Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
In this graph, the number of containers is plotted along the x-axis and the amount of water in the containers is along the y-axis.



The proportionality constant of the graph (y to x) is

Answer:

The equation of a parallel line is y = x

Step-by-step explanation:

Parallel lines have the same slope

hence the new lines slope is = 1

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

          b represents the y-intercept

where the format of a point is (x, y)

Given:

we need to find b, y = 1x + b

we can plug in the point (2, 2)

2 = 1(2) + b

2 = 2 + b

0 = b

Hence, the equation of the line through point

(2, 2) and parallel to y = x+4 is y = x

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The distance between B and C is 26.926 units.

The distance between coordinate P(x1 , y1) and coordinate Q(x2 , y2) is calculated using the distance formula: d = √[(x2 - x1)² + (y2 - y1)²]

The zip-line course distance from platform A to platform F are given

Coordinates of B = (-25, -20)

coordinates of C = (-15, 5)

Now, the distance between B and C is

= `√(5-(-20))² +((-15)-(-25))²

=√25² + 10²

= √725

= 26.926 units.

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Step-by-step explanation:

(4²-x²)³/²

or,(4+X) (4-X)

Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to

[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]

Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and

[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]

(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])

So, the integral we want transforms to

[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]

Expand the integrand using the identity

[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]

to write

[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]

Now integrate to get

[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]

Recall the double angle identity,

[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]

[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]

By the Pythagorean identity,

[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]

Finally, put the result back in terms of [tex]x[/tex].

[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]

The average rate of change for this function for the interval from x = 2

to x = 4 is 20

The function is given as:

x   y

0  18

2   32

3    50

4   72

The average rate of change at the interval from x = 2 to x = 4 is calculated using:

m = (f(4) - f(2))/(4 - 2)

Using the table values, we have:

m = (72 - 32)/(4 - 2)

Evaluate

m = 20

Hence, the average rate of change is 20

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Using it's concept, it is found that the probability that the button is either pink or blue is:

[tex]p = \frac{26}{29}[/tex]

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

In this problem, we have that:

There are six times as many pink buttons as yellow books, hence:

z = 6x.

Considering the ratio of yellow buttons to blue buttons, we have that:

[tex]\frac{x}{y} = \frac{3}{8}[/tex]

3y = 8x

[tex]y = \frac{8x}{3}[/tex]

The total number of buttons is given by:

[tex]T = x + \frac{8x}{3} + 6x[/tex]

[tex]T = \frac{29x}{3}[/tex]

The number of pink or blue is given by:

[tex]y + z = \frac{8x}{3} + 6x = \frac{26x}{3}[/tex]

Hence the probability is given by:

[tex]p = \frac{\frac{26x}{3}}{\frac{29x}{3}} = \frac{26}{29}[/tex]

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Answer:

Step-by-step explanation:

Write the number as [tex]abc[/tex] and use the divisibility rules for 10 and 3. From the rule for 10, we know that the last digit of [tex]abc+cba[/tex] is [tex]o[/tex], hence [tex]a+c=10[/tex]. Thus the options are [tex]a=1[/tex] & [tex]c=9[/tex], [tex]a=2[/tex], & [tex]c=8[/tex], etc.

From the rule for 3, namely that the digit sum must be divisible by 3, we find that [tex]2a+2b+2c=20+2b[/tex]  is divisible by [tex]3[/tex]. By hand it's easy to check that [tex]b=2,5,8[/tex] are the only options that work.

So there are 9 choices for [tex]a[/tex] and [tex]c[/tex] and [tex]3[/tex] for [tex]b[/tex] , giving 27 total.

Answer:

1/a+ 1/b = 1/2

Adding the fractions we get

b+a/ab=1/2

cross Multiplying the denominator we get,

b+a=ab/2

a= ab/2 -b

Answer:

a = 1/(1/2 + 1/b)

Step-by-step explanation:

1/a + 1/b = 1/2

1/a = 1/2 - 1/b

1 = a(1/2 - 1/b)

1/(1/2 + 1/b) = a

Answer:

1/4 or 0.25

Step-by-step explanation:

The total possibilities of any 7 digit number using 0-9 is :

9×10×10×10×10×10×10=9000000

To work out the total possibilities in this question :

We look at the conditions :

The first digit can only be 5 numbers :

1 , 3 , 5 , 7 , 9

Now we subtract 5 from 9 :

9-5 = 4

Since no repeats for 2 , 3 , 4, 5, 6:

9 , 8 , 7 , 6 , 5,  

5 possibilities for the last digit :

Total possibilities for this code :

4 × 9 × 8 × 7 × 6 × 5 × 5 = 302400

If it begins with 5 that is only 1 possibility for the first digit

1 × 9 × 8 × 7 × 6 × 5 × 5 = 75600

Now we make a fraction :

75600÷302400

Dividing top and bottom by 75600 gives you 1/4 or 0.25

Hope this helped and have a good day

Answer:

Step-by-step explanation:

Comment

The first digit and the last digit are both odd. That tells you that so far what you have is one of 5 digits for the first digit and and one of 4 for the last digit. 4 because you can't repeat the first digit.

5, , , , , ,4

2 digits are gone 8 remain.

5* 8 * 7* 6* 5* 4* 4 = 134400

Part 2

Only one number can go at the beginning, and that is a 5. Everything else remains the same.

1 * 8 * 7 * 6 *5 * 4 * 4 = 26880

P(picking a number beginning with a 5 is  25880 /13440) = 0.2

The difference of two squares expression is (d) 25a^2-36b^6

The difference of two squares is represented as:

x^2 - y^2

Where x and y are perfect square expressions.

From the list of options, we have:

25a^2-36b^6

The terms of the above expression are perfect squares

i.e.

25a^2 = (5a)^2

36b^6 = (6b^3)^2

Hence, the difference of two squares expression is (d) 25a^2-36b^6

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Answer:

Step-by-step explanation:

sin θ=1/4,tan θ>0

so θ lies in first quadrant.

cos θ=√(1-sin²θ)=√(1-(1/4)²)=√(1-1/16)=√(15/16)=√15/4

[tex]2cos^2 \frac{\theta}{2} =1+cos \theta[/tex]

[tex]2~cos^2\frac{\theta}{2} =1+\frac{\sqrt{15} }{4} =\frac{4+\sqrt{15}}{4} \\cos~\frac{\theta}{2} =\sqrt{\frac{4+\sqrt{15} }{4 \times 2} } \\cos\frac{\theta}{2} =\frac{\sqrt{8+2\sqrt{15}} }{4}[/tex]

Answer:

[tex]\huge\boxed{\sf x =5 \ \ \ OR \ \ \ x = 1}[/tex]

Step-by-step explanation:

[tex]x^2-6x+5=0[/tex]

[tex]x^2-5x-x+5=0\\\\Take \ common\\\\x(x-5)-1(x-5)=0\\\\Take \ (x-5) \ common\\\\(x-5)(x-1)=0[/tex]

Either,

x - 5 = 0         OR         x - 1 = 0

[tex]\rule[225]{225}{2}[/tex]

Answer:

64 degrees

Step-by-step explanation:

90-32=58

180-58-58=64

Answer:

x = 64°

Step-by-step explanation:

supplementary angles is two angles whose sum is 180° (straight line)

90 + 32 = 122°

To find angle A,

A + 122 = 180

subtract 122 from both sides,

A + 122 - 122 = 180 - 122

A = 58°

This is an isosceles triangle, two angles are equal in measure (A and B). These angles lie opposite to the equal sides.

A triangles angles add up to 180°

58° + 58° + x° = 180°

116° + x = 180°

116 - 116 + x = 180 - 116

x = 64°

The values of f(3.52)=26.61 and f(-8.77)=257.05

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the argument x.

The given function is f(x) = 3x²-3x =3x(x-1)

f(3.52)=3*(3.52)(3.52-1)

=26.61

f(-8.77)=3*(-8.77)(-8.77-1)

=257.05

Therefore, the values of f(3.52)=26.61 and f(-8.77)=257.05

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The maximum profit will be 956 birrs for both cows and sheep.

The amount of money earned by any seller on the cost price is called the profit.

Given that:-

From the given data we can see that the total number of animals cows and sheep is 16.

C + S = 16

To raise a cow need 2 Br

To raise Sheep need 5 Br

The number of sheep is 12 and cows 4.

So the amount required to raise sheep and cows is:-

Sheeps = 12 x 2 = 24 Br

Cows = 4 x 5 = 20 Br

Total = 44 Br

The selling price of cows and sheep are 100 and 50 Br.

Cows = 100 x 4 = 400Br

Sheeps = 50 x 12 = 600 Br

Total = 1000 Br

So the profit will be calculated as follows:-

P = 1000 - 44 = 956 Br

Therefore the maximum profit will be 956 birrs for both cows and sheep.

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Answer:

The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is 3. option (C)

Step-by-step explanation:

Echelon Form : it is used to find the rank of matrix by reducing rows into zeros then the number of non zero rows is the rank of the matrix

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\2&-2&-2&5&1\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

apply row operations:

R₂= R₂ - 2 R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

R₃= R₃ -  R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\-1&1&7&-7&1\end{array}\right][/tex]

R₄ = R₄ +R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&12&-9 &3\end{array}\right][/tex]

R₄ = R₄ +R₃

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&0&0 &0\end{array}\right][/tex]

we can clearly see that after performing row operations there are 3 non zero rows,

therefore the Rank of the given matrix is 3

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Answer:

a) Cat

b) 4 (unless there is a key that says otherwise)

c) 3 more people

Step-by-step explanation:

a) It has the least number of shapes (only 5)

b) Cat has 1 small square which stands for 1 person and 4 small squares put together make a big square so a big square is 4 people. Unless a key says that a small square is more or less 1, then it should be 4.

c) If one big square is 4 people, then there are 10 people for giraffes and 7 people for dogs. 10 - 7 = 3 more people.

Answer:

-3 is a zero of the function  False

-1 is a zero of the function  True

1 is a zero of the function   False

2 is a zero of the function  True

4 is a zero of the function   False

The solution will be x= -10

Simplifying the given expression

[tex]1.8(1.1x - 1.3) - 1.88 = - 24.02[/tex]

Step1: Convert decimal to fraction

[tex]1.8( \frac{11x}{10} - 1.3) - 1.88 = - 24.02[/tex]

[tex]1.8( \frac{11x}{10} - \frac{13}{10} ) - 1.88 = - 24.02[/tex]

[tex]\frac{18}{10} ( \frac{11x}{10} - \frac{13}{10} ) - 1.88 = - 24.02[/tex]

Step2: Make denominator common

[tex]\frac{18}{10} ( \frac{11x - 13}{10}) - 1.88 = - 24.02[/tex]

Step3: Simplifying the fraction

[tex]\frac{9}{5} ( \frac{11x - 13}{10}) - 1.88 = - 24.02[/tex]

Step4: Make denominator common

[tex] \frac{9(11x - 13)}{5 \times 10} - \frac{1.88 \times 50}{50} = - 24.02[/tex]

[tex] \frac{9(11x - 13)}{50} - \frac{94}{50} = - 24.02[/tex]

[tex] \frac{9(11x - 13 - 94)}{50} = - 24.02[/tex]

[tex] \frac{99x - 117 - 94}{50} = - 24.02[/tex]

Step5: Simplifying

[tex] \frac{99x - 211}{50} = - 24.02[/tex]

[tex] 99x - 211 = - 24.02 \times 50[/tex]

[tex] 99x - 211 = - 1201[/tex]

[tex] 99x = - 1201 + 211[/tex]

[tex] 99x = - 990[/tex]

[tex] x = \frac{ - 990}{99} [/tex]

[tex]x = - 10[/tex]

Hence, the solution x=-10

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Answer:

a. b = 2A/a

b. 30

Step-by-step explanation:

a. to solve for b:

[tex]A = 1/2 ab[/tex]

multiply both sides by 2

[tex]2A = ab[/tex]

divide both sides by a

[tex]2A/a=b[/tex]

so b = 2A/a

b. using the equation b = 2A/a

[tex]b = 2*18/(6/5)\\= 36/(6/5)\\= 30[/tex]

The match is shown in the picture for the function of a parabola and the graph of a parabola.

It is defined as the graph of a quadratic function that has something bowl-shaped.

As we know the standard form of the parabola is:

y = a(x - h)² + k

If a > 0 (parabola opens upwards)

If a < 0 (parabola opens downwards)

or

x = a(y - h)² + k

If a > 0 (parabola opens right side)

If a < 0 (parabola opens left side)

Here (h, k) is the vertex of the parabola and a is the leading term.

Thus, the match is shown in the picture for the function of a parabola and the graph of a parabola.

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Answer:

f(x) = -3x + 5

Step-by-step explanation:

The slope of the function is -3 as the outputs decrease by three for each iteration.

The constant is 5 and can be determined if you plug in 1 as an x value and solve for c in an equation like this: -3(1) + c = 2

Answer:

x=12

Step-by-step explanation:

Given that there is only one expression given in each triangle, if we only use the information in a single triangle, there is no way to set up an equation that we could solve to find the expression.  (For this situation, at best we could use the triangle sum theorem to say that the three angles in one triangle added to 180°, but since we don't know the other two angles, that's 3 unknowns with only 1 equation... that's not solvable)

The only way to solve this problem is to make a relationship of some sort between the two triangles.

Proving a relationship between triangles - option 1

You may have a theorem about the Third angles of two triangles... "Given two arbitrary triangles, [tex]\triangle ABC[/tex] and [tex]\triangle D E F[/tex], if [tex]\angle A \cong \angle D[/tex] and [tex]\angle B \cong \angle E[/tex],  then [tex]\angle C \cong \angle F[/tex] "

If you have this, then the third angles are congruent.

In a more general situation of a similar problem (one in which you don't know two of the angles to begin with), it might be easier to prove triangle congruence, or triangle similarity.

Other Relationships between triangles

There are two main relationships between triangles: similarity and congruence.

Most people learn about congruence first.

In the situation for this problem, the two triangles happen to be congruent (we'll prove it shortly), which implies that all corresponding angles between shapes are congruent (and all corresponding sides between shapes are congruent).

For the purpose of solving for things related to angles, proving that the two triangles are similar is enough to know that angles between triangles are congruent (sides wouldn't necessarily be equal, but would be proportional, and since we're not solving for anything related to side lengths, proving that the triangles are similar would be enough).

Proving a relationship between triangles - option 2 - congruence

Notice that the triangle on top has two angles with markings (a single mark, and a double mark), and one side with a marking (a single tick).  These three pieces are in a configuration of ASA (the side is between the two angles).

Looking at the bottom triangle, it also has angles and sides with corresponding markings, and they are also in an ASA configuration.

Thus, by ASA congruence, these triangles are congruent triangles.

Knowing the triangles are congruent (even though we only used 3 parts), the rest of the corresponding parts (including the third angles) are also congruent.

Proving a relationship between triangles - option 3 - Similarity

For similarity, the process is similar to proving congruence, however the theorems we have for proving similarity are different.

SSS, SAS, or AA similarity.

Since the triangles in our problem do have two angles that are congruent, by AA similarity, the triangles are "similar".

Knowing the triangles are similar (even though we only used 2 parts), the last set of corresponding angles are also congruent.

Building our equation

Since the third angle of each triangle is congruent, by definition of congruent angles, the measures of each of those two angles are equal, and so we can build an equation knowing that the two expressions are equal to each other:

[tex]3x-7=2x+5[/tex]

Solving for x

From there, we need some algebraic properties equality to solve for x.

Subtract 2x from both sides...

[tex](3x-7)-2x=(2x+5)-2x\\x-7=5[/tex]

add 7 to both sides...

[tex](x-7)+7=(5)+7\\x=12[/tex]

Extension

Knowing the value for x, we could solve for the measure of the angles, if that had been requested.  Simply substitute 12 back into the expressions for the angle measure (the results should be the same for both angles, since they were congruent angles)

[tex]3(12)-7\\36-7\\29[/tex]         [tex]2(12)+5\\24+5\\29[/tex]

So, if we had been asked, the measure of the angle is 29°

The following statements accurately compare the three functions on the graph: option A and C.

In Geometry, the following statements are true about the graph of a function:

By critically observing the graph of a function, we can logically deduce that the following statements accurately compare the three functions on the graph:

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Answer:

I iitiriririrrifjjrjr idiocy jdkthink 179.86

The ship is 88.8 miles far from the port at 4 pm.

Given,

The displacement from 1 to 3 in the afternoon.

D1 = 30 miles/hr × 2 hr

     = 60 miles to the north

The displacement from 3 till 4 in the afternoon.The ship changes its course 20 degrees eastward at 3 o'clock.

Therefore, D2 = 30 miles/hr × 1 hr

                       = 30 miles to the 20° north eastward

By combining two vectors, the resulting displacement:

D = √((D1 ₊ D2 × cos(20°))² ₊ (D2 × sin(20°))²

D = √((60 ₊ 30 × cos (20°))² ₊ (30 × sin(20°))²

D = 88.8 miles

Hence the ship is 88.8 miles far away from the port at 4 pm.

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The value of the probability P(x > 2) is 0.8369

The given parameters are:

n = 5

p =0.7

The probability is calculated as:

[tex]P(x) = ^nC_x *p^x * (1 - p)^x[/tex]

Using the complement rule, we have:

P(x > 2) = 1 - P(0) - P(1) - P(2)

Where:

[tex]P(0) = ^5C_0 *0.7^0 * (1 - 0.7)^5[/tex]

P(0) = 1 *1 * (1 - 0.7)^5 = 0.00243

[tex]P(1) = ^5C_1 *0.7^1 * (1 - 0.7)^4[/tex]

P(1) = 5 *0.7^1 * (1 - 0.7)^4 = 0.02835

[tex]P(2) = ^5C_2 *0.7^2 * (1 - 0.7)^3[/tex]

P(2) = 10 *0.7^2 * (1 - 0.7)^3 = 0.1323

Recall that:

P(x > 2) = 1 - P(0) - P(1) - P(2)

So, we have:

P(x > 2) = 1 - 0.00243 - 0.02835 - 0.1323

Evaluate

P(x > 2) = 0.83692

Approximate

P(x > 2) = 0.8369

Hence, the value of the probability P(x > 2) is 0.8369

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