If 2^m = 4x and 2^w = 8x, what is m in terms of w?
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Related Questions
The equation of a given circle in general form is x2+ y2 − 8x + 12y + 27 = 0. Write the equation in standard form, (x − h)2 + (y - k)2 = r2, by completing the squares in the equation. Show your work in a table.
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we take x-es and y-s 'close' to each other, and complete the square:
[tex]x^{2}+8x + y^{2} +12y+27=0[/tex]
write the coefficients of the linear terms (the x and y with degree 1) as 2*'something', to see how to complete the square:
[tex]x^{2}+2*4*x + y^{2} +2*6*y+27=0[/tex]
which means that [tex]x^{2}+2*4*x[/tex] needs [tex] 4^{2} [/tex]
and [tex]y^{2} +2*6*y[/tex] needs [tex] 6^{2} [/tex] to become perfect square trinomials:
[tex](x^{2}+2*4*x + 4^{2})-4^{2} + (y^{2} +2*6*y+ 6^{2})-6^{2} +27=0[/tex]
[tex] (x+4)^{2}+ (y+6)^{2}=16+36-27 [/tex]
[tex] (x+4)^{2}+ (y+6)^{2}=25 [/tex]
[tex](x-(-4))^{2}+ (y-(-6))^{2}= 5^{2} [/tex]
Answer: [tex](x-(-4))^{2}+ (y-(-6))^{2}= 5^{2} [/tex]
Answer:
Step Reason
x2 + y2 - 8x + 12y + 27 = 0 given
x2 - 8x + y2 + 12y = -27 Isolate the constant term
x2 - 8x + 16 + y2 + 12y + 36 = -27 + 16 + 36 Complete the square by adding . 16 and 36 to both sides.
(x2 - 2∙4∙x + 42) + y2 + 12y + 36 = 25 Group and rearrange terms in x.
(x - 4)2 + y2 + 12y + 36 = 25 (a - b)2 = a2 - 2ab + b2
(x - 4)2 + (y2 + 2∙6∙y + 62) = 25 Group and rearrange terms in y.
(x - 4)2 + (y + 6)2 = 25 (a + b)2 = a2 + 2ab + b2
(x - 4)2 + (y + 6)2 = 52 Take the square root to find r = 5.
Step-by-step explanation:
this is the exact answer from plato
hope this helps a little bit :))
Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.
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Answer:
Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.
Step-by-step explanation:
From 512 to 68, there are a total of 444 houses, of which 222 are pairs, which is half, if it is even with the previous two, would be 224, otherwise, 222, if one yes and the other does not, 223.
A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second. Write an equation to model the height h in feet of the ball t seconds after it has been punted. The football is caught at 5.5 feet above the ground. How long was the football in the air?
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The equation for the height of a football punted with initial conditions is calculated, and the time the football spent in the air is determined.
Given: Initial height = 2.5 feet
Initial vertical velocity = 45 ft/s
The height at which the ball is caught = is 5.5 feet
Equation to model height: h(t) = -16t² + 45t + 2.5 where h(t) is the height at time t seconds.
Time in the air: To find how long the ball is in the air, solve for t when h(t) = 5.5 feet.
Final answer: The football was in the air for approximately 1.9 seconds.
if I'm going to the lake that is 60 miles away and I'm driving 40 miles per hour how long would it take for me to get there
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How to simplify?
2a - 4b - 16 + (3a + 7 ) - 8
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= 5a -4b -17
Tina is placing 30 roses and 42 tulips in vase for table decorations in her restaurant each vase will hold the same number of flowers each vase will have only one type of flower what is the greatest number of flowers She can place it each vase
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Answer: 6
Step-by-step explanation:
Given : Tina is placing 30 roses and 42 tulips in vase for table decorations in her restaurant .
Each vase will hold the same number of flowers and each vase will have only one type of flower .
Then, the greatest number of flowers she can place it each vase will be the greatest common factor of 30 and 42.
Prime factorization of 30 and 42 :
[tex]30=2\times3\times5\\\\42=2\times3\times7[/tex]
We can see that greatest common factor of 30 and 42 = [tex]2\times3=6[/tex]
Hence, the greatest number of flowers she can place it each vase =6
A pallet stacked with bags of cement weighing a total of 5501 N must be pushed up a 2.30-m incline to a 75.0-cm high platform. What force, in Newtons, must be applied to get the job done?
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Refer to the diagram shown below.
Note that 75 cm = 0.75 m.
Therefore the angle of the incline is given by
sin(x) = 0.75/2.3 = 0.3261.
The weight pushed up the incline is W = 5501 N.
The component of the weight acting down the incline is
W*sin(x) = 5501*0.3261 = 1793.9 N
The force, F, should overcome this weight acting along the incline, therefore
F = 1794 N (nearest integer)
Answer: 1794 N
Select true and false for each question.
a.) LN(x^a) = a + LN x
b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y)
c.) (ln a)^3b = 3b ln a
d.) log_a b^2 = (log_a b)^2
Answers
a.) LN(x^a) = a + LN x
b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y)
c.) (ln a)^3b = 3b ln a
d.) log_a b^2 = (log_a b)^2 = True
Write down all elements of ({9, 10, 11} ∩ {10, 11, 12, 13}) ∪ {14, 15}. (enter your answer in set notation.)
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Let set A = {9, 10, 11}
Let set B = {10, 11, 12, 13}
Let set C = A∩B. This means: the intersection of A & B.
Let set D = {14, 15}
Let set Universal = C∪D. This means: the union of C & D where C is the intersection of A & B.
Solution:
Let us first solve for set C.
C = A∩B
C = {9, 10, 11} ∩ {10, 11, 12, 13}
C = {10, 11} <--- New value for set C
Let us now solve for set Universal.
Universal = C∪D
Unviversal = {10, 11} ∪ {14, 15}
∴ Universal = {10, 11, 14, 15} <--- What we are looking for.
Therefore, the answer is Universal = {10, 11, 14, 15}.
The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs is allowed for team who will play, which of the following function notation matches the situation?
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For this problem, you are to find the total cost which consists of cost for the gun rent and cost for the paintballs. Hence, your equationmust consist of two terms. The equation must be:
Total cost = 100x + 1000
The term x denotes the number of guns. Hence, it must be multiplied with 100 to determine the cost. On the otherhand, the constant 1000 is for the paintballs. Since it was given that each team must have 2000 paintballs, then it follows that they must pay 1000 Php.
Prove the identity
cos(-x)/[1+sin(-x)]=secx+tanx
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The length of the shorter side of a parallelogram is 29 cm. Perpendicular line segment, which goes through the point of intersection of the diagonals to the longer side divides this longer side into two segments: 33cm and 12cm. What is the area of the parallelogram?
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The area of the parallelogram is calculated by multiplying the base (45 cm) and the height (29 cm), giving us a total area of 1305 cm².
Explanation:The area of a parallelogram is the product of the base and height.
The base is the longer side of the parallelogram, which is 33cm +12cm = 45cm.
And, the height would be the shorter side, which is 29cm.
Therefore, the area of the parallelogram can be calculated with the
formula base x height = 45cm x 29cm = 1305 cm².
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Find an implicit and an explicit solution of the given initial-value problem. (use x for x(t).) dx dt = 2(x2 + 1), x(π/4) = 1
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We'll use [tex]x(\pi/4)=1[/tex], considering that [tex]x_0=1, t_0=\dfrac{\pi}{4}[/tex]:
[tex]t-t_0=\dfrac{1}{2}\left[\arctan(x)-\arctan(x_0)\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\left[\arctan(x)-\arctan(1)\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\left[\arctan(x)-\dfrac{\pi}{4}\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\arctan(x)-\dfrac{\pi}{8}\\\\ t-\dfrac{\pi}{8}=\dfrac{1}{2}\arctan(x)\\\\ \boxed{\arctan(x)=2t-\dfrac{\pi}{4}}[/tex]
Applying tan in the both sides:
[tex]\arctan(x)=2t-\dfrac{\pi}{4}\\\\ \tan(\arctan(x))=\tan\left(2t-\dfrac{\pi}{4}\right)\\\\ \boxed{x(t)=\tan\left(2t-\dfrac{\pi}{4}\right)}[/tex]
let log P/N=8 and log M/N=5
What is the relationship between P and M?
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log(a)-log(b)= log(a/b),
so log(P/N) - log(M/N) = log( P/N:M/N) = log(P/M),
Then: 8-5 = log(P/M), log(P/M)=3.
If log here means natural logarithm (base e), then P/M = e^3,
If log here means basis 10, decimal logarithm, then P/M = 10^3 = 1000.
Tim is employed at an annual salary of $23999.04.his regular workweek is 36 hours and he is paid semi monthly. What is caseys remineration of gross per pay period ? What is his hourly rate of pay ? What is his gross pay for a period in a which he worked
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Tim's gross pay per pay period is $999.96. His hourly rate is approximately $12.82. This was calculated by dividing his annual salary by the number of pay periods and dividing his pay per period by the number of work hours per period respectively.
Explanation:First, we start by finding Tim's pay per pay period. Since he is paid semi-monthly, this means he is paid twice a month and since there are 12 months in a year, he will have 24 pay periods in a year. To calculate his gross pay per pay period, we divide his annual salary by the number of pay periods: $23999.04 ÷ 24 = $999.96 per pay period. Next, we calculate Tim's hourly rate. Since he works 36 hours in a week, and there are roughly 4.33 weeks in a month (52 weeks in a year / 12 months = 4.33), his monthly work hours would be 36 hours * 4.33 = roughly 156 hours. Since he's paid twice a month, his total work hours per pay period would be 156 / 2 = 78 hours. If we divide his pay per period by the number of work hours per period, we get his hourly rate: $999.96 ÷ 78 hours = roughly $12.82 per hour.Learn more about Pay Calculation here:https://brainly.com/question/32700496
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Rotating Light A searchlight rotates through one complete revolution every 4 seconds. How long does it take the light to rotate through 90°?
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A computer repairman makes $25 per hour. Which equation models the situation? Let h represent the hours worked. Let d represent the total amount earned.
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d(h)=25h
HELP PLEASE???? Jayla has a USB stick that transfers data at 2.4 x 109 bytes per second. Her modem transfers data at 1.2 x 107 bytes per second. Which statement is true?
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Answer:
The transfer rate of USB is 200 times the transfer rate of Modem
Step-by-step explanation:
Jayla has a USB stick that transfers data at 2.4 x 10^9 bytes per second. Her modem transfers data at 1.2 x 10^7 bytes per second.
To compare the transfer rate we divide the transfer rate of USB by modem
[tex]\frac{2.4*10^9}{1.2*10^7}[/tex]
2.4 divide by 1.2 is 2
10^9 divide by 10^7 = 10^2
So its 2* 10^2 = 200
The transfer rate of USB is 200 times the transfer rate of Modem
The USB stick transfers data at a rate which is significantly faster than the modem.
Explanation:The statement that is true is that Jayla's USB stick transfers data much faster than her modem. This is because the data transfer rate of the USB stick, which is 2.4 x 109 bytes per second, is greater than the modem's transfer rate of 1.2 x 107 bytes per second. We can compare the two rates directly because they are given in the same units. We can see that the USB's speed is two decimal places further to the right than the modem's speed, meaning it is 100 times faster.
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A collection of nickels, dimes, and quarters consist of
11
coins with a total of
$1.35
. If the number of dimes is equal to the number of nickels, find the number of each type of coins.
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q + n + d = 11 coins
25*q + 10*n + 5*d = 135 cents
d = n
Then:
q + 2n = 11 and 25q + 15n = 135
q+2n=11 and 5q + 3n = 27
q = 11-2n -----> 5*(11-2n)+3n = 27
55 -10n+3n=27, or -7n = -28, n = 4 (nice!)
So, 4 nickle, 4 dime and 3 (11-2*4) quarters.
Check it works! ($1.35!)
Translate the sentence into an equation. Nine more than the quotient of a number and 7 is equal to 3 . Use the variable y for the unknown number.
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Nine more = 9 +
Quotient of a number and 7 = y/7
Equal to three = = 3
Put it together:
9 + y/7 = 3
^ the answer
Bonus points if you can tell me what y equals ;)
Hope this helps! :)
The equation is 9+ y/7 = 3
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S
Given statement:
Nine more than the quotient of a number and 7 is equal to 3.
let the number be y
The 9+ y/7 = 3
quotient of a number and 7 is y/7
and, nine more than= 9+ y/7
So, 9+ y/7 = 3
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459 randomly selected lightbulbs were tested in a laboratory 291 lasted more than 500 hours find a point estimate of the true proportion of all lightbulbs in that last more than 500 hours
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Final answer:
The point estimate of the true proportion of all lightbulbs that last more than 500 hours is approximately 0.634, calculated using the sample data of 291 out of 459 lightbulbs lasting more than 500 hours.
Explanation:
To find a point estimate of the true proportion of all lightbulbs that last more than 500 hours, we use the sample data provided. Out of 459 randomly selected lightbulbs, 291 lasted more than 500 hours.
The point estimate is calculated by dividing the number of successes in the sample by the total number of trials. In this case, the point estimate (p-hat) would be 291 divided by 459, which gives us an estimate of the true proportion.
The calculation would be as follows:
Point estimate (p-hat) = Number of successes / Total number of trialsp-hat = 291 / 459p-hat = 0.633987 (rounded to six decimal places)The point estimate for the true proportion of all lightbulbs that last more than 500 hours is approximately 0.634.
I thought of a number, doubled it, then decreased by 17. Then I divided the result by 3. I got 15. What was my number?
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The number person thinking about is 14.
Given that, I thought of a number, doubled it, and then decreased it by 17. Then I divided the result by 3. I got 15.
What is the equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number be x.
Double it=2x
Decreased it by 17=2x+17
Divided the result by 3=(2x+17)/3
The result is equal to 15.
(2x+17)/3=15
⇒2x+17=45
⇒2x=28
⇒x=14
Therefore, the number person thinking about is 14.
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What related number sentence shows the commutative property addition 3+9=12
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Please take note, the commutative property of addition is
a + b = c
b + a = c
a + b = b + a
Commutative originates from the word move around or commute, therefore, commutative property refers to the act of moving stuff around. In addition, the rule is a + b = b + a; wherein from the example above, means 9 + 3 = 3 + 9. They want to say that the computation uses the Commutative Property, if at any time, a computation depends on moving stuff around
A ball is thrown from a height of 255 feet with an initial downward velocity of 21/fts . The ball's height h (in feet) after t seconds is given by the following. How long after the ball is thrown does it hit the ground?
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The time it takes for a ball thrown downwards at a velocity of 21 ft/s from a height of 255 ft to reach the ground is approximately 4.05 seconds.
Explanation:The physics problem presented is a classic example of a vertically descending projectile. Here, we can use the formula of motion to find the solution. The formula is h = vt + 0.5gt², where v is the initial velocity, g is the acceleration due to gravity, and h is the height.
Since the ball is thrown downwards, the initial velocity will be negative, -21 ft/s. We're also working in feet, so the gravitational acceleration should be in feet/s², which is approximately -32.2 ft/s² (remember it's negative as it's acting downwards).
So, substituting the values into the equation, we have 255 = (-21*t) + 0.5*(-32.2)*t². Simplifying this gives us a quadratic equation: 16.1t² - 21t - 255 = 0.
The roots of this equation represent the times at which the ball will be 255 ft below its starting point. We solve the equation and get t ≈ -3.9s or t ≈ 4.05s. Clearly, time cannot be negative, so the ball hits the ground after approximately 4.05 seconds from being thrown.
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The ball thrown from a height with initial downward velocity hits the ground after 3.79 seconds. This was found by solving the quadratic equation that stems from principles of physical motion (height vs time).
Explanation:The problem can be solved using the principles of kinematics in physics. The height of the ball after t seconds is given by the equation of motion, which is a quadratic equation. If we let h be 0 (height when the ball hits the ground), we can solve the equation for t.
Given: initial height = 255 feet, initial velocity = 21 feet/s, acceleration due to gravity = 32.2 ft/s² (downward); The equation of motion is: h = 255 + 21t - 16t²; We have to find the time when the ball hits the ground i.e when h=0. So, the equation becomes: 0 = 255+21t-16t².
On solving this quadratic equation, we get two roots. Assuming upward direction is positive, the negative time value reflects the time before the ball was launched and the positive value is the time it takes for the ball to hit the ground. The positive root gives us the answer, t = 3.79 s.
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10 raised to negative 3 in standard notation
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10^-3= 1/10^3
1/10^3=1/1000
1/1000=0.001
Final answer: 0.001
True or false The coefficient of (x^(k)) (y^(n-k)) in the expansion of (x+y)^n equals (n choose k)
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nCk a^(n-k) b^k, where k is the kth term of the expanded form, n is the nth power. The coefficient of the term in the binomial expansion is nCk or n!/k!(n-k)!.
What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25
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Answer:
x= -5
Step-by-step explanation:
Suppose you buy a 1.25-pound package of ham at $5.20 per pound.What fraction of a pound did you buy
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You bought [tex]\( \frac{25}{104} \)[/tex]of a pound of ham, which is approximately 0.2404 pounds.
To find the fraction of a pound you bought, divide the total weight by the price per pound.
Given:
Total weight = 1.25 pounds
Price per pound = $5.20
[tex]\[ \text{Fraction of a pound} = \frac{\text{Total weight}}{\text{Price per pound}} \]\[ \text{Fraction of a pound} = \frac{1.25}{5.20} \]\[ \text{Fraction of a pound} \approx \frac{125}{520} \][/tex]
Now, simplify the fraction:
[tex]\[ \text{Fraction of a pound} \approx \frac{25 \times 5}{104 \times 5} \]\[ \text{Fraction of a pound} = \frac{25}{104} \][/tex]
So, you bought [tex]\( \frac{25}{104} \)[/tex] of a pound of ham.
A local grocer wants to find out whether how many mixed flower bouquets in his inventory everyday. To that end, kept records of the daily bouquet sales for the last 27 days. The average number of bouquets sold every day was 11.8 and the sample standard deviation is 2.3. Construct a 99% confidence interval for the number of bouquets sold on a given day..
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n = 27, sample size
df = n-1 = 26, degrees of freedom
xb = 11.8, sample mean
s = 2.3, sample standard deviation.
Because population statistics are not known, we should use the Student's t-distribution.
At 99% confidence interval, the t-value = 2.779 (from tables).
The confidence interval is
11.8 +/- 2.779*(2.3/√(27)) = 11.8 +/- 1.23 = (10.57, 13.03)
Answer: (10.6, 13.0) to the nearest tenth
whats the solution of the equation
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3x+9-7x=2(x+6)
3x-7x = -4x
-4x+9 =2x+12
9=6x+12
-3 = 6x
x=-3/6 = - 1/2
x = - 1/2