Find y please help !!!

Answer:

[tex]3^2=x+5[/tex]

Step-by-step explanation:

Given equation:

[tex]\log_3(x+5)=2[/tex]

Method 1

[tex]\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b[/tex]

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^2=x+5[/tex]

Method 2

Make both sides of the equation the index to base 3:

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^{\log_3(x+5)}=3^2[/tex]

Apply the log law [tex]a^{\log_ax}=x[/tex] :

[tex]\implies x+5=3^2[/tex]

Swap sides:

[tex]\implies 3^2=x+5[/tex]

Solve for x

Although the question hasn't asked to solve for x, here is the solution:

[tex]\implies 3^2=x+5[/tex]

[tex]\implies 9=x+5[/tex]

[tex]\implies x=9-5[/tex]

[tex]\implies x=4[/tex]

Check

Substitute the found value of x into the original equation:

[tex]x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}[/tex]

[tex]\\ \rm\Rrightarrow log_3(x+5)=2[/tex]

[tex]\\ \rm\Rrightarrow x+5=3^2[/tex]

[tex]\\ \rm\Rrightarrow x+5=9[/tex]

[tex]\\ \rm\Rrightarrow x=9-5[/tex]

[tex]\\ \rm\Rrightarrow x=4[/tex]

Answer:

All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are  ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex] by using rational zeroes theorem.

Step-by-step explanation:

Rational zeroes theorem gives the possible roots of polynomial f(x) by taking ratio of p and q where p is a factor of constant term and q is a factor of the leading coefficient.

The polynomial f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex]

Find all factors (p) of the constant term.

Here we are looking for the factors of 4, which are:

±1 , ±2 and ±4

Now find all factors (q) of the coefficient of the leading term

we are looking for the factors of 3, which are:

±1 and ±3

List all possible combinations of ± [tex]\frac{p}{q}[/tex]  as the possible zeros of the polynomial.

Thus, we have ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex] as the possible zeros of the polynomial

Simplify the list to remove and repeated elements.

All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are  ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex]

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Work Shown:

|x+2| + 7 > 10

|x+2| > 10-7

|x+2| > 3

x+2 > 3 or x+2 < -3

x > 3-2 or x < -3-2

x > 1 or x < -5

The graph for x > 1 has an open circle at 1 and shading to the right.

The graph for x < -5 has an open circle at -5 and shading to the left

Both of these facts combine to describe Choice C

In other words, we have open circles at -5 and 1, with nearly everything shaded except for the region between the open circles.

The open circles are used to exclude those x values mentioned.

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{1}{r^4^2}[/tex]  (option B)

Step-by-step explanation:

[tex]\left(a^b\right)^c=a^{bc},[/tex]

So, we need to first multiple -7 × 6 (= -42)

our new value is [tex]r^{-42\\}[/tex]

[tex]\:a^{-b}=\frac{1}{a^b}[/tex]

So, we simplify [tex]r^{-42\\}[/tex] to [tex]\frac{1}{r^4^2}[/tex]

Answer:

that makes no sence at all i read it over 3 times and still font understand a word of it

sorry :(

The average rate of change for this function for the interval from x = 2

to x = 4 is 20

The function is given as:

x   y

0  18

2   32

3    50

4   72

The average rate of change at the interval from x = 2 to x = 4 is calculated using:

m = (f(4) - f(2))/(4 - 2)

Using the table values, we have:

m = (72 - 32)/(4 - 2)

Evaluate

m = 20

Hence, the average rate of change is 20

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Answer:

D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens

r = 14 miles / hour

Problem

Convert to feet per second.

Solution

Later on, you will learn how to solve these kinds of conversion problems using a method called Unit Analysis. Since you likely have not been taught this method, will just use proportions.

1 mile = 5280 feet

14 miles = x                          Cross multiply

x = 14 * 5280                       Simplify

x = 73920 feet

1 hour = 3600 seconds

Answer

r = 73920 feet / 3600 seconds

r = 20.533 feet  / secpmd

Example:

[tex](f+g)(x)=f(x)+g(x)[/tex]

To add this, we can substitute in the functions and combine like terms.

We're given:

Add k to k:

[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]

Input x as 4:

[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]

[tex](k+k)(4)=28[/tex]

(k+k)(4) is equivalent to 28.

If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.

Addition of two functions : If f(x) & g(x) be two functions, then

(f+g)(x) = f(x)+g(x)

Given, k(x) = 5x-6

Now, Adding function k with k we get,

(k+k)(x) = k(x)+k(x)

           = (5x-6)+(5x-6)

           = 5x-6+5x-6

           = 10x-12

We have to find, (k+k)(4)

∴  (k+k)(4) = (10×4)-12

                = 40-12

                = 28

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Answer:

22/7

Step-by-step explanation:

22/7 is not very close to pi, but it is sometimes used as an estimation for pi

Answer:

22/7 is estimation

Answer:

m3+5

Step-by-step explanation:

m is miles

take the number of miles  multiply by3

take that answer add 5

The equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

A statement that relate two expressions with an equal sign is called an Equation.

It is given that

A cab company charges a $5 boarding

Charges for every mile is $3 per mile

Let x be the mile travelled

The cab's total charge is represented by y

then y = 3x + 5

Therefore the equation that represents the cab's total charge is  y = 3x + 5 , Option A is the correct answer.

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Answer:

x = [tex]\frac{172-2y}{6}[/tex]

Step-by-step explanation:

6x + 2y + 8 = 180 ( subtract 8 from both sides )

6x + 2y = 172 ( subtract 2y from both sides )

6x = 172 - 2y ( divide both sides by 6 )

x = [tex]\frac{172-2y}{6}[/tex]

Step-by-step explanation:

Anything which has a decimal point is not a whole number

6830 is

66 is

717.59 is not

808 is

42.3 is not

1/10 = 0.1 ergo is not

Answer:

Sum of all the angles of a triangle = 180° ( angle sum property).

Angle D + Angle E + Angle F = 180°

8x - 1 + 5x + 90° = 180°

8x + 5x + 89 = 180

13x = 180 - 89

13x = 91

x = 7.

Angle D = 8x - 1

= 8(7)-1

= 56 - 1

= 55

Angle E = 90° ( given)

Angle F = 5x

= 5 * 7

= 35

Answer:

m∠E: 90°

m∠D: 55°

m∠F: 35°

Step-by-step explanation:

Since the interior angles of a right triangle sum up to 180°, the sum of angles D, E, F will equal 180°. We can then form an equation from that information.

[tex]90+(8x-1)+5x=180\\13x-1=90\\13x=91\\x=7[/tex]

From this, we can plug in the variable.

[tex]mE=90\\mD=55\\mF=35[/tex]

Answer:

(3, 0) and (−1, −8)

Equation's:

2x − (x² − 9) = 6

2x - x²  + 9 = 6

-x² + 2x + 9 - 6 = 0

-x² + 2x + 3 = 0

x² - 2x - 3 = 0

x² - 3x + x - 3 = 0

x(x - 3) + 1(x - 3) = 0

(x + 1)(x - 3) = 0

x = -1, x = 3

If x = -1, then y = (-1)² - 9 = -8

If x = 3, then y = (3)² - 9 = 0

(x, y) = (-1, -8), (3, 0)

It is wider and shifted 3 units to the left , Option A is the right answer.

Function is a mathematical statement that shows relation between two variables.

The parent function given is

f(x) = |x|

The transformed function is given by

f(x) = 0.1|x -3|

The function is shifted towards the left

and as the scale factor is 0.1 therefore , It is wider

Therefore Option A is the right answer.

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Answer:

The answer for this is B.

Step-by-step explanation:

Figured it out the hard way on EDGE. 2022

(╯‵□′)╯︵┻━┻

Answer:

x is approximately 20.89

Step-by-step explanation:

cos(40°) = 16/x

x cos(40°) = 16

x = 16 / cos(40°) = 16/.766 = 20.89

The approximate value of x in the diagram is,

⇒ x = 20.77

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We can formulate by the given figure;

⇒ sin 50° = 16 / x

⇒ 0.77 = 16 / x

⇒ x = 16 / 0.77

⇒ x = 20.77

Thus, The approximate value of x in the diagram is,

⇒ x = 20.77

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The area of a trapezium with base 8 top 6 height 4 is 28 cm².

Given that, base of trapezium (b)=8 cm, top of trapezium (a)=6 cm and height of trapezium = 4 cm.

What is the area of a trapezium?

The trapezium is a quadrilateral with pair of sides parallel. The area of a trapezium is the area enclosed within its four sides.

We know that area of a trapezium [tex]=\frac{1}{2}(a+b) \times h[/tex]

Where a and b are parallel sides of a trapezium.

Now, the area of a given trapezium [tex]=\frac{1}{2}(6+8) \times 4[/tex] cm²

=14×2=28 cm²

Therefore, the area of a trapezium with base 8 top 6 height 4 is 28 cm².

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Answer: [A] addition property of equality

Step-by-step explanation:

    Mitch used the addition property of equality because he added 43 to both sides of the equation.

         75r - 43 = 332

         43 + (75r - 43) = (332) + 43

         75r = 375

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The 2 colors can be chosen in 6 different ways.

Here we need to identify the selections and the numbers of options for each.

Here the selections are:

And the numbers of options for each are:

The total number of combinations is:

C = 3*2 = 6

The 2 colors can be chosen in 6 different ways.

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Answer: Yes.

Step-by-step explanation: However, charging your battery to high voltages except for the first time can significantly decrease your battery's lifespan. According to some studies charging a battery to only 85% to 90% can improve its discharge cycle from 300 to even an extra 1000 recharges.

Answer:

  -5

Step-by-step explanation:

Substituting x=4 into the equation gives a 2-step linear equation in y. It is solved by isolating the variable and making its coefficient be 1.

__

When x=4, the equation becomes ...

  -3x +9y = -57

  -3(4) +9y = -57

  -12 +9y = -57

The first step is to "isolate" the variable term (9y) by adding the opposite of the constant that is on the same side of the equation. The result is that the variable term is by itself on one side of the equal sign.

  -12 +12 +9y = -57 +12 . . . . . add the opposite of -12

  9y = -45 . . . . . . . . . . . . . . simplify

The second step is to make the coefficient of y be 1. We do that by multiplying by its inverse, 1/9. Equivalently, we divide by 9.

  (1/9)(9y) = (1/9)(-45) . . . . multiply by the inverse of 9

  y = -5 . . . . . . simplify

Yes, by using the factor theorem and synthetic division method, x + 3 is a factor of -x³ + 4x - 15.

According to the factor theorem, a given polynomial of f(x) has a factor if and only if f=0.

From the given information:

Using the synthetic division method:

[tex]\mathbf{= \dfrac{-x^3+4x - 5}{x+3} }[/tex]

[tex]\mathbf{\implies \dfrac{-(x+3) (x^2-3x + 5)}{x+3} }[/tex]

Cancel out the common factors, we have:

[tex]\mathbf{\implies - (x^2-3x + 5)}[/tex]

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The long leg and the hypotenuse of the isosceles right triangle will be 7.07 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The short leg of a 90-45-45 triangle is 5.

The right triangle is an isosceles right triangle. Then the two side will be same.

Then the long leg and the hypotenuse will be

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 7.07 units

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185.4m  (rounded to 1dp)

Circumference of a circle is the diameter times by pi. 59×pi=185.4

Answer:

59 meters

or approximately 185.26 ( using 3.14 for pi)

or 185.3539666 meters using the pi button

Step-by-step explanation:

The circumference is given by

C = pi *d where d is the diameter

C = pi * 59 m

C = 59 pi meters

We can approximate pi by 3.14

C =185.26 meters

or by using the pi button the calculator

185.3539666 meter

D

Step-by-step explanation:

The points dx are at -1, 1, 2 and 3 so it must be D

Answer:

To find the range,

first see the value of each points -

first = (3,5)

second = (2,0)

third = ( 1,3)

fourth, ( -1, 2)

let's take X Axix to find the range

so the range is ( -1, 1 , 2 ,3)

Option D is correct

The half life of the radioactive substance is 10.22 years.

Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).

It is given that

y = ae⁻ᵇˣ

here a is the initial amount , y is the amount remaining after x years

a = 90mg at x =0

Value of y = 12.6 mg at x = 29 years

On substitution of value

12.6 = 90 e⁻²⁹ᵇ

0.14 = e⁻²⁹ᵇ

b = 0.0678

The equation is

[tex]\rm y = 90 e^{-0.0678 * x}\\[/tex]

Half life is when the concentration is reduced to half

On 1st half life , the concentration = 90/2 = 45 mg

[tex]\rm 45 = 90 e^{-0.0678 * x}\\[/tex]

x = 10.22 years

Therefore the half life of the radioactive substance is 10.22 years.

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Answer:

1/7

Step-by-step explanation:

Alternative Form: 0.142857, 7^-1

Answer:

445

Step-by-step explanation:

I think it is 445 because each term is +1 and time is the number of terms you want to find.

So

(2+1) time 2 = 6

(6+1) time 3 = 7

(88+1)  time 5 = 445