Answer:
[tex]x_1 = -t[/tex]
[tex]x_2 = s[/tex]
[tex]x_3 = 0[/tex]
[tex]x_4 = t[/tex]
Step-by-step explanation:
Given
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]
Required
Determine x1 to x4
First, we write the augmented matrix
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right] = \left[\begin{array}{c}0&0&0\end{array}\right][/tex]
Taking the position of each column, we have:
[tex]x_1 + 0 + 0 +x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex]
There is no explicit equation for [tex]x_2[/tex]
So: [tex]x_2 = s[/tex] ----- arbitrary variable
[tex]x_1 + 0 + 0 +x_4 = 0[/tex] implies that:
[tex]x_1 + x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex] implies that
[tex]x_3 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex] implies that
[tex]0 = 0[/tex]
So, we have:
[tex]x_1 + x_4 = 0[/tex]
[tex]x_3 = 0[/tex]
[tex]x_1 + x_4 = 0[/tex] becomes
[tex]x_1 = -x_4[/tex]
Let
[tex]x_4 = t[/tex]
So:
[tex]x_1 = -x_4[/tex]
[tex]x_1 = -t[/tex]
Where t , s are real numbers
find the surface area of the composite figure
Answer:
[tex]=280[/tex] [tex]in^2[/tex]
Step-by-step explanation:
----------------------------------------
Let's find the surface area of the pink rectangular prism first.
[tex]2*10=20+20=40[/tex]
[tex]4*10=40+40=80[/tex]
[tex]4*2=8+8=16[/tex]
[tex]40+80+16=136[/tex]
The surface area for the pink rectangular prism is [tex]136[/tex] [tex]in^2[/tex].
-------------------->>>>>
Now, let's find the surface area of the green rectangular prism.
[tex]4*7=28+28=56[/tex]
[tex]4*7=28+28=56[/tex]
[tex]4*4=16+16=32[/tex]
[tex]56+56+32=144[/tex]
The surface area for the green rectangular prism is 144 [tex]in^2[/tex].
-------------------->>>>>
Now let's add the surface area of both rectangular prisms to find the surface area of the composite figure.
[tex]136+144=[/tex]
[tex]=280[/tex] [tex]in^2[/tex]
----------------------------------------
Hope this is helpful.
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Answer:
224 in²
Step-by-step explanation:
There are a couple of ways to go at this. Here, we choose to figure the areas of each of the prisms individually, then subtract the "hidden" area where they are joined together.
The area of a prism is ...
A = 2(LW +H(L+W))
Pink area:
A = 2(10·4 +2(10+4)) = 2(40 +28) = 136 . . . square inches
Green area:
A = 2(7·4 +4(7+4)) = 2(28 +44) = 144 . . . square inches
One 4 in × 7 in face of the green prism meets with a similar area of the pink prism, so the area hidden at that interface is 2(4·7) = 56 square inches. Then the total surface area of the composite figure is ...
SA = 136 in² +144 in² -56 in² = 224 in²
in a club there are seven women and five men. A committee of 3 women and 2 men as to be chosen. how many different possibilities are there?
Answer:
Step-by-step explanation:
What is a number divided by 3
gives a remainder of 1, divided by 4
gives a remainder of 2, divided by
5 gives a remainder of 3?
Answer:
58
Step-by-step explanation:
58/3 gives a remainder of 1
58/4 gives a remainder of 2
58/5 gives a remainder of 3
Is 4 over 5 equals 48 over 60 a true proportion?
Answer:
0.8 you yes both of them has the same answer , so it is a true portion
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
[tex]\frac{4}{5} =\frac{48}{60}[/tex]
This is a true proportion because when you cross multiply you get the same product.
[tex]48*5=240[/tex]
[tex]4*60=240[/tex]
PLEASE CAN SOMEONE HELP ME??????????????
Answer: 180 degrees rotation, center (1.5, -0.5)
=====================================================
Explanation:
Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)
Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2
--------------
Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11
--------------
We have this system of equations
[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]
Equate the right hand sides and solve for x
7x-11 = x-2
7x-x = -2+11
6x = 9
x = 9/6
x = 3/2
x = 1.5
which leads to
y = x-2 = 1.5-2 = -0.5
or
y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5
Either way, x = 1.5 leads to y = -0.5
We get the ordered pair (x,y) = (1.5, -0.5)
This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)
Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that
AD = A''D
BD = B''D
CD = C''D
7/7q+21= x /5q^2-45 then x=?
Answer:
x = 5q - 15
Step-by-step explanation:
[tex]\frac{7}{7q+21}=\frac{x}{5q^{2}-45}\\\\\frac{7}{7(q+3)}=\frac{x}{5 (q^{2} -9)}\\\\frac{1}{q+3}=\frac{x}{5*(q^{2}-3^{2})}\\\\\frac{1}{q+3}=\frac{x}{5(q+3)(q-3)}\\\\\frac{1}{q+3}*5*(q+3)(q-3)=x\\\\5(q-3)=x\\\\x= 5q-15[/tex]
Evaluate the given equation for the indicated function values. pls help
Answer:
The answer in each numeral is:
f(4) = 28f(10) = -19f(-5) = -33f(9) = -9Step-by-step explanation:
To obtain the result in each case, you must replace the variable (n) by the value that appears in the second case, I'll explain it with the first exercise:
1. f(n) = 5n + 8 f(4) = ?As you can see, in the second doesn't appear f(n), but f(4), that means you must replace the "n" in the equation by 4, if we do this, we obtain:
1. f(4) = 5*(4) + 8f(4) = 20 + 8f(4) = 28The first answer is 28, now we'll continue with the next exercises:
2. f(n) = -2n + 1f(10) = -2*(10) + 1f(10) = -20 + 1f(10) = -193. f(n) = 6n - 3f(-5) = 6*(-5) - 3f(-5) = -30 - 3f(-5) = -334. f(n) = -nf(9) = -9In this form, you can prove the answers are: 28, -19, -33, and -9 respectively.
identify the 3D shape
Answer and Step-by-step explanation:
The 3D shape shown is a rectangle. This is the net-form of a rectangle.
#teamtrees #PAW (Plant And Water)
Answer:
rectangular prism
Step-by-step explanation:
a rectangle is not 3d. a rectangle is 2d. the correct answer is a rectangular prism.
easy math questions please help me:)! solve for x and show work
Answer:
4) 93°
5) 1°
6) 51°
7) 6°
Step-by-step explanation:
4)
180 - 36 - 51 = 93
93 °
5)
(4x + 27 ) = 180 - 64 - 85
4x + 27 = 31
x = 1
6)
theory of exterior angles in a triangle:
21 + 30 = x
x = 51
7)
3x + 42 = 46 + 44
3x + 42 = 90
3x = 48
x = 16
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which of the data sets below has a mean of 48? Select all that apply.
A) 51, 53, 43
B) 24, 91, 18, 65, 52
C) 65, 18, 72, 33, 52
D) 72, 18, 56, 46
can someone help me with this?
Answer: 22
Step-by-step explanation: 44:2=22
given that abc=def what is the measure of d
Answer:
C. 47 deg
Step-by-step explanation:
m<A = 180 - 94 - 39 = 47
m<D = m<A = 47
Graph the Image of AKLM after a translation 1 unit left and 7 units up.
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Answer:
see attached
Step-by-step explanation:
Pick a point (such as K, L, or M). Count one grid square to the left and 7 up. That is its new location.
What’s the domain of the function?
Answer:
domain of function refers to the various values that can be passed through to the function.
Step-by-step explanation:
someone pls help ill give you a kiss and a cookie fi you help meee
for the point (6,8) find the csc theta and sec theta
Answer:
cscθ = 5/4, secθ = 5/3
Step-by-step explanation:
First, let's view the drawing that I have attached, with the dot in the bottom left representing the origin. We know that cosecant and secant are the reciprocals of sin and cos respectively, and in order to find sin and cos, we must find the opposite, adjacent, and hypotenuse sides. The hypotenuse is opposite the right angle, equal to √(8²+6²) = 10
Next, we can find sin and cos of θ . sinθ = 8/10=4/5, making cscθ the reciprocal of 4/5, or 5/4
Similarly, cosθ = 6/10=3/5, and secθ = 5/3
Solve the inequality –8 < x – 14.
Answer:
x=6
Step-by-step explanation:
Answer:
Interval Notation:
(6,∞)
Inequality Form:
x>6
there ya go
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Task #3 Mariam’s Job
Date Completed:
Mariam makes $50 a week.
a) Show this relationship in a graph below.
b) What is the unit rate of the line in the equation?
c) What is the connection between the unit rate and the amount of money Mariam makes per week?
d) Write the equation for this relationship.
e) Is this a proportional relationship? Justify your answer.
Answer:
a
Step-by-step explanation:
Consider the following sets of sample data: A: $30,500, $27,500, $31,200, $24,000, $27,100, $28,600, $39,100, $36,900, $35,000, $21,400, $37,900, $27,900, $18,700, $33,100 B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answer:
[tex]CV=0.2[/tex] ---- dataset 1
[tex]CV = 7.2[/tex] --- dataset 2
Step-by-step explanation:
Given
[tex]A: 30500, 27500, 31200, 24000, 27100,28600, 39100, 36900, 35000, 21400, 37900, 27900, 18700,[/tex][tex]33100[/tex]
[tex]B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11[/tex]
Required
The coefficient of variation of each
Dataset A
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{30500+ 27500+31200+24000+ 27100+28600+ 39100+ 36900+ 35000+ 21400+ 37900+ 27900+ 18700+33100}{14}[/tex][tex]\mu = \frac{418900}{14}[/tex]
[tex]\mu = 29921.43[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(30500 - 29921.43)^2 +.................+ (18700- 29921.43)^2 + (33100- 29921.43)^2}{13}}[/tex]
[tex]\sigma= \sqrt{\frac{487723571.42857}{14}}[/tex]
[tex]\sigma= \sqrt{34837397.959184}[/tex]
[tex]\sigma= 5902.32[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV=\frac{5902.32}{29921.43}[/tex]
[tex]CV=0.2[/tex] --- approximated
Dataset B
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{4.29+ 4.88+ 4.34+ 4.17+ 4.52+ 4.80+ 3.28+ 3.79+ 4.84+ 4.77+ 3.11}{11}[/tex]
[tex]\mu = \frac{46.79}{11}[/tex]
[tex]\mu = 4.25[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{(4.29 - 4.25)^2 + (4.88- 4.25)^2 +.........+ (3.11- 4.25)^2}{11}}[/tex]
[tex]\sigma = \sqrt{\frac{3.859}{11}}[/tex]
[tex]\sigma = \sqrt{0.35081818181}[/tex]
[tex]\sigma = 0.593[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV = \frac{4.25}{0.5903}[/tex]
[tex]CV = 7.2[/tex] -- approximated
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6y - 3x = 30
Answer:
y=(x/2)+5
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept form. To get that, we need y by itself so we have to add 3x to both sides: 6y=30+3x. Now we divide by 6 and rearrange the right side: y=(3x+30)/6.
y = (3x/6)+(30/6) => y = (x/2)+5. We also know that the slope is 1/2 and the y-intercept is 5 because of the slope-intercept equation.
100 Brainly points!! Need help ASAP :)
In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B’. What is the scale factor of dilation?
A. 1
B. 2
C. 0.5
D. -0.5
Answer:
B
Step-by-step explanation:
I'm not really shure tho
Answer:
D. -0.5
Step-by-step explanation:
AB dilated by scale factor -0.5 to produce AB'.
the length of AB = 4 units and the length of AB' = 2 units, the direction is backward, so the scale factor is - 2/4 = -0.5
Let a, b, c be the three observations. The mean of these observations is.
(a) a+b+c2 (b) a×b×c2 (c) a+b+c3 (d) a+bc
Answer: a+b+c/3
Step-by-step explanation:
mean= sum of all values/number of values
Having trouble with these questions, please help.
Answer:
(a)=50%(b)=2.1and(c)=16.1
Step-by-step explanation:
Hope this helps
if u can answer all them correctly ill make a post for u and u can have all my coins just pls answer them all im begging
Answer: this is a continuation starting in number 4 (use the same steps as example 3)
Step-by-step explanation:
-12
45
-12
14
32
-2
5
Which of the following best represents the relationship between functions f and g?
g(x) = -f(x) - 1
g(x) = f(x - 1)
g(x) = -f(x) + 1
g(x) = -f(x)
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Answer:
(c) g(x) = -f(x) +1
Step-by-step explanation:
We really only need to consider one point on f(x) and/or g(x). We can look at the y-intercepts.
f(0) = 4 and g(0) = -3
Looking at the answer choices, we see ...
A. -f(0) -1 = -4 -1 = -5 ≠ g(0)
B. f(0 -1) = f(-1) = 1 ≠ g(0)
C. -f(0) +1 = -4 +1 = -3 = g(0) . . . . . matches requirements
D. -f(0) = -4 ≠ g(0)
The relation between f(x) and g(x) is g(x) = -f(x) +1.
Which is the graph of the function y = 3x?
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Answer:
see attached
Step-by-step explanation:
The graph that includes the point (1, 3) will be the one that is a graph of ...
y = 3^x
Helppppppp
Which choice is equivalent to the product below
Step-by-step explanation:
jkkkkkkkkkkkkkkkkkkkkk
Answer:
[tex]2 \sqrt{35} [/tex]
find the value of c to the nearest tenth
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Answer:
x ≈ 9.3
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(50°) = 6/x
Solving for x gives ...
x = 6/cos(50°) ≈ 9.3343
x ≈ 9.3
__
There is no 'c' to find the value of.
Answer:
x ≈ 9.3
Step-by-step explanation:
Since , this is right triangle, we can use trigonometry functions;
cos θ = Adjacent side / Hypotenuse
Where, θ = 50°
Hypotenuse = xAdjacent side = 6Solve for x
cos 50° = 6 / x
Multiply both side by x
cos 50° × x = 6 / x × x
cos 50° × x = 6
divide cos50° by both sides
cos 50° / cos 50° × x = 6 / cos 50°
x = 6 / cos 50°
x ≈ 9.33434296
Nearest tenth :- x ≈ 9.3
a country’s population in 1990 was 123 million in 2002 it was 128 million
Answer:
whats the question
Step-by-step explanation:
4(2x + 3) ÷ 5y
The expression above provides an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write "not present."
Answer:
8xy+12y/5
Step-by-step explanation:
write the division as a fraction
4(2x+3)/5 y
Calaucte the product
4y(2x+3)/5
Distbtute 4y through the parentheis
8xy+12y/5
which gives you 8xy+12y/5
There are approximately 1.35 billion people in China. If the world population is 7.1 billion people, what percent of the world population is in China?
Answer:
19.01%
Step-by- step explanation:
[tex]Percentage = \frac{1.35 billion }{ 7.1 billion } \times 100[/tex]
[tex]= \frac{ 1.35 \ times 1, 000, 000, 000} {7.1 \times 1,000,000,000} \times 100\\\\\\=\frac{1.35}{7.1} \times 100 = 19.01 \%[/tex]
