What is number 61 and a step by step explaination please?
1/3 ln(x) + ln(2) - ln(3) = 3
Recall that [tex]m\log_b(n)=\log_b(n^m)[/tex], so
ln(x ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
[tex]\log_b(m)+\log_b(n)=\log_b(mn)[/tex]
[tex]\log_b(m)-\log_b(n)=\log_b\left(\dfrac mn\right)[/tex]
Then
ln(2/3 x ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant e. (I'm using exp(x) = e ˣ so I can write it all in one line.)
exp(ln(2/3 x ¹ʹ³)) = exp(3)
Now exp(ln(x)) = x for all x, so this simplifies to
2/3 x ¹ʹ³ = exp(3)
Now solve for x. Multiply both sides by 3/2 :
3/2 × 2/3 x ¹ʹ³ = 3/2 exp(3)
x ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(x ¹ʹ³)³ = (3/2 exp(3))³
x = 3³/2³ exp(3×3)
x = 27/8 exp(9)
which is the same as
x = 27/8 e ⁹
Find tan 0.
(Marking brainliest if correct)
8/17
15/17
15/8
8/15
Answer:
15/8
Step-by-step explanation:
Assuming you mean tan theta
Tan(theta) = opposite/adjacent
We know the adjacent side is 8 so the bottom of the fraction must also be 8
C: 15/8 is the only option that fits this criteria
The value of tangent of the angle θ, i.e., tan θ = 15/8.
Hence the correct option is c.
Given is a right triangle, with base = 8 units and the hypotenuse is 17 units,
The angle θ which is between the base and the hypotenuse,
We need to find the value of tangent of the angle θ, i.e., tan θ.
To find the value of tangent (tan) of the angle θ, we can use the definition of tangent in a right triangle.
The tangent of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the base of the triangle is given as 8 units, and the hypotenuse is given as 17 units.
To find the length of the side opposite θ, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we can calculate the length of the side opposite θ:
(side opposite θ)² + (base)² = (hypotenuse)²
(side opposite θ)² + 8² = 17²
(side opposite θ)² + 64 = 289
(side opposite θ)² = 289 - 64
(side opposite θ)² = 225
side opposite θ = √225
side opposite θ = 15 units
Now that we have the lengths of the side opposite θ and the side adjacent to θ, we can calculate the tangent of the angle θ:
tan θ = (side opposite θ) / (base)
tan θ = 15 / 8
Therefore, the value of tangent (tan) of the angle θ is 15/8.
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Please help ASAP this is due today
Answer:
good luck
Step-by-step explanation:
the mean is all of them added up then divided by how many numbers there are the median is where you put them in order putting the numbers in order then finding the middlel mode is the most of the same numbers and range is the biggest number
Answer:
mean- 104.83
median- 102
mode- 101
range- 28
Step-by-step explanation:
mean is all numbers added together then divided by however many numbers there are. sum of all numbers is 629, divided by 6 is 104.83 repeating.
median is the number in the middle. since there are six numbers and no middle one, the two in the middle (when ordered smallest to largest) are 101 and 103. the number between those two is 102 and therefore the median.
mode is the number that appears the most in the data set, which is 101 in this case.
range is the difference between the largest number and the smallest. the largest number is 121, minus 93, the smallest number, gives you 28.
hope this helps!
How much is 2/9th of 234.900?
Given:
The number is 234.900.
To find:
The [tex]\dfrac{2}{9}[/tex]th of 234.900.
Solution:
We need to find the [tex]\dfrac{2}{9}[/tex]th of 234.900. So, multiply [tex]\dfrac{2}{9}[/tex] and 234.900 to get the required value.
[tex]\text{Required value}=\dfrac{2}{9}\times 234.900[/tex]
[tex]\text{Required value}=\dfrac{469.800}{9}[/tex]
[tex]\text{Required value}=52.200[/tex]
Therefore, the [tex]\dfrac{2}{9}[/tex]th of 234.900 is 52.200 or it can be written as 52.2.
Which is the graph of y= 2 8x - 3?
Graph B.
Graph C
Graph A
Please help!
Answer:
Graph C
Step-by-step explanation:
We can tell because the equation states that the y intercept is -3 and has a steep slope
What is the area of rectangle PQRS?
A.
20.25 square inches
B.
21.375 square inches
C.
27.00 square inches
D.
42.75 square inches
Answer:
D
Step-by-step explanation:
(4.5+3+2) x4.5 = 42.75
hope this helps
Answer:
D. 42.75 square inches
Step-by-step explanation:
Area = height x width
Height = 4.5 inches
Width = 3 + 4.5 + 2 = 9.5 inches
4.5 x 9.5 = 42.75 square inches
Convert grams (g) and milligrams (mg) to grams.
Answer:
1mg= 1000g
Step-by-step explanation:
1000 grams makes up 1miligram
Find the measure of angles T and V.
W is 90
Full equation
90+ 2x +3x =180
5x = 180-90
5x = 90
X= 90/5
X= 18
T = 3 (18)
T= 54
V=2(18)
=36
To get ready for school, Traci spent 1/20th
of an hour getting dressed and 1/10th of an
hour doing her hair. What is the total
amount of time she spent getting ready?
Give your answer in simplest form.
Answer:
3/5
Step-by-step explanation:
1/10+1/20=3/5
Find the area of the sector.
Answer:
359.1887600604 so D should be right
Four points are graphed on the number line below.
Which point is located closest to the value of -v5?
A point w
B. point x
C. point Y
D. point Z
Answer:
It's close between Y and Z, but I'd go with Z
Step-by-step explanation:
[tex]-\sqrt{5}[/tex]≈-2.2360679775
THIS IS DUE IN AN HOUR PLS HELP !
Answer:
27
Step-by-step explanation:
Answer:
22°
Step-by-step explanation:
<1 is a secant-secant angle (it lies outside the circle, created by two lines that cut through the circle). The measure of a secant-secant angle is half the difference of the measures of the intercepted arcs:
<1=(0.5)(98-54)
<1=(0.5)(44)
<1=22°
What is the value of z?
Answer
61
Step-by-step explanation:
subtract 180-73.8-46.2
Answer:
The value of z is 26.6
Step-by-step explanation:
72.6 - 46.2=26.6
Find the product? y ^4 · y ^3
Answer:
if it will help
y^7
Step-by-step explanation:
y^4+3 = y^7
Suppose f(x) = x2 and g(x)=(6)
. Which statement best compares the
graph of g(x) with the graph of f(x)?
O A. The graph of g(x).js the graph of f(x) horizontally stretched by a
factor of 5.
O B. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 5.
O c. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 5.
O D. The graph of g(x) is the graph of f(x) shifted
units left.
Answer:
In Exercises 1-9, describe the transformation of f(x) = x² represented by g. ... 14. f(x) = 4x2 + 5; horizontal stretch by a factor of 2 and a translation 2 units up, ... graph of g be a horizontal shrink by a factor of the graph of f(x) = x2 x 2x ... 4(x-3)?–4.
Step-by-step explanation:
Solve for each variable and tell how you found the value of each.
Answer:
A:38 c:54
Step-by-step explanation:
First off, I did the easiest which was a. i found the value of A by subtracting 180 by 142. because a flat line is 180 degrees.
For C, It was more difficult. I subtracted 88 by the value of A, since the value of A is the same as the one next to 88. So I subtracted 126 (88+38) and got 54.
Fortunately, I couldn't figure out B though, but i think it is a similar answer to c.
.
In each row, decide whether the expression in column A is equivalent to the expression in column B. If they are not
equivalent, show how to change one expression to make them equivalent.
A
B
A.
3x-2x +0.5x
1.
1.5x
B.
3(x + 4)-2(x + 4)
2. x + 3
C.
6(x+4)-2(x + 5)
3. 2(2x + 7)
D.
3(x + 4)-2(x + 4) + 0.5(x + 4)
4. 1.5
For each situation write an eynression for the new balance using as few terms as possible
A. [tex]3x-2x+0.5x=1.5x[/tex], so the expressions are equivalent.
B. [tex]3(x+4)-2(x+4)=x+4[/tex], so the expressions are not equivalent. To make the expressions equivalent, add 1 to expression B.
C. [tex]6(x+4)-2(x+5)=6x+24-2x-10=4x+14=2(2x+7)[/tex], so the expressions are equivalent.
D. [tex]3(x+4)-2(x+4)+0.5(x+4)=1.5(x+4)[/tex], so the expressions are not equivalent. To make the expressions equivalent, multiply expression B by (x+4).
PLEASE HELP !! ILL GIVE 40 POINTS ; PLUS BRAINLIEST !! DONT SKIP ANSWER.
Which two shapes are equivalent fractions?
Answer:
B. 1 and 3
Step-by-step explanation:
The price of milk has been increasing by 4% per year. If he gallon of milk cost exactly 3 dollars right now, how much should it cost in 4 years?
different solution of salt are made up what valumo of
Answer:
Salt is sodium.
Answer:
Salt is Sodium.
Step-by-step explanation:
When you break down the compounds of salt you find molecules of sodium thus saying that salt is made up of sodium molecules.
A man is in a lighthouse tower that is 65 ft. He spots a ship at sea at an angle of depression of 20°. How far is the ship from the base of the lighthouse to the nearest foot?
Answer:
24 feet
Step-by-step explanation:
distance away is x
tan(20)=x/65
65*tan(20)=x
x=23.65806... feet
round to the nearest foot
x=24
Estimate 58.311+49.35 by first rounding each number to the nearest whole number.
Answer:
≈107
Step-by-step explanation:
58.311 will round down since 0.311 is less than half or 0.5. It will become 58. 49.35 will also round down since 0.35 is less than 0.5. This will be 49. 58+49=107. Since 107 is not the exact answer, you will use the approximately sign, or ≈.
For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots. The meat costs $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound. You spend $48.50 on 13.5 pounds of food. You buy twice as many carrots as potatoes.
Answer:
6lb meat2.5lb potatoes5Ib carrotsStep-by-step explanation:
M + P + C = 13.5
6M + 3P + C = 48.50
OM + 2P - C = O
2P = C
Therefore, there are 6 pounds of meat, 2.5 pounds of potatoes, and 5 pounds of carrots.
Find the area of the shaded region and choose the appropriate result.
Answer:
B) 12 cm²
Step-by-step explanation:
find area of shaded region, which is 4x4, or 16 cm² then subtract out the area of the unshaded region, which is 2x2, or 4 cm²; you get 12 cm²
3. How many solutions does the equation
2(x – 5) = 2x + 3 have?
A. O
C. 2
B. 1
D. infinitely many
This is my work: -10 does not equal 3, so therefore there is no solution
(03.06)
Using the completing the square method, rewrite f(x) = x2 + 4x - 1 in vertex form,
f(x) = (x + 2)2 + 1
Oь
f(x) - (x + 2)2
oc
f(x) = (x + 2)2 + 4
Od
f(x) = (x + 2)2 - 5
Natalie is almost always on time for class. In fact, the probability that she is on time for a given class is 90%. If there are 50 classes during the semester, what is the best estimate of the number of times out of 50 that Natalie is on time to class?
Answer:
45 out of 50
Step-by-step explanation:
First, 90/100 x 50 which = 45.
You could also do 5 x 9 which equals 45.
Hope this helps!!
Uhh help?? I’m highly confused I just want answers
Answer:
1) x = 5√3, y = 5
2) x = 16, y = 8
3) x = 10, y = 5
4) m = 9√15/10, n = 9√5/10
5) x = 3√3/2, y = 3/2
6) x = 6√5, y = 3√5
7) x = 5, y = 5
8) x = 5√2, y = 5
9) a = 2, b = √2
10) m = 10√6/3, n = 5√6/3
Explanation:
For special right triangles, there is a certain side ratio that applies due to the angle measurements which are opposite of the corresponding angles.
For 30° - 60° - 90° triangles (Scalene Right), we can use x as a marker for the side opposite of 30°, the side opposite of the 60° angle will be x√3, and the side opposite of the 90° angle will be 2x.
For 45° - 45° - 90° triangles (Isosceles Right),
Both 45° angles can be thought of as x, and the 90° angle can be thought of as x√2.
This is all computed as a result of the trigonometric functions:
SOH CAH TOA.
This is a shortcut for these specific triangles.
If you do not have the side marked as x, just do the inverse operation to get it.
90° is always opposite of the hypotenuse (longest side of a triangle; looks like a slant)
convert the following recurring decimal to a rational number 0,72
Answer:
The repeating decimal 0. 72 can be written as a ratio of two integers with numerator 8 and denominator 11 as the numerator and denominator, respectively. As a result, it is a logical number (named after ratio). If a number's decimal representation repeats or terminates, it may be seen to be rational.
Step-by-step explanation:
0.72 equals 8 /11
as a fraction.
How do you turn 0.72 repeating into a fraction?
Detailed Answer:
Step 1: To convert 0.72 repeating into a fraction, begin writing this simple equation:
n = 0.72 (equation 1)
Step 2: Notice that there are 2 digits in the repeating block (72), so multiply both sides by 1 followed by 2 zeros, i.e., by 100.
100 × n = 72.72 (equation 2)
Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.
100 × n = 72.72
1 × n = 0.72
99 × n = 72
72 /99
could be the answer, but it still can be put in the simplest form, i.e., reduced.
To simplify this fraction, divide the numerator and denominator by 9 (the GCF - greatest common factor).
n = 72
99 = 72 ÷ 9
99 ÷ 9 = 8 11 .
So, 0.72 = 8 /11
as the lowest possible fraction.
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(hope this helps can i plz have brainlist :D hehe)