A cylindrical vase has a volume of 192.5 cubic centimeters. The height of this vase is 5 centimeters. The formula for the volume of the cylinder is πr^2h where r is the radius and h is the height of the vase. Find the radius of this vase.(Given that π ≈ 22 / 7 )

Hi there!

[tex]\large\boxed{(-3, 8.25)}[/tex]

Solve for the vertex by completing the square:

y = -0.25x² - 1.5x + 6

Factor out a negative:

y = -(0.25x² + 1.5x) + 6

Remember that a square binomial is:

a² + 2ab + b²

We know that:

a² = 0.25, so a = 0.5

1.5 = 2ab, so:

1.5 = 2(0.5)b

b = 1.5

b² = 2.25

Thus:

y = -(0.25x² + 1.5x + 2.25) + 6 - (-2.25)

Simplify:

y = -(0.5x + 1.5)² + 8.25

Find the vertex by factoring out 0.5:

y = -0.5(x + 3)² + 8.25

Thus, the vertex is:

(-3, 8.25)

Answer:

22 m/s

Step-by-step explanation:

Take the distance and divide by the time

1210 m/55s

22 m/s

Answer:

Step-by-step explanation:

[tex]speed = \frac{distantce}{time} \\ = \frac{1210m}{55s} \\ = 22m {s}^{ - 1} [/tex]

Solution:-10

As <AGQ and <EQG are corresponding interior angles

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 60°+a=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow a=180-60[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow a=120}[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow b=75°}[/tex]

According to angle sum property

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow b+c+<PQR=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+75+60=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c+135=180[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow c=180-135[/tex]

[tex]\\ \qquad\quad\boxed{\sf{:}\twoheadrightarrow c=45°}[/tex]

Answer:

solution,

(X1,y1)= (-4,5)

(X2,Y2)=(2,-3)

slope of the line(m)= y2-y1/x2-x1

=-3-5/2-(-4)

=-8/6

=-4/3

Answer:

f(-8) = 64

Step-by-step explanation:

Since x =-8, we need to use x^2 since -8 <0

(-8)^2 = 64

When x = -8 f(-8) = 64

Answer:

B

Step-by-step explanation:

There are 2 functions, one if x > 0 and one if x < 0

The x we are given is -8, and -8 is less than 0

Plug -8 into the function for if x < 0, which is x^2

(-8)^2=64

Circumference of a circle = 2πr

So,

[tex]circumference = 2\pi \: r \\ = > circumference = 2 \times \frac{22}{7} \times \frac{63 \: cm}{2} \\ = > circumference = 2 \times \frac{11}{7} \times 63 \: cm \\ = > circumference = 2 \times 11 \times 9 \: cm \\ = > circumference = 198 \: cm[/tex]

Answer: Therefore, the circumference of circle is 198 cm.

Step-by-step explanation:

diameter = 63 cm

radius = 63/2 = 31.5 cm

circumference = ?

circumference or perimeter of circle = 2*pi*r

= 2*(22/7)*31.5

= (44/7)*31.5

= 198 cm

Answer:

1 ) 0.023

2 ) 0.1004

Step-by-step explanation:

2 / 100 + 3 / 1000

= 0.02 + 0.003

= 0.020 + 0.003

= 0.023

1 / 10 + 4 / 10,000

= 0.1 + 0.0004

= 0.1000 + 0.0004

= 0.1004

Answer:

360 feets

Step-by-step explanation:

Given :

Scale : 1 inch = 12 feets

This means 1 inch on paper (model) represents 12 feets in real life

If the model height = 30 inches ;

The actual height of the Saturn V rocket will be :

1 inch = 12 feets

30 inch = x

x = (30 * 12)

x = 360 feets

Actual height = 360 feets

Answer:m

Step-by-step explanation:m

Step-by-step explanation:

-23 is the answer

√18=9

√16=4

-3×9+4= -23

Answer:

-23 is right on edg

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

divide 76 by 4

Answer:

The third one

Step-by-step explanation:

Just took the quiz

Answer: i would go with the third one

Answer:

18 pages

Step-by-step explanation:

that means you can read 2 pages in 10 minutes.

an hour and a half is 90 minutes.

90 is 9 times more than 10.

so we do 2 * 9 = 18 pages

Answer:

1st option

Step-by-step explanation:

3×2+5y=15

5y=15-6

y=9/5

Answered by GAUTHMATH

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.

Step-by-step explanation:

There are mistakes in the statement, correct form is presented below:

[tex]5+\frac{\sqrt{3}}{7} + 2\sqrt{3} = a - b\cdot \sqrt{3}[/tex].

By direct comparison we have the following system of equations:

[tex]a = 5[/tex] (1)

[tex]\frac{\sqrt{3}}{7}+2\sqrt{3} = -b\cdot \sqrt{3}[/tex] (2)

In (2) we solve for [tex]b[/tex]:

[tex]\left(\frac{1}{7}+2 \right)\cdot \sqrt{3} = -b\cdot \sqrt{3}[/tex]

[tex]b = -\frac{15}{7}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.

Answer:

Step-by-step explanation:

Table I

Given function is,

f(x) = [tex]b^x[/tex]

From the table attached,

For x = 0.827, value of function f(0.827) = 5,

f(0.827) = [tex]b^{0.827}[/tex]

Therefore, [tex]b^{0.827}=5[/tex]

[tex]\text{log}(b^{0.827})=\text{log}(5)[/tex]

0.827[log(b)] = log(5)

log(b) = 0.8452

b = [tex]10^{0.8452}[/tex]

b = 7

Therefore, function 'f' will be,

f(x) = [tex]7^x[/tex]

For f(x) = 9,

9 = [tex]7^x[/tex]

log(9) = log([tex]7^x[/tex])

log(9) = x[log(7)]

x = 1.129

Table II

Given function is g(x) = [tex]\text{log}_b(x)[/tex]

From the given table,

For x = 7, g(x) = 1

1 = [tex]\text{log}_b(7)[/tex]

[tex]b^1=7[/tex]

b = 7

Therefore, the function 'g' will be,

g(x) = [tex]\text{log}_7(x)[/tex]

For g(x) = 1.318

1.318 = [tex]\text{log}_7(x)[/tex]

[tex]x=7^{1.318}[/tex]

[tex]x=12.9968[/tex]

[tex]x=13.997[/tex]

Your answer is attached above. hope it helps

Point-slope form

y -24 = -4/5(x -0)

Find x when y is 0 (X-intercept)

0 -24 = -4/5(x -0)

-24 = -4/5x

x = -120/-4

x = 30

Answer: A. 30 minutes

Answer:

14.88 km

Step-by-step explanation:

add both base 1 and base 2 together divide them by 2 then multiply by the height.

y = x^2 - 2x - 3

Factored Form: y = (x - 3)(x + 1)

X-Intercepts: (3, 0) and (-1, 0)

Axis of Symmetry: x = 1

Vertex: (1, -4)

Domain: All Real Numbers (or negative infinity to infinity)

Range: y > -4

Hope this helps!

Answer: 159

Step-by-step explanation:

We have to find the surface area of two triangles and 3 rectangles

To find the surface areas of the triangles, we use the formula: base x height / 2

6 x 5.5 / 2 = 16.5

Multiply that by 2 since there are 2 of them

16.5 x 2 = 33

To find the surface area of the rectangles, we multiply the length and width

7 x 6 = 42

Multiply that by 3 since there are 3 of them

42 x 3 = 126

Add up all the surface areas

126 + 33 = 159

c) y= -2x +1

Step-by-step explanation:

y= -2x +1

m= (- 3 -5)/2+2

= -2

c=1

y-(-3)= -2(x-2)

y= -2x +4 -3

y = -2x+1

Answer:

[tex]a. \ \dfrac{1}{36}[/tex]

[tex]b. \ \dfrac{4}{9}[/tex]

[tex]c. \ \dfrac{5}{6}[/tex]

Step-by-step explanation:

The given probabilities are; P(Orange) = 1/3, P(Blue) = 1/6, P(Purple) = 1/2

The probability of rolling any of the six numbers of the six-sided die = 1/6

a. The probability of simultaneously 'rolling a 3' and 'spinning blue', P(3 and Blue) is given as follows;

P(rolling a 3) = 1/6, P(Blue) = 1/6

∴ P(3 and Blue) = (1/6) × (1/6) = 1/36

P(3 and Blue) = 1/36

[tex]P(3 \ and \ Blue) = \dfrac{1}{36}[/tex]

b. The probability of either 'rolling a 1' or 'spinning Orange', P(1 or Orange), is given as follows;

P(rolling a 1) = 1/6, P(Orange) = 1/3

P(1 or Orange) = P(rolling a 1) + P(Orange) - P(1 and Orange)

Where;

P(1 and Orange) = (1/6) × (1/3) = 1/18

∴ P(1 or Orange) = 1/6 + 1/3 - 1/18 = 4/9

P(1 or Orange) = 4/9

[tex]P(1 \ or \ Orange) = \dfrac{4}{9}[/tex]

c. The probability of not spinning a blue, P(not Blue) is given as follows;

P(not Blue) = P(rolling all outcomes of the die) and (The sum of the spin probabilities - P(Blue)

∴ P(not Blue) = 1 × ((1/3 + 1/6 + 1/2) - 1/6) = 1 × (1 - 1/6) = 5/6

P(not Blue) = 5/6

[tex]P(not \ Blue) = \dfrac{5}{6}[/tex]

Answer:

The total value of quarters that Samantha took is $3.75

Step-by-step explanation:

Timothy has 72 coins.

He has:

Q quarters

D dimes

N nickels

8 pennies.

Then:

Q + D + N + 8 = 72

Samantha takes:

3 dimes

2 nickels

Leaves him with one penny, then she takes 7 pennies.

all of the quarters, so she took Q quarters.

So now Timothy has 45 coins.

And for each particular type of coin, Thimothy now has:

D - 3 dimes

0 quarters

1 penny

N - 2 nickels

And we know that he has 45 coins, then:

(N - 2) + 1 + ( D - 3) = 45

Which we can rewrite as:

N + D + 1 - 2 - 3 = 45

N + D - 4 = 45

N + D = 45 + 4 = 49

So we have two equations:

Q + D + N + 8 = 72

N + D = 49

Now we can replace the second equation into the first one:

(N + D) = 49

then:

Q + D + N + 8 = 72

Q + (D + N) + 8 = 72

Q + 49 + 8 = 72

Now we can solve this for Q

Q = 72 - 49 - 8 = 15

So Samantha took 15 quarters.

Each quarter has a value of $0.25

Then Samantha took:

15*$0.25 = $3.75

The total value of quarters that Samantha took is $3.75