What is the value of f(3) in the function below? f(x) = 1/2 .2^x O A. 4 B. 2 O c. 133 3 2 D. 8​

Answer:

k = -2

Step-by-step explanation:

f(x) = (x − h)² + k

(h, k) is the (x, y) coordinate of the vertex

For a vertex of (4, -2)

h = 4

k = -2

Answer:

[tex]x = \frac{19-2y}{3}[/tex]

[tex]y=-\frac{3x+19}{2}[/tex]

Step-by-step explanation:

4x + y = 22

y = x - 3

4x + y + y = 22 + x - 3

4x + 2y = 19 + x

4x - x + 2y = 19 + x - x

3x + 2y ÷ 3 = 19 ÷ 3

[tex]x = \frac{19-2y}{3}[/tex]

[tex]y=-\frac{3x+19}{2}[/tex]

Answer:

a)Let's solve for x.

4x+y=22

Step 1: Add -y to both sides.

4x+y+−y=22+−y

4x=−y+22

Step 2: Divide both sides by 4.

4x

4

=

−y+22

4

x=

−1

4

y+

11

2

a)y=x−3

b)y=

−1

2

x+6

b)x=y-12

Answer:

[tex] y = 6 \sqrt{3} \: units[/tex]

Step-by-step explanation:

In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.

By geometric mean theorem:

Length of the perpendicular

[tex] =\sqrt{9\times 3}[/tex]

[tex] =\sqrt{27}\: units [/tex]

Next, by Pythagoras theorem:

[tex] {y}^{2} = {9}^{2} + {( \sqrt{27} )}^{2} \\ \\ {y}^{2} = 81 + 27 \\ \\ {y}^{2} = 108 \\ \\ y = \sqrt{108} \\ \\ y = \sqrt{36 \times 3} \\ \\ y = \sqrt{ {6}^{2} \times 3} \\ \\ y = 6 \sqrt{3} \: units[/tex]

Answer:

option A

Step-by-step explanation:

y = k . f( x )

• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k.

• if k < 0, the vertical stretch or shrink is followed by a reflection across the x-axis.

Given g(x ) = - |x |

                = -1 × f(x)

k < 0 , therefore the graph g (x) is a vertical shrink ( or compression ) of graph f

Answer:

5.74

Step-by-step explanation:

The value of AC in the given right triangle is 5.74 units.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) - a² + b² = c².

Given that, the right triangle ABC, AB = 4 and BC = 7.

According to Pythagoras theorem,

AC² = AB²+BC²

AC² = 7²+4²

AC = √33 = 5.74

Hence, The value of AC in the given right triangle is 5.74 units.

For more references on Pythagoras theorem, click;

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Answer:

below

Step-by-step explanation:

a.. it divides the triangle into two equal parts

b.. it is an isosceles triangle

c.. the base line of a mid point are equal

d.

g. two angles are equal in isosceles triangle

Answer: [tex]\dfrac{6}{26}[/tex]

Step-by-step explanation:

Given

Denominator is 4 more than twice its numerator

Suppose the numerator is x. So, it follows above condition, fraction becomes

[tex]\Rightarrow \dfrac{x}{2x+4}[/tex]

If both numerator and denominator are reduced by 6, they become equal

[tex]\Rightarrow 12(x-6)=2x+4-6\\\Rightarrow 12x-72=2x-2\\\Rightarrow 10x=70\\\Rightarrow x=7[/tex]

The fraction is

[tex]\Rightarrow \dfrac{x}{4x+2}=\dfrac{6}{4\times 6+2}\\\\\Rightarrow \dfrac{6}{26}[/tex]

Answer: 68,819 rabbits

Step-by-step explanation:

First find the annual rate of growth that took the number of rabbits from 9,400 in 1998 to 32,000 in 2006.

Use the future value formula:

Number of years = 2006 - 1998 = 8 years

Future value formula:

Future value = Current value * ( 1 + rate) ^ number of years

Assume 2006 is the future and 1998 is present.

32,000 = 9,400 * (1 + r) ⁸

32,000 / 9,400 = (1 + r)⁸

(1 + r)⁸ = 3.404255319

1 + r = ⁸√3.404255319

r = ⁸√3.404255319 - 1

r = 16.55%

Use that rate to find the number of rabbits in 2011:

= Current value * (1 + rate) ^ number of years

Number of years = 2011 - 2006 = 5 years

= 32,000 * ( 1 + 16.55%)⁵

= 68,819 rabbits

Answer:

the equation as intercept form is

y = 3x + 5

Answer:

20

Step-by-step explanation:

L times W

length times width

so 5 x 4 = 20

Answer:

Fluffy is longer than Muffy

Step-by-step explanation:

There are 1000 millimeters in a meter

Fluffy = 2000 millimeters

Muffy = 900 millimeters

Fluffy is longer than Muffy

2000 > 900

If my answer is incorrect, pls correct me!

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-Chetan K

Fluffy is longer than Muffy

There are 1000 millimeters in a meter

There are 1000 millimeters in a meterFluffy = 2000 millimeters

There are 1000 millimeters in a meterFluffy = 2000 millimetersMuffy = 900 millimeters

There are 1000 millimeters in a meterFluffy = 2000 millimetersMuffy = 900 millimetersFluffy is longer than Muffy

There are 1000 millimeters in a meterFluffy = 2000 millimetersMuffy = 900 millimetersFluffy is longer than Muffy2000 > 900

Given:

Consider the expression is:

[tex]\sqrt{-9}[/tex]

To find:

The equivalent expression.

Solution:

We have,

[tex]\sqrt{-9}[/tex]

It can be written as:

[tex]\sqrt{-9}=\sqrt{-1\times 9}[/tex]

[tex]\sqrt{-9}=\sqrt{-1}\times \sqrt{9}[/tex]

[tex]\sqrt{-9}=i\times 3[/tex]                 [tex][\because \sqrt{-1}=i][/tex]

[tex]\sqrt{-9}=3i[/tex]

The expression [tex]3i[/tex] is equivalent to the given expression.

Therefore, the correct option is A.

Answer:

15 weeks

Step-by-step explanation:

First, calculate the total that is needing to be saved not including the money she already has.

So 700 minus 175 is 525.

Next, to find the number of weeks, divide 525 by 35 which gives you 15 even.

So if Kalon continues to save $35 a week, it will take him 15 weeks to reach his goal of $700.

Answer:

4/12

Step-by-step explanation:

add up all the marbles, and take how many blue marbels there are and put both numbers in fraction form

Answer:

scale factor is 3/2

YZ=15

JL=12

Step-by-step explanation:

JK=XY

ZY=LK

XZ=JL

15/10=3/2 (scale factor)

3/2=x/10

now cross multiply

30/2=2x/2

15=x or YZ

3/2=18/y

cross multiply

3y/3=36/3

JL or y=12

Answer:

x=-20

Step-by-step explanation:

x=-10•2

• means multipled

Answer: x=2

Step-by-step explanation:

15x-10=10 + 6+ 2x

15x-2x=20+6

13x=26

X=2

Answer:

x = 2

Step-by-step explanation:

2.5(6x - 4) = 10 + 4(1.5 + 0.5x)

Distribute the 2.5

15x - 10 = 10 + 4(1.5 + 0.5x)

Distribute the 4

15x - 10 = 10 + 6 + 2x

Combine like terms

15x - 10 = 16 + 2x

Add 10 to both sides

15x = 26 + 2x

Subtract 2x from both sides

13x = 26

Divide both sides by 13x

x = 2

Answer:

3.32+8÷2-(4+3)

=3.32+8÷2-7

=3.32+4-7

=7.32-7

=0.32

this is the correct answer but unfortunately it's not in the options, maybe you need to check the options again :)

Answer:

1260

hope this helps

have a good day :)

Step-by-step explanation:

Step-by-step explanation:

2 x 2 x 3 x 3 x 5 x 13

= 2340

................

9514 1404 393

Answer:

Step-by-step explanation:

A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.

OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.

__

As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.

Answer:

261.5 ft^2

Step-by-step explanation:

Surface Area of a rectangular prism = Length x Width x Height

= 8.5ft x 6ft x 5.5ft

= 261.5 ft

Answer:

62.8

Step-by-step explanation:

The formula of finding the volume of a cylinder v= pi*r^2*h

So substitute the values:

r is 2, and h is 5

v=pi*2^2*5

Then solve the equation:

v=pi*4*5

v=pi*20

v=62.8 (I multiplied 20 by 3.14, or pi)

So the answer is 62.8

Answer:

87.95479

Step-by-step explanation:

10.3% of 853.93 km

Expand 10.3÷100 by multiplying both numerator and denominator by 10.

[tex] \small \sf \frac{10.3 \times 10}{100 \times 10} = 853.93 \\ [/tex]

[tex] \small \sf \frac{103}{1000} = 853.93 \\ [/tex]

convert decimal number 853.93 to fraction 85394÷100

[tex]\small \sf \frac{103}{1000} = \frac{85393}{100} \\[/tex]

Multiplying 103÷1000 and 85393÷100 by numerator times numerator and denominator times denominator.

[tex]\small \sf \frac{103 \times 8539 3}{1000 \times 100} \\[/tex]

Do the multiplication in the fraction

[tex]\small \sf \frac{8795479}{100000} \\ [/tex]

Divide we get

87.95479

Another way to solve it

10.3% 853.93

we know that ; % = whole no. ÷ 100

then,

10.3 ÷ 100 × 853.93

Divide the numbers

0.103 × 853.93

multiply the numbers

87.95479

Given:

The height, in feet, of each rocket at t seconds after launch is given by the polynomial equations:

Rocket A: [tex]-15t^2+100t[/tex]

Rocket B: [tex]-14t^2+85t+3[/tex]

To find:

The equation to find the "difference" in height of Rocket A and Rocket B.

Solution:

The difference in height of Rocket A and Rocket B is:

Difference = Height of Rocket A - Height of Rocket B

[tex]\text{Difference}=(-15t^2+100t)-(-14t^2+85t+3)[/tex]

[tex]\text{Difference}=-15t^2+100t+14t^2-85t-3[/tex]

[tex]\text{Difference}=(-15t^2+14t^2)+(100t-85t)-3[/tex]

[tex]\text{Difference}=-t^2+15t-3[/tex]

Therefore, the difference in height of Rocket A and Rocket B is [tex]-t^2+15t-3[/tex].

Hope this helps please mark me brainliest

Answer:

x = -3

Answer:

60 cm^2

Step-by-step explanation:

let are of big figure be x .

area of small figure / area of big figure = 15 / 18

50/x = 15/18

do cross multiplication

x*15 = 18*50

x = 900/15

x = 60 cm^2

Answer:

(x + 7)² + (y - 1)² = 1

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 7, 1) and r = 1 , then

(x - (- 7) )² + (y - 1)² = 1² , that is

(x + 7)² + (y - 1)² = 1