16. A car leaves a parking lot and travels directly north for
6 miles. It then turns and travels 8 miles east. How many
miles is the car from the parking lot?
Answers
Answer:
The car is 10 miles from parking lot.
Step-by-step explanation:
Given that:
The car travels 6 miles north and 8 miles east.
This forms the two legs of a right angled triangle.
The distance from car to parking lot will be hypotenuse.
Using Pythagorean theorem;
\(a^2+b^2=c^2\\(6)^2+(8)^2= c^2\\c^2 = 36 + 64 \\c^2 = 100\)
Taking square root on both sides
\(\sqrt{c^2}=\sqrt{100}\\c=10\)
Hence,
The car is 10 miles from parking lot.
Related Questions
What can you do to solve the equation x/5 = -2
Answers
Answer: x=-10
Step-by-step explanation:
Given that x/5=-2
multiply both sides of equation with 5
(x/5)*(5)=(-2)*(5)
x=-10
Need Help please, here is screenshot
Answers
1)
The axis of symmetry is x = -6.
2)
Vertex is (-6, 26).
3)
f(x) has a maximum value.
4)
f(x) is concave down.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
f(x) = -x² - 12x - 10
This is in the form of ax² + bx + c.
a = -1, b = -12, c = -10
The axis of symmetry is x = -b/2a
x = 12/(-2)
x = -6
Now,
f(x) = -x² - 12x - 10
f(x) = -(x² + 12x + 10)
f(x) = - { (x² + 12x + 36) - 36 + 10}
f(x) = -(x + 6)² + 26
This is in the form of f(x) = a (x - h)² + k
a = -1, h = -6, k = 26
Vertex = (h, k) = (-6, 26)
Now,
f(x) = -x² - 12x - 10
f'(x) = -2x - 12
f''(x) = -2
It is a negative value.
This means f(x) has a maximum value.
Now,
From the graph, we see that f(x) is concave down.
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I don’t know how to do this and I need know know how quick!!
Answers
600 raffle tickets were sold. There will be one first prize of $500 and three second prizes of $200. The rest of the tickets will win nothing. Use the chart to calculate the expected value.
Answers
The expected value of the tickets is -$3.17.
What is the expected value?Expected value (EV), which is based on a random variable's probability distribution, describes the long-term average level of that variable. The expected value of a stock or other investment is a crucial factor in investing and is taken into account while performing scenario analysis.An expected value provides a rapid understanding of a random variable's behavior without requiring knowledge of its discreteness or continuity. The probability distributions of two random variables with the same expected value can so vary.So, we can calculate as:
500-5=495200-5=195The remainder of the tickets is -$5.
The expected value is $495 x 1/600 + $ 19583/600 + (-$5) 596/600= -$3.17.
Therefore, the expected value of the tickets is -$3.17.
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Iff (x) = 3x + 2 and g(x) = x? – x, find the value.
=
f (4)
Answers
I hope this helps (:
Which expressions are equivalent to -4(3d-2)-7
Answers
Answer:
C, none of the above
Step-by-step explanation:
-4(3d-2) after expression should be -12d+8 and then add -7, so combine like terms would be -12d+1, which is not the choice, so the answer is none of the above.
Answer:
The answer is C (none of the above)!
Step-by-step explanation:
calculate the percentage change of a movie tickets of $6 is now $8?
Answers
Answer:
33.33%
Step-by-step explanation:
Formula for calculating Percentage change =
New Price - Old Price x 100
Old Price 1
Where new price is $8
Old Price is $6
Step 2: Input the variables in the above formula
$8 - $6 x 100
$6 1
= $2 x 100
$6
= $0.333 x 100 = 33.33%
Percentage change = 33.33%
Bruce's hourly wage increased from $12.00 to $13.00. What is the percent of increase?
Answers
Answer:
13-12 = 1
1/12 = 0.08333... = 8 1/3%
Step-by-step explanation:
plz mark branliest
SOMEONE HELP ME PLEASE
The XYZ Car Rental Agency charges a flat rate of $29 per day plus $0.32 per mile driven. Write an algebraic expression for the rental cost of a car for x days that is driven y miles.
Answers
Answer:
Total Cost = 29x + 0.32y
Step-by-step explanation:
It is 29x since you pay $29 per day, and x represents the number of days.
It is 0.32y since you pay $0.32 per mile, and y represents the number of miles.
a passenger train leaves a railway station at 12 p.m and travels 3 hours on the Northbound tracks. A second passenger train leaves the same railway station at 12:45 p.m. and travels 2 hours and 15 minutes on the southbound tracks at a speed of 20 kilometers per hour faster than the first train. At 3:00 pm the two trains were 360 kilometers apart. How fast was each train traveling? include units in answer
Answers
Answer:
Step-by-step explanation:
Train A is northbound at S km/hr S = speed and travels for 3 hours
S is the speed of Train A
Train B is southbound at (S + 20) km/hr
Train B starts later 45 min and travels for 2 and 1/4 hours so 3/4 hour plus 2 1/4 hour equals 3 hours
After 3 hours since Train A left the station Train A and Train B are 360 km apart
A + B = 360 km Equation 1
A = S km/hr x 3 hr
B = (S +20) km/hr x (2 1/4) hr
Plug A and B into the first equation
3S (km/hr) + (2 1/4)(S + 20) (km/hr)= 360 km
3S + (9/4)(S + 20) = 360 i dropped the units to make easier to read
3S + 9S/4 + 180S/4 = 360 I just multiplied 9/4 time the S +20
12S + 9S + 180 = 1440 multiply both sides by 4
12S + 9S = 1440 - 180 subtract 180 from both sides
21S = 1260 collecting terms
S = 60 km/hr S = Speed of Train A equal 60 km/hr I added the units back into the answer
S + 20 is the speed of
Train B = 80 km/hr
Extra credit
now using the same train speeds, if Train B was now headed NORTH, a what time would it crash into Train A?
S km/hr x T hr = (S+20) km/hr x (T-3/4) hr solve for T T = time in hr
When is Train A equal the same location as Train B
Trani A = Train B don't forget the start time differential
ST = (S + 20)(T-3/4) plug in train a and b speeds
60T = 80(T-3/4)
60T = 80T - 60
60 = 80T - 60T
60 = 20T
3 = T
after 3 hrs Train B will catch Train A
2. 7 cm In triangle ABC, AC = 7 cm, BC = 10 cm, angle ACB = 73° C 73° 10 cm Calculate the length of AB Give your answer correct to 3 significant figures. Diagram NOT accurately drawn B (Total 3 marks
Answers
Answer:
AB = 10.398
Step-by-step explanation:
By cosine rule, we have:
AB² = AC² + BC² - 2(AC)(BC)cos(ACB)
⇒ AB² = 7² + 10² - 2(7)(10)cos(73)
⇒ AB² = 49 + 100 - 140cos(73)
⇒ AB² = 149 - 140cos(73)
⇒ AB² = 149 - 140cos(73)
⇒ AB² = 149 - 140(0.292)
⇒ AB² = 149 - 40.88
⇒ AB² = 108.12
⇒ AB = √(108.12)
⇒ AB = 10.398
what is the answer to x+2=17-4x
Answers
Answer:
x = 3
Step-by-step explanation:
Move all terms containing x to the left
5x + 2 = 17
Move all terms not containing x to the right
5x = 15
Divide each term by 5 and simplify
x = 3
Jared draws a rectangle. Explain how
to find the area using the Distributive
9 ft length
5 ft height
Answers
45 feet is the answer
A right triangle has side lengths 6 centimeters and 8 centimeters. Is it possible for there to be more than one right triangle with whole-number side lengths that includes the given side lengths? Explain.
Answers
The given side lengths, 6 cm and 8 cm, satisfy the Pythagorean theorem because $6^2 + 8^2 = 100 = 10^2$, which means that the triangle is a right triangle.
To determine if there is more than one right triangle with whole-number side lengths that includes these given side lengths, we need to check if there exist other pairs of whole numbers that satisfy the Pythagorean theorem and include 6 cm and 8 cm as two of their sides.
Let's call the third side of the right triangle x. Then we have:
62+82=x26^2 + 8^2 = x^262+82=x2
which simplifies to:
36+64=x236 + 64 = x^236+64=x2
100=x2100 = x^2100=x2
x=100=10x = \sqrt{100} = 10x=100
=10
So the only other possible triangle with whole-number side lengths that includes the given side lengths has side lengths of 6 cm, 8 cm, and 10 cm.
Therefore, there is only one other right triangle with whole-number side lengths that includes the given side lengths, and it is unique.
At the movie theater, child admission is $5.30 and adult admission is $9.90. On Wednesday, 172 tickets were sold for a total sales of $1344.00. How many child tickets were sold that day?Number of child tickets:?
Answers
We have
x- number of child admissions
y= number of adult admissions
Therefore we have the next equation
x+y=172
5.30x+9.90y=1344
We isolate x from the first equation
x=172-y
we susbtitute in the second equation
5.30(172-y)+9.90y=1344
we simplify
911.6-5.30y+9.90=1344
4.6y=1344-911.6
4.6y=432.4
y=432.4/4.6
y=94
Then we substitute y in the equation with x isolated
x=172-94=78
ANSWER
The number of child tickets is 78
7(6x-1)+x=36
Please help
Answers
Answer:
x=1
I think that's what you're looking for.
Isolate the variable by dividing each side by factors that don't contain the variable.
Good luck, hope this helped.
What is your favorite song and why? Does it mean something to you or do you just enjoy the sound of it/the lyrics? Enjoy the points :)
Answers
Answer:
Step-by-step explanation:
my favorite song is Sia's unstoppable song. I think it conveys a lot of energy and always while I listen to it I get points and am inspired to do better.
-16 + the quotient of a number and 2 is 35
Answers
Answer:
Step-by-step explanation:
Hamid has 20 T-shirts. The information shows the colours of his T-shirts. 7 black 4 red 1 light blue 2 grey Hamid is going to take one of his T-shirts at random. a) What is the probability that the T-shirt will be grey? b) What is the probability that the T-shirt will not be red? c) He takes one of his blue T-shirts at random. What is the probability that the T-shirt is light blue? 4 dark blue 2 white
Answers
Answer:
a) The probability that the T-shirt will be grey is 2/20 or 1/10. This is because Hamid has 2 grey T-shirts out of 20 total T-shirts.
b) The probability that the T-shirt will not be red is 1 - (4/20) or 16/20, which can be simplified to 4/5. This is because Hamid has 4 red T-shirts out of 20 total T-shirts, so the probability of not selecting a red T-shirt is equal to the probability of selecting one of the 16 non-red T-shirts.
c) Hamid has only one light blue T-shirt out of the total 20 T-shirts. So, the probability of selecting a light blue T-shirt is 1/20.
Answer:
Step-by-step explanation:
a) The probability that Hamid pulls out a grey T-shirt is 2/20, or 1/10 in simplified form since there are 2 grey T-shirts out of 20 total.
b) The probability that the T-shirt will not be red is 16/20, or 4/5 in simplified form since there are 4 red T-shirts and 16 T-shirts that are not red.
c) Hamid has only 1 light blue T-shirt out of the 20 total T-shirts. So, the probability that he takes out the light blue T-shirt is 1/20. Note that the numbers of dark blue and white T-shirts are not needed to answer this question.
Suppose that a loan of $5500 is given at an interest rate of 13% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
(b) Find the amount owed at the end of 2 years.
?
Answers
Answer:
11,990
9% of 5500 is 495
(495+5500) [one year] x 2 [two years] = $11,990
At the end of 2 years, Aldo will owe $11,990.
Hope it helps
Graph the function f(x) = x^3+2x^2-3
Answers
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
Answers
W(x) - C(x) = 2(W(x) - C(x))
Solving this equation for C(x), we get:
C(x) = (W(x) - 2W(x))
= W(x)(1 - 2)
= (5x3 + 9x2 - 14x + 9)(1 - 2)
= (5x3 + 7x2 - 14x + 6)
Therefore, the function C(x) to model the water used by the car wash on a shorter day is:
C(x) = (5x3 + 7x2 - 14x + 6)
There are 4 pink, 5 yellow, 2 violet and 3 gray marbles
in a hat. You pick 2 marbles from the hat. Marbles are
NOT returned to the hat.
P(pink, then violet)
P(gray, then gray)
P(not yellow, not yellow)
P(yellow, not yellow)
Answers
================================================
Work Shown for problem 1
P(pink, then violet) = P(pink)*P(violet given 1st was pink)
= (4/14)*(2/13)
= 8/182
= 4/91
------------------------------
Work Shown for problem 2
P(gray, then gray)
= P(gray)*P(gray given 1st was gray)
= (3/14)*(2/13)
= 6/182
= 3/91
-------------------------------
Work Shown for problem 3
P(not yellow, not yellow)
= P(not yellow)*P(not yellow given 1st was not yellow)
= (9/14)*(8/13)
= 72/182
= 36/91
-------------------------------
Work Shown for problem 4
P(yellow, not yellow)
= P(yellow)*P(not yellow given 1st was yellow)
= (5/14)*(9/13)
= 45/182
Which linear inequality is represented by the graph?
Answers
If 2x-y=9 and 3x+4y=19, then y=
Answers
Answer:
x = 5
y = 1
Step-by-step explanation:
2x - y = 9
3x + 4y = 19
We multiply the first equation by 4
8x - 4y = 36
3x + 4y = 19
11x = 55
x = 5
Now we put 5 in for x and solve for y
2(5) - y = 9
10 - y = 9
-y = -1
y = 1
Let's Check the answer
2(5) - 1 = 9
10 - 1 = 9
9 = 9
So, x = 5 and y = 1 is the correct answer.
A copy machine can print 480 copies every 4 minutes.
A teacher printed 720 copies. How long did it take to print?
Answers
Find the circumference of the circle. Use 3.14 for PI .
Circle Is 18 feet
Answers
Answer: pie
Step-by-step explanation: mcdonald.
yeet is good and feet is also good
AUTUMN ALSO SAVED $500 THAT SHE KEEPS AT HOME DOES NOT ADD TO IT WRITE A FUNCTION G(X) TO MODEL THIS SITUATION
Answers
The mathematical function that models Autumn's situation of saving $500 that she keeps at home and does not add to the savings is G(x) = 500 + 0x.
What is a mathematical function?A mathematical function is an equation, expression, rule, or law defining the relationship between the independent variable and the dependent variable.
There are many types of mathematical function, including:
Cubic functionLinear functionQuadratic functionPolynomial function.The amount that Autumn saved = $500
The amount that Autumn adds to the savings = $0
Let the number of periods that Autumn saves the above amount = x
Function:G(x) = 500 + 0x
Thus, based on the linear function above, the amount that Autumn saved would remain $500 after many periods.
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If a woman makes $32,000 a year receives a cost of living increase 2.2% what will her new salary be?
Answers
Answer:
$32 704
Step-by-step explanation:
(102.2÷100) × 32 000 = $32 704
They are attached below.
Answers
14)The sum of the tangent and the sine of the angle is obtained as 1.21.
15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.
16)The angle opposite the largest side is 130°.
What is the trigonometric ratios?The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.
14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;
a = √2^2 + 3^2
a = √ 4 + 9
a = 3.6
We know that;
tan θ = 2/3 = 0.66
sin θ = 2/3.6 = 0.55
Then;
tan θ + sin θ
0.66 + 0.55
= 1.21
We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.
15)
The area of the segment is obtained as;
Area of the triangle;
1/2r^2 sinθ
r= radius of the circle
θ = angle of inclination
1/2 * (10)^2 * sin 60
= 43.3
Area of the sector;
60/360 * 3.142 * (10)^2
= 52.3
Therefore the area of the triangle is;
43.3 + 52.3 = 95.6 m
b)The perimeter of the segment;
(2πr * θ/360) + 2rsin(θ/2)
(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))
1.047 + 10
= 11.047 m
16)
Using;
c^2 = a^2 + b^2 - 2abcos C
20^2 = 13^2 + 9^2 - 2(13 * 9) cos C
400 = 250 - 234cosC
400 - 250 = - 234cosC
150 = - 234cosC
Cos C = -(150/234)
C = Cos-1-(150/234)
C = 130°
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