The values of x, EC, and AC determined using the ratio of similar triangles are 21, 22, and 33 respectively.
What is the value of x, EC, and AC?The value of x is determined using the ratio of similar triangles as follows:
x / 7 = (12 + 6) / 6
x / 7 = 18 / 6
x * 6 = 18 * 7
x = 18 * 7 / 6
x = 21
EC + 11 / 11 = 21 / 7
(EC + 11) * 7 = 21 * 11
EC + 11 = 231 / 7
EC = 33 - 11
EC = 22
AC = 11 + EC
AC = 33
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Look at the situation below. Which equation determines how far they travel in feet (F) per second (S)? Mary walks her dog every morning before school. They travel 4 feet per second.
Answer:
Feet / per second
4 feet/per second
Step-by-step explanation:
. 16 is 20% of what number? Show your work and/or explain your reasoning.
Answer:
0.8
Step-by-step explanation:
.16/.2 = 0.8
check
0.8 x .2 = 0.16
A total of 255 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold? answer ASAP will give brainliest!!!
Answer:
85
Step-by-step explanation:
255 ÷ 3 = 85
85×2= 170 This is how much student tickets were sold.
255 - 170= 85
85 adult tickets were sold.
I need help please ?!!!!??!
Answer:
68
Step-by-step explanation:
x = original number of marbles
x = 104 - 36
x = 68
29.5 - 2.1 × (4.7 - 2.7)3 A. 219.2 B. 21.1 C. 12.7 D. 25.3
The expression is simplified to 25.3. Option D
What is BODMAS?BODMAS is simply a mathematical acronym which represents;
BracketOrderDivisionMultiplicationAdditionSubtractionNote that when carrying out mathematical operations, the order must be followed for a correct solution.
We have to simply the expression;
29.5 - 2.1 × (4.7 - 2.7)
solve the bracket
29.5 - 2.1 × ( 2. 0)
Multiply the bracket
29. 5 - 2.1(2)
29. 5 - 4. 2
25. 3
Thus, the expression is simplified to 25.3. Option D
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Age of Senators The average age of senators in the 108th Congress was 56.5 years. If the standard deviation was 12.5 years, find the Z-scores corresponding to the oldest and youngest senators of age 85 and 39. Round z scores to two decimal places. Part: 0/2 Part 1 of 2 The Z-score corresponding to the oldest senator of age 85 is oll
Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.
To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:
Z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation.
Part 1 of 2: For the oldest senator of age 85:
Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28
Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.
Part 2 of 2: For the youngest senator of age 39:
Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4
Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.
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A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is 4.5 days, the average brightness (or magnitude) of the star is 5.4, and its brightness varies by ±0.30 magnitude. Find a function that models the brightness of the star as a function of time (in days), t. (Assume that at t = 0 the brightness of the star is 5.4 and that it is increasing.)
Answer:
f(t) = 5.4 + 0.3sin (2π/4.5t)
Step-by-step explanation:
See attachment
How do we know if a function is a parabola like for instance, this one x^2 + x?
What equation of the line which passes through the point (-1, 2) and is parallel to the line y=x+4
Answer:
Thus, the equation of line for point (-1, 2) is y = x + 3.
Step-by-step explanation:
Answer:
The equation of the line is y = x + 3.
Step-by-step explanation:
A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.
y = mx + b
y = 1 * -1 + b
y = -1 + b
b = y + 1
b = 2 + 1
b = 3
A delivery driver makes $78 each day that he works and makes approximately $10 in tips for each delivery that he makes. If he wants to make at least $238 in one day, at least how many deliveries does he need to make?
Answer:
16 deliveries
Step-by-step explanation:
We can model the situation using a linear inequality. Since we're told that the driver makes $10 in tips for each delivery.Thus, this is the slope.Since he makes $78 each day, this number is a constant and he makes it even when no deliveries are made. Thus, this is the y-interceptSince he wants to make at least #238, we want to find a value of d (number of deliveries) which would cause his wages to equal #238. Thus, we can use the following equation to find:238 ≤ 10d + 78
160 ≤ 10d
16 ≤ d
Thus, he needs to make at least 16 deliveries to make at least $238 in one day. Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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the circumference of circle x in which a = 49pi in squared
Answer:
C = 14 pi inches
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
49 pi = pi r^2
Divide each side by pi
49 pi/pi = pi /pi r^2
49 = r^2
Take the square root of each side
7 = r
The circumference is given by
C = 2 * pi *r
C = 2 * pi *7
C = 14 pi inches
The Heflin household is laying down mulch around their garden. The following image depicts the shape and dimension of their garden and the area they want to place the mulch:
A triangular garden inside a rectangular mulch area. The garden has a base of 6 feet and a height of 5 feet, and the mulch area has a height of 9 feet and a base of 12 feet.
If the mulch costs $0.59 per square foot, determine the total cost.
Answer:
$54.87
Step-by-step explanation:
The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.
The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.
The total area to be covered with mulch is 108 - 15 = 93 square feet.
The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.
Therefore, the total cost of the mulch will be $54.87.
Solve for x. Write both solutions, separated by a
comma.
6x² + 5x - 6= 0
Answer:
\(x=\dfrac{2}{3},-\dfrac{3}{2}\)
Step-by-step explanation:
Given equation:
\(6x^2+5x-6=0\)
First, factor the left side of the given equation.
To factor a quadratic in the form \(ax^2+bx+c\) find two numbers that multiply to \(ac\) and sum to \(b\):
\(\implies ac=6\cdot-6=-36\)
\(\implies b=5\)
So the two numbers are: 9 and -4
Rewrite \(b\) as the sum of these two numbers:
\(\implies 6x^2+9x-4x-6=0\)
Factorize the first two terms and the last two terms separately:
\(\implies 3x(2x+3)-2(2x+3)=0\)
Factor out the common term \((2x+3)\):
\(\implies (3x-2)(2x+3)=0\)
To solve for x:
\(\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}\)
Therefore:
\(x=\dfrac{2}{3},-\dfrac{3}{2}\)
there's 240 candy bars 1/4 of candy bars are snickers 1/3 of the candy bars are twix 1/8 of the candy bars are hershey. how many candy bars are Mars? explain not with a lot of words but in numbers please.
Answer:
you have to add all the fractions of the candy1/4+1/3+1/8
=17/24
subtract from 1Step-by-step explanation:
1-17/24
=7/24
multiply with the total number of candy7/24×240
=70
i need some help pls :'(
Answer:
a
Step-by-step explanation:
UVT equals what?....
Answer:
m<UVT = 114°
Step-by-step explanation:
½(sum of intercepted arcs) = measure of vertex of an angle inside a circle
Thus:
½(FS + UT) = m<UVT
Substitute
½(53 + 175) = m<UVT
½(228) = m<UVT
114 = m<UVT
m<UVT = 114°
Need help with number 80
Answer:
a no
b. no
c.no
d. yes
Step-by-step explanation:
A cone has a diameter of 16 cm and a height of 35 cm. What is its volume?
Answer: if with 3.14 v= 37512.5333
if with pi v= 37531.56
Step-by-step explanation:
the formula is 1/3hπr^2
r= 2d so radius is 32
plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)
graph and find the equation of a line with a slope of 1/2 that passes through (6,0)
The equation of a line with slope m that passes thorugh the point (x1,y1) is given as:
\(y-y_1=m(x-x_1)\)Plugging the values we know we have:
\(\begin{gathered} y-0=\frac{1}{2}(x-6) \\ y=\frac{1}{2}x-3 \end{gathered}\)Therefore the equation of the line is:
\(y=\frac{1}{2}x-3\)To find the graph we need another point. If x=0, then:
\(\begin{gathered} y=\frac{1}{2}(0)-3 \\ y=-3 \end{gathered}\)Then we have the point (0,3). Plotting the points (0,3) and (6,0) and join them with a straign
PLEASE HELP ME WITH THIS PLEASE
Answer:
y = -x - 2
this is because the m is the slope and the b is the intersection of the y axis
Answer:
y=-1x-2
Step-by-step explanation:
First find the slope by using the formula (y2-y1)/(x2-x1). Choose the 2 intercepts to calculate the slope. replace the y's and x's with your points so it would look like this or this: (-2-0)/(0-(-2)) or 0-(-2))/(-2-0). They both give the same slope which is -1. Then, since the graph tells us the y-intercept(when the x is equal to 0), we replace it with b to get y=-1x-2.
rearrange the following numbers in order from greatest (top)to least (bottom) -1, 2, -2,-4
Answer:
2,-1,-2,-4
Step-by-step explanation:
How many 11-card hands are possible with a 20-card deck?
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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You lease a car at $23,495 for 3 years at $429.95 a month with a $500 down payment. The interest is 30% of the payments and $4,643.46 in interest is paid over 3 years. What is the remaining balance when the lease ends? How did you arrive at $12,160.26?
Answer:
Step-by-step explanation:
total interest paid is given as $4,643.46.
total payments = $429.95 x 36 months = $15,478.20
total lease payments = total payments - total interest
total lease payments = $15,478.20 - $4,643.46 = $10,834.74
Remaining balance = Total cost of the lease - Total lease payments
$23,495 - $10,834.74 = $12,660.26
the top of an electric pole is s supported by a wire of 26 ft long on the ground level. how far is tightened spot from the foot of the pole if its height is 24 ft?
Answer:
The tightened spot is 10 feet away from the foot of the pole.
Step-by-step explanation:
1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.
2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.
⭐What is the Pythagoras' Theorem?
\((C)^2 = (A)^2 + (B)^2\)An equation to find a 3rd side lengthC = hypotenuseA = one legB = another leg3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.
Let B= the distance from the tightened spot to the foot of the pole.
\((C)^2 = (A)^2 + (B)^2\)
\(26^2 = 24^2 + B^2\)
\(676 = 576 + B^2\)
\(100 = B^2\)
\(\sqrt{100} = \sqrt{(B)^2}\)
\(10 = B\)
∴ The tightened spot is 10 feet away from the foot of the pole.
Diagram:
What is the domain of the square root function graphed below?
On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3).
x less-than-or-equal-to negative 1
x greater-than-or-equal-to negative 1
x less-than-or-equal-to 0
x greater-than-or-equal-to 0
Mark this and return
The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.
The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.
From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).
The x-values of these points are 0, 1, and 4.
Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.
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There were 5 winners in a lottery drawing. The prize was $12 million. What is each winner's share of the prize?
heres the clearer version
Answer:
The midpoint of FH is (3;1)
Step-by-step explanation:
Please help will give brainliest it’s for a test
Round 29.20 to 30
Show work please
Answer:
you cant round that to 30
Step-by-step explanation
29.20
29.2 2 is less than 5
so you cant round you can only round if the .tens place is 5 or more
A swiming pool has a length of 12meters width of 6 meter and a height of a 5 meter how much water is needed to fill the swiming pool?
Answer:
\(\boxed {360 m^{3}}\)
Step-by-step explanation:
Water needed to fill the pool = volume of pool
Volume :
Volume = Length × Width × HeightVolume = 12 m × 6 m × 5 mVolume = 12 m x 30 m²Volume = 360 m³Hence, 360 m³ of water has to be filled.
Answer:
360 m³
Step-by-step explanation:
The swimming pool can be modeled as a rectangular prism with the following dimensions:
length = 12 mwidth = 6 mheight = 5 mTo find how much water is needed to fill the pool, calculate the volume of the rectangular prism using the given dimensions:
\(\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf length \times width \times height\\\implies \textsf{Volume of pool} & = \sf 12 \times 6 \times 5 \\& = \sf 72 \times 5\\& = \sf 360 \:\: m^3\end{aligned}\)
Therefore, 360 m³ of water is needed to fill the swimming pool.