You want to pull out the square roots of each term since they are both perfect squares.
Factor using the difference of squares formula: a2-b2=(a+b)(a-b)
This formula allows the middle term to cancel out.
=x2 - 49
=(x + 7)(x - 7)
ANSWER: (x + 7)(x - 7)
Hope this helps! :)
((3.55)^2+(4.12)^2+(4.41)^2)/2(3.55)*(4.12)
Answer:
((3.55)^2+(4.12)^2+(4.41)^2)/2(3.55)*(4.12)
=358.519825
Step-by-step explanation:
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Help anyone can help me do this question,I will mark brainlest.
Answer:
11. 40.5
12. 84
Step-by-step explanation:
[tex]5x- \dfrac{ \sqrt{ 9 { x }^{ 2 } -6x+1 \phantom{\tiny{!}}} }{ 1-3x }[/tex]
Answer:
[tex]=5x+1[/tex] or [tex]=5x-1[/tex]
Step-by-step explanation:
One is given the following equation:
[tex]5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]
The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation. Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]
[tex]=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}[/tex]
Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,
[tex]=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}[/tex]
[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]
Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:
[tex]|a-b|\\=a -b[/tex] or [tex](-a-b) = b-a[/tex]
[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]
[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex] or [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]
Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,
[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex] or [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]
[tex]=5x-(-1)[/tex] or [tex]=5x-(1)[/tex]
Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.
[tex]=5x-(-1)[/tex] or [tex]=5x-(1)[/tex]
[tex]=5x+1[/tex] or [tex]=5x-1[/tex]
For what value of k does the linear system below have infinite solutions?
2x - 6y = k
6x - 18y = 30
Answer:
10
Step-by-step explanation:
The first equation should be the same with the second one, then we will have an infinite number of solutions of this system.
So if I multiply the first equation by 3, it'll be
6x-18y=3k
So if they should be the same, 30=3k
K=10
An iceberg weighs 450,000 pounds if it loss 0.2% of its weight in a day, what is its new weight at the end of the day
Answer:
449 100
Step-by-step explanation:
0.2% × 450000÷ 100=900
450000-900= 449 100
Answer:
Step-by-step explanation:
The answer is 449100 pounds .
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
Can someone help me with this answer?
[tex](4.2 \times {10}^{5}) \times (3.2 \times {10}^{6}) = 15.54 \times {10}^{11} = 1.554 \times {10}^{12} [/tex]
I hope I helped you ^_^
In how many years will the interest of a sum Rs 3600 at the rate of 5.5% per year be Rs 594.8?
Answer:
in 3.04 years the will give required intrest
Working together, Nadia and Olivia can clean a horse stable in 8 hours. Had Nadia cleaned it alone, it would have taken her 12 hours Find out how long it would take Olivia to clean the horse stable by herself.
Answer:
24 hours
Step-by-step explanation:
The formula is
1/a + 1/b = 1/c where a and b are the times alone and c is the times together
1/12 + 1/b = 1/8
Multiply by 24b to clear the fractions
24b(1/12 + 1/b = 1/8)
2b + 24 = 3b
Subtract 2b from each side
2b +24-2b = 3b-2b
24 = b
Find the area of each.
Answer:
14
Step-by-step explanation:
The formula for the area of a triangle is: 1/2 times base times height.
1/2x8x3.5=14
A 100m mast is supported by six cables in two sets of three cables. They are anchored to the ground at an equal distance from the mast. The top set of three cables is attached at a point 20m below the top of the mast. Each cable in the lower set of three cables is 60m long and is attached at a height of 30m above the ground. If all the cables have to be replaced, find the total length of cable required?
Answer:
60
would be right
Step-by-step explanation:
Total length of cable required is 466.18 m.
What is Pythagoras theorem?Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
According to the question
A 100m mast is supported by six cables in two sets of three cables.
They are anchored to the ground at an equal distance from the mast.
The top set of three cables is attached at a point 20m below the top of the mast.
Each cable in the lower set of three cables is 60m long and is attached at a height of 30m above the ground.
One set of guy wires (1 upper and one lower have two right triangles which can solve
The lower right triangle
a = distance from the pole to guy tie point
b = 30 m
c = 60 m the lower guy wire (the hypotenuse)
Using Pythagoras theorem
[tex]a^{2} +30^{2} =60^{2}[/tex]
⇒ [tex]a^{2} = 3600 - 900[/tex]
⇒ [tex]a^{2} =2700[/tex]
⇒ [tex]a = \sqrt{2700}[/tex]
⇒ [tex]a = 51.96[/tex] m from the pole to the tie point.
The other triangle using upper guy wire as the hypotenuse (h) tied to a point on the pole 80 m from the ground (20 m from the top) and also 50m from the tie point.
Using Pythagoras theorem
[tex]h^{2} =(51.96)^{2} +80^{2}[/tex]
⇒ [tex]h^{2}=2700+6400[/tex]
⇒ [tex]h^{2}=9100[/tex]
⇒ [tex]h = \sqrt{9100}[/tex]
⇒ [tex]h = 95.39[/tex] m , the length of the upper guy wire
For one set of guy wires (1 upper & 1 lower):
= 95.39 + 60
= 155.39 m
For 3 sets of guy wires :
= 3(155.39)
= 466.18 m of wire required
Hence, total length of cable required is 466.18 m.
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An expression is shown below: \sqrt(50)+\sqrt(2) is it irrational or rational
Answer:
Irrational
Step-by-step explanation:
It's an irrational number since both of them are irrational
What is the average rate of change of the function over the interval x = 0 to x = 8?
f(x)=2x−1/3x+5
Enter your answer, as a fraction, in the box.
====================================================
Work Shown:
Plug in x = 0
[tex]f(x) = \frac{2x-1}{3x+5}\\\\f(0) = \frac{2*0-1}{3*0+5}\\\\f(0) = \frac{0-1}{0+5}\\\\f(0) = -\frac{1}{5}\\\\[/tex]
Repeat for x = 8
[tex]f(x) = \frac{2x-1}{3x+5}\\\\f(8) = \frac{2*8-1}{3*8+5}\\\\f(8) = \frac{16-1}{24+5}\\\\f(8) = \frac{15}{29}\\\\[/tex]
Now use the average rate of change formula
[tex]m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(8)-f(0)}{8-0}\\\\m = \frac{15/29 - (-1/5)}{8}\\\\m = \frac{15/29 + 1/5}{8}\\\\m = \frac{(15/29)*(5/5) + (1/5)*(29/29)}{8}\\\\m = \frac{75/145 + 29/145}{8}\\\\[/tex]
[tex]m=\frac{104/145}{8}\\\\m = \frac{104}{145} \div \frac{8}{1}\\\\m = \frac{104}{145} \times \frac{1}{8}\\\\m = \frac{104*1}{145*8}\\\\m = \frac{104}{1160}\\\\m = \frac{13}{145}\\\\[/tex]
Which expressions are equivalent to 5+(-3)(6x-5)5+(−3)(6x−5)5, plus, left parenthesis, minus, 3, right parenthesis, left parenthesis, 6, x, minus, 5, right parenthesis ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 18x-2018x−2018, x, minus, 20 (Choice B) B 3x-33x−33, x, minus, 3 (Choice C) C None of the above
5+(-18x+15)5 + (-18x +15)5
5+ (-90x +75) + (-90x + 75)
-180x +155
let's see the alternatives:
a) -2000x - 2018 -> -200x - 201,8
b) -30x - 33 -> -180x -198
c) none of the above
so, c is the right one
hope it helps :)
Answer:
ITS C
Step-by-step explanation:
Which three lengths could be the lengths of the sides of a triangle? 21 cm, 7 cm, 11 cm 7 cm, 23 cm, 11 cm, 12 cm, 7 cm, 19 cm 10 cm, 15 cm, 23 cm
Answer:
(d) 10 cm, 15 cm, 23 cm
Step-by-step explanation:
21 cm, 7 cm, 11 cm — 7+11 < 21 . . . not a triangle
7 cm, 23 cm, 11 cm — 7+11 < 23 . . . not a triangle
12 cm, 7 cm, 19 cm — 7+12 = 19 . . . not a triangle
10 cm, 15 cm, 23 cm — 10+15 > 23 . . . can form a triangle
__
The sum of the two shortest sides must exceed the length of the longest.
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
Must click thanks and mark brainliest
using trig to solve for the missing angle
Step-by-step explanation:
Since there is a 45 and 90 degree angle, this is a 45-45-90 triangle. The legs are equal in a 45-45-90 ttiangle. The hypotenuse sqr root of 2 times more than the legs. So this means the hypotenuse measure is
[tex]18 \sqrt{2} [/tex]
So we can set up a equation.
[tex] {18}^{2} + {x}^{2} = ({18 \sqrt{2}) }^{2} [/tex]
[tex]x = 18[/tex]
So the missing side is 18
chứng minh đường thẳng a là tiếp tuyến của ( O,R) tại điểm C
state the equation, in slope-intercept form of each of the following graph
Answer:
A) y=(1/4)x-1, 4y=x-4
B) y=-2x
Members of a band class were arguing over which
instruments are played by the best academic students. A
survey was conducted, and here are the results:
All 13 flute players had a grade point average (GPA)
between 3.84 and 3.88.
There were only 3 percussionists. One had a GPA of
2.4, one had a GPA of 2.8, and one had a GPA of 3.2.
Among the saxophone players, 4 had a GPA of 3.9,
and the other 5 had a GPA of 4.0.
h
The median GPA of the percussionists is 2.8
This question appears incomplete.
Here is the complete question :
Members of a band class were arguing over which instruments are played by the best academic students. A survey was conducted, and here are the results:
All 13 flute players had a grade point average (GPA) between 3.84 and 3.88.
There were only 3 percussionists. One had a GPA of 2.4, one had a GPA of 2.8, and one had a GPA of 3.2.
Among the saxophone players, 4 had a GPA of 3.9, and the other 5 had a GPA of 4.0.
For percussionists, the median GPA is _____.
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
Median is a measure of central tendency
Other measures of central tendency include mean and mode.
The GPA of the 3 percussionists are 2.4, 2.8 and 3.2
This data has already been arranged in ascending order.
The number that is in the middle is 2.8
Conversely, if the GPA is arranged in descending order, it is 3.2, 2.8 and 2.4
The number that is in the middle is 2.8
For more information on how to calculate median, check : https://brainly.com/question/12528427?referrer=searchResults
Write an algebraic model based off this numerical model
Step-by-step explanation:
T0 = a³+4
T1 = a⁴x a¹ +4
T2= a³ + a³ + 4
T3= a⁴ + a⁴* a² + 4
T4= a⁴ + a⁴ x a¹ + 4
T5= a³ + a³ + a⁴+4
Answer:
hello,
Step-by-step explanation:
c(1)=5
c(2)=9
c(2)-c(1)=9-5=4
c(2)=9
c(3)=13
c(3)-c(2)=13-9=4
c(3)=13
c(4)=17
c(4)-c(3)=17-13=4
c(4)=17
c(5)=21
c(5)-c(4)=21-17=4
for n=1,2,...,k :
c(n+1)-c(n)=4 and c(n+1)=4*(n+1)+1=4n+5
c(1)=1
(x+8)^2-2(x-8)(x-2)+(x+2)^2=15
Lem is playing a board game and needs to roll two dice and get a six on both die in order to win the game. What is the probability that Lem will win the game on the next roll? Write your answer as a simplified fraction.
The probability of getting a 6 on one dice is 1/6
The probability of getting a 6 on both dice would be 1/6 x 1/6 = 1/36
Answer: 1/36
Which function represents g(x), a refection of f(x)=1/2(3)^x across the y-axis
Answer: g(x) = (1/2)3^-x reflection over y axis yields (-x,y)
Given the a center (-1, -2) and a radius r = 2. Identify the circle.
Answer:
1st option
1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2
Answered by GAUTHMATH
-6>t-(-13)
slove for the inequality
Answer:
-19>t
Step-by-step explanation:
-6>t-(-13)
-6>t +(13)
Subtract 13 from each side
-6-13 > t+13-13
-19>t
the difference of 8 and 3 is multiplied by one quarter of the sum of 7 and 5
Answer:
15
Step-by-step explanation:
the difference of 8 and 3 : 8-3 = 5
sum of 7 and 5 : 7+5 = 12
a quarter of that sum : 12/4 = 3
the difference from before is now multiplied by that quarter : 5 × 3 = 15
I know, you are a beginner, but you don't know basic arithmetic calculation of +, -, × , / ? really ?
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The solution of the difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 is 15.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The statement can be solved as shown below,
1. The difference between 8 and 3,
8 - 3 = 5
2. The difference between 8 and 3 is multiplied by one-quarter of the sum of 7 and 5,
[tex](8-3) \times \dfrac{(7+5)}{4}\\\\= 5 \times \dfrac{12}{4}\\\\= 15[/tex]
Hence, the solution of the difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 is 15.
Learn more about Multiplication:
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Rebecca can paint a room in 12 hours Guadalupe can paint the same room in 16 hours how long does it take for both Rebecca and Guadalupe to paint the room if they are working together
Please help me with this on the image
Step-by-step explanation:
The total of the number of computers he sold in 2015 is 67.
The total of the number of computers he sold in 2016 is 61.
The total of the number of computers he sold in 2017 is 71.
He sold 35 computers in Quarter 1, 24 in Quarter 2, 61 in Quarter 3, and 79 in Quarter 4.
He sold the most computers in 2017 and the least in Quarter 2.
Therefore, to find the total number of computers he sold all time, we add 67, 61, and 71 together to get 199.
Hope this helped!
Answer with Step-by-step explanation:
From the given table
(a)
In quarter 1
Computer sold in 2015=12
Computer sold in 2016=15
Computer sold in 2017=8
Total computer sold in quarter 1=12+15+8=35
In quarter 2
Computer sold in 2015=9
Computer sold in 2016=10
Computer sold in 2017=5
Total computer sold in quarter 2=9+10+5=24
In quarter 3
Computer sold in 2015=21
Computer sold in 2016=17
Computer sold in 2017=23
Total computer sold in quarter 3=21+17+23=61
In quarter 4
Computer sold in 2015=25
Computer sold in 2016=19
Computer sold in 2017=35
Total computer sold in quarter 4=25+19+35=79
In 2015
Total number of computer sold=12+9+21+25=67
In 2016
Total number of computer sold=15+10+17+19=61
In 2017
Total number of computer sold=8+5+23+35=71
(b)He sold the most computers in 2017
(c) He sold the least computers in quarter 2.
2. Use factoring to determine the x-intercepts and vertex of the quadratic function
y = 2x2 + 5x -3
(answer plsss)
Step-by-step explanation:
I solved for the x hope it's correct
