Answer:
x = 6
Step-by-step explanation:
log2(x + 5) + log2(x − 5) = log2 11.
We know that loga (b) + log a(c) = log a( bc)
log2(x + 5) (x − 5) = log2(11)
Multiply
log2(x^2 -25) = log2(11)
Raise each side to the power of 2
2^log2(x^2 -25) = 2^log2(11)
x^2 - 25 = 11
Add 25
x^2 -25 +25 = 25+11
x^2 = 36
Taking the square root of each side
x = ±6
But x cannot be negative because then the log would be negative in log2(x-5) and that is not allowed
x = 6
Answer:
x = 6
Step-by-step explanation:
[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] 11
Determined the define range.
[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] (11), x ∈ ( 5, + ∞ )
We know that [tex] log_a ( b ) + log_a ( b ) [/tex] = [tex] log_a( bc) [/tex]
[tex] log_2[/tex] ( x + 5 ) ( x - 5 ) = [tex] log_2[/tex] ( 11).
[tex] log_2[/tex] ( ( x + 5 ) × ( x - 5 ) ) = [tex] log_2[/tex] ( 11).
Use indentity :- ( a + b ) ( a - b ) = a² - b².
[tex] log_2[/tex] ( x² + 25) = [tex] log_2[/tex] ( 11).
Since , the base of the logarithm are the same. set the arguments equal.
x² - 25 = 11.
Move constant to the right-hand side and change their sign.
x² = 11 + 25
x² = 36.
Take square root of each side.
√x² = √36
x = ± 6
x = 6
x = -6, x ∈ ( 5, + ∞ )
Check if the solutions is in determine range.
x = 6
Using the diagram below, which of the following parts of the triangles are
congruent?
7 miles
B
С
16 ft
12 ft
D
21 ft
E
1 mile = 5280 ft
Given:
1. ACAB-ACED
2. AB ||ED
A. ZA ZB
B. ZASZC
y
Answer: Choice D. [tex]\angle A \cong \angle E[/tex]
Explanation: Since AB is parallel to ED, this means the alternate interior angles A and E are congruent as marked below.
Angle A is congruent to angle E by alternate interior angle theorem. Therefore, option D is the correct answer.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, triangle CAB is similar to triangle CED and AB is parallel to ED.
From the given figure, AB=7 miles, DC=16 ft, EC=12 ft and DE=21 ft.
Here, in figure,
∠A ≅ ∠E (Alternate interior angles)
∠B ≅ ∠D (Alternate interior angles)
∠ACB ≅ ∠DCE (Vertically opposite angles are congruent)
Therefore, option D is the correct answer.
To learn more about the similar triangles visit:
https://brainly.com/question/25882965.
#SPJ7
Sue was paid $384 for working 32 hours. How many hours will she have to work to earn $672?
Answer:
56
Step-by-step explanation:
Answer:
56 hours
Step-by-step explanation:
I divided 384 dollars by 3w hours and then was Sue made 12 an hour. Then I tried mukyiplong different times until I discovered 12×56=672. So, 56 hours
Chris is saving for a down payment to buy a house. The account earns 3.9% interest compounded semi-annually, and he wants to have $8,000 in 10 years. What must his principal be? Round your answer to the nearest cent. Do not round at any other point in the solving process; only round your answer.
Answer:
$5436.82
Step-by-step explanation:
8000 = P(1 + .039/2)^10*2
[tex]\frac{8000}{\left(1+\left(\frac{0.039}{2}\right)\right)^{20}}=5436.82538[/tex]
is the value of x=3 find the value of 4x³-2x²+3x
Answer:
99
Step-by-step explanation:
4x³-2x²+3x
4×3³-2×3²+3×3
4(27)-2(9)+9
108-18+9
99
99
=(4)(27)−2(32)+(3)(3)
=108−2(32)+(3)(3)
=108−(2)(9)+(3)(3)
=108−18+(3)(3)
=90+(3)(3)
=90+9
=99
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = 18x
B.
y = 9x
C.
y = -9x
D.
y = - x
E.
y = -18x
F.
y = x
Answer:
a
Step-by-step explanation:
i took this and got a 100
Answer:
y = 9x
Step-by-step explanation:
other person is so wrong, hope this helps.
CAN SOMENE PLESAE ANSWER B ITS URGERT MARKING BRAINLIEST
(4*10^4)+(6*10^2) Standard form
Answer:
40600
Step-by-step explanation:
(4 * 10^4) + (6 * 10^2) =
= 4 * 10000 + 6 * 100
= 40000 + 600
= 40600
Answer:
4.06 x 10^4
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
A ___________________ summarizes all values in a data set and lists how many times they occur.
A. tally chart
B. data value
C. data summary
D. frequency table
Answer:
Step-by-step explanation:
B) data summary its in the words it sums up the answers to all the data you've collected over timew
Sz – [32 – (10z + 2)]
You put $5000 in an investment account with interest compounded
continuously. Calculate the approximate annual interest needed for the
account to grow to $10,000 after 20 years.
Answer:
3.465 %
Step-by-step explanation:
10000 = 5000 [tex]e^{20r}[/tex]
2= [tex]e^{20r}[/tex]
ln(2) = 20r ln(e)
r = ln(2)/20
r = 0.03465
What is the slope of a line parallel to line B?
can u help me on this... I will mark u as brilliant students.. plz
Answer:
For number 5 . a= 3 and b = -1
Sandra has developed a program designed to increase reading comprehension scores in 6th graders. She randomly selects three students and has them participate in her program. When she compares the mean score from the students who completed her program to three students who did not participate in the program, she finds no significant difference between their mean scores. What is most likely the reason for the non-significant finding
Answer:a small sample size
Step-by-step explanation:
From the information given in the question, we are informed that Sandra developed a program that was designed to increase reading comprehension scores in 6th graders and she then randomly selects three students and has them participate in her program.
After comparing the mean score from the students who completed her program to three students who did not participate in the program, she finds no significant difference between their mean scores, it should be noted that the reason for this will be because the sample size is small.
If a large sample size was used, this could have been different as thsi could result in a significant difference between their mean scores.
5√27-2√48-5√3-√(3-2√3)2
Answer:
4√3
Step-by-step explanation:
5√27-2√48-5√3-(√3-2√3)2
= 5√(3x9)-2√(3x16)-5√3-2√3+4√3
= 5(3)√3-2(4)√3-5√3-2√3+4√3
= 15√3-8√3-5√3-2√3+4√3
= 4√3
please can someone help me?
Answer:
∠ 3 = 90°
Step-by-step explanation:
∠ 3 and ∠ 4 are adjacent angles on a straight line and sum to 180° , then
∠ 3 + ∠ 4 = 180°
∠ 3 + 90° = 180° ( subtract 90° from both sides )
∠ 3 = 90°
the actual length of wall c is 4 m . to represent wall c noah draw a segment 16cm long what scale is he using explain your reasoning
Answer:
1/25
Step-by-step explanation:
1 m = 100 cm
4m x 100 = 400 cm
If it is 16 cm long, then the scale factor is 16/400, which simplifies to 1/25.
Find the length of AD in the figure.
A. √26 units
B. √34 units
C. √122 units
D. √130 units
Answer:
√122
Step-by-step explanation:
To find the distance/length between two points
Use this formula: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]\sqrt{(1 - 2)^2 + (3 + 8)^2}[/tex]
[tex]\sqrt{(-1)^2 + (11)^2}[/tex]
[tex]\sqrt{1 + 121}[/tex]
[tex]\sqrt{122}[/tex]
What is the volume of the solid? Let π=3.14
Answer:
V = 7234.56 km^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 (3.14) (12)^3
V = 7234.56 km^3
Answer:
7234, 56 km³
Step-by-step explanation:
π×R³×4/3=3.14×1728×4/3=7234, 56 km³
all I've found is 1 but how do I work that out properly beaides guess and check
Answer:
1
Step-by-step explanation:
(1-x)/x=0
or, 1-x=0
or, -x=-1
or, x=1
Answer:
F(x) = 0 when x=1
Step-by-step explanation:
We need the numerator to equal zero
1-x = 0
Add x to each side
1-x+x = 0+x
1 =x
The denominator cannot equal zero( The denominator does not equal zero when x =1)
F(x) = 0 when x=1
Convert 110011 no decimal number System
(110011)2 = (51)10
Step by step solution
Step 1: Write down the binary number:
110011
Step 2: Multiply each digit of the binary number by the corresponding power of two:
1x25 + 1x24 + 0x23 + 0x22 + 1x21 + 1x20
Step 3: Solve the powers:
1x32 + 1x16 + 0x8 + 0x4 + 1x2 + 1x1 = 32 + 16 + 0 + 0 + 2 + 1
Step 4: Add up the numbers written above:
32 + 16 + 0 + 0 + 2 + 1 = 51.
So, 51 is the decimal equivalent of the binary number 110011.
Please hurry I will mark you brainliest
What is the value of p so that the line passing through (6, 2) and (9, p) has a slope of -1?
Answer:
-1
Step-by-step explanation:
im pretty sure its right
sry if it not good luck!!
A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length of the box has been increased by 30%, the height has been increased by 20%, and the width remains the same.
By what percentage does the volume of the box increase from the regular box to the value box? Round your answer to the nearest percent.
70% - Rounded Answer
I need two people to help me… brainliest….
Does this graph represent a function (scatter)
A. Yes
B. No
Answer:
A. Yes
Step-by-step explanation:
it is always yes because no os negative
Answer
a
Step-by-step explanation:
it does represent a function
8^x times 2^(4-x) = 1
Find x.
With detailed steps.
Answer: x= -1
Step-by-step explanation:
In mathematics when you have bases that are the same while multiplying you add the powers. In this case we do not have the same bases so we are going to make it look like 8 is 2. So we sort of simplify it. So we get 8 and put into like 2^4. We do not eliminate the power x that was already there though. So we will have 2^4x × 2^4-x. So like I said earlier we add the powers. Soo we will have
4x +4-x4x-x=13x+4-4 =1-43x/3 = -3/3x= -1Hope that helped!John read the first 144 pages of a novel, which was 3 pages less than 1/3 of the novel. Write an equation to determine the total number of pages (p in the novel.
Find the total number of pages in the novel.
Answer: 441 pages
Step-by-step explanation:
[tex]\frac{1}{3}p-3=144\\\frac{1}{3}p=147\\3(\frac{1}{3})p=147(3)\\p=441[/tex]
could someone please answer this
Answer:
Step-by-step explanation:
draw a parallel line to x at a distance of 23 cutting the quadrilateral in two points.
A right angle is formrd at the bottom.
Hypotenuse=59
one side=45-23=22
x= other side=√(59²-22²)=√(59-22)(59+22)=√((37)(81))=9√(37)≈54.74
PLZ HELP, GIVING BRAINLIEST!!!
Find the length of the intercepted arc.
pi/6, r = 2.5
Answer:
4pi
Step-by-step explanati
Ed takes five 100-point tests in his algebra class. He scores 87, 85 and 87 points on the first three tests. If the scores of his last two tests differ by three points and he has a 90% average on his five tests, what was his highest test score?
PLS ANSWER QUICK WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
When we take an average of something, we have to add up all the data on the somethings and then divide by the number of somethings we have. Ed takes 5 tests, and we have scores for them; we also have his current average. What we don't know for sure are 2 of the 5 test scores, but we have enough to determine what they are.
If one test has a score of x, and the other test is 3 points less than that, the score on that last test is x - 3. Putting all of that together into an average problem:
[tex]\frac{87+85+87+x+(x-3)}{5}=90[/tex] and simplfiying a bit:
[tex]\frac{256+2x}{5}=90[/tex]. Multiply both sides by 5 to get
256 + 2x = 450; subtract 256 from both sides to get
2x = 194 and divide by 2:
x = 97
The one test score was a 97 and the other one, which was 3 less than that, was a 94.
help me pleaseeeeee!!!!!!
Step-by-step explanation:
AC = 20
AB = 18
BC² = 20²+ 18² -2•20•18•cos(52°)
BC² = 280.72
BC = √280.72
BC ≈ 16.75
Angle C:
18² = 20² + 16.75² -2•20•16.75•cos(C)
324 = 400 + 280.72 -670•cos(C)
cos(C) = -356.72/-670
cos(C) ≈ 0.53
acos(0.53) = C
C = 57.8°
Angle B:
180-52-57.8 = 70.2°
