Suppose the diameter of a circle is 6 units. What is its circumference?

Answer:

Step-by-step explanation:

6x² + 40 = 31x

6x² - 31x + 40 = 0

6x² - 16x - 15x + (-5)*(-8) = 0

2x(3x - 8) - 5(3x -8) = 0

(3x - 8) (2x - 5) = 0

Answer: Center (0, -8) and Radius = 2

The standard equation of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

You can write the equation as (x-0)² + (y-( -8))² = 2². From this, you can conclude that the center is (0,-8) and the radius is 2.

Answer:

She receives $47.5 less

Step-by-step explanation:

Now, the first thing to do here is to calculate what 15% if the total amount is

That would be 15/100 * 950 = $142.5

The amount she receives less is thus $142.5 -$95 = $47.5

Answer:

The amount less that she received than if she had received 15% of the cost of the meal is $47.5

Step-by-step explanation:

Here we have the amount of dinners served by the waitress = $950

Amount received in tips = $95.00

Amount the waitress would have received if she had gotten 15% of the cost of meals served = 15/100 × $950 = $142.5

Therefore, since she received $95.00, the amount less that she received than if she had received 15% of the cost of the meal is thus;

$142.5 - $95 = $47.5.

Hey there! I'm happy to help! :D

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OVERVIEW

A complex number is a real number combined with an imaginary number (such as i, a number that will equal -1 when squared).

The complex plane is an interesting thing we use to graph complex numbers. The horizontal axis is where you plot the real part of the complex number, and the y-axis is where you plot the coefficient of the imaginary number.

For example, if I had the complex number 4+3i, I would plot the point (4,3) on the complex plane.

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MODULI

The modulus (plural is moduli) is the distance of a complex number from the origin on the complex plane. To find the modulus, you take the real number and the coefficient (basically the points of your graph), square them, add the results, and then you find the square root of that! Here's a little checklist so that you can always find the modulus of any complex number!

STEPS TO FIND MODULUS GIVEN COMPLEX NUMBER

STEP 1: PLOT THE COMPLEX NUMBER

Let's use our complex number 4+3i. If we plot it, the point will be (4,3)

STEP 2: TAKE YOUR VALUES OF X AND Y AND SQUARE THEM

4²=16

3²=9

STEP 3: ADD THESE SQUARES

16+9=25

STEP 4: SQUARE ROOT IT

√25=5

Therefore, the modulus (distance from the origin on the complex plane) of 4+3i is 5.

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SOLVING THE PROBLEM

In our case, we are given a modulus but not a point on the line. Our modulus is the square root of seventeen. We are going to have to the steps to find the modulus backwards to find our points. I will put the steps for finding a complex number given the modulus below.

STEPS TO FIND COMPLEX NUMBER GIVEN MODULUS

STEP 1: SQUARE THE MODULUS

√17²=17

STEP 2: FIND THE SQUARES THAT MAKE UP THE NUMBER

Before, we could just add things we found. Now, we have to find the things that were added! How do we know what things were added to find 17?  Well, we know that we added two squares to find the modulus, so we will subtract a square of some sort and hopefully come up with another square.

Let's see what squares exist that are less than seventeen.

1, 4, 9, 16

(Note that one is 1², 4 is 2², 9 is 3², and 16 is 4²)

Which of these can we add to get 17?

Well, we can do 1 and 16, so this is our result so far.

STEP 3: SQUARE ROOT THE RESULTS

Now, we just find the square roots of what we found in the last problem!

√1=1

√16=4

STEP 4: PLOT THE GIVEN NUMBERS ON THE PLANE AND FIND THE COMPLEX NUMBER

We can plot these either way because the modulus of 1+4i will be the same distance from the origin as 4+i because we only use the commutative property (adding order doesn't matter) when looking for the modulus. You can also have the negative version of either number because you immediately square it, so it can also be -4+i or 4-i! You can also rearrange the equation in tons of ways to figure it out. You could also have both be negative, flip the coefficient placement, etc.!

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SOLUTION

Therefore, the complex numbers that have a distance of √17 from the origin on the complex plane are ±4±i and ±1±4i. So, why did I write all of these funny plus and minus signs? Well, it's so that I didn't have to write all of the possible equations. I believe those equations actually represent 8 possible points we can create with the solution we got.

4+i

-4+i

4-i

-4-i

1+4i

-1+4i

1-4i

-1-4i

You can plug these complex numbers back in and find the modulus with my instructions to find the modulus given a complex number. Now, you will be able to deal with moduli and complex numbers for the rest of your life!

I hope that this helps! Have a wonderful day! :)

Answer:

Step-by-step explanation:

389

Answer. 3/89

Step-by-step explanation:

HEY FREN

Answer:

8

Step-by-step explanation:

f(x)=5x^2−3x+8

Let x=0

f(0) = 5(0) -3(0) +8

     = 8

Answer:

V= 1/3 pi*r^2*

Step-by-step explanation:

The reason the volume of a cone involves using the fraction 1/3, is because it takes three cones to fill up a cylinder. So, if the volume of a cylinder is pi*r^2*h, and a cone is 1/3 the size, then the volume of a cone(which uses the same formula) has to have the 1/3rd in front.

Answer:

2/5*180=72

360/72=5

as simple as that you just need to read on polygons

Step-by-step explanation:

pls give me brainlyist

Answer:

50 ft2

Step-by-step explanation:

im not sure if this is right but this is what i got when i worked it out

Answer: [tex]150ft^2[/tex]

Step-by-step explanation:

length: [tex]7\frac{1}{2}in[/tex] Convert to an improper fraction. [tex]\frac{7*2+1}{2}=\frac{15}{2}[/tex]

width: [tex]5 in[/tex]

[tex]Formula: A=w*l[/tex]

[tex]A=(5in)(\frac{15}{2}in)\\A=\frac{75}{2}in^2[/tex]

Convert to ft. I assume your conversion factor is [tex]\frac{1}{2}in. : 1ft[/tex]. However, the unit we need is squared. Square both sides.

[tex](\frac{1}{2}in.)^2 : (1ft)^2[/tex]

[tex]\frac{1}{4}in^2 : 1ft^2[/tex]

Convert.

[tex]\frac{75}{2}in^2(\frac{1ft^2}{\frac{1}{4}in^2 } )=[/tex]

Invert the fraction in the denominator and multiply it by the numerator.

[tex]\frac{75}{2}in^2*1ft^2*4in^-^2=75*2ft^2=150ft^2[/tex]

Answer:

48.048

Step-by-step explanation:

multiply 77 time 0.60 since 60%in decimal form is 0.60. you then get the answer of that(46.2) and mutiply 0.04 since that the decimal form for 4%. you get 1.848 and add it to 46.2 and get the final answer 48.048. Hope this helped you

Answer:

The answer is A

Step-by-step explanation:

Answer:

Area of parallelogram A = base x height = 2 x 1 = 2 (in2)

Hope this helps

:)

Answer:

r: radius of balloon

V = (4/3)*pi*r^3 =  288000

=> r^3 = 288000*(3/4)/pi

=> r^3 = 68754.94

=> r = [tex]\sqrt[3]{68754.94}[/tex] = ~40.97 cm

[tex] {x}^{2} = 11x \\ {x}^{2} - 11x = 0 \\ x(x - 11) = 0[/tex]

Product is equal to 0 when one of multipliers is equal to 0, so

[tex]x = 0[/tex]

Or

[tex]x - 11 = 0 \\ x = 11[/tex]

Answer: x=0 or x=11

Answer:

Step-by-step explanation:

x^2 = 11x

x ( x − 11 ) = 0

x = 0  (by transposing)

x − 11 = 0

x=11  (by transposing)

therefore, x= 0,11

Hope it Helps...pls Mark as Brainliest!!

Answer:

Option B

The directrix of the parabola is parallel to the axis of symmetry

Step-by-step explanation:

The directrix of the parabola is not parallel to the axis of symmetry. It is as a matter of fact, perpendicular to it.

A parabola is actually a set of points that are equidistant from a given point, the focus, and a given line the directrix.

The axis of symmetry is a line that divides the parabola into two equal halves and it always passes through the focus.

The directrix of the parabola is always perpendicular to this axis of symmetry as they always intersect at right angles.

We want to see which one of the given statements is false. We will see that the false one is B: "The directrix of the parabola is parallel to the axis of symmetry"

So in a parabola, we define the axis of symmetry as the vertical line that divides the parabola in two equal parts.

For a general parabola:

y = a*x^2 + b*x + c

The line of symmetry is at:

x = -b/2a

While we know that in a parabola the directrix is a horizontal line.

So the axis of symmetry and the directrix are perpendicular lines.

Then the statement that is false is B: "The directrix of the parabola is parallel to the axis of symmetry"

If you want to learn more, you can read:

https://brainly.com/question/3283347

Answer:

[tex]\sin B=\dfrac{3\sqrt{58}}{58}[/tex]

[tex]\cos B=\dfrac{7\sqrt{58}}{58}[/tex]

[tex]\tan B=\dfrac{3}{7}[/tex]

Step-by-step explanation:

The sine of an angle is the length of the opposite side divided by the length of the hypotenuse, which in this case is[tex]\frac{3}{\sqrt{58}}=\frac{3\sqrt{58}}{58}[/tex]. The cosine is the adjacent side divided by the hypotenuse, which in this case is [tex]\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}[/tex]. The tangent is the length of the opposite side divided by the length of the adjacent side, which in this case is simply [tex]\frac{3}{7}[/tex]. Hope this helps!

Answer:

He sold 7 more small boxes than large boxes

Step-by-step explanation:

Let x be the no of small boxes sold .

Cost of 1 small boxes of oranges = $5

Cost of x small boxes of oranges = 5x

Let y be the no. of large boxes sold

Cost of 1 large boxes of oranges = $9

Cost of y large boxes of oranges = 9y

He sold 17 boxes in all total for 105

So,x+y=17 ---1

So,5x+9y=105 ---2

Substitute the value of x from 1 in 2

5x+9(17-x)=105

5x+153-9x=105

153-105=4x

[tex]\frac{153-105}{4}=x[/tex]

12=x

Substitute value of x in 1

12+y=17

y=17-12

y=5

Difference in no. of boxes = 12-5 = 7

So, He sold 7 more small boxes than large boxes

Answer:

the answer is 0

Step-by-step explanation:

she had -27 in her bank the she added  27

Answer:

what grade are you in so i can help

Step-by-step explanation:

Answer:

Step-by-step explanation:

x three point shots: 8*3=24

x two point shots: 2*2=4

The point would Anthony score is : 24+4=28

I hope it'll help you much

Thank you for asking

Step-by-step explanation:

(5x+2y=6)2

10x+4y=12

10x+4y=12 then substract

10x+4y=12

0=0 true so, it have infinite s/n

Option B. is correct

Polynomial equation are equation of number independent variables having relationship with dependent variable.

Since,
A monomial can have higher exponents so its exponents has probability to get divisible by 3 so when cube root for monomial performed.  
for example [tex]\sqrt[3]{x^3}[/tex] = x

Thus, Miguel is correct. Any monomial can be a perfect cube root because, when it is cubed, the variables will have exponents divisible by 3.

Learn more about polynomial here:

brainly.com/question/11536910

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Answer:

option B

Step-by-step explanation:

edge 2023

Answer:

m∠DEH= 128.6°

Step-by-step explanation:

∠GHJ and ∠DEH are both congruent to each other because lines DF and GI are both parallel to each other.

This means, if m∠GHJ is 128.6°, m∠DEH is also 128.6°.

Answer:

128.6

Step-by-step explanation:

GHJ= DEH

adjasent angle

Answer:

We equate the two expressions since they both pass through the center of the circle.

The coordinate of the center of the circle is (2,4)

Step-by-step explanation:

From circle theorem, we know that the perpendicular bisector of a chord passes through the center of the circle.

Since both equations would pass through the center of the circle, we equate them.

So, -2x+8 = 3x-2

Solving for x, we have

3x + 2x = 8 + 2

5x = 10

x = 10/5

x = 2

Substituting x = 2 into any of the equations, we find the y- coordinate of the center of the circle.

y = -2x + 8 = -2(2) + 8 = -4 + 8 = 4

So, the coordinate of the center of the circle is (2,4)

Personal Answer:

The perpendicular bisector of a chord passes through the center of the circle/plate, meaning that both expressions can contribute to the finding the center. By solving for x and y, one can find the coordinates of the center of the circle.

Plato Sample Answer:

Because the perpendicular bisector of any chord of a circle passes though the center of the circle, these two perpendicular bisectors intersect at that point. You can set up a system of equations and solve to find the coordinates of the center.

I hope this helps!

Answer:

6

Step-by-step explanation:

Answer:

6 students read 2 books

Answer:

Slant height = 33 inches

Step-by-step explanation:

r = 12 inches

Lateral Surface Area of cone = 396π square inches

πrl = 396π

π * 12 * l = 396π

[tex]l=\frac{396\pi }{12*\pi }\\[/tex]

l = 33 inches

Answer:

4 is the length of a side.

Step-by-step explanation:

16 divided by 4 equals 4

Answer:

4 units

Step-by-step explanation:

The area of a square is denoted by: A = s², where s is the side length.

Here, we know that the area is 16, so plug this in for A:

A = s²

16 = s²

s = √16 = 4

Thus, the side length is 4 units.

~ an aesthetics lover

Answer:

9

Step-by-step explanation:



Answer:

9 hours per night

Step-by-step explanation:

Assuming a week is 7 days

7 * 12 = 14 days

126/14=9

She slept 9 hours per night

Using the normal distribution, it is found that 0.35% of the testers scored a perfect score.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 20.9, \sigma = 5.6[/tex]

The proportion of scores above 36(perfect scores) is given by one subtracted by the p-value of Z when X = 36, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{36 - 20.9}{5.6}[/tex]

Z = 2.7

Z = 2.7 has a p-value of 0.9965.

1 - 0.9965 = 0.0035 = 0.35.%.

Hence, 0.35% of the testers scored a perfect score.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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Answer:

Engineers use the Pythagorean Theorem to figure out measurements of objects.