Answer:
[tex]\|a\| = 5\sqrt{13}[/tex].
[tex]\|b\| = 3\sqrt{29}[/tex].
Step-by-step explanation:
Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:
[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].
[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].
[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].
The question states that [tex]\| a + b \| = 34[/tex]. In other words:
[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].
[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].
[tex]289\, k^{2} = 34^{2}[/tex].
Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].
[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].
[tex]k^{2} = 2^{2}[/tex].
The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].
Therefore:
[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].
[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:
[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].
[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].
Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:
[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].
[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].
Hence:
[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].
[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].
May anyone help me with this
Answer:
Step-by-step explanation:
y=3(x−3)^2+75
Answer:
(x - 3)² = - 25
Step-by-step explanation:
Given
- 3x² = - 18x + 102 ( add 18x to both sides )
- 3x² + 18x = 102 ( divide through by - 3 )
x² - 6x = - 34
To complete the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 3)x + 9 = - 34 + 9
(x - 3)² = - 25
I'LL GIVE BRAINLIEST !! FASTER
please provide explaination
Answer:
532
A
Step-by-step explanation:
A=86
B=180
C=94
D=266
now,
a+b+c+d_94
=86+180+94+266_94
=532
ntroduction to Functions
Assignment Active
Creating a Function from a Mapping
The mapping shows a relationship between input and
output values.
Input
Output
Which ordered pair could be removed to make this
relation a function?
O (-5,0)
0 (-1, -3)
O (4, -2)
O (6,-1)
Answer:
To be a function, each input must only have one output. In this case, input 4 has two outputs, so (4 , -2) can be removed for it to be a function.
Let me know if you have any other questions!
The ordered pair (4,2) could be removed to make the given relation a function.
What is the relation?A relation is a function if for every input (x-value) there is exactly one output (y-value).
If there are two or more ordered pairs with the same x-value but different y-values, then the relation is not a function. In this case, one of those ordered pairs would need to be removed in order to make it a function.
As per the question, the relation was given as {(-5,0), (2, -3), (-1, -3), (4, -2), (4, -2), (6,-1)}, the ordered pair (4,-2) would need to be removed because there are two outputs (-2 and 2) for the input of 4.
Thus, removing (4,2) would result in the function.
Learn more about the relations here:
https://brainly.com/question/29207494
#SPJ7
These prisms are similar. Find the surface
area of the larger prism. Round to the
nearest tenth.
5 in.
Surface Area = 572 m2 Surface Area = [ ? ] m2
6 in.
Answer:
823.7 m^2
Step-by-step explanation:
The ratio of the side lengths is 6/5.
The ratio of the areas is the square of the ratio of the side lengths, 36/25.
572 m^2 * 36/25 = 823.7 m^2
Given the graph of a radical function, which statement is correct?
Radical function going from the point negative 4 comma negative 3 up to the right through the point 5 comma 0
R colon open bracket y is an element of all real numbers close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to 5 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 4 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
Answer:
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
[tex]x - \frac{3\\}{8} = \frac{13}{2}[/tex]
X - 3/8 = 13/2
Add 3/8 to both sides:
X = 13/2 + 3/8
Rewrite 13/2 to have 8 as the denominator:
13/2 x 4 = 52/8
X = 52/8 + 3/8
X = 55/8
Answer:
55/8
Step-by-step explanation:
Add 3/8 to both sides
X - 3/8 = 13/2
X = 13/2 + 3/8
make sure the denominators are equal so we can add. so multiply 4/4 by 13/2 and that equals 52/8
X = 52/8+3/8
X= 55/8
Help meh pweeeeaaaasssseeee!
Answer:
The name of the given figure in two different ways are - J⇔U and U⇔J
Solve the equation for x.
(x - 4) - (x + 7) = 8x
11
a.
c.
11
8
2
AlE NE
b.
1
d.
11
coin
8
4
Answer:
[tex]x=-\frac{11}{8}[/tex]
Step-by-step explanation:
Hi there!
[tex](x - 4) - (x + 7) = 8x[/tex]
Open up the parentheses
[tex]x - 4 - x - 7 = 8x[/tex]
Combine like terms
[tex]x -x - 4 - 7 = 8x\\-4-7=8x\\-11=8x[/tex]
Divide both sides by 8 to isolate [tex]x[/tex]
[tex]-\frac{11}{8}=x[/tex]
I hope this helps!
A wall of a building is 34 inches wide Sixteen inches is concrete, 12 inches is brick, and 6 inches is limestone What fraction of the wall is concrete?
Can someone please help me with these 7 questions please?
The solution to each of the question takes different approach, as the questions are taken from different concepts; however, a common operation among all questions, is factorization.
[tex](1)\ (-xy)^3(xz)[/tex]
Expand
[tex](-xy)^3(xz) = (-x)^3* y^3*(xz)[/tex]
[tex](-xy)^3(xz) = -x^3* y^3*xz[/tex]
Rewrite as:
[tex](-xy)^3(xz) = -x^3*x* y^3*z[/tex]
Apply law of indices
[tex](-xy)^3(xz) = -x^4y^3z[/tex]
[tex](2)\ (\frac{1}{3}mn^{-4})^2[/tex]
Expand
[tex](\frac{1}{3}mn^{-4})^2 =(\frac{1}{3})^2m^2n^{-4*2}[/tex]
[tex](\frac{1}{3}mn^{-4})^2 =\frac{1}{9}m^2n^{-8[/tex]
[tex](3)\ (\frac{1}{5x^4})^{-2}[/tex]
Apply negative power rule of indices
[tex](\frac{1}{5x^4})^{-2}= (5x^4)^2[/tex]
Expand
[tex](\frac{1}{5x^4})^{-2}= 5^2x^{4*2}[/tex]
[tex](\frac{1}{5x^4})^{-2}= 25x^{8[/tex]
[tex](4)\ -x(2x^2 - 4x) - 6x^2[/tex]
Expand
[tex]-x(2x^2 - 4x) - 6x^2 = -2x^3 + 4x^2 - 6x^2[/tex]
Evaluate like terms
[tex]-x(2x^2 - 4x) - 6x^2 = -2x^3 -2x^2[/tex]
Factor out x^2
[tex]-x(2x^2 - 4x) - 6x^2 = (-2x-2)x^2[/tex]
Factor out -2
[tex]-x(2x^2 - 4x) - 6x^2 = -2(x+1)x^2[/tex]
[tex](5)\ \sqrt{\frac{4y}{3y^2}}[/tex]
Divide by y
[tex]\sqrt{\frac{4y}{3y^2}} = \sqrt{\frac{4}{3y}}[/tex]
Split
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{\sqrt{4}}{\sqrt{3y}}[/tex]
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{2}{\sqrt{3y}}[/tex]
Rationalize
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{2}{\sqrt{3y}} * \frac{\sqrt{3y}}{\sqrt{3y}}[/tex]
[tex]\sqrt{\frac{4y}{3y^2}} = \frac{2\sqrt{3y}}{3y}[/tex]
[tex](6)\ \frac{8}{3 + \sqrt 3}[/tex]
Rationalize
[tex]\frac{8}{3 + \sqrt 3} = \frac{3 - \sqrt 3}{3 - \sqrt 3}[/tex]
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{(3 + \sqrt 3)(3 - \sqrt 3)}[/tex]
Apply difference of two squares to the denominator
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{3^2 - (\sqrt 3)^2}[/tex]
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{9 - 3}[/tex]
[tex]\frac{8}{3 + \sqrt 3} = \frac{8(3 - \sqrt 3)}{6}[/tex]
Simplify
[tex]\frac{8}{3 + \sqrt 3} = \frac{4(3 - \sqrt 3)}{3}[/tex]
[tex](7)\ \sqrt{40} - \sqrt{10} + \sqrt{90}[/tex]
Expand
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =\sqrt{4*10} - \sqrt{10} + \sqrt{9*10}[/tex]
Split
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =\sqrt{4}*\sqrt{10} - \sqrt{10} + \sqrt{9}*\sqrt{10}[/tex]
Evaluate all roots
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =2*\sqrt{10} - \sqrt{10} + 3*\sqrt{10}[/tex]
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =2\sqrt{10} - \sqrt{10} + 3\sqrt{10}[/tex]
[tex]\sqrt{40} - \sqrt{10} + \sqrt{90} =4\sqrt{10}[/tex]
[tex](8)\ \frac{r^2 + r - 6}{r^2 + 4r -12}[/tex]
Expand
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r^2 + 3r-2r - 6}{r^2 + 6r-2r -12}[/tex]
Factorize each
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r(r + 3)-2(r + 3)}{r(r + 6)-2(r +6)}[/tex]
Factor out (r+3) in the numerator and (r + 6) in the denominator
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{(r -2)(r + 3)}{(r - 2)(r +6)}[/tex]
Cancel out r - 2
[tex]\frac{r^2 + r - 6}{r^2 + 4r -12}=\frac{r + 3}{r +6}[/tex]
[tex](9)\ \frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14}[/tex]
Cancel out x
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x^2 - 5x - 14}[/tex]
Expand the numerator of the 2nd fraction
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x^2 - 7x+2x - 14}[/tex]
Factorize
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{x(x - 7)+2(x - 7)}[/tex]
Factor out x - 7
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4x + 8}{x} \cdot \frac{1}{(x + 2)(x - 7)}[/tex]
Factor out 4 from 4x + 8
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4(x + 2)}{x} \cdot \frac{1}{(x + 2)(x - 7)}[/tex]
Cancel out x + 2
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4}{x} \cdot \frac{1}{(x - 7)}[/tex]
[tex]\frac{4x + 8}{x^2} \cdot \frac{x}{x^2 - 5x - 14} = \frac{4}{x(x - 7)}[/tex]
[tex](10)\ (3x^3 + 15x^2 -21x) \div 3x[/tex]
Factorize
[tex](3x^3 + 15x^2 -21x) \div 3x = 3x(x^2 + 5x -7) \div 3x[/tex]
Cancel out 3x
[tex](3x^3 + 15x^2 -21x) \div 3x = x^2 + 5x -7[/tex]
[tex](11)\ \frac{m}{6m + 6} - \frac{1}{m+1}[/tex]
Take LCM
[tex]\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m(m + 1) - 1(6m + 6)}{(6m + 6)(m + 1)}[/tex]
Expand
[tex]\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m^2 + m- 6m - 6}{(6m + 6)(m + 1)}[/tex]
[tex]\frac{m}{6m + 6} - \frac{1}{m+1} = \frac{m^2 - 5m - 6}{(6m + 6)(m + 1)}[/tex]
[tex](12)\ \frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}}[/tex]
Rewrite as:
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} \div \frac{2}{y^2 - 9}[/tex]
Express as multiplication
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{y^2 - 9}{2}[/tex]
Express y^2 - 9 as y^2 - 3^2
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{y^2 - 3^2}{2}[/tex]
Express as difference of two squares
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{y - 3} * \frac{(y - 3)(y+3)}{2}[/tex]
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{1}{1} * \frac{(y+3)}{2}[/tex]
[tex]\frac{\frac{1}{y - 3}}{\frac{2}{y^2 - 9}} = \frac{y+3}{2}[/tex]
Read more at:
https://brainly.com/question/4372544
I need help ASAP!!Please explain the answer
Answer:
348
Step-by-step explanation:
Volume = Area of cross section x height
Area of cross section = 1/2bh
1/2 (12x5.8) = 34.8
34.8 x 10 = 348
Volume = 348km^3
Answered by g a u t h m a t h
A hamburger and a soda cost $1.45. Two hamburgers and one soda cost $2.50. What is the price of one soda?
$0.60
$0.40
$0.50
Answer:
$0.40
Step-by-step explanation:
let a hamburger be X and soda b y
then X + Y is equals to 1.45
2 X + Y is equals to 2.50
using elimination method we will fine the value of x
2 X + Y = 2.50
- X + Y= 1.45
X = 1.05
now how to find the value of Y
we know that X + Y = 1.45
putting the value of x
we get Y is equals to 1.45-1.05
$0.40
What is the equation of a line that passes through the point (5,3) and has a slope of -2?
Answer:
y = -2x +13
Step-by-step explanation:
you know the point is (5,3) and slope is -2
sub into the linear equation y=mx+b
3 = -2(5) +b
rearrange and solve for b
b= 3 + 10
b = 13
what is the commutative property for 4xy
PLEASE ANSWER QUICKLY
Answer:
[tex]we \: know \: that \: commutative \: prop \\ = x + y = y + x \\ then \\ 4xy + 0 = 0 + 4xy \\ thank \: you[/tex]
Round the number 553 to the tens place.
is it 550? because 3 is less than 5 so I replace it with a 0
Answer:
550
Step-by-step explanation:
To round 553 to the tens place, we would need to identify the value of the digit in the ones place.
If the digit in the ones place is greater than 5, we increase the tens place by 1 & convert the ones place into a 0.
If not, we leave the tens place as is & convert the ones place into a 0.
Since 3 is less than 5, we round 553 to 550 so you are correct.
Answer:
Yes
550 has 2 sig figs
553 has 3
Step-by-step explanation:
Solve the equation 40 = 2x^2+ 2x by factoring.
What are the solutions?
Answer:
x=4, -5
Step-by-step explanation:
Factor and set each factor equal to zero
Answer:
X = -4 , x= 4
Step-by-step explanation:
20=x^2-x=0
-20+x^2+x=0
x^2+x-20=0
x×(x+5)-4(x+5)=0
(x+5)×(x-4)=0
x+5=0
×-4=0
x=-5
x=4
46°
X
Х
X =
degrees.
Answer:
x = 67°
Step-by-step explanation:
The 2 base angles x are congruent , then
x = [tex]\frac{180-46}{2}[/tex] = [tex]\frac{134}{2}[/tex] = 67°
Answer:
X= 67 degrees.
Step-by-step explanation:
All triangles must add up to 180°. This is an isosceles triangle which means once you have one degree you can find the other two.
In order to get the answer start with 180°-46°
180-46=134
The two x's equal each other. So you can divide the remaining degrees by 2 to get the answer.
134÷2=67.
So the answer is 67°.
Combine like terms to simplify the following polynomial.
x + y + z + x + 2z + 3y
2x + 4y + 3z
9xyz
4x + 2y + 3z
x2 + y4 + z3
Step-by-step explanation:
Answer 1
x+x+y+3y+z+2z
2x+4y+3z
Answer 2
2x+4y+3z
( no like terms are there so it cannot be added)
Answer 3
9xyz
last two answers will also be similar as the question because unlike terms cannot be added..
Which of the following is equivalent to the expression below?
Answer:
4
Step-by-step explanation:
ln(e)=1 since ln= log_e
log(x^y)=y*log(x) so ln(e^4)=4*ln(4)=4*1=4
Answer:
D
Step-by-step explanation:
ln(e^4)
The 4 comes down in front of the natural log (ln). You get 4 ln(e)
The natural log of e (ln e ) is 1.
So the answer is 4 * 1 = 4
That may not be clear to you. We could try it another way.
e = 2.718281828
ln (2.718281828) = 1
ln(2.718281828)^4 = 4. The calculator gags until you get it right. You need the y^x key (or the x^y key of ^) It does come back with 4.
You have to monkey around with the calculator to get this to happen.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The amount of lemonade left in a pitcher would be considered ________ data.
A. neither continuous nor discrete
B. discrete
C. continuous
D. both continuous and discrete
Find the length of the third side. If necessary, round to the nearest tenth.
12
13
Answer:
Submit Answer
attempt 1 out of 2
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PLS HELP ASAP
Answer:
5
Step-by-step explanation:
Use pythagorean theorem. A^2+B^2=C^2
13 is c because it is the hypotenuse and across from the right angle
a is unknown and b is 12
A^2+12^2=13^2
A^2 +144 = 169
A^2 = 169- 144
A^2= 25
now take the sq root of both side
A = 5
Answer:
17.7
Step-by-step explanation:
Whoever can answer this question gets 100 Points!!!!!!!
question: What is 2 + 2 - 1
Answer:
3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Consider the function fx) = -2x + 6x3 + 2x.
The function is
because
Answer:
This is an odd function because f (–x) = f (x)
Step-by-step explanation:
This is an odd function because f (–x) = f (x)
f(x) = -2x^5 + 6x^3 + 2x.
All the powers are odd powers and the sum of odd functions is odd
All of the terms are odd functions so the total function is odd
Answer:
CORRECT
Step-by-step explanation:
Help plz!!!!!!!!!!!!
Answer:
Option A, 90
Step-by-step explanation:
105×2-120
= 210-120
= 90
Simplify x + (7+14x)
Answer:
15x + 7
Step-by-step explanation:
x + (7 + 14x)
x + 7 + 14x
15x + 7
Answer:
15x + 7
Step-by-step explanation:
Remove parenthesis:
x + 7 + 14x
Combine like terms:
14x + x = 15x
Add the seven:
15x + 7
Hope this helped.
pls help :: geometry summer assignment
Answer:
140
Step-by-step explanation:
Left column = x
Right column = y
Rule = 3.5x = y
Because 42/12 = 3.5
3.5 * 40 = 120 + 20 = 140
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
2. The ? states that the product of the extremes is equal to the product of the
means.
Answer:
proportion
Step-by-step explanation:
In a proportion, the means or the extremes (or both) may be interchanged. In proportion, the product of the means equals the product of the extremes.
hope it helps :)
mark brainliest!
Need help with VOCAB!!! Please make sure it's correct
Hey there!
I believe your answer would be a transformation, and not a translation.
A transformation is an operation that moves, flips, or otherwise changes a figure to create a new figure.
Hope this helps!
Have a wonderful day! :)
someone measured the living room of their house and it is 12ft by 16 feet. what will the dimensions of the doll house living room be if every foot of the actual house is equal to 1/2 inch in the doll house?
Answer:
6ft by 8ft
Step-by-step explanation:
12 / 2 is 6 and 16 / 2 is 8
Helpppoplplllllpppllppppppppplpppppppppp
Work Shown:
tan(angle) = opposite/adjacent
tan(x) = 17/29
x = arctan(17/29)
x = 30.379 which is approximate
x = 30
Side note: arctan is the same as inverse tangent [tex]\tan^{-1}[/tex]
