Find the value of Z

Answer:

x² - 3x - 18 = 0

Step-by-step explanation:

x/3 - 6/x = 1

x²/3 - 6 = x

x² - 18 = 3x

x² - 3x - 18 = 0

Answer:

2+2+2=6

4+52-32+2=26

finally add 26+6=32

Answer:

y = 3 and x = - 5

Step-by-step explanation:

(a)

[tex]\frac{5-7y}{2+4y}[/tex] = [tex]\frac{-8}{7}[/tex] ( cross- multiply )

- 8(2 + 4y) = 7(5 - 7y) ← distribute parenthesis on both sides

- 16 - 32y = 35 - 49y ( add 49y to both sides )

- 16 + 17y = 35 ( add 16 to both sides )

17y = 51 ( divide both sides by 17 )

y = 3

-----------------------------------------------

(b)

x + 7 - [tex]\frac{8x}{3}[/tex] = [tex]\frac{17}{6}[/tex] - [tex]\frac{5x}{2}[/tex]

Multiply through by 6 to clear the fractions

6x + 42 - 16x = 17 - 15x

42 - 10x = 17 - 15x ( add 15x to both sides )

42 + 5x = 17 ( subtract 42 from both sides )

5x = - 25 ( divide both sides by 5 )

x = - 5

Answer:

EF = 58 units

Step-by-step explanation:

Given:

DF = 9x - 39

DE = 47

EF = 3x + 10

Find:

EF

Computation:

DF = DE + EF

9x - 39 = 47 + 3x + 10

9x - 3x = 47 + 39 + 10

6x = 96

x = 16

EF = 3x + 10

EF = 3(16) + 10

EF = 58 units

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos2Θ = 1 - 2sin²Θ, then

1 - 2sin²([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )

= cos [2([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )]

= sos([tex]\frac{\pi }{2}[/tex] - Θ )

= cos[tex]\frac{\pi }{2}[/tex]cosΘ + sin

= 0 × cosΘ + 1 × sinΘ

= 0 + sinΘ

= sinΘ = right side

Answer:  see proof below

Step-by-step explanation:

Use the Difference Identity: sin (A + B) = sin A cos B - cos A sin B

Use the following Half-Angle Identities:  

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

Use the Pythagorean Identity: cos²A + sin²A = 1   -->   sin²A = 1 - cos²A

Use the Unit Circle to evaluate: [tex]\cos\dfrac{\pi}{4}=\sin\dfrac{\pi}{4}=\dfrac{1}{\sqrt2}[/tex]

Proof LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad 1-2\sin^2\bigg(\dfrac{\pi}{4}-\dfrac{\theta}{2}\bigg)\\\\\text{Difference Identity:}\quad 1-2\bigg(\sin\dfrac{\pi}{4}\cdot \cos \dfrac{\theta}{2}-\cos \dfrac{\pi}{4}\cdot \sin\dfrac{\theta}{2}\bigg)^2\\\\\text{Unit Circle:}\qquad \qquad 1-2\bigg(\dfrac{1}{\sqrt2}\cos \dfrac{\theta}{2}-\dfrac{1}{\sqrt2}\sin \dfrac{\theta}{2}\bigg)^2\\\\\\\text{Half-Angle Identity:}\quad 1-2\bigg(\dfrac{\sqrt{1+\cos A}}{2}-\dfrac{\sqrt{1-\cos A}}{2}\bigg)^2[/tex]

[tex]\text{Expand Binomial:}\quad 1-2\bigg(\dfrac{1+\cos A}{4}-\dfrac{2\sqrt{1-\cos^2 A}}{4}+\dfrac{1-\cos A}{4}\bigg)\\\\\text{Simplify:}\qquad \qquad \quad 1-2\bigg(\dfrac{2-2\sqrt{1-\cos^2 A}}{4}\bigg)\\\\\text{Pythagorean Identity:}\quad 1-\dfrac{1}{2}\bigg(2-2\sqrt{\sin^2 A}\bigg)\\\\\text{Simplify:}\qquad \qquad \qquad 1-\dfrac{1}{2}(2-2\sin A)\\\\\text{Distribute:}\qquad \qquad \qquad 1-(1-\sin A)\\\\.\qquad \qquad \qquad \qquad \quad =1-1+\sin A\\\\\text{Simplify:}\qquad \qquad \qquad \sin A[/tex]

RHS = LHS:   sin A = sin A  [tex]\checkmark[/tex]

Answer:

105 ways

Step-by-step explanation:

Because the order of selection does not matter, we know that we will be using a combination instead of a permutation.

₁₅C₂ = 15! / (2! * 13!)

= 15 * 14 * ... * 2 * 1 / 2 * 1 * 13 * 12 * ... * 2 * 1

= 15 * 14 / 2 * 1 (The 13! cancels out)

= 105

Answer:

105 ways, because the order of selection does not matter, we know that we will be using a combination instead of a permutation.

1) multicropping

2)soilconservation

3)High carbon farming

4) clay particle

Hope it helps

Answer:

B. ∠ABC

Step-by-step explanation:

When naming an angle using three points, the points should be given in order, with the vertex of the angle in the middle. B is the only option that has the letters in the right order.

∠CBA would also be a valid name for the angle, but that's not one of the options.

The diagram below shows what the problem is describing.

Rays BA and BC will form an angle named B. <ABC.

Therefore, the letter of the vertex will be in the middle of the three letters used in naming the angle.

The name of the angle formed by BA and BC is B. <ABC.

Learn more about naming of angles here:

https://brainly.com/question/19350659

Answer:

7 1/5

Step-by-step explanation:

You said that she poured 1 1/5 pouches in each cup. There are 5 cups, so multiply 1 1/5 by 5.

(e.g)

1 1/5+1 1/5= 3 because 1+1=2 & 1/2+1/2=1 so you add them and get 3

Do that twice and you get 6

then you have 1 one more cup left so add 1+6=7 then add the half 7+1 1/2=7 1/2

Your Welcome

Answer:

9

Step-by-step explanation:

21 x 3/7

= 9 ( goldfish )

Answer:

9 goldfishes

Step-by-step explanation:

Total fish = 21

Number of goldfish = 3/7 of 21

                                [tex]= \frac{3}{7}*21\\\\= 3 * 3\\\\= 9[/tex]

la primera sale 1/3

la segunda 1/4

la tercera tambien 1/4

en la cuarta se puede hacer un grafico o un planteo de ecuacionas de igual manera te va a salir 1/5

y en la quinta tambien se puede hacer un grafico o un planteo de ecuacionas de igual manera te va a salir 1/8

Answer:

X= 7

Step-by-step explanation:

Answer:

18 values for n are possible.

Step-by-step explanation:

Given the quadratic polynomial:

[tex]$x^2 - mx + n$[/tex]

such that:

Roots are positive prime integers and

[tex]$m < 20$[/tex]

To find:

How many possible values of [tex]n[/tex] are there ?

Solution:

First of all, let us have a look at the sum and product of a quadratic equation.

If the quadratic equation is:

[tex]Ax^{2} +Bx+C[/tex]

and the roots are: [tex]\alpha[/tex] and [tex]\beta[/tex]

Then sum of roots, [tex]\alpha+\beta = -\frac{B}{A}[/tex]

Product of roots, [tex]\alpha \beta = \frac{C}{A}[/tex]

Comparing the given equation with standard equation, we get:

A = 1, B = -m and C = n

Sum of roots,  [tex]\alpha+\beta = -\frac{-m}{1} = m[/tex]

Product of roots, [tex]\alpha \beta = \frac{n}{1} = n[/tex]

We are given that [tex]m<20[/tex]  

[tex]\alpha[/tex] and [tex]\beta[/tex] are positive prime integers such that their sum is less than 20.

Let us have a look at some of the positive prime integers:

2, 3, 5, 7, 11, 13, 17, 23, 29, .....

Now, we have to choose two such prime integers from above list such that their sum is less than 20 and the roots can be repetitive as well.

So, possible combinations and possible value of [tex]n (= \alpha \times \beta)[/tex] are:

[tex]1.\ 2, 2\Rightarrow n = 2\times 2 = 4\\2.\ 2, 3 \Rightarrow n = 6\\3.\ 2, 5 \Rightarrow n = 10\\4.\ 2, 7\Rightarrow n = 14\\5.\ 2, 11 \Rightarrow n = 22\\6.\ 2, 13 \Rightarrow n = 26\\7.\ 2, 17 \Rightarrow n = 34\\8.\ 3, 3\Rightarrow n = 3\times 3 = 9\\9.\ 3, 5 \Rightarrow n = 15\\10.\ 3, 7 \Rightarrow n = 21\\[/tex]

[tex]11.\ 3, 11\Rightarrow n = 33\\12.\ 3, 13 \Rightarrow n = 39\\13.\ 5, 5 \Rightarrow n = 25\\14.\ 5, 7 \Rightarrow n = 35\\15.\ 5, 11 \Rightarrow n = 55\\16.\ 5, 13 \Rightarrow n = 65\\17.\ 7, 7 \Rightarrow n = 49\\18.\ 7, 11 \Rightarrow n = 77[/tex]

So,as shown above 18 values for n are possible.

This is the idea that any segment is the same length as itself (in this case, segment VO is the same length as segment VO). Think of a mirror reflecting an identical image of something in front of the mirror.

It might seem redundant to say VO = VO, but it's useful when you want to break up a figure into smaller more manageable pieces to do the proof.

The measure of angle MRS exists equivalent to the measure of the angle MRO or m∠MRS = m∠MRO.

It exists described as the four-sided polygon in geometry containing four edges and four corners.

∠MRS ≅ ∠MRO (given)

From the given figure, we get

∠MRS + ∠MRO = ∠SRO

∠MRS + ∠MRO = 180 (as SRO exists a straight line segment)

Given: ∠MRS exists congruent to ∠MRO

2∠MRS = 180 degree

∠MRS = 90 degree

∠MRO = 180 - 90 = 90 degree

m∠MRS = m∠MRO

Therefore, the measure of angle MRS exists equivalent to the measure of the angle MRO or m∠MRS = m∠MRO.

To learn more about quadrilateral

https://brainly.com/question/27891143

#SPJ2

Answer:

27%

Step-by-step explanation:

27/100

Percent means out of 100

27%

Answer:

27 percent

Step-by-step explanation:

:)

Answer:

5 buses

Step-by-step explanation:

Total number of 6th graders going for the field trip = 184

Step 1

Divide the total number of students by 4

184/4 = 46

We have 46 groups of six graders.

Step 2

There needs to be one chaperone for every four students.

We have 46 groups of six graders

This means there is need for 1 chaperone per group

Hence, we have 46 chaperones

Step 3

Find total number of people going for the field trip

184 students + 46 chaperones

= 230 people

Step 4

If a bus can hold 50 people, how many buses will they need for the trip?

50 people = 1 bus

230 people = ??y

50 × y = 230

y = 230/50

y = 4.6 buses

Hence, 4.6 buses would be needed but since we can't have 0.6(part) of a bus figuratively, as buses come in whole numbers, we approximate to the nearest whole number

= 4.6 ≈ 5

Therefore, they would be needing 5 buses for the trip.

5 buses

Step-by-step explanation:

i got 10 out of 10

Answer:

see explanation

Step-by-step explanation:

Using the double angle identity for cosine

cos2x = 2cos²x - 1

Given

cos( [tex]\frac{0}{2}[/tex] ) = [tex]\frac{1}{2}[/tex]( p + [tex]\frac{1}{p}[/tex] ) , then

cosΘ = 2[ [tex]\frac{1}{2}[/tex](p + [tex]\frac{1}{p}[/tex] ) ]² - 1

         = 2 [ [tex]\frac{1}{4}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) ] - 1  ← distribute by 2

         = [tex]\frac{1}{2}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) - 1 ← distribute by [tex]\frac{1}{2}[/tex]

         = [tex]\frac{1}{2}[/tex] p² + 1 + [tex]\frac{1}{2p^2}[/tex] - 1

        = [tex]\frac{1}{2}[/tex] p² + [tex]\frac{1}{2p^2}[/tex] ← factor out [tex]\frac{1}{2}[/tex] from each term

        = [tex]\frac{1}{2}[/tex] ( p² + [tex]\frac{1}{p^{2} }[/tex] ) ← as required

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]cos(\theta)=2cos^2(\dfrac{\theta}{2})-1\\\\=2\left(\dfrac{p+\dfrac{1}{p}}{2}\right)^2-1\\\\=\dfrac{p^2+\dfrac{1}{p^2}+2}{2}-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})+1-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})[/tex]

Thank you

Answer:

1.) The slope of an equation expressed in the form of y= mx+b is m.

==========================================

Explanation:

The two smaller circles have a height of h, so one circle has a height of h/2 = 0.5h

The radius of each smaller circle is (0.5h)/2 = 0.25h

Draw an xy axis. Place the bottom left corner of the rectangle at the origin (0,0)

The center of the lower smaller circle is at location (0.25h, 0.25h). Call this point A.

Let B be the center of the larger circle. It has coordinates (x,y). We don't know x, but we know that y = 0.5h since the center must be at the halfway point in terms of the height of this rectangle. So the larger circle has a radius of 0.5h

Draw a line segment connecting A and B. The length of this segment, call it d, is d = 0.5h + 0.25h = 0.75h. Note how I added the two radius values mentioned earlier.

-------------

Summarizing everything so far, we have

A = (0.25h, 0.25h)

B = (x, 0.5h)

d = 0.75h

The distance formula is then used

d = distance from A to B

d = length of segment AB

d = sqrt( (x1-x2)^2 + (y1-y2)^2 )

0.75h = sqrt( (0.25h - x)^2 + (0.25h - 0.5h)^2 )

(0.75h)^2 = (0.25h - x)^2 + (-0.25h)^2

0.5625h^2 = 0.0625h^2 - 0.5hx + x^2 + 0.0625h^2

x^2 - 0.5hx + 0.4375h^2 = 0

From here you use the quadratic formula to get x = 0.9571067811865h approximately (the other solution is ignored as it's negative). See the attached image below if you're curious what the quadratic formula steps would look like.

This x value is the x coordinate of point B, which is the center of the larger circle. This spans the horizontal distance from the left edge of the rectangle to the center of the larger circle. The remaining horizontal distance is h/2 as it is the radius of the larger circle.

Therefore,

w = 0.9571067811865h + 0.5h

w = 1.4571067811865h

-------------

We have turned w into a roughly equivalent expression that has an h in it, allowing us to find the ratio of h to w

h/w = h/(1.4571067811865h) = 1/1.4571067811865 = 0.68629150101527

When rounding to two decimal places, we get roughly 0.69

49,400-20,000=29400

29400/24=1225 average miles per month

hi my litler friend

[tex](x-5)^2=3\\(x-5)=+-\sqrt{3} \\\\x-5=\sqrt{3} \\x=5+\sqrt{3} \\\\x-5=-\sqrt{3} \\x=5-\sqrt{3} \\\\\\S=(5-\sqrt{3},5+\sqrt{3})\\[/tex]

if in doubt, let me know. I really like to help.

Exact solutions: [tex]x = 5+\sqrt{3} \ \text{ or } \ x = 5-\sqrt{3}[/tex]

Approximate solutions: [tex]x \approx 6.732051 \ \text{ or } \ x \approx 3.267949[/tex]

==================================================

Work Shown:

Apply the square root to both sides, then add 5 to both sides

Don't forget about the plus/minus so you can get two solutions.

[tex](x-5)^2 = 3\\\\\sqrt{(x-5)^2} = \sqrt{3}\\\\|x-5| = \sqrt{3}\\\\x-5 = \pm\sqrt{3}\\\\x-5+5 = \pm\sqrt{3}+5\\\\x = 5\pm\sqrt{3}\\\\x = 5+\sqrt{3} \ \text{ or } \ x = 5-\sqrt{3}\\\\x \approx 6.732051 \ \text{ or } \ x \approx 3.267949\\\\[/tex]

Use a calculator for the last step.

Answer:

A graph that goes through (4, 0), (8, -3), (0, 3), and (-4, 6)

Step-by-step explanation:

Hello!

To find what this looks like it is easier to put it into slope-intercept form which is y = mx + b

To get our equation to look like that we have to get y by itself

3x + 4y = 12

Subtract 3x from both sides

4y = -3x + 12

Divide both sides by 4

[tex]y =- \frac{3}{4}x + 3[/tex]

We now know the y-intercept is (0, 3)

Now we follow the slope to give us more points

More points are (4, 0), (8, -3), and (-4, 6)

The answer would be a graph that goes through those points.

Hope this helps!

Answer:

-32

Step-by-step explanation:

Negative plus negative = Negative

Just add those 2 together,

(-)18 + (-) 14

Which is -32

(-) 32 = -32

Answer:

c. 40°

Step-by-step explanation:

The information given has been illustrated in the figure drawn in the attachment below.

m<BAD = 50° (angle bisector theorem)

m<ADB = 90° (perpendicular bisector)

m<ABD = 180 - (m<BAD + m<ADB) (sum of angles in a triangle)

m<ABD = 180° - (90° + 50°)

= 180° - 140°

= 40°

B = 40°

Answer:

Rate of return = 16%

Step-by-step explanation:

The computation of the rate of the return is shown below:

Data provided in the question

Current value of the investment = $20,880 = C

Originally cost = $18,000 = O

N = Net earnings = C - O

= $20,880 - $18,000

= $2,880

Based on the above information, the rate of return is

[tex]= \frac{N}{O} \\\\ = \frac{\$2,880}{\$18,000}[/tex]

= 16%

Hence, the rate of return is 16%

Answer:

24:12 = 24/12

24/12 = 2/1 or 2

Step-by-step explanation:

Answer:

x > 7/3   or x < -11/3

Step-by-step explanation:

|3x + 2| > 9

There are two solutions, one positive and one negative, remembering to flip the inequality when taking the negative solutions

3x+2 > 9         or         3x+2 < -9

Subtract 2

3x+2-2 >9-2   or      3x+2-2 < -9-2

3x >7                           3x>-11

Divide by 3

3x/3 > 7/3                    3x/3 < -11/3

x > 7/3   or x < -11/3

Answer:

To make a true equation, check your math to make sure that the values on each side of the equals sign are the same. Ensure that the numerical values on both sides of the "=" sign are the same to make a true equation. For example, 9 = 9 is a true equation. 5 + 4 = 9 is a true equation.You will be able to determine if an equation has one solution (which is when one variable equals one number), or if it has no solution (the two sides of the equation are not equal to each other) or infinite solutions (the two sides of the equation are identical).

Answer:

[tex]\huge \boxed{{y=2x+5}}[/tex]

Step-by-step explanation:

y = mx + b (slope-intercept form of a line)

m is slope

b is y-intercept

The y-intercept of the line is (0, 5) or 5.

y = mx + 5

The slope of the line can be found through rise over run.

(1, 7) and (2, 9) are two points on the line.

m = (y2-y1)/(x2-x1)

m = (9 - 7)/(2 - 1)

m = 2/1 = 2

The slope of the line is 2.

y = 2x + 5

Answer: Hi! The equation for this line would be c), y = 2x + 5.

Step-by-step explanation:

Slope - intercept form: y = mx + b, where m is the slope and b is the y - intercept.

First, we should determine the y - intercept. We can observe using the graph that the line intercepts the y - axis at point (0, 5), so we take the y - coordinate (5) and insert it into our equation.

y = mx + 5

This automatically rules out options d) and b).

Next, we find the slope. The formula for finding the slope is (y2 - y1) ÷ (x2 - x1).

We need to choose two coordinates before we can calculate the slope.

Let's use (1, 7) and (0,5).

We will not insert the values into or slope formula:

(7 - 5) ÷ (1 - 0)

When we solve this, the quotient is 2.

This is our slope, and we can insert the value into our slope equation - -

y = 2x + 5

This rules out option a). So, your answer is option c), y = 2x + 5.

Hope this helps!