Subtract: (2x2 − 7x + 5) − (−6x2 − 4x − 2)
Answer:
8x^2 - 3x + 7
Step-by-step explanation:
I took the test.
Solve 4 log12 2 + log12 x = log12 96. Choose one answer.. a. x = 88. b. x = 80. c. x = 12. d. x = 6
Answer:
Option (d) is correct.
The solution of x for the given equation [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex] is 6.
Step-by-step explanation:
Given : [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex]
We have to solve for x.
Consider the given equation [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex]
Subtract [tex]4\log _{12}\left(2\right)[/tex] both side, we have,
[tex]4\log _{12}\left(2\right)+\log _{12}\left(x\right)-4\log _{12}\left(2\right)=\log _{12}\left(96\right)-4\log _{12}\left(2\right)[/tex]
Simplify, we have,
[tex]\log _{12}\left(x\right)=\log _{12}\left(96\right)-4\log _{12}\left(2\right)[/tex]
Consider Right side of above,
[tex]\log _{12}\left(96\right)-4\log _{12}\left(2\right)[/tex]
Apply log rule, [tex]\:a\log _c\left(b\right)=\log _c\left(b^a\right)[/tex]
[tex]4\log _{12}\left(2\right)=\log _{12}\left(2^4\right)[/tex]
[tex]=\log _{12}\left(96\right)-\log _{12}\left(2^4\right)[/tex]
Again applying log rule, [tex]\log _c\left(a\right)-\log _c\left(b\right)=\log _c\left(\frac{a}{b}\right)[/tex]
[tex]\log _{12}\left(96\right)-\log _{12}\left(2^4\right)=\log _{12}\left(\frac{96}{2^4}\right)[/tex]
Simplify, we have,
[tex]=\log _{12}\left(6\right)[/tex]
[tex]\log _{12}\left(x\right)=\log _{12}\left(6\right)[/tex]
when log have same base,
[tex]\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)[/tex]
Thus, x = 6
Thus, The solution of x for the given equation [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex] is 6.
Answer:
D is the correct answer for the given equation.
1)The square shown has a perimeter of 32 units. The square is rotated about line k.
What shape is created by the rotation and what is the approximate circumference of the base?
Circumference of a circle: C = 2πr
a cone with a base circumference of about 25 units
a cone with a base circumference of about 50 units
a cylinder with a circumference of about 25 units
a cylinder with a circumference of about 50 units
2) The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm.
What shape is created by the rotation and what is the approximate circumference of the base?
Circumference of a circle: C = 2πr
a cylinder with a circumference of about 63 mm
a cylinder with a circumference of about 126 mm
a cone with a base circumference of about 63 mm
a cone with a base circumference of about 126 mm
1) The shape created by rotating a square about a line is a right circular cylinder. The approximate circumference of the base is about 25 units.
2) The shape created by rotating an equilateral triangle about a line is a cone. The approximate circumference of the base is about 63 mm.
How to determine solid formed after rotating a plane shape1) The shape created by rotating a square about a line is a right circular cylinder. The approximate circumference of the base is about 25 units.
Rotating a square about line k creates a right circular cylinder. The base, retaining the square's shape, has a circumference equal to the square's perimeter. With a square perimeter of 32 units
Perimeter of square = 4L
32 = 4L
L = 32/4 = 8 units
Radius of circular base of cylinder = 8/2 = 4 units
Circumference = 2πr
C = 2 * 3.142 * 4 = 25.136 units
The cylinder's base circumference is about 25 units,
2) The shape created by rotating an equilateral triangle about a line is a cone. The approximate circumference of the base is about 63 mm.
Rotating an equilateral triangle about a line creates a cone. The base retains the triangle's shape, and the circumference is equal to the triangle's perimeter.
With each side measuring 20 mm
Radius of cone = 20/2 = 10 mm
Circumference of base = 2πr
C = 2*3.142*10 = 62.884 mm
So,
Circumference of the base is approximately 63 mm
learn more about rotating a square here
https://brainly.com/question/16626275
#SPJ3
Complete question
Mason and Nora decided to swim across the river. Mason began swimming 8 seconds earlier than Nora.
Mason swam at a speed of 5 feet per second.
Nora swam at a speed of 9 feet per second.
For how many seconds had Mason been swimming at the moment when the two swimmers had swam exactly the same distance?
please help on b (left of c) and c !!!
rewrite each of the following expressions so that your answer has no negative or fractional exponents
i need help find the volume of this hexagon based pyramid!
please write steps and its ok to have more than one person answering
A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?
Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.
What is unitary method?The unitary method is a technique in mathematics for solving a problem by finding the value of a single unit, I.e.,1,(by dividing) and then finding the necessary value by multiplying the single unit value.A method of solving a problem that involves first determining the value of a single unit, And then multiplying that value to determine the required value.According to the question,
A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?let the number of paper be "X".$4=500$2000= 250,000Hence we can say that Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.
Know more about unitary method click here:
https://brainly.com/question/23423168
#SPJ2
How do I solve this? (Geometry)
Constantine picks two letters at random from the word constantinople with replacement. what is the probability that both letters picked are consonants?
The area of one circle is 4 times as large as a smaller circle with a radius of 3 inches. the radius of the larger circle is
A polynomial p(x) has a remainder of 4 when divided by (x+1) and a remainder of 7 when divided by (x-2) what will be the remainder when divided by (x+1)(x-2)
Use Gauss-Jordan elimination to solve the following system of equations. 3x + 5y = 7 6x − y = −8 A. x = 2, y = 1 B. x = 5, y = 6 C. x = 3, y = −1 D. x = −1, y = 2
A kayaker spends a morning paddling on a river. She travels 9 miles upstream and 9 miles downstream in a total of 6 hours. In still water, she can travel at an average speed of 4 miles per hour. What is the average speed of the river's current in miles per hour?
A) 1 mi/h
B) 2 mi/h
C) 3 mi/h
D) 1.5 mi/h
Average speed is the ratio of the total distance traveled to the total time taken. The average speed of the river's current is 2 mi/h.
What is Average speed?Average speed is the ratio of the total distance traveled to the total time taken.
As we know that the total time taken by the boat to travel upstream and downstream is 6 hours. And the distance traveled by Kayaker is 9 miles, each time while going upstream and downstream.
We know that when the boat is traveling upstream the water current will try to resist the boat, therefore, the speed of the boat while going upstream is (4-x), where x is the speed of the boat. Similarly, the speed of the boat when going downstream will be (4+x), as the water stream will try to provide a push to the boat. Therefore, the total time taken by the Kayaker can be written as,
Total Time
= Time taken while going upstream + Time taken while going downstream
[tex]\rm 6 = \dfrac{Distance\ upstream}{Speed\ upstream} + \dfrac{Distance\ Downstream}{Speed\ Downstream}[/tex]
[tex]\rm 6 = \dfrac{9}{(4+x)} + \dfrac{9}{(4-x)}[/tex]
Taking the LCM,
[tex]6 = \dfrac{9(4+x)+9(4-x)}{(4+x)(4-x)}\\\\6\times (4+x)(4-x) = 9(4+x)+9(4-x)\\\\6(16-x^2) = 36+9x+36-9x\\\\96 - 6x^2 = 72\\\\-6x^2 = 72-96\\\\6x^2 = 24\\\\x^2 = 4\\\\x =2[/tex]
Hence, the average speed of the river's current in miles per hour is 2 mi/h.
Learn more about Average Speed:
https://brainly.com/question/12322912
There are 7 black marbles and 9 white marbles in a bag. what is the probability of drawing 2 black marbles then a white marble without replacement
The perimeter of a square is 96 inches. if the side length is 2x + 4, what is the value of x and the length of each side?
A club decides to sell T-Shirts for 15$ as a fund-raiser. It cost $20 plus $9 per T-Shirt to make them. How many T-Shirts need to be made to make a profit of at least $150?
The lengths of the sides of a triangle are 6, 8, 10. Can the triangle be a right triangle? Yes or no?
In the diagram, PN¯¯¯¯¯ is the perpendicular bisector of AB¯¯¯¯¯ and is also the angle bisector of ∠CPD. If m∠CPD = x, which quantity is equal to sin ∠DPB?
sin x2
sinx2
cosx2
cos x2
Since ∠CPD = x and segment PN is the angle bisector of this angle, therefore segment PN equally divides ∠CPD into two angles. Which means that:
∠CPN = ∠NPD = x / 2
Further, segment PN is also the perpendicular bisector of AB which further means that the intersection formed by PN and AB creates a right angle (90°). Therefore:
∠NPD + ∠DPB = 90°
x/2 + ∠DPB = 90°
∠DPB = 90 – x/2
Therefore:
sin∠DPB = sin(90 – x/2) which is not in the choices
However we know that the relationship of sin and cos is:
sin(π/2 - θ) = cos θ
Where,
π/2 = 90
θ = x/2
Therefore:
sin(90 – x/2) = cos(x/2)
Answer:
cos(x/2)
The quantity which is equal to sin ∠DPB is:
cos(x/2)What is an Angle?This refers to the figure which is formed by two rays with a common endpoint.
Hence, we know that
∠CPN = ∠NPD = x / 2If we segment PN which is the bisector of AB, it would crerate angle 90 and this would give us:
∠NPD + ∠DPB = 90°x/2 + ∠DPB = 90°
∠DPB = 90 – x/2
With this in mind, there is the relation between sin and cos, which would be:
sin(π/2 - θ) = cos θWe are aware that
π/2 = 90θ = x/2Hence,
sin(90 – x/2) = cos(x/2)
=cos(x/2)
Read more about degrees and angles here:
https://brainly.com/question/25770607
What is the solution to 2x-8<12 ?
A. X<2
B. X<8
C. X<10
D. X<40
Answer:
x < 10
Step-by-step explanation:
HELP if f(x)=-14x-2, then f^-1(x)=?
Which value is in the domain of f(x)?
A.) –7
B.) –6
C.) 4
D.) 5
Answer:
C) 4
Step-by-step explanation:
The given function is
[tex]f(x)=\left \{ {{2x+5,\:-6\:<\:x\le0} \atop {-2x+3,\:0\:<x\le4}} \right.[/tex]
The function is defined on two intervals.
The first interval is
[tex]-6\:<\:x\le0[/tex] and the second interval is [tex]\:0\:<x\le4[/tex].
[tex]-7[/tex] does not belong to any of these intervals.
[tex]-6[/tex] does not also belong to any of these intervals.
[tex]4[/tex] belongs to the interval [tex]\:0\:<x\le4[/tex].
Hence 4 is in the domain of f(x).
[tex]5[/tex] does not also belong to any of the intervals.
Therefore the correct answer is C.
A ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. 1.97 is the time taken by the ball to hit the ground.
What is Distance?Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given that a ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t²
Now we can take h=0
h=-16t²+70-4t
-16t²+70-4t
Divide by 2
-8t²-2t+35
Now apply quadratic formula
a=-8, b=-2, c=35
t=-b±√b²-4ac/2a
t=2±√-2²-4(-8)(35)/2(-8)
t=2±√4+1120/-16
we get t= 1.97 and t= -2.22
You get the numbers to be : 1.97 and -2.22
We do not consider negative values. So the correct answer is 1.97
Hence 1.97 is the time taken by the ball to hit the ground.
To learn more on Distance click:
https://brainly.com/question/15172156
#SPJ2
James wants to go to a concert with his friends. The tickets to the show cost $10 each. If James buys x tickets at a cost of c dollars, represent c as a function of x.
Answer:
C = f(x)=10x
Step-by-step explanation:
plato answer
Two less than twice a number is the same as four times the number
Final answer:
The algebraic expression representing 'two less than twice a number is the same as four times the number' is solved, resulting in the number being -1.
Explanation:
The student's question involves solving a simple algebraic equation. We are given that two less than twice a number is the same as four times the number. To represent this algebraically, let's let the unknown number be n. The phrase 'twice a number' can be written as 2n. 'Two less than' this expression would be 2n - 2. The statement implies this is equal to four times the number, which is 4n. Therefore, the equation we need to solve is 2n - 2 = 4n. To solve this equation, we need to isolate the variable n on one side of the equals sign.
Subtract 2n from both sides: -2 = 2n.
Divide both sides by 2 to find the value of n: n = -1.
In conclusion, the number that satisfies the condition given is -1.
Melissa exercises for 20 minutes every day. She decides to increase her daily exercise time by 5 minutes each week. However, according to her doctor’s orders, she can spend no more than 45 minutes a day exercising. For how many weeks can Melissa increase her exercise time this way?
Answer:
at most 5 weeks
Step-by-step explanation:
Calculate the upper and lower limit for a 95% confidence interval about this mean. a family needs a new car, but isn't sure they can fit the payment into their budget. a sample of 36 months of grocery bills yields a mean of $94 with a standard deviation of $10. if the upper limit of a 95% confidence level is below $100, the family can afford to buy the car. standard error = (standard deviation)/(square root of sample size) upper limit (dollars and cents) lower limit (dollars and cents)
To find the upper and lower limits of a 95% confidence interval for the given data, calculate the standard error, use the multiplier of 2, and apply the formula Sample mean ± Multiplier * Standard error.
To calculate the upper and lower limit for a 95% confidence interval, we use the formula: Confidence interval = Sample mean ± Multiplier * Standard error. For this case, the sample mean is $94 and the standard deviation is $10. The standard error is calculated as $10 / √36 = $10 / 6 ≈ $1.67.
With a 95% confidence level, the multiplier is approximately 2. Therefore, the upper limit would be $94 + 2($1.67) = $94 + $3.34 ≈ $97.34, and the lower limit would be $94 - $3.34≈ $90.66.
I need to know the solution
An airline claims that the no-show rate for passengers booked on its flights is less than 6%. of 380 randomly selected reservations, 18 were no-shows. assuming that this data is used to test the airline's claim, find the p-value for the test. 0.3508 0.1499 0.1230 0.0746
The p-value in this context represents the probability that the no-show rate is indeed less than 6%, given the collected sample data. It is calculated using a test statistic formula and compared to a chosen significance level to determine whether to reject or not reject the null hypothesis (the airline's claim). The correct p-value can't be identified from the provided options without further details or calculations.
Explanation:To answer your question, we first need to understand the concept of a p-value and how to calculate it. The p-value is calculated in a hypothesis test and it's the probability of getting sample data like ours, or more extreme, if the null hypothesis is true.
The null hypothesis, in this case, would be the claim that the airline's no show rate is less than 6%.The alternative hypothesis would be that the no-show rate is 6% or higher.We know that 18 out of 380 randomly selected reservations were no-shows. So, we can use the test statistic formula to calculate the p-value which represents the probability that the no-show rate is less than 6% if our null hypothesis is true. The options provided here (0.3508, 0.1499, 0.1230, 0.0746) seem to be possible outcomes of that calculation.
Depending on the result of this calculation, we would then determine whether to reject the null hypothesis or not. If the p-value is less than or equal to our significance level (say 0.05 or 5%), then we reject the null hypothesis. Conversely, if the p-value is greater than our significance level, we do not reject the null hypothesis and we can say there is not enough evidence to support the claim.
Unfortunately, without further information or calculations, we can't definitively identify the correct p-value from the options provided in your question.
Learn more about P-value calculation here:https://brainly.com/question/33322273
#SPJ12
Stacy needed to fill her gas tank for a road trip. if she spent $45.87 and purchased 11 gallons how much did each gallon cost?
One student can paint a wall in 10 minutes. another student can paint the same wall in 15 minutes. working together, how long will it take for them to paint the wall?
Answer:
6 days
Step-by-step explanation:
Given that one student can paint a wall in 10 minute and another student in 15 minutes.
Since if number of persons increase, painting time decreases, this is a question of inverse proportion
Hence if they work together they can paint in one day
[tex]\frac{1}{10} +\frac{1}{15}[/tex] part of the work
i.e. work completed in 1 day when they work together
=[tex]\frac{1}{10} +\frac{1}{15} \\=\frac{9+6}{90} \\=\frac{1}{6}[/tex]
Hence in 6 days they can together complete the full work