Give an example of two 2×2 matrices A and B, neither of which is the zero matrix or the identity matrix, such that AB=BA.

Answer: 62°

Step-by-step explanation:

apply concept: the interior angle sum of triangle is = 180°

          a+b+c=180

a+68.5+49.5=180

            a+118=180

                  a=62

Answer:

Step-by-step explanation:

Since it's a triangle it's interior angles sum up to 180° .

In order to find x add up all it's known interior angles and subtract it from 180° to find x.

That's

x + 68.5 + 49.5 = 180

x + 118 = 180

x = 180 - 118

We have the final answer as

Hope this helps you

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

[tex]\triangle ABC[/tex] represents the 1st angle of elevation of sun i.e.  58°

[tex]\triangle ABD[/tex] represents the 2nd angle of elevation of sun i.e.  36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = [tex]h[/tex] m

Let side BC = [tex]x[/tex] m

Now, let us apply tangent rules in [tex]\triangle ABC, \triangle ABD[/tex] one by one:

[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)[/tex]

[tex]tan36^\circ = \dfrac{h}{x+90}[/tex]

Putting value of [tex]x[/tex] using equation (1):

[tex]tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}[/tex]

119.45 m is the height of pole.

Answer:

C

Step-by-step explanation:

Here we have the question,

7x+4 = -19 + 5x

Now we add 19 to both sides,

7x + 4 + 19 = -19 + 19 + 5x

7x + 23 = 5x

Now we subtract 7x from both sides,

23 = -2x

We divide -2 from both sides,

x = -23/2

Now we plug this in into 2x - 14,

2(-23/2) - 14 = -23-14 = -37

Our answer is C

Answer:

y2=16-x

x=0

y2=16-0

y2=16

y2/2=16/2

y=8

Step-by-step explanation:

(2) (x+2)^2 + (-15x -3)

I hope this will be helpful for you.

Answer:

[tex]2(x + 2)^{2} + (-15x - 3)[/tex]

The guy above is correct

Proof :

[tex]2(x + 2)^{2} - 15x - 3 \\ 2((x + 2)(x + 2) - 15x - 3 \\ 2( {x}^{2} + 4x + 4) - 15x - 3[/tex]

[tex]2 {x}^{2} + 8x - 15x + 8 - 3 \\ 2 {x}^{2} - 7x + 5[/tex]

My workings are in the picture

My asnwer was 5/2 and -1

Answer:

X=2

Step-by-step explanation:

First, distribute the 3 to get

3x+3-2=x+5

Solve for 3-2 to get

3x+1=x+5

subtract 1 from both sides to get

3x=x+4

subtract x from both sides to get

2x=4

divide both sides by 2 to finalily get

x=2

Answer:

Standard form:

Simplify the words.

6,090,036

Expanded form:

Take the standard number and expand it.

6000000 + 90000 + 30 + 6

I'm sorry if I misunderstood.

Good luck though! :)

Please add Brainliest if you'd like, not that it matters.

Answer:

4 units

Step-by-step explanation:

The volume of a square pyramid is (a²)*h/3

256=a²*12/3

256=a²*4

256/4=a²

64=a²

a=8

Now we know that the square is 8 by 8.

The volume of a square prism is a²h

256=64h

256/64=h

h=4

Also, a square pyramid is 1/3 the volume of a square prism.

12÷3=4

Answer:

the answer is C    4 units

Step-by-step explanation:

Answer:

$578.87

Step-by-step explanation:

Find the area made by the circle made by the 3 ft. walk:

Radius = 17 + 3 = 20

Area = 22/7 x 20 x20 = 1257.14

Find the area made by the pond:

Area = 22/7 x 17 x 17 = 908.29

Subtract area 2 from area 1:

1257.14 - 908.29 = 348.85

Muliply this area by the cost er squar foot:

348.85 x $1.66 = 579.09

It depends on the value of pi used

Answer:

Length= 30 ft

Width= 18ft

Step-by-step explanation:

The perimeter of the rectangular patio is to be 96 feet.

the length is to be 6 feet less than twice the width

Perimeter=2(length+width)

But

Length= 2(width)-6

Substituting in perimeter equation

Perimeter=2(length+width)

Perimeter=2((2(width)-6)+width)

Perimeter= 96 feet

Let width= x

Perimeter=2((2(width)-6)+width

96=2((2(x)-6)+x)

96= 4x-12+2x

108= 6x

18= x

Width= 18ft

Length= 2(width)-6

Length= 2(18)-6

Length= 36-6

Length= 30 ft

Answer:

the answer is 8. just think of it as subtraction. subtract +6 from +14. then you get the answer for +14+-6.

Answer:

RK= 13      SK= 12

Step-by-step explanation

First, we find the missing length of RK using the given information: 65-52=13

Then we divide 65 by 13 to get a scale factor: 65/13=5

(To check, we multipuly: 13*5=65)

We then apply the scale factor to MK to find SK: 60/5=12

(To check we multipuly: 5*12=60)

We now have our answers: RK:13, SK:12

Answer:

5

Step-by-step explanation:

The leading coefficient is the coefficient with a variable with the greatest exponent.The exponent is the number you would say "the power to". What I mean is let's say you have this number: [tex]3^{2}[/tex] . The exponent would be 2 in this equation because it's saying what power 3 is too. Therefore, 5 is the leading coefficient.

Answer:

1/6

Step-by-step explanation:

For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.

C1a + C2b + C3c = 0

From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)

The values in parenthesis are the ccoefficients of w, v and u respectively.

On writing this vector as a linear combination, we will have;

C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)

0-2C2+C3 = 0........ 1

-3C1+C2 = 0 ........... 2

C1-kC3 = 0 ….......... 3

From equation 2, 3C1 = C2

Substituting into 1, -2(3C1)+C3 = 0

-6C1+C3 = 0

-6C1 = -C3

6C1 = C3.…..4

Substitute 4 into 3 to have

C1-k(6C1) = 0

C1 = k6C1

6k = 1

k = 1/6

Hence the value of k for the set of vectors to be linearly dependent is 1/6

Answer:

3

Step-by-step explanation:

because it's being intersected

hope I helped?

Answer:

The heaviest 5% of fruits weigh more than 747.81 grams.

Step-by-step explanation:

We are given that a particular fruit's weights are normally distributed, with a mean of 733 grams and a standard deviation of 9 grams.

Let X = weights of the fruits

The z-score probability distribution for the normal distribution is given by;

                              Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean weight = 733 grams

            [tex]\sigma[/tex] = standard deviation = 9 grams

Now, we have to find that heaviest 5% of fruits weigh more than how many grams, that means;

                    P(X > x) = 0.05       {where x is the required weight}

                    P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-733}{9}[/tex] ) = 0.05

                    P(Z > [tex]\frac{x-733}{9}[/tex] ) = 0.05

In the z table the critical value of z that represents the top 5% of the area is given as 1.645, that means;

                               [tex]\frac{x-733}{9}=1.645[/tex]

                              [tex]{x-733}}=1.645\times 9[/tex]

                              [tex]x = 733 + 14.81[/tex]

                              x = 747.81 grams

Hence, the heaviest 5% of fruits weigh more than 747.81 grams.

Answer:

5/14

Step-by-step explanation:

you would just add the number of marbles which is 14 and add the green and red marbles which is 5 and your answer is 5/14

Probability helps us to know the chances of an event occurring. The probability of choosing a green or red marble from the bag is 5/14.

Probability helps us to know the chances of an event occurring. It is always the ratio of desired outcomes or the sample that is needed to the total number of outcomes.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that the bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles.

Now, the total number of marbles in the bag is 14.

Therefore, the probability of choosing a green or red marble from the bag is,

Probability = (Number of green and red marbles)/(Total number of marbles)

                  = (1+4)/(2+1+7+4)

                  = 5/14

Hence, the probability of choosing a green or red marble from the bag is 5/14.

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Answer: 3 people ordered soup.

Step-by-step explanation:

Let x be the number of people ordered salad and y  be the number of people ordered soup.

As per given,

x=2y           (i)

7.50x+6.25y= 63.75          (ii)

Substitute value of c =2y in (ii) , we get

7.50(2y)+6.25y= 63.75

⇒ 15y+6.25y =  63.75

⇒21.25y =  63.75

⇒ y= 3   [divide both sides by 21.25]

Then, x= 2(3) =6

So 6 people ordered salad and 3 people ordered soup.

Answer:

[tex]\huge\boxed{\rho=1.6125\dfrac{g}{cm^3}}[/tex]

Step-by-step explanation:

The formula of a density:

[tex]\text{density}=\dfrac{mass}{volume}\Rightarrow\rho=\dfrac{m}{V}[/tex]

We have

[tex]\text{mass}\ m=12.9g\\\\\text{volume}\ V=8cm^3[/tex]

Substitute:

[tex]\rho=\dfrac{12.9g}{8cm^3}=\dfrac{12.9\cdot10}{8\cdot10}\dfrac{g}{cm^3}=\dfrac{129}{80}\dfrac{g}{cm^3}=1.6125\dfrac{g}{cm^3}[/tex]

The the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]

Given the following data:

To find the density of the brown sugar;

Density can be defined as mass all over the volume of an object.

Simply stated, density is mass per unit volume of an object.

Mathematically, the density of a substance is given by the formula;

[tex]Density = \frac{Mass}{Volume}[/tex]

Substituting the values into the formula, we have;

[tex]Density = \frac{12.9}{8}[/tex]

Density =  [tex]1.6125 \;g/cm^3[/tex]

Therefore, the the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]

Find more information: brainly.com/question/5995838

Answer:8,2,0,2,8; Graph A

Step-by-step explanation:

The graph of the given equation best represents a parabola.

A graph represents the nature of the equation graphically by plotting the points of it.

Given, y = 2x²

For x = - 2, y = 2(- 2)² = 8

For x = - 1, y = 2(- 1)² = 2

For x = 0, y = 2(0)² = 0

For x = 1, y = 2(1)² = 2

For x = 2, y = 2(2)² = 8

Therefore, the given table will be:

x  - 2   - 1   0   1   2

y    8     2   0  2   8

By plotting the graph, it is clear that, the graph best represents a parabola.

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Answer:

0 belongs to the set of whole number,set of rational numbers,set of real numbers and integers

Step-by-step explanation:

Answer:

y = 4x + 3

Step-by-step explanation:

If he has x seed packets, Johnny can grow 4 * x = 4x plants. The 3 is a constant because he already has 3 so the equation is y = 4x + 3.

Answer:  The difference is approximately $44. Remember that is not an exact amount because the weeks are approximated and the second offer was also approximated.

Step-by-step explanation:

If one has $61,100 and the other has 63,400 annually which means that is the amount they will be offered a year. So first we need to determine how many weeks are in a year.There are approximately 52 weeks in one year so we will divide the salaries by 52 to find how much they each offer in one week.

First Offer:  61,100 / 52 =  1175  

Second Offer:  63,400/52=  approximately 1219    

Now find the difference between the numbers

1219. - 1175 =  $44

The difference in weekly pay for these two job will be around $0.04k.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Number of weeks in 1 year = number of weeks in 1 month × 12

Number of weeks in 1 year = 4 × 12 = 48

Annual salary in the first job = $61.1k

So weekly salary of first job =$1.28k

Annual salary in the second job = $63.4k

So weekly salary of second job = $1.32k per week

Difference between weekly pay = 1.32 - 1.28 = 0.04k

Hence "The difference in weekly pay for these two job will be around $0.04k".

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Answer:

Hey there!

The correct answer would be a line from (0, 0) to (-1, 2)

Let me know if this helps :)

Answer:

y= -7

Step-by-step explanation:

This line is a horizontal line.

Horizontal lines all have the same form of y=k (where k is the y-intercept of the horizontal line).

The y-intercept is the point where the line meets the y-axis (the vertical axis). For this line, the y-intercept is in between -6 and -8, making it: (0,-7) or just -7.

Let's return to the form for horizontal lines.

y= k

The y-intercept is -7. Substitute -7 in for k.

y= -7

The equation of the line is y= -7

Answer:

0.33

Step-by-step explanation:

We would like to find the probability that both beads are aqua.

There are 6 aqua beads. Let's calculate the number of ways we can select 2 aqua beads from these 6. We use combinations, which is [tex]_6C_2=\frac{6!}{(6-2)!*2!}[/tex], where the n! means n * (n - 1) * (n - 2) * ... * 2 * 1.

The value of the expression is:

[tex]_6C_2=\frac{6!}{(6-2)!*2!}=\frac{720}{24*2} =15[/tex]

So there are 15 ways to choose 2 aqua beads.

Now let's calculate the number of ways we can select any 2 beads. There are 6 + 4 = 10 beads in total, so we do the same thing as before using combinations:

[tex]_{10}C_2=\frac{10!}{(10-2)!*2!} =\frac{3628800}{40320*2} =45[/tex]

Our fraction is thus:

15 / 45 = 1/3 ≈ 0.33

The answer is thus 0.33.

~ an aesthetics lover

Answer:

6.25

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides.

For a rectangle, it's the two widths plus the two heights.

P = 2W + 2H

Plugging in values:

52 = 2(3x − 1) + 2(x + 2)

52 = 6x − 2 + 2x + 4

52 = 8x + 2

50 = 8x

x = 6.25

Find the value of x.

Perimeter of rectangle = 2 ( l + b )

We know that,

Perimeter of rectangle = 52 [ Given ]

⇒ 2 ( l + b ) = 52

⇒ 2 ( 3x - 1 + x + 2 ) = 52

⇒ 2 ( 4x + 1 ) = 52

⇒ 8x + 2 = 52

⇒8x = 52 - 2

⇒ 8x = 50

⇒ x = 50/8

⇒ x = 6.25 inches

Answer:

0.00387

To convert from meters to kilometers, you must divide the number pf meters by 1000.

3.87 ÷ 1000 = 0.00387.

So, that is the answer. Hope it helps!

Answer:

Total number of votes- 145,000

Votes secured by winning candidate- 76,850

Step-by-step explanation:

Candidate A- 47%

Candidate B- 53%

6% difference or 8700 votes so

6%=8700

1%=1450

100%=145,000

53%= 76,850

Answer:

quantity of red paint =  12.5 gallons

quantity of blue paint =  7.5  gallons

Step-by-step explanation:

Ratio of red and blue paint : 5:3

in ratio

a:b = ax:bx

let the

quantity of red paint be 5x

quantity of blue paint be 3x

then quantity of purple paint = quantity of red paint  + quantity of blue paint

                                                  = 8x

given quantity of purple paint is 20 gallons

thus,

8x = 20

x = 20/8 = 2.5

thus,

quantity of red paint = 5x = 5*2.5 = 12.5 gallons

quantity of blue paint = 3x = 3x*2.5 = 7.5  gallons

Answer:

7 and 12.5

Step-by-step explanation: