The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
How to find the equivalent of a quotient?We want to find the equivalent quotient of the given expression; √16 / √8
Now, we know that the square root of 16 is equal to 4 i.e. √16 = 4
Thus, applying that to our expression gives;
√16/√8 = 4/√8
Now, square root of 8 which is √8 can also be expressed as; 2√2
Thus;
4/√8 = 4/2√2 = 2/√2
The steps to rationalize the denominator, to get rid of all radicals that are in the denominator are as follows;
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
Step 2: Make sure all radicals are simplified.
Step 3: Simplify the fraction if needed.
If we rationalize the denominator of our expression, we have;
2/√2 × √2/√2 = 2√2/ 2 = √2
Also, 2/√2 can be expressed as √4 /√2
Therefore, The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
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Use a triple integral to find the volume of the wedge bounded by the parabolic cylinder yx and the planes zy and z0.
The volume of wedge is 4/15 by use of Triple integral.
According to the statement
we have to find the volume of wedge which is bounded by the parabolic cylinder.
So, because of the given shape of z=√y
the plane y=0 is a boundary, in addition to the given x = 0, z = 0.
so we are in the first octant for all of this. and the further constraint is the plane x + y = 1
Triple integrals are 3 successive integrations, used to calculate a volume, or to integrate in a 4th dimension, over 3 other independent dimensions.
but as a triple integral you would write:
∫x=0 ∫y=0∫z=0 dz dy dx
And after put the values in it and solving it we get the
[−4/15(1−x)^5/2] at x=0
Then after that the answer will become 4/15.
So, The volume of wedge is 4/15 by use of Triple integral.
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Juan bought a sweater for $15.95 and two shirts for $9.00 each. how much did juan spend on clothes?
Answer:
Step-by-step explanation:
Well first you have:
$15.95 for one sweater
$9.00 each for two shirts
You would double the amount $9.00 which would be:
9 + 9 = 18 or Multiply 9 x 2 = 18
So this would total to 15 + 18 = $33
Write an absolute value inequality for each of the following. Then graph the
solution set on a number line.
all numbers less than 7and greater than -7
An absolute value inequality for "all numbers less than 7 and greater than -7" is given by |x| < 7.
How to write an absolute value inequality?Based on the information provided, we can logically deduce that the statement describes an intersection of set because the word "and" was used.
This ultimately implies that, we would use the less than (<) symbol to write an absolute value inequality for the given statement:
|x| < 7
Therefore, this can be translated as follows:
-7 < x < 7 or x < 7 and x > -7.
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HALP URGENT PLS im dum
x =x=x, equals
^\circ
∘
Answer:
x = 55°
Step-by-step explanation:
That square box indicates a right angle.
A right angle is 90°.
We know that angle x and the 35° angle are making up this 90° angle together.
So, the equation to show what this ship looks like is the following:
[tex]x+35=90[/tex]
This is a simple equation, that if we solve, we get:
[tex]x=55[/tex]
So, x is 55°.
Considering the angle of the ray, it is found that the value of x is of x = 55º.
What is the angle of the ray?The ray has an angle of 180º. It is composed by:
Angle x.An angle of 35º.An angle of 90º.Hence:
x + 35 + 90 = 180
x = 180 - 125
x = 55º.
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There are 86,400, frames of animation in 1 hour of anime.
How many frames are there per second?
There are 3,600, seconds in 1 hour.
Answer:
There are 24 frames of animation in 1 second of anime. Step-by-step explanation: There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.
All the students in a science class complete a 15-point extra-credit assignment to raise their test scores the new test score is 15 points more than the original score let x = original score let y = new score ehich equation represents this situation?
The equation that represents the situation is,
y = x + 15
Given Information
It is given that the students complete a 15-point extra-credit assignment in order to raise their test scores.
The new test score is 15 more than the old test score.
We have to find an equation for this situation. A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.
Forming Equation
Original Score = x
New Score = y ................... (1)
Thus, after the test, the score is raised by 15 points.
⇒ New score = x + 15 .................... (2)
The following equation can be deduced from (1) and (2)
y = x + 15
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Find the odds against hitting the ball if you have made 3 out of 19 attempts
We conclude that the odds of hitting the ball are 0.158
How to find the odds?
The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.
Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:
P = 3/19 = 0.158
We conclude that the odds of hitting the ball are 0.158
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100 POINTS!!! PLEASE HELP ASAP EXPERTS! PLEASE I'M BEGGING!!
The function H(t) = −16t2 + 64t + 12 shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by g(t) = 10 + 10.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answer:
A)
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
Between 3 and 4 seconds.
B) The baseballs will collide between 3 and 4 seconds.
Step-by-step explanation:
Given functions:
[tex]H(t)=-16t^2+64t+12[/tex]
[tex]g(t)=10+10.4t[/tex]
Part ASubstitute the values of t = 1, 2, 3 and 4 into the two functions:
[tex]H(1)=-16(1)^2+64(1)+12=60[/tex]
[tex]H(2)=-16(2)^2+64(2)+12=76[/tex]
[tex]H(3)=-16(3)^2+64(3)+12=60[/tex]
[tex]H(4)=-16(4)^2+64(4)+12=12[/tex]
[tex]g(1)=10+10.4(1)=20.4[/tex]
[tex]g(2)=10+10.4(2)=30.8[/tex]
[tex]g(3)=10+10.4(3)=41.2[/tex]
[tex]g(4)=10+10.4(4)=51.6[/tex]
Create a table with the found values:
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
The solution to H(t) = g(t) is between 3 and 4 seconds as:
When t = 3, H(t) > g(t)
When t = 4, H(t) < g(t)
To prove this, equate the equations and solve for t:
[tex]\implies -16t^2+64t+12=10+10.4t[/tex]
[tex]\implies -16t^2+53.6t+2=0[/tex]
Using the Quadratic Formula to solve for t:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-53.6 \pm \sqrt{53.6^2-4(-16)(2)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{53.6 \pm \sqrt{3000.96}}{32}[/tex]
[tex]\implies t=3.39, -0.04\:\:(\sf 2\:d.p.)[/tex]
As time is positive, t = 3.39 s (which is between 3 and 4 seconds).
Part BWhen the two baseballs are at the same height they will collide.
Therefore, the baseballs will collide between 3 and 4 seconds (when t = 3.39 s).
The formula m =1/2(a+b) gives the mean M of two numbers a and b
a.express a in terms of m and b
b.hence find a when m=19 and
b=23
Answer:
a = 2m - b , a = 15
Step-by-step explanation:
(a)
m = [tex]\frac{1}{2}[/tex] (a + b) ← multiply both sides by 2 to clear the fraction
2m = a + b ( subtract b from both sides )
2m - b = a
(b)
when m = 19 and b = 23 , then
a = 2(19) - 23 = 38 - 23 = 15
a. 'a' in terms of m and b is given by: a = 2m - b.
b. when m = 19 and b = 23, the value of 'a' is 15.
a. To express a in terms of m and b, we can rearrange the mean formula:
m = (1/2)(a + b)
Now, we'll solve for 'a':
Multiply both sides by 2 to eliminate the fraction:
2m = a + b
Subtract 'b' from both sides:
2m - b = a
So, 'a' in terms of m and b is given by: a = 2m - b.
b. Now that we have the expression for 'a', we can find its value when m = 19 and b = 23:
a = 2m - b
a = 2(19) - 23
a = 38 - 23
a = 15
So, when m = 19 and b = 23, the value of 'a' is 15.
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Charlotte is solving the following equation for X (x+3)^2-10=2 her first steps are given below (x+3)^2=12 x+3= + square root 12
The values of the x in the given equation are x = 6.46 and x = -0.46
Solving an equationFrom the question, we are to solve the equation for x
The given equation is
(x+3)² -10 = 2
First, add 10 to both sides of the equation
(x+3)² -10 +10 = 2 +10
(x+3)² = 12
Now, take the square root of both sides to get
x + 3 = ±√12
∴ x = 3 ± √12
x = 3+√12 OR 3-√12
x = 3 + 3.46 OR 3 - 3.46
x = 6.46 OR -0.46
Hence, the values of the x in the given equation are x = 6.46 and x = -0.46
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Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).
The area of the convex polygon is 21.5 square units
How to determine the area of the convex polygon?The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |
So, we have:
A = 0.5 * |-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 +2 * -4 - 0 * -3 - 3 * 2 + 4 * 1|
Evaluate
A = 0.5 * |-43|
Remove the absolute bracket
A = 0.5 * 43
This gives
A = 21.5
Hence, the area of the convex polygon is 21.5 square units
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Find the coefficient of t to the 4th power in the expansion of (-9t-9) to the 7th power select one: a. -25,515 b. -100,442,349 c. -167,403, 915 d. -4,782, 969
The coefficient of t to the 4th power in the given expansion is -167403915.
Option (c) is the correct answer.
What is an expansion?An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.
Given expansion=[tex](-9t-9)^{7}[/tex]
Coefficient of the 4th power of t in the expansion,
=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]
=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]
=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]
=[tex]35t^{4}(-9)^{7} \\[/tex]
=[tex]35t^{4}(4782969)[/tex]
= -167403915[tex]t^{4}[/tex]
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The sum of a number and its reciprocal is 122/11. Find the
number.
O -11
09
O 11
Answer:
11
Step-by-step explanation:
if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11
Store A has sold 67 mugs and sells 11
mugs every week. Store B has sold 13
mugs and sells 17 mugs every week.
How many weeks (w) will it be before
Store B sells as many mugs (m) as
Store A?
m = 11w + 67
m = 17w + 13
[?] weeks
Answer:
9 weeks.
Step-by-step explanation:
m = 11w + 67
m = 17w + 13
So:
11w + 67 = 17w + 13
67 - 13 = 17w - 11w
54 = 6w
w = 9.
Jagrit is looking at two computer repair stores.
Store 1: Data-Fix
The total cost charged by Data-Fix is represented by the graph
as shown.
a) Write an equation to model the relation of total cost, C, and
number of hours, n as shown in the graph.
b) One of the points on the graph is (3, 60). Explain the
meaning of this point, in the context of this scenario.
Store 2: Comput-Repair
It charges a fixed cost of $10 plus $15 per hour for repair
services.
c) Write an equation to model the relation of total cost, C, and
number of hours, n, in Comput-Repair.
d) On the grid provided, graph the line that describes the fee structure for Compu-Repair.
e) What are the coordinates of the point of intersection?
f) What does it mean in this scenario?
g) Based on the point of intersection, how would you advise Jagrit when trying to choose between the two
computer repair stores? Fully explain your answer supported by the information from the graph.
PLEASE I DON'T HAVE TIME
See below for the solution of each question
The equation of the modelThe points are given as:
(3,60) and (5, 80)
The equation is calculated as:
[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]
This gives
[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]
Evaluate the quotient
C(n) = 10 * (n - 3) + 60
Expand
C(n) = 10n - 30 + 60
Evaluate
C(n) = 10n + 30
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30
Explain the points on (3, 60)The point (3, 60) means he paid $60 for 3 hours
The equation of the model for Comput-RepairHere, we have:
Fixed = $10
Hourly rate = $15
The equation is calculated as:
C(n) = Fixed + Rate * Number of hours
This gives
C(n) = 10 + 15n
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n
The graph of the fee structure for Compu-RepairThe equation is represented as:
C(n) = 10 + 15n
See attachment for the graph
The coordinates of the point of intersectionThis is the point where the two lines intersect.
From the graph, we have the point of intersection to be:
(n, C(n)) = (4, 70)
The meaning in this scenarioThis means that the charges for Comput-Repair and Data-Fix are the same after 4 hours
Advice JargitBased on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate
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The lengths of three sides of a triangle are 2x + 1/5 feet , 4x + 1/2 feet , and x+ 1 5 . what is the perimeter of the triangle? the drondown menuto complete the answer
Answer:
7x + 9/10 ft
Step-by-step explanation:
To find the perimeter of a triangle, add the lengths of the three sides
P = 2x + 1/5 + 4x + 1/2 + x+ 1/ 5
Combine like terms
P = 7x + 2/5 +1/2
Get a common denominator
P = 7x + 2/5(2/2) + 1/2 * (5/5)
= 7x + 4/10 + 5/10
= 7x + 9/10
By use of technology, we investigated Mary’s investment and created the model, M(x) = 3.03(1.28)2x, in thousands of dollars. What was Mary’s initial investment? $4.96 $3,030 $4,960 $3.03
Using an exponential function, it is found that Mary's initial investment was of $3,030.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.Her investment model, in thousands of dollars, is:
[tex]M(x) = 3.03(1.28)^{2x}[/tex]
Then a = 3.03, since we measure the amount in thousands of dollars, Mary's initial investment was of $3,030.
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Find the equation of the line through point (−1,4) and parallel to 5x+y=4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
The equation of the parallel line is y = -5x - 1
How to determine the line equation?The equation is given as:
5x + y = 4
Make y the subject
y = -5x + 4
The slope of the above equation is
m = -5
Parallel lines have equal slope.
This means that the slope of the new line is 5
The equation is then calculated as:
y = m(x - x1) + y1
So, we have:
y = -5(x + 1) + 4
Expand
y = -5x - 5 + 4
Evaluate
y = -5x - 1
Hence, the equation of the parallel line is y = -5x - 1
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which of the following is equivalent to the logarithmic equation below?
Answer:
A
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then
[tex]log_{2}[/tex] 8 = 3 ⇒ 2³ = 8
Answer:
A
Step-by-step explanation:
loga(b)=x
a^x=b
since the answer to log2(8)=3
a^3=8
b=8
a=2
so 2^3=8
I hope this helped!
Question 12 of 20
Subtract.
(2x²+5)-(4x-3)
OA. 2x²-4x+2
OB. -2x² +8
OC. 2x2²-4x+8
OD. -2x²+2
Answer:
C
Step-by-step explanation:
Distribute the negative, (2x^2 + 5) + (-4x+3)
Add like terms, 2x^2 - 4x +(5+3)
2x^2-4x+8
Solve for this equation:
x(x+3)(x+3)=0
Answer:
x^3+6x^2+9x
if you are trying to find the original function
if not, and you are trying to find the zeros is
x=-3
x=0
Step-by-step explanation:
multiply x(x+3)
x^2+3x
then multiply that by x+3 and that should give you the answer
Answer:
x = 0 or x = -3 or x = -3
Step-by-step explanation:
set up factors as:
x = 0
x + 3 = 0
x + 3 = 0
the first will remain as x = 0 while the others become x = -3 once subtracted
i hope this helped!
The formula d=1/2n+26 relates the nozzles pressure n (in pounds per square inch) of a free hose and the maximum horizontal distance the water reaches d (in feet). How much pressure is needed to reach a fire 50 feet away?
The pounds of pressure needed to reach a fire 50 feet away is 48 pounds
Formulad = 1/2n + 26
where
n = nozzle pressure in pounds per square feetd = distance the water reachesIf d = 50 feet
d = 1/2n + 26
50 = 1/2n + 26
50 - 26 = 1/2n
24 = 1/2n
n = 24 ÷ 1/2
n = 48 pounds
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If Avogadro's number of pennies is divided equally among the 246 million men, women, and children in the United States, how many dollars would each receive
USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].
What is the US dollar?The US dollar is the official currency of the United States and a number of other countries. The Coinage Act of 1792 established the United States dollar on equal footing with the Spanish silver dollar, divided it into 100 cents, and authorized the minting of coins denominated in dollars and cents.To find how many dollars would each receive:
Avogadro's number of pennies is divided equally among 261 million people.
Avogadro's number is [tex]6.022[/tex] × [tex]10^{23}[/tex].
To find the number of pennies each person will receive, we divide [tex]6.022[/tex] × [tex]10^{23}[/tex] by 261 million.
Pennies per person = [tex]\frac{6.022 * 10^{23} }{261 million} = \frac{6.022 * 10^{23} }{261 * 10^{6} } = 2.31 * 10^{15}[/tex]
This is equal to the number of cents each person receives.
To convert pennies into dollars, 1 USD = 100 pennies, divide [tex]2.31 * 10^{15}[/tex] by [tex]100[/tex].
USD per person = [tex]\frac{2.31 * 10^{15} }{100} = $2.31 * 10^{13}[/tex]
Therefore, USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].
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The question you are looking for is here:
If Avogadro's number of pennies is divided equally among the 261 million men, women, and children in the United States, how many dollars would each receive?
what is the volume of a sphere with a radius of 6 inches
Answer:
288pi in^3 , which is 904.78 in^3 to nearest hundredth.
Step-by-step explanation:
V = 4/3 pi r^3
= 4/3 pi * 6*3
= 288pi in^3
= 904.7786842 in^3
Player A throws the ball 25 yards to Player B. After catching the ball, Player B immediately turns 90 degrees to his left
and runs with the ball for 30 yards. At the end of the play, how far away is the ball from where it started? Round your
answer to the nearest whole number.
Answer:
39
Step-by-step explanation:
Sofa co is selling sofas with a 33% discount off the original price to reduce its stock. Calculate the discounted price of a sofa originally selling for £999.00. Please show your working.
A machine in a candy company creates 9,328 pieces of candy each hour. if a box holds 98 pieces of candy, how many boxes can be filled in one hour?
Answer:
Step-by-step explanation:
9,328 and you would divide that by 98 and the answer would be 95.18367347 boxes
The citizens of a state may only register to vote after proving to have submitted their census survey.
The citizens of a state may only register to vote after proving to have submitted their census survey is a "false" statement.
What is census survey?In order to create statistics that define populations and their characteristics, such as age, education, housing, and income, the U.S. Census Bureau compiles data from households.
The purpose of census survey are-
We obtain this information by posing questions to members of the household regarding the occupants of the home, apartment, mobile home, or group housing.The census helps our communities decide where to build everything from homes to hospitals, from schools to supermarkets, and it provides information about who we are as a country and where we are headed. It aids in the government's decision-making about the allocation of cash and assistance to cities and states.It aids in predicting the nation's economic needs, such as those for electricity, housing, food, etc. figuring out the country's population size, standard of life, and number of unemployed people.To know more about census, here
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The complete question is-
The citizens of a state may only register to vote after proving to have submitted their census survey.(True/False)
Can someone help me please
Answer:
D. (4,0) and (-4,0)
C. there is one discontinuity at x=3
Step-by-step explanation:
Roots can be found by setting f(x)=0:
f(x)=(x^2-16)/(x^2-2x-3)
0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator
0=x^2-16, use difference of squares to factor it
0=(x+4)(x-4)
x=4,-4
Therefore the roots are (4,0) and (-4,0)
Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0
Set the denominator equal to 0:
0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor
0=(x-3)^2
x=3
Therefore, there is a discontinuity at x=3
Someone do this please
Answer: 102 degrees
Step-by-step explanation:
The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.
51 + 51 = Angle 4
Angle 4 = 102 degrees