For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.

Answer:

[tex](x-1)^2+(y-2)^2=6.25[/tex]

Step-by-step explanation:

The equation for a circle is given by:

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

Where (h,k) is the center and r is the radius.

The center is the red dot, which is (1,2). Thus, h=1 and k=2.

To find the radius, you need to use the distance formula. We are given two coordinates: the center (red dot) at (1,2) and a blue dot on the circle at (2.5,4). Find the radius by using the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let (1,2) be x₁ and y₁ and let (2.5,4) be x₂ and y₂. Therefore:

[tex]d=\sqrt{(2.5-1)^2+(4-2)^2}\\d=\sqrt{(1.5)^2+2^2}\\d=\sqrt{2.25+4}\\d=\sqrt{6.25}=2.5[/tex]

Thus, r is 2.5.

Plugging these numbers into the equation, we have:

[tex](x-h)^2+(y-k)^2=r^2\\(x-1)^2+(y-2)^2=2.5^2\\(x-1)^2+(y-2)^2=6.25[/tex]

Answer:

The period of the function y = 2×tan x is π

Step-by-step explanation:

The tangent function, generally has a period of π radians such that a cycle of the tangent function is completed every π radians

Therefore, where a required number of periods is required to be completed within the π radians range, the number is used to multiply the trigonometric function[ parameter.

From the question, we have;

y = 2×tan x

Which gives the multiplier of the variable x as 1

Therefore, the period of the function y = 2×tan x is π.

Answer:

answer what

Step-by-step explanation:

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Answer:

w>10

length = 40

Step-by-step explanation:

Let

Width=w

Length=4w

Perimeter is less than 100 inches

Perimeter of a rectangle= 2( Length + width)

100 < 2(4w+w)

100 < 8w+2w

100 < 10w

w > 10

Length =4w

=4 × 10

=40 inches

Answer:

5/2l <100

Step-by-step explanation:

PLATO

Answer:

Each book weighs 1/2 lbs

Step-by-step explanation:

Take the total weight and divide by the number of books

10 lbs/20 books

1/2 lbs per book

Each book weighs 1/2 lbs

A regular heptagon (7-sided figure) cannot be constructed with a compass and straightedge.

Answer:

n = 12 nickels

d = 11 dimes

q = 7 quarters

Step-by-step explanation:

.05n + .1d + .25q = 3.45

n + d + q = 30

n = q + 5

n = 12

d = 11

q = 7

Answer:

B

Step-by-step explanation:

The side you have drawn in is 4√3 (calculate via pythagoras as √(8²-4²) = √48 = √16·3 = √4²·3 = 4√3)

So the area of the small triangle is 4*2√3 and the area of the small rectangle is 2*4√3. Together makes 4*2√3 + 2*4√3 =  16√3

Greetings from Brasil...

As stated in the statement:

HEIGHT = CONSTANT ÷ WIDTH

H = C ÷ W

so, isolating the variable C....

C = H · W

choosing any point on the graph...

(2; 30)  ⇒ W = 2 and H = 30

C = H · W

C = 30 · 2

The value of the constant in the equation shown in the figure would be, 60. Hence option C is true.

Given that,

The graph is the relation between Height and width.

As is given in the graph:

Height = Constant / Width

We observe that the graph passes through (2,30), (5,12), (10,6), (30,2)

So, by using any one point we may get the value of constant( since it is a fixed quantity)

Hence, using the point (2,30)

Width = 2

And, Height = 30

So, we get:

Constant = 2 × 30

= 60

To learn more about multiplication visit:

https://brainly.com/question/10873737

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Answer:

[tex]3\frac{7}{10}[/tex]

Please tell me if I'm wrong, and maybe consider brainliest if it's correct of course.

All of 4x+8 is under a cube root sign.

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

Work Shown:

To find the inverse, we swap x and y, then solve for y.

[tex]y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\[/tex]

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

Side note:

If [tex]f(x) = \frac{1}{4}x^3 - 2[/tex] and [tex]g(x) = \sqrt[3]{4x+8}[/tex], then [tex]f(g(x)) = x[/tex] and [tex]g(f(x)) = x[/tex]for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.

Greetings from Brasil...

In a triangle the sum of the internal angles is 180 °.... Thus,

Ô = 180 - 30

Ô = 60

The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60

A1 = area of the rectangle triangle

TG B = OA/AB

AB = OA / TG B

AB = 6 / TG 30

AB = 6√3

A1 = (AB . OA)/2

A1 = (6√3 . 6)/2

A2 = area of the circular sector

(rule of 3)

 º                       area

360    ------------   πR²

60     ------------    X

X = 60πR²/360

X = 6π

So,

Then the area shaded is:

A = A1 - A2

Answer:

343

Step-by-step explanation:

7^3 =

7*7*7

343

Answer:

41 inches

Step-by-step explanation:

Let the point at the top of the door on the left be x

Wx + xH = 45

Let the point at the top of the door  on the right be c

Yc + cZ = 37

We know the door is

xH +  plus the width of the tile

The width of the tile is Yc

xH + Yc

On the right door

cZ +  the height of the tile

cZ + Wx

Add the two doors together

xH + Yc + cZ + Wx = 2 times the height of the door

Rewriting

xH +  Wx +  Yc + cZ = 2 times the height of the door

45+ 37 = 2 times the door height

82 = 2 times the door height

Divide by 2

41 = door height

Answer:

the other factor is (x+7)

Step-by-step explanation:

Given x^2+11x+28

factor into

x^2+7x + 4x + 28

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

= (x+4)(x+7)

Answer: the other factor is (x+7)

Answer:

Step-by-step explanation:

Let the number be x

The product of two numbers is 16/9

That's

x × y = 16/9

One of the numbers is 5/2

That's

y = 5/2

So we have

[tex] \frac{5}{2} x = \frac{16}{9} [/tex]

Multiply through by the LCM

The LCM of 2 and 9 is 18

That's

[tex]18 \times \frac{5}{2} x = \frac{16}{9} \times 18[/tex]

9 × 5x = 16 × 2

45x = 32

Divide both sides by 45

we have the final answer as

[tex]x = \frac{32}{45} [/tex]

Hope this helps you

Answer: a=5

Step-by-step explanation:

1/12a=10/24

24a=120

a= 5

Answer:

m = 4

Step-by-step explanation:

9/6=6/m

9m = 36

m = 4

Answer:

14

Step-by-step explanation:

RS = QS - QR

RS = 17 - 3

RS = 14

Answer:

[tex]\large \boxed{14}[/tex]

Step-by-step explanation:

Point R is on the line segment QS.

QS = QR + RS

Solve for RS.

RS = QS - QR

RS = 17 - 3

RS = 14

Answer:

Chemistry

Step-by-step explanation:

To solve the above question, we use the z score formula

Andy took two Exams, Chemistry and Spanish. So we find the z score for both exams.

a) Chemistry Exam

On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

z = (45 - 30)/5

z = 15/5

z = 3

b) On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65.

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

z = (65 - 60)/6

z = 5/6

z = 0.8333333333

Comparing the z score of both Exams,

Andy had a z score of 3 in the Chemistry exam and 0.8333333333 in the Spanish exam.

Therefore, Andy should be expecting a better grade in the Chemistry exam because his z score in the Chemistry exam was higher than that of the Spanish exam.

Answer:

[tex]3^7[/tex]

Step-by-step explanation:

[tex]3^2*3^5[/tex]

[tex]\text {Apply Product Rule: } a^b+a^c=a^{b+c}\\\\3^2*3^5=3^{2+5}=3^7[/tex]

Answer:

71/84

Step-by-step explanation:

Answer:

1229/1764,  1231/1764, 179/252,  1255/1754 and 185/252.

Step-by-step explanation:

(5/6)^2 = 25/36

(6/7)^2 = 36/49

LCM of 36 and 49 is 1764

So 25/36 =   25 * 49 / 1764 = 1225/1764

and 36/49  =   36 * 36 / 1764 = 1296/1764

So the 5 rational numbers could be:

1229/1764,  1231/1764, 1253/1764 ( = 179/252),  1255/1764 and 1295/1764 (= 185/ 252).

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Let's solve your equation step-by-step.

[tex]3(x+7)-14=22[/tex]

Step 1: Simplify both sides of the equation.

[tex]3 ( x + 7 ) - 14 = 22\\(3)^(x) + (3) (7) + - 14 = 22[/tex] (Distribute)

[tex]3x + 21 + -14 = 22[/tex]

[tex]( 3x) + (21 + -14 ) = 22[/tex] (Combine Like Terms)

[tex]3x + 7 = 22\\3x + 7 = 22[/tex]

Step 2: Subtract 7 from both sides.

[tex]3x + 7 - 7 = 22 - 7 \\3x = 15[/tex]

Step 3: Divide both sides by 3.

[tex]\frac{3x}{3} = \frac{15}{3} \\x = 5[/tex]

So your answer would be : [tex]\boxed {x = 5}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

48 portions of salad

Step-by-step explanation:

4 bags spinach = 18 cherry tomatoes = 7.2 lb of chicken

7.2/.75 = 9.6 x 5 = 48

Answer:

The graph of x=4 is a vertical line parallel to y-axis and having a x-intecept:(4,0) and having no y-intercept

Step-by-step explanation:

So I think that the answer would be this, which means answer 1!! Hope this helps

The answer is option c.

Answer:

see below

Step-by-step explanation:

The formula for a geometric sequence is

an = a1 * r^ (n-1)  where a1 is the first term and r is the common ratio

The common ratio is  found by taking the second term and dividing it by the first term

a) 1, 2,4.........

a1 = 1

r = 2/1 = 2

an = 1 * ( 2) ^ (n-1)

Let n = 4

a4 = 1 * 2^ (4-1) = 1 * 2^3 = 8

b)50, 20, 8.........

a1 = 50

r = 50/20= 5/2

an = 50 * ( 5/2) ^ (n-1)

Let n = 4

a4 = 50 * (5/2)^ (4-1) = 50 * (5/2)^3 = 3125/4

Answer:

Yes this is a Triangle

36 degrees of any side then 41 would connct to 36 and 17 would connects to 36 and 41! If this is Khan Academy your asking out of its a Yes, it is a Triangle

Answer:

It is a triangle:

Step-by-step explanation:

b² = a² + c² - 2(a)(c)cos(B)  

b² = 41² + 20² - 2(41)(20)cos(36)

b² = 754.2121292

b = 27.46292281

b = 27.463

A = 41, B = 27.4, C = 17

Your answer is x + 12

Hope this helped!

Answer:

x+12

Step-by-step explanation:

Correct on test