Write the ratios for sin X, cos X,and tan X

Answer:

Step-by-step explanation:

[tex]d(z_1,\ z_2)=|z_1-z_2|\\\\z=a+bi\to|z|=\sqrt{a^2+b^2}\\------------------\\\\\text{We have:}\\\\z_1=2-3i,\ z_2=9+21i\\\\\text{substitute:}\\\\|(2-3i)-(9+21i)|=|2-3i-9-21i|\\\\=|(2-9)+(-3i-21i)|=|-7-24i|\\\\=\sqrt{(-7)^2+(-24)^2}=\sqrt{49+576}=\sqrt{625}=25[/tex]

Answer:

25.

Step-by-step explanation:

For two complex numbers z=([tex]x_{1},y_{1}[/tex]) and w=([tex]x_{2},y_{2}[/tex]) we have that the distance between z and w is equal to

|z-w| =  [tex]\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}[/tex]

So, in this case we have that [tex](x_{1},y_{1})=(2,-3)[/tex] and  [tex](x_{2},y_{2})=(9,21)[/tex], then the distance

|z-w| =  [tex]\sqrt{(2-9)^{2}+(-3-21)^{2}}[/tex]

= [tex]\sqrt{(-7)^{2}+(-24)^{2}}[/tex]

=  [tex]\sqrt{49+576}[/tex]

=  [tex]\sqrt{625}[/tex]

= 25.

Answer:

3,500 no votes

Step-by-step explanation:

There were 7 yes votes to every 4 no votes.  There were a total of 6,125 yes votes, so set up a proportion to find the number of no votes

Let x represent the number of no votes

7 is to 4 as 6,125 is to x

We get

7/4 = 6,125/x

Now solve for x

First cross multiply

7x = 24,500

Divide both sides by 7 to isolate x..

x = 3,500 no votes

Answer:

B.) 27ft

Step-by-step explanation:

The labeled points given: (5,18) and (1.5, 7.5)

Slope = (18 - 7.5)/(5-1.5) = 10.5 / 3.5 = 3

A linear model:

y - 18 = 3(x - 5)

y - 18 = 3x - 15

y = 3x + 3

If x = 8 seconds then the distance in feet (y) would be: (plug in x = 8 into the equation y = 3x + 3)

y = 3(8) + 3

y = 24 + 3

y = 27 ft

Answer:

B.) 27ft

A person would be at a distance of 27 feet, 8 seconds after the experiment begins.

A scatter plot diagram is a graph in which the coordinates of a point are marked and the regression or correlation between these points is observed.

The labeled points that are given are (5,18) and (1.5, 7.5)

m = Slope of the given scatter plot = (18 - 7.5)/(5 - 1.5)

= 10.5 / 3.5

= 3

The linear model of the scatter plot can be found by substituting the values of x and y using the labelled coordinates.

y - y_1 = m( x - x_1 )

y - 7.5 = 3(x - 1.5)

y - 7.5 = 3x - 4.5

y = 3x - 4.5 + 7.5

y = 3x - 3

The value of x is given as 8. Substitute x in the equation above:

y = 3(8) + 3

y = 24 + 3

y = 27 feet

Therefore, a person would be at a distance of 27 feet, 8 seconds after the experiment begins. The correct answer is option B.

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Answer:

parallel

Step-by-step explanation:

Solve both equations for y to make it easier to compare them.

2x - 5y = 0 ↔ 5y = 2x, or y = (5/2)x.

y = (5/2)x - 3

Since the slopes are the same, the two lines are parallel.

Answer:

6 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

chance of rolling a 6 once on a die: 1/6

1/6 * 1/6 * 1/6 * 1/6 = 1/(36^2)= 1/1296

Answer:

4/3 or 1.33333333333333333333.....

Step-by-step explanation:

Answer:

[tex]\large\boxed{C.\ \left(\dfrac{14}{3},\ 0\right)}[/tex]

Step-by-step explanation:

[tex]\text{The x-intercept is for y = 0.}\\\\\text{Put y= 0 to the equation}\ 3x + 3y = 14:\\\\3x + 3(0) = 14\\\\3x + 0 = 14\\\\3x = 14\qquad\text{divide both sides by 3}\\\\x =\dfrac{14}{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

Option A is incorrect.

Step-by-step explanation:

Length of the given parts is l and width is w meters.

It is given in the question that Sanjay needs 90 meters of fence to go around the rectangular park.

It means perimeter of the park is 90 meters.

Since perimeter of a rectangle = 2(length + width)

                                                  =  2(L + w)

It is given that length of garden is three times of width so l = 300

therefore, equation will be

Perimeter = 2[3w + w]

           90 =  2[3w + w]

Option A ⇒ w + 3w = 90   ⇒ incorrect

Option B ⇒ w + 3w + w + 3w = 90

                   2(w + 3w) = 90  ⇒ Correct option

Option C ⇒ 2w + 2 (3w) = 90

                  2 [w + 3w] = 90   ⇒ Correct option

Option D ⇒ 2(3w + w) = 90  ⇒ Correct option

therefore Option A is incorrect option.

Answer:

w+3w+w+3w=90

Step-by-step explanation:

correct

Answer:

x = - 7, x = - 4

Step-by-step explanation:

To factor the quadratic

Consider the factors of the constant term ( + 28) which sum to give the coefficient of the x- term ( + 11)

The factors are + 7 and + 4, since

7 × 4 = 28 and 7 + 4 = 11, hence

(x + 7)(x + 4) = 0

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 4 = 0 ⇒ x = - 4

Answer:

5

Step-by-step explanation:

We need to use Pythagoras' theorem.

For this we can use the pythagoras formula a^2+b^2=c^2 and rearrange this

We then will have 8^2+b^2=89

(because 89(sqrt) squared is 89)

We can then solve for what x is.

We take away 64 from 89 which is 25

the square root of 25 is 5

Therefore x=5

I’m not 100% sure but I think it’s 14/49

Pythagoras' Theorem

[tex]c^{2} =\sqrt{a^{2}+b^{2}}[/tex]

a = 5

b = 7

[tex]c^{2} =\sqrt{5^{2}+7^{2}}[/tex]

[tex]c^{2} =\sqrt{25+49}[/tex]

[tex]c^{2} =\sqrt{74}[/tex]

c = 8.6 to 1d.p.

The distance is 8.6 units

see the image

The solution to the set of equations is (0,2).

Reasoning:

m + 4n = 8 -> 0 + 4(2) = 8

m = n - 2 -> 0 = 2 - 2

Answer:

Yes, B is correct.

Step-by-step explanation:

Answer:  [tex]\bold{\dfrac{7}{9}}[/tex]

Step-by-step explanation:

[tex]\sqrt{\dfrac{49}{81}}=\dfrac{\sqrt{49}}{\sqrt{81}}=\large \boxed{\dfrac{7}{9}}[/tex]

The answer is D 5:2

4:16

10:4

5:2

Answer:

180 degrees and interior

Step-by-step explanation:

X and y equal 180 and make the shape C therefor are interior angles

Without specific details like an equation or diagram, we can't find the actual values of x and y. But we can talk about how angles can relate to each other generally - they can be complementary (add up to 90 degrees), supplementary (add up to 180 degrees), or vertical (equal when two lines intersect).

The question is missing specific details like an equation or a diagram that we can use to find the actual values of x and y. Without these, it's not possible to provide a direct answer. However, we can discuss how angles relate to each other in a general sense.

These are just a few examples of the relationship between angles that could help guide your understanding. If you have a specific problem involving angles and variables, please provide it so we can assist you more accurately.

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The correct answer is D.

There are 32 fluid ounces in a quart so 2 quarts would have 64 fluid ounces and the last equation represents this.

I hope this makes sense and is helpful.

Answer:

D

Step-by-step explanation:

Answer:   a)  k(x) = 2ˣ

Step-by-step explanation:

[tex]g(x) = 3(2^x)\qquad h(x)=2^{x+1}\\\\k(x) = (g-h)(x)\\.\qquad =3(2^x)-2^{x+1}\\.\qquad =3(2^x)-2^x\cdot 2^1\\.\qquad =3(2^x)-2(2^x)\\.\qquad =1(2^x)\\.\qquad =\large\boxed{2^x}[/tex]

Answer:

2 - y = 4x

y - 2 = -4x

y = -4x + 2

Answer:

Step-by-step explanation:

xy = 42

x+y = - 2                   Substitute into the top equation

y = -2 - x                   Put in for y

x(-2 - x) = 42             Remove the brackets

-2x - x^2 = 42           Subtract 42 from both sides.

-2x - x^2 - 42 = 0      Put in the more normal order.

-x^2 - 2x - 42 = 0      Multiply by -1

x^2 + 2x + 42 = 0

This cannot be factored. It gives complex roots as it is written. I will give you the answer but I kind of doubt the question is correct.

x1 = - 1 + 6.40i

x2 = -1 - 6.40i

Leave a comment if you have a correction.

Answer:

1) He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2) He did not multiply the numerator and denominator by the correct number to equal 1,500.

5) He should have multiplied the numerator and denominator by 75, not 30,  because 20 x 75 = 1,500.

Step-by-step explanation:

Final answer:

Josiah made errors in predicting the number of rock songs on his MP3 player by not averaging the samples correctly and by using the wrong multiplication factor in his proportion calculation. The correct average should be 5, and he should have used a factor of 75 to scale his samples up to the total number of songs.

Explanation:

The student has used a proportion to predict the number of rock songs on his MP3 player based on a sample. However, the prediction method has a few mistakes that should be corrected for an accurate estimate.

Josiah's initial prediction did not consider averaging the number of rock songs from both samples, which would have given a better representation of the average occurrence in the sample set. The correct average is (4+6)/2 = 5 rock songs per sample.

The proportion set up by Josiah is 10/20 = x/1,500, which implies that the 10 rock songs in his samples represent half of all songs played. This should have been compared to the total number of songs on the MP3 player, 1,500, requiring him to multiply by a specific number. Yet, the multiplication factor used (30) was incorrect. To scale up 20 to 1,500, he should use the factor of 75, because 20 × 75 = 1,500.

The correct proportion should be 5/20 = x/1,500, which simplifies to 1/4 = x/1,500, and then x = 1,500/4 = 375. Hence, the predicted number of rock songs based on the sample should be 375.

You are correct! It’s C

Answer: OPTION B

Step-by-step explanation:

The red graph shows the parent function of a quadratic function (which is the simplest form of a quadratic function), whose vertex is at the origin.

The function g(x) is the result of shift the parent function 2 units to the right and shift it 1 unit up.

Therefore, keeping the above on mind you have that the transformation has the following form:

[tex]g(x)=(x-h)^2+k[/tex]

Where the horizontal shift depends on the value of h and the vertical shift depends on the value of k.

Therefore, you obtain the function:

[tex]g(x)=(x-2)^2+1[/tex]

Answer:

B. [tex]g(x)=(x-2)^2+1[/tex]

Step-by-step explanation:

The equation of the red graph is [tex]f(x)=x^2[/tex].

The blue graph has its vertex at (2,1)

Hence its equation is of the form;

[tex]g(x)=a(x-2)^2+1[/tex]

This graph has y-intercept (0,5).

[tex]5=a(0-2)^2+1[/tex]

[tex]5-1=a(-2)^2[/tex]

[tex]4=4a[/tex]

[tex]1=a[/tex]

The blue graph therefore has equation;

[tex]g(x)=(x-2)^2+1[/tex]

Answer:

First Equation: [tex]\frac{3}{4} \div \frac{1}{8} =6[/tex]

Step-by-step explanation:

From the given number line we can see that there are 6 arrows/jumps of equal sizes to reach from 0 to [tex]\frac{3}{4}[/tex]

Each small jump is equivalent to [tex]\frac{1}{8}[/tex]. This is because from 0 to [tex]\frac{1}{4}[/tex] there are 2 jumps, so 1 jump will be equal to [tex]\frac{1}{4}[/tex] divided by 2 which is equal to [tex]\frac{1}{8}[/tex]

From 0 to [tex]\frac{3}{4}[/tex], 6 jumps of [tex]\frac{1}{8}[/tex] are made. In other words we can say [tex]\frac{1}{8}[/tex] is added to itself 6 times to reach to [tex]\frac{3}{4}[/tex].

Adding [tex]\frac{1}{8}[/tex] 6 times to itself also means multiplying [tex]\frac{1}{8}[/tex] by 6. So we can set up the equation as:

[tex]\frac{1}{8} \times 6 = \frac{3}{4}[/tex]

Dividing both sides by [tex]\frac{1}{8}[/tex]  we get:

[tex]6=\frac{3}{4} \div \frac{1}{8} \\\\ or\\\\ \frac{3}{4} \div \frac{1}{8} =6[/tex]

Hence, the first equation represents the given number line.

Answer:

A

Step-by-step explanation:

Answer:

Always

Step-by-step explanation:

They never intersect

Answer:

Always

Step-by-step explanation:

The solution to a system of equations graphically is at the point of intersection of the graphs.

If the lines are parallel then they never intersect and so there is no solution.

Answer: the probability of green would be 4/13 the probability of red would be 6/12

Step-by-step explanation:

The probability of green would be 4/13 the probability of red would be 6/12.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of samples

Given that a bag contains 6 red balls, 4 green balls, and 3 blue balls. If we choose a ball, then another ball without putting the first one back in the bag.

Total outcomes for green ball = 6 + 4 + 3 = 13

The probability of choosing a green ball is,

Probability = 4 / 13

The probability of choosing the red ball is,

Probability = 6 / 12

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Answer:

The system of inequalities is

[tex]y\leq -\frac{1}{3}x+2[/tex]

[tex]y>\frac{2}{3}x+3[/tex]

Step-by-step explanation:

step 1

Find the equation of the solid red line

Let

[tex]A(0,2),B(3,1)[/tex]

Find the slope

[tex]m=(1-2)/(3-0)=-1/3[/tex]

The equation of the line is

[tex]y=-\frac{1}{3}x+2[/tex]

The solution of the inequality is the shaded area below the solid red line

therefore

The inequality is

[tex]y\leq -\frac{1}{3}x+2[/tex]

step 2

Find the equation of the dashed blue line

Let

[tex]A(0,3),B(3,5)[/tex]

Find the slope

[tex]m=(5-3)/(3-0)=2/3[/tex]

The equation of the line is

[tex]y=\frac{2}{3}x+3[/tex]

The solution of the inequality is the shaded area above the dashed blue line

therefore

The inequality is

[tex]y>\frac{2}{3}x+3[/tex]

The system of inequalities is

[tex]y\leq -\frac{1}{3}x+2[/tex]

[tex]y>\frac{2}{3}x+3[/tex]

Answer:

C

Step-by-step explanation:

You can reason your way through this without a calculator:

A: the absolute function turns everything positive, then you can see that 5/6 cannot be larger than 1 5/6

B: Realizing that √25=5, √18 cannot be larger than 5

C: 5.6x10³ means shifting to the left 3 positions: 5600 > 1000 so this one is true.

D: A negative number is always smaller than a positive number.

Answer:

Your answer would be C because simplified:

5,600 is greater than 1,00

Step-by-step explanation:

Your answer wouldn't be A because simplified:

0.833 > 1.833 is an incorrect statement.

Your answer wouldn't be B because simplified:

4.243 > 5.875 is an incorrect statement.

Your answer WOULD be C because simplified:

5,600 > 1,000 is a true statement

Your answer wouldn't be D because simplified:

-2.45 > 4.4 is an incorrect statement