Answer:
The function is y = -6 / x.
Step-by-step explanation:
Since (-2, 3) belongs to the function, we know that x = -2, y = 3 is a solution to the function so when we plug those values in to solve for a, we get:
3 = a / (-2)
3 * (-2) = a / (-2) * (-2)
-6 = a so the function is y = -6 / x.
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
which of the following could be the value of |x-3|+4 for some value of x? A) -2 B) 1 C) 3 D) 5
Answer:
5
Step-by-step explanation:
|x-3|+4
The minimum value that an absolute value can take is zero
0+4
4
The smallest value is 4
The answer must be 4 or greater
The only answer that is possible is 5
Chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine. a. About how much medicine did he make in grams? Estimate the amount of each chemical by rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.
Answer:
30.0g
Step-by-step explanation:
In order to determine the amount of each chemical to the nearest tenth of gram prior to computing the sum is shown below:
Like
10.357, 57 > 50, rounded to 10.4
12.062, 62 > 50, rounded to 12.1
7.506, 06 < 50, rounded to 7.5
Now
The Sum is
= 10.4g + 12.1g + 7.5g
= 30.0g
Hence, 30.0g medicine required to make in grams
Fill in the blank with a number to make the expression a perfect square.
u^2+8u+?
Answer:
16
Step-by-step explanation:
Hello, do you remember that result?
For any a and b real numbers,
[tex](a+b)^2=a+2\cdot a \cdot b+b^2[/tex]
In this example, we have.
[tex]u^2+8u=u^2+2\cdot 4 \cdot u\\\\\text{ This is the beginning of ... } u^2+8u+4^2=u^2+8u+16\\\\\text{ So, we need to add 16 to make a perfect square}\\\\u^2+8u+\boxed{16}=u^2+2\cdot 4\cdot u +4^2=(u+4)^2[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Both figures shown below are trapezoids. ABCD - WXYZ. Find the
value of y.
A
B
30 mm
7 mm
15 mm
30 mm
А
С
Z
15 mm
15 mm
X
D
30 mm
w
Answer:
Y*x -2x=40min
Three years from now Tom will be twice as old as Jean and two years ago the sum of their ages was 26. How old is Tom now?
Answer:
21
Step-by-step explanation:
Tom'age: a
Jean'age: b
3+a=2(b+3)
a-2+b-2=26
or
a =2b+3
2b+3-2+b-2=26
or
a=2b+3
3b=27
or
a=21
b=9
Thus the required present age of Tom and Jean is 21 years and 9 years.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the present age of Tom and Jean is x and y.
Three years from now Tom will be twice as old as Jean.
x + 3 = 2 ( y + 3 )
x = 2y + 6 - 3
x = 2y + 3 - - - - - - - - -(1)
two years ago the sum of their ages was 26.
x - 2 + y - 2 = 26
x + y = 26 + 4
x + y = 30 - - - - - - -(2)
From equation 1 put x in equation 2.
2y + 3 + y = 30
3y = 30 - 3
3y = 27
y = 9
Put y in equation 2
x + 9 = 30
x = 30 - 9
x = 21
Thus the required present age of Tom and Jean is 21 years and 9 years.
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Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
-Khan Academy
Answer:Astrid needs 280 tons of wood
Step-by-step explanation:
Because:
1 ship requires 40 tons of wood=accomodates 300 sailors
We must:
2100, sailors needed to be accomodated
÷
300, sailors that can be accomodated by 1 ship that requires 40 tons of wood
=7 groups of 300 sailors that can be accomodated by 1 ship that requires 40 tons of wood.
So:
I ship that requires 40 tons of wood × the 7, groups = 280 tons of wood.
I hope this helps! Im sorry its too complicated.
Simplier:
2100 ÷ 300= 7
40 × 7= 280
Answer:
280 tons of wood or 10 ships
Step-by-step
khan academy
what is y when X is 5? The Graph below shows the answer. Y=2 when X=10
━━━━━━━☆☆━━━━━━━
▹ Answer
Y = 1
▹ Step-by-Step Explanation
[tex]\frac{10}{2} = \frac{5}{y} \\\\10/5 = 2\\2/2 = 1\\\\Y =1[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 150 miles from the point and has a speed of 300 miles per hour. The other is 200 miles from the point and has a speed of 400 miles per hour.(a) At what rate is the distances between the planes decreasing?(b) How much time does the air traffic controller have to get one of the planes on a different flight path?
Answer:
The answer to this question can be defined as follows:
In option A, the answer is "- 357.14 miles per hour".
In option B, the answer is "-0.98".
Step-by-step explanation:
Given:
[tex]\frac{dx}{dt} =- 300 \text{ miles per hour}[/tex]
[tex]\frac{dy}{dt} =- 400 \text{ miles per hour}[/tex]
find:
[tex]\frac{ds}{dt} =?[/tex] when
[tex]x= 150 \\y= 200\\s=x+y\\\\[/tex]
[tex]= 150+200 \\\\=350[/tex]
[tex]\to s^2=x^2+y^2\\[/tex]
differentiate the above value:
[tex]\to 2s\frac{ds}{dt}= 2x \frac{dx}{dt}+2y \frac{dy}{dt}[/tex]
[tex]\to 2s\frac{ds}{dt}= 2(x \frac{dx}{dt}+y \frac{dy}{dt})\\\\\to \frac{ds}{dt}= \frac{(x \frac{dx}{dt}+y \frac{dy}{dt})}{s}\\\\[/tex]
[tex]= \frac{(150 \times -300 +200 \times -400 )}{350}\\\\= \frac{-45000+ (-80000) }{350}\\\\= \frac{- 125000 }{350}\\\\= - 357.14 \ \text{miles per hour}[/tex]
In option B:
[tex]\to d=rt\\\\ \to t= \frac{d}{r}[/tex]
[tex]\to \ \ d= 350 \ \ \ \ \ \ r= -357.14\\[/tex]
[tex]\to t= - \frac{350}{357.14}\\\\\to t= - 0.98[/tex]
Find all values of $x$ such that $3x^2 + 16x + 5=0$. If you find more than one value, then list your solutions, separated by commas.
answer
x = {-5, -⅓}
explanation
[tex]3 {x}^{2} + 16x + 5 = 0[/tex]
[tex]3 {x}^{2} + 15x + x + 5 = 0[/tex]
[tex]3x(x + 5) + 1(x + 5) = 0[/tex]
[tex](x + 5)(3x + 1) = 0[/tex]
[tex]x = - 5 \: or \: - \frac{1}{3} [/tex]
[tex]x = \{ - 5 \: , - \frac{1}{3} \}[/tex]
HOPE IT HELPS...
BRAINLIEST PLEASE ;-)Directions: Simplify each expression by combining like
Terms (pls help if u can )
Answer:
1. -y
3. 9a-7
5. 14x-2
7. 7d-6
Step-by-step explanation:
1. 8y-9y=-y
3. 8a-6+a-1
=(8a+a)-(6+1)
=9a-7
5. -x-2+15x
=(-x+15x)-2
=14x-2
7. 8d-4-d-2
=(8d-d)-(4+2)
=7d-6
Answer:
1. -x
3. 9a-7
5. 14x-2
7. 7d-6
Step-by-step explanation:
To do the first one you would just subtract 8 by 9 which is -1 so you would get -x as 1.
To do the third one would would just move the numbers around so you get 8a+a-6-1 and when you simplify you get 9a-7.
To do the fifth one you just have to move the numbers so you get -x+15x-2 and when you simplify you get 14x-2
To do the seventh one you just have to move the numbers so you get 8d-d-4-2 and when you simplify you get 7d-6.
a broker gets rs 20000 as commission from sale of a piece of land which costs rs 8000000. Find the rate of commission.
Answer:
0.25%
Step-by-step explanation:
Rate of commission
= (commission*100)/cost of land
=( 20000*100)/8000000
= 2000000/8000000
=2/8
= 0.25%
Side AB of square ABCD is parallel to the Y axis and the perimeter of ABCD is 36. If the coordinates of point B is (5,17) . What is the coordinates of Pont D ?
============================================
Explanation:
The perimeter of the square is 36, so each side length is 36/4 = 9 units.
Point B is located at (5,17). We move down 9 units to get to (5,8), which is the location of point A. Then we move 9 units to the right to arrive at (14,8) which is point D's location.
Or we could go from B = (5,17) to C = (14,17) and then to D = (14,8). Each time we move 9 units.
What is the volume of the sphere below?
500/3 π units
Step-by-step explanation
first state the formula wic is 4/3πr^3 then after u multiply 4 times the radius wic is
4×5^3
=500/3π units
Julissa is thinking about getting her Master’s degree. She will give up making $28,000 a year for the 2 years it takes to complete the program. She will also pay $34,000 in total costs to get the degree. Assuming that she will make $60,000 a year after she completes her degree, how long will it take for her to recover her investment?
Answer:
1.5 years
Step-by-step explanation:
She will give up making $28,000 per year for 2 years. This means that she will give up making $56,000 in total.
$28,000 × 2 = $56,000
She also pay $34,000 in total to costs to get her degree. She invested a total of $90,000.
$56,000 + $34,000 = $90,000
After graduating, she makes $60,000 a year. It will take her 1.5 years to recover her investment.
90,000/60,000 = 1.5
50 POINTS!!! Use the quadratic formula above to solve for h(t) = -4.9t^2 + 8t + 1 where h is the height of the ball in meters and t is time in seconds. Round to the nearest hundredth second!
Answer:
1.75 seconds
Step-by-step explanation:
Lets apply the quadratic formula-
- 8 +_ (sqrt of 64 + 19.6)
__________________
-9.8
-8 +_ 9.1433
__________________
-9.8
x = 1.74931972 ( since x can only be positive in real life situations like when throwing a ball)
x = 1.75 rounded in seconds
Answer:
Step-by-step explanation:
h(t)= -8±√8^2-4(-4.9)(1)/2(-4.9)
h(t)=-8±√64-19.6/ -9.8
h(t)=-8±√44.4 / -9.8
h(t)=-8±6.6633325/ -9.8
h(t)= 0.14
The height will be 0.14
The time will be 2.02 seconds per meter
Hope that helps.
solve for v. 27= -v/2
Answer:
v = -54
Step-by-step explanation:
27= -v/2
Multiply each side by -2
27 *-2= -v/2 *-2
-54 = v
Answer:
-54
Step-by-step explanation:
[tex]27=\frac{-v}{2}[/tex] .... Equation to start with
[tex]27 x 2= \frac{-v}{2} x2[/tex] ..... Cancelling out the denominator and multiplying on the other side
[tex]54 = -v[/tex] .... Multipling
[tex]-54 =v[/tex] ..... Solving for v, not -v, so bring the negative over to the other side
Hope you understood:)
Please Show your work, equations, etc. I will name Brainliest!!!! (: A pyramid has a square base that measures 10 feet on a side. The height of each face is five feet. What is the surface area of the pyramid?
Answer:
200 ft^2
Step-by-step explanation:
The surface area of the pyramid is the sum of the area of the base and the areas of the 4 congruent triangular sides.
SA = LW + 4 * bh/2
SA = 10 ft * 10 ft + 4 * (10 ft)(5 ft)/2
SA = 100 ft^2 + 2(50 ft^2)
SA = 200 ft^2
(P.S. It's impossible to make a pyramid with these dimensions.)
Answer:
[tex]\boxed{\sf 200 \ feet^2}[/tex]
Step-by-step explanation:
The 3D shape is a square-based pyramid.
The surface area of a square-based pyramid is given as:
[tex]\sf SA=2 \times (base \ length) \times (slant \ height) + (base \ length)^2[/tex]
Plug in the values.
[tex]\sf SA=2 \times 10 \times 5 + 10^2[/tex]
[tex]\sf SA=100 + 100[/tex]
[tex]\sf SA=200[/tex]
A company is making a new label for one of their containers. The container is a cylinder that is 9 inches tall and 5 inches in diameter. What is the area of the label that needs to be printed to go around the new container? Use π = 3.14.
Answer:
180.55 in².
Step-by-step explanation:
Data obtained from the question include the following:
Height (h) = 9 in.
Diameter (d) = 5 in
Pi (π) = 3.14
Area of the label =..?
Next, we shall determine the radius.
Diameter (d) = 5 in
Radius (r) =.. ?
Radius (r) = Diameter (d) /2
r = d/2
r = 5/2
r = 2.5 in.
Next, we shall determine the area of the label that needs to be printed to go around the new container by calculating the surface area of the cylinder.
This is illustrated below:
Height (h) = 9 in.
Pi (π) = 3.14
Radius (r) = 2.5 in.
Surface Area (SA) =.?
SA = 2πrh + 2πr²
SA = (2×3.14×2.5×9) + (2×3.14×2.5²)
SA = 141.3 + 39.25
SA = 180.55 in²
The surface area of the cylinder is 180.55 in².
Therefore, the area of the label that needs to be printed to go around the new container is 180.55 in².
Answer:
Step-by-step explanation:
i dont have the work but the answer is 182.6
Find the measure of a. A. 48 B. 90 C. 44 D. 84
Answer:
A. 48
Step-by-step explanation:
There is a diameter of the circle through point O. The bottom right angle is an inscribed and that intersects a diameter, so its measure is 90 deg.
a + 90 + 42 = 180
a + 132 = 180
a = 48
The measure of angle 'a' is 48°.
We need to find the measure of 'a'.
What is the circle theorem of diameter?Angles are formed by drawing lines from the ends of the diameter of a circle to its circumference from a right angle.
There is a diameter of the circle through point O. The bottom right angle is inscribed and that intersects a diameter, so its measure is 90°.
Now, a + 90°+ 42° = 180°
⇒a + 132°= 180°
⇒a = 48°
Therefore, the measure of angle 'a' is 48°.
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What is the 1st mistake...
Answer:
[tex]\huge\boxed{Step \ 3}[/tex]
Step-by-step explanation:
In Step # 3, We need to divide rather than to subtract. So, the first mistake is done in step 3.
Answer:
[tex]\Large \boxed{\mathrm{Step \ 4}}[/tex]
Step-by-step explanation:
[tex]20 +20 \div 4-2[/tex]
Division should be performed first, not subtraction.
[tex]20+5-2[/tex]
explain the difference between legs and the hypotenuse of a right triangle
Answer:
The difference between the legs and the hypotenuse of a right triangle is that the hypotenuse will always be the longest side. Also, it will always be less than the two legs added together.
Step-by-step explanation:
How many of the positive integer factors of 15552 are perfect squares? (WILL MARK BRAINLIEST IF CORRECT)
15552|2
7776|2
3888|2
1944|2
972|2
486|2
243|3
81|3
27|3
9|3
3|3
1
[tex]15552=2^6\cdot 3^5=(2^3\cdot3^2)^2\cdot 3[/tex]
[tex](3+1)\cdot(2+1)=4\cdot 3=12[/tex]
It's 12
In a chocolate chip cookie recipe flour,brown sugar, and chocolate chips are mixed in the ratio 5:3:4 if the total volume of the three ingredients is 720 ML how many mL of Chocolate chips are in the mix
Answer:
240 mL.
Step-by-step explanation:
The following data were obtained from the question:
Ratio of Flour = 5
Ratio of brown sugar = 3
Ratio of chocolate = 4
Total volume = 720 mL
Next, we shall determine the total ratio. This can be obtained as follow:
Total ratio = ratio of flour + ratio of brown sugar + ratio of chocolate
Total ratio = 5 + 3 + 4
Total ratio = 12
Finally, we shall determine the volume of the chocolate chips in the mixture as shown below:
Volume of chocolate chips = ratio of chocolate /total ratio x total volume
Ratio of chocolate = 4
Total ratio = 12
Total volume = 720 mL
Volume of chocolate chips =..?
Volume of chocolate chips = ratio of chocolate /total ratio x total volume
Volume of chocolate chip = 4/12 x 720
Volume of chocolate chip = 240 mL
Therefore, the volume of the chocolate chips in the mixture is 240 mL.
what is the value of x ?
Answer:
28 degrees
Step-by-step explanation:
there is a square in the corner which means it is a right angle, 90 degrees.
90-62=28
Answer:
28 deggrees
Step-by-step explanation
© A boy has N800. He spends N160. What
fraction of his original money does he have
ter
left?
Answer:
4/5
Step-by-step explanation:
[tex]800 - 160 = 640 \\ \frac{640}{800} = \frac{4}{5} [/tex]
URGENT! What is the period for the cotangent function? (Answer in radians.)
it is [tex]\pi[/tex]
since period of tangent is $\pi$ ,so the period of reciprocal will also be same
The period for the cotangent function is π radians.
How do I find the period of a function?
The period for function y = A sin(Bx + C) and y = A cos(Bx + C) is 2π/|B| radians. Frequency is described as the wide variety of cycles completed in one 2d. If the duration of a function is denoted via P and f is its frequency, then –f =1/ P.
What is the period of tangent and cotangent?The tangent function has period π. f(x)=Atan(Bx−C)+D is a tangent with vertical and/or horizontal stretch/compression and shift. The cotangent function has period π and vertical asymptotes at 0,±π,±2π, The range of cotangent is (−∞,∞), and the function is decreasing at each point in its range.
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Hii, can you help me ?
Answer:
100, 101, 102, 103, 104
Step-by-step explanation:
Basically, if the units (or ones, it's the same thing) digit of the first number is 0, the units digit of the second number should be 1, then 2, and so on. Therefore, one possible list of numbers is as follows: 100, 101, 102, 103, 104.
1) Complete the table
2) find the mean of the random variable x. Use the formula in the photo
Answer:
a. Please check the explanation for filling of the empty column on the table
b. The mean of the random variable x is 7/11
Step-by-step explanation:
a. Firstly, we are concerned with completing the table.
To do this, we simply need to multiply the values in the column of x by the values in the column of p(x)
Thus, we have the following;
2. 3 * 2/36 = 6/36
3. 4 * 3/36 = 12/36
4. 5 * 4/36 = 20/36
5. 6 * 5/36 = 30/36
6. 7 * 6/36 = 42/36
7. 8 * 5/36 = 40/36
8. 9 * 4/36 = 36/36
9. 10 * 3/36 = 30/36
10. 11 * 2/36 = 22/36
11. 12 * 1/36 = 12/36
b. We want to find the mean of the random variable x.
All what we need to do here is add all the values of x•P(x) together, then divide by 11.
Thus, we have
(2/36 + 6/36 + 12/36 + 20/36 + 30/36 + 42/36 + 40/36 + 36/36 + 30/36 + 22/36 + 12/36)/11
Since the denominator is same for all, we simply add all the numerators together;
(252/36) * 11 = 252/396 = 63/99 = 7/11
Micha is playing a game with five cards numbered 1 through 5. He will place the cards in a bag and draw one card at random three times, replacing the card each time. To win a prize, he must draw the number 5 all three times. What is the probability he will draw the number 5 all three times?
Answer: 0.008
Step-by-step explanation:
We have 3 experiments.
Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".
in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:
p = 1/5.
And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:
P = (1/5)*(1/5)*(1/5) = 1/125 = 0.008
