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 = -9Answer:
[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]
does anyone know the answer?? i’ll mark brainlists
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?
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.
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!
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!!!!!!!!!!!!!!!!
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
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
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
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.
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!
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
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.)
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.
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
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
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.
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 feetCircumference 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.
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.
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
Answer:
(2a+b)^2
4a^2 + 4ab + b^2
product=4
Answer:
4a²+b²+4abStep-by-step explanation:(2a+b)²=(2a)²+(b)²+2×2a×b(a+b)²=a²+b²+2abanswer:- 4a²+b²+4abTen times the square of a non zero number is equal to fifty times the number.
What is the number?
Answer:
5
Step-by-step explanation:
10x^2=50x
10x=50
x=5
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
is the Square root of 18 divided by 3 a rational or irrational number? explain using full sentences
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
find the slope, y-intercept. write the equation :).
slope: -4/5
y-int: 4
y=-4/5x+4
pls help with this !!
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?
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°
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?
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
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
Answer:
(5x + 6) (x + 3)
hope it helps