step-by-steps to Solve a system of linear equations using matrices.

Answer:

6 friends can share the pizza

Step-by-step explanation:

1 1/2 ÷ 1/4 =6

Answer:

Divide 1 1/2 by 1/4. Note that 1 1/2 = 1 2/4 = 6/4. So now we divide 6/4 by 1/4, obtaining 6.

6 friends can enjoy an equal share.

Answer:

ez pts tysm

Step-by-step explanation:

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Answer:

66-26 = 40

Step-by-step explanation:

u = 40 degrees

let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

\(\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill\)

\(\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}\)

\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

16 new releases and 22 classic movies.

Answer:

-10

Step-by-step explanation:

Answer:

 309

Step-by-step explanation:

-42 x -7 = 294 + 15 = 309

Answer: 52 ounces

multiply the mass value by 16

The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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Answer:

Isoceles

Step-by-step explanation:

Use the distance formula for each side

\(\sqrt{(x_{2} -x_{1} )^2 + (y_{2} - y_{1})^2\)

(x1, y1)  (x2, y2)

Answer:

Step-by-step explanation:

Answer: 40%

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

what I did is that I added 6 and 2 (2 males and 6 women) so that's 8, then I put it as a fraction of 6/8, and I just searched what 6/8 as a percentage was :b  

I'm really sorry if u don't understand what I'm trying to say, I'm really bad when it comes to write in English x,d

Answer:

5.25ft

Step-by-step explanation:

i got the question right so thats it

Answer:

5 1/4

Step-by-step explanation:

5 1/4 to decimal form is 5.25

Answer:

2009

Step-by-step explanation:

The question can be interpreted as:

\(f(x) = -1.330x^2 + 5.149x + 5.517\)

Required

Determine x when f(x) = 10.5

Substitute 10.5 for f(x) in \(f(x) = -1.330x^2 + 5.149x + 5.517\)

\(10.5 = -1.330x^2 + 5.149x + 5.517\)

Collect Like Terms

\(-1.330x^2 + 5.149x + 5.517-10.5=0\)

\(-1.330x^2 + 5.149x -4.983=0\)

Using quadratic formula

\(x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}\)

Where

\(a = -1.330\)

\(b = 5.149\)

\(c = -4.983\)

\(x = \frac{-5.149 \± \sqrt{5.149^2 - 4*-1.330*-4.983}}{2*-1.330}\)

\(x = \frac{-5.149 \± \sqrt{0.002641}}{-2.660}\)

\(x = \frac{-5.149 \± 0.0514}{-2.660}\)

Split:

\(x = \frac{-5.149 + 0.0514}{-2.660}\ or\ x = \frac{-5.149 - 0.0514}{-2.660}\)

\(x = \frac{-5.0976}{-2.660}\ or\ x = \frac{-5.2004}{-2.660}\)

\(x = 1.92\ or\ x = 1.96\)

Both values of x approximates to 2.

So:

\(x = 2\)

2 years after 2007 is 2009.

Hence, the funding is about $10.5 billion in 2009

Answer:

it's 61+61

Step-by-step explanation:

i hope this helps

Answer:

yes it is because the second triangle is the base and the other three triangles are the sides of the three dimensional shape

Answer:

1.5

Step-by-step explanation:

\(9 \div 6 = 1.5 \\ the \: length \: of \: each \: rope \: is \: 1.5\)

The length of each piece of rope equal to 2/3 feet OR 0.66 feet

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that Amelie has a rope that is 6 feet long.

She needs to divides her rope into 9 equal pieces.

i.e. 9 pieces of rope has length = 6 feet

1 piece of rope has length= 6/9 feet

                                         = 2/3 feet = 0.66 feet

Hence, the length of each piece of rope equal to 2/3 feet OR 0.66 feet.

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The dimensions of each half rectangular brick are, length 15 cm, and height 10 cm.

Let the original dimensions of the rectangular brick be length L, breadth B, and height H.

According to the problem statement, each dimension of the original brick is 5 cm larger than the desired dimensions of each half brick.

Therefore, the dimensions of each half brick are;

(L-5)/2, (B-5)/2, and (H-5)/2.

Since the two half bricks have identical dimensions, we have:

(L-5)/2 = (B-5)/2 = (H-5)/2

Simplifying this equation, we get:

L-5 = B-5 = H-5

Therefore, L = B = H + 5.

Now, the volume of the original brick is L x B x H, and the volume of each half brick is [(L-5)/2] x [(B-5)/2] x [(H-5)/2].

Since the two half bricks have the same dimensions, their volumes are equal. Thus, we have:

(L-5)/2 x (B-5)/2 x (H-5)/2 = (L x B x H)/2

Substituting L = B = H + 5, we get:

(H+5-5)/2 x (H+5-5)/2 x (H-5)/2 = (H x H x (H+5))/2

Simplifying this equation, we get:

(H+5)/2 x (H-5)/2 x H/2 = (H x H x (H+5))/2

Cancelling out the factor of 1/2, we get:

(H+5)(H-5)H = H x H x (H+5)

Simplifying this equation, we get:

H³ - 125H = H³ + 5H²

Subtracting H³ from both sides, we get:

-125H = 5H²

Dividing both sides by 5H, we get:

H = -25 or H = 0

Since H represents the height of the brick, it must be positive. Therefore, we have H = 0, which implies that the original brick has zero height. This is not a valid solution, so we reject it.

Therefore, the only valid solution is:

H = 25 cm

Substituting this value of H in the equation L = B = H + 5, we get:

L = B = 30 cm

Therefore, the dimensions of the original brick are:

Length = L + 5 = 35 cm

Breadth = B + 5 = 35 cm

Height = H + 5 = 30 cm

And the dimensions of each half brick are:

Length = Breadth = 15 cm

Height = 10 cm

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The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

\((2x+1)+29=90\\2x+1=61\\2x=60\\x=30\)

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The motion of the skier from point A to point B, then to point C, and then point D, indicates that the distances and displacement traveled are;

a) The distance from A to C is 280 meters

b) The distance from point A to point D is 360 meters

c) The displacement of the skier from point B to point C is 120 meters.

Displacement is the change in the position or location of the object.

The possible diagram of the skier in the question can be presented as follows;

A \({}\)                            C                                                   D                          B

t = 0 min      \({}\)         t = 2 min                                       t = 3 min            \({}\)t = 1 min

ʂ         \({}\)                     ʂ                                                     ʂ                           ʂ

-|-------|------|------|------|-----|------|-----|------|------|-------|-------|--------|-------|-------|-----

0           \({}\)   20           40         60          80            100    120    140           160

The above diagram indicates that we get;

a) The distance from point A (t = 0 min) to point C(t = 2 min) is can be found as follows;

The skier moves from point A to point B then from point B to point C, therefore,

The distance from point A to point B = 160 m - 0 m = 160 m

The distance from point B to point C = 160 m - 40 m = 120 m

The distance from point A to point C is therefore;

b) The distance from point A to point D = The distance from point A to point C + The distance from point C to point D as follows;

AD = AC + CD

CD = 120 m - 40 m = 80 m

Therefore;

AD = 280 m + 80 m = 360 m

c) The displacement of the skier from point B (t = 1 min) to C (t = 2 min) can be found as follows;

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The meaning of the statement, "if the function has no parameters, then the class C is definable" is that if there are no parameters given then the class c can be defined with an empty set but if there are no parameters, then the class cannot be defined.

The meaning of the above statement is that if no parameters are provided for this function, then the given class represented as c can be defined with an empty set that is enclosed in parameters.

Also, if the parameters are given then the class c is not defined.

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Answer: 3.42x10^11

Step-by-step explanation:

The number 0.0000000000342 is equivalent to 3.42 × 10^-11. Hence, option B is the correct answer.

This type of conversion is called scientific notation.

Firstly we have to place a decimal between the two non-zero numbers which is 3.42.

And then, count the number of decimals that were moved. That is 11.

And then, determine whether the decimal point is to be moved to the left or right to return to the original number. If the decimal is moved right then the exponent is negative. If the decimal is moved left then the exponent is positive.

Here, the exponent is moved right and the decimal will be negative.

In this case, it is written as 3.42 × 10^-11.

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Answer: See below

Step-by-step explanation:

To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:

Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.

Then, the addition problem becomes:

A B C

D E F

We know that the sum of each column must be the same, so:

C + F = 10 + B

B + E = 10 + A

We can rewrite these equations as:

C - B + F = 10

B - A + E = 10

Since we are given that the sum of the two numbers is the same, we know that:

C + F + D + E = 1112

We can substitute C and F in terms of A and B using the equations above:

C = 10 + B - F

F = 10 + C - B

Substituting these expressions into the equation for the sum, we get:

10 + B - F + C + D + E = 1112

Simplifying this equation, we get:

B - F + C + D + E = 1102

Now we can substitute in the expressions for C and F in terms of A and B:

B - (10 + B - F) + (10 + C - B) + D + E = 1102

Simplifying and canceling out terms, we get:

F - C - D - E = -92

We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.

Trying different values for A and D, we find that A = 2 and D = 3 works:

A B C

D E F

2 7 9

1 7 3

The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:

2 7 9

1 7 3

4 5 2

Answer:

9/5 (K-273.15) + 32=F

Step-by-step explanation:

K=5 /9(F−32)+273.15

Subtract 273.15 from each side

K-273.15=5/9(F−32)+273.15-273.15

K-273.15=5/9(F−32)

Multiply by 9/5 on each side

9/5 (K-273.15)= 9/5 *5/9(F−32)

9/5 (K-273.15)=(F−32)

Add 32 to each side

9/5 (K-273.15) + 32=F−32 +32

9/5 (K-273.15) + 32=F

Answer:

f=1/59k+27.370339

Step-by-step explanation:

k=59(f−32)+273.15

Step 1: Flip the equation.

59f−1614.85=k

Step 2: Add 1614.85 to both sides.

59f−1614.85+1614.85=k+1614.85

59f=k+1614.85

Step 3: Divide both sides by 59.

59f/59=k+1614.85/59

f=1/59k+27.370339