Answer:
600km/h
546.807 fps
0.1666667 km/s
Step-by-step explanation:
Use which ever unit youd want to in this scenereo, I'd use 600km/h
3000 / 5 = 600
Find all real $x$ that satisfy $$(2^x - 4)^3 (4^x - 2)^3 = (4^x 2^x - 6)^3. $$
The polynomial-like expression is satisfied by the real value x = 1.
How to determine the real solution of a polynomial-like expression
In this question we must apply the concepts of logarithms and algebra properties to solve the entire expression. Initially, we expand the right part of the expression:
[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (4^{x}+2^{x}-6)^{3}[/tex]
[tex](2^{x}-4)^{3} + (4^{x}-2)^{3} = [(2^{x}-4)+(4^{x}-2)]^{3}[/tex]
[tex](2^{x}-4)^{3}+(4^{x}-2)^{3} = (2^{x}-4)^{3}+3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2}+(4^{x}-2)^{3}[/tex]
[tex]3\cdot (2^{x}-4)^{2}\cdot (4^{x}-2)+3\cdot (2^{x}-4)\cdot (4^{x}-2)^{2} = 0[/tex]
[tex]2^{x}-4 + 4^{x}-2 = 0[/tex]
[tex]2^{x}\cdot 2^{x} + 2^{x}-6 = 0[/tex]
[tex]u^{2}+u - 6 = 0[/tex]
[tex](u+3)\cdot (u-2) = 0[/tex]
Hence, the roots of the pseudopolynomial are [tex]u_{1} = -3[/tex] and [tex]u_{2} = 2[/tex]. Only the second one have a real value of x. Hence, we have the following solution:
[tex]2^{x} = 2[/tex]
[tex]x\cdot \log 2 = \log 2[/tex]
[tex]x = 1[/tex]
The polynomial-like expression is satisfied by the real value x = 1. [tex]\blacksquare[/tex]
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write an expression that is equivalent to 21h - 10h + 16 - 9 + 14h + 5 .
Answer:
25h+12
Step-by-step explanation:
Add the numbers :
21h-10h + 16-9 + 14h+ 5
21h-10h + 12 + 14h
Combine like terms:
25h + 12
If the figures below are similar, find the scale factors
HELP PLEASE
Answer: 3:2 and 2:3
Step-by-step explanation:
Scale factor is image/preimage.
So from A to B, the image is B and the preimage is A, so the scale factor is 6/4 = 3/2.
Similarly, from B to A, the scale factor is 4/6=2/3
Find the inverse of the function, no solutions doesn't work and things like sqrt(9-x^2) doesn't either.
Answer:
The range of [tex]f(x)[/tex] is [tex]f(x)\in[0,3][/tex]
[tex]f^{-1}(x)=-\sqrt{-x^2+9}[/tex] with a domain [tex]x\in[0,3][/tex]
Step-by-step explanation:
Domain: set of input values (x-values)
Range: set of output values (y-values)
Given function:
[tex]f(x)=\sqrt{9-x^2}\quad(x\in[-3,0])[/tex]
Therefore, as the original function has a restricted domain, its range is also restricted:
[tex]f(-3)=\sqrt{9-(-3)^2}=0[/tex]
[tex]f(0)=\sqrt{9-0}=3[/tex]
[tex]\therefore\textsf{Range}\:f(x)\in[0,3][/tex]
To determine the inverse of a function
Change [tex]x[/tex] to [tex]y[/tex]:
[tex]\implies x=\sqrt{9-y^2}[/tex]
Square both sides:
[tex]\implies x^2=9-y^2[/tex]
Switch sides:
[tex]\implies 9-y^2=x^2[/tex]
Subtract 9 from both sides:
[tex]\implies -y^2=x^2-9[/tex]
Divide both sides by -1:
[tex]\implies y^2=-x^2+9[/tex]
Therefore:
[tex]\implies y=\sqrt{-x^2+9}\textsf{ and }y=-\sqrt{-x^2+9}[/tex]
As the range of the inverse function is the same as the domain of the original function:
[tex]\implies f^{-1}(x)=-\sqrt{-x^2+9}[/tex] only as the range is [-3, 0]
The domain of the inverse function is the same as the range of the original function.
[tex]\therefore\textsf{Domain of}\:f^{-1}(x):x \in [0,3][/tex]
The inverse of a function is ordinarily the reflection of the original function in the line [tex]y=x[/tex].
**Please see attached graph**
40 POINTS HELPP ME ITS BEEN SO LONG HELP PLEASEEE HELP PLEASEE HELPP Stevie needed twine for the gifts she was wrapping for a family party. The lengths of Stevie’s twine are shown on the line plot below. How many feet of twine does Stevie have total?
Answer:
Your answer would be:
57.75 or 57 3/4
(I will show how many of each length of twine that is on the graph)
Point 2 1/4:
2
Point 2 3/4:
4
Point 3:
1
Point 3 1/2:
2
Point 3 3/4:
3
Point 4:
1
Point 4 1/4:
4
We can show how much length in total Stevie used with the following equation:
(2 1/4 x 2) + (2 3/4 x 4) + ( 3 x 1 ) + ( 3 1/2 x 2 ) + (3 3/4 x 3 ) + (4 x 1 ) + (4 1/4 x 4)
Each smaller equation in paraphrases shows how much of each length of twine at each point with x's on the number line. Altogether it would equal 57.75 or 57 3/4.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Is 1,-9 a solution to y=-9
Answer:
yes
Step-by-step explanation:
(x,y) -> (1,-9) y=-9
Measure of angle U . Help quick
Answer:
72 degrees
Step-by-step explanation:
all triangles have angles adding up to 180
that does not look like a right triangle
only possible answer is 72
Answer:
angle U = 72°
Step-by-step explanation:
The sum of the internal angles in a pentagon is 540°
[tex]x^{o} +(2x)^{o} +(2x)^{o} +90^{o}+90^{o} =540^{o}[/tex]
[tex](5x)^{o} =540^{o} -180^{o}[/tex]
[tex]x^{o} =\frac{360^{o} }{5} =72^{o}[/tex]
Hope this helps
10. Ryan inherited land from his grandfather. He decided to sell the land for $160,000, then place
the money in a new account that earns 1. 2% interest compounded bimonthly. How much
interest will he have earned after 30 years?
The amount of interest Ryan would earn at the end of 30 years given the interest rate is $69,250.27.
What is the interest rate on the new account?When an account earns an interest that is compounded bimonthly, it means that it earns an interest every 2 months.
The formula that can be used to determine the interest earned is:
Future value - amount deposited
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate = 1.2/6m = number of compoundingN = number of yearsFV = 160,000(1.002^180) = $229,250.27
Interest = $229,250.27 - $160,000 = $69,250.27
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A soup can has a radius of 4.3 cm and a height of 11.6 cm. What is the approximate volume of the soup can?
Answer:
673.82 cm³
Explanation:
soup can are usually in the form of a cylinder.cylinder volume : [tex]\sf \pi r^2h[/tex]
[tex]\rightarrow \sf \pi (4.3)^2(11.6)[/tex]
[tex]\rightarrow \sf 673.82 \ cm^3[/tex]
If the number of bacteria in a
colony doubles every 25 hours
and there is currently a population
of 10,000 bacteria, what will the
population be 75 hours Trom now?
Answer:
The population of 75 hours from now would be 40,000.
Step-by-step explanation:
The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.
The equation 4x – 45 = y is used to find your profit, y, in dollars from buying $45 of supplies and washing cars for $4 each. What does the x stand for?
A farmer plants wheat and corn. It costs about $150 per acre to plant wheat and about $350 per acre to plant corn. The farmer plans to spend no more than $250,000 planting wheat and corn. The total area of corn and wheat that the farmer plans to plant is less than 1200 acres
The inequality that models this situation is 150x + 350 y ≤ 250000 and x + y < 1200
What is an inequality?
An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
Let x represent the number of wheat acres and y represent the number of corn acres, hence:
150x + 350 y ≤ 250000 (1)
Also:
x + y < 1200 (2)
The inequality that models this situation is 150x + 350 y ≤ 250000 and x + y < 1200
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If in a certain year, 400 000 high school seniors took a test in the NSAT and 240 000 scored above the cut-off score, what is the cut-off score for that year?
Answer:
160 000
Step-by-step explanation:
400 000 - 240 000 = 160 000
A equals 10. Find the measure of ZWY
Answer:
8a-9=7a+1 (inscribed angle are equal standing on the arc)
8a-7a=1+9
a=10
What is the median of the following numbers? 1, 2, 4, 6, 41,2,4,6,41, comma, 2, comma, 4, comma, 6, comma, 4
Answer:
4
Step-by-step explanation:
Here are the Numbers: 1,2,4,6,41,2,4,6,41,2,4,6,4
First we order from least to greatest;
1,2,2,2,4,4,4,4,6,6,6,41,41
Since the amount of numbers are odd, we just take the middle number:4
La distancia entre dos ciudades A y B es de 255 km. Un automovil sale de A hacia B a una velocidad de 90 km/h. Al mismo tiempo sale, otro automovil de B hacia A a una velocidad de 80 km/h. Suponiendo su velocidad constante , calcula la distancia que ha recorrido cada uno hasta el momento del encuentro
Usando proporciones, hay que:
El auto A hay recorrido 135 km.El auto B hay recorrido 120 km.¿Qué es una proporción?Una proporción es una fracción de la cantidad total.
En este problema, dos automovis, en sentidos opostos, salen al mismo tiempo. Por eso, su velocidad relativa es de 90 km/h + 80 km/h = 170 km/h.
La distancia es de 255 km, por eso, el tiempo en que se encontraran, en horas, es dado por:
t = 255/170 = 1.5h
La distancia recorrida por cada auto es dada por:
dA = 90 x 1.5 = 135 km.
dB = 80 x 1.5 = 120 km.
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What is 5 x 3/20 as a fraction in its simplest form
Answer:
3/4
Step-by-step explanation:
You can form the product, then cancel common factors, or you can cancel common factors before you form the product.
__
[tex]5\times\dfrac{3}{20}=\dfrac{15}{20}=\dfrac{3\cdot5}{4\cdot5}=\boxed{\dfrac{3}{4}}\\\\\textsf{or ...}\\\\5\times\dfrac{3}{20}=\dfrac{5}{20}\cdot\dfrac{3}{1}=\dfrac{1}{4}\cdot\dfrac{3}{1}=\boxed{\dfrac{3}{4}}[/tex]
You have decided to purchase a car for $22,346. 16. The credit union requires a 10% down payment and will finance the balance with a 5. 4% annual interest loan for 36 months. The sales tax in your city is 7. 6%, and the license and title charges are $125. 13. Determine the amount that the credit union will finance you for. Round your answer to the nearest cent. A. $24,179. 10 c. $21,761. 20 b. $24,169. 60 d. $21,752. 64.
The amount that the credit union will finance is $24169.60
We have given that the cost of the car is $22,346. 16
and the credit union required 10% down payment
and sale tax=7.6%
The license and title charges are $125. 13.
We have to determine that the amount that the credit union will
finance Now we have sale tax 7.6% for $22,346. 16
Therefore, we get
[tex]\frac{7.6}{100} \times 22,346. 16=1698.31[/tex]
What is the amount that the credit union finance ?credit union finance=cost of car+sales tax+the license and title charges.
[tex]=22346.16+1698.31+12.13\\=24169.60[/tex]
Therefore, the amount that the credit union will finance is $24169.60
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I need help please. i will give brainliest
Answer:
1) There were 120 customers per night when the restaurant opened
2) y = -2x + 24
Step-by-step explanation:
1) x represents the # of months since a restaurant opened, and y represents the average number of nightly customers.
y=mx+b
120 is b in this situation, which is the y-intercept of the line. This means that 120 is the starting number of customers when the restaurant first opened.
what is
Find p(rolling a 4)
Answer: 4/6
Step-by-step explanation: This because most dice have a 6 sides on them and others have more and if you roll a 6-sided dice you will get 4/6 of a probabilty that you will role a 4.
Hope This Helps!Which ratio below is equivalent to the ratio 7 : 350?
Answer:
7/350 7 to 350
Step-by-step explanation:
there are 3 ways to write a ratio
:
to
/
Find yolanda’s finance charge in november using the previous balance method, the adjusted balance method, and the daily balance method. among those three possible finance charges, what is the value of the one which is neither lowest nor highest? a. $12.53 b. $11.59 c. $12.05 d. $10.91
Answer:
i believe its B
Step-by-step explanation:
Answer:
The Answer is B. $11.59
Step-by-step explanation:
Edge 2022
The equation to model Exponential Decay is:
y = a[1 – r)
y= total amount
a= starting amount
r= the growth rate as a decimal
t= number of growth periods
Question 1 (1 point)
Sarah takes 550 mg of an antibiotic. Every hour,
her body breaks down 25% of the remaining drug.
How much will be left after 12 hours?
Guys help me please I really don’t understand this
Exponential functions are used to represent growth or decay of a substance. The amount that will be left after 12 hours is 17.42mg
How to model exponential equationsThe standard form of an exponential equation is given as:
[tex]y=a(1-r)^t[/tex]
where;
y= total amounta= starting amountr= the growth rate as a decimalt= number of growth periodsGiven the following parameters
a = 550mg
r = 0.25
t = 12
Substitute into the formula
[tex]y=550(1-0.25)^{12}\\y = 550(0.75)^{12}\\y=17.42mg[/tex]
Hence the amount that will be left after 12 hours is 17.42mg
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What percent represents the shaded part of the hundredths grid shown? Please help asap!
Answer:
C. 5%
Step-by-step explanation:
if u count the shaded part it is 5 shaded out of 100 so that fraction is 5/100 which is .05 as a decimal and 5% as a percent
type of angle that has the sallest measure
Answer: acute angle
Step-by-step explanation: acute angle is the smallest starting from 0 to 90 DDegrees .
Which expression is equivalent to 9 ( w + 8)?
72 w
9 w + 72
9 w + 8
17 w
Answer:
A) 72w
Step-by-step explanation:
1. Which transformation would take point A(5,-4) to A’(5,-4)
Answer:
that would be A. 360.
Step-by-step explanation:
when you think about it, a 360 is doing a full circle which is the only option here, because the point stays the same.
the glass forms a cylinder with a radius of 1.5 inches. the volume of the glass is approximately 45.95 cubic inches. what is the height of the drinking glass in inches? round your answer to the nearest tenth.
Answer:6.80
Step-by-step explanation:
Between 11 P.M. and 8:45 A.M., the water level in a swimming pool decreased by 3/8
. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
find the volume of the cubes or rectangular prisms in cubic centimeters.36/125 cm 3 6/125 cm 3 8/125 cm 3 1/125 cm 3cube with a side length of cmrectangular prism with a length,width, and height of cm, cm,and cm, respectivelycube with a side length of cmrectangular prism with a length,width, and height of cm, cm,and cm, respectively
Applying the formula for volume of a rectangular prism and volume of a cube, we would have:
a. 6/125 cm³
b. 8/125 cm³
c. 1/125 cm³
d. 36/125 cm³
What is the Volume of a Rectangular Prism and a Cube?Volume of rectangular prism = length × width × height.Volume of cube = (side length)³a. Volume of rectangular prism = length × width × height = (1/5) × (2/5) × (3/5)
Volume of rectangular prism = 6/125 cm³
b. Volume of cube = (side length)³ = (2/5)³
Volume of cube = 8/125 cm³
c. Volume of cube = (side length)³ = (1/5)³
Volume of cube = 1/125 cm³
d. Volume of rectangular prism = length × width × height = (3/5) × (4/5) × (3/5)
Volume of rectangular prism = 36/125 cm³
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