Answer:
x = 6.5 cmStep-by-step explanation:
The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm[/tex]
Substitute:
[tex]x^2+20.2^2=(14.7+x)^2[/tex] use (a + b)² = a² + 2ab + b²
[tex]x^2+408.04=14.7^2+(2)(14.7)(x)+x^2[/tex] subtract x² from both sides
[tex]408.04=216.09+29.4x[/tex] subtract 216.09 from both sides
[tex]191.95=29.4x[/tex] divide both sides by 29.4
[tex]x\approx6.5\ cm[/tex]
Find the missing side length. When the area is 12ft.
Answer: Since you are finding the missing side of a rectangle, it is 3.
Step-by-step explanation:
Area of rectangle= (l)(w)
The length of the missing side is 3ft.
What is Area ?Area is defined as the space occupied by a flat surface .
It is measured in square units.
It is given in the question
A rectangle with one side as 4ft.
Area of the rectangle = 12 sq.ft
Other side = ?
Area of a rectangle is given by Length * Breadth
Area = one side * other side
Substituting the values
12 = 4 * other side
other side = 3 ft.
Therefore the length of the missing side is 3ft.
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Can someone help me on 8,12 please
Step-by-step explanation:
8.
[tex]\triangle CHF\sim\triangle YWS\\\\\angle C\cong\angle Y\\\angle H\cong\angle W\\\angle F\cong\angle S\\\\\dfrac{CH}{YW}=\dfrac{HF}{WS}=\dfrac{CF}{YS}[/tex]
Although it does not look like the picture.
From the picture ∠F ≅ ∠Y...
We must stick to the correct writing:
Δ → Δ
C → Y
H → W
F → S
12.
ΔMLK and ΔYWZ are not similar because they have different angles (different shape).
given f(x)=x+2 and h(x)=1/x-1 evaluate the following function at x=2
[h(x)]^2/f(x)
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Substitute x = 2 into both h(x) and f(x)
h(2) = [tex]\frac{1}{2-1}[/tex] = 1 ⇒ (h(2))² = 1
f(2) = 2 + 2 = 4
Hence
[tex]\frac{h(x)^2}{f(x)}[/tex] when x = 2
= [tex]\frac{1}{4}[/tex]
1/4 is the following function at x=2
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and co domain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Given
Substituting x = 2 into both h(x) and f(x)
h(2) = 1(2-1) = 1 ⇒ (h(2))² = 1
f(2) = 2 + 2 = 4
Hence
h(x)²/f(x) when x = 2
=1/4
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what is the difference r+2/r+4-3/r+1
Answer:
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\frac{r+2}{r+4}-\frac{3}{r+1}[/tex]
We collect the least common multiple of the denominators to get:
[tex]\frac{(r+2)(r+1)-3(r+4)}{(r+4)(r+1)}[/tex]
Expand the numerator:
[tex]\frac{r^2+3r+2-3r-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-3r+3r+2-12}{(r+4)(r+1)}[/tex]
[tex]\frac{r^2-10}{(r+4)(r+1)}[/tex]
Answer:
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
Step-by-step explanation:
[tex]\frac{r+2}{r+4} - \frac{3}{r+1}[/tex]
To simplify the fractions we take common denominator
LCD is (r+4)(r+1)
we try to get same denominator on both fraction
multiply the first fraction by r+1 and second fraction by r+4
[tex]\frac{(r+2)(r+1)}{(r+4)(r+1)} - \frac{3(r+4)}{(r+1)(r+4)}[/tex]
(r+2)(r+1) becomes r^2 +3r+2
3(r+4) becomes 3r+12
[tex]\frac{ r^2 +3r+2}{(r+4)(r+1)} - \frac{3r+12)}{(r+1)(r+4)}[/tex]
[tex]\frac{ r^2 +3r+2-3r-12}{(r+4)(r+1)}[/tex]
combine like terms
[tex]\frac{ r^2-10}{(r+4)(r+1)}[/tex]
For the z-score for the 11.6 data point
Answer:
z = 1.3345
Step-by-step explanation:
The z-score for a given data point, say x, from a normal distribution with a given mean and population standard deviation is usually calculated using the formula;
[tex]z=\frac{x-mean}{standard deviation}[/tex]
The following information is available;
mean = 7
population standard deviation = 3.522
x = 11.7
We simply employ the above formula to determine the z-score associated with the 11.7 data point;
[tex]z=\frac{11.7-7}{3.522}=1.3345[/tex]
FIRST CORRECT ANSWER GETS BRAINLIEST!! (Please don't rush to answer, I've gotten a lot of incorrect answers from people who answer within the minute)
Which table shows a proportional relationship between x and y?
Answer:
B
Step-by-step explanation:
y is 3 times the x
Answer:
B
Step-by-step explanation
1/3=3
6/2=3
12/4= 3
15/5=3
The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. The events are not independent because the .
Answer:
The events are not independent because the product of their marginal probabilities is not equal to their joint probability
Step-by-step explanation:
Two events A and B are said to be independent with respect to probability if the product of their marginal probabilities is equal to their joint probability. In the question presented we have;
Pr(A) = 0.4
Pr(B) = 0.2
Pr(A n B) = 0.1
The product of their marginal probabilities is;
Pr(A) * Pr(B) = 0.4 * 0.2 = 0.08
Their joint probability is given as;
Pr(A n B) = 0.1
Clearly, Pr(A) * Pr(B) ≠ Pr(A n B) and thus the events are not independent.
Answer:
Product of P(A) and P(B) is not equal to P(A and B)
Step-by-step explanation:
it would be option C on E2020
15. Cody and his wife are purchasing a home. The cost
of the home is $145,900. They will be required to
pay a down payment of 5% of the purchase price
and to pay closing costs of 6% of the purchase
price. How much cash will they need for the down
payment and closing costs?
$16,049
$8,754
$7,295
$145,900
$161,949
They would need $16,049!
Price of the home is $145,900.
Percentage of the down payment is 5%
Subtract 5% from $145,900 = $138,605
That mean 5% of $145,900 is $7,295
Percentage of the closing cost is 6%.
Subtract 6% from $145,900 = 137,146
That mean 6% of 145,900 is $8,754
Add the down payment ($7,925) and closing cost ($8,745)
$16,049!
Mark me Brainliest!! Please!
they will need to pay $16,049
multiply $145,900 by 5%
multiply $145,900 by 6%
now add the totals to get $16,049
If the mean of this distribution is 7, which could be the median? A) 1.5 B) 5 C) 8 D) 10
PLEASE HELP
Answer:
Tationia Rolon
Step-by-step explanation:
I think its C because the median is the number in the middle
Answer
6
Step-by-step explanation:
I got is correct on usatestprep
Answer choices
F(x) or G(x)
for both A and B
Answer:
A. f(x)
B. g(x)
Step-by-step explanation:
The initial amount if the value of the function at x = 0.
Here that value is 2000 for the f(x) and 1000 for the g(x), so the f(x) has the higher initial value.
For the second part, by looking at the graph, you can determine that the function for the g(x) is 1000(3)^x (because the g(1) is 3000). Plugging in two for both the function, you get the f(x) = 8,000 and the g(x) = 9,000, so the g(x) has the greater amount of bacteria after two days.
Answer:
A. f(x)
B. g(x)
Step-by-step explanation:
The initial amount if the value of the function at x = 0.
Here that value is 2000 for the f(x) and 1000 for the g(x), so the f(x) has the higher initial value.
For the second part, by looking at the graph, you can determine that the function for the g(x) is 1000(3)^x (because the g(1) is 3000). Plugging in two for both the function, you get the f(x) = 8,000 and the g(x) = 9,000, so the g(x) has the greater amount of bacteria after two days.
Which of the following is the solution to the inequality below?
Answer:
C.
Step-by-step explanation:
distribute.
-3x+9 > 5-5x
put the x's to one side.
2x+9 > 5
put the number to the other side.
2x > -4
x > -2
Carly wins 1282 tickets at a arcade. For each group of 65 tickets she will receive a prize. Carl solve the problem 1282÷65 and determines that she has enough tickets right now for 19 prices. What is the least number of additional tickets that current needs to win to have enough tickets for a 20th prize?
18 is correct because 1300/65=20 1300-1282=18.
Find the value of X in the circle
Answer:
x=7 units
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The triangles AMN and APQ are congruent by SAS similarity postulate
The include angle
∠MAN=∠PAQ
Because
Arc MN=Arc PQ
therefore
MN=PQ
substitute the values
38=4x+10
solve for x
4x=38-10
4x=28
x=7 units
x would be 7 units because 4 × 7 = 28 And 28 + 10 = 38
The ratio of red cars to blue cars in a parking lot was 5:3.if there were 40 red cars, how many blue cars were there??
Every 5 red cars there are 3 Blue cars,
So if there are 40 red cars,
there are going to be 24 Blue cars
40 divided by 5 which is 8
Multiply 3 × 8 which is ( 24 blue cars )
Answer:
24
Step-by-step explanation:
The 5 part of the ratio represents 40 cars, thus
40 ÷ 5 = 8 cars ← value of 1 part of the ratio
3 parts = 3 × 8 = 24 ← number of blue cars
To the nearest hundred what is the value of X
Answer:
41.51
Step-by-step explanation:
We can find the value of x using the trigonometry identify.
Cos (41) = x/55
x = 55cos (41)
x = 41.51
ANSWER
[tex]x = 41.51[/tex]
EXPLANATION
The given triangle has a right angle.
We were given an acute angle that measures 41°
The hypotenuse of the given right triangle is 55.
Since x is adjacent to the given angle and we also know the hypotenuse, we use the cosine ratio to find x.
[tex] \cos(41 \degree) = \frac{x}{55} [/tex]
Therefore
[tex]x = 55 \cos(41 \degree) [/tex]
[tex]x = 41.509[/tex]
We round to the nearest hundredth to obtain,
[tex]x = 41.51[/tex]
Convert 7pi/5 to degrees.
Answer: 252 degrees!
7pi/5 is 252degrees.
What is radians?The standard unit of angular measure used in many branches of mathematics is the radian, indicated by the symbol rad. The radian is the SI unit for measuring angles. The radian has replaced the unit as a SI derived unit, which was previously a SI supplementary unit.
Given
To convert radians to degrees, multiply by 180/π, since a full circle is
360° or 2π radians.
(7π/5)⋅180°/π
Cancel the common factor of π.
Rewrite the expression.7/5⋅180
7⋅36
Multiply 7 by 36.
252
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The manager of a company that sells movie tickets online releases a report. The report states that the company's customers do not want the option of reserving a seat when they buy tickets. The report was based on a survey of 200 customers chosen at random from the company's database. Participants were asked the question, "Are you willing to spend the extra time and effort to reserve a seat when you buy tickets?" Select all statements that correctly evaluate the report. The question is biased toward a Yes response.
A) The sample is biased because it does not represent the population.
B) The question is biased toward a No response.
C)The question is not biased.
D) The sample is not biased.
Answer:
the question is biased towards a no response, because they're asking participants "are you willing to spend the extra time to blah blah" obviously they're going to say no, and the second answer is the sample is not biased because they're not giving the consumers any reason to want the product they're selling.
Step-by-step explanation:
Answer:
The sample is not biased.
The question is biased toward a No response
Step-by-step explanation:
I took the test!
How many terms are in the arithmetic sequence 7, 1, −5, …, −161?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
27
28
29
30
Answer:
29
Step-by-step explanation:
The n th term of an arithmetic sequence is
• [tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = 1 - 7 = - 5 - 1 = - 6 and a₁ = 7, [tex]a_{n}[/tex] = - 161, hence
7 - 6(n - 1) = - 161 ← solve for n
7 - 6n + 6 = - 161
13 - 6n = - 161 ( subtract 13 from both sides )
- 6n = - 174 ( divide both sides by - 6 )
n = 29
There are 29 terms in the sequence
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
22 feet
26 feet
33 feet
44 feet
22 feet is the answer I hope this helps
Answer:
Longest rope is 44 feet. 1 piece is 1/2(44)=22. 22+44=66
Step-by-step explanation:
What is the surface area of the cylinder in term of pi? Radius of 11 and height of 23
Answer:
The surface area of the cylinder is [tex]748\pi[/tex].
Step-by-step explanation:
Given : Radius of the cylinder is 11 unit and height of the cylinder is 23 unit.
To find : What is the surface area of the cylinder in term of pi?
Solution :
The formula of surface area of cylinder is
[tex]A=2 \pi r^2+2\pi rh[/tex]
Where, r is the radius of the cylinder r=11 unit.
h is the height of the cylinder h=23 unit.
Substitute the value in the formula,
[tex]A=2 \pi r^2+2\pi rh[/tex]
[tex]A=2\pi(r^2+rh)[/tex]
[tex]A=2\pi(11^2+11(23))[/tex]
[tex]A=2\pi(121+253)[/tex]
[tex]A=2\pi(374)[/tex]
[tex]A=748\pi[/tex]
Therefore, The surface area of the cylinder is [tex]748\pi[/tex].
y = 3x-5
6x + 3y= 15
y = 3x - 5
So substitute 3x-5 for y:
6x + 3(3x-5) = 15
Simplify:
6x + 9x - 15 = 15
15x - 15 = 15
x - 15 = 1
x = 16
THEN find y by plugging the value of x back into the first equation:
y = 3(16) - 5
y = 48 - 5
y = 43
Find the perimeter of the polygon ??
Answer:
35.5 m
Step-by-step explanation:
The perimeter of the polygon is the sum of all the sides of the polygon. The sides are given as
11 m , 5 m ,7.5 m , 5m and 7m
Hence the perimeter would be,
11+5+7.5+5+7
= 35.50 m
In the figure, angle A measures 41° and angle D measures 32°. What is the measurement of angle E?
triangles angles always add up to 180° that being said,
41+32=73
180-73=107
angle e= 107°
hope this helps!
In a lottery game, a player picks six numbers from 1 to 20. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1.
What is the expected value of this game?
The expected value of the lottery game is -$0.62, suggesting a long-term average loss of 62 cents per game played. This value is calculated by considering the probability of each outcome and the associated gain or loss.
Explanation:In order to calculate the expected value of the lottery game, we must first understand what expected value truly represents. The expected value is essentially a description of the average outcome of a series of events if these events are repeated many times. It's a statistical concept used to predict the long-range behavior of random events, such as lottery games.
The expected value is calculated as the sum of all possible values each multiplied by the probability of its occurrence. For the lottery game described, there are two possible outcomes: a win of $30,000 or a loss of $1.
The probability of winning is extremely low. In this game, the player is attempting to choose the correct 6 numbers out of 20, which is a 1 in 38,760 chance. Whereas, the probability of losing is extremely high, practically 38,759 out of 38,760.
Thus, the Expected Value (E) can be calculated as follows: (probability of winning x winnings) + (probability of losing x loss). Plugging in our values gives us an expected value of -$0.62, rounded to the nearest cent. This figure indicates that if one were to play this game repeatedly, their average loss per game would be about 62 cents.
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a penny is dropped from the top of the statue of liberty which is 305 feet tall . the height of the penny, (h,) at time (t) seconds can be repesented by the equation h(t) = -16t^2 + 305. After 4 seconds how much further does the penny need to travel before it hits the ground.
Answer: Penny need to travel 49 feet before it hits the ground.
Step-by-step explanation:
Since we have given that
[tex]h(t)=-16t^2+305[/tex]
Here, h denotes the height of the penny
t denotes the time in seconds.
Now, t = 4 seconds
So, the penny needs to travel before it hits the ground is given by
[tex]h(4)=-16(4)^2+305\\\\h(4)=-16\times 16+305\\\\h(4)=256-+305\\\\h(4)=49\ feet[/tex]
Hence, Penny need to travel 49 feet before it hits the ground.
After 4 seconds, the penny needs to travel an additional 49 feet before it hits the ground.
Explanation:The equation h(t) = -16t^2 + 305 represents the height of the penny at time t seconds. To find out how much further the penny needs to travel before it hits the ground after 4 seconds, we need to substitute t = 4 into the equation and solve for h.
h(4) = -16(4)^2 + 305
h(4) = -256 + 305
h(4) = 49 feet.
Therefore, the penny needs to travel an additional 49 feet before it hits the ground.
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What is the value of x?
x = 16.
Hope this helps!
Answer:
x = 16
Step-by-step explanation:
Since the triangles are similar then the ratio of corresponding sides are equal, that is
[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] ( cross- multiply )
5x = 80 ( divide both sides by 5 )
x = 16
Tell whether each equation represents a direct proportion. If so, identify the
constant of proportionality.
1. 0.4y = x
2. x = 1 - 2y
Answer:
Step-by-step explanation:
1. 0.4y = x is a direct proportion. It'd be more appropriate to write this as
y = x / 0.4, or y = 2.5x, in which case 2.5 is the constant of proportionality.
2. x = 1 - 2y is not a direct proportion because of the offset (1). A line representing a direct proportion must go through the origin (0, 0); this particular line does not do that.
The first equation, 0.4y = x, represents a direct proportion with the constant of proportionality being 2.5. The second equation, x = 1 - 2y, does not represent a direct proportion since it does not have the form y = kx.
When we talk about two quantities being directly proportional, we mean that as one quantity increases, the other increases by a constant rate, and vice versa. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.
For the first equation, 0.4y = x, this is rearranged as y = (1/0.4)x or y = 2.5x. This is indeed a directly proportional relationship, with the constant of proportionality being 2.5.
The second equation x = 1 - 2y does not describe a directly proportional relationship because it is not of the form y = kx. Instead, it shows that x decreases as y increases, which is suggestive of an inverse relationship, rather than a direct one.
A ________ is a transformation of a figure by turning it around a given point.
A. dilation
B. reflection
C. rotation
D. translation
Answer:
Translation
Step-by-step explanation:
What is the answer to this?
Answer:
90°
Step-by-step explanation:
The angles at the intersection of a kite will always be 90°
write the equation for an exponential function, in the form axb^x, whose graph passes through the coordinates points (1, 7.5) ( 3, 16.875)
Answer:
see explanation
Step-by-step explanation:
The equation of the exponential function in the form
y = a[tex]b^{x}[/tex]
Substitute the given points into the equation and solve for a and b
Using (1, 7.5), then
7.5 = ab → (1)
Using (3, 16.875), then
16.875 = ab³ → (2)
Divide (2) by (1)
[tex]\frac{ab^3}{ab}[/tex] = [tex]\frac{16.875}{7.5}[/tex], hence
b² = 2.25 ( take the square root of both sides )
b = 1.5
Substitute b = 1.5 into (1)
1.5a = 7.5 ⇒ a = 5
The exponential function is y = 5[tex](1.5)^{x}[/tex]