log subscript-4 (m^2)=log subscript-4 (18-7m)?

Answers

Answer 1

Answer:

m = {-9, 2}

Step-by-step explanation:

log₄ (m²) = log₄ (18 - 7m)

18 - 7m > 0 ⇒ 7m < 18 ⇒ m < 18/7

m² = 18 - 7mm² + 7m - 18 = 0m² + 2*3.5m + 12.25 = 30.25(m + 3.5)² = 5.5²m = - 3.5 ± 5.5m = 2 m = -9
Answer 2

Answer:

[tex] \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9[/tex]

Step-by-step explanation:

we are given a logarithm equation

[tex] \displaystyle \log_{4}( {m}^{2} ) = \log_{4}(18 - 7m) [/tex]

notice that, we have [tex]\log_4[/tex] both sides therefore we can get rid of it

[tex] \displaystyle {m}^{2} = 18 - 7m[/tex]

in order to solve it we should make it standard form we know that

[tex] \displaystyle a {x}^{2} + bx + c = 0[/tex]

so right hand side expression to left hand side and change its sign:

[tex] \displaystyle {m}^{2} + 7m- 18=0[/tex]

now we can solve it by using factoring method

to do so rewrite the middle term as sum or subtraction of two different terms

in that case -2m+9m is good to use

[tex] \displaystyle {m}^{2} - 2m + 9m - 18 = 0[/tex]

factor out m:

[tex] \displaystyle m({m}^{} - 2 )+ 9m - 18 = 0[/tex]

factor out 9:

[tex] \displaystyle m({m}^{} - 2 )+ 9(m - 2)= 0[/tex]

group:

[tex] \displaystyle (m - 2)(m + 9) = 0[/tex]

hence,

[tex] \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9[/tex]

remember that,

when we deal with logarithm equation we should always check the roots

let's check the root 1:

[tex] \displaystyle \log_{4}( {2}^{2} ) \stackrel{?}{=} \log_{4}(18 - 7.2) [/tex]

simplify square:

[tex] \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(18 - 7.2) [/tex]

simplify multiplication:

[tex] \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(18 - 14) [/tex]

simplify substraction:

[tex] \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(4) [/tex]

simplify logarithm:

[tex] \displaystyle 1 \stackrel{ \checkmark}{=} 1[/tex]

let's check root 2:

[tex] \displaystyle \rm \log_{4}( { - 9}^{2} ) \stackrel{?}{=} \log_{4}(18 - 7.( - 9)) [/tex]

simplify square:

[tex] \displaystyle \rm \log_{4}( 81 ) \stackrel{?}{=} \log_{4}(18 + 63) [/tex]

simplify addition:

[tex] \displaystyle \rm \log_{4}( 81 ) \stackrel{ \checkmark}{=} \log_{4}(81) [/tex]

therefore,

[tex] \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9[/tex]


Related Questions

does anyone know the answer?? i’ll mark brainlists

Answers

I’d say D as the answer

It costs Eduardo 2 d 3 dollars to go to the carnival for d days. How many dollars does the carnival cost if Eduardo goes for d 5 days?

Answers

Answer:

$250

Step-by-step explanation:

Given:  Cost for d days carnival = $2d^3 .....(i)

where d is number of days

Now we have to calculate the total cost incured for 5 days of carnival

we can simply put d = 5 in above equation (i)

= 2×5^3 = 2×125 = $250.

Therefore carnival cost if Eduardo goes for d 5 days = $250

Find the area of the right triangle.

Answers

54 is th answer because ther is 6 units on one side and 9 units in the other and when you times you get this I think

Answer:

[tex] \frac{1}{2} \times 9 \times 6 = 27 \\[/tex]

You have to count the units then put the rule

[tex] \frac{1}{2} \times base \: \times hight[/tex]

I need help finding the answer!

Answers

Answer: x=4

Step-by-step explanation:

Since this is a rectangle we already know that all the angles are 90, so we can do this:

46+10x+4=90

50+10x=90

10x=40

x=4

HELPP!!!!!!!!!!!!!!!!

Answers

Answer:

D.4 3/4

Step-by-step explanation:

hope it helps you

What is the value of x in the
equation below?
5x +9= 74

Answers

The answer is 13 because 74-9= 65. 65/5 = 13

HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP

Answers

Answer and Step-by-step explanation:

Let's put the information given into equations.

Let's also denote x as individual songs and y as albums.

Charlene -  6x + 2y = 25.92

Keisha -  4x + 3y = 33.93

Those above equations is answer choice option, which is D.

So, D is the correct Answer.

#teamtrees #PAW (Plant And Water)

f(x) = 3 x e^2x
That's the problem​

Answers

Answer:

6 e (*2)x

Step-by-step explanation:

i hope this helps and the 2 is a square unit

Answer:

y = 0

Step by step explanition:

I want its solution and the unit is about algebraic fraction.

Answers

Answer:

3x²/(3x - 9y)

This should be the simplest form.

Step-by-step explanation:

Combine the fractions:

(5x² - 2x²)/((6x - 6y) - (3y - 3x))

Combine like terms:

3x²/(6x - 3x - 6y - 3y)

Solve.

3x²/(3x - 9y)

Answer:

9x^2      

======

6(x - y)

Step-by-step explanation:

Begin by switching the - to a plus. Switch the x and y in the second denominator.

5x^2              2x^2

=====      +    ======

6x - 6y          3x - 3y

Pull out the common factors in both denominators. Use the distributive property.

5x^2              2x^2

=====      +    ======

6(x - y)          3(x - y)

Multiply both the numerator and denominator by 2 on the left had fraction.

5x^2              2*2x^2

=====      +    ======

6(x - y)          2*3(x - y)

5x^2                4x^2

=====      +    ======

6(x - y)          6(x - y)

Put both numerators over a common denominator. Notice that the + sign shifts up.  It shifts up because both fractions have been changed to a common denominator.

5x^2        +        4x^2

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

          6(x - y)

Combine the two numerators since they are of the same power.

9x^2      

======

6(x - y)

please help me with this math problem, the question is on the picture that i attached, ill mark brainliest if the answer is correct. NO links!

Answers

Answer:

5/12

Step-by-step explanation:

Think SohCahToa

Soh- Sin: opposite/hypotenuse

Cah- CoSin: adjacent/hypotenuse

Toa- Tan: opposite/adjacent

Opposite: The length on the opposite side of the angle.

Adjacent: The length next to the angle.

Hypotenuse: The longest side of the angle.

I need more answers and I don’t know how to make an account

Answers

Answer:

Well if your on chrome book sign out and select add person and make your new email and password and you have a new account.

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

Account for what, brain ly

Step-by-step explanation:

step 1: Go to sign up

step 2: create a email

step 3: create password

Bryan calculated the area of a square to be 18/32 square foot. Which shows the side length of the square? (Hint: Simplify. Also, area of a square is side x side.)

Answers

Answer:

x = 0.75 feet

Step-by-step explanation:

The area of a square is 18/32 square foot

We need to find the side length of the square.

The area of a square of side x is given by :

[tex]A=x^2[/tex]

Substitute all the values,

[tex]x=\sqrt{A} \\\\x=\sqrt{\dfrac{18}{32}} \\\\x=0.75\ feet[/tex]

So, the side length of the square is equal to 0.75 feet.

Jesse has a storage container in the shape of a right rectangular prism. The volume of the container is 43.875 cubic meters, the length is 5 meters and the width is 3.9 meters.

Answers

Note: Consider we need to find the height of the container.

Given:

The volume of container in the shape of right rectangular prism = 43.875 cubic meters.

Length = 5 meters.

Width = 3.9 meters.

To find:

The height of the container.

Solution:

We know that the volume of a rectangular prism is:

[tex]V=l\times w\times h[/tex]

Where, l is length, w is width and h is height.

Putting [tex]V=43.875,l=5,w=3.9[/tex] in the above formula, we get

[tex]43.875=5\times 3.9\times h[/tex]

[tex]43.875=19.5\times h[/tex]

[tex]\dfrac{43.875}{19.5}=h[/tex]

[tex]2.25=h[/tex]

Therefore, the height of the rectangular container is 2.25 meters.

Help plzz need the answer and that explanation plz don't send a file I need help with question 21!! thx so much

Answers

Answer:

No, they cannot be becuase the points are too different- no same numerical

values.

Step-by-step explanation:

HELP MEEEEEEEEE I REALLY DONT KNOW THIS ONE

Answers

Answer:

[tex]volume = \pi {r}^{2} h \\ = \pi( {5}^{2} ) \times 6 \\ 150\pi \: cubic \: units[/tex]

Answer:

471

Step-by-step explanation:

Using Pi=3.14

First find the area of the bottom circle:

3.14*([tex]5^{2}[/tex])

=78.5

Then multiply the result by the height

78.5*6=471

therefore,

Volume of clylinder: 471 units squared

Please give me brainliest if corrrect :)

PLEASE HELP ASAP THANK YOUU: A unicycle wheel makes five rotations. The unicycle travels 37.94 feet. Find the diameter of the wheel in inches.
Show your work and write your answer in a sentence.

Answers

Answer:

diameter of the wheel = 28.98 in (2 d.p.)

Step-by-step explanation:

Given information:

A unicycle wheel makes five rotationsThe unicycle travels 37.94 feet

Circumference of a circle = πd  (where d is the diameter)

One rotation of the wheel is equal to the circumference of the wheel.

Therefore, 5 rotations is equal to the sum of 5 circumferences.

To find the diameter of the wheel in feet, equate the expression for 5 circumferences to the total distance traveled and solve for d:

[tex]\begin{aligned}\textsf{5 circumferences} & = \textsf{total distance traveled}\\\implies 5 \pi d & = \sf 37.94\: ft\\d & = \sf \dfrac{37.94}{5 \pi}\\d & = \sf 2.415335416... \:ft \end{aligned}[/tex]

As 1 foot = 12 inches, multiply the found diameter in feet by 12 to calculate the diameter in inches:

[tex]\begin{aligned}d & =2.415335416... \times 12\\\implies d & = \sf 28.98\:\:in\:(2\:d.p.)\end{aligned}[/tex]

Therefore, the diameter of the wheel is 28.98 in (2 d.p.).

A square pyramid has a volume of 297 cubed feet. The width and length of the pyramid are
both 9. feet. Find the height of the pyramid.

Answers

Answer:

11

Step-by-step explanation:

H =V/(LxW)/3

H = 297/(9x9)/3

H = 297/(81)/3

H = 297/27

H = 11

Therefore, the height of the pyramid is 11ft square

Oliver has created a plot of his backyard on the given coordinate plane, so that each unit length is one yard. He wants to design a right triangular plant bed for his backyard that has an area of eight square yards. After placing one vertex of the base of the plant bed at (3, 8) and one vertex at (7, 8) on his coordinate plane, he has to determine where to place the last vertex. Locate the possible locations of the last vertex on the coordinate plane.

Answers

Answer:

The possible locations are;

(3, 4), (3, 12), (7, 4), and (7, 12)

Please find attached the plot of the points created with Microsoft Excel      

Step-by-step explanation:

The given parameters of the plot of Oliver's backyard are;

The area of the right triangular plant bed Oliver wants to design, A = 8 yd²

The length of a/each unit of the plot = 1 yard

The location of one of the vertex of the right triangular area = (3, 8)

The location of the other vertex of the right triangular area = (7, 8)

We note that the area of a triangle, A = 1/2 × Base length, B × Height, h

Let the distance between the two plotted point represent the base length, 'B', therefore;

B = 7 - 3 = 4 (We subtract only the x-values (7 and 3) given that the y-values (8 and 8) are the same;

Therefore, the base length, B = 4 yards

A = 1/2 × B × h

∴ A = 8 yd.² = 1/2 × 4 yd. × h

h = 8 yd.²/ 2 yd. = 4 yd.

The height of the right triangle, h = 4 yd.

Therefore the possible locations of the last vertex the right triangle on the coordinate plane, given that the first two points are parallel with the x-axis, are points 4 units above or the y-axis value of the plotted points with the x-value of the last vertex being either 3, or 7 as follows;

(3, 8 ± 4) or (7, 8 ± 4) which give points, (3, 4), (3, 12), (7, 4), and (7, 12).

Answer:

3,4 7,4

Step-by-step explanation:

Find the product of (2a+b)^2

Answers

Answer:

(2a+b)^2

4a^2 + 4ab + b^2

product=4

Answer:

4a²+b²+4ab

Step-by-step explanation:

(2a+b)²=(2a)²+(b)²+2×2a×b

(a+b)²=a²+b²+2ab

answer:- 4a²+b²+4ab

Ten times the square of a non zero number is equal to fifty times the number.

What is the number?

Answers

Answer:

5

Step-by-step explanation:

10x^2=50x

10x=50

x=5

x=5 hsjsbseinsosnsiwnskdbisndisnsdjd

A graph of f(x) = 6^2 - 11x + 3 is shown on the grid
What are the zeros of f?

A. 3
B. 2 and 9
C. 11/12
D. 1/3 and 3/2

Answers

The answer is D
Use Conects

is the Square root of 18 divided by 3 a rational or irrational number? explain using full sentences

Answers

Answer:

irrational

Step-by-step explanation:

[tex]\sqrt{18}[/tex] = [tex]\sqrt{9}[/tex] · [tex]\sqrt{2}[/tex] which is the same as 3[tex]\sqrt{2}[/tex]

3[tex]\sqrt{2}[/tex] divided by 3 equals [tex]\sqrt{2}[/tex], which is irrational

Classify the triangle with the given side lengths: 5, 9, 10

Answers

This can be a right triangle

find the slope, y-intercept. write the equation :).

Answers

y=mx+b
m=2/5
b= y-intercept witch is 4

y=2/5x+4

slope: -4/5

y-int: 4

y=-4/5x+4

pls help with this !!

Answers

Answer:

25.12 so the nearest 10 is 25.10

Margo wants new carpet and a new wallpaper border for her bedroom. The room is 5.7 yards long and 6 7 8 yards wide. About how many square yards of carpet will she need? About how many yards of wallpaper border will she need?

Answers

Answer:

39.19 yards^2

25.15 yards

Step-by-step explanation:

To determine the squares square yards of carpet needed, we have to determine the area of the room

The room is shaped like a rectangle

area of a rectangle = length x breadth

5.7 x 6 7/8

To multiply, convert 6 7/8 to a  decimal

to do this, divide 7 by 8. Add the value gotten to 6

5.7 x 6.875 =39.19 yards^2

To determine the yards needed for the border, calculate the perimeter of the room

Perimeter = 2 x (length + breadth)

2 x(5.7 + 6.875) = 25.15 yards

Lines CD and DE are tangent to circle A shown below: Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 112 degrees. Point B lies on circle A. If Arc CE is 112°, what is the measure of ∠CDE? (4 points) Question 5 options: 1) 124° 2) 136° 3) 68° 4) 56°

Answers

Answer:

Option (3)

Step-by-step explanation:

By the theorem, angle between two tangents intersecting each other outside the circle is half of the difference between intercepted arcs.

From the figure attached,

Two tangents CD and DE are intersecting each other at point D outside the circle A.

Two intercepted arcs are minor arc CE and major arc CBE,

Measure of arc CE = 112°

Therefore, measure of major arc CBE = 360° - 112°

                                                               = 248°

m(∠CDE) = [tex]\frac{1}{2}(\text{arcCBE}-\text{arcCE})[/tex]

                 = [tex]\frac{1}{2}(248-112)[/tex]

                 = [tex]\frac{1}{2}\times 136[/tex]

                 = 68°

Option (3) will be the correct option.

Answer:

C

Step-by-step explanation:

Can someone please help me on this problem?

Answers

Answer:

$5820.07

Step-by-step explanation:

Substitute 243 into the equation for n:

[tex]c=117\sqrt[3]{243^{2} }+1264\\c=117\sqrt[3]{59049}+1264\\c=117*38.9407384+1264\\c=4556.06639+1264\\c=5820.06639[/tex]

Round 5820.06639 to the nearest hundredth:

5820.07

$5820.07

-2x+6y=12 x-3y=3 graph the equations

Answers

Answer:

here ya go bruv:

Step-by-step explanation:

:3

Answer:

The graph, with the answers, is in the picture below.

Step-by-step explanation:

−2x + 6y = 12

Slope:  [tex]\frac{1}{3}[/tex]    y-intercept: (0, 2)

LINE COLOR: RED

x − 3y = 3  

Slope:  [tex]\frac{1}{3}[/tex]   y-intercept: (0, −1)

LINE COLOR: BLUE

The factor by grouping method found the GCF's of the original polynomial to be "5x" and "+6."

When you factor those out, you have this remaining:

5x(x + 3) + 6(x + 3).

What is the final answer?

Group of answer choices

(x + 3)(30x)

(x + 3)(5x + 6)

(x + 3)(11x)

Prime

Answers

Answer:

(5x + 6) (x + 3)

hope it helps

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