Answers
======================================================
Work Shown:
[tex]\log_{4}(x+10)+\log_{4}(x-2)=\log_{4}(64)\\\\\log_{4}\left((x+10)(x-2)\right)=\log_{4}(64)\\\\(x+10)(x-2)=64\\\\x^2-2x+10x-20=64\\\\x^2-2x+10x-20-64=0\\\\[/tex]
[tex]x^2+8x-84=0\\\\(x+14)(x-6)=0\\\\x+14=0 \ \text{ or } \ x-6=0\\\\x=-14 \ \text{ or } \ x=6\\\\[/tex]
Those are the possible solutions, but plugging x = -14 back into the original equation will lead to an error. So we rule x = -14 out
x = 6 works as a solution however
Related Questions
if there are 25 members in a club and 40% are girls how many girls are in the club
Answers
Answer:
there are 10 girls in the club
Step-by-step explanation:
25*40% is equal to 10
The first 3 numbers in a sequence are 30000, 12000, and 4800. Use percent to describe the pattern in the sequence. List the next 2 terms.
Answers
Answer:
1920 and 768
Step-by-step explanation:
its 40% of the numbers
40% of 30000 = 12000
40% of 12000 = 4800
next numbers
40% of 4800 = 1920
40% of 1920 = 768
Mr Mason asks 240 year 11 students what they want to do next year. 15% of the students want to go to college. ¾ of the students want to stay at school. The rest of the students do not know. Work out the number of students who do not know.
Answers
Answer:
Number of students who do not know = 24
Step-by-step explanation:
Year II students = 240
15% of the students want to go to college.
Number of year II students who wants to go to college = 15% of 240
= 15/100 × 240
= 0.15 × 240
= 36
¾ of the students want to stay at school.
Number of students who wants to stay at the school = 3/4 × 240
= (3 × 240) / 4
= 720 / 4
= 180
Number of students who do not know = Total year II students - Number of year II students who wants to go to college - Number of students who wants to stay at the school
= 240 - 36 - 180
= 24
Number of students who do not know = 24
A student bought some pens at 8 each and some pencils at 31.50 each. If the total
number of pens and pencils purchased is 16 and their total cost is 50, how many pens
did he buy?
be
as his
Answers
Step-by-step explanation:
Letthenumberofpensbexand
numberofpencilsbey
then
x+y=16ory=16−x
andtheirvalue
8x+1.5y=50
8x+(
2
3
)(16−x)=50
8x+24−(
2
3
)x=50
8x−(
2
3
)x=50−24
(
2
13x
)=26∴x=4
theny=16−x=16−4=12
uhmmmm... yea............
Answers
Answer:
You add 12.5+12.5+3.02+3.02 which equals 31.04
Step-by-step explanation:
WILL GIVE BRAINLIEST FOR RIGHT ANSWER
What is the solution to this system of equations?
Answers
Answer:
A) (-2, 4)
Step-by-step explanation:
hope this helped
15PTS PLEASE HELP ASAP!
(dont write random answers pls)
look at the pic attached:
Answers
Answer:
120
Step-by-step explanation:
a^2 + b^2 = c^2
48^2 + x^2 = 52^2
2304 + x^2 = 2704
x^2 = 2704-2304
x^2 = 400
x = 20
52 + 48 + 20 =
120
which is equivalent to √3/√8 when denominator is "rationalized"?
Answers
Step-by-step explanation:
[tex]\dfrac{\sqrt3}{\sqrt8}=\dfrac{\sqrt3\cdot\sqrt2}{\sqrt8\cdot\sqrt2}=\dfrac{\sqrt{3\cdot2}}{\sqrt{8\cdot2}}=\dfrac{\sqrt6}{\sqrt{16}}=\dfrac{\sqrt6}{4}[/tex]
Used:[tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{16}=4\ \text{because}\ 4^2=16[/tex]
What is the equation of this line? Carlos started at 1 meter and he rode for 5 meters for 2 seconds. y = mx + b
Answers
Y = 5/2x + 1
Help Please! Solve For Y.
Answers
Answer:
i think 7
Step-by-step explanation:
pls help this is due soon
Answers
Answer:
1/2^4
Step-by-step explanation:
I need help ASAP !!!!!
Answers
Answer:
you will get the football
Step-by-step explanation:
On Sunday it was 89°F. On Monday it was 15° colder. What temperature was it on Monday?
°
I need help I dont understand
Answers
Answer:
74F
Step-by-step explanation:
If it is 89F on Monday and it went DOWN 15 degrees, you subtract. 89-15= 74. The temp on Monday is 74 degrees F
60 over 100 as a decimal
Answers
Answer:
0.6
Explanation: 60 over 100 would be 60/100, so when converting this into a decimal, the 60 would be in the hundreths place. Therefore, the decimal would be 0.6.
Hope this Helps!
Is y=2x+3 proportional
Answers
Answer:
no
Step-by-step explanation:
I calculated
No because something proportional can't have a y-intercept, the 3 is the y intercept so your statement is not proportional.
Given w= √ 2(cos(pi/4)+isin(pi/4)) and z=2(cos (pi/2)+i sin (pi/2)) what is w-z expressed in polar form?
Answers
Answer:
It is B.
Step-by-step explanation:
Edge2021
[tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
What is complex number?"The number of the form a + ib where a, b are real numbers and [tex]i=\sqrt{-1}[/tex] "
What is polar form of complex number?"The polar form of complex number z = x + iy is [tex]z=r~(cos\theta+i~sin\theta)[/tex] where [tex]r=\sqrt{x^{2} +y^{2} }[/tex] and [tex]\theta=tan^{-1}(\frac{y}{x} )[/tex]"
For given question,
We have been given two complex numbers in polar form.
[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} ))[/tex] and [tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))[/tex]
We simplify above complex numbers.
[tex]w=\sqrt{2}(cos(\frac{\pi}{4} )+i~sin(\frac{\pi}{4} )) \\\\w=\sqrt{2}(\frac{1}{\sqrt{2} } +i~ \frac{1}{\sqrt{2} } ) \\\\w=1+i[/tex]
And the second complex number is,
[tex]z=2(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))\\\\z=2(0+i~1)\\\\z=0+2i[/tex]
Now if we find the value of w - z
⇒ w - z = (1 + i) - (0 + 2i)
⇒ w - z = 1 - i
Now we find the polar form of complex number.
[tex]r=\sqrt{1^{2} +(-1)^{2} } \\\\r=\sqrt{2}[/tex]
And the value of [tex]\theta[/tex] would be,
[tex]\theta=tan^{-1}(\frac{-1}{1} )\\\\\theta=tan^{-1}(-1)\\\\\theta=\frac{3\pi}{4}[/tex]
So, w - z in the polar form would be [tex]1+i=\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
Therefore, [tex]w -z =\sqrt{2}(cos(\frac{3\pi}{4} )+i~sin(\frac{3\pi}{4} ))[/tex]
Learn more about the complex numbers here:
https://brainly.com/question/17162901
#SPJ3
Tiana’s car traveled 111 miles on 3/8 of a tank of gas. How far will she be able to go on a full tank of gas?
Answers
Answer:
Hiiiiiii
Step-by-step explanation:
So to get the answer you have to turn the 3/8 into a mixed number and divide it by 111
Which statements are true regarding the diagram? Check all that apply.
1. ΔXYZ ≅ ΔLMN
2. ∠Y ≅ ∠M
3. ∠X ≅ ∠L
4. ∠Z ≅ ∠L
5. YZ ≅ ML
6. XZ ≅ LN
Answers
Answer:
1, 2, 3, 6
Step-by-step explanation:
I don't really know how to explain this but if the only change between the two triangles is that it was reflected, then there was no change of any of the angles or side lengths, you just have to make sure you match up the rights angles and the right sides.
Answer:
Hi how are you doing today Jasmine
Find that x and y intercept 4x-5y=40
Answers
Answer:
x intercept: 10, y intercept: -8
Step-by-step explanation:
make into y = mx + b
4x = 5y + 40
4x - 40 = 5y
y = 4/5x - 8
plug in 0 for x, to find y intercept
y = -8
plug in 0 for y, to find x intercept
0 = 4/5x - 8, x = 10
Peter is a beekeeper who sells jars of honey and combs at the market. For each 10 jars of honey that he takes to the market carries 3 honeycombs. Which of the following could be what Peter brings to market?
Answers
Charles charges 4 an our to baby sit he also adds an extra 10 dollars onto the total for families with more than 3 children. How much will charles charge to baby sit 4 children for 4 hourss
Answers
Answer:
i beleve 26 or 48
good luck
What is the value of x?
A. 88
B. 68
C. 38
D. 112
Answers
Answer:
B. 68
Step-by-step explanation:
Find the measurements of angles a, b and c. PLZ HELP
Answers
yo im timed please help!! at the top it says "car A is traveling east at a steady speed of 45 mph. after 2 hours it is 100 miles east of Johnstown . car B is traveling east on the same road. its distance east of Johnstown is represented by the graph" il give 20 more points if you're correct
Answers
Answer:
it could be C or a
Step-by-step explanation:
more likey c be sorry if it's wrong
Which expression shows 24 + 36 as a product of the greatest common factor (GCF) and a sum? *
A. 3(8+12)
B. 4(6+9)
C. 12(2+3)
D. 6(4+6
Answers
Answer:
D
Step-by-step explanation:
The product of the greatest common factor and a sum is 12 (2 + 3).
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
24 + 36
We have the following cases:
2 (12 + 18)
3 (8 + 12)
4 (6 + 9)
6 (4 + 6)
12 (2 + 3)
Now,
The greatest common factor.
12 x 2 = 24
12 x 3 = 36
Thus,
12(2 + 3) is the product of the greatest common factor and a sum of (2 + 3).
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
pls answer both parts of this problem for a brainliest !!
Bianca can walk 5/6 of a mile in of an hour. What is her walking speed, in miles per hour?
Answers
Step-by-step explanation:
please see it, i work on paper worksheet
Answer:
2 1/2 miles
24 minutes per mile
April took out a $600 loan from the bank.At the end of 5 years, she pays back the principle,plus $60 simple interest.What was the annual interest rate?
Answers
Answer:
April took out a loan of $600 and paid it back with simple interest of $60 after 5 years. The formula to calculate interest is given the principal and the time and the interest rate is . For this problem we have to find the interest rate given . To archive that , we can just solve the equation making the interest rate the subject of the formula as shown below,
I= Prt
=> r= I/Pt
=> r= 60/600x5 = 1/50
The interest rate is 1/50 or 0.02 as a decimal. The interest rate is 2% as a percentage.
If 3x+2=7x then what is x
Answers
Answer:
take the x together
then
2=7x-3x
2=4x
2/4=x
2=x
2 is your ans
I hope it helps mate
I will always help you understanding your assingments
have a great day
#Captainpower:)
What is it will mark Brainliest
Answers
Answer:
1
Step-by-step explanation:
[tex]y \times 3 = 27 \times 10[/tex]
Answers
y = 270 ÷ 3 = 90
Y = 90
Hope it helps