Final answer:
To find the time it took for Austin to catch up with Amber, we calculated the distance Amber had covered before Austin started, and then divided that distance by the difference in their speeds, yielding a catch-up time of 5.5 hours.
Explanation:
The question is asking after how many hours Austin will catch up with Amber if they are driving the same route, but start at different times and drive at different speeds. To solve this problem, we can use the concept of relative speed and the equation Distance = Speed × Time. Since Amber left 2 hours earlier, by the time Austin starts, Amber has already covered a certain distance. We can calculate this distance by multiplying Amber's speed (55 mph) by the time she drove alone (2 hours), which gives us 110 miles. Now, Austin catches up by covering the difference in the distance at a relative speed, which is the difference of their speeds. So, the relative speed is Austin's speed (75 mph) minus Amber's speed (55 mph), resulting in 20 mph.
Now we can find the time it took Austin to catch up by dividing the distance Amber covered alone (110 miles) by the relative speed (20 mph). This comes out to 5.5 hours. Thus, Austin catches up with Amber after driving for 5.5 hours.
Use the theorem below to answer the question. Suppose θ is an acute angle residing in a right triangle. If the length of the side adjacent to θ is a, the length of the side opposite θ is b, and the length of the hypotenuse is c, then cos(θ) = a c and sin(θ) = b c . If θ = 13° and the side adjacent to θ has length 4, how long is the hypotenuse? (Round your answer to three decimal places.)
Answer:
c ≈ 4.105
Step-by-step explanation:
You want to find c in ...
cos(13°) = 4/c
Multiply the equation by c/cos(13°) and evaluate.
c = 4/cos(13°) ≈ 4.105
Answer:
Solve the equation where the sine of 30 degrees is equal to YZ/50.
Solve 180 – (30 + 90) = 60 to find the measure of angle Z. Then use the cosine of Z to write and solve an equation.
Use the 30°-60°-90° triangle theorem to find that YZ = 50/2.
Step-by-step explanation:
These are the sample answers, use how you would like :)
A box contains 3 cherry frozen treats and 2 grape frozen treats. Maggie takes a treat from the box without looking, gives it to her brother, and then selects another treat. What is the probability that Maggie and her brother gets a grape treat
Answer:
1/10
Step-by-step explanation:
When Maggie gives a grape treat to her brother, there are 2 grape treats out of 5 total treats.
When Maggie selects another treat, there is 1 grape treat out of 4 treats left.
So the probability that both happen is:
2/5 × 1/4
1/10
Kevin sold a box of 28 books at a yard sale for a total of $54.64. He sold the paperback books for $1.68 each and sold the hardcover books for $2.44 each. Which system of equations can be used to determine the number of $1.68 paperback books, x, and the number of $2.44 hardcover books, y, that were sold at the yard sale?
A.
x + y = 28
1.68x + 2.44y = 54.64
B.
2.44x - 1.68y = 28
x + y = 54.64
C.
x + y = 28
2.44y = -1.68x + 54.64
D.
y = x - 54.64
1.68x + 2.44y = 28
Answer:
A.
x + y = 28
1.68x + 2.44y = 54.64
Step-by-step explanation:
Let x = paperback books and y = hardback books
x+y =28
We know that paperbacks cost 1.68 and hardback cost 2.44
1.68x + 2.44y = 54.64
We have 2 equations and 2 unknowns
x+y =28
1.68x + 2.44y = 54.64
Which transformation is a isometry?
Answer:
A. The two triangles.
Step-by-step explanation:
Isometry can be divided into two words: iso = same and metry = measure
So, isometry means "same measure".
In this case, that means the transformation didn't change the measures of the object.
In B, they kept the same shape, but not the same side.
In C, you can see the figure has been transformed,.
A bit if not A them it’s C (sorry I tried)
According to legend, in 1626 Manhattan Island was purchased for trinkets worth about $24. If the $24 had been invested at a rate of 6% interest per year, what would be its value in 2006? Compare this with a total of $802.4 billion in assessed values for Manhattan in 2006.
Answer:
Its value in 2006 would be $99, 183, 639, 920
Step-by-step explanation:
Use the compounding interest formula for this one, which looks like this in its standard form:
[tex]A(t)=P(1+r)^t[/tex]
Our P is the initial amount of $24, the r in decimal form is .06, and the time between 2006 and 1626 in years is 380. Fitting this into our formula we get:
[tex]A(t)=24(1+.06)^{380}[/tex] or
[tex]A(t)=24(1.06)^{380}[/tex]
First raise the 1.06 to the power of 380 on your calculator and then multiply in 24.
As for the second part of the question, I'm not quite sure how it's supposed to be answered. But maybe you can figure that out according to what the unit normally asks you to do.
What is the length of the base of an isosceles triangle if the center of the inscribed circle divides the altitude to the base into the ratio of 12:5 (from the vertex to the base), and the length of a leg is 60 cm?
Answer:
50 cm
Step-by-step explanation:
Consider isosceles triangle AEF in the attachment. Point B is the center of the incircle, and it divides altitude AC into segments having the ratio 12:5.
Triangle ABD is similar to triangle AEC by AA similarity. (Angle A is the same for both right triangles. Then the ratio of hypotenuse to short leg will be the same for each. In triangle ABD, that ratio is 12:5, as given by the problem statement. Since we know AE = 60 cm, also from the problem statement, we know that ...
AB/BD = AE/EC
12/5 = 60 cm/EC
so ...
EC = (60 cm)·(5/12) = 25 cm
Base length EF is twice that, or 50 cm.
Please help!!
What is the value of x? Enter your answer in the box. x = NOTE: Image not drawn to scale. Triangle G E H with segment E D such that D is on segment G H, between G and H. Angle G E D is congruent to angle D E H. E G equals 44.8 millimeters, G D equals left parenthesis x plus 4 right parenthesis millimeters, D H equals 35 millimeters, and E H equals 56 millimeters.
Answer:
x = 24
Step-by-step explanation:
The segments on either side of an angle bisector are proportional:
(x +4)/44.8 = 35/56
x +4 = 44.8·(35/56) = 28 . . . . multiply by 44.8
x = 24 . . . . . subtract 4
Answer:
The value of x is 24.
Step-by-step explanation:
Given information: In ΔGHE, ED is angle bisector, EG=44.8 millimeters, GD=(x+4) millimeters, DH=35 millimeters, and EH=56 millimeters.
According to the angle bisector theorem, an angle bisector divide the opposite side into two segments that are proportional to the other two sides of the triangle.
In ΔGHE, ED is angle bisector, By using angle bisector theorem, we get
[tex]\frac{GD}{DH}=\frac{EG}{EH}[/tex]
[tex]\frac{x+4}{35}=\frac{44.8}{56}[/tex]
Multiply both the sides by 35.
[tex]x+4=\frac{44.8}{56}\times 35[/tex]
[tex]x+4=28[/tex]
Subtract 4 from both the sides.
[tex]x=28-4[/tex]
[tex]x=24[/tex]
Therefore the value of x is 24.
Complete the identity
Answer: [tex]cos(\pi-x)=-cos(x)[/tex]
Step-by-step explanation:
We need to apply the following identity:
[tex]cos(A - B) = cos A*cos B + sinA*sin B[/tex]
Then, applying this, you know that for [tex]cos(\pi-x)[/tex]:
[tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex]
We need to remember that:
[tex]cos(\pi)=-1[/tex] and [tex]sin(\pi)=0[/tex]
Therefore, we need to substitute these values into [tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex].
Then, you get:
[tex]cos(\pi-x)=(-1)*cos(x)+0*sin(x)[/tex]
[tex]cos(\pi-x)=-1cos(x)+0[/tex]
[tex]cos(\pi-x)=-cos(x)[/tex]
kong took 15% fewer seconds that Nolan took to complete his multiplication timed test. Kong took 85 seconds.
How many seconds did Nolan take?
Answer:
Answer: Nolan took 97.75 Seconds
Step-by-step explanation:
85 x .15 = 12.75
85 + 12.75 = 97.75
Determine whether each ordered pair is a solution of the given linear equation?
Answer:
(1,2) is the only solution to the given linear equation
Step-by-step explanation:
To see whether an ordered pair is a solution to an equation, the easiest thing to do would be to plug the pair into the equation and see if it equals the right hand side.
(1,2):
[tex]4*x+7*y=18\\4*(1)+7*(2)=18\\\therefore (1,2) \text{ is a solution}[/tex]
(8,0):
[tex]4*(8)+7*(0)=32\\\therefore (8,0) \text{ is not a solution}[/tex]
(0, -2):
[tex]4*(0)+7*(-2)=-14\\\therefore (0,-2) \text{ is not a solution}[/tex]
The pair (1,2) is a solution to the linear equation 4x+7y=18. However, the pairs (8,0) and (0,-2) are not solutions because they do not satisfy the equation.
Explanation:a. To determine if the ordered pair (1, 2) is a solution to the linear equation 4x + 7y = 18, we substitute the values of x and y into the equation: 4(1) + 7(2) = 18. This simplifies to 4 + 14 = 18, which is true. Therefore, (1, 2) is a solution to the given linear equation.
b. To determine if the ordered pair (8, 0) is a solution, we substitute the values of x and y into the equation: 4(8) + 7(0) = 18. This simplifies to 32 + 0 = 18, which is false. Therefore, (8, 0) is not a solution to the given linear equation.
c. To determine if the ordered pair (0, -2) is a solution, we substitute the values of x and y into the equation: 4(0) + 7(-2) = 18. This simplifies to 0 - 14 = 18, which is false. Therefore, (0, -2) is not a solution to the given linear equation.
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The complete question is here:
Determine whether each ordered pair is a solution of the given linear equation.
4 x+7 y=18 ;(1,2),(8,0),(0,-2)
a. Is (1,2) a solution to the given linear equation?
No
Yes
b. Is $(8,0)$ a solution to the given linear equation?
Yes
No
c. Is (0,-2) a solution to the given linear equation?
No
Yes
A square playing field has an area of 1255 square yards. About how long is each side of the field? Please explain how to do this problem
Answer:
about 35.4 yards
Step-by-step explanation:
Make use of the formula for the area of a square and solve for the side length. The area (A) of a square of side length s is given by ...
A = s²
You are given A and asked to find s. So you have
1255 yd² = s²
To find s, you take the square root of both sides of the equation.
√(1255 yd²) = √(s²)
35.426 yd ≈ s . . . . . the square root of 1255 is irrational, so we have shown an approximation rounded to 3 decimal places.
Each side of the field is about 35.4 yards long.
_____
Any scientific or graphing calculator can compute the square root for you, as can any spreadsheet program or any of a number of on-line calculators. A Google or Bing search box will also compute the square root for you. (see attachment)
Please, I need it ASAP!!!! I will give brainliest if correct!!!
Answer:
recursive: f(0) = 7; f(n) = f(n-1) -8
explicit: f(n) = 7 -8n
Step-by-step explanation:
The sequence is an arithmetic sequence with first term 7 and common difference -8. Since you're numbering the terms starting with n=0, the generic case will be ...
recursive: f(0) = first term; f(n) = f(n-1) + common difference
explicit: f(n) = first term + n·(common difference)
To get the answer above, fill in the first term and common difference values.
The perimeter of a rectangle is 32 feet. The length is 6 feet longer than the width. Find the dimensions.
To find the dimensions of the rectangle, express its length in terms of its width as 'width + 6'. Substitute this in the formula for perimeter and solve to get width = 5 feet and length = 11 feet.
Explanation:The problem stated relates to the geometric concept of perimeter and involves a bit of algebra. First, remember that the formula for the perimeter of a rectangle is 2(length + width). If the total perimeter is 32 feet, and the length is 6 feet longer than the width, we can describe the length as 'width + 6'.
Substitute these into the perimeter formula: 2((width + 6) + width) = 32. Simplify this to 2(width + width + 6) = 32, then simplify further to 2(2width + 6) = 32. Divide both sides by 2 to get 2width + 6 = 16. Solving for 'width', we get width = 5 feet. Therefore, the length (which is width + 6) would be 5 + 6 = 11 feet.
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Which of the following is a solution of y - x < -3?
A. (6,2)
B. (2,6)
C. (2,-1)
Thanks
Answer:
Option A. (6,2)
Step-by-step explanation:
We have the following inequality:
[tex]y- x <-3[/tex]
Solving for y we have:
[tex]y<x-3[/tex]
The line that limits the region of inequality is
[tex]y = x-3[/tex]
Then the region of inequality are all values of y that are less than [tex]f (x) = x-3[/tex]
In other words, the points belonging to the inequality are all those that lie below the line.
To find out which point belongs to this region substitute inequality and observe if it is satisfied
A. (6,2)
[tex]2<6-3[/tex]
[tex]2<3[/tex] is satisfied
B. (2, 6)
[tex]6<2-3[/tex]
[tex]6<-1[/tex] it is not satisfied
C. (2, -1)
[tex]-1<2-3[/tex]
[tex]-1<-1[/tex] it is not satisfied
The answer is the option A
Slove these one step equation for the variable listed: Show your work
1. 14-7= k
2. 21+ W = 36
3. -5= G+3
4. 2b = 12
5. 35 = 5R
6. Q/2 =6
1. 7=k
2. 21+w=36
-21 -21
----------------------
w=15
3. -5 =G+3
-3 -3
---------------------
-8=G
4. 2b/2=12/2
b=6
5. 35/5=5R/5
7= R
6. Q/2 (2) = 6 (2)
Q=12
Answer:
Step-by-step explanation:
1) 14-7 = 7 = k
2) 21 + W = 36 → W = 36 - 21 → W = 25
3) -5 = G + 3. Add 5 to both sides, obtaining G = 8.
4) 2b = 12. Div. both sides by 2: b = 6
5) 35 = 5R. Div. both sides by 5: 7 = R
6) Q/2 = 6; Mult both sides by 2: Q = 12
Need help ASAP!! (Geometry) *Attachments*
Answer:
option b 5√2
option a 20
option c 4
option d 3/4
option b 3
Step-by-step explanation:
To solve all these questions we will use trigonometry identity which says that
sinΔ = opposite / hypotenuse
1)
sin45 = 5 / KL
Kl = [tex]\frac{5}{\frac{\sqrt{2}}{2} }[/tex]
KL = 5√2
2)
TanФ = opp / adj
Ф = Tan^-1(5/14)
Ф = 19.65
≈ 20
3)
sin(30) = rq / 8
rq = sin(30)(8)
rq = 4
4)
tan(Ф) = 6/8
5)
angle 3
If you know the radius, r, of a circle, what do you multiply r by to get the circle's CIRCUMFERENCE?
A) 2
B) π
C) 2π
D) 3π
E) 4π
Answer:
C
Step-by-step explanation:
When you have the radius of a circle, you find the circumference by multiplying the radius by 2PI.
The answer is C.
What is wrong with this “proof”? “Theorem” For every positive integer n, if x and y are positive integers with max(x, y) = n, then x = y. Basis Step: Suppose that n = 1. If max(x, y) = 1 and x and y are positive integers, we have x = 1 and y = 1. Inductive Step: Let k be a positive integer. Assume that whenever max(x, y) = k and x and y are positive integers, then x = y. Now let max(x, y) = k +1, where x and y are positive integers. Then max(x – 1, y – 1) = k, so by the inductive hypothesis, x – 1 = y – 1. It follows that x = y, completing the inductive step. Online Discussion Guidelines: Post your logical argument on the discussion forum. Read the logical argument of your peers. Reply the results posted by at least two of your peers.
The assumption of the inductive step is not correct. If [tex]\mathrm{max}(x,y)=2[/tex], for instance, it's entirely possible that [tex]x=1[/tex] and [tex]y=2[/tex].
If A = {x | x is an even integer}, B = {x | x is an odd integer find a u b
Answer:
A U B = {x|x is an integer}
Step-by-step explanation:
If A={x|x is an odd integer} then:
A = 1, 3, 5, 7, 9, 11, etc.
(Negative odd integers are also included)
and B= {x|x is an even integer}
A = 2, 4, 6, 8, 10, 12, 14, etc.
(Negative even integers are also included)
We have that a u b is going to be the set of all integer numbers. That is to say:
A U B = {x|x is an integer}
20pts + brainliest PLEASE HELP
1. Find the 70th percentile for the values below:
26 37 18 45 20 36 22 25 50 41
2. Find the 40th percentile for the values below:
26 37 18 45 20 36 22 25 50 41
Answer:
1. 37
2. 25
Step-by-step explanation:
In order to find a percentile of a given number set, you must first put the values in ascending order:
18, 20, 22, 25, 26, 36, 37, 41, 45, 50
70% = 0.7
Since there are 10 numbers in the set, we'll multiply 10 by 0.7
10 × 0.7 = 7
So we are going to look at the seventh number in the set.
18, 20, 22, 25, 26, 36, 37, 41, 45, 50
1 2 3 4 5 6 7 8 9 10
The seventh number in the set is 37.
We're going to do the same for finding the 40th percentile:
40% = 0.4
10 × 0.4 = 4
Finding the fourth number in the set...
18, 20, 22, 25, 26, 36, 37, 41, 45, 50
1 2 3 4 5 6 7 8 9 10
... We get 25
And those are you answers, 37 and 25.
OH ⊥ BC , OB=10, OH=6, EF=9, AB=2 Find: AE.
Answer:
AE = 3
Step-by-step explanation:
A soccer ball is kicked off from the ground in an arc defined by the function, h(x)=-8x^2+64x. At what point does the ball hit the ground?
(0,4) , (0,8) , (4,0) , (8,0)
Answer:
(8,0)
Step-by-step explanation:
The equation that models the path traced by the ball is
[tex]h(x)=-8x^2+64x[/tex]
To find the point at which the ball hit the ground, we must equate the function to zero.
[tex]-8x^2+64x=0[/tex]
Factor;
[tex]-8x(x-8)=0[/tex]
[tex]-8x=0,(x-8)=0[/tex]
This implies that;
x=0,x=8,
At x=0, the ball was not yet kicked.
So we take x=8, to be the time the ball hit the ground.
We substitute x=8 into the function to get;
[tex]h(8)=-8(8)^2+64(8)=0[/tex]
Hence the point at which the ball hit the ground is (8,0)
I really need help with these three questions, urgent!
6.
Intersecting chords:
RT x ST = PT x TQ
2 x 6 = 3 x TQ
12 = 3TQ
TQ = 12/3
TQ = 4
7.
AD = 90 -BE = 90-18 = 72
ADE = 180. DE = 180 - AD = 180-72 = 108
AE = 180. AB = 180-18 = 162
DE = 108
BD = BE +DE = 18 + 108 = 126
DAB = 72 + 162 = 234
ADE = 90 degrees
8.
AB^2 = BC* (BC +x)
8^2 = 2 * (2 +x)
64 = 4 + 2x
60 = 2x
X = 60/2
X = 30
what is the perimeter of the figure
Answer:
As we can see in the picture, we already knew 4 out of 6 sides of the figure so we need to find the other sides.
So the first missing side (the one near the 3 m one) should be:
7 - 4 = 3 (m)
The second missing side (the one near the 4m one) should be:
6 - 3 = 3 (m)
Now that we know all of the side lengths of the figure, the perimeter of the figure will be:
7 + 3 + 3 + 3 + 4 + 6 = 26 (m)
You are asked to draw a triangle with the side lengths of 6 inches and 8 inches. What is the longest whole number length that you're third side can be?
Answer:
13
Step-by-step explanation:
The longest side must be less than the sum of the shorter sides:
c < a + b
c < 6 + 8
c < 14
So the largest whole number length is 13.
Please help this is my last question
Answer:
y = 90°
Step-by-step explanation:
The angle y subtends an arc of 180°, so its measure is 180°/2 = 90°. (We know the arc is 180° because the end points of it are on a diameter, so it is half a circle.)
A circle has a radius of 119.3 millimeters. What is the circumference of this circle? Use 3.14 for pi. Round your final answer to the nearest tenth.
Answer:
0.74 m
Step-by-step explanation:
The distance around a circle on the other hand is called the circumference (c).
A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d) .
Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).
The circumference of a circle is found using this formula:
C=π⋅d
or
C=2π⋅r
Given r = 119.3 mm
So, C = 2 * 3.14 * 119.3 = 749.2 mm = 0.74 m
A 12-foot ladder is leaning up against a wall, as shown. how high does the ladder reach up the wall when x is 30°? 45°? 60°? round decimal answers to the nearest tenth, if necessary.
Answer:
6ft for 30°
8.5ft for 45°
10.4ft for 60°
Step-by-step explanation:
12(sin 30°)=x
x=6
12(sin 45°)=x
x=8.5
12(sin 60°)=x
x=10.4
By using right angle trigonometry and the cosine function (x = L cos θ), we find that a 12-ft ladder reaches 10.4 ft, 8.5 ft and 6 ft up a wall when it is leaned at 30°, 45° and 60° respectively.
Explanation:The problem described here involves the use of right angle trigonometry, specifically the use of the cosine function. In order to determine how high up the wall the ladder reaches at an angle of 30°, 45° and 60°, we can use the formula: x = L cos θ.
Firstly, let's calculate the height at 30 degrees (θ = 30°). We know that cos 30° = √3/2, so we substitute into the formula: x = 12ft * √3/2 which approximately equals 10.4 ft.
Next, for 45 degrees (θ = 45°), cos 45° = √2/2. Substituting into the formula: x = 12ft * √2/2 = 8.5 ft.
Finally, for 60 degrees (θ = 60°), cos 60° = 1/2. Therefore, x = 12ft * 1/2 = 6ft). So, the ladder reaches 10.4 ft up the wall when the angle is 30°, 8.5 ft when the angle is 45°, and 6 ft when the angle is 60°.
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Hannah and Heather are sisters. Hannah's age is four less than twice Heather's age. The sum of their ages is 30. Which system of equations can be used to determine Hannah's age, x, and Heather's age, y?
A.
x + 30 = y
x = 2 - 4y
B.
x + y = 30
x - 2y = 4
C.
x + y = 30
x = 2y - 4
D.
x + y = 4
y = 30 - 2x
Let Hannah = X and Heather = Y.
The sum of their ages is 30, so you would have x + y = 30
Then Hannah's age is 4 less than 2 times Heather's age so X = 2y-4
The equations are :
X + Y = 30 and X = 2y - 4
The answer is C.
200 tickets were sold to a concert. Floor seats cost $32 and stadium seats cost $20. Ticket sales totaled $5440. Find how many of each type we’re sold.
Answer:
120 floor seats, 80 stadium seats
Step-by-step explanation:
use extreme values
if all were floor seats, then cost would be 32*200, or 6400
6400-5440=960
32-20=12
960/12=80
200-80=120
120 floor seats and 80 stadium seats were sold.
Let's designate F as the number of floor seats and S as the number of stadium seats.
Given :
F + S = 200 (Equation for the total number of tickets)
32F + 20S = 5440 (Equation for the total sales amount)
We can use substitution or elimination to solve this system. If we multiply the first equation by 20 to get
20F + 20S = 4000
and subtract it from the second equation, we get:
12F = 1440
F = 120
We found the number of floor seats sold. We can then substitute F back into the first equation to find the number of stadium seats:
120 + S = 200
S = 80.
So, 120 floor seats and 80 stadium seats were sold.