Answers
Answer:
see belowStep-by-step explanation:
Question-6:we are given a equation
[tex] \sf \displaystyle \: \log_{4}( - x) + \log_{4}( 6 - x) = 2[/tex]
to solve so
recall logarithm multiplication law:
[tex] \sf \displaystyle \: \log_{4}( - x \times (6 - x)) = 2[/tex]
simplify multiplication:
[tex] \sf \displaystyle \: \log_{4}( - 6 x + {x}^{2} ) = 2[/tex]
remember [tex]\displaystyle \log_{4}(4^2)=2[/tex]
so
[tex] \sf \displaystyle \: \log_{4}( - 6 x + {x}^{2} ) = \log_{4}( {4}^{2} ) [/tex]
cancel out [tex]\log_4[/tex] from both sides:
[tex] \sf \displaystyle \: - 6 x + {x}^{2} = {4}^{2} [/tex]
simplify squares:
[tex] \sf \displaystyle \: - 6 x + {x}^{2} = 16[/tex]
move left hand side expression to right hand side and change its sign:
since we are moving left hand side expression to right hand side there'll be only 0 left in the left hand side
[tex] \sf \displaystyle \: - 6 x + {x}^{2} - 16 = 0[/tex]
rewrite it to standard form i.e ax²+bx+c=0
[tex] \sf \displaystyle \: {x}^{2} - 6x - 16 = 0[/tex]
rewrite -6x as 2x-8x:
[tex] \sf \displaystyle \: {x}^{2} + 2x - 8x - 16 = 0[/tex]
factor out x and 8:
[tex] \sf \displaystyle \: x {(x}^{} + 2) - 8(x + 2) = 0[/tex]
group:
[tex] \sf \displaystyle \: (x - 8){(x}^{} + 2) = 0[/tex]
[tex] \displaystyle \: x = 8 \\ x = - 2 [/tex]
[tex] \therefore \: x = - 2[/tex]
Question-7:move left hand side log to right hand side:
[tex] \displaystyle \: \log(x ) + \log(x - 21) = 2 [/tex]
use mutilation logarithm rule;
[tex] \displaystyle \: \log( {x}^{2} - 21x) = 2 [/tex]
[tex]\log(10^2)=2[/tex] so
[tex] \displaystyle \: \log( {x}^{2} - 21x) = \log({10}^{2} )[/tex]
cancel out log from both sides:
[tex] \displaystyle \: {x}^{2} - 21x = 100[/tex]
make it standard form:
[tex] \displaystyle \: {x}^{2} - 21x - 100= 0[/tex]
factor:
[tex] \displaystyle \: {(x} + 4)(x - 25)= 0[/tex]
so
[tex] \displaystyle \: x = 25[/tex]
Related Questions
uhmm...hi... can someone plss answer this...
plss don't waist ma póints.
Answers
1: 6, because both are congruent
2: 14, because if half is seven then the whole line is double.
3: (Sorry, I’m not sure on this one).
4: Right triangle
5: 42, because A = (xy) / 2
So HT=6
2) a kite’s diagonals are perpendicular so GH= 7
7+7=14
3)AMH divides into two equal parts so we divide by 2
35/2 = 17.5
17.5
4)scalene triangle
5)area = 0.5 d1xd2
0.5 x 12x 7=42
Can someone explain to me how Slope Rise over Run works? I just don’t understand it no matter how many times I look into it.
Answers
Answer:
slope= rise over run means divide rise by run
Answer:
when there is a linear equation and line. first, find where you see a point that has whole numbers. graph them or circle them. Next, go to point to pint using the lines. do not use the slanted line. go up (rise) and count how many boxes you passed (be careful it could go by 2's) and then go across to the other point (run). count how many boxes you passed. now you put the up number or rise number over the run number. Rise/run. you'll get a fraction, simplified it if needed.
or do slope form which is just find 2 points that have whole numbers. Label the first one (x1,y1) and the second one (x2,y2) the you do (Y2 - Y1) over (X2 - X1). you'll get a fraction and you'll simplified it if needed
Step-by-step explanation:
What is the formula for this pattern.
Term: 1, 2, 3, 4, 5, 6, 7, 8, 9
Number: 1, 2, 3, 1, 2, 3, 1, 2, 3
Answers
Hope it helps u understand ask if u have any doubts
50 POINTS: Please help thank you so much!! (Image attached) The polygons are similar. Find the values of the variables.
I know from the answer key that the answers are x=
[tex]3 \sqrt{10} [/tex]
and y=
[tex]2 \sqrt{10} [/tex]
but I'm not sure how to get there...
Answers
Step-by-step explanation:
9 + y^2 = 49
y^2 = 40
y = √40 = 2√10
4.5/3 = 2√10/5x
22.5x = (3) 2√10
22.5x = 6√10
x = 6√10/22.5 = 3√10/11.5
What is the angle of 1,2,3, and 4?
Answers
Answer:
1=72
2=36
3=36
4=54
A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 34
centimeters, and the length of the other leg is 24 centimeters. The student incorrectly says that the
length of the hypotenuse is 7.6 centimeters. Answer parts a and b.
a. Find the length of the hypotenuse of the right triangle to the nearest tenth of a centimeter.
Answers
Answer:
41.6 centimeters
Step-by-step explanation:
The right triangle formula: c^2 = a^2 + b^2
c is the hypotenuse side of the triangle
a and b are the legs of the triangle.
Find the hypotenuse : c^2 = (24)^2 + (34)^2
c = square root of ( (24)^2 + (34)^2)
c = square root of ( 576 + 1,156)
c = 41.6173
An item is regularly priced at $70. Chang bought it on sale for 60% off the regular price. How much did Chang pay?
Answers
Answer: $42
Step-by-step explanation:
You need to find 60% of 70
10%= 7 (70/10)
60% = 42 (7x6)
so the answer is $42
60% as a decimal is 0.6
70 x 0.6 = 42
That is the amount taken off the full price.
70 - 42 = 28
Another way to solve is by considering that if 60% of the price is gone, 40% remains. Then you can multiply by 0.4
70 x 0.4 = 28
Please let me know if you have any questions
Solve for x. Round to the nearest tenth.
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 8) 64.2
10) 51.3
Explanation:
I hope this helped!
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Business owners use percents to calculate markup, discount, and sales tax. A shoe store owner buys a pair of shoes for $20. There is a sale on the item for 20% off.
Answers
Answer:
$16
Step-by-step explanation:
Given data
The cost price of the shoe= $20
Discount = 20%
Let us find the amount of the 20% discount
=20/100*20
=0.2*20
=$4
Hence the selling price will be
=20-4
=$16
The dimensions of Jared's classroom are shown in the diagram.
12 m
4 m
6 m
4 m
2 m
8 m
What is the area of the classroom?
A. 36 m2
B. 48 m2
OC.-64 m2
OD. 72 m2
Answers
Answer:
64 m2
Step-by-step explanation:
12x6=72m2
2x4=8m2
72-8=64m2
The area for the given dimensions of Jared's classroom is, 64 m²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Given that,
The dimensions of Jared's classroom are,
12 m, 4 m, 6 m, 4 m, 2 m, 8 m
we can divide the area of classroom in two parts,
first A₁, having side lengths of 6 m & 8 m
second A₂, having side lengths of 4 m & 4 m
Jared's classroom area = A₁ + A₂
A₁ = 6 × 8
= 48
A₂ = 4 × 4
= 16
A = A₁ + A₂
= 16 + 48
= 64
The area of classroom is 64 m²
To learn more about Area check:
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If you buy a necklace for $400 on your credit card, which charges 21.3% simple interest, how much interest will be added after 15 months?
Answers
Answer:
C
Step-by-step explanation:
400*0.213=85.2
Ken makes 75 cookies. He gives 35 of them to his classmates and 13 of them to his teachers. He brings the rest home. He brings home
cookies.
Answers
So ken would bring home 27 cookies
Can someone help me? Please? TwT
Answers
(a)
Perimeter: 2l + 2w = 2(77 yd) + 2(24 yd) = 154 yd + 48 yd = 202 yd.
Area: 77 yd × 24 yd = 1848 yd².
———
(b) To determine how long it will take to walk around the field, one would need to know the total distance of the edges that make up the field. That would be the perimeter, which is the measure that would be used here.
———
(c) To determine the amount of turf needed to cover the field, one needs to know the size or extent of the surface of the region to be covered. That is the definition of area, which is the measure that would be used here.
If mpho is the 50th fastest and slowest runner in her school,how many students are there in her school
Answers
Answer:
Step-by-step explanation:
i need points lol
There are 99 students in her school.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
mpho is the 50th fastest and slowest runner in her school.
Now,
Since, mpho is the 50th fastest and slowest runner in her school.
Hence, Total number of students = (50 + 50) - 1
= 100 - 1
= 99
Thus, There are 99 students in her school.
Learn more about the mathematical expression visit:
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Volume of the cylinder? Use 3.14 as pi.
Answers
Answer:
V≈8906.42
Step-by-step explanation:
V=πr2h=π·92·35≈8906.41517
plz give the brainliest
Have a great day!
what is the simplified ratio of 6:4 please explain step by step
Answers
Answer:
3:2
Step-by-step explanation:
Answer:
3:2
Step-by-step explanation:
6 and 4 can be both divided by 2
A marble has a volume of 524 cubic feet. What is the approximate diameter of the marble?
Answers
262
Step-by-step explanation:
in half a circle will get the answer
A local taxi company charges a base fare of $3.20. The taxi company charges $0.40 for every minute the taxi is in service. If a passenger has $20, how many minutes can he travel in the taxi?
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 42 minutes
Explanation:
0.40x + 3.20 = 20
0.40x = 16.8
x = 42 minutes
I hope this helped!
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*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Each cube in the prism is one cubic unit.
What is the volume of this rectangular prism?
Answers
Select ALL choices that are zeros of this function y=x2 +12x +32
Answers
Answer:
{-8, -4}
Step-by-step explanation:
Rewrite this function y=x2 +12x +32 as y = x^2 + 12x + 32; " ^ " indicates exponentiation.
Set this x^2 + 12x + 32 equal to zero (to find the zeros):
x^2 + 12x + 32 = 0. Let's solve this using the quadratic formula, which applies when ax^2 + bx + c = 0:
-b ± √(b^2 - 4·a·c)
x = -------------------------------
2a
The coefficients of the given quadratic are {1, 12, 32}. Thus, the discriminant is
b^2 - 4ac, or 12^2 - 4(1)(32), or 144 - 128, or 16. Therefore, we have:
-12 ± √16 -12 ± 4
x = -------------------- which simplifies to: x = --------------- = { -8, -4}
2 2
The zeros are {-8, -4}
the common factor of 6x 66xy
Answers
Answer:
6x and 1x or x
Step-by-step explanation:
the highest common factor of 6x and 66xy in 6x
6x ÷ 6x = 1
66xy ÷ 6x = 11y
the lowest common factor of 6x and 66xy is 1x or x
6x÷ 1x =6
66xy÷ 1x = 66y
6x÷ x = 6
66xy ÷ x = 66y
NOTE
1x and x is the same
The diameter of a circle is 2 inches. What is the circle's circumference? d=2 in
Answers
Answer:
2π or 6.2831 (I don't know which since I don't know what to round to or if it is supposed to be in terms of π soooo)
Step-by-step explanation:
[tex]2\pi(1) = 2\pi = 6.2831[/tex]
PLZ HELP !!!! WILL MARK BRAINLIEST, THIS IS DUE IN 15 MINUTIES !!!ANYONE PLEASEPLZ HELP !!!! WILL MARK BRAINLIEST, THIS IS DUE IN 15 MINUTIES !!!ANYONE PLEASEPLZ HELP !!!!
Answers
Answer:
J
Step-by-step explanation:
i looked it up on a graphic calculator, just trust me lolz
good luck!!!
f(x) = 9x+7
find 20-3)
09c + 7
0 18c + 20
18c + 7
O -
180 - 20
Someone help?
Answers
Answer:
18c - 20
Step-by-step explanation:
substitute 2c - 3 into x,
f(2c - 3) = 9(2c - 3) + 7
=> f(2c - 3) = 18c - 27 + 7
=> f(2c - 3) = 18c - 20
HELPPP PLEASE I NEED AN ANSWER
Answers
Answer:
C
Step-by-step explanation:
What would be the volume of a sphere if the radius is 6 in? Round to nearest tenth if needed
Answers
Answer:
904.8cm
Step-by-step explanation:
The volume of a sphere is given as
[tex] \frac{4}{3}\pi {r}^{2} [/tex]
There is only one variable, the radius, which we are given in the problem.
since the radius is 6 cm, we can plug that in to the formula
[tex] \frac{4}{3} \pi {6}^{2} [/tex]
Put this into the calculator, and we see that the volume is 904.8cm rounded to the nearest tenth.
which of the following statements are true
A tangent line is perpendicular to the radius of a circle at the point of tangency.
A tangent line is perpendicular to the diameter of a circle at the point of tangency.
A tangent line is the perpendicular bisector of the radius of a circle.
A tangent line intersects a circle at one point.
A tangent line intersects a circle at two points.
Every circle has exactly one tangent line to that circle.
Answers
The tangent line and radius or diameter of the circle intersect at a right angle and the tangent intersects the circle at a single point only. Then the correct option is A, B, and D.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
The tangent line and radius or diameter of the circle intersect at a right angle.
And the tangent line intersects the circle at a single point only.
The number of the tangent line depends on the point from which the tangent is drawn.
More about the circle link is given below.
https://brainly.com/question/11833983
Sasha drinks 2 liters of water each weekend how many milliliters of water does Sasha drinks each weekend?
Answers
Answer:
2,000 ml
Step-by-step explanation:
'milli' indicates 'thousands'
2 x 1000 = 2000
f(x)=2x-8 find a function help ;-;
Answers
(I think this is the answer)
It takes a bear 9 more days to eat a barrel of honey alone than it takes the bear and a second bear to eat the barrel of honey together. It takes the first bear 7 fewer days to eat a barrel of honey alone than it takes the second bear to eat a barrel of honey alone. In how many days can the two bears eat a barrel of honey together?
No links please.
Answers
Answer:
it takes the bears 12 days to eat honey together.
Step-by-step explanation:
1/x+9+1/x+16=1/x
(solve this using cross multiplication)
= x^2 = 144
x=12
answer: 12
explanation:
let x=two bears eating honey together
let x+9=first bear
let (x+9)+7=second bear **because we know the second day takes 7 more days to eat the same amount of honey as the first bear**
since the bears can finish a barrel of honey over multiple days, they can only finish part of the barrel of honey in one day.
therefore...
x/(x+9)+x(x+16)=1 or x*1/(x+9)+x*1/(x+16)=1 **the equation equals 1 because you are trying to find how much honey they eat in one day aka 1=single day**
if you solve, you get x=-12; x=12. it can only be the positive value so x=12 is your answer. your welcome fellow rsm students.