Answer:
Step-by-step explanation:
Slope is the rate of change. For us, this rate of change is inches of water per minute. If this rate of change is 2/1, that means that the rate is changing 2 inches every minute (aka The height of the water increases 2 inches per minute, first choice in your list of possibilities).
if f(x)=2x/x-5 find f^-1(x)
Answer:
[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = [tex]\frac{2x}{x-5}[/tex] ( multiply both sides by x - 5 )
y(x - 5) = 2x ← distribute left side
xy - 5y = 2x ( subtract 2x from both sides )
xy - 2x - 5y = 0 ( add 5y to both sides )
xy - 2x = 5y ← factor out x from each term on the left side )
x(y - 2) - 5y ← divide both sides by y - 2
x = [tex]\frac{5y}{y-2}[/tex]
Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]
Look into the image. I hope it helps❤
#CarryOnLearningFind d:
d=| 5 1 |
|-1 10 |
D= 51
[2 4 ]
[-3 9]
the determinant of the above matrix: 30
Answer:
D = 51, other = 30
Step-by-step explanation:
d = | 5 1 |
|-1 10|
D = (5 x 10) - ( 1 x -1) = 50 + 1 = 51
| 2 4|
|-3 9|
(2 x 9) - (4 x -3) = 18 + 12 = 30
Please help me!
The Farmer's Ranch House
9. The farmer's house is shown in the diagram below. He wants to build a screened-in patio on the back of his house.
Use the figure to answer the questions. (6 points)
a The area of the patio is planned to be (x + 10x - 200) square feet. What will the length be?
Patio
Patio
**10) - 0-10)
Original
House
b.
What is the area of the original house in simplest form?
Terigth
c
The farmer decides to extend the width of the patio. The area of the patio with the extension is now (x2 + 12x-160) square feet. By how
many feet will the patio be extended from what you found in part a?
Answer:
The answer is below
Step-by-step explanation:
a) The patio is in the form of a rectangle. The patio has a width of (x - 10) ft. Therefore given that the area of the patio is x² + 10x - 200, hence:
[tex]Area=length*breadth\\\\x^2+10x-200=length*(x -10)\\\\x^2+20x-10x-200=length*(x -10)\\\\x(x+20)-10(x+20)=length*(x -10)\\\\(x-10)(x+20)=length*(x -10)\\\\length=x +20[/tex]
b) Area of original house = length of house * breadth of house
The length of house = length of patio = x + 20; breadth of house = x + 10; therefore:
Area of original house = (x + 20)(x + 10) = x² + 10x + 20x + 200
Area of original house = x² + 30x + 200
c) If the width is extended, hence:
[tex]Area=length*breadth\\\\x^2+12x-160=(x+20)*width\\\\x^2+20x-8x-160=(x+20)*width\\\\x(x+20)-8(x+20)=(x+20)*width\\\\(x-8)(x+20)=(x+20)*width\\\\width=x-8\\\\Extended \ width=(x-8)-(x-10)\\\\Extended \ width=2\ feet[/tex]
pLZ HELPPPPPPPPPPPPPPPPPPPPPPPPP.
Answer:
x^4+4x^3+6x^2+7x+2
Which expression is equivalent to this polynomial?
16x2 + 4
A.
(4x + 2i)(4x − 2i)
B.
(4x + 2)(4x − 2)
C.
(4x + 2)2
D.
(4x − 2i)2
Answer:
A.
Step-by-step explanation:
C and D do not create any x² terms when doing the multiplications. so, they are out.
B stands for (a+b)×(a-b) = a² - b².
so, that would give us a "-4" at the end and is not fitting to the "+4" term at the end of the original expression.
that leaves us with A.
let's verify :
(4x+2i)(4x-2i)
it follows the same rule as B :
(a+b)(a-b) = a² - b²
a = 4x
b = 2i
you remember, i = sqrt(-1).
so, we get
(4x)² - (2i)² = 16x² - 4×(sqrt(-1))² = 16x² - 4×(-1) = 16x²+4
bingo !
Answer:
Step-by-step explanation:
the answer is A
WILL GIVE BRAINLIEST AND 30 POINTS!
PLEASE SHOW WORK!
f(x)=x2+10 and g(x)=|x|
Find (f+g)(2).
Answer:
14
Step-by-step explanation:
[tex]f(x) = {x}^{2} + 10 \\ \therefore \: f(2) = {2}^{2} + 10 \\ \therefore \: f(2) = 4 + 10 \\ \therefore \: f(2) = 14 \\ \\ g(x) = |x| \\ \therefore \:g(2) = |2| \\ \therefore \:g(2) = 2 \\ \\ f(2) + g(2) = 14 + 2 \\ \red{ \bold{(f + g)(2) = 14}}[/tex]
Step by step Explanation:
[tex]f(x) = x2 + 10g(x) = 1[/tex]
[tex](f + g)(2).[/tex]
Step 1
The equation is in standard form.
[tex]xf = 10gx + x2[/tex]Step 2
Divide both sides by x.
[tex] \frac{xf}{x} = \frac{10gx + x2}{x} [/tex]Step 3
Dividing by x undoes the multiplication by x.
[tex]f = \frac{10gx + x2}{x} [/tex]Step 4
Divide x 2 + 10 g x by x.
[tex]f = 10g + \frac{x2}{x} [/tex]My Answer is.
[tex]\color{green}f \ = \frac{10g + \frac{x2}{x} }{f€g} x2 = {14}^{x} [/tex]Tariq wants to make some purple paint.
He mixes blue, red and white paint in the ratio 5:3:2
Tariq needs 60 litres of purple paint.
He gets a discounted price of 60% on the red paint.
Calculate how many litres of red paint he buys at the discounted price.
Answer:
18 liters
Step-by-step explanation:
Blue : red : White = 5 : 3 : 2
Quantity of Blue paint = 5x
Quantity of Red paint = 3x
Quantity of White paint = 2x
Total paint = 5x + 3x + 2x = 10x
10x = 60 liters
x = 60/10
x = 6
Quantity of red paint = 3x = 3*6 = 18
Can someone help me with this math homework please!
1. f(-6)=8
2.-2
3. 4
Hope this helps you...
A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 65°. If the string is 350 ft long, how high is the kite above the ground? (Round your answer to the nearest foot.) ft
Answer: [tex]317.2\ ft[/tex]
Step-by-step explanation:
Given
Angle of elevation [tex]\theta=65^{\circ}[/tex]
Length of string [tex]L=350\ ft[/tex]
Suppose the height of kite from the ground level is h
from the figure, we can write
[tex]\Rightarrow \sin \theta=\dfrac{h}{L}\\\\\Rightarrow \sin 65^{\circ}=\dfrac{h}{350}\\\\\Rightarrow h=350\sin 65^{\circ}\\\Rightarrow h=317.2\ ft[/tex]
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x ≈ 28.8°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{3.9}{8.1}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{3.9}{8.1}[/tex] ) ≈ 28.8° ( to the nearest tenth )
help please!!! :)
2x + 6 = 4x - 2
Answer:
[tex]2x + 6 = 4x + -2[/tex]
[tex]\Longrightarrow2x+6-6=4x-2-6[/tex]
[tex]\Longrightarrow 2x=4x-8[/tex]
[tex]\Longrightarrow 2x-4x=4x-8-4x[/tex]
[tex]\Longrightarrow -2x=-8[/tex]
[tex]\Longrightarrow \frac{-2x}{-2}=\frac{-8}{-2}[/tex]
[tex]\hookrightarrow \underline{ANSWER: x=4}[/tex]
-------------------------
hope it helps...
have a great day!!
Find the value of cos C rounded to the nearest hundredth, if necessary
[tex]\bold{\frac{5}{13} or 0.38}[/tex]
Answer:
Solution given:
here
by using Pythagoras law
hypotenuse =
[tex]\displaystyle\sqrt{adjacent ²+opposite ²}\\=\sqrt{15²+36²}=39[/tex]
Cos C=[tex]\frac{adjacent} {hypotenuse}=\frac{15}{39}=\frac{5}{13} or{0.38}[/tex]
Need help on this question asap pleasee
Answer:
option c is correct ,,,,,,Four pounds of tea and 5 pounds of coffee cost $88.30, while 9 pounds of tea and
six pounds of coffee cost $144.60. What is the cost of each per pound?
Cost of 1 pound of tea = $4.78 and cost of 1 pound of coffee = $12.88
Cost of 1 pound of tea = $9.20 and cost of 1 pound of coffee = $10.30
O Cost of 1 pound of tea = $8.20 and cost of 1 pound of coffee = $10.30
O Cost of 1 pound of tea = $9.20 and cost of 1 pound of coffee = $9.30
Answer:
Cost of 1 pound tea is $ 9.2.
Cost of 1 pound coffee is $ 10.3.
Step-by-step explanation:
Let the cost of tea is $ per pound and cost of coffee is $ q per pound.
4 p + 5 q = 88.30 .... (1)
9 p + 6 q = 144.60 ....(2)
Solving (1) and (2) we get
p = $ 9.2
q = $ 10.3
The composite figure is made up of a rectangle and two pentagons. Find the area. 5 5 34 S 5 A. 129 sq. units O B. 122.4 sq. units C. 225 sq. units D. 140 sq. units
Answer:
Option D, 140 sq. units
Step-by-step explanation:
Area of the rectangle part, 11*5 = 55 sq. units
Area of the pentagon part (3.4*5)*5/2 = 42.5 sq. units
Total area,
55+2*42.5 sq. units (since there are two pentagons)
= 55+85 sq. units
= 140 sq. units
Thank you for the help!
Answer:
see explanation
Step-by-step explanation:
cosM = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{MN}{LM}[/tex] = [tex]\frac{8}{17}[/tex]
sinM = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{LN}{LM}[/tex] = [tex]\frac{15}{17}[/tex]
tanM = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{LN}{MN}[/tex] = [tex]\frac{15}{8}[/tex]
what is the value of b?
Answer: The b-value is the middle number, the number next to the X
Find the measure of the indicated angle
Answer:
[tex]given\Longrightarrow AB=AC[/tex]
[tex]\angle \;C=\angle \:B=60\ [isosceles ~triangle][/tex]
[tex]\angle~A+\angle~B+\angle~C=180[/tex]
[tex]x+60+60=180[/tex]
[tex]x+120=180[/tex]
[tex]x=180-120[/tex]
[tex]x=60[/tex]
-------------------------
HOPE IT HELPS
HAVE A GREAT DAY!!
Can someone help me with this math homework please!
Answer:
2nd option
{(-8, -2), (-4, 1), (0, -2), (2, 3), (4, -4)}
Step-by-step explanation:
For a function to exist, every value of input must have exactly one value of output.
The rest of the relations(1, 3, and 4) have 2 outputs for 1 input so they dont make a function.
Answer:
(B)
Step-by-step explanation:
If you noticed, all the other input values have one input value that has two output values. This doesn't represent a function. Only (B) has one output for each input.
Hope that helps (●'◡'●)
According to a survey of 1000 families of any town in 2010 A.D.,794 families have radio and 187 families have television.lf 63 families do not have any one of them,then how many families will have both radio and television?Find it.
Answer:
the families who use both radio and television is 44.
I NEED HELP!!! Can someone please help me
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Here you have to use the Pythagorean Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
STEP 1: Define your variables
a and b are the legs of the triangle, and c is the hypotenuse
a = 7
b = x
c = 9
STEP 2: Plug the variable into the equation
7^2 + x^2 = 9^2
STEP 3: Solve
7^2 + x^2 = 9^2
49 + x^2 = 81
49 - 49 + x^2 = 81 - 49
[tex]\sqrt{x}[/tex]^2 = [tex]\sqrt{32}[/tex]
x = [tex]\sqrt{32}[/tex]
STEP 4: Simplify
Since the questions asks you to put it in simplified radical form, you do not have to approximate the answer, but you do have to simplify the radical.
x = [tex]\sqrt{32}[/tex]
x = [tex]\sqrt{16}[/tex] * [tex]\sqrt{2}[/tex]
x = 4[tex]\sqrt{2}[/tex]
Hope this helps
solve x in the diagram below
Answer:
60
Step-by-step explanation:
180-100 = 80
80-20 = 60
Kenneth ran a marathon (26.2) miles) in 5.5 hours. What was Kenneth’s average speed? (Round your answer to the nearest tenth.)
Answer:
4.8 miles per hour.
Step-by-step explanation:
Average speed=Total distance/Time taken
=26.2miles/5.5hour
=4.8 miles per hour
Sam has 24 ball he gives 1/3 to Rita. How many ball did he give to Rita?
Answer:
8
Step-by-step explanation:
Find 1/3 of 24, which is 8.
Answer:
Sam gave 8 balls to Rita.
Step-by-step explanation:
24 / 3 = 8
1/3 of 24 is 8, therefore Sam gave 8 balls to Rita.
In a clinic, a doctor charges Rs 1200 for every 15 minutes. If he attends to the clinic 2 hours per day for seven days, how much will he earn during a week?
Answer:
67,200 (please note you did not specify the currency this is figured in so that is important to include in your answer. If this answer is in dollars, then make sure you add a dollars sign and specify "dollars" in your answer. If it is in another currency then put that in).
Step-by-step explanation:
First, we need to figure out how much the doctor makes per hour. Since there are 4, 15 minute billing periods per hour, we multiple to find the hourly billing charges:
4[tex]4*1200=4800[/tex] (this is the amount the doctor makes per hour)
Next, we have to take that hourly charge and multiply it by 2 because we know the doctor works two hours per day:
[tex]4800*2=9600[/tex] (this is the amount the doctor makes per day working two hours)
Finally, we know the doctor attends to the clinic two hours per day and seven days per week. We have to multiply the amount of money earned in two hours (9600) by 7 days:
[tex]9600*7=67,200[/tex] (this is the amount the doctor makes in seven days, billing two hours per day)
an object falls from a height, h m, varies directly as the square of its time, t s on planet Q. given that the object falls from the height of 5 m in 2 s, calculate the time taken in seconds, for the object to fall from a height of 45 m on the planet.
Answer:
18 seconds
Step-by-step explanation:
5x9=45 so 2x9=18
Which of the following equations represents a line that is parallel to y = -4x-1
and passes through the point, (2, 2)?
O A. y = -4x+10
O B. y = 1/4x+2
O C. y = -4x + 4
O D. y = -4x - 6
Answer:
A
Step-by-step explanation:
Parallel lines have the same gradient
For line y=-4x-1, the gradient is -4 and so that of this new line will also be -4
Now,
y-y1=m(x-x1)
y-2=-4(x-2)
y-2=-4x+8
y=-4x+8+2
y=-4x+10
i'm kinda confused in this question, please help me.
Answer:
there you go
Step-by-step explanation:
angle DOB is 60 degree.
Answer:
see explanation
Step-by-step explanation:
Given ∠ DOC = 90° then
∠ DOB = 90 - p and
Since AOB is a straight angle , then
4p + 90 - p = 180
3p + 90 = 180 ( subtract 90 from both sides )
3p = 90 ( divide both sides by 3 )
p = 30
4p = 4 × 30 = 120
Then
∠ DOB = 180° - 4p = 180° - 120° = 60°
Please help!!!!!!!!!!!!!!!!
Given:
For two events X and Y,
[tex]P(X)=\dfrac{2}{3}[/tex]
[tex]P(Y)=\dfrac{2}{5}[/tex]
[tex]P(X|Y)=\dfrac{1}{5}[/tex]
To find:
The probabilities [tex]P(Y\cap X), P(Y)\cdot P(X)[/tex].
Solution:
Using the conditional probability:
[tex]P(X|Y)=\dfrac{P(Y\cap X)}{P(Y)}[/tex]
[tex]P(X|Y)\times P(Y)=P(Y\cap X)[/tex]
Substituting the given values, we get
[tex]\dfrac{1}{5}\times \dfrac{2}{5}=P(Y\cap X)[/tex]
[tex]\dfrac{2}{25}=P(Y\cap X)[/tex]
And,
[tex]P(Y)\times P(X)=\dfrac{2}{5}\times \dfrac{2}{3}[/tex]
[tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex]
Therefore, the required probabilities are [tex]P(Y\cap X)=\dfrac{2}{25}[/tex] and [tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex].
Lshonda sells beaded necklaces. Each large necklace sells for 4.70 and each small necklace sells for 4.20. How much will she earn from selling 4 large necklaces and 1 small necklace