f(x)=-x2+1 what’s f(2) ?

Answer:

x = [tex]\frac{ln(16)}{ln(2)}[/tex]

Step-by-step explanation:

[tex]4^{2x-1} =8^{x+2}[/tex]

ln both sides like you would add the same number to both sides to keep the equation equivalent

[tex]ln4^{2x-1} = ln 8^{x+2}[/tex]

using log rules, exponents can be brought down as a constant multiplying ln

[tex](2x-1)ln(4) =(x+2)ln(8)[/tex]

use distributive property to remove parentheses

2xln(4) - ln(4) = xln(8) + 2ln(8)

isolate x

2xln(4) - xln(8) = 2ln(8) + ln(4)

rewrite the logs using log rules: ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex]) and the exponent rule stated above

xln([tex]4^{2}[/tex])-xln(8) = ln([tex]\frac{8^{2} }{4}[/tex])

factor out x

x(ln[tex]4^{2}[/tex]-ln8) = ln([tex]\frac{8^{2} }{4}[/tex])

again use log rules:  ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex])

x* [tex]ln(\frac{4^{2} }{8}[/tex][tex])[/tex]=  ln([tex]\frac{8^{2} }{4}[/tex])

now simplify the stuff inside the ln parentheses

x*ln(2) = ln(16)

x = [tex]\frac{ln(16)}{ln(2)}[/tex]

Answer: multiplies

Explain: this is because exponentially is multiplication.

The table of exponential multiplies by the same amount each time to get to the next number.

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

In another meaning, an exponential function is that function above which a variable x has imposed.

For example [tex]3^{x}[/tex] , [tex]7^{x}[/tex] like that.

Let a general exponential function [tex]a^{x}[/tex] where a is constant.

Let x = 1,2,3,4,5....

At x = 1 ⇒ a¹ = a

At x = 2 ⇒ a² = a × a = previous numebr ×  (a)

At x = 3 ⇒ a³ = a² × a = previous number × (a)

So,

It is clear that in exponential function each term multiplies the same amount each time to get to the next number.

For more about exponential function,

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Answer:

4/5

Step-by-step explanation:

Since the total of all the balls are 2 + 5 + 3 = 10

The probability of choosing not a red ball is (5 + 3)/10 which is 8/10 or 4/5

The easier way is to go like this:  1 - 1/5 = 4/5

Answer:  4/5

Answer:

4/5

Step-by-step explanation:

If the probability of choosing a red ball is 1/5, then the probability of this not happening is 1 - 1/5, or 4/5.

Answer:

SU = 26 meters

Step-by-step explanation:

Based on the definition of a parallelogram, we know that the diagonals bisect each other, so we know that:

UV = VS

x + 3 = 2x - 7

10 = x

Now that we know "x", we can find the length of SU:

SU = x + 3 + 2x - 7

SU = (10) + 3 + 2(10) - 7

SU = 13 + 20 - 7

SU = 33 - 7

SU = 26 meters

Answer:♣ = Vertical angles theorem

♦ =SAS

♠ =CPCTC

Step-by-step explanation:

Answer: _(32)(16)=(4)/(5)

Step-by-step explanation:

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

since [tex]\frac{5}{8}[/tex] has been completed

the remaining would be :

[tex]\frac{8}{8} -\frac{5}{8}[/tex]

since denominators are the same

= [tex]\frac{8 - 5}{8} \\\\[/tex]

= [tex]\frac{3}{8}[/tex]

the fraction of the race that is remaining is 3/8

Answer:

There are 13 cards for each suit so the first fraction is 13/52 and the next one is 13/51 as there is no replacement for the first card you pulled.

Multiplying them you get: 13/52*13/51= 169/2652,

Then you divide both sides by 13 to get: 13/204

So, the answer is C.

I hope this helps!

The probability of drawing a club and then a diamond consecutively from the deck without replacement is 13/204.

Option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of cards = 52

Number of clubs = 13

Number of diamonds = 13

Now,

The probability of drawing a club.

= 13/52

And,

The probability of drawing a diamond consecutively from the deck without replacement.

= 13/51

[ There will be only 51 cards in total since we are not replacing ]

Now,

The probability of drawing a club and then a diamond consecutively from the deck without replacement.

= 13/52 x 13/51

= 13/4 x 1/51

= 13/204

Thus,

13/204 is the probability of drawing a club and then a diamond consecutively from the deck without replacement.

Learn more about probability here:

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Answer:

-9

Step-by-step explanation:

-8 - -3 equals -5, -5 - (+2) so just do -5 + 2 because the + 2 is in parenthesis and that means to do that first so that will equal -3, -3 - (6) = -9

Answer:

Perimeter = 63.9 cm.

Area = 166.96 cm^2 to the nearest hundredth.

Step-by-step explanation:

The perimeter = 16+20.9+27 = 63.9 cm.

To find the area you can use Heron's Formula.

Area = √ [ s(s-a)(s-b)(s-c)]  where  s = the semi-perimeter and a, b and c are the lengths of the 3 sides.

s = 63.9 / 2 =  31.95.

Area of the triangle = √ (31.95(31.95-16)(31.95-20.9)(31.95-27)]

 = 166.96 cm^2.

Answer:

Option B, i

Step-by-step explanation:

sqrt(-1) is i

Answer:  Option B, i

Answer: i got this square root(negative 1) =

i

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number be n.

Then:

99 + n > 199

if you wish to solve this, subtract 99 from both sides, obtaining n > 100

Answer:

15

Step-by-step explanation:

2:3

X2 4:6

X5 10:15

Answer:

15 miles

Step-by-step explanation:

Divide 10 by 2, which equals 5. This gives you the amount of times she walks. Thus, if you multiply 3 miles times 5 (the amount of times she walks) it equals 15.

Answer:

f(4) = 11

Step-by-step explanation:

To evaluate f(4) substitute x = 4 into f(x)

f(4) = 3(4) - 1 = 12 - 1 = 11

Answer:

550

Step-by-step explanation:

so we know that 17% of everyone who applies (3,240) will be accepted.

0.17*3,240= 550.8

550 students will be accepted

we have to round down as only 17% can be accepted and u cant have 0.8th of a person

hope this helps

The right answer is Option C: 3 units

Step-by-step explanation:

Given coordinates are;

A polygon has the following coordinates: A(3,-3), B(-3,-2), C(-5,1), D(-5,4), E(-4,6), F(-2,6), G(3,2).

For finding length of CD, we will find the distance between C and D.

C(-5,1) and D(-5,4)

Here;

[tex]x_1=-5, y_1=1\\x_2=-5, y_2=4[/tex]

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

[tex]Distance=\sqrt{(-5+5)^2+(4-1)^2}\\Distance=\sqrt{(0)^2-(3)2}\\Distance=\sqrt{(3)^2}\\Distance = 3[/tex]

Therefore;

The length of CD is  units.

The right answer is Option C: 3 units

Answer:

2

Step-by-step explanation:

The answers to the blanks are

1. 600,

2. 120,

3. 120,

4. 180.

Explanation:

To find the length of the hypotenuse in Bill's right triangular garden, the Pythagorean theorem is used with the sides measuring 24 and 25 feet. The calculation shows that the hypotenuse is 35 feet.

Bill is planning a right triangular garden with two perpendicular sides measuring 24 and 25 feet. To find the length of the other side, which is the hypotenuse, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The formula is expressed as:

c2 = a2 + b2

Plugging in the values provided:

c2 = 242 + 252

c2 = 576 + 625

c2 = 1201

To find the length of the hypotenuse, we take the square root of 1201:

c = [tex]\\(sqrt{1201}\\[/tex]

Since 1201 is a perfect square, c = 35

Therefore, the length of the hypotenuse of the garden is 35 feet.

We can use the Copy Dot Flip Method to solve this.

Steps to solve:

1 3/4 ÷ 2/3

~Turn 1 3/4 into an improper fraction

1 3/4 = 7/4

~Change the symbol and flip 2/3

7/4 * 3/2

~Multiply both numerators and denominators

21/8 or 2 5/8

Best of Luck!

Answer:

21/8 or 2 5/8

Step-by-step explanation:

1 3/4 ÷ 2/3

Convert to improper fractions

7/4 ÷ 2/3

Find the reciprocal of 2/3 and multiply

7/4 * 3/2

Multiply (numerator * numerator) / (denominator * denominator)

21/8

Convert to a mixed fraction

2 5/8

Hope this helps :)

Answer:

20-8 = 12 , he waste $12 if he got 4 cans 12 divide by 4 equal 3 so the one can cost $3

Step-by-step explanation:

Answer:

18 servings

Step-by-step explanation:

Because 6 divided by 1/3 is the same as 6*3, we can just do it that way so it makes more sense.

6*3= 18

And there you have your answer!

Answer:

It's choice A.

Step-by-step explanation:

Kevin is 3 years older than Daniel gives:

k = d + 3.

2 years ago kevin is  aged k - 2 and daniel d - 2  years.

So:

k - 2 = 4(d - 2).

Answer:

300

Step-by-step explanation:

Let the number be X

62/100 × X = 186

X = 186 × 100/62

X = 300

Answer: 62% of 300 is 186

Step-by-step explanation:

62% of x = 186

62/100 x = 186

0.62x=186

×=300

The fish is 2.25 ft above the water surface.

Step-by-step explanation:

⇒ y = -16(0.375)² + 12 × 0.375

     = -2.25 + 4.5

     = 2.25 ft

Answer:

the answer for this is 80 m^3

Answer:

40 and 60

Step-by-step explanation:

the answers are 40 and 60

Answer:

First column is 40, and the second one is 60

Step-by-step explanation:

Got it right on edge:)

Answer:

2.3 is the answer

Step-by-step explanation:

Name the unknown package n

[1.8 + 3.2 + 2.7 + n]/4 = 2.5

[7.7 + n] = 2.5 × 4

7.7 + n = 10

n = 10 - 7.7

n = 2.3

Answer:

2 hours.

Step-by-step explanation:

There is no way a car can travel 100 miles away in minutes or seconds, and 70 minutes seems ridiculous. Although there are some exceptions, the best answer is two hours.

Answer:

-5.238

Step-by-step explanation:

Step 1:  First multiply

1.567 + 2.345 - 1.83(5)

1.567 + 2.345 - 9.15

Step 2:  Add the first two numbers

(1.567 + 2.345) - 9.15

3.912 - 9.15

Step 3:  Add the next two numbers

3.912 - 9.15

-5.238

Answer:  -5.238

Answer:

-5.238

Step-by-step explanation:

1.567+2.345=3.912-1.83(5)=