Twice a number plus three times a second number is twenty two. Three times the first number plus four times the second is thirty one. Find the numbers

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answer:

yeyyyaya

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D because they are congruent try measuring it.

Answer:

[tex]\boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

The triangles are congruent.

The angles that are corresponding on both triangles must be congruent.

Angle Q in triangle PQR must be congruent to angle T in triangle STU.

Answer:

The probability of the event BC

= the probability of B * C = 48.6667% * 70%

= 34.0667%

Step-by-step explanation:

Probability of A, students with children = 44/150 = 29.3333%

Probability of B, students enrolled in at least 12 credits = 73/150 = 48.6667%

Probability of C, students working at least 10 hours per week = 105/150 = 70%

Therefore, the Probability of BC, students enrolled in 12 credits and working 10 hours per week

= 48.6667% * 70%

= 34.0667%

Answer:  m = -5

Step-by-step explanation:

[tex]\dfrac{m+3}{m^2+4m+3}-\dfrac{3}{m^2+6m+9}=\dfrac{m-3}{m^2+4m+3}\\\\\\\dfrac{m+3}{(m+3)(m+1)}-\dfrac{3}{(m+3)(m+3)}=\dfrac{m-3}{(m+3)(m+1)}\quad \rightarrow m\neq-3, m\neq-1[/tex]

Multiply by the LCD (m+3)(m+3)(m+1) to eliminate the denominator. The result is:

(m + 3)(m + 3) - 3(m + 1) = (m - 3)(m - 3)

Multiply binomials, add like terms, and solve for m:

(m² + 6m + 9) - (3m + 3) = m² - 9

    m² + 6m + 9 - 3m - 3 = m² - 9

                  m² + 3m + 6 = m² - 9

                           3m + 6 =  -9

                                  3m = -15

                                    m = -5  

Answer:

[2.5 ,4]

Step-by-step explanation:

The graph in this interval has a vertex while opening up wich means it's a minimum

Answer:

The center is (1,4)

Step-by-step explanation:

The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.

Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:

[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]

So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:

[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]

Answer:

14 Quarters and 28 dimes

Step-by-step explanation: 14 quarters $3.50

28 dimes is $2.80 total is $6.30

Answer:

b. (10,10,0)

Step-by-step explanation:

r+v can be evaluated if the vectors/matrices have the same dimensions.

These do. They are both 1 by 3 vectors.

Just add first to first in each.

Just add second to second in each.

Just add third to third in each.

Example:

(5,-5,6)+(1,2,3)

=(5+1,-5+2,6+3)

=(6,-3,9)

Done!

In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).

r+v

=(7,3,9)+(3,7,-9)

=(7+3,3+7,9+-9)

=(10,10,0)

Done!

Answer:

x^2 + 2x - 20 = 0

x^2 + 2x - 20 + 20 = 0 + 20  ( add 20 to both sides)

x^2 + 2x = 20

x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)

( x + 1 )^2 = 21

x = [tex]\sqrt{21}-1[/tex]

x = [tex]-\sqrt{21}-1[/tex]

Answer:

A)  x = –1 ± square root 21

is the answer:)

Answer:

[tex] x = 2 [/tex]

Step-by-step explanation:

Given a right-angled triangle as shown above,

Included angle = 60°

Opposite side length = 3

Adjacent side length = x

To find x, we would use the following trigonometric ratio as shown below:

[tex] tan(60) = \frac{3}{x} [/tex]

multiply both sides by x

[tex] x*tan(60) = \frac{3}{x}*x [/tex]

[tex] x*tan(60) = 3 [/tex]

Divide both sides by tan(60)

[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]

[tex] x = \frac{3}{tan(60} [/tex]

[tex] x = 1.73 [/tex]

[tex] x = 2 [/tex] (approximated to whole number)

Answer:

Step-by-step explanation:

Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B

Answer: 32

Step-by-step explanation:

Answer:

1312 feet

Step-by-step explanation:

41 ft=1 sec

how about 32 sec

41 x 32=1312/1=1312

Answer:

2√137

Step-by-step explanation:

To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:

22² + 8² = c²

484 + 64 = c²

548 = c²

c = ± √548 = ± 2√137

c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.

Answer:

x=3.9 or 39/10 and   y=3.13333 or 47/15

Step-by-step explanation:

Since both expressions (6x-3y) and (3-2x+6y) are equal to 14, separate the equations:

       6x-3y=14 and 3-2x+6y=14

Simplify the equations

       6x-3y=14 and -2x+6y=11

Now, line the equations up and pick a variable (either x or y) to eliminate

        6x-3y=14

        -2x+6y=11

In this case, let's eliminate y first. To do so make the y values in both equations the same but with opposite signs. Make both be 6y but one is +6y and the other -6y

Multiply (6x-3y=14) by 2 to get:

      12x-6y=28

Line the equations up and add or subtract the terms accordingly

      12x-6y=28

      -2x+6y=11

This becomes:

     10x+0y=39

Isolate for x

   x= 39/10 or x= 3.9

Now substitute the x value into either of the original equations

    6x-3y=14

    6(3.9)- 3y=14

Isolate for y

   23.4-14=3y

   3y= 9.4

  y= 3.1333 (repeating)  or y= 47/15

Answer: x = 39/10, y = 94/30

Step-by-step explanation:

6x - 3y = 3 - 2x + 6y,

Now solving this becomes

6x + 2x -3y - 6y = 3

8x - 9y = 3 ------------------- 1

3 - 2x + 6y. = 14

-2x + 6y = 14 - 3

-2x. + 6y = 11

Now multiply both side by -1

2x. - 6y = -11 ----------------- 2

Solve equations 1 & 2 together

8x - 9y. = 3

2x - 6y = -11

Using elimination method

Multiply equation 1 through by 2 ,and equation 2 be multiplied by 8

16x - 18y = 6

-16x - 48y = -88 ------------------------- n, now subtract

30y = 94

Therefore. y = 94/30.

Now substitute for y in equation 2

2x - 6y = -11

2x - 6(94/30) = -11

2x - 94/5 = -11

Now multiply through by 5

10x - 94 = -55

10x = -55 + 94

10x = 39

x = 39/10

Answer:

Step-by-step explanation:

Hello,

We can write three equations thanks to Pythagoras

   [tex]AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\[/tex]

So it comes

[tex]x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\[/tex]

Hope this helps

Answer:

x = [tex]\sqrt{21}[/tex]

Step-by-step explanation:

Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{CD}{BD}[/tex] , substitute values

[tex]\frac{x}{7}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )

x² = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex]

Answer:

Nx = λx

Nx = 0, with x≠0

if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions

Step-by-step explanation:

given that

let N be a square matrix in order of n

note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N

let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ

Nx = λx (x≠0)

N²x =  λNx = λ²x

∴[tex]N^{k}x[/tex] =  (λ^k)x

[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector

where x = 0, (λ^k) = 0

λ = 0

therefore, Nx = λx

Nx = 0, with x≠0

note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution

Answer:

Loss = $80000

Step-by-step explanation:

To determine if it's a profit or loss is simple.

He predicted the sugar cane stock to fall so he sold , but few days later the stock grew and went bullish.

He sold at$ 40 for 2000 shares

=$ 80000

But the stock went up to $80 per share that is gaining extra $40

So it was actually a loss.

The loss is =$40 * 2000

The loss = $80000

Answer:

x = -3 and x = 9.

Step-by-step explanation:

2|x - 3| - 5 = 7

2|x - 3| = 12

|x - 3| = 6

x - 3 = 6

x = 9

-(x - 3) = 6

-x + 3 = 6

-x = 3

x = -3

Hope this helps!

Answer:

x=9            x=-3

Step-by-step explanation:

2|x-3|-5=7

Add 5 to each side

2|x-3|-5+5=7+5

2|x-3|=12

Divide by 2

2/2|x-3|=12/2

|x-3|=6

There are two solutions to an absolute value equation, one positive and one negative

x-3 =6           x-3 = -6

Add 3 to each side

x-3+3 = 6+3      x-3+3 = -6+3

x=9                     x = -3

Answer:

Step-by-step explanation:

g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:

8 unit right

6 units up

a parent absolute value function has a vertex at (0,0)

if the function is moved so is the vertex:

(0+8,0+6)

(8,6)

So, the vertex of this function is at (8,6)

Answer:  vertex = (8, 6)

Step-by-step explanation:

The Vertex form of an absolute value function is: y = a|x - h| + k   where

g(x) = |x - 8| + 6 is already in vertex form where

h = 8 and k = 6

so the vertex (h, k) = (8, 6)

Answer:

Q(1,1), N(3,2) A(2,5)

Step-by-step explanation:

Explanation:

The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.

A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.

Answer: B.) Circumcenter

Step-by-step explanation:

Answer:

105.6

Step-by-step explanation:

If the mean is 8.8, than that means that in total the sum must be (8.8 * 12) which equals 105.6.

This is because the sum of all the numbers in a list divided by the amount of numbers in a list equals the mean.

Answer:

Option (3)

Step-by-step explanation:

[tex](x-i\sqrt{3})[/tex] is a factor of a polynomial given in the options, that means a polynomial having factor as [tex](x-i\sqrt{3})[/tex] will be 0 for the value of x = [tex]i\sqrt{3}[/tex].

Option (1),

3x⁴ + 26x² - 9

= [tex]3(i\sqrt{3})^{4}+26(i\sqrt{3})^2-9[/tex] [For x = [tex]i\sqrt{3}[/tex]]

= 3(9i⁴) + 26(3i²) - 9

= 27 - 78 - 9 [Since i² = -1]

= -60

Option (2),

4x⁴- 11x² + 3

= [tex]4(i\sqrt{3})^4-11(i\sqrt{3})^2+3[/tex]

= 4(9i⁴) - 33i² + 3

= 36 + 33 + 3

= 72

Option (3),

4x⁴ + 11x² - 3

= [tex]4(i\sqrt{3})^4+11(i\sqrt{3})^2-3[/tex]

=  4(9i⁴) + 33i² - 3

= 36 - 33 - 3

= 0

Option (4),

[tex]3x^{4}-26x^{2}-9[/tex]

= [tex]3(i\sqrt{3})^4-26(i\sqrt{3})^{2}-9[/tex]

= 3(9i⁴) - 26(3i²) - 9

= 27 + 78 - 9

= 96

Therefore, [tex](x-i\sqrt{3})[/tex] is a factor of option (3).

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.

Power and chain rule (where the power rule kicks in because [tex]\sqrt x=x^{1/2}[/tex]):

[tex]\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'[/tex]

Simplify the leading term as

[tex]\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}[/tex]

Quotient rule:

[tex]\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}[/tex]

Chain rule:

[tex](\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)[/tex]

[tex](1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)[/tex]

Put everything together and simplify:

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

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

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

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

[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}[/tex]

[tex]=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}[/tex]

[tex]=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}[/tex]

Answer:

option: D

51200

Step-by-step explanation:

64000 x 80/100 = 51200

Answer:

Hi there!!!

your required answer is option D.

explanation see in picture.

I hope it will help you...

Answer:

43\ 12 , 35/ 6

Step-by-step explanation:

43\ 12 , 35/ 6

Answer:  B: (3, -7)

Step-by-step explanation:

4x + 4y = -9

         y = 2x - 13

Use Substitution:

4x + 4(2x - 13) = -9

4x + 8x - 52 = -9

       12x - 52 = -9

               12x = 43

                   [tex]x=\dfrac{43}{12}[/tex]

None of the options provided are valid so either there is a typo on your worksheet or you typed in one of the equations wrong.

Plan B: Input the choices into the equation to see which one makes a true statement.

               4x + 4y = -9

A) (x, y) = (-3, -7)

               4(-3) + 4(-7) = -9

                -12   +   -28 = -9

                             -40 ≠ -9

B) (x, y) = (3, -7)

               4(3) + 4(-7) = -9

                12   +   -28 = -9

                             -16 ≠ -9

C) (x, y) = (3, 7)

               4(3) + 4(7) = -9

                12   +   28 = -9

                            40 ≠ -9

D) (x, y) = (-3, 7)

               4(-3) + 4(7) = -9

                -12   +   28 = -9

                              16 ≠ -9

Obviously there is something wrong with the first equation because none of the options provide a true statement.

               y = 2x - 13

A) (x, y) = (-3, -7)

               -7 = 2(-3) - 13

               -7  = -6    -13

                -7 ≠ -19

B) (x, y) = (3, -7)

               -7 = 2(3) - 13

               -7  = 6    -13

                -7 = -7                   this works!!!

C) (x, y) = (3, 7)

               7 = 2(3) - 13

               7  = 6    -13

                7 ≠ -7

D) (x, y) = (-3, 7)

               7 = 2(-3) - 13

               7  = -6    -13

                7 ≠ -19

Option B is the only one that provides a true statement so this must be the answer.

Answer:

Correlation Coefficient

Step-by-step explanation: