Answer:
AC = 18.Step-by-step explanation:
The problem is about proportions, because we have two parallels line being intercepted by two transversal. So, the proportion would be:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}[/tex]
Solving for [tex]x[/tex]:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}\\(x+1)(x+8)=x(x+13)\\x^{2} +8x+x+8=x^{2} +13x\\9x+8=13x\\8=13x-9x\\4x=8\\x=\frac{8}{4}=2[/tex]
Now, to find the length of AC, we just have to use the value found and replace it in the proper expression:
[tex]AC=x+13+x+1=2x+14=2(2)+14=4+14=18[/tex]
Therefore, the length of AC is 18.
how are the integers and rational numbers different? ...?
Is the ordered pair a solution to the system of linear equations?
Select Yes or No.
Ordered pair: (−2,2)(−2,2)
System of equations:
−7x+2y=0
6x+6y=0
Eric bought 300 t-shirts, which were sold in packs of 12. How many packs did Eric buy?
A) 20
B) 25
C) 28
D) 30
Answer is B, 25, because 300 Divided 12 is 25 & 25x12=300.
One more and I should be good, i'm pretty familar with this but i'd like to make sure,
Two brothers, Bill and Eric, are 4 years apart, and Bill is the older of the two. If the sum of the boys' ages is 28, how old is bill and how old is eric?
Both boys age is unknown, yet we can mark both with say,
x = Eric's age
y = Bills' age
There are many ways to solve this, but we DO know they're 4 years apart, so it'd have to be
x + y4 = ?,
actually that's off but you understand what i'm saying... Thanks!
Using the properties of equality to solve the equation -2b + 7 = -13, you would _____.
add 13 and then divide by -2
add 13 and then add 2
subtract 7 and then add 2
subtract 7 and then divide by -2
To solve the equation, firstly subtract 7 from both sides, converting the equation into -2b = -20. Then divide both sides by -2 to find the value of b, which is 10.
Explanation:To use the properties of equality to solve the given equation, -2b + 7 = -13, follow these steps:
First, isolate the term containing the variable b on one side of the equation. This is done by subtracting 7 from both sides of the equation. The equation becomes -2b = -20.Next, to find the value of the variable b, divide both sides of the equation by -2. So, the final equation becomes b = 10.Learn more about Properties of Equality here:https://brainly.com/question/10617252
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Kayla has a bowl of beads that contains 42 yellow beads, 28 green beads, 12 white beads, and 18 red beads. She randomly draws a bead from the bowl.
The probability of Kayla not drawing a yellow or a green bead is______ %. The probability of Kayla drawing a red or a green bead is______ %.
Answer:
1. 30%
2.46%
Step-by-step explanation:
The probability of Kayla not drawing a yellow or a green bead is 30 %. The probability of Kayla drawing a red or a green bead is 46 %.
Correct for plato! :)
What is the difference? -2/15 -(-9/15)
a.-11/15
b. -7/15
c. 7/15
d. 11/15
Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln1.38.
L(x)= ?
ln1.38 approximately = ? ...?
a certain game consists of rolling a single fair die and pays off as follows: $5 for a 6, $2 for a 5, $1 for a 4, and no payoff otherwise. find the expected winnings for this game.
The expected winnings for this game is calculated by multiplying the value of each possible outcome by their probability, providing an overall expected value of $1.33. This indicates that over a long period of repeated games, the average winnings per game would be $1.33.
Explanation:In this question, we're dealing with calculating the expected value in a game of probability. The game involves rolling a dice with outcomes ranging from 1 to 6 and the associated payoffs for roll outcomes of 4, 5, and 6 are $1, $2, and $5 respectively.
We calculate the expected winnings (value) for a single round of the game by multiplying all possible outcomes by their respective probabilities, then summing these products. In this case, symbols represent the payout (in $) and P represents the probability of each outcome.
(6) $5*P(1/6) = $0.83 (5) $2*P(1/6) = $0.33 (4) $1*P(1/6) = $0.17 (1-3) $0*P(1/2) = $0.00Adding up these expected outcomes gives us our overall expected winnings: $0.83 + $0.33 + $0.17 + $0.00 = $1.33 per game
If you play this game repeatedly, over the long term, you'd expect to win around $1.33 on average each game. Note that the exact winnings in a single instance of the game could be $0, $1, $2, or $5, and this value simply provides an average expected outcome over time.
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At sumer camp the ratio of boys to girls is 7:3 if there were 63 boys how many girls were there
Explain why all linear angle pairs must be supplementary, but all supplementary angles do not have to be linear pairs?
Final answer:
Linear angle pairs are always supplementary and formed by intersecting lines, while supplementary angles can be any two angles that add up to 180 degrees.
Explanation:
In mathematics, linear angle pairs are formed by two adjacent angles that add up to 180 degrees. This is known as supplementary angles. Linear angle pairs always occur when two lines intersect, creating opposite angles or a straight angle, such as in the case of a triangle.
On the other hand, supplementary angles do not have to be linear pairs. Supplementary angles are any two angles that add up to 180 degrees, regardless of their position or relation to each other. They can be adjacent angles, non-adjacent angles, or angles across parallel lines.
For example, two angles measuring 60 degrees and 120 degrees are supplementary angles but not a linear pair, since they are not adjacent to each other or formed by intersecting lines.
In the game of roulette, a player can place a $4 bet on the number 22 and have a 1/38 probability of winning. If the metal ball lands on 22, the player gets to keep the $4 paid to play the game and the player is awarded $140. Otherwise, the player is awarded nothing and the casino takes the players $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? ...?
Final answer:
The expected value of the game to the player is $3.68. If played 1000 times, the player would expect to lose $320.
Explanation:
Expected value for the game:
Probability of winning (landing on 22): 1/38Payout for winning: $140 + $4 initial bet = $144Cost of playing (losing bet): -$4Expected value = (Probability of winning * Payout for winning) + (Probability of losing * Cost of losing)Expected value = (1/38 * $144) + (37/38 * -$4)Expected value = -$0.2105 per gameExpected Loss in 1000 Games:
Expected loss per game = -$0.2105Expected loss in 1000 games = Expected loss per game * Number of gamesExpected loss in 1000 games = -$0.2105 * 1000Expected loss in 1000 games = -$210.50Therefore, you can expect to lose an average of $210.50 if you play this game 1000 times.
Express answer in exact form.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)
Answer:
A = { 3/2 π - 9/4 √ 3 } in^2
Step-by-step explanation:
Hope it helps, sorry for answering late.
What is 1036.50 rounded the the nearest whole number?
A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b?
Answer:
Hence the values of a and b are given by:
a=240
and b=1.16.
Step-by-step explanation:
It is given that:
A population of 240 birds increases at a rate of 16% annually.
i.e. the initial population of birds is 240.
Also they are increasing at a rate of 16% =0.16.
Hence, it clearly implies that the growth is exponential and the function that represents the population of the birds after x years is given by:
[tex]f(x)=240\times (1+0.16)^x\\\\\\f(x)=240\times (1.16)^x[/tex]
Hence, on comparing our function with the exponential function:
[tex]f(x)=ab^x[/tex]
we have:
a=240
and b=1.16.
Last year, Gena’s food cart business was $225 in debt. This year, the debt has tripled. Which expressions show how much Gena’s business is currently in debt? Check all that apply.
A. 225(3)
B. (3)(–225)
C. –225 + 3
D. 3 – 225
E. –225(3)
Both B & E; They are both using -225 which represents debt
The expression that shows the given statement will be equal to -225(3). Hence, options B and E are correct.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Gena's food cart business last year = $225 in debt = -225
The dept has tripled this year.
Then, the equation according to the statement will be,
(-225) × 3
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Find the sum of the first 50 terms of the sequence below.
An = 3n + 2
Answer:
3925
Step-by-step explanation:
this arithmetic sequence the first term is : A1 = 3(1)+2=5
and common difference is r = 3
the sum of the first 50 terms is : S50 = 50/2(A1 + A50)
A50 = 3(50)+2 = 152
S50 = 50/2(5 + 152)= 3925
Simplify (4xy^-2)/(12x^(-1/3)y^-5) and Show work ...?
4(x+3)=20
Help? Solve the equation
the quotient of a number and four decreased by ten is two
In 2009, the population of a country passed the 307.5 million marker. The total area of the country is 3.79 million square miles. What is the population density for that country for 2009? Find the number of people per square mile. Round to the nearest hundredth as needed. ...?
The population density for a country with a population of 307.5 million and an area of 3.79 million square miles is approximately 81.14 people per square mile. This figure is calculated by dividing the population by the area and is rounded to the nearest hundredth.
Explanation:To calculate the population density of a country for 2009, when the population was reported to be 307.5 million and the total area was 3.79 million square miles, you must divide the population by the total area. The formula for population density is:
Population Density = Population / Area
In this case, the calculation would be:
Population Density = 307,500,000 people / 3,790,000 square miles
When you do the math, you get:
Population Density ≈ 81.14 people per square mile
This result has been rounded to the nearest hundredth as requested. Comparing this with other countries' population densities, such as those of South Asian countries, can provide a remarkable insight into how population distribution and globalization impact living conditions and resource availability.
The population density of a country with a population of more than 307.5 million and an area of 3.79 million square miles, in 2009, was approximately 81.14 people per square mile after rounding to the nearest hundredth.
Explanation:To calculate the population density of a country for the year 2009 when the population was more than 307.5 million and the total area was 3.79 million square miles, we use the following formula:
Population Density = Population / Area
Now, let's substitute the given values:
Population Density = 307.5 million people / 3.79 million square miles
To proceed with the calculation, we need to convert the population into a number without the word 'million' since 'million' is also part of the area's units. Therefore, 307.5 million people become 307,500,000 people and 3.79 million square miles become 3,790,000 square miles.
Population Density = 307,500,000 people / 3,790,000 square miles
After doing the division, we get:
Population Density ≈ 81.14 people per square mile (rounded to the nearest hundredth)
Therefore, the population density for that country in 2009 was approximately 81.14 people per square mile.
WHICH CONSTRUCTION DOES THE IMAGE BELOW DEMONSTRATE??
A square circumscribed about a circle
A square inscribed in a circle
The circumcenter of a square
The incenter of a square
Answer:
This is a square inscribed in a circle.
Step-by-step explanation:
If (x-y)^2=71 and x^2+y^2=59 what is the value of xy?
Which is a correct first step in solving 5 – 2x < 8x – 3?
choices
5 < 6x – 3
3x < 8x – 3
5 < 10x – 3
2 – 2x < 8x
Which three statements below are true about an acute isosceles triangle?two side measures are the sameall angle measures are less than 90°one angle is obtusetwo angle measures are the sameall angle measures are different
Answer:
two side measures are the same
all angle measures less than 90°
two angle measures are the same
Step-by-step explanation:
The three true statements about an acute isosceles triangle are:
- Two side measures are the same:
- All angle measures are less than 90°:
- Two angle measures are the same:
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
About an acute isosceles triangle are:
- Two side measures are the same:
In an isosceles triangle, two sides have the same length.
In an acute isosceles triangle, all angles are acute, which means they are less than 90°.
Therefore, the two sides that are the same length must be the two sides opposite the acute angles.
- All angle measures are less than 90°:
An acute triangle is a triangle in which all angles are less than 90°.
Since an acute isosceles triangle has two equal acute angles, all three angles in the triangle are less than 90°.
- Two angle measures are the same:
An isosceles triangle is a triangle in which two sides have the same length. In an acute isosceles triangle, the two sides that have the same length are opposite the two equal acute angles.
Therefore, the two angles opposite those sides must also have the same measure.
Thus,
The three true statements about an acute isosceles triangle are:
- Two side measures are the same:
- All angle measures are less than 90°:
- Two angle measures are the same:
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20 % of 2 is equal to
A. 20
B. 4
C. 0.4
D. 0.04
What is the average rate of change of the function f(x)=2(3)^x from x = 2 to x = 4?
The average rate of change of the given function will be 72.
What is the average rate of change of the function?It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.
The given function is f(x)=2(3)ˣ and the interval is x ∈ [2,4].
The formula to calculate the average rate of change is (f(b)-f(a))/(b-a).
Here, a = 2 and b = 4
So,f (2) = 2.3² = 18
Now,f (4) = 2.3⁴ = 162
The average rate of change = (162 - 18)/(4 - 2)
The average rate of change = 144/2
The average rate of change = 72
Therefore, the average rate of change of the given function will be 72.
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The average rate of change of the function f(x) = 2(3)ˣ from x = 2 to x = 4 is 72. This means the secant line that intersects the graph of the function at x = 2 and x = 4 has a slope of 72.
Step 1: Formula for Average Rate of Change
The average rate of change of a function f(x) over the interval [a, b] is calculated using the following formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where:
f(b) is the function's value at the upper bound (x = 4 in this case).f(a) is the function's value at the lower bound (x = 2 in this case).b is the upper bound of the interval (x = 4).a is the lower bound of the interval (x = 2).Step 2: Find f(b) and f(a)
We are given the function f(x) = 2(3)ˣ . Let's find the function's values at x = 4 (upper bound) and x = 2 (lower bound):
f(4) = 2(3)⁴ = 2 × 81 = 162f(2) = 2(3)⁴ = 2 × 9 = 18Step 3: Calculate the Average Rate of Change
Now that we have f(b) and f(a), we can plug them into the formula along with the interval's bounds:
Average rate of change = (f(4) - f(2)) / (4 - 2)Average rate of change = (162 - 18) / (2)Average rate of change = 144 / 2Average rate of change = 72The surface area of two similar solids are 340yd^2 and 1,158yd^2. The volume of the larger solid is 1,712yd^2. What is the volume of the smaller solid? ...?
What multiplies to 9 and adds to 1
A wire 24inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of x:
Determine the domain of the function and use a graphing utility to graph the function over that domain
Use the graph of the function to approximate the maximum area of the rectangle. Make a conjecture about the dimensions that yield a maximum area. ...?
Answer:
Area function : [tex]A(x)=12x-x^2[/tex]
Domain: (0,6)
The area of rectangle is maximum at x=6. The area of a rectangle is maximum if it is a square.
Step-by-step explanation:
It is given that the length of wire is 24 inches. It is to be cut into four pieces to form a rectangle.
Let x be the length of shortest side.
Perimeter of a rectangle is
Perimeter = 2( Shortest side + longest side).
[tex]24 = 2( x + \text{longest side})[/tex]
[tex]12 = x + \text{longest side}[/tex]
[tex]12 - x = \text{longest side}[/tex]
So, length of longest side is (12-x) inches.
Area of a rectangle is
[tex]A=length \times width[/tex]
Area function is
[tex]A(x)=x(12-x)[/tex]
The area of rectangle and dimensions of a rectangle can not be a negative.
[tex]A(x)>0[/tex]
[tex]x(12-x)>0[/tex]
It means,
[tex]x>0[/tex]
[tex]12-x>0\Rightarrow 12>x[/tex]
One side is less that the other side.
[tex]x<12-x[/tex]
[tex]2x<12[/tex]
[tex]x<6[/tex]
It means the domain of the function is (0,6).
The simplified form of the area function is
[tex]A(x)=12x-x^2[/tex]
Differentiate with respect to x.
[tex]A'(x)=12-2x[/tex]
[tex]A'(x)=0[/tex]
[tex]12-2x=0[/tex]
[tex]x=6[/tex]
Differentiate A'(x) with respect to x.
[tex]A''(x)=-2<0[/tex]
Therefore the area of rectangle is maximum at x=6.
[tex](12-x)=12-6=6[/tex]
It means the area of a rectangle is maximum if it is a square.