What is the solution set to this equation?
log_4(x + 3) + log_4x = 1

Answer: x= 2/5 or x= 3

how?

Step 1: Subtract 17x from both sides

5x² + 6 -17x = 0

*PUT THEM IN ORDER* --> 5x² -17x + 6= 0

Step 2: Factor left side of equation:

(5x-2) (x-3) = 0

Step 3: Set factors equal to 0.

5x−2=0 or x−3=0

which gives us an answer of x= 2/5 or x=3

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{5x^2 + 6 =17x}\\\\\large\textsf{SUBTRACT 17x to BOTH SIDES}\\\\\mathsf{5x^2 + 6 - 17x = 17x - 17x}\\\\\mathsf{5x^2 - 17x + 6 = 0}\\\\\large\textsf{SET the LEFT SIDE to equal 0}\\\\\mathsf{(5x -2)(x -3)=0}\\\\\large\textsf{SET the FACTORS to EQUAL to 0}\\\\\mathsf{5x - 2 = 0\ or\ x - 3 = 0}\\\\\large\textsf{SIMPLIFY ABOVE AND YOU HAVE YOUR RESULT}\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf x = \dfrac{2}{3}\ or\ x = 3}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Option c is correct

Step-by-step explanation:

From the screenshot I attached.

sinA/a=SinC/c

a/c=SinA/SinC

Thus a=cSinA/SinC

Answer:

y = 0.8x – 2

Step-by-step explanation:

Slope (m) =  

ΔY/ ΔX =  4 /5 = 0.8

y=.8x+b

plug in point

b=-2

Answer:

If x is the required number, equation will be 9+4x=8

Answer:

Have you gotten the answer. if yes Hmu... Aihs I sit beside you

Step-by-step explanation:

Step-by-step explanation:

hope this helps you thank you

[tex]\boxed{ \sf{Answer}} [/tex]

[tex] \large{\sf\frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1}} [/tex]

Use the algebraic identities ⟶

Squaring on both the sides

[tex] {\sf\frac{(a + 1 {)}^{2} + ( {a - 1)}^{2} }{(a - 1)(a + 1)}} [/tex]

[tex]=\frac{ {a}^{2} + 2a + 1 + {a}^{2} - 2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} +\bcancel 2a + 1 + {a}^{2} - \bcancel2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} + {a}^{2} + 1 + 1 }{ {a}^{2} - 1}[/tex]

[tex]\large\boxed{\sf{⟹\frac{ {2a}^{2} + 2}{ {a}^{2} - 1 }}} [/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

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

Step-by-step explanation:

x = -3 & 1; f(x) = 9

f(x) = a(x-r1)(x-r2)

f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)

9 = a(3)(-1); 9 = a(-3)

a = -3

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

Answer:

f(x) = -3x^2 - 6x + 9.

Step-by-step explanation:

As the x intercepts are - 3 and 1 we can write it as:

f(x) = a(x - 1)(x + 3)    where a is a constant to be found.

As the - intercept is at (0, 9),  x =0 when f(x) = 9 so we can also write:

a( 0 - 1)(0 + 3) = 9

(-1)(3)a = 9

a = 9 / -3

= -3.

So the equation is f(x) = -3(x - 1)(x + 3)

In expanded form it is

-3(x^2 + 2x - 3)

= -3x^2 - 6x + 9.

502.5 = -502.5

Now

x = -502.5

= -5025/10

= -1005/2 feet

Answered by Gauthmath must click thanks and mark brainliest

Answer:

[tex]\angle 72=BC-86/2[/tex]

[tex]144+86=BC[/tex]

[tex]BC=230[/tex]

[tex]BC=230/2[/tex]

[tex]\angle BAC= 115[/tex]°

~OAmalOHopeO

Answer:

7/6

Step-by-step explanation:

(7x/12)/(x/2)

=7/6

Answer:

The area of D is 36 times bigger than C

Step-by-step explanation:

The scale factor is 1:6

We know the ratio of the areas is the ratio of the scale factor squared

1^2 : 6^2

1:36

The area of D is 36 times bigger than C

Answer:

[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]

Hence b^3=-1

Answer:

c part ....

please mark brainlest

For a cyclic quadilateral, the combination of opposite angles = 180°. So <G is opposite to <E so G must be 153°

Answer:

B

Step-by-step explanation:

Using the identities

sec x = [tex]\frac{1}{cosx}[/tex] , csc x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex] , then

sec²x cot²x

= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{cos^2x}{sin^2x}[/tex] ( cancel out cos²x )

= [tex]\frac{1}{sin^2x}[/tex]

= csc²x → B

Answer:

A.

[tex]{ \tt{slope = \frac{ - 4 - 2}{ - 1 - 2} }} \\ \\ = { \tt{ \frac{ - 6}{ - 3} }} \\ = 2[/tex]

Answer:

Smaller factor/larger figure = 3/6 = ½

Step-by-step explanation:

Scale factor of similar figures is usually the ratio of one to the other.

In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.

Length of smaller figure = 3

Corresponding length of larger figure = 6

Scale factor = smaller figure/larger figure = 3/6

Simplify

Scale factor = ½

Answer:

4.5, - 27, 162, - 972, 5832

Step-by-step explanation:

Using the recursive rule and a₁ = 4.5 , then

a₂ = - 6a₁ = - 6 × 4.5 = - 27

a₃ = - 6a₂ = - 6 × - 27 = 162

a₄ = - 6a₃ = - 6 × 162 = - 972

a₅ = - 6a₄ = - 6 × - 972 = 5832

The first 5 terms are 4.5, - 27, 162, - 972, 5832

Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

Answer:

y=4

Step-by-step explanation:

you multiply through by 3y^2

3y^4 - 18y^2 =30y^2

Collect like terms

3y^4=48y^2

divide through by y^2

3y^2=48

divide through by 3

y^2=16

take the square root of both sides

y=4

Answer:

4

Step-by-step explanation:

Hi there!

Range = largest number from data given - smallest number from data given

From the given data, 58, 59, 57, 59, 55,

59 is the largest number and 55 is the smallest number

So the range = 59 - 55 = 4

Answer:

4x² - 8x - 60

Step-by-step explanation:

Given :-

Simplify ,

Trinomial expression :-

The polynomial function [tex](2x-10)(2x+6)[/tex] expressed as a trinomial is [tex]4x^2 - 8x - 60[/tex].

Given data:

The polynomial function is represented as A.

Now, the value of [tex]A=(2x-10)(2x+6)[/tex].

On simplifying the equation:

From distributive property to multiply the terms:

[tex]A=2x * 2x + 2x * 6 - 10 * 2x - 10 * 6[/tex]

[tex]A=4x^2 + 12x - 20x - 60[/tex]

On simplifying the equation:

[tex]A=4x^2 - 8x - 60[/tex]

Hence, the trinomial is [tex]4x^2 - 8x - 60[/tex].

To learn more about polynomial equations, refer:

https://brainly.com/question/13199883

#SPJ6

Answer:

None.

Step-by-step explanation:

There is no expression for the square root of negative numbers. In other words it is undefined.

Answer:

4√5

Step-by-step explanation:

Answer:

$ 645.85

Step-by-step explanation:

First you would plug 6,500 into P. The plug 2.5% as 0.025 into i. And plug the years (5) into n.

A = 6500 (1 + 0.025)^5 = 7354.15

That is the amount that would be in the account at the end of the 5 years.

Then you take the cost of the car (8,000) and subtract the money left in the account (7,354.15).

8000 - 7354.15 = 645.85

Your final answer would be rounded to the nearest cent, or the hundredths place.

9514 1404 393

Answer:

  a) 30.7 million

  b) 1.5% per year

  c) 42.0 million

  d) 2017

Step-by-step explanation:

a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.

__

b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.

The population is growing by 1.5% per year.

__

c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.

  P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0

The population in Canada in 2021 is predicted to be 42.0 million.

__

d) For this we need to solve for t when P(t) = 40.

  40 = 30.7·1.015^t

  40/30.7 = 1.015^t

Taking logarithms gives ...

  log(40/30.7) = t·log(1.015)

  t = log(40/30.7)/log(1.015) ≈ 17.773

In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.

_____

Additional comment

The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.

Answer:

[tex]f(x)=\begin{cases}x^2 + 3; & \text{ } x<1 \\ -2\cdot x+5; & \text{ } x\geq 1 \end{cases}[/tex]

Step-by-step explanation:

The y-intercept (when x = 0) on the quadratic graph is 3, the upper quadratic graph does not intersect the x-axis, and the endpoint of the function has an open circle that stops at x = 1. The starting point extends to the boundaries of the graph

Therefore, the piecewise function shown in the quadratic graph is given as follows;

f(x) = x² + 3; x < 1

The straight line graph has a negative slope and starts at x = 1, with a closed circle, extending to higher values of x to the boundaries of the graph

Two points on the straight line graph are (1, 3) and (5, -5), therefore, the slope is (-5 - 3)/(5 - 1) = -2

The equation of the function is y - 3 = -2·(x - 1)

∴ y = f(x)  -2·x + 2 + 3 = -2·x + 5

f(x) = -2·x + 5; x ≥ 1

# Sin θ = 9/15.

# Cos θ = 12/15.

# Cosec θ = 15/9.

# Sec θ = 5/4

Step-by-step explanation:

[tex]by \: using \: pythagorian \: triplets[/tex]

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {9}^{2} + {12}^{2} = {c}^{2} [/tex]

[tex]81 + 144 = {c}^{2} [/tex]

[tex]225 = {c}^{2} [/tex]

[tex]c = 15.[/tex]

[tex] \sin θ = \frac{9}{15} [/tex]

[tex] \cos θ = \frac{12}{15} = \frac{4}{5} [/tex]

[tex] \csc θ = \frac{15}{9} [/tex]

[tex] \secθ = \frac{5}{4} [/tex]

Answer:

cột số 2

Step-by-step explanation:

Answer:

1. 90-68= 22

2. 90-80= 10

3. 90-3= 87

Step-by-step explanation:

A complement angle is found by their sum being 90 degrees. So, you are looking for the angle that would add to the given angle to = 90.