (5x-6.9) to the terms in the second set (2x+12.2) So when you're doing it 5x gets multiplied by 2x and 12.2 and -6.9 gets multiplied by 2x and 12.2. Then you simplify as much as possible
PLS HURRYYYYY
Think about what you know about ratios and comparisons. Fill in each box. Use
words, numbers, and pictures. Show as many ideas as you can.
two concentric circles have radii 11 and 22 two points on the outer circle are chosen independently and uniformly at random. what is the probability that the chord joining the two points intersects the inner circle?
Answer: Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?
$\textbf{(A)}\ \frac{1}{6}\qquad \textbf{(B)}\ \frac{1}{4}\qquad \textbf{(C)}\ \frac{2-\sqrt{2}}{2}\qquad \textbf{(D)}\ \frac{1}{3}\qquad \textbf{(E)}\ \frac{1}{2}\qquad$
Solution
Let the center of the two circles be $O$. Now pick an arbitrary point $A$ on the boundary of the circle with radius $2$. We want to find the range of possible places for the second point, $A'$, such that $AA'$ passes through the circle of radius $1$. To do this, first draw the tangents from $A$ to the circle of radius $1$. Let the intersection points of the tangents (when extended) with circle of radius $2$ be $B$ and $C$. Let $H$ be the foot of the altitude from $O$ to $\overline{BC}$. Then we have the following diagram.
[asy] scale(200); pair A,O,B,C,H; A = (0,1); O = (0,0); B = (-.866,-.5); C = (.866,-.5); H = (0, -.5); draw(A--C--cycle); draw(A--O--cycle); draw(O--C--cycle); draw(O--H,dashed+linewidth(.7)); draw(A--B--cycle); draw(B--C--cycle); draw(O--B--cycle); dot("$A$",A,N); dot("$O$",O,NW); dot("$B$",B,W); dot("$C$",C,E); dot("$H$",H,S); label("$2$",O--(-.7,-.385),N); label("$1$",O--H,E); draw(circle(O,.5)); draw(circle(O,1)); [/asy]
We want to find $\angle BOC$, as the range of desired points $A'$ is the set of points on minor arc $\overarc{BC}$. This is because $B$ and $C$ are part of the tangents, which "set the boundaries" for $A'$. Since $OH = 1$ and $OB = 2$ as shown in the diagram, $\triangle OHB$ is a $30-60-90$ triangle with $\angle BOH = 60^\circ$. Thus, $\angle BOC = 120^\circ$, and the probability $A'$ lies on the minor arc $\overarc{BC}$ is thus $\dfrac{120}{360} = \boxed{\textbf{(D)}\: \dfrac13}$.
See Also
Nine friends vote on their favorite fruit. Only one person in the group votes for kiwi.
Choose the decimal that is equivalent to this fraction.
0.1
The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111.
What is a fraction?It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
As per the given,
Number of people who vote on their favorite fruit = 9
Number of people who vote for kiwi = 1
The fraction of person vote kiwi to vote on their favorite fruit = 1/9
In decimal form 1/9 = 0.1111111.
Hence "The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111".
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Grace and Kian are building towers. Each one of Grace’s blocks is 8cm tall. Each one of Kian's blocks is 12 cm tall.
They both build towers that are exactly the same height. What is thensmallest height that their towers could be? Give your answer in centimetres.
The smallest height of the tower is 24 cm.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 44 + 3x + 4y = 7 is an expression.
We have,
Grace:
Blocks = 8 cm
Kian:
Blocks = 12 cm
Now,
Grace and Kian both have the same height.
This means,
The least common multiples of 8 and 12.
4 x 2 = 8
4 x 3 = 12
So,
4 x 2 x 3 = 24
Thus,
The smallest height of the tower is 24 cm.
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2 (x + 1) <\= 12
X <\= ?
Answer: x<1
Step-by-step explanation:
The average income of 5 members in a family is $36,500. The average income of a neighboring family with 2 members is $52,000. What is the average income of both families combined?
Answer:
$40928.57
Step-by-step explanation:
(5·36500 + 2·52000) / (5 + 2) = 40928.57
5. What is an equation of the line in slope-intercept form?
m=2/7 and the y-intercept is (0, -12)
Oy=2/7x+12
Oy=2/7x-12
Oy=12x-2/7
Oy=12x+2/7
Answer:
[tex]y=\dfrac{2}{7}x-12[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given:
slope = ²/₇y-intercept = (0, -12)The y-intercept is the y-value when x = 0.
Substitute the slope and y-intercept into the formula to create the equation of the line in slope-intercept form:
[tex]\implies y=\dfrac{2}{7}x-12[/tex]
If f(x) = |x|, what is the equation of the graphed function?
A. y = f(-x+3)
B. y=f(-x) +3
C. y= -f(x+3)
D. y = -f(x) +3
The equation of the graphed function is y = -f(x) +3.
What is translation?Translation is the act of moving a form or a figure from one location to another. A figure can move in translation up, down, right, left, or anyplace else in the coordinate system. Only the object's location changes during translation; its size stays the same.
In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered.
Given:
f(x) = |x|
The graph given here is reflected over x- axis.
Now, to make it up- side down the parent function should be negative.
So, g(x)= -f(x)
then, the graph is also shifted 3 units up.
Thus, g(x)= -f(x) + 3
y = -f(x) +3
Hence, the equation of the graphed function is y = -f(x) +3.
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7. What is the cost of a book that was sold for $500 and at a profit of $ 230?
The most appropriate choice for Profit and loss will be given by-
Cost price of the book is $270
What is Profit and loss?
The price at which an article is bought is known as cost price and the price at which the article is sold is known as selling price.
If the selling price of an article is more than the cost price, the difference between the selling price and the cost price gives the profit.
If the selling price of an article is less than the cost price, the difference between the cost price and the selling price gives the loss.
Here,
Selling price of book = $500
Profit = $230
In case of profit, cost price is always less than the selling price
Cost price of the book = Selling price - profit
= $(500 - 230)
= $270
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ABCDE is a circle centre O. The diameter, AC, is extended to the point F so that CF = 16 cm. The line BF is the tangent to the circle at B and FDE is a straight line such that FD = 18 cm and DE = 14 cm. The radius of the circle is r
Answer:
r = 10 cmStep-by-step explanation:
It is assumed you are looking for the missing value of r.
Use the intersecting secants theorem:
[tex]FA*FC = FE*FD[/tex]Substitute known values and solve for r:
(2r + 16)*16 = (14 + 18)*1832r + 256 = 57632r = 320r = 10Answer:
(a) FB = 24 cm
(b) r = 10
Step-by-step explanation:
Part (a)Find the length, in cm, of FB.
Intersecting Secant and Tangent Theorem
When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Given:
Tangent segment = FBSecant segment = FE = 18 + 14 = 32 cmExternal secant segment = FD = 18 cm[tex]\begin{aligned}\implies FB^2 & =FE \cdot FD\\FB^2&=32 \cdot 18\\FB^2&=576\\\sqrt{FB^2}&=\sqrt{576}\\FB&=24\end{aligned}[/tex]
Therefore, the length of FB is 24 cm.
Part (b)Find the value of r.
Triangle FBO is a right triangle with side lengths:
BO = r cmFB = 24 cmOF = (r + 16) cmPythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Therefore, substitute the side lengths of triangle FBO into Pythagoras Theorem and solve for r:
[tex]\begin{aligned}\implies BO^2+FB^2&=OF^2\\r^2+24^2&=(r+16)^2\\r^2+576&=r^2+32r+256\\576&=32r+256\\32r&=320\\r&=10\end{aligned}[/tex]
Therefore, the value of r is 10.
Please help me with this asappppp
The perimeter of the rectangle is 32 feet.
Perimeter of the rectangle:
The perimeter of a rectangle is stated that the sum of all the sides of a rectangle.
Through the definition, the perimeter of a rectangle,
P = 2 (a + b) units
where
“a” is the length of the rectangle
“b” is the width of the rectangle
Given,
Here we have the diagram of the rectangle and the measurements are given in it.
And we need to find the perimeter of the rectangle.
Through the given diagram, we know that, the values of
length = 12 feet
width = 4 feet
Now, we have to apply the values on the formula in order to solve it,
So, the perimeter is,
P = 2 ( 12 + 4)
When we simplify it then we get,
P = 2 (16)
After the multiplication we get the result as
P = 32 feet.
Therefore, the perimeter of the rectangle is 32 feet.
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daisy has one cucumber that is 3 inches long and another cucumber that is 5 inches long she cuts the cucumbers into (3)/(8)-slices and adds them to a salad how many (3)/(8)-inches thick slices does daisy have
Answer:
21 slices of 3/8 inch
Step-by-step explanation:
Daisy would have 21.This is because 3 times 8 divided by 3 is 8.And 5 times 8 divided by 3 is 13 (you have to ignore the remainder) 8 plus 13 is 21
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough. ft3/min
Given:
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
The volume of the trough will be as follows:
[tex]undefined[/tex]PLS HELP ME... just confused on this question about what I need to do
Find the measure of angle b
Juan paid 13.46 for a 3.47-pound bag of shrimp at one store. the following week, he paid 18.75 for a 5.15-pound bag at another store. find the unit price for each bag is the better buy based on the unit price. round the answers to the nearest cent.
The unit price for a 5.15 pound bag is the better buy for Juan
Juan paid $13.36 for a 3.47 pound bag of shrimp:
So, cost of one pound bag of shrimp= [tex]\frac{1*13.46}{3.47}[/tex]
=$3.88
Hence, unit price for the 3.47 pound bag=$3.88
Following week, Juan paid $18.75 for a 5.15 pound bag at another store:
So, cost of one pound bag of another store= [tex]\frac{1*18.75}{5.15}[/tex]
=$3.64
Hence, unit price for the 5.15 pound bag at another store=$3.64
It is clear from the above result that second buy (5.15-pound bag at another store) is the better buy for Juan because it cost less per pound.
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On a map, Elmwood Drive passes through R(4,-11) and S(0,-9) and Taylor Road passes through
J(6,-2) and K(4,-5). If the streets are straight lines, determine if the streets are parallel or
perpendicular.
The streets where Elmwood and Taylor drive are neither perpendicular nor parallel.
Elmwood Drive passes through R(4,-11) and S(0,-9)
Slope of this line is (y₁-y₂)/(x₁-x₂)
Here (x₁,y₁) is (4,-11) and (x₂,y₂) is (0,-9)
slope of this line is (-11 - (-9))/(4-0)
= (-11 + 9)/4
= -2/4 = -1/2
Taylor Road passes through J(6,-2) and K(4,-5)
Slope of this line is (y₁-y₂)/(x₁-x₂
Here (x₁,y₁) is (6,-2) and (x₂,y₂) is (4, -5)
slope of this line is (-2 - (-5))/(6 - 4)
= (5 - 2)/2
= 3/2
The slopes of both the line is not same, so they are not parallel.
The product of slopes of both the lines is equal to 1, then it can be said as perpendicular lines.
The product of slope of streets passed by Elmwood and Taylor is
- 1/2 x 3/2 = -3/4
The result is not equal to 1, so they are not perpendicular lines.
Therefore, the streets where Elmwood and Taylor drive are neither perpendicular nor parallel.
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Simplify the expression √9x^3/25y^2 and be sure to explain your steps!
The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the value of the expression?The expression is given as
√9x^3/25y^2
Evaluate the square root of 9 in the expression
So, we have the following equation
√9x^3/25y^2 = 3x^3/25y^2
The above expression cannot be further simplified
Hence, the solution to the expression is 3x^3/25y^2
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PLEASE HELP! What is one over seven raised to the third power equal to?
one over ten
three over twenty-one
one over three hundred forty-three
three over two thousand four hundred one
Answer: 1/343
Step-by-step explanation:
Let and .
Which transformations are needed to transform the graph of f(x) to the graph of g(x)?
Select EACH correct answer.
Question 3 options:
Horizontal translation 1 units right.
Vertical translation 1 unit down.
Horizontal translation 3 units right.
Horizontal translation 1 unit left.
Vertical translation 3 units up.
Vertical translation 3 units down.
The transformations that are needed to transform the graph of f(x) to the graph of g(x) include the following:
Horizontal translation 1 unit left.Vertical translation 3 units down.What is a translation?In Mathematics, the translation of a geometric figure to the right simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image and translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
Given the following function:
Function, f(x) = 4^x
Next, we would translate f(x) 1 unit left based on this horizontal translation rule:
f'(x) = f(x + 1)
f'(x) = 4^{x + 1}
Now, we would apply a vertical translation 3 units down based on this horizontal translation rule:
f''(x) = f'(x) - 3
f''(x) = 4^{x + 1} - 3
Therefore, function g(x) = 4^{x + 1} - 3
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The table shows the cost for ordering a certain number of pieces of chicken. What is the value of x if the cost is proportional to the number of chicken pieces ordered?
Answer:
$9.00
Step-by-step explanation:
if 2 pieces of chicken ordered --> $3.00
6 pieces of chicken ordered --> x
(cross multiplication)
[tex]x= \frac{6*3}{2}[/tex]
so x = 9
then, 6 pieces of chicken ordered is $9.00
6. Given the area of the rectangle is 52 ft², find
the value of x.
(4x - 2) ft
2 ft
Answer:x=7
Step-by-step explanation: 2(4x-2)=52
8x-4=52
8x=56
x=7
the coefficient of x³ in the expansion (2x-1)³
Answer: 8
Step-by-step explanation:
Since the expression is raised to the 3rd power, the highest exponent x will have will be 3. So in order to get the coefficient you multiply 2x by itself 3 times, getting (2x)³ = (2 * 2 * 2)(x * x * x) = (8)(x³) = 8x³
[tex]\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (2x-1)^{3}~\hspace{4em} \begin{array}{cccl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(2x)^{3 }(-1)^0\\ 2&+3&(2x)^{2}(-1)^1\\ 3&+3&(2x)^{1}(-1)^2\\ 4&+1&(2x)^{0}(-1)^3 \end{array} \\\\\\ 1(8x^3)+3(-4x^2)+3(2x)+1(-1)\implies \text{\LARGE 8}x^3-12x^2+6x-1[/tex]
Alyssa buys 3 bottles of orange juice at the corner store for a total cost of $3.54. If
each bottle costs the same amount, how much is 19 bottles of juice?
ASAP help with 8th grade math, 50 points
Answer:
The height is 7 units the length is 12 units.
Step-by-step explanation:
It's 6 and 6 for the graph one.
Casho went shopping for a new pair of sneakers because of a sale. The price on the tag was $25, but Casho paid $22.50 before tax. Find the percent discount
The percentage discount for the pair of sneakers is 10%.
What is percentage?A percentage is a value per hundredth. Percentages can also be fractions and decimals by decimals by dividing by 100 and vice versa. To obtain a percentage of a given value we divide the given percentage by a hundred and multiply the value with it.
The percentage discount can be determined by putting the discounted value upon the price multiplied by a hundred and subtracting the obtained percentage from the hundred percentage.
∴ The percentage discount on the pair of sneakers is,
= (22.50/25)×100.
= 0.9×100.
= 90%.
So, the percentage discount is (100 - 90)% = 10%.
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yo ___ 14 anos (expressing age
Answer:
tengo
Step-by-step explanation:
i am hispanic
Solve this equation for x in terms of the other pronumerals.
x/a - x/2a = b
Answer:
x=2a*b
Step-by-step explanation:
(2x-x)/2a=b
x=2a*b
At lunch time a restaurant sold 6 times as many salads as they sold cups of soup . If they sold two cups of soup how many salads did they sell
Stephanie is helping her band collect money to fund a field trip the band decided to sell chocolate bars each bar sells for $1.50 and each box contains 20 bars below is a partial table of monies collected for the different number of boxes sold
O P=20($1.50)
If they sell 100 boxes of chocolates, they will make $3,000 in profit.
Given that each chocolate bar costs $1.50 and that there are 20 chocolate bars in a box, multiplication is required to get the profit for the entire box. Using this information, we discover that each chocolate box costs $30, multiplied by 100 boxes to equal $3000.
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