Answer:
0.5km
Step-by-step explanation:
[tex]1km = 1000m \\ x = 50m \\ \\ 50m \times 1km = x \times 1000m \\ x = 0.5km[/tex]
2. The value of C when y= 2x+C is tangent to the parabola y²=8x is: (a)-1 (b) 1 (c) 2 (d)-2
Answer:
B. The value of C is 1
Step-by-step explanation:
Given:
[tex]\displaystyle \large{y=2x+C}\\\displaystyle \large{y^2=8x}[/tex]
y = 2x + C is a tangent to parabola y² = 8xTo find:
value of CA line being a tangent to curve means both equations are equal but there has to be only one interception between both graphs.
Therefore, substitute y = 2x+C in y² = 8x:
[tex]\displaystyle \large{(2x+C)^2 =8x}[/tex]
Expand the expression (2x+C)² using perfect square:
[tex]\displaystyle \large{4x^2+4xC+C^2=8x}[/tex]
Simplify the equation:
[tex]\displaystyle \large{4x^2+4xC-8x+C^2=0}\\\displaystyle \large{4x^2+(4C-8)x+C^2=0}[/tex]
The discriminant says:
If b²-4ac > 0 then there are two real rootsIf b²-4ac = 0 then there is only one real rootIf b²-4ac < 0 then the are no real rootsFor this, we choose b²-4ac = 0 since tangents only have one intersection.
[tex]\displaystyle \large{b^2-4ac = (4C-8)^2-4(4)C^2 = 0}\\\displaystyle \large{16C^2-64C+64-16C^2=0}\\\displaystyle \large{-64C+64=0}[/tex]
Solve the equation for C:
[tex]\displaystyle \large{-64C=-64}\\\displaystyle \large{C=1}[/tex]
Therefore, the value of C is 1
what is this its to hard :|
Answer:
25
Step-by-step explanation:
We take both medians and subtract.
53-28=25
Can yall help me with this pls
What is the square root of a number if it is in ratio form
The square root of 25 is 5. It is the positive solution of the equation x2 = 25. The number 25 is a perfect square.
...
Square Root of 25 in radical form: √25.
The difference between two consecutive cube numbers is always odd or even?
Answer:
odd
Step-by-step explanation:
take example of 2^3 +3^3 it's odd
now others try yourself
According to the rules of NCAA volleyball, there must be exactly 6 players on the court at all times and each player has a unique designated position on the court. How many different starting position configurations are possible for the 6 starting players of an 8-member volleyball team that follows this rule? Please answer quick.
Answer:
20160Step-by-step explanation:
This is a permutation of 6 out of 8
Use formula
P(n, r) = n!/(n-r)!Find the number of starting positions
P(8,)6 = 8!/(8 - 6)! = 8!/2! = 1*2*3*4*5*6*7*8/1*2 = 20160I need help it's due tomorrow!!!!
Answer:
56
Step-by-step explanation:
All You Need To Do Is Count intill You Reach That Point
A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, “ In addition to the 60% discount you are receiving for purchasing these items on sale today you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!
If we were getting 60% discount early and then again we are receiving 20% discount for using credit card then it means that we are getting 80% discount.
What is discount?Discount means the amount which is deducted by sellers from the amount to be payable by buyers.
How to calculate discount?Let the total price to be paid by us to store is $100.
Discount received because on purchase on sale day=100*60%
=60
Discount received due to use of credit card=100*20%
=20
Total discount received from store=60+20
=80
Percentage=80/100*100
=80%
Hence the total discount received by us from store is 80%.
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The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is y+7= -5/2(x-10)What
is the standard form of the equation for this line ?
One way we can organize a linear equation is in standard form:
[tex]Ax+By=C[/tex]
A, B and C are typically integersAnother way we can organize a linear equation is in point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m is the slope[tex](x_1,y_1)[/tex] is a point that falls on the lineSolving the QuestionWe're given:
Line passes through (-5,-1) and (10,-7)Point-slope form is [tex]y+7=-\dfrac{5}{2}(x-10)[/tex]We only need the point-slope form equation to find the stand form of the equation for this line. All we have to do is rearrange the numbers to get them in the right places.
[tex]y+7=-\dfrac{5}{2}(x-10)[/tex]
⇒ First, multiply both sides by 2 to get rid of the fraction:
[tex]2y+14=-5(x-10)[/tex]
⇒ Now, open up the parentheses:
[tex]2y+14=-5x+50[/tex]
⇒ Move -5x to the other side:
[tex]5x+2y+14=50[/tex]
⇒ Move 14 to the other side:
[tex]5x+2y=50-14[/tex]
⇒ Combine like terms:
[tex]5x+2y=36[/tex]
Answer[tex]5x+2y=36[/tex]
Pls help me
Pls show your answer pls and thank you
Answer:
Step-by-step explanation:
Beth's position over time is constant, which makes the problem a lot easier. You are asked for the rate of position versus time, so begin by doing that. Since the rate is constant, clearly from the table, you can take any two data points and take their ratio. Her rate would be 11 feet every 5 seconds, or equivalently 2.2 feet every second. To graph the data, put position on the x-axis and time on the y-axis. The slope will be 2.2 at every point along her bike ride.
Moving on to the third part. If Amy traveled at a rate of 75 feet every 30 seconds, then she would be traveling 2.5 feet every second. Amy's rate is larger than Beth's rate. Since the rate corresponds to the slope of the postion vs. time graph, Amy's graph will have a steeper incline since the slope is 2.5
solve
-2(x + 2)(x - 1)
Answer:
-2x^2 -2x + 4
Step-by-step explanation:
Distributive prop.
(-2x-4)(x-1)
-2x^2 + 2x - 4x + 4
-2x^2 -2x + 4
The cost of beef decreases weekly at a rate of 10.2%. If beef cost $15.75 per pound today. How much will it cost in 2 years? ( round to the nearest cent (2 decimal places) )
Answer:
$ 383 854.28 per pound ====> See below !!
Step-by-step explanation:
Increases 10.2 % per WEEK (?? Per WEEK?))
2 years is 104 weeks (this is going to be a HUGE number)
15.75 (1+.102)^104 =
If increase is YEARLY
15.75 ( 1 + .102)^2 = $ 19.13 per pound <<<<after two years
Is 10, 20, 40, 80... an arithmetic sequence?
Answer:
No.
Step-by-step explanation:
A arithmetic sequence is a sequence of numbers that go up by the same value each time. We can clearly see that this set of numbers does not go up by the same value each time, therefore ruling it out as an arithmetic sequence. This sequence is a geometric sequence in case you're wondering.
A standard deck of cards has 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) in each
of 4 suits (hearts, clubs, diamonds, spades). The hearts and diamonds cards are red. The
clubs and spades cards are black. You choose a card from a standard deck of cards at
random. What is the probability that you do not choose a club?
The probability that you do not choose a club is
Answer:
3/4
Step-by-step explanation:
Prob to pick a club is 13/52
Prob not to pick a club is 1 - 13/52
1 - 13/52 = 3/4
On the map below 1/4 inch represents one mile. Candler, Canton, and Oteen are three cities on the map. If Candler and Oteen are 3 1/2 inches apart on the map, what is the actual distance between Candler and Oteen in miles?
14 miles
Step-by-step explanation:Let "Candler" be known as "C" and "Oteen" as "O"
Given:
0.25 inch = 1 mileDistance between "C" and "O" (In inches): 3.5 inches3.5 ------> 3.50
⇒ Distance between "C" and "O" (In inches): 3.50 inchesComparing the rate (inches/mile) and the distance:
⇒ 0.25x = 3.50Multiplying both sides by 100:
⇒ 25x = 350Clearly, 350 is divisible by 25 as "50" is divisible by 25.
Divide both sides by 25 to isolate x:
⇒ 25x/25 = 350/25⇒ x = 14The actual distance between the two cities is 14 miles.
Answer:
14 miles
Step-by-step explanation:
Given:
[tex]\sf Scale=\dfrac14\:in : 1\:mile[/tex]distance between Candler and Oteen is 3 1/2 inLet [tex]x[/tex] be the distance between Candler and Oteen in miles.
[tex]\implies \dfrac14:1=3 \frac12:x[/tex]
[tex]\implies \dfrac{\frac14}{1}=\dfrac{\frac72}{x}[/tex]
[tex]\implies \dfrac14x=\dfrac72[/tex]
[tex]\implies x=\dfrac72 \div \dfrac14[/tex]
[tex]\implies x=\dfrac72 \times \dfrac41[/tex]
[tex]\implies x=\dfrac{28}{2}[/tex]
[tex]\implies x=14[/tex]
A rectangular tabletop will be made of maple
wood that weighs 43 pounds per cubic foot. The
tabletop will have a length of eight feet, a width
of three feet, and a thickness of one inch.
Determine and state the weight of the tabletop,
in pounds.
A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot. The weight of the tabletop, in pounds, is 1032.
What is the volume of the rectangular tabletop?The volume of the rectangular tabletop is the product of the length, breadth, and height of the given tabletop.
Volume of rectangular tabletop= (length x width x height)
The tabletop will have a length of eight feet, a width of three feet, and a thickness of one inch.
Volume of rectangular tabletop= (length x width x height)
= [tex]8 \times 3 \times 1\\\\24[/tex]
A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot.
The weight of the tabletop, in pounds = 43 x 24
= 1032 pounds
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A regular hexagon has an area of approximately
20 square centimeters. If the apothem measures
2.4 centimeters, find the approximate length of
each side.
Answer:
The side is approx 2.78cm
Step-by-step explanation:
There is an area formula for regular polygons that uses the apothem:
A = 1/2•a•s•n
a is the apothem.
s is the side length.
n is the number of sides.
The area, A is given and also the apothem is given, as well as the number of sides.
The shape in your problem is a hexagon, so it has 6 sides.
A = 1/2 asn
20 = 1/2(2.4)s(6)
Multiply.
20 = 7.2s
Divide.
20/7.2 = s
2.78 = s
s = 2.78
Change the following fraction to a mixed number with the fraction part reduced to lowest terms. 84/42
Answer:
2
Step-by-step explanation:
since you have 84/42, and you are supposed to convert the improper fraction to a mixed number, the easiest place to start is to divide the two numbers and find the remainder. In this case, however, there is no remainder, as 84 divided by 42 is exactly 2. Therefore, the most simplified fraction would be 2 (although it does not look like a fraction the most simplified form of the fraction is 2/1 --> which is just 2). Hope this helps!
[-32] <,>,= [15] what is the answer
Answer:
-32 < 15
Step-by-step explanation:
Whenever in the negatives, it's always less than zero. Because 15 is positive, it would be greater than -32.
Use log 2=a, log 3=b to evaluate log 216
Answer:
answer = 3(a +b)
Step-by-step explanation:
[tex] log(2) = a \: log(3) = b \: \: \\ log(216) = log(2 \times 2 \times 2 \times 3 \times 3 \times 3) \\ = log( {2}^{3} \times {3}^{3} ) \\ = log(2^{3} ) + log( {3}^{3} ) \\ = 3 log(2) + 3 log(3) \\ = 3(a) + 3(b) \\ = 3(a + b) \\ \\ log(216) = 3(a + b)[/tex]
Really need help anybody!?!
Answer:
it's got to be 3........
What does 4! Equal?show the equation and what it equals
Answer:
[tex]\boxed{\sf{24}}[/tex]Step-by-step explanation:
To solve this problem, first, you have to use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract4!Use the fractional rule.
[tex]\Longrightarrow: \sf{n!= 1*2*3*4}[/tex]
First, multiply.
1*2=2
2*3*4
2*3=6
6*4=24
[tex]\Longrightarrow: \boxed{\sf{24}}[/tex]
Therefore, the correct answer is 24.I hope this helps. Let me know if you have any questions.
The prism below is made of cubes which measure 1/2 of an inch on one side. What is the volume?
Note: Figure is not drawn to scale.
OA. 15/2 cubic in
OB. 6 cubic in
OC. 30 cubic in
OD. 60 cubic in
the answer is B. 6 cubic in
|x-20| if x<-20
I need help with the opposite equation
Find the value of X.
Answer:
Step-by-step explanation:
Vertically opposite angles are congruent.
-2x - 6 = 40
Add 6 to both sides
-2x = 40 + 6
-2x = 46
Divde both sides by (-2)
x = 46/(-2)
x = -23
if X varies inversely as the cube root of y and X=1 when y=8. find y when X =3
Answer:
The work is straight forward once you know the formular
Here are the test scores for 15 students in Mr. M's class.
96, 85, 59, 63, 76, 68, 94, 97, 89, 100, 93, 96, 72, 46, 78
What is the percentage of these test scores that are less than 90?
Answer:
60%
Step-by-step explanation:
If you look through the data, it is clear that 46, 59, 63, 68, 72, 76, 78, 85, and 89 are all less than 90. There are 9 elements total that are less than 90.
For percentages, you take the number you have and divide by the total. Since we know that there are 15 students, we can do 9 / 15. This gives us 0.6 which is 60%
Help! This one step for solving standard deviation I don't understand...
When I got it wrong it tells me what to do but I don't get it? (2nd image)
x = 10
hope it helps...!!!
solve for x ~
[tex]x {}^{2} - 16x = 0[/tex]
thankyou ~
Step-by-step explanation:
Mark me brainliest please[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
[tex]\qquad \tt \dashrightarrow \: {x}^{2} - 16x = 0[/tex]
[tex]\qquad \tt \dashrightarrow \: x(x - 16) = 0[/tex]
Now, there are two possibilities ~
[tex]\qquad \tt \dashrightarrow \:x = 0[/tex]
or
[tex]\qquad \tt \dashrightarrow \:x - 16 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 16[/tex]
50 points each question. Please help. How do I solve?
[tex]~~~~~7e^{xy} +2x^2 -4y^2 =13\\\\\\\implies \dfrac{d}{dx}\left(7e^{xy} +2x^2 -4y^2\right) =\dfrac d{dx} (13)\\\\\\\implies 7\left[e^{xy} \dfrac{d}{dx} ( xy)\right] +2 \cdot 2x -4\cdot 2y \dfrac{dy}{dx} = 0\\\\\\\implies 7e^{xy} \left( x \dfrac{dy}{dx} +y\right) +4x -8y \dfrac{dy}{dx} =0\\\\\\\implies 7xe^{xy}\dfrac{dy}{dx} + 7ye^{xy} +4x -8y\dfrac{dy}{dx} = 0\\\\\\\implies \left(7xe^{xy} -8y \right) \dfrac{dy}{dx}=-7ye^{xy} -4x\\\\\\[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{-7ye^{xy} -4x}{7xe^{xy} -8y }[/tex]