The results were as follows: a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.
What are square root of a number?Get a number that, when multiplied twice by itself, equals the original number in order to find the square root of any integer. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any integer. equivalently for 4throots and so on.
We have
a)
\(x^{2}\) = 36
so x= \(\sqrt{36}\)
x = +6, -6
b)
\(x^{2}\) = \(\sqrt{50}\)
x = \(\sqrt[4]{50}\)
x = +-2.6591
c)
\(x^{2}\) = \(\sqrt{100}\)
x = \(\sqrt[4]{100}\)
x = +- 3.1622
d)
2\(x^{2}\) = 50
\(x^{2}\) = 50/2
\(x^{2}\) = 25
x =+-5
Thus a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.
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1 dollar bill is 6.14 inches long 2.61 wide and 0.00043 thick. If you had 1 billion in 100 dollar bills the the number of bills would be
The number of 100 dollar bills in one billion dollars is 10 million hundreds or 70,900 hundred dollar bills.
To find the number of 100 dollar bills in one billion dollars, we can use the following steps:
First, we need to find the value of one billion dollars in terms of hundreds. Since each hundred dollar bill has a value of $100,
we can divide one billion by 100 to get the number of hundreds
\(:$$\frac{1\text{ billion}}{100}=10\text{ million}$$\)
So one billion dollars is equal to 10 million hundreds.
Now we need to find the volume of one hundred dollar bill. To do this, we multiply its length, width, and thickness:\($$6.14 \text{ in} \times 2.61 \text{ in} \times 0.00043 \text{ in}=0.00709 \text{ in}^3$$\)
The volume of one hundred dollar bill is approximately 0.00709 cubic inches.
Finally, we need to find the total volume of 10 million hundreds:\($$0.00709 \text{ in}^3 \times 10,000,000=70,900 \text{ in}^3$$\)
Therefore, the total volume of 10 million hundred dollar bills is approximately 70,900 cubic inches.10 million hundreds or 70,900 hundred dollar bills.
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By how much is a piece of land covering 7.5 hectares shorter than another one which is 540 m long and 360 m wide?
Step-by-step explanation:
To determine the difference in size between the two pieces of land, we need to calculate the area of each.
The first piece of land covers 7.5 hectares. To convert hectares to square meters, we multiply by 10,000 (since 1 hectare = 10,000 square meters):
Area of the first piece of land = 7.5 hectares * 10,000 square meters/hectare
= 75,000 square meters
The second piece of land is given in length and width:
Area of the second piece of land = length * width
= 540 m * 360 m
= 194,400 square meters
To find the difference in size, we subtract the smaller area from the larger area:
Difference = Area of the second piece of land - Area of the first piece of land
= 194,400 square meters - 75,000 square meters
= 119,400 square meters
Therefore, the first piece of land is shorter by 119,400 square meters compared to the second piece of land.
f y = mx + b is the equation of a line perpendicular to the line y = 5x – 2, what is the value of m?
Answer:
5
Step-by-step explanation:
What is the volume of the following rectangular prism? (please help)
Answer:
?
Step-by-step explanation:
i think ljhh ako naiintindihan
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Enter your Teacher.. libaray
Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be
27.75 meters. She stands 23.5 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
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27.75 m
(Diagram is not to scale.)
1.65 m
23-5 m
Crest
Dashboard | Kham
Trigonometry is the application of certain functions to determine the value of a quantity. The tree stands 10.77 meters tall.
What is trigonometric function?Some trigonometric functions can be used to solve the given problem. Let s represent the distance from the tip of the tree's shadow to where Aria stands, so that;
s = 27.75 - 23.5
= 4.25 m
s = 4.25 m
Also, let the angle formed by the line connecting the tree's tip and the shadow's tip be, so that;
Tan θ = opposite / adjacent
Here given,
Opposite side = 1.65
Adjacent side = 4.25
= 1.65 / 4.25
= 0.3882
θ = Tan⁻¹ 0.3882
= 21.216
θ = 21.216°
We get θ = 21.216°
The tree's height, h, can be calculated as follows:
Tan 21.216° = h/27.75
h = Tan 21.216° x 27.75
= 0.3882 x 27.75
h = 10.77m
As a result, the tree's height is 10.77m.
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Which of the following Statements are true?
Statement 1: Every trapezoid is a parallelogram.
Statement 2: An equilateral triangle is also an acute
triangle.
Only Statement 1 is true.
Only Statement 2 is true.
Both Statements are true.
Neither Statement is true.
Answer:
only statement 2 is correct
Step-by-step explanation:
trapezoids only have one equal side to be a parallelogram it must have 2
A equilateral triangle has angels which are 60 degrees which is less that 90 (right angle)
Triangle RST has vertices R(-3,2), S(0,-5),and T(4,5).When translated R’ has coordinates (4, 1). Find the coordinates of S’ and T’.
Which number cannot be written as a ratio of Integers? Please Help!
a
0.14444444.....
b
√121
c
0.125
d
0.14151617...
The number 0.14151617... cannot be written as a ratio of Integers, which is the correct answer that would be an option (D).
What are Integers?Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer. Fractional numbers are not included in integers. Integers are represented by the symbol Z.
As per the given question, we have to determine the ratio of Integers
⇒ 0.14444444.....
This number can be written as a ratio of Integers
⇒ 18/125
⇒ √121
⇒ √(11 x 11)
⇒ 11 = 11/1
This written as a ratio of Integers
⇒ 0.125
⇒ 125/100
⇒ 0.14151617...
This number cannot be written as a ratio of Integers.
Hence, the correct answer would be an option (D).
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it’s a -10 btw and a positive 9
Answer: -1 and -9
Step-by-step explanation:
(- 1) + (-9) = -10
(-1) * (-9) = +9
hope this helps!
Find the value of x and y in simplified radical form.
x and y have the values 7 and 7√2, respectively.
The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.
We can use this information to determine the values of x and y because the base is specified as being 7.
Let's give the perpendicular side the value of x, and the hypotenuse the value of y.
The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.
Consequently, x = 7.
We can determine that x:y:2x using the ratio of 1:1:2.
When we enter the value of x, we may calculate y:
7:y:√2(7)
Simplifying even more
7:y:7√2
Given that the hypotenuse (y) equals 72, we can write:
y = 7√2
Thus, x and y have the values 7 and 7√2, respectively.
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Given the following functions:
f(x) = 2x+6
Find (h-f)(x).
○ 4x² - 3x + 7
O 4x² 2x - 1
O 4x² + 3x + 3
O 4x² + 2x + 11
g(x) = 3x - 2
h(x) = 4x² + 5
12121211.ooooooooooo
the ages (in years) of the 5 employees at a particular computer store are the following 35, 32, 37, 37, 34assuming that these ages constitute an entire population, find the standard devation of the population. round your answer to two decimal places.
The standard deviation is 1.90
The first thing we would do here is to find the mean of the given set
The mean can simply be calculated by adding all the numbers and dividing these numbers by their count
Mathematically, we have this as follows;
\(\frac{35+32+37+37+34}{5}\text{ = }\frac{175}{5}\text{ = 35}\)What we have to do next is to subtract the mean from each of the numbers
This would be;
35-35 = 0
32-35= -3
37-35 = 2
34-35 = -1
0 , -3 , 2 , 2 and -1
square each of these
0, 9 , 4 , 4 ,1
Sum of these is 18
Now, we use the standard deviation formula;
\(\sigma\text{ = }\sqrt[]{\frac{\Sigma f(x-\operatorname{mean})^2}{N}}\)As we can see , the summation of all the numbers after subtracting the mean is 18
So, we have;
\(\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{18}{5}} \\ \sigma\text{ = }\sqrt[]{3.6} \\ \sigma\text{ = }1.90 \end{gathered}\)please help? :( Thanks in advance
Answer: Proportional!
Step-by-step explanation:
1.8/7.2=0.25
0.4/1.6=0.25
0.25=0.25
In
= 2n+2n²
find the first five terms
\(t(n) = 2 {n}^{2} + 2n \)
_________________________________
\(t(1) = 2 ({1})^{2} + 2(1) \)
\(t(1) = 2 \times 1 + 2 \times 1\)
\(t(1) = 2 + 2 = 4\)
##############################
\(t(2) = 2 ({2})^{2} + 2(2) \)
\(t(2) = 2 \times 4 + 2 \times 2\)
\(t(2) = 8 + 4 = 12\)
##############################
\(t(3) = 2 ({3})^{2} + 2(3) \)
\(t(3) = 2 \times 9 + 2 \times 3\)
\(t(3) = 18 + 6 = 24\)
##############################
\(t(4) = 2 ({4})^{2} + 2(4)\)
\(t(4) = 2 \times 16 + 2 \times 4\)
\(t(4) = 32 + 8 = 40\)
##############################
\(t(5) = 2 ({5})^{2} + 2(5) \)
\(t(5) = 2 \times 25 + 2 \times 5\)
\(t(5) = 50 + 10\)
\(t(5) = 60\)
_________________________________
And we're done.
Thanks for watching buddy good luck.
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The equation Y= X^2/2 - 8 and Y= 2X -2 are graphed below what are the solutions to the equation X^2/2 - 8 = 2X -2 
The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.
To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.
The equation is:
X^2/2 - 8 = 2X - 2
To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:
X^2 - 16 = 4X - 4
Next, we rearrange the equation to have all terms on one side:
X^2 - 4X - 12 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:
(X - 6)(X + 2) = 0
Setting each factor equal to zero gives us two possible solutions:
X - 6 = 0 --> X = 6
X + 2 = 0 --> X = -2
So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.
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The function f(x) = 1.85x^2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answer:
I helped you last time so I'll help you again.
Step-by-step explanation:
We can find the average rate of change of f(x) over the interval [10, 20] using the formula:
average rate of change = (f(b) - f(a))/(b - a)
where a = 10 and b = 20.
So, we have:
f(a) = f(10) = 1.85(10)^2 = 185
f(b) = f(20) = 1.85(20)^2 = 740
average rate of change = (740 - 185)/(20 - 10) ≈ 55.5
Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.
Please Do this : (2x3 + 3x 4)(1/9)
Answer: 2
Step-by-step explanation:
Alright, so assuming that "x" in this equation means multiplication you would solve this using PEMDAS. PEMDAS is basically the order in which you solve everything so first is parentheses, then exponent, then multiplication and division and then addition and subtraction.
So lets go to the first parentheses- (2x3 + 3x4):
Inside the parentheses we should use PEMDAS. This means that we perform multiplication first.
It should now look like this: (6+12)
Next you just add so now the whole thing is (18)(1/9)
It is important to note that (1/9) is the same as the fraction one ninths. Next you just perform multiplication of fractions so now it should be 18/9 which simplifies to 2.
Hope this helps :)
Answer:
2
Step-by-step explanation:
(2x3+3x4)(1/9)
=(6+12)(1/9)
=(18)(1/9)
=18/1x1/9
=18/9
=2
what is the estimated sum of 4 5/12 + 3 8/14
A.7
B.7 1/2
C.8
D.9
The estimated sum of 7 83/84 is 8 to the nearest whole number.
Addition of mixed fractions:Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.
Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.
Using the first process:
= 4 5/12 + 3 8/14
The whole number are 4 and 3, adding those two together, we have:
= 7 (5/12 + 8/14)
The L.C.M of 12 and 14 is 84.
= 7( (7×5)+ (6*8) ) /84
= 7 (35+ 48/84)
= 7 (83/84)
To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.
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please help me with i’ll give you brainlist
The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.
What is whisker plot?A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.
Here,
To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:
Minimum value: the smallest value in the data set.
First quartile (Q1): the median of the lower half of the data set.
Median: the middle value in the data set.
Third quartile (Q3): the median of the upper half of the data set.
Maximum value: the largest value in the data set.
First, we need to put the data in order:
10, 12, 14, 15, 16, 18, 22, 24, 25, 28
The minimum value is 10 and the maximum value is 28.
The median is the middle value, which is 18.
To find the first quartile, we need to find the median of the lower half of the data set, which is:
10, 12, 14, 15, 16
The median of this lower half is 14.
To find the third quartile, we need to find the median of the upper half of the data set, which is:
22, 24, 25, 28
The median of this upper half is 24.
So, the five-number summary for this data set is:
Minimum value = 10
First quartile (Q1) = 14
Median = 18
Third quartile (Q3) = 24
Maximum value = 28
Now we can use this information to create the box and whisker plot:
| |
----+----+----+----+----
10 14 18 24 28
The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.
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Julie made 25 international long-distance phone calls to London last month. The scatterplot below shows the length and cost of each phone
call she made.
Cost of International
Long Distance Phone Calls
3
Cost of Call (dollars)
.
N
.
.
0
6 12 18 24
Length of Call (minutes)
Which conclusion is best supported by the scatterplot?
Answer:b
Step-by-step explanation:
Answer:d there is no relationship time and cost varies
Step-by-step explanation:
its conman sense
Plzz help me I well mark brainliest if you are correct!
NO LINKS
adult tickets to the game are sold for $7 and student tickets are sold for $5. what combination of tickets must be sold to have total sales of at least $5000?
The combination of tickets that must be sold to have total sales of at least $5000 is 7x + 5y ≥ 5000
How to construct inequality?
The situation forms an inequality. Inequality expression has <, >, ≤ or ≥. Therefore,
let
x = number of adult ticket sold
y = number of students ticket sold
Therefore, the combination of tickets must be sold to have total sales of at least $5000 is as follows:
7x + 5y ≥ 5000
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PLEASE HELP ME I AM IN DIRE NEED OF ASSISTANCE EXTRA POINTS INCLUDED BRAINLIEST GUARANTEED. Explain how to solve 5x − 2 = 8 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answer:
5x - 2 = 8
5x = 8 + 2
5x = 10
x = 10/5
x = 2
Which answer is an equation in point-slope form for the given point and slope?
Point (1, 9), Slope: 5
(A) y - 9 = 5(x + 1)
(B) y+9 -5(x - 1)
(C) y-9=5(x - 1)
(D) y-1-5(x +9)
Answer:
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀,y₀):
y-y₀ = m(x-x₀)
In your case, m=5 and (x₀,y₀)=(1,9):
y-9 = 5(x-1)
Is 8(3x+2) and 4(6x÷4) equivalent?
Answer:
x= - 8/9
Step-by-step explanation:
Can someone please actually help me?
Answer:
\(x^{2}\) + \(-2x^{2}\) = \(-x^{2}\)
and 3x + 9x = 12x
5 will not change
so
\(-x^{2}\)+12x+5
HELPPPPPPPPPPPPPPPPPPP
Answer:
15
Step-by-step explanation:
What is the area, in square feet, of the shaded part of the rectangle below?
5ft
17 ft
11 ft
Every month, Helen budgets $110 for coffee from the coffee bar located in the lobby of her apartment building. If she stops by the bar every morning and her average order costs $3.88, how much money will she have left after 16 days?
answer:
$47.92
explanation:
$3.88 × 16=$62.08
$110-$62.08=$47.92
the 16 is the days
110is the budget
3.88 is the cost
hope that helps
The total money Helen have left after 16 days will be $47.92
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Helen budgets for coffee from the coffee bar located in the lobby of her apartment building was $110. And she stops by the bar every morning and her average order costs $3.88.
The budget = 110 dollars
The average cost = 3.88 dollars
Then the average order costs for 16 days;
$3.88 × 16 = $62.08
Therefore, the money she have left after 16 days;
$110-$62.08=$47.92
Hence, The total money she have left after 16 days will be $47.92
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what is (1/2 + isqrt3/2)^5?
Answer:
\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)
Step-by-step explanation:
Convert 1/2 + i√3/2 to rectangular form
\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)
Use DeMoivre's Theorem
\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)