(20 points) You are writing a research paper on plant cells. You got 48,600,000 results on the online search. How do you write 48,600,000 in scientific notation?
Which expression is equivalent to 34 ⋅ 3−9?
1 over 3 to the 13th power
1 over 3 to the 5th power
35
313
Answer:
b.1 over 3 to the 5th power.
Step-by-step explanation:
We are given that an expression
[tex]3^4\cdot 3^{-9}[/tex]
We have to find that which expression is equivalent to given expression
[tex]3^4\cdot 3^{-9}[/tex]
We know that [tex]a^b+a^c=a^{b+c}[/tex]
Using this identity
Then, we get [tex]3^4\cdot 3^{-9}=3^{4-9}=3^{-5}[/tex]
[tex]3^4\cdot 3^{-9}=\frac{1}{3^5}[/tex]
Using [tex]a^{-b}=\frac{1}{a^b}[/tex]
Hence, option b is true.
Answer:b.1 over 3 to the 5th power.
Are the traingles congruent? Why or why not?
Yes, A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
No, C is not congruent to any angle in DEF.
No, the congruent sides do not correspond.
Yes , A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
What are Congruent Triangles?
Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
• Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
• Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
• A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
From the given data ,
AB ≅ DE
and , ∠BAC = 33°
∠EDF = 33°
Therefore by rules of congruent triangles
The two angles are the same and the corresponding sides are same
Hence , The two triangles ΔABC and ΔDEF are congruent
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If you put down 20% on a $7000 car and pay monthly payments of $109.40 for 60 months, what is the total price of the car?
Answer:
7964
Step-by-step explanation:
Express -2 in triganomic form
Final answer:
To express -2 in trigonometric form, we find the magnitude (absolute value) and the argument (angle) of the complex number.
Explanation:
The trigonometric form of a complex number is expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the argument or angle.
In this case, to express -2 in trigonometric form, we first find the magnitude, which is the absolute value of -2, so |-2| = 2. The argument can be found using the arctan function, which is θ = arctan(b/a), where a is the real part and b is the imaginary part.
For -2, the real part is -2 and the imaginary part is 0. Thus, the argument is θ = arctan(0/(-2)) = arctan(0) = 0. Therefore, -2 in trigonometric form is 2(cos0 + isin0), which simplifies to just 2.
The measure of ______________ in a circle is half the measure of the intercepted arc.
A. a central angle
B. an interior angle
C. an inscribed angle
YES slay5 is correct the answer is : C. an inscribed angle
Answer: C. An inscribed angle
Step-by-step explanation:
Central angle is an angle that is subtended by an arc in a circle, it is also known as the arc's angular distance.
Interior angle is an angle between two sides inside a polygon or a shape.
Inscribed angle is an angle formed by two chords in a circle which have a common endpoint, and by the inscribed angle theorem, the measurement of inscribed angle is half the measure of the intercepted arc.
Cannon took out a mortgage for $85,290 on his new house. If the interest rate is 8.5 percent and the loan is for 25 years, how much will he pay monthly if he must pay $8.05 per $1,000?
Answer:
The answer is $686.584
Step-by-step explanation:
Given is, Cannon pays $8.05 per month for every $1,000, so we have a ratio: 8.05 / 1000
Now, we will find the second ratio which is an unknown payment per month over the price: x / 85290
Equaling them to solve for x :
[tex]\frac{8.05}{1000}=\frac{x}{85290}[/tex]
[tex]1000x=8.05*85290[/tex]
[tex]1000x = 686584.50[/tex]
So, x = 686.584
Hence, the answer is $686.584
f(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i
Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.
The zeros are:
x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*iFirst, for a given function f(x), we define the zeros as the values of x such that:
f(x) = 0.
Then we must solve:
f(x) = 16*x^4 - 81 = 0
Solving this for x leads to:
16*x^4 = 81
x^4 = 81/16
x^2 = ±√(81/16) = 9/4
x = ±√±(9/4) = ±3/2 and ±(3/2)*i
So there are 4 zeros, and these are:
x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*iWhere the two complex zeros come from evaluating the second square root on -9/4.
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Melanie is flying from washington,
d.c., to seattle. her flight leaves at 10
a.m. when her plane lands, the pilot announces that it is 2 p.m. in seattle. how long did her flight take
What is equivalent to xy/a - 1/b
A jacket that regularly cost $40 is on sale for $32 what is the percent decrease in the price of the jacket?
Which statement is 1?
option 5 btw is none of these
THIS IS TIMED AND I NEED HELP!!!
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)
Find the exact length of the curve. y = 3 + 2x3/2, 0 ≤ x ≤ 1
The exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\(\frac{2}{27} (10\sqrt{10} - 1)\)[/tex].
To find the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex], we can use the formula for arc length of a curve:
[tex]\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx \][/tex]
where a and b are the lower and upper bounds of the interval, respectively.
First, we need to find [tex]\(\frac{dy}{dx}\)[/tex], which represents the derivative of y with respect to x:
[tex]\[ \frac{dy}{dx} = \frac{d}{dx}(3 + 2x^\frac{3}{2}) = 0 + 3x^\frac{1}{2} = 3\sqrt{x} \][/tex]
Next, we substitute this derivative into the formula for arc length:
[tex]\[ L = \int_{0}^{1} \sqrt{1 + (3\sqrt{x})^2} dx = \int_{0}^{1} \sqrt{1 + 9x} dx \][/tex]
Now, we need to integrate [tex]\(\sqrt{1 + 9x}\)[/tex]L with respect to \(x\). We can do this by making a substitution. Let u = 1 + 9x, then du = 9dx and \(dx = \frac{du}{9}\). Substituting these into the integral, we get:
[tex]\[ L = \frac{1}{9} \int_{1}^{10} \sqrt{u} du \][/tex]
Now, we can integrate [tex]\(\sqrt{u}\)[/tex]:
[tex]\[ L = \frac{1}{9} \left[\frac{2}{3}u^\frac{3}{2}\right]_{1}^{10} = \frac{2}{27} \left[10^\frac{3}{2} - 1^\frac{3}{2}\right] \][/tex]
[tex]\[ L = \frac{2}{27} (10^\frac{3}{2} - 1) \][/tex]
[tex]\[ L = \frac{2}{27} (10\sqrt{10} - 1) \][/tex]
So, the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\( \frac{2}{27} (10\sqrt{10} - 1) \)[/tex].
To which part of the prism are the arrows pointing
the function f (x) =830(1.2)x represents the number of students enrolled at a university xyears after it was founded. each year the number of students is ----- the number the year before
Step-by-step explanation: Apex 9/25/19
How do I find the terms?
A. 15
B. 125
C. 135
D. 45
Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half hour. how many bacteria will the colony contain at the end of 24
A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.
Explanation:The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.
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You give your friend a head start of 20 feet in a race. A linear equation representing your friend’s progress (in feet) after x seconds is y = 9x + 20. A linear equation representing your progress (in feet) after x seconds is y = 9x. Will you catch up to your friend? Explain.
To catch up to your friend or not in a race explained with equations and steps.
The question is: Will you catch up to your friend? Explain.
Step-by-step explanation:
Friend's progress equation: y = 9x + 20
Your progress equation: y = 9x
To catch up, set the equations equal: 9x + 20 = 9x
Solve for x: 20 = 0 (This equation has no solution)
You will not catch up to your friend.
Mateo is studying a human hair with a diameter of 6.5 x 10^-4 inches and a horse hair with a diameter of 1.3 x 10^-3 inches. Which statement is true?
A.The horse hair is 2 times as thick as the human hair.
B.The horse hair is 5 times as thick as the human hair
C.The human hair is 2 times as thick as the horse hair
D.The human hair is 5 times as thick as the horse hair
Answer:
A.The horse hair is 2 times as thick as the human hair.
Step-by-step explanation:
We have been given that Mateo is studying a human hair with a diameter of [tex]6.5\times 10^{-4}[/tex] inches and a horse hair with a diameter of [tex]1.3\times 10^{-3}[/tex] inches.
Since proportions states that two fractions are equal, So we will use proportions to solve our given problem.
[tex]\frac{\text{Diameter of horse hair}}{\text{Diameter of human hair}}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}\times \text{Diameter of human hair}[/tex]
Now we will quotient rule of exponents to simplify our given problem.
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3--4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3+4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{1}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{13}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=2\times \text{Diameter of human hair}[/tex]
We can see that the diameter of horse hair is 2 times the diameter of human hair. Therefore, the horse hair is 2 times as thick as the human hair and option A is the correct choice.
The sum of two numbers is 49 . the smaller number is 17 less than the larger number. what are the numbers?
Final answer:
To solve the student's algebra problem, we defined variables, set up an equation based on the given conditions, and then solved for the larger number. Ultimately, we found the two numbers to be 33 and 16.
Explanation:
The student asked a problem that involves finding two numbers given that their sum is 49 and the smaller number is 17 less than the larger number. To solve this problem, we will use algebra.
Let the larger number be x and the smaller number be x - 17. According to the problem, the sum of these two numbers is 49:
x + (x - 17) = 49
Combine like terms: 2x - 17 = 49
Add 17 to both sides: 2x = 66
Divide by 2: x = 33
Since the larger number is 33, the smaller number is 33 - 17, which is 16.
Therefore, the two numbers are 33 and 16.
The table below shows the surface area y, in square feet, of a shrinking lake in x days:
Time (x)
(days) 5 10 15 20
Surface area (y)
(square feet) 90 85 70 61
Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points)
Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points)
Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
If a triangle has legs measuring 8 inches and 15 inches and has a hypotenuse measuring 17 inches, what is the ratio, in simplest form, of the shorter leg to the hypotenuse?
Roger owns a one acre piece of land . The length of the land is 484 feet. What is the width of his property
1 acre = 43560 square feet
43560 = 484 * X
X=43560/484 = 90
the width = 90 feet
Answer:
90 feet
Step-by-step explanation:
How old am i if i was born in 05/22/1965?
Answer:
In 2021 you would be 56 or 55 years old
Step-by-step explanation:
2021-1965=56 or the other way you could do it 52+4 because the other person said you would be 52 in 2017 so 4 years after you would be 55 or 56
Alicia drove 265 miles in 5 hours What is the average rate that she traveled 49 miles per hour 51 miles per hour 53 miles per hour 55 miles per hour
The function f(x) is represented by this table of values .Match average rate of change of f(x) with corresponding intervals
ms johnson and ms smith were folding report cards to send home to parents. the ratio of the number of report cards ms johnson folded to the number of report cards ms smith folded is 2:3. At the end of the day , ms Johnson and ms smith folded at total of 300 report cards. How many did each person fold?
Which of the following is a description of the data with a correlation coefficient of -0.3?
A.)low positive correlation
B.)low negative correlation
C.)high positive correlation
D.)high negative correlation