The simplified form of the expression √(100x³⁶) will be 10x¹⁸. Then the correct option is A.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ √(100x³⁶)
Then the simplified form of the expression will be
⇒ √[(10x¹⁸)²]
⇒ 10x¹⁸
Then the correct option is A.
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Answer:
Step-by-step explanation:
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The simplified form of √(400x¹⁰⁰) is;
D; 20x⁵⁰
We want to find the simplified form of √(400x¹⁰⁰)
Now, according to laws of indices;
√ab = √a × √b
Thus;
√(400x¹⁰⁰) = √400 × √(x¹⁰⁰)
⇒ 20√(x¹⁰⁰)
Also according to law of indices;
a⁴ = a² × a²
Thus;
x¹⁰⁰ = x⁵⁰ × x⁵⁰
Thus;
√(x¹⁰⁰) = √(x⁵⁰ × x⁵⁰)
⇒ x⁵⁰
Our final answer is;
20x⁵⁰
f(x)= 2x^3 + 6x^2 -5x - 3, g(x)= 3x-4 find (f-g)(x)
The difference in the given functions is 2x^3 + 6x^2 -8x + 1
Difference of functionsGiven the following function a shown
f(x)= 2x^3 + 6x^2 -5x - 3
g(x)= 3x-4
Take the difference
(f-g)(x) = f(x) - g(x)
Substitute
(f-g)(x) = 2x^3 + 6x^2 -5x - 3 - (3x - 4)
Expand
(f-g)(x) = 2x^3 + 6x^2 -5x - 3 - 3x + 4
(f-g)(x) = 2x^3 + 6x^2 -8x + 1
Hence the difference in the given functions is 2x^3 + 6x^2 -8x + 1
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HELP pls. Which statement correctly demonstrates using limits to determine a vertical asymptote of
Answer:
Step-by-step explanation:
Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?
Answer:
28 feet
Step-by-step explanation:
Area of a rectangle is :
A = L × W
We are given A and a expression for L, so let's substitute :
448 = (2W-4) × W
Now we expand the left side :
2W²-4w = 448
Subtract 448 from both sides :
2W²-4W-448 = 0
Divide everything by 2 :
W²-2W-224 = 0
Now we factorise :
Find 2 numbers that multiply to give -224 and add to give -2 :
-16 and 14
Rewrite -2W with -16W and +14W :
W² - 16W + 14W -224 = 0
W(W-16) +14(W-16) = 0
(W+14)(W-16) = 0
W = -14 , W = 16
Only take positive value since this is lengths :
W = 16
Now we substitute W into the expression to find L :
L = (2W -4)
L = 2(16) - 4
L = 32 - 4
L = 28
Units will be feet since it is a length
Hope this helped and have a good day
Which formula finds the probability that a point on the grid below will be in the blue area? A grid contains 20 squares. 10 squares are shaded blue. P (blue) = StartFraction total number of squares over number of blue squares EndFraction P (blue) = StartFraction number of blue squares over total number of squares EndFraction P (blue) = StartFraction number of blue squares over number of white squares EndFraction P (blue) = StartFraction number of white squares over number of blue squared EndFraction
The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:
P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.
The probability = 1/2.
The probability of an event defines the chance of the occurrence of that event. It is given by the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.
If we suppose an event to be A, the total number of possible outcomes favorable to A be n, and the total number of outcomes in the experiment be S, then the probability of event A can be given as:
P(A) = n/S.
In the question, we are asked to find the formula that defines the probability that a point on the grid will be in the blue area, where the grid contains 20 squares, 10 of them being shaded blue.
We take the event that the chosen point is in the blue area as A.
The total number of outcomes favorable to this event A can be given by n, which will be equal to the number of blue squares = 10
The total number of outcomes in the experiment can be given by S, which will be equal to the number of squares = 20.
Now, the formula for the probability of event A can be written as
P(A) = n/S = 10/20 = 1/2.
The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:
P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.
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what is the sign of f on the interval -5/9 < X < 2/3
Note that the sign of f on the interval -5/9 < x < 2/3 is negative. (Option B)
What is the explanation for the above?To determine the sign of f(x) on the interval -5/9 < x < 2/3, we need to evaluate f(x) at a test point within this interval and determine if it is positive or negative.
Since we know that f(x) has zeros at x = -4, x = -5/9, and x = 2/3, we can use these points as our reference to choose test points.
Specifically, since the zeros at x = -5/9 and x = 2/3 are not included in the interval -5/9 < x < 2/3, we can choose any test point within this interval, such as x = 0.
Evaluating f(x) at x = 0, we get:
f(0) = (3(0) - 2)(0 + 4)(9(0) + 5)
= (-2)(4)(5)
= -40
Since f(0) is negative, we can conclude that f(x) is negative on the interval -5/9 < x < 2/3.
Therefore, the sign of f on the interval -5/9 < x < 2/3 is negative
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Full Question:
f(x) = (3x - 2) (x+4) (9x +5) has zeros at x = -4, x = -5/9, and x = 2/3, that is the sign of f on the interval -5/9 < x < 2/3?
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic charge if they worked 10 hours in one day?
$450
$400
$550
None of these choices are correct.
Answer:
$800
Step-by-step explanation:
per hour $40×10hours=$400
$400÷$50=8 times initial fee
8×$50=$400 total initial fee
$400hours fee+$400 initial fee=$800 total payment
Translate and solve using proportions what percent of 120 is15
Answer:
12.5%
Step-by-step explanation:
To find what percent of 120 15 is, we must find what 15/120 is.
15/120 = 0.125. To convert to a percent, we move the decimal two places to the right. So, the answer is 12.5%.
Brainliest, please :)
Answer:
12.5%
Step-by-step explanation:
Christine splits 4/5 pounds of candy with 5 people. What is the unit rate in pounds per person. In simplest form
Answer:
4/25
Step-by-step explanation:
4/5 ÷ 5 = 4/5 × 1/5 = 4/25
Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard
Please answer both questions I will give u brainliest if ur right
first one b 315, second d
Step-by-step explanation:
18*=3*+315
7*+4*=a*
I keep putting in the formula but I keep getting the answer wrong
Answer:
314 in² (nearest whole number)
Step-by-step explanation:
Radius of a regular polygon: The distance from the center of the polygon to any vertex. The radius of a hexagon is equal to the length of one side.
Therefore, from inspection of the given diagram:
radius = 11 in ⇒ side length = 11 inTo find the area of a regular polygon, we first need to calculate the apothem. The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.
[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]
where:
s = length of one siden = number of sidesGiven:
s = 11 inn = 6Substitute the given values into the formula and solve for a:
[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]
Area of a Regular Polygon
[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]
where:
n = number of sidess = length of one sidea = apothemGiven:
n = 6s = 11[tex]\textsf{a}=\dfrac{11\sqrt{3}}{2}[/tex]Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]
[tex]\implies \sf A=314.3672216...[/tex]
[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]
NEED HELP ASAP !!!
Simplify: √16r
O 47²
O 473
87²
O 8-3
Answer:
4 r^3
Step-by-step explanation:
sqrt ( 16 r^6 ) = sqrt ( 4^2 * (r^3)^2 ) = 4 r^3
find sin(x/2), cos (x/2), and tan(x/2) from the given information.
Sin(x)= 15/17, 0 < x <90
sin(x/2)= ?
cos(x/2)=?
tan(x/2)= 0.6
I need help with sin and cos. I know what tan is.
Step-by-step explanation:
sin(x/2) = sqrt((1 - cos(x))/2)
cos(x/2) = sqrt((1 + cos(x))/2)
tan(x/2) = sin(x/2)/cos(x/2)
sin(x) = 15/17
so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.
via Pythagoras we get the 3rd, horizontal side :
17² = 15² + side²
289 = 225 + side²
64 = side²
side = 8
cos(x) = 8/17
sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =
= 0.514495755...
cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =
= 0.857492926...
tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =
= 3/5 = 0.6
A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
Answer:
1/(7^5)=1/16807
Step-by-step explanation:
Assuming 7-key mean zero up to 7,
# of possible codes = 17^5 = 16807
=====
Probability of first try correct = 1/7^5
pls someone help me asap :)
Answer:
right angle
acute
acute
obtuse
obtuse
Step-by-step explanation:
Since angle <ABC is a straight line, the angle is 180 degrees. This means all the angles in between should also add up to 180 degrees. Using this knowledge you can solve for the value of angle <FBE which is going to be equal to 180 - (40 + 25 + 50) = 65.
< DBF = <DBE + <EBF
< DBF = 25 + 65 = 90 (right angle)
<EBD = 25 (given) (acute)
<DBC = 50 (given) (acute)
<ABE = <ABF + <FBE
<ABE = 40 + 65
<ABE = 105 (obtuse)
<CBF = <CBD + <DBE + <EBF
<CBF = 50 + 25 + 65
<CBF = 140 (obtuse)
height of 24cm with a radius of 7cm. What is the total surface area of the cone?
Answer:
the answer to this problem is 703.7 in^2
Let −5, 3 be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.
The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have (−5, 3) be a point on the terminal side of θ.
Perpendicular = -5
Base = 3
From Pythagoras' theorem:
Hypotenuse² = (3)² + (-5)²
Hypotenuse = √34
cosθ = 3/√34
cscθ = -√34/5
tanθ = -5/3
Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.
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A company had the following purchases and sales during its first year of operations:
Purchases Sales
January: 10 units at $120 6 units
February: 20 units at $125 5 units
May: 15 units at $130 9 units
September: 12 units at $135 8 units
November: 10 units at $140 13 units
The final answer of the Inventory is $3540.
What is Inventory?The term inventory refers to the raw materials used in production as well as the goods produced that are available for sale.
FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold
Ending inventory comprises of goods bought in May, September and November
cost of the ending inventory :
(4 x $130) + (12 x $135) + (10 x$140) = $3540
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What is the measure of complemnt angle
a)42° b) 35°
Answer:
90°
Step-by-step explanation:
A complement angle is the same as a right angle
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex][tex]\sf 55\textdegree[/tex]Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complements of these two angles by setting up an equation.
x+42=90
Subtract 42 from both sides
x=48
This problem can be solved the same way!
x+35=90
Subtract 35 from both sides
x=55
--
Hope that this helped! Best wishes.
--
Let f(t) represent the temperature of a turkey baking in an oven as a function of time (t) in the oven (in minutes). This means time (t) is the independent variable and temperature of the turkey f(t) is the dependent variable. The turkey was in the oven for 360 minutes and then removed. Note that when something is baked in an oven, the temperature of the oven stays constant. The graph of the function is shown below.
Describe the rate of change pattern over each interval of the graph listed below.
a. 0 < t < 345
b. 345 < t < 360
c. t > 360
Explain what is happening in each interval of your graph in terms of the turkey and its temperature, using complete sentences.
Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation.
Answer:
a. When the time is greater than 0, but less than 345 minutes, the temperature of the turkey is increasing at roughly a linear rate.
b. When the time ranges from 345 to 360 minutes, the temperature of the turkey stays constant, at 165 degrees.
c. When the time is greater than 360 minutes, the temperature of the turkey decreases.
which of the following are identities? check all that apply A. cot^2x+1=csc^2x B.tan^2=1-sec^2x C.sin2^x=1=cos^2x D.sin^2x+cos^2x=1
What is the midpoint of AB?
Answer: Point G.
Step-by-step explanation:
Count the number of spaces between points A and B. Then divide that number by 2 and count that many spaces from one point.
14/2=7
I hope this helps!! Pls mark brainliest :)
Jack and Susan bought together 28 books. Susan bought 11 books. Which one of the
following equations represents the number of books bought by Jack? Let x be the
number of books bought by Jack.
Answer:
11 + x = 28
Step-by-step explanation:
The number of books they bought must add to 28.
If f(x) =
√2x+3
6x-5
a. 1
b. -2
then f() =
C. -1
d. - 13
Answer:
put 1/2as a value of x in the equation and then solve .then the answer will be -1
Answer:
[tex]C.\ f\left( \frac{1}{2} \right) =-1[/tex]
Step-by-step explanation:
[tex]f\left( x\right) =\frac{\sqrt{2x+3} }{6x-5}[/tex]
In order to calculate f(1/2) ,all we have to do
is replacing x by 1/2 in the expression of f.
Then
[tex]f\left( \frac{1}{2} \right) =\frac{\sqrt{2\left( \frac{1}{2} \right) +3} }{6\left( \frac{1}{2} \right) -5 }[/tex]
[tex]=\frac{\sqrt{1+3} }{3-5}[/tex]
[tex]=\frac{\sqrt{4} }{-2}[/tex]
[tex]=\frac{2}{-2}[/tex]
[tex]=-1[/tex]
Which of the following is a correctly written algebraic equation?
2 + 0.2x
5b - 5x + 2
a - 3x=0
3(x/5)
what is the least common multiple of the numbers 8 and 12?
A. 24
B. 8
C. 4
D.96
Answer:
A. 24
Step-by-step explanation:
Least common multiple of 8 and 12 = 24
8× 1 = 8 12×1 = 12
8×2 = 16 12×2=24
8×3 = 24
L.C.M (8,12) = 24
The greatest multiple that occurs in both the multiples of 8 and 12, is 24.
Hence, the least common multiple here is 24.
Find x and y please help
Answer:
x is 130°,y is 60°
Step-by-step explanation:
x is corresponding to 130° therefore they are equal to find y since the angle on a straight line is 180° you subtract 180 from 130 and get 50 then you have gotten the other interior angle then add both interior angles and subtract by180 then you get the y
Answer:
X = 130° Y = 60°both the lines are parallel
therefore, X= 130° ( if two lines are parallel their corresponding angles are equal)
Y + 70° = X ( sum of tow interior angle is equal to exterior)
Y + 70= 130
Y = 130 - 70
Y = 60°
Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The best buy is (d) a 9 oz box of rice $1.25
How to determine the best buy?The best buy is the product that has the least unit rate.
The unit rate is calculated as:
Unit = Price/Weight
So, we have:
Box 1:
Unit rate = $0.90/6 oz = $0.150 per oz
Box 2:
Unit rate = $1.93/12 oz = $0.161 per oz
Box 3:
Unit rate = $2.42/16 oz = $0.151 per oz
Box 4:
Unit rate = $1.25/9 oz = $0.139 per oz
The least unit price is $0.139 per oz for box 4
Hence, the best buy is (d) a 9 oz box of rice $1.25
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Number of Potatoes
36
24
12
5
10
Number of Pounds
x
15
Use the graph to find the unit rate.
potatoes per pound
Answer this! Thanks so much in advance (:
Answer:
ai) m = 17, applicable past x = 23/17; aii) m = 4; applicable past 3 dad jokes
Step-by-step explanation:
to calculate slope you use the (y2 - y1) / (x2 - x1) equation
so for the first one
(62 - 11) / (5 - 2)
51 / 3 = 17
the equation for this is y = 17x + b
plug in values to find b
11 = 34 + b
b is -23
y = 17x - 23
because distance cannot be negative we must find when x is exactly 0 to find where it is applicable
17x = 23
x = 23/17
for the second one we can subtract again
(10 - 2) / (5 - 3)
8 / 2
4 is the slope
like before we must find b and then find where y is 0
y = 4x + b
2 = 12 + b
b = -10
y = 4x - 10
4x = 10
x = 5/2
since you cannot have 1/2 a dad joke we round up from 2 1/2 to 3
