PLZZ HELPPP

Which matrix equation can be used to solve the system?
x+y=21
5x+4y=20

PLZZ HELPPPWhich Matrix Equation Can Be Used To Solve The System?x+y=215x+4y=20

Answers

Answer 1

Answer:

[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]

Step-by-step explanation:

Given the simultaneous equation

x+y=21

5x+4y=20

To write in matrix form, it must be in the form AX= b

X = A⁻¹b

A⁻¹ is the inverse of matrix A

A is a 2by2 matrix

X is the variables

b is a column matrix

The expression will therefore be written as;

[tex]A=\left[\begin{array}{ccc}1&1\\5&4\\\end{array}\right] \\\\|A| = 1(4)- 5(1)\\|A| = 4-5\\|A| = -1\\A^{-1} = -\left[\begin{array}{ccc}4&-1\\-5&1\\\end{array}\right] \\\\A^{-1} = \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \\[/tex]

Hence the required product matrix that represent X is;

[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]


Related Questions

Financial software can do all of the following except ____.


A.
prepare your taxes


B.
apply for loans


C.
keep track of expenses


D.
monitor your savings

Answers

Answer: Apply for loans

Step-by-step explanation:

I just took the quiz off gradpoint :) trust me its right!!!!

1. Which two points fail the VLT here in this graph?


PLEASE HELP!!!!

Answers

Kiki and Rose's points

They are on the same vertical line so they fail

can you help me do this Q I can't seem to get it :)

Answers

9514 1404 393

Answer:

x = 3∠IEH = 61°∠IHE = 35°

Step-by-step explanation:

There are a couple of useful facts about parallelograms that can be used here.

1) The diagonals bisect each other.

2) Opposite sides are parallel, so each diagonal can be considered a "transversal" with respect to parallel lines. That means all of the angle relationships involving parallel lines apply.

__

The two marked sections of diagonal GIE are congruent, so you have ...

  3x +1 = 10

  3x = 9 . . . . subtract 1

  x = 3 . . . . . divide by 3

__

Angles IEH and IGF are "alternate interior" angles, so are congruent.

  angle IEH = 61°

__

Angles IHE and IFG are "alternate interior" angles, so are congruent.

  angle IHE = 35°

is 15 over -4 negative

Answers

Answer:

15 is larger than -4

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

15 ÷ (-4) = -3.75

1. Solve for x.
55°
(3r + 23)
75°

Answers

Answer:

The value of x is 9.

Step-by-step explanation:

55°

(3 x + 23)

75°

The sum of all the angles of triangle is 180°.

55 + 3 x + 23 + 75 = 180

3 x = 27

x = 9

So, the value of x is 9.

A fair dice is rolled 3 times in a row. The outcomes are shown below.
Calculate the probability of all three events occurring.

Answers

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{1}{6} + \frac{1}{6} + \frac{1}{6} =\frac{1}{2}[/tex]

Kate is 1 year and six months younger than her sister. If her sister is 14 years and 2 months old, how old is Kate?

Answers

Answer:

Kate is 13years and 4 months old,I suggest.

Which equation represents a line that passes through the two points in The table

Answers

Answer:

y = mx + by= mx+ b

Step-by-step explanation:

since we know the two points on the line. we use the two points formed to find its equation. the final equation.the slope intercept form ,y=mx+by = mx+b

Name the marked angle in 2 different ways.

Answers

1) Angle UWV

2) Angle VWU

angle uwv

yepyepyep!

7. From eye level 5 feet off the ground, a person has to look up at an angle of 35
degrees to see the top of a tree 60 feet away. How tall is the tree.​

Answers

Answer:

47.01 ft

Step-by-step explanation:

answer in photo above

An aeroplane travels on a bearing of 295o so that it is 200 km west of its starting point. How far has it travelled on this bearing?
please use diagrams to explain

Answers

Answer: Approximately 221 km

The more accurate value is roughly 220.675583792499 km but even that isn't an exact value.

===============================================

Explanation:

Refer to the diagram below.

The plane starts at point A, which is the origin (0,0)

Directly north is the bearing 0 degrees, which it sometimes written as triple zeros and a degree symbol at the end, so we'd write 000° to mean directly north.

Let's say we face directly north. When turning clockwise (turn toward the east), the bearing angle increases. That means directly east is the bearing 090° and 180° is directly south.

The bearing 270° is directly west. Another 25 degrees gets us to 270+25 = 295°

This plane is facing the northwest direction, as the diagram indicates below (the plane is aimed at point C while it's located at point A initially).

------------

Triangle ABC has the horizontal component AB = 200 km, since we're told that the plane is 200 km west of its starting point (and some unknown distance north of the starting point).

We use the cosine ratio to help determine the hypotenuse length AC

cos(angle) = adjacent/hypotenuse

cos(A) = AB/AC

cos(25) = 200/x

x*cos(25) = 200

x = 200/cos(25)

x = 220.675583792499 which is approximate.

x = 221

I'm rounding to the nearest whole number since every other value given to you is a whole number. Round as your teacher instructs.

This means the plane is roughly 221 km away from its starting point. In other words, side AC is about 221 km long.

If a is an odd number, b is not divisible by 3 and LCM of a and b is P, what is the LCM of 3a and 2b?

Answers

Answer:

The LCM of 3a and 2b = 6P

Step-by-step explanation:

LCM of  3 a  and  2 b  will be  6 p

Since  a  is odd, which means it's not divisible by 2. Therefore a can be number 1, 3, 5, 7, 9, 11, .......

b  is not divisible by  3, which means b can be number 1, 2, 4, 5, 7, 8, 10, 11, .....

LCM of a and b is P

Factors of 2b can be 2 multiplied by (1, 2, 4, 5, 7, 8, 10, 11, ..... )  

Factors of 3a can be 3 multiplied by (1, 3, 5, 7, 9, 11, .......)

So, to get the LCM of 3a and 2b, since we already show the factors of a and b, Then, 3 X 2 X P (remember P is the LCM of a and b)

The LCM of 3a and 2b = 6P

       

Line x line y find the measures of angle 4

Answers

Answer: The measure of angle 4 is 95 degrees.

Step-by-step explanation:

Knowing that the lines are parallel that means the alternate exterior angles are congruent. The alternate exterior angle of the angle marked with 95 degrees is angle 1. That means angle one is 95 degrees. Angle 1 and Angle 4 are vertical angles. All vertical angles are congruent so this mean angle 4 is also 95 degrees.

When 345 is multiplied by a power of 10 the number of zeros in the product is related to the power of 10. Explain how the number of zeros relates to the power of 10.

Answers

Answer:

The Number of Zeroes In The Results is Always equal To the Powers of 10.

Step-by-step explanation:

Example:-

345*[tex]10^{2}[/tex] = 34500

345*[tex]10^{5}[/tex] = 34500000

345*[tex]10^{7}[/tex] = 3450000000

345*[tex]10^{8}[/tex] = 34500000000

(In the Above examples, There is All The Numbers of Zeroes In The Results is equal To the Powers of 10)

Seventh Grade Students
Instrument # of Students
Guitar 12
Bass 10
Drums 9
Keyboard 12
Eighth Grade Students
Instrument # of Students
Guitar 5
Bass 6
Drums 15
Keyboard 5

Based on these results, express the probability that a seventh grader chosen at random will play the drums as a fraction in simplest form.

Answers

Answer:

3/11

Step-by-step explanation:

FORMULA= P(A)=

NUMBER OF FAVORABLE OUTCOMES

-------------------------------------------------------------

NUMBER OF POSSIBLE OUTCOMES

GIVEN: 12 Guitars, 10 Bass, 9 Drums, 12 Keyboards

WANT: The probality a seventh grader chosen at randome will play drums

add all the instruments

12+10+9+12=33

there are 9 drums

FOLLOW THE FORMULA

9 3

---- = ---- SIMPLIFIES FORM

33 11

pls answer by step by step

Answers

Answer:

[tex]\frac{\sqrt{5}-\sqrt{2} }{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{\sqrt{5} + \sqrt{2} }[/tex]

[tex]\frac{1}{\sqrt{5} + \sqrt{2} } * \frac{\sqrt{5} - \sqrt{2} }{\sqrt{5} - \sqrt{2} }[/tex]

[tex]\frac{\sqrt{5} - \sqrt{2} }{(\sqrt5)^{2} - \sqrt{2})^2 } }[/tex]

[tex]\frac{\sqrt{5} - \sqrt{2} }{5-2}[/tex]

[tex]\frac{\sqrt{5}-\sqrt{2} }{3}[/tex]

classify the expression by both degree and terms 2x4 - x +5

Answers

Answer:

x=3

Step-by-step explanation:

What's the domain of the graph?

Answers

Step-by-step explanation:

In interval form, the domain of f is (−∞,∞).

the question is on the image​

Answers

Answer:

70

Step-by-step explanation:

the fraction 7/10 turns into 70% which means 70 out of 100 tickets were sold.

Answer:

70 tickets sold

Step-by-step explanation:

Multiply the number of tickets by the fraction of tickets sold

100 *7/10

Rewriting

100/10 * 7

10*7

70

The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240. A) Find the first term. B) Find the common ratio. C) Justify your answers by showing steps that demonstrates your answers generate S8=19680 and S4=240.

Answers

Answer:

First Term = 6

Common Ratio = 3

Step-by-step explanation:

According to the Question,

Given, The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240 .

Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .

The Sum of n-term of Geometric Mean is [tex]S_{n} = \frac{a(r^{n-1)} }{r-1}[/tex] Where, r>1 , a=First term of G.P & r=common Ratio .

Now, on solving  [tex]\frac{S_{8} }{S_{4} }[/tex]  we get,

[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]  

[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]

[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )

So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .

Which conversion factor would you use to convert from meters to feet?

Answers

Answer:

To convert a meter measurement to a foot measurement, multiply the length by the conversion ratio. The length in feet is equal to the meters multiplied by 3.28084.

Step-by-step explanation:

IF YOU ANSERW MY MATH QUESTIONS ILL GIVE ADTINAL 50) POINTS FOR each question and crown evry question.
A scientist uses a submarine to study ocean life.
*She begins at sea level, which is an elevation of 0 feet.
*She descends for 91 seconds at a speed of 2.2 feet per second.
*She then ascends for 32 seconds at a speed of 0.7 feet per second.

At this point, what is her elevation, in feet?

Answers

Answer:

-177.8 feet below sea level.

Step-by-step explanation:

First, we know that descend means to lower. Anything lower than 0 has to be negative. It says that she descends for 91 seconds at a speed of 2.2 feet per second. So first to find out how many feet she descended in those 91 seconds, you need to multiply 91*-2.2= -200.2. Then, it says that she ascends for 32 seconds at the speed of 0.7 feet per second. It's the same thing, but ascend means to go up. So, we multiply 32*0.7=22.4. Now we add the two numbers together to get -177.8.

Answer:

220.4 feet below sea level

Step-by-step explanation:

use the following formula:

rate x time = distance

(rate going down)(time going down) = distance going down.

so if she starts at 0 feet above sea level, and descends for 91 seconds at a speed of 2.2 ft/sec. you would plug that in as:

(2.2 ft/sec)(91 seconds) = distance of 198 feet.

she then ascends for 32 seconds at a speed of 0.7 feet/second.

so, substitute that;

(0.7 ft/sec)(32sec) = distance of 22.4 feet.

distance traveled downward + distance traveled upward = total distance of location.

198 + 22.4 feet = 220.4 feet

Please help I wanna pass

Answers

Answer:

Everything is correct except for the second one and the ones you checkmarked.

Step-by-step explanation:

The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.

Answers

Answer:

x = -5; y = 4, z = 1

Step-by-step explanation:

Given the row echelon form as:

[tex]\left[\begin{array}{cccc}1&0&\ \ 4|&-1\\0&1&-1|&3\\0&0&\ \ 1|&1\end{array}\right][/tex]

This matrix can be represented as:

[tex]\left[\begin{array}{ccc}1&0&4\\0&1&-1\\0&0&1\end{array}\right]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right] \\\\Performing\ matrix\ multiplication\ gives:\\\\\left[\begin{array}{c}x+4z\\y-z\\z\end{array}\right] =\left[\begin{array}{c}-1\\3\\1\end{array}\right][/tex]

Therefore:

z = 1

y - z = 3;  

y = 3 + z = 3 + 1 = 4.

Hence, y = 4

x + 4z = - 1;

x = -1 - 4z = -1 - 4(1) = -5

x = -5

sin 145° rounded to the nearest hundredth

Answers

Answer:

0.57

You could use a calculator ya know

Step-by-step explanation:

I need help on this hurry please

Answers

Answer:

x=70

Step-by-step explanation:

sum is angles of a Pentagon=540°

x°+138°+2x°+80°+112°=540°

3x°+330°=540°

3x°=540°-330°

3x°=210°

3x°/3°=210°/3°

x=70

hope this is helpful

(1.3) Sequence A: 4; 7; 10; 13; 16; Sequence B: 5; 10; 20; 40; 80; .......... Sequence C: 2; 5; 10; 17; 26; (1.3.1) Write down the next three numbers in each of given sequences. (3) Sequence A Sequence B: Sequence C: (1.3.2) Write down how you decided what the next number would be in each of the three sequences. (3) Sequence A: Sequence B: Sequence C ​

Answers

Answer with Step-by -step explanation:

Sequence A;4,7,10,13,16

[tex]a_2-a_1=7-4=3[/tex]

[tex]a_3-a_2=10-7=3[/tex]

The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.

Common difference, d=3

a=4

[tex]a_n=a+(n-1)d[/tex]

[tex]a_6=a+5d=4+5\times 3=19[/tex]

[tex]a_7=a+6d=4+6(3)=22[/tex]

[tex]a_8=a+7d=4+7(3)=25[/tex]

Sequence B: 5,10,20,40,80,...

[tex]a_1=5,a_2=10,a_3=20[/tex]

[tex]\frac{a_2}{a_1}=\frac{10}{2}=2[/tex]

[tex]\frac{a_3}{a_2}=\frac{20}{10}=2[/tex]

The ratio  of two consecutive terms is equal. Therefore, it forms geometric sequence.

Common ratio, r=2

a=5

[tex]a_n=a r^{n-1}[/tex]

[tex]a_6=ar^5=5(2)^5=160[/tex]

[tex]a_7=ar^6=5(2^6)=320[/tex]

[tex]a_8=ar^7=5(2^7)=640[/tex]

Sequence C:2,5,10,17,26,..

a1=2

[tex]a_2=5=2+3=a_1+3[/tex]

[tex]a_3=10=5+5=a_2+5[/tex]

[tex]a_4=17=10+7=a_3+7[/tex]

[tex]a_5=26=17+9=a_4+9[/tex]

From the following pattern

We can get

[tex]a_6=a_5+11=26+11=37[/tex]

[tex]a_7=a_6+13=37+13=50[/tex]

[tex]a_8=a_7+15=50+15=65[/tex]

30 POINTS + BRAINLIEST!!! PLEASE HELP ASAP!!!

Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule.

Answers

Answer:

CNBD

Step-by-step explanation:

From the diagram, we can see that:

[tex]\displaystyle BL\parallel CA[/tex]

Then by Alternate Interior Angles:

[tex]\angle LBA\cong \angle CAB\text{ and } \angle BLC\cong \angle ACL[/tex]

From vertical angles, we also know that:

[tex]\displaystyle \angle BKL\cong \angle AKC[/tex]

This is all we can gather from the given image. Knowing only three pairs of angles cannot prove congruence, as proving congruence requires at least one side.

Congruence cannot be determined.

Answer:

Cannot be determined

Step-by-step explanation:

With BL and AC being parallel, we can deduce that the two triangles in question share all three of their angles. However, there is no information given that implies any of the sides are equal. AAA (Angle-Angle-Angle) is a proof of similarity, but not congruence, therefore the two triangles cannot be determined to be congruent.

URGENT: If θ is a second-quadrant angle and cosθ = -2/3, then tanθ = _____.

Answers

In the second quadrant, both cos and tan are negative while only sin is positive.

To find tan, we will use the following property below:

[tex] \large \boxed{ {tan}^{2} \theta = {sec}^{2} \theta - 1}[/tex]

Sec is the reciprocal of cos. If cos is a/b then sec is b/a. Since cos is 2/3 then sec is 3/2

[tex] \large{ {tan}^{2} \theta = {( - \frac{3}{2}) }^{2} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - \frac{4}{4} \longrightarrow \frac{5}{4} } \\ \large{tan \theta = \frac{ \sqrt{5} }{ \sqrt{4} } } \\ \large \boxed{tan \theta = \frac{ \sqrt{5} }{2} }[/tex]

Since tan is negative in the second quadrant. Hence,

[tex] \large{ \cancel{ tan \theta = \frac{ \sqrt{5} }{2} } \longrightarrow \boxed{tan \theta = - \frac{ \sqrt{5} }{2} }}[/tex]

Answer

tan = -√5/2

Edna has a new St. Bernard puppy. He found a mud puddle on their last walk, so Edna needs to give him a bath. She buys a bottle of dog shampoo that costs $3.99. The bottle contains 28.5 ounces of shampoo. What is the cost per ounce of shampoo?

Answers

Answer: 7.142857142857143

Step-by-step explanation: all you have to do is divide 28.5 by 3.99

The cost per ounce of shampoo is 7.15 ounce.

Assume that the cost per ounce of shampoo is ${x}.

Total cost of bottle of a dog shampoo is $3.99.

Amount of shampoo in the bottle is 28.5 ounces.

So, we can write the cost per ounce of shampoo as

x = 28.5/3.99

x = 7.15 ounce

The cost per ounce of shampoo is 7.15 ounce.

To solve more questions on division, visit the link below-

https://brainly.com/question/15381501

#SPJ2

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