HELPPP!!!!

Solve this system of equations using the inverse of a matrix.
-x +y = 8
4x + 3y = 12
x - 7y + z = 15

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

( i )

now ,

since diameter = 10 cm

[tex]\implies \: radius = \frac{10}{2} = 5 \: cm \\ [/tex]

now ,

[tex]slant \: height \: ( \: l \: ) = \sqrt{h {}^{2} + r { }^{2} } \\ \\ \implies \: \sqrt{(12) {}^{2} + (5) {}^{2} } \\ \\ \implies \: \sqrt{144 + 25} \\ \\ \implies \: \sqrt{169} \\ \\ \implies \: 13 \: cm[/tex]

now ,

[tex]CSA \: of \: cone = \pi \: \times r \times l \\ \\ \implies \: \pi \: \times 5 \times 13 \\ \\ \implies \: 65\pi \: cm {}^{2} [/tex]

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( ii )

now when we flatten the cone ,

the slant height becomes the radius of the sector , while the arc becomes the circumference of cone !

[tex]\therefore \: radius = l = 13 \: cm \\ \\ arc \: length = circumference = 2\pi \: r[/tex]

now ,

[tex]s = d \: \theta \: ( \: for \: a \: sector \: ) \\ \\ \therefore \: l\theta \: = 2\pi \: r \\ \\ \implies \: \theta = \frac{2\pi \: r}{l} \\ \\ \implies \: \theta = \frac{2 \times \pi \times 5}{13} \\ \\ \implies \: \theta \: = \frac{10\pi}{13} \\ \\ \implies \theta \: = \: 0.77 \pi [/tex]

hope helpful :D

Step-by-step explanation:

i)

remember, the radius is half the diameter !

the overall surface area of a cone (base circle + "mantle", the lateral, curved surface) is

A = pi×r × (r + sqrt(h² + r²))

so, only the "mantle" or lateral curved stave area is

pi×r × sqrt(h² + r²) = pi×5 × sqrt(12² + 5²) = pi×5×sqrt(169) =

= pi×5×13 = 65×pi cm²

ii)

the length of the arc of the sector is the circumference of the circle, that was the base of the original cone.

that is

2×pi×r = 2×pi×5 = 10×pi cm

the total circumference of the large circle containing that sector is

2×pi×r' = 2×pi×sqrt(h² + r²)

as the radius r' of the circle containing the sector (representing the "mantle" of the cone) is the lateral height of the cone (the distance along its side from the base to the top). and that is per Pythagoras simply the square root of the sum of the square of the inner height and the square of the base radius.

in our case that is

2×pi×sqrt(12² + 5²) = 2×pi×13 = 26×pi cm

the angle of the sector is then 10/26 of the total of 360° for the whole circle :

360 × 10/26 = 138.4615385...°

or, if you need this in terms of pi too, remember that 360° are represented by 2×pi (the arc length of the standard circle).

2×pi × 10/26 = pi × 20/26 = pi × 10/13 =

= 0.769230769... × pi

The correct option for this questions is Option C

1/3, 2/6, 3/9, 4/12, 5/15, 6/18, 7/21, 8/24, 9/27, 10/30, 11/33, 12/36, 13/39, 14/42, 15/45, 16/48, 17/51, 18/54, 19/57, 20/60, and so on ...

Two frations are equivalent when they have the same value when written in lowest terms. The fraction 8/24 is equal to 1/3 when reduced to lowest terms. To find equivalent fractions, just multiply the numerator and denominator of that reduced fraction (1/3) by any interger number, ie, multiply by 2, 3, 10, 30.

Equivalent fractions may look different, but when you reduce then to the lowest terms you will get the same value. If any fraction is not reduced to lowest terms, you can get other equivalent fractions just dividing both numerator and denominator by the same number.

Thus, option c is your answer

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Answer:

The correct answer is B

Step-by-step explanation:

The blue line points to the left and has a closed circle, so the value of x has to be less than or equal to -4.

Answer:

x-axis

Step-by-step explanation:

The lateral line on a graph is known as the x-axis

Answer:

f(x)=x-24

Step-by-step explanation:

It is decreasing by 24. Hope this helps!

Answer:

The formula is f(x) = x-24

Step-by-step explanation:

72-24=48

48-24=24 and so on

Answer:

1) 14π

2) 47.1

Step-by-step explanation:

1)

Circumference = 2πr

where r = radius

given radius is 7mi

So we have C = 2πr and r = 7

==> plug in 7

C = 2π(7)

==> multiply 2 and 7

C = 14π

we leave our answer in terms of pi so this is our final answer.

2)

Again Cicumference = 2πr

The given radius here is 7.5

So C = 2πr

R = 7.5 and π = 3.14

==> plug in values

C = 2(3.14)(7.5)

==> multiply 2 and 3.14

C = 6.28(7.5)

==> multiply 6.28 and 7.5

C = 47.1

Answer: y= -7   y= -5   y= -3   y= -1

Step-by-step explanation:

Answer:

47.15%

Step-by-step explanation:

Getting a raise of 15% would increase the teacher's salary by 300. 943 of 2300 is 47.15%.

Answer:

∠A + ∠B = 90°

Step-by-step explanation:

Complementary angles are angles which, combined, add to 90°. Therefore, an equation displaying the relationship between two complementary angles may look like this: ∠A + ∠B = 90°.

Answer:

C

Step-by-step explanation:

Plug in x, for example if you plug in x in 3x+1 you will get  y which is 4, and the same for the rest.

The amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.

Let the three dimensions(height, length, width) be x, y,z units respectively.

The surface area of the cuboid is given by

[tex]S = 2(a\times b + b\times c + c\times a)[/tex]

For this case, tissue box is almost cuboid shaped.

Also, its dimensions are given being 8 inches, 3 inches and 3 inches.

Suppose we measure the amount of cardboard needed in terms of area, then, the amount of cardboard needed to make that box(without any whole, full cuboid) is equal to the area of its surface(either outer or inner if we assume 0 inches thickness of cardboard),

Thus, we get:

Amount of cardboard needed = surface area of cuboid box with dimensions 8 by 3 by 3 (in inches)

= [tex]2(8 \times 3 + 3 \times 3 + 3 \times 8) = 114 \: \rm in^2[/tex]

Thus, the amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.

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Answer:

5 shaded region area = 100 - 78.5 = 21.5 sqm

6 c

Step-by-step explanation:

5. area of square = 10 x 10 = 100 sqm

area of circle = pi * r^2 = pi (5)^2 = 78.5 sqm (take pi as 3.14)

shaded region area = 100 - 78.5 = 21.5 sqm

6. for a straight line, equation is y = mx + b

m = 5, b = -12 in this case

Answer:

B

Step-by-step explanation:

took the test >:)

Answer:

a) 15h 45m gap

b) 06h 15m gap

c) 14h 30m gap

d) 16h 25m gap

Answer:

a) 3 hours and 45 mins

b) 18 hours and 15 minmins

c) 2 hours and 30 mins

d) 16 Hours and 20 mins

I might be wrong...

Answer:

[tex]f = 2.48[/tex]

Step-by-step explanation:

Step 1:  Subtract 4.02 from both sides

[tex]f + 4.02 = 6.5[/tex]

[tex]f + 4.02 - 4.02 = 6.5 - 4.02[/tex]

[tex]f = 2.48[/tex]

Answer:  [tex]f = 2.48[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

∠POS = 128°

Step-by-step explanation:

Angles on a straight line always add up to 180°

Therefore:

∠POS + ∠POQ = 180°  (as they are the angles on line SOQ)

∠POS + 52° = 180°

∠POS = 180° - 52°

∠POS = 128°

[tex]\huge{\color{magenta}{\fbox{\textsf{\textbf{Answer}}}}}[/tex]

To find :-

The value of ∠POS

Given :-

∠POQ = 52°

Solution :-

The ∠POQ + ∠POS lies on same line SOQ. So they are linear pair and linear pair angle forms sum of 180°.

∠POS + ∠POQ = 180° {linear pair}

∠POS + 52° = 180°

∠POS = 180° - 52°

∠POS = 128°

Result :-

The angle ∠POS is 128°.

Answer:

12

Step-by-step explanation:

Answer:

The inequality true is -5-3x > 10-3 (I hope thats the selection kinda hard to tell with spaces.

Step-by-step explanation:

By solving each side of each inequality your able to compare if the statements are true. -5-3x Is 13 and 10-3 is seven making that inequality the only true one in the selection.

The scale on the y-axis overemphasizes the difference in salaries between different experience levels.

The histogram is one of the ways of data presentation. Usually, it utilizes rectangles plotted on the x and the y axis.

In this case, the graph is misleading in the sense that; the scale on the y-axis overemphasizes the difference in salaries between different experience levels.

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Answer:

A

Step-by-step explanation:

Answer:

1480m^2

Step-by-step explanation:

1. Fine the area of the full lot: 35 x 50 = 1750

2. Find the area of the house: 270

3. Subtract the area of the house from the lot: 1750 - 270 = 1480

Your answer is 1480m^2.

[tex]\begin{cases} p= < 6,6 > \\ q= < -5,-3 > \end{cases}\qquad \qquad \stackrel{2p}{2 < 6,6 > }~~ + ~~\stackrel{3q}{3 < -5,-3 > } \\\\\\ \stackrel{2p}{ < (2)(6)~~,~~(2)(6) > }~~ + ~~\stackrel{3q}{ < (3)(-5)~~,~~(3)(-3) > } \\\\\\ < 12~~,~~12 > ~~ + ~~ < -15~~,~~-9 > \implies < 12-15~~,~~12-9 > \\\\\\ \stackrel{2p~~ + ~~3q}{\boxed{ < -3~~,~~3 > }}\qquad \qquad ||\stackrel{magnitude}{ < -3,3 > }||\implies \sqrt{(-3)^2 + (3)^2}\implies 3\sqrt{2}[/tex]

The expected number of times to select a green pencil when the pencils are selected 1350 times is 450

The distribution of the pencils is given as:

Red = 4

Blue = 6

Green = 5

The total number of pencil is:

Total = 4 + 6 + 5

Evaluate the sum

Total = 15

The probability of selecting a green pencil is:

P(Green) = 5/15

Evaluate

P(Green) = 1/3

So, the expected number of times is:

E(x) = 1/3 * 1350

Evaluate

E(x) = 450

Hence, the expected number of times to select a green pencil is 450

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Answer: The Answer is 450

Explanation: I took the test and got it right

Hope this helps :)

Answer:

635.2 cm^3.

Step-by-step explanation:

Volume of the cylinder = π r^2 h

= 3.14 * 4^2 * 5 = 251.2

Volume of the prism = 4 *8 * 12

= 384

Total volume = 384 + 251.2

[tex]v = \pi {r}^{2} h[/tex]

[tex]v = 3.14 \times {4}^{2} \times 5[/tex]

[tex]v = 251.2 \: {cm}^{3} [/tex]

[tex]v = lwh[/tex]

[tex]v = 12 \times 8 \times 4[/tex]

[tex]v = 384 \: {cm}^{3} [/tex]

[tex]v = 251.2 + 384[/tex]

[tex]v = 635.2 \: {cm}^{3} [/tex]

The amount that will be there in Henry's account after a period of 6 years will be $1,925.765.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,

[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]

The amount that Henry put in the account is $1700, while the compound interest on that account is 2.1% annually. Also, the time for which the amount is kept in the account is 72 months which is equal to 6 years.

Now, the total amount in Henry's account after a period of 6 years will be,

[tex]\rm Account\ Balance = \$1700(1+0.021)^6[/tex]

                           [tex]= \$1700(1.021)^6\\\\= \$1,925.765[/tex]

Hence, the amount that will be there in Henry's account after a period of 6 years will be $1,925.765.

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Answer:

10 + 6 - 3

Step-by-step explanation:

Using it's concept, it is found that there is a 0.4545 = 45.45% probability that the person is from Texas, given that the person prefers brand A.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 176 people who prefer brand A, and of those 80 are from Texas, hence the probability is given by:

p = 80/176 = 0.4545.

0.4545 = 45.45% probability that the person is from Texas, given that the person prefers brand A.

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The value of the integration for a non closed path abcd will be -88

Cyclic integration is the integration over a closed loop.Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is

[tex]\oint_c(Sin(x)+9y)dx+(4x+y)dy\\\\\\[/tex]

[tex]=\int\int \dfrac{\partial (4x+y)}{\partial x} -\dfrac{\partial (Sin(x)+9y)}{\partial y}dxdy[/tex]

[tex]=-5\int\int dxdy[/tex]

(where int(C ) denotes the region interior to the path C )

The remaining double integral is -5 times the area of the trapezoid, which is

[tex]-5 \int\int dxdy=\dfrac{-5}{2}\times (12+4)\times 4=-160[/tex]

To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to

[tex]\int _{DA} ydy=\int\limits^0_{12} y dy=-\int\limits^{12}_0ydy =-72[/tex]

Then

[tex]\int_{ABCD}9Sin(x)+9y)dx+(4x+y)dy=-160-(-72)=-88[/tex]

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