Answer:
Step-by-step explanation:
[tex]\sqrt{8}-\sqrt{72}+\sqrt{50}[/tex] These cannot combine the way they are. The rule for adding and subtracting radicals is really picky. Not only does the index have to be the same (the little number that is sitting outside in the bend of the radical {ours is a 2, which isn't usually there, but is instead understood to be a square root}), but the radicand, the expression under the square root (or cubed root, or fourth root, etc) has to the same as well. All of our radicals are square roots, so that's good, but the radicands are all different. The first one is an 8, the next one is a 72, and the last one is a 50. BUT if we can rewrite them by simplifying them and then the radicands are the same, we're in good shape.
Simplify by taking the prime factorization of each of those numbers.
8: 4*2 and 4 is a perfect square, so we'll stop there
72: 36*2 and 36 is a perfect square, so we'll stop there
50: 25*2 and 25 is a perfect square, so we'll stop there.
Now, rewrite each one of them in terms of their prime factorization:
[tex]\sqrt{4*2}-\sqrt{36*2}+\sqrt{25*2}[/tex] and then pull out each perfect square as its root:
[tex]2\sqrt{2}-6\sqrt{2}+5\sqrt{2}[/tex] and now all the radicands are the same, so we can add them to get
[tex]1\sqrt{2}[/tex] or simply [tex]\sqrt{2}[/tex]
Answer:
[tex]A: \sqrt{2}[/tex]
Step-by-step explanation:
sqrt 8 = sqrt (2 * 2 *2 ) = [tex]2\sqrt{2}[/tex]
sqrt 72 = sqrt (2 * 2 *2 * 3 * 3 ) = [tex]6\sqrt{2}[/tex]
sqrt 50= sqrt (2 * 5 *5 ) = [tex]5\sqrt{2}[/tex]
What is the missing coefficient? See photo!! Thanks
Answer:
4x + 2x would be 6x
Step-by-step explanation:
Which graph represents a line with a slope of and a y-intercept equal to that of the line y = x – 2?
Answer:
y=x-2,
so'n
y-x=2 answer you haven't write value.
Which of the following is a point-slope equation for a line with the point (-2, 4) and a slope of 3?
Answer:
y=3x+10
Step-by-step explanation:
y-4=(x+2)3
y-4=3x+6
y =3x+10
Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49
Câu 1: Trong các mệnh đề sau, mệnh đề nào là không đúng ?
A. Nếu a // b và (α) vuông góc a thì (α) vuông góc với b
B. Nếu (α) // (β) và a vuông góc với (α) thì a vuông góc với (β)
C. Nếu a và b là hai đường thẳng phân biệt và a vuông góc (α), b vuông góc với (α) thì a // b
D. Nếu a // (α) và b vuông góc a thì b vuông góc (α)
Answer:
Hey can you ask this question in English so I can no answer this question in English and then you can convert that my answer in your language as you're I'm Indian so I don't know this language
Step-by-step explanation:
Please don't you think that I'm doing this for points I think I should know this question so can you please answer this you're this and English
b)
Diberi bahawa ungkapan surd
1+3
adalah sama dengan P-Q dengan keadaan P
1-3
dan Q adalah pemalar. Cari nilai bagi P4Q
Given the expression of surd
1+√3
is equal to P - where P and Q are constants. Find
1-73
the value of P+Q.
[4 m ]
anyone please help me with this question I will give brainliest if you got the right answer
Jawapan / Answer:
Answer:
P + Q = 1
Step-by-step explanation:
Given: [tex]\frac{1+\sqrt{3} }{1-\sqrt{3} }[/tex] = P - [tex]\sqrt{Q}[/tex]
This is a question on surd, so we need to rationalize the denominator to have;
[tex]\frac{1+\sqrt{3} }{1-\sqrt{3} }[/tex] * [tex]\frac{1+\sqrt{3} }{1+\sqrt{3} }[/tex] = [tex]\frac{1+\sqrt{3}+\sqrt{3} + 3}{1+\sqrt{3}-\sqrt{3} -3 }[/tex]
= [tex]\frac{4+ 2\sqrt{3} }{1-3}[/tex]
= [tex]\frac{4+2\sqrt{3} }{-2}[/tex]
= -2 - [tex]\sqrt{3}[/tex]
Thus,
-2 - [tex]\sqrt{3}[/tex] = P - [tex]\sqrt{Q}[/tex]
⇒ P = -2 and Q = 3
Therefore, the value of P + Q = -2 + 3
= 1
Thus,
P + Q = 1
The two-way table shows information about the languages studied b
some people.
French
German
Spanish
Total
Male
12
9
16
37
Female
16
11
16
43
Total
28
20
32
80
a
a)
How many people are female OR study French OR both?
Answer:
Step-by-step explanation:
1
There are 71 people who are female OR study French OR both.
To find the number of people who are female OR study French OR both, we need to add the numbers in the Female row (excluding the "Total" column) and the numbers in the French column (excluding the "Total" row), and then subtract the number of people who study both French and are female, as they were counted twice.
Number of people who are female = 43
Number of people who study French = 28
Number of people who study both French and are female = 16
Total = Number of people who are female + Number of people who study French - Number of people who study both French and are female
Total = 43 + 28 - 16
Total = 71
So, there are 71 people who are female OR study French OR both.
To know more about people here
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the length of a rectangle is 8 cm longer than its width. find the dimensions of the rectangle if its area is 108cm
!!no links!!
Answer:
[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]
Or about 15.136 centimeters by 7.136 centimeters.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length is 8 centimeters longer than the width. In other words:
[tex]\ell = w+8[/tex]
And we are also given that the total area is 108 square centimeters.
Thus, substitute:
[tex](108)=w(w+8)[/tex]
Solve for w. Distribute:
[tex]w^2+8w=108[/tex]
Subtract 108 from both sides:
[tex]w^2+8w-108=0[/tex]
Since the equation is not factorable, we can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]
So, our two solutions are:
[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]
Since width cannot be negative, we can eliminate the second solution.
And since the length is eight centimeters longer than the width, the length is:
[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]
So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.
Jimmy, who is five and a half feet tall, sees a bird at the top of a tree and wonders how tall the tree is. Jimmy stands 18 feet from the tree. Jimmy takes an inclinometer (a device used to calculate angles of elevation) and measures the angle created from his horizontal gaze and the bird to be 50 degrees. How tall is the tree?
Answer:
100
Step-by-step explanation:
it is 50 when he sees it in a horizontal line so double it to see how much it is if it where straight
In a test containing 10 questions, (+5) marks are awarded for every correct answer, (-1) mark for every incorrect answer and 0 for not attempting the questions. If Rashid gets 4 correct answers and 6 incorrect answers, what is his score?
Answer:
14
Step-by-step explanation:
10 questions = 4 correct + 6 incorrect
4 correct = 4* 5 = 20
6 incorrect = 6* (-1) = -6
His score is 20 -6 = 14 points
a bag contains 10 white balls and 14 red balls.a ball is taken out of the bag,what is the probability that it is a red ball
Answer:
7/12
Step-by-step explanation:
10 white balls and 14 red balls = 24 balls
P( red) = number of red balls / total balls
=14/24
=7/12
Hey plz could you help me with this???? Tysm
Answer:
25.71
Step-by-step explanation:
πr + d
3.142(5) + 10
= 25.71
i think
(x⁴ + 3x³ – 2x² + 5) + (2x⁴ – 5x³ + 4x – 15).
Answer:
[tex]\left(x^4+3x^3-2x^2+5\right)+\left(2x^4-5x^3+4x-15\right)[/tex]
[tex]=[/tex] [tex]x^4+3x^3-2x^2+5+2x^4-5x^3+4x-15[/tex]
[tex]=x^4+2x^4+3x^3-5x^3-2x^2+4x+5-15[/tex]
[tex]=x^4+2x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x-10[/tex]
[tex]OAmalOHopeO[/tex]
Can someone help me with this math homework please!
Answer:
D
Step-by-step explanation:
The line is decreasing. Option B is wrong because if it was true, it means that the entire candle burns in an hour
Find the distance between the points (2, 4) and (8, -8) on a coordinate plane, to the nearest whole number.
A.7
B.11
C.13
D.16
Answer:
C
Step-by-step explanation:
distance between two points formula:
[tex]d = \sqrt{( x2 - x1) ^{2} + (y2 - y1) ^{2} } [/tex]
where the x and y values are derived from the known points
we are given the points (2, 4) and (8, -8)
given these two points let's define each variable
x1 = 2
x2 = 8
y1 = 4
y2 = -8
we now substitute in these values into the formula
[tex]d = \sqrt{(8 - 2) ^{2} + ( - 8 - 4)^{2} } [/tex]
now we evaluate the expression using PEMDAS
first we do the subtraction inside of the parenthesis
8 - 2 = 6
-8 - 4 = -12
d = sqrt(6)^2 + (-12)^2
next we do the exponents
6^2 = 36
-12^2 = 144
d = sqrt( 144 + 36 )
next do the addition inside of the parenthesis
144 + 36 = 180
d = sqrt ( 180 )
finally we do the square root of 180
sqrt ( 180 ) = 13 ( rounded to the nearest whole )
d = 13
The perimeter of a rectangular garden is 4534 m. The length is 1125 m more than thrice the width. Find the length and the width of the rectangular garden. (Estimate to the nearest tenths place and verify the reasonableness).
Answer:
length = 1696 m
breadth = 571 m
Step-by-step explanation:
perimeter = 4534 m
let breadth be b
so length = b + 1125 m
so
perimeter of rectangular garden = 2(l+b)
4534 m = 2(b+1125m+b) {substituting the value}
or, 4534 m = 2(2b+1125m)
or, 4534 m = 4b + 2250 m
or, 4534 m - 2250m = 4b
or, 2284m = 4b
or, b = 2284m/4
so, b = 571m
so, l = b + 1125 m
= 571 m + 1125m
= 1696 m
The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
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PLEASE HELP!
The distance to the nearest exit door is less than 100 feet.
Use d to represent the distance (in feet) to the nearest exit door.
Answer:
d < 100
Step-by-step explanation:
the distance is less than (<) 100 ft
d < 100
The sentence translates to the inequality d < 100
There's not much else to say about this problem. We just simply replace the "less than" wording with its corresponding symbol. We can think of the inequality sign as an alligator mouth that always wants to eat the larger value (so the open ended side is facing toward the larger value).
write the equation of the line that goes through points (0,4) (6,16)
Answer: Y= 2x
Step-by-step explanation:
Answer:
y=2x-4
Step-by-step explanation:
firstly find the gradient
m=y2-y1/x2-x1
16-4/6-0
12/6
m=2
then use the equation to find the answer
y-y1=m(x-x1)
y-4=2(x-0)
y-4=2x-0
y=2x-4
Find the perimeter of \triangle SOW△SOWtriangle, S, O, W.
If entering your answer as a decimal, round your final answer to the nearest hundredth.
Answer:
the perimeter is 30 units
If you use the addition property of equality , what number would you add to both sides of the equal sign to isolate the variable
Answer:
The answer is "[tex]\frac{26}{7}[/tex]"
Step-by-step explanation:
The whole question can be found in the file attached.
[tex]\to x + \frac{5}{7} = \frac{31}{7}\\\\[/tex]
Subtracting the [tex]\frac{5}{7}[/tex] from both sides of the equations:
[tex]\to x +\frac{5}{7} - \frac{5}{7} = \frac{31}{7} - \frac{5}{7} \\\\[/tex]
[tex]= \frac{31-5}{7} \\\\= \frac{26}{7} \\\\[/tex]
A block has a mass of 880g and a volume of 80 cm Calculate the density
Answer:
Density formula (p=m÷v). ---[ p= Density, m= Mass, v= volume]
so, 880g/80cm³
=11gcm³
PLEASE HELP solve step by step
Answer:
-3y/x^2
Step-by-step explanation:
-5/15 = -3
When dividing variables with powers, subtract the powers.
x^2 - x^4 = x^-2
y^3 - y^2 = y
z^4 - z^4 = 0
therefore we have -3 x^-2 y
Since we can't have negative powers, divide (move the x^-2 to the bottom and make positive)
-3y / x^2
Hope this helps! Let me know if I am wrong ^w^
Answer:
- y/3x^2
Step-by-step explanation:
The negative sign goes between y and 3x^2
Find the missing length indicated
Answer:
x =1 08
Step-by-step explanation:
Please help ASAP
Which pairs of rectangles are similar polygons?
Answer:
D is the answer
Step-by-step explanation:
39 is 3 times greater than 13 and 27 is 3 times greater than 9
Can someone help me out
Answer:
60
Step-by-step explanation:
Plz help out will give brainliest
Answer:
4
Step-by-step explanation:
Sum of interior angles in a triangle is 180,
41 + 26u + u + 31 = 180
26u + u + 41 + 31 = 180
27u + 72 = 180
27u = 180 - 72
27u = 108
u = 108 / 27
u = 4
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Here given
one angle =26u2nd angle =41°3rd angle=u+31°.we know that
[tex]\sf{ sum~ of~ 3 ~angles ~of~ a ~triangle~ is ~180° }[/tex]
According to the question,
26u+41+u+31=18027u+72=18027u=180-7227u=108u=108/27u=4°Therefore:-
The value of u is 4°
What is the solution to the inequality?
-x/4 < 6
O A. x<-24
O B. x<-2
O C. x>-24
O D. x>-2
Answer:
x > -24
Step-by-step explanation:
-x/4 < 6
Multiply each side by -4, remembering to flip the inequality
-x/4 *-4> 6*-4
x > -24
[tex]\boxed{\large{\bold{\red{ANSWER~:) }}}}[/tex]
x>-24Step-by-step explanation:[tex]\sf{\dfrac{-x}{4}<6 }[/tex] [tex]\sf{\dfrac{-x}{4}×(-4)>6×(-4) }[/tex] [tex]\sf{ x>-24 }[/tex][tex]\bold{ Note - }[/tex]
By multiply negetive number,we need to change the side of the inequality.sipho made a 12.5% when he sold a coat for E437.50 .calculate original cost of the coat
Answer:
E500
Step-by-step explanation:
Given x the original price of the coat
437.5 + 0.125x = x
437.5 = 0.875x
x = E500
Graph the data set.
{(−1, 0.5), (0, 1), (1, 2), (3, 8), (5, 32)}
Which kind of model best describes the data?
A. Cubic
B. Exponential
C. Linear
D. None
Answer: It is Exponential
Step-by-step explanation: There is a graph provided below.
The kind of model which describes the given data best is exponential.
What is exponential graph?An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid. It always cuts the y-axis at some point but it may or may not cut the x-axis. i.e., an exponential graph always has a y-intercept but it may or may not have the x-intercept.
According to the given question.
We have a data set {(-1, 0.5), (0,1), (1, 2), (3, 8), (5, 52)}.
So, if we locate this points on the graph.
We see that, when 'x' varies 'y' varies as [tex]2^{x}[/tex].
Hence, the kind of model which describes the given data best is exponential.
Thus, option B is correct.
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