Work out the area of this circle with a radius of 6mm. Give your answer in terms of pi

Answer:

[tex](2, 17)[/tex]

Step-by-step explanation:

A parabola has the general function: [tex]f(x)=ax^2+bx+c[/tex]

In this case we have: [tex]f(x) = x^2 - 4x + 21[/tex]

where

[tex]a=1[/tex]

[tex]b=-4[/tex]

[tex]c=21[/tex]

the vertex of a parabola is in the coordinates:

[tex](\frac{-b}{2a}, \frac{-b^2+4ac}{4a} )[/tex]

substituting all of the known values, we get the following:

[tex](\frac{-(-4)}{2(1)} ,\frac{-(-4)^2+4(1)(21)}{4(1)} )\\\\(\frac{4}{2} ,\frac{-16+84}{4} )\\\\\\(2 ,\frac{68}{4} )\\\\\\(2,17)[/tex]

the vertex of  [tex]f(x) = x^2 - 4x + 21[/tex] is at the point (2,17) which is the second option.

Answer:

2,17

Step-by-step explanation:

Step-by-step explanation:

The quotient is 0.125

I think this should be the answer

Answer:

0.125

Step-by-step explanation:

Answer:

so 2a+3b=±13

Step-by-step explanation:

4a²+9b²=97

ab=6

2a+3b=?

by using formula

(a+b)²=a²+b²+2ab

(2a+3b)²=(2a)²+(3b)²+2(2a)(3b)

(2a+3b)²=4a²+9b²+12ab

putting values

(2a+3b)²=97+12(6)

(2a+3b)²=97+72

(2a+3b)²=169

taking square root on both sides

√(2a+3b)²=√169

2a+3b=±13

i hope it will help you

Answer:

2a+3b = 13

Step-by-step explanation:

Using this formula

[tex](x+y)^2 = x^2+y^2+2xy[/tex]

Where,

x = 2a and y = 3b

Putting in the above formula

=> [tex](2a+3b)^2=4a^2+9b^2+12ab[/tex]

Putting  4a²+9b² = 97 and ab = 6

=> (2a+3b)² = 97+12(6)

=> (2a+3b)² = 97+72

=> (2a+3b)² = 169

Taking sqrt on both sides

=> 2a+3b = 13

Answer: 0.5

Step-by-step explanation:

Total bags (U) = 140

Number of bags with both button and zip:

(48 + 47 + x + 22) = 140

117 + x = 140

x = 140 - 117

x = 23

Therefore, probability that bag has button :

Total Number of bags with button:

(Bags with button alone + bags with both button and zip)

(47 + 23) = 70

Probability = (required outcome / Total possible outcomes)

P(bag has button) = (number of bags with button / total number of bags)

P(bag has button) = 70/140 = 0.5

P(bag has button) = 0.5

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x

Answer:

t ≤ 4.24

Step-by-step explanation:

P(t) ≥ 40000 implies

500t/(2t²+9) ≥ 40000

Multiplying through by t², we have

500t ≥ 40000(2t²+9)

500t/40000 ≥ 2t²+9

Collecting like terms

0.0125t  ≥ 2t²+9

0  ≥ 2t²+ 9 - 0.0125t

2t²+ 9 - 0.0125t  ≤ 0

2t²- 0.0125t + 9 ≤ 0

Using the quadratic formula,

[tex]t = \frac{-(-0.0125) +/-\sqrt{(-.0125)^{2} - 4 X 2 X 9} }{2 X 2} \\= \frac{0.0125 +/-\sqrt{(0.00015625 - 288} }{4}\\= \frac{0.0125 +/-\sqrt{-287.9998} }{4}\\= \frac{0.0125 +/-16.97i }{4}\\=0.00313 + 4.24i or 0.00313 - 4.24i[/tex]

The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)

So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0

(t - 0.00313)² - 4.24² ≤ 0

(t - 0.00313)² ≤ 4.24²

taking square-root of both sides,

√(t - 0.00313)² ≤ √4.24²  

t - 0.00313 ≤ 4.24

t ≤ 4.24 + 0.00313

t ≤ 4.24313 ≅ 4.24

t ≤ 4.24

Answer:

(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

Step-by-step explanation:

When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]

PART A

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]

PART B

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]

ii) Not a perfect square  

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]

iii) A multiple of 5  

Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

[tex]=\dfrac{15}{64}\\=0.234375[/tex]

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]

Answer:

x = -1/8

Step-by-step explanation:

The greater than sign can be replaced with an equal sign to solve.

5x + 4 < 3 – 3x =>

5x + 4 = 3 - 3x =>

+3x  -4    +3x - 4

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

8x = -1

x = -1/8

Step-by-step explanation:

We have,

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :

[tex]h=-16t^2 + 36t + 10[/tex] ......(1)

Part (a) :

The maximum height reached by the ball is given by :

[tex]\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s[/tex]

Part (b) :

The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :

[tex]h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m[/tex]

1 pound = 1.62 dollars.

Multiply total pounds by 1.62 for total dollars.

650 x 1.62 = $1,053

Answer: y = 1/2x - 6

Step-by-step explanation:

#4 We are going to use slope intercept form, (y = mx+b)

1. The line crossing the y-intercept at (0,-6)

2. The slope is 1/2 (increasing by 1 then over 2 --> RISE OVER RUN)

3. Make the equation: y= 1/2x - 6

Answer: 3 . y = -1/3 + 4/3   4. y= 1/2x -6

Step-by-step explanation:

3.   In the first graph  they have the coordinates,  (-2,2)  and (4,0). We have to solve for the slope and the y-intercept in other to write and equation.

To find the slope we have to find the change in the y values  and divide it by the difference in the x values.

2-0 = 2

-2 -4 = -6

2/-6 =  -1/3  Now we know that the slope is -1/3  so we need to  find the y-intercept.

2= -1/3(-2) +b   where be is the y intercept.

2= 2/3 + b

-2/3  -2/3

b= 4/3  

Now we could write the equation as  y= -1/3 + 4/3  

4. The same with number 4.  

We will find the slope and the y intercept by using some points on the number line.

(0,-6)  This already have the y-intercept graphed so we will need to just find the slope.

(0,-6)

(4,-4)  

-6 - (-4) = -2

0 - 4 =  -4

-2/-4 = 1/2

Equation: y = 1/2x  -6

Answer:

believe its 2x cause 1 was wrong

Answer:

Equation of a line y = mx + c

m = slope

m = 2

Using point ( -4,3)

Equation of the line is

y - 3 = 2(x +4)

y - 3 = 2x + 8

y = 2x + 8 + 3

y = 2x + 11

Hope this helps.

Answer:

B. Y = 2x + 11

Step-by-step explanation:

Got it right on edg.

Step-by-step explanation:

8x(7y+2)-4(7y+2)

=56xy+16x-28y-8

Answer:

56xy+16x-28y-8

Step-by-step explanation:

you have to use the FOIL method to solve this is problem which is

F-First

O-Outer

I-Inner

F-Last

Answer:

280 ft2

Step-by-step explanation:

The lateral area of this prism consists of seven rectangles, each one with dimensions 4 feet by 10 feet.

The area of one of these rectangles is:

[tex]A = base * height = 4 * 10 = 40\ ft^2[/tex]

Then, the area of the seven rectangles is:

[tex]Lateral\ area = 7*A = 7*40 = 280\ ft^2[/tex]

So the lateral area of this prism is 280 ft2.

Answer:

A. <

Step-by-step explanation:

The symbol "<" means less than.

Comparing 4.589 with 4.958, 4.958 is greater than 4.589 by 0.369 (4.958 - 4.589).

So therefore, if we are to write 1 statement for both, we would say "4.589 is less than 4.958".

This can be written by using just symbols without words, thus, we have:

4.589 < 4.958.

The correct option is A. <

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

https://brainly.com/question/17615619

#SPJ2

Answer:

[tex]900[/tex]

Step-by-step explanation:

[tex]892/10=89.2\\893/10=89.3\\894/10=89.4\\895/10=89.5\\896/10=89.6\\897/10=89.7\\898/10=89.8\\899/10=89.9\\900/10=90\\901/10=90.1\\902/10=90.2\\903/10=90.3\\904/10=90.4\\905/10=90.5\\906/10=90.6\\907/10=90.7\\908/10=90.8\\909/10=90.9[/tex]

Answer:

-1.67

Step-by-step explanation:

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

Step-by-step explanation:

If a function has a positive slope, that means the y value is increasing with respect to x. As you go down the x-axis, the y value will continuously increase.

First you want to plot the two sets of coords that they gave you, or else you wont know what the line looks like. Or, you could visually do it in your head. We're going down -4 on the x-axis and down 1 on the y-axis. Then for our second coords, we are going to 0 on the x-axis, then up 3 on the y-axis.

You could plot this for yourself, but im going to do it in my head for simplicity. We also need to find the slope of this function in order for us to find the y-intercept. The slope is change in y divided by the change in x. Subtract the initial position from the final position.

3 - 1 = 2

0 - (-4) = 4

2/4 = 1/2

The new equation is:

[tex]y=\frac{1}{2} x+b\\plugin(0,3)\\3=\frac{1}{2} (0)+b\\b=3[/tex]

Everything is shaded below and to the right of the line. They said the line was solid, so that means less than or equal to, [tex]\leq[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Y=15 when x=5

Step-by-step explanation:

if y= -6 when x= -2

So y=? When x=5

Y=15

Hope this helps

Good Luck

Answer:

2.5*10^7

Step-by-step explanation:

Answer:

Brainliest!!!

Step-by-step explanation:

See picture

Answer:

a: -3n+1

b:-5n-2

Step-by-step explanation:

a: it is -3+1 because you can see that the sequence is going down by 3, so it is the 3 times table, but because the number is 4, and 4 is 1 more than 3, you put plus one at the end. :)

b: similar to the last, it's going down by five, but it is two less this time, so you put minus two instead.

Hope this helps :),

Lily

Answer:

35 cm

Step-by-step explanation:

As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,

The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:

2(length + width) = Perimeter

2(2x + x) = 21

2(3x) = 21

6x = 21

x = 21/6 = 3.5 cm

x = 3.5 cm

From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:

2(length + width) = Perimeter

2(3x + 2x) = Perimeter

Perimeter = 2(5x)

Perimeter = 10x

Perimeter = 10(3.5)

Perimeter = 35 cm

Answer: Option B.

Step-by-step explanation:

The price per ounce can be calculated as the amount of you paid divided the number of ounces that you get.

A) we have a table:

ounces          price

18                     $1.5

36                    $3.00

54                    $4.5

We can see that here we have a linear relationship. for example, the price for 18 ounces is $1.5

Then the price per ounce is:

p = $1.5/18 = $0.083

B) here we know that 15 oz cost $0.75, the price per ounce is:

p = $0.75/15 = $0.05

C) here we have 11 ounces, and the price is $2.20

then we have:

p = $2.2/11 = $0.2

Then we can conclude that the least expensive is option B.

Answer:b

Step-by-step explanation:

did it on khan

Answer:

Do it your self

Step-by-step explanation:

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer:

x = 12:15=×5

36

060

Step-by-step explanation:

12:15=0

x=0

Answer:

4

Step-by-step explanation:

Divide the left side by 3

12:15

12/3 : 15/3

4:5

x would be 4