Answer:
[tex] \sqrt{50} + \sqrt{18} - 8 \sqrt{2} \\ \\ 5 \sqrt{2} + 3 \sqrt{2} - 8 \sqrt{2} \\ \\ 8 \sqrt{2} - 8 \sqrt{2 } \\ \\ = 0[/tex]
Given the expression:
[tex] \displaystyle \large{ \sqrt{50} + \sqrt{18} - 8 \sqrt{2} }[/tex]
Since we have 2 in the square root from 8√2. We will be converting terms in √2 form so we can. evaluate.
As we know, 50 comes from 5×10 = 5×5×2
and 18 comes from 9×2 = 3×3×2.
[tex] \displaystyle \large{ \sqrt{5 \times 5 \times 2} + \sqrt{3 \times 3 \times 2} - 8 \sqrt{2} }[/tex]
In the square root, if there are two same numbers, we can pull it out as one.
Ex. √5×5 would be 5. Refer to below:
[tex] \displaystyle \large{ \sqrt{a \times a} = \sqrt{ {a}^{2} } = |a| }[/tex]
Since there are two fives and two threes in the square root, we pull these numbers out only one.
[tex] \displaystyle \large{ 5\sqrt{2} + 3 \sqrt{2} - 8 \sqrt{2} }[/tex]
Because these terms have the same square root of 2, we can evaluate 5+3-8.
[tex] \displaystyle \large{ 8 \sqrt{2} - 8 \sqrt{2} } = 0[/tex]
Of course, like term - like term = 0
Hence, the answer is 0.
what is the opposite of
A) 7 & B) -3
A -7 , -3
B -7 -3
C -7 , 3
D 7 , 3
Define the domain and range of the function and state whether it is one-to-one, onto, both or neither.
Answer:
Neither
Step-by-step explanation:
how many axes of symmetry does a square have
Answer:
four lines axes of symmetry does a square have
Find the sum Sn of the first n terms from the given sequence.
1, 1+2, 1+2+3, 1+2+3+4, ...
Please show your work and use Sigma Notation too. Thank you!
The Sequence:
1 , 1+2 , 1+2+3 , 1+2+3+4, ...
here, every term is an AP. finding the general formula for the sum of the elements of each term is:
Sₙ = [tex]\frac{x}{2}(2a + (x-1)d)[/tex] [where x = number of term, a = first term and d = common difference]
here, the first term is always 1 and so is the common difference.
Sₙ = [tex]\frac{x}{2}(2 +x-1)[/tex]
Sₙ = [tex]\frac{x}{2}(1 +x)[/tex] = [tex]\frac{1}{2}(x + x^{2})[/tex]
which is the formula for a general term in our series
now, we need to find the sum of the first n terms of this series
[tex]\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})][/tex]
[tex]\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})][/tex]
in this formula, for the first term, it's just an AP from x = 1 to x = n
for the second term, we have a general formula [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
[tex]\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
in this AP (first term), the first term and the common difference is 1 as well
[tex]\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex]\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex][\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ][/tex]
[tex]\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ][/tex]
[tex]\frac{n}{2}(n+1) [\frac{(n+2)}{3} ][/tex]
[tex]\frac{n(n+1)(n+2)}{6}[/tex]
which is the sum of n terms of the given sequence
Find the exact solution of -x^2+3x+7=0 by using the Quadratic Formula?
if a=3x and b = 3x-4i, find the value of a3b In fully simplified form
C^-24 times c^9 times c^-87 answer using positive exponents
Answer:
1/c^102
Step-by-step explanation:
C^-24 * c^9 * c^-87
When we multiply exponents with the same base, we add the exponents
c^(-24+9+-87)
c^(-102)
We know that a^-b = 1/a^b
1/c^102
Answer:
Step-by-step explanation:
[tex]a^{m} *a^{n} = a^{m+n}\\\\\ a^{-m}=\dfrac{1}{a^{m}}\\\\\\c^{-24}*c^{9}*c^{-87}=c^{-24+9-87}\\\\=c^{-102}\\\\=\dfrac{1}{c^{102}}[/tex]
42.3952 to the nearest thousandths
Answer:
42.395
Step-by-step explanation:
What is the measure of angle A?
Select the best answer from the choices provided.
A.26°
B.32°
C.64°
D.78°
Angle B is 90 degrees so angle A and c when added also equal 90:
7x + 8 + 3x + 2 = 90
Simplify:
10x + 10 = 90
Subtract 10 from both sides
10x = 80
Divide both sides by 10
X = 8
Now you have x calculate angle A:
7x + 8 = 7(8) + 8 = 56 + 8 = 64
Answer: C. 64
Answer:
C
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , so
7x + 8 + 3x + 2 + 90 = 180 , that is
10x + 100 = 180 ( subtract 100 from both sides )
10x = 80 ( divide both sides by 10 )
x = 8
Then
∠ A = 7x + 8 = 7(8) + 8 = 56 + 8 = 64° → C
if you rolled a die what is the probability that you would roll a 4 or 5
Answer:
1/3
a dice has 6 sides and the probability of getting 4 or 5 is just 2/6 which simplifies to 1/3
To verify Pythagoras theorem.
Answer:
The proof of Pythagorean Theorem in mathematics is very important. In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. States that in a right triangle that, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²).
The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is the area of the original rectangle?
ty<3
[tex]thank \: you[/tex]
which expression is equivalent to 2•2 3 •8
Answer:
2^7
Step-by-step explanation:
2 * 2^3 *8
Rewriting 8
8 = 2^3
2 * 2^3 * 2^3
We know that a^b * a^c = a^(b+c)
2^1 * 2^3*2^3
2^(1+3+3)
2^7
please help with these 5 math questions for 25 points!
Answer:
1)C 2)A 3)D
Step-by-step explanation:
3/4x + 4/7y = 5/4x -1...solve for y
Answer:
[tex] \frac{3}{4} x + \frac{4}{7} y = \frac{5}{4} x - 1 \\ \frac{4}{7} y = \frac{5}{4} x - 1 - \frac{3}{4} x \\ \\ \frac{4}{7} y = \frac{5x - 4 - 3x}{4} \\ \frac{4}{7} y = \frac{2x - 4}{4} \\ \\ y = \frac{2x - 4}{4} \div \frac{4}{7} \\ y = \frac{2x - 4}{4} \times \frac{7}{4} \\ \\ y = \frac{14x - 28}{16} \\ \\ y = \frac{14x}{16} - \frac{28}{16} [/tex]
I hope I helped you^_^
What is 7 divided by 329
Answer:
47
Step-by-step explanation:
Do long division.
7 goes into 32, 4 times.
32 - 28= 4
7 goes into 49, 7 times.
Therefore 47 is correct.
help!! i really don’t know how to do this!!
if this trapezoid is moved through the translation (x+3,y-2) what will the coordinates of B` be
Answer:
-2, 2
Step-by-step explanation:
Kai took a trip from Stratford to Paris in 2013, and needed to exchange 500 British
pounds for euros. The exchange rate was 1 pound to 1.23 euros. How many euros did Kai
receive in this exchange?
Answer:
500pounds×1.23euros
=615eurosMelany wants to hang a canvas, which is 8 feet wide, on his wall. Where on the
canvas should Melany mark the location of the hangers if the canvas requires a
hanger every 1/5 of its length, excluding the edges? Justify your answer.
The length of the canvas where Melany will mark the position of the hanger is 1.6 feet.
The given parameters:
length of the canvas = 8 feet
dimension of the hanger = [tex]\frac{1}{5} \ of \ the \ shoe's \ length[/tex]
To find:
the length of the canvas where Melany will mark the position of the hanger.The length of the canvas where Melany will mark the position of the hanger is calculated as follows:
[tex]location \ of \ the \ hanger = \frac{1}{5} \times 8\ ft\\\\location \ of \ the \ hanger = 1.6 \ ft[/tex]
Thus, the length of the canvas where Melany will mark the position of the hanger is 1.6 feet.
Learn more here: https://brainly.com/question/17765207
A wedding planner uses 72 ivy stems for 18 centerpieces. When sh arrives at the venue , she realizes she will only need 16 centerpieces. How many ivy stems should she use so that the ratio of ivy stems to centerpieces stays the same ?
Answer:
64 ivy stems
Step-by-step explanation:
72 ivy stems / 18 centerpieces = 4 ivy stems / 1 centerpiece
Create an equation with x being the amount of ivy stems needed.
x / 16 = 4
x = 64
5.
A bank statement shows transactions of -$10.40 and $8.50.
A. Do these transactions represent deposits or withdrawals?
Plz help
A negative value is when money is taken out ( withdrawal). A positive value is when money is added to the account(deposit)
-10.40 is a withdrawal
8.50 is a deposit
Answer:
Hint :- Withdrawal is denoted as the -ve sign and deposit are denoted by the +ve sign. This is because if we deposit money then the money increase and if we withdraw then the money decreases.
-10.40
See there is a negative sign. This means it is a withdrawal
8.50
See there is a positive sign. This means it is a deposit
I need help With math
Answer:
Step-by-step explanation:
0.919191....It can be represented as a fraction. You can always make repeating decimals into fractions.
It does not terminate. 91 will go on forever. It's a repeating decimal
We don't know what the second one does. You are likely not supposed to say it repeats; it certainly does not terminate. It cannot be made into a fraction.
0.555 This terminates. It can be written as a fraction.
It can be written as a fraction. It repeats. It contains a repeating decimal which can always be written as a fraction.
can anyone help me please on this function.
USE (m a t h w a y) its real easy to use
Step-by-step explanation:
can any one solve this please....I kinda need this
9514 1404 393
Answer:
t₂ = 2t₃ = 2Step-by-step explanation:
The given expression says ...
[tex]t_n+1=3\\\\t_n=2\qquad\text{for any value of n}\\\\t_2=2\\\\t_3=2[/tex]
Answer:
[tex]here \: tn + 1 = 3 \\ tn = 2 \\ put \: n = 1 \\ t1 = 2 \\ n = 2 \\ t2 = 2 \\ n = 3 \\ t3 = 2 \\ for \: all \: n \: values \: = 2 \\ thank \: you[/tex]
Pls help me in this my math exam is Tom and I wanna know how to solve theese
Step-by-step explanation:
[tex]thank \: you[/tex]
Someone please help.
Hi there!
[tex]f(x)+f(x+1)=4f(x)[/tex]
There are 3 parts to this equation:
f(x)
f(x+1)
4f(x)
We must first determine these three parts separately.
1) f(x)
We're given that [tex]f(x)=3^x[/tex]:
⇒ [tex]f(x)=3^x[/tex]:
2) f(x+1)
Now, we must find f(x+1). To do so, add 1 to x in the original function [tex]f(x)=3^x[/tex]:
⇒ [tex]f(x+1)=3^x^+^1[/tex]
3) 4f(x)
To find 4f(x), multiply the original function [tex]f(x)=3^x[/tex] by 4:
[tex]4f(x)=4*3^x[/tex]:
4) Put it all together
Now, plug each of the three parts into the equation [tex]f(x)+f(x+1)=4f(x)[/tex]:
[tex]f(x)+f(x+1)=4f(x)[/tex]
[tex]3^x+3^x^+^1=4*3^x\\3^x+3^x*3=4*3^x[/tex]
Factor the left side
[tex]3^x*(1+3)=4*3^x[/tex]
Divide both sides by 3^x
[tex]1+3=4\\4=4[/tex]
Because this equation is true, [tex]f(x)+f(x+1)=4f(x)[/tex] is therefore true.
I hope this helps!
600 miles/day into miles per hour
Find the value, n(A), if n(B)=33, n(A intersectionB)=12 and n(A union B) =59
Answer:
38
Step-by-step explanation:
nAuB=nA+nB-nA∩B. take nA as x
now substitute
59=x+33-12
59=x+21
x=59-21
x=38
(7x2 - 2x - 5)(3x2 + 2x - 3)
Answer:
21x4 + 8x3 - 40x2 + 15
Step-by-step explanation:
expand using distributive property.