Answer:
Step-by-step explanation:
[tex]\large \boldsymbol{ \boxed{\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b} }} \\\\\\ \sqrt{25x+75} +3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9x-18} \\\\ \sqrt{25} \cdot \sqrt{x+3}+3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9}\cdot \sqrt{x-2} \\\\5\sqrt{x+3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4\sqrt{x-3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5\sqrt{x+3})^2 =(2+4\sqrt{x-3} )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5\sqrt{t} \ \big)^2=(2+\sqrt{t-6} )^2 \\\\[/tex] [tex]\large \boldsymbol{} 25t=4+16\sqrt{t-6} +16(t-6) \\\\(9t+92)^2=(16\sqrt{t-6} )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions[/tex]
How do you calculate an antilog?
eg: antilog 2.1423
9514 1404 393
Answer:
138.77
Step-by-step explanation:
Your scientific or graphing calculator will have exponential functions for bases 10 and e. On the calculator shown in the first attachment, they are shifted (2nd) functions on the log and ln keys. Consult your calculator manual for the use of these functions.
The value can be found using Desmos, the Go.ogle calculator, or any spreadsheet by typing 10^2.1423 as input. (In a spreadsheet, that will need to be =10^2.1423.) The result using the Go.ogle calculator is shown in the second attachment.
You can also use the y^x key or the ^ key (shown to the left of the log key in the first attachment). Again, you would calculate 10^2.1423.
__
We have assumed your log is to the base 10. If it is base e (a natural logarithm), then you use the e^x key instead. Desmos, and most spreadsheets, will make use of the EXP( ) function for the purpose of computing e^( ). You can type e^2.1423 into the Go.ogle calculator.
_____
Additional comment
There are also printed logarithm tables available that you can use to look up the number whose log is 0.1423. You may have to do some interpolation of table values. You should get a value of 1.3877 as the antilog. The characteristic of 2 tells you this value is multiplied by 10^2 = 100 to get the final antilog value.
The logarithm 2.1423 has a "characteristic" (integer part) of 2, and a "mantissa" (fractional part) of 0.1423.
What is the product of the polynomials below?
(3x2 - 2x - 3)(5x2 + 4x + 5)
Answer
15x^4+2x^3+8x^2-15
Answer:
15^4+2^3−8^2−22−15
Step-by-step explanation:
(3^2−2−3)(5^2+4+5)
Distribute:
3(5^2+4+5) ⋅ ^2−2(5^2+4+5) − 3(5^2+4+5)
15^4+12^3+15^2 − 2(52+4+5) − 3(52+4+5)
15^4+12^3+15^2 − 10^3−8^2−10 − 3(52+4+5)
15^4+12^3+15^2 − 10^3−8^2−10 − 15^2−12−15
Combine like terms:
15^4+12^3−10^3+15^2−8^2−15^2−10−12−15
15^4+2^3+15^2−8^2−15^2−10−12−15
15^4+2^3−8^2−10−12−15
15^4+2^3−8^2−22−15
15^4+2^3−8^2−22−15
hope it helps :)
please mark brainliest!
Describe and correct the error in finding the volume of the pyramid.
Can someone quickly answer this please
Answer:
Step-by-step explanation:
Hello !
(4,4*2,4) + (3,14 * 2,2² )/2 =
10,56 + 7,60 = 18,2 m²
The volume of a box(v) varies directly with its length(l). If a box in the group has a length of 35 inches and k=15, what is its volume?
Answer:
525 in³
Step-by-step explanation:
Use the direct variation equation, y = kx.
Substitute y with v (volume) and substitute x with l (length) to represent this situation:
y = kx
v = kl
Plug in 35 as l and 15 as k, then solve for v (the volume):
v = kl
v = 15(35)
v = 525
So, the volume of the box is 525 in³
A Ferris wheel is boarding platform is 2 meters above the ground, has a diameter of 48 meters, and rotates once every 5 minutes. How many minutes of the ride are spent higher than 38 meters above the ground
Answer:
Step-by-step explanation:
I discounted the 2-m ramp. If we are supposed to be looking for the length of time the ride is above 38 m from the ground, that translates to 36 m from the very bottom of the circle that is the Ferris wheel (where the wheel would meet the "ground"). I first found the circumference of the circle:
C = 48(3.1415) so
C = 150.792 m
I enclosed this circle (the Ferris wheel is a circle) in a square and then split the square in 4 parts. Each square has a quarter of the circle in it. If you divide the circumference by 4, that means that the arc length of each quarter circle is a length of 37.698 m. But that doesn't put us 36 m above the ground, that only puts us 24 m above the ground (remember the diameter of the circle is 48, so half of that is 24, the side length of each of the 4 squares). What that means to us (so far, and we are not at the answer yet) is that when the height off the ground is 24 m, a car that starts at the bottom of the ride has traveled 37.698 m around the circle. Traveling in an arc around the outside of the circle is NOT the same thing as a height off the ground. Going around a circle takes longer because of the curve. In other words, if the car has traveled 37.698 m around the outside of the circle, it is NOT 37.698 m above the ground...it's only 24 m above the ground. Hence, the reason I enclosed the circle in a square so we have both the circle's curve {arc length} and height above the ground {side of the square}). As the car travels farther along the outside of the circle it gets higher off the ground. If one quarter of the circle is 24 m above the ground, we need to figure out how much farther around the circle we need to go so we are 36 m above the ground. The height difference is 36 - 24 = 12m. we need now to find how long the arc length of the circle is that translates to another 12 m (the difference between the 24 we found and the 36 total). Using right triangle trig I found that arc length to be 12.566. The total arc length on the circle that translates to 36 m above the ground is 50.26437 m.
Going back to the beginning of the problem, the circumference of the circle is 150.792, and it makes one complete revolution in 5 minutes. That means that a car will travel 30.1584 m in 1 minute. Since this is the case, we can use proportions to solve for how long it takes to get 36 m above the ground:
[tex]\frac{m}{min}:\frac{30.1584m}{1min}=\frac{50.26437m}{xmin}[/tex] and cross multiply:
30.1584x = 50.26437 so
x = 1.6667 minutes, the time it takes to reach a height of 36 m. BUT this is not what the question is asking. The question is asking how long it's HIGHER than that 36 m. Let's think.
The car starts at the bottom of the ride, gets to a height of 36 m, keeps going around the circle to its max height of 48 m, then eventually comes back down and keeps going til it's back on the ground. That means that there is a portion at the top of the wheel that is above 36 m. If it goes 50.2647 m around the circle til it's at 36 m, then when it passes the max height and drops back to 36 m, it's 50.2647 m around the other side of the circle. We just found that to travel that 50.2647 m, it took the car 1.6667 minutes. We travel this distance twice (once meeting the height going up and then again coming down) so that takes up 3.3334 minutes.
5 minutes - 3.3334 minutes leaves us off 36 m above the ground for 1.6664213 minutes.
convert 17.25base base two to base 2
Answer:
could you explain your question better please
(Picture) Could someone help me solve this I need to use Inverse Operations but I don't fully understand? I'll mark brainliest, 10 Points.
Answer:
[tex]x = - 8[/tex]
Step-by-step explanation:
First,Step write the given equation.
[tex] \frac{x}{2} + 7 = 3[/tex]
In Algebra, we learn how to solve for a missing term called a variable. We must use inverse operations to undo terms to isolate our variable. Inverse operations means that we do the opposite of the given.
Opposite of Addition is Subtraction, vice versa.Opposite of Multipication is Division, vice versa.For example, say we have a equation
[tex]x + 2 = 3[/tex]
We would subtract 2 from both sides. E.g( remember the golden rule of algebra). What we do to one side, we do the other. This applies when we solving for a variable.
This means that
[tex]x = 1[/tex]
And if we substitute 1 in for x, it is indeed true.
[tex]1 + 2 = 3 = 3[/tex]
Now, back to the question.
[tex] \frac{x}{2} + 7 = 3[/tex]
First, we subtract 7 from both sides to get rid of the 7 on the left side. Also remeber to undo terms that aren't included in the variable when solving these problems.
So now we got
[tex] \frac{x}{2} = - 4[/tex]
Then we multiply 2 by both sides since that the opposite of division.
[tex] \frac{x}{2} \times 2 = x = -4 \times 2 = - 8[/tex]
So this means that
[tex]x = - 8[/tex]
If we plug this in, this is true.
[tex] \frac{ - 8}{2} + 7 = 3[/tex]
If V=πh²(r-h\3) make r subject of formula
Making r the subject of formula, we have; [tex]r = \frac{V}{\pi h^{2} } \; + \;\frac{h}{3}[/tex]
In Mathematics, making a variable the subject of formula simply means making the particular variable to be equal to all the other variable contained in an algebraic expression or mathematical equation. Thus, the subject of a formula is typically on the left-hand side of a mathematical equation while the other variables on the right-side.
Given the mathematical expression;
[tex]V = \pi h^{2}(r \; - \;\frac{h}{3} )[/tex]
To make "r" subject of formula;
First of all, we would divide both sides by [tex]\pi h^{2}[/tex]
[tex]\frac{V}{\pi h^{2} } = r \; - \;\frac{h}{3}[/tex]
Next, we would rearrange the equation;
[tex]r = \frac{V}{\pi h^{2} } \; + \;\frac{h}{3}[/tex]
For more on subject of formula visit: https://brainly.com/question/17148850
I need help I don't understand it.
These angles are corresponding angles, and we know that corresponding angles are equal when a transversal intersects two parallel lines.
So,
8x - 12 = 6x + 8
=> 8x - 6x = 8 + 12
=> 2x = 20
=> x = 20/2
=> x = 10
So, the value of x is 10.
please mark this answer as brainlist
The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).
A) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
B) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
C) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
D) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground
Answer:
A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground
Step-by-step explanation:
f(t) = 4t^2 − 8t + 7
Factor out 4 from the first two terms
f(t) = 4(t^2 − 2t) + 7
Complete the square
(-2/2)^2 =1 But there is a 4 out front so we add 4 and then subtract 4 to balance
f(t) = 4( t^2 -2t+1) -4 +7
f(t) = 4( t-1)^2 +3
The vertex is (1,3)
This is the minimum since a>0
The minimun is y =3 and occurs at t =1
Answer:
The above answer is correct.
Step-by-step explanation:
In 32 days, a field is cleared by 8 workers. How many workers would clear the same field in 8 days if working at the same time
Answer: 32
No of workers = 8
No of days = 32
Now no of days = 8
Let the number of workers be x
ATQ
256/x = 8
x = 256/8
x = 32
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Find the length of CV
Answer:
sinΘ = opposite/ hypotenuse
sin (37)= CV/55
55 sin (37) = CV
CV=33.1
OAmalOHopeO
Find the median, first quartile, third quartile, interquartile range, and any outliers for each set of data. 111, 68, 93, 88, 74, 152, 119, 87, 88, 105, 84, 102, 151, 115, 112 A. Median: 102, Q1: 87, Q3: 113, IR: 28, outliers: none B. Median: 102, Q1: 87, Q3: 115, IR: 28, outliers: 68 C. Median: 102, Q1: 87, Q2: 115, IR: 28, outliers: none D. Median: 102, Q1: 87, Q3: 115, IR: 27, outliers: none
Answer:
Q1 = 87 ;
Q2 = 102 ;
Q3 = 115 ;
IQR = 28
OUTLIER = None
Step-by-step explanation:
Given the data:
111, 68, 93, 88, 74, 152, 119, 87, 88, 105, 84, 102, 151, 115, 112
Ordered data : 68, 74, 84, 87, 88, 88, 93, 102, 105, 111, 112, 115, 119, 151, 152
Sample size, n = 15
The first quartile, Q1 = 1/4(n+1)th term
Q1 = 1/4(15+1)th term
Q1 = 1/4(16) = 4th term
Q1 = 87
The Median , Q2 = 1/2(n+1)th term
Q2 = 1/2(15+1)th term
Q2 = 1/2(16) = 8th term
Q2 = 102
The third quartile, Q3 = 3/4(n+1)th term
Q3 = 1/4(15+1)th term
Q3 = 3/4(16) = 12th term
Q3 = 115
The interquartile range, IQR = Q3 - Q1
IQR = (115 - 87) = 28
Q1 = 87 ;
Q2 = 102 ;
Q3 = 115 ;
IQR = 28
OUTLIER = None
help please :) try to explain and answer math coordinates
In the diagram what is the length of the 3rd side?
Answer:
Step-by-step explanation:
Use Pythagorean's Theorem:
[tex]c^2=15^2+8^2[/tex] and
[tex]c^2=225+64[/tex] and
[tex]c^2=289[/tex] so
c = 17
What are the values of a, b, and c in the quadratic equation 0 = 1 / 3x² – 3x – 2?
O a = 3,6 =3, c= 2
O a = 1, b =-3, c= -2
O a= 2,6 = 3, c= -2
O a = 1, b = -3, c = 2
W
Answer:
[tex]a = \frac{1}{2} \\ b = - 3 \\ c = - 2[/tex]
Step-by-step explanation:
The explanation is in the picture!
can you help me please.
Answer:
-86
Step-by-step explanation:
-102-
98 so the answer is -86
I need help to find n =
Answer:
n = √108
Step-by-step explanation:
Use similar triangles or the right triangle altitude theorem.
18/n = n/6
n^2 = 18 * 6
n^2 = 108
n = √108
Find the number in which 4 has highest value.
6050.4837
6834.2590
6986.0432
6748.9251
Step-by-step explanation:
the number in which 4 has the highest value is
6748.9251
Answer:
6834.2590
Step-by-step explanation:
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PLS HELP ASAP!!!!!!!!!!!!!!!!
2. Write down the supplementary angle of each of the following angles are 105 degree.
Answer:
75
Step-by-step explanation:
Answer:
75°Step-by-step explanation:
Supplementary angles add up to 180°.
The angle x, supplementary with 105°:
x + 105° = 180°x = 180° - 105°x = 75°(3[tex]\sqrt{7} \\[/tex]+7[tex]\sqrt{3}[/tex])/[tex]\sqrt{21}[/tex]
Answer:
sqrt(3) + sqrt(7)
Step-by-step explanation:
3*sqrt(7) / sqrt(21) = 3/sqrt(3)
If you rationalize the denominator, you get 3*sqrt(3)/3. The threes cancel
You are left with sqrt(3)
7sqrt(3)/sqrt(21) = 7 / sqrt(7)
If you rationalize the denominator, you get
7 sqrt(7)/ 7 = sqrt(7)
The 7s have been canceled out
The answer is
sqrt(3) + sqrt(7)
Mis Gurung is a bank Manager in a development bank. She draws Rs 75000 every month and a Dashain bonus of one months salary. Find her income tax in a year.
Answer:
With new regime is 183,750Rs
Step-by-step explanation:
I. 75,000 * 13 [12 months + 1 month bonus] = 975,000
II. Ms.Gurung tax rate will be ₹37500 + 15%
III. Perform ratio x/975,000 = 15/100 [15% is 15/100] = 146,250
IIII. ₹37500 + 146,250 = 183,750Rs
It depends on how tax rate will costs, could be more or less.
If s = 6 and t = 4, find the value of x.
x = 4 + s - t
Answer:
x = 6
Step-by-step explanation:
s = 6
t = 4
x = 4 + s - t
Substituting s and t in equation,
x = 4 + 6 - 4
x = 6
Answer:
6
Step-by-step explanation:
s=6
t=4
x= 4+6-4
x=10-4
x=6
Therefore; the final result is 6
Practice multiplying numbers by powers of 10.
Please help will give brainliest
Answer:
16p - 2
Step-by-step explanation:
Answer:
20p - 2
Step-by-step explanation:
To find a perimeter, you take the values of each side and add them together.
Let's start there.[tex](p-8)+(9p-7)+(p-8)+(9p-7)[/tex]
Bring all values with a p to one side[tex]p+9p+9p+p-8+7-8+7[/tex]
Simplify, knowing values with an attached variable cannot be added to values without an attached variable.[tex]20p-8+7-8+7[/tex]
Simplify the other numbers.[tex]20p-2[/tex]
Which choices are equivalent to the expression below? 3sqrt5 + 8sqrt5
A. 24 start 5
B. 24 sqrt 10
C. 11 sqrt 10
D. 11 sqrt 5
Answer:
B. 24 sqrt 10
Step-by-step explanation:
Hope this helped.
Answer:
11√5
Step-by-step explanation:
just putting the question with the symbols here so its easier to find for others
Which choice is equivalent to the expression below? 3√5+8√5
A. 24√5
B. 24√10
C. 11√10
D. 11√5
Please help me thank you xx
Answer:
A
Step-by-step explanation:
the brigde means anything in between
how to evaluate 4(x+2−5x) when x=2
Answer:
-24
Step-by-step explanation:
4(x+2−5x)
Combine like terms
4(2 -4x)
Distribute
8 -16x
Let x=2
8 - 16(2)
8 - 32
-24
how to evaluate 4(x+2−5x) when x=2
To Find :The value after evaluating Solution :We are provided that x equals 2 so have to put 2 instead of x to the desired result4(x + 2 - 5x)
Putting the value of x we get
4(2 + 2 - 5 × 2)
According to BODMAS multiplication comes first then addition
So 5 × 2 will be solved after that we will simplify 2 added with 2
4(2 + 2 - 10)
4(4 - 10)
4(-6)
- 24
Henceforth, the required answer is -24
