Expressions with exponents can be simplified using rules of exponents, and numbers can be converted into scientific notation by recognizing how to move the decimal point and denote magnitude with the power of ten.
To simplify expressions with exponents and convert numbers into scientific notation, we apply the rules of exponents and understand the format of scientific notation.
(2t)⁻⁶: Using the negative exponent rule, which states that a⁻⁶ = 1/a⁶, we can simplify this expression to 1/(2⁶t⁶).
(w⁻²j⁻⁴)⁻³(j⁷j³): To deal with the negative and compounded exponent, we invert and take the cube, resulting in w⁶j¹². Then, multiply the j terms together to get w⁶j¹⁵.
To simplify a²b⁻⁷c⁴ / a⁵b³c⁻², we subtract exponents when dividing like bases, resulting in a⁻³b⁻¹°c⁶.
For the expression z⁻ᵗ(mᵗ)¹, when any variables are raised to the zero power, the result is 1. Thus, the entire expression evaluates to 1 due to (mᵗ)¹ becoming 1.
Converting to scientific notation: To express 0.0002603 in scientific notation, it becomes 2.603 × 10⁻⁴. The number 5.38 × 10² in standard notation is 538.
By applying these step-by-step procedures, we can simplify expressions using positive exponents and accurately convert between standard notation and scientific notation.
Please Help!!!
The figure shows a line graph and two shaded triangles that are similar:
Which statement about the slope of the line is true? (5 points)
Select one:
a. It is fraction 1 over 2 throughout the line.
b. It is 2 throughout the line.
c. The slope from point O to point A is fraction 1 over 2 time the slope of the line from
point A to point B.
d. The slope from point O to point A is two times the slope of the line from point A to point B.
Help see the picture
The table below represents the displacement of a bird from its nest as a function of time: time (hours) x displacement from nest (miles) y 0 12 1 20 2 28 3 36 4 44 part
a.what is the y-intercept of the function, and what does this tell you about the bird? part
b.calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. part
c.what would be the domain of the function if the bird continued to fly at this rate until it traveled 172 miles from the nest?
Place the indicated product in the proper location on the grid.
(5c +2/3 )(5c -2/3 )
Answer:
The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]
Step-by-step explanation:
given : The polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]
We have to place the indicated product in the proper location o the grid.
Consider the given polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]
Apply identity of difference of square
[tex]\left(a+b\right)\left(a-b\right)=a^2-b^2[/tex]
We have,
[tex]=\left(5c\right)^2-\left(\frac{2}{3}\right)^2[/tex]
Simplify, we have,
[tex]=25c^2-\frac{4}{9}[/tex]
Thus, The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]
Location on gris shown below.
What is the slope of the line that contains the points (4,-1) and (-1,4)?
Answer:
-1
Step-by-step explanation:
Write the equation of a line that includes the point (1, 5) and has a slope of 3 in standard form. 3x + y = 5 –3x + y = 5 3x + y = 2 –3x + y = 2
Use the quadratic formula to determine the exact solutions to the equation. 6x2+4x−3=0
The correct answer is [tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]
To find the exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex]using the quadratic formula, we can follow these steps:
Given quadratic equation: [tex]6x^2 + 4x - 3 = 0[/tex]
[tex]a = 6, b = 4, c = -3[/tex]
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-4 \pm \sqrt{4^2 - 4(6)(-3)}}{2(6)}[/tex]
[tex]x = \frac{-4 \pm \sqrt{16 + 72}}{12}[/tex]
[tex]x = \frac{-4 \pm \sqrt{88}}{12}[/tex]
[tex]x = \frac{-4 \pm \sqrt{4 \cdot 22}}{12}[/tex]
[tex]x = \frac{-4 \pm 2\sqrt{22}}{12}[/tex]
Solution 1: [tex]x = \frac{-4 + 2\sqrt{22}}{12}[/tex]
Solution 2: [tex]x = \frac{-4 - 2\sqrt{22}}{12}[/tex]
Therefore, the two exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex] are:
[tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]
Please help me. I'm confused. Consider the following geometric sequence. -5, 10, -20, 40,... If the recursive formula for the sequence above is expressed in the form a^n=b*^n-1, determine the value of B. B= (choices are 2, -2, 5, -5)
Answer:
-2
Step-by-step explanation:
If a line crosses the y-axis at (0,8) and has a slope of -1/8,what is the equation of the line?
A.y= 1/8x+8
B.y=-1/8x-8
C.y=8x-8
D.y=-1/8x+8
Please help me!!!!!!
Answer:
d
Step-by-step explanation:
what is the area of a regular pentagon with an apothem of 25.1 and a perimeter of 182mm
A globe in a brass stand has a diameter of 40 in . what is the volume of the globe to the nearest cubic inch?
Suppose the line of best fit is being found for some data points that have an r-value of 0.876. If the standard deviation of the x-coordinates is 5.559, and the standard deviation of the y-coordinates is 7.163, what is the slope of the line to three decimal places?
Answer: 1.129
Step-by-step explanation:
In statistics, the slope of the line is given by :-
[tex]b=r\dfrac{\sigma_y}{\sigma_x}[/tex],
[tex]\text{where r is correlation coefficient,}\\\sigma_y\text{ is standard deviation of the y-coordinates,}\\\sigma_x\text{ is standard deviation of the x-coordinates,}[/tex]
[tex]\text{Given: }r=0.876\\\sigma_x=5.559\\\sigma_y=7.163[/tex]
Now, the slope of the line will be :-
[tex]b=0.876\times\dfrac{7.163}{5.559}\\\\\Rightarrow\ b =1.12876200756\approx1.129[/tex]
Hence, the lope of the line to three decimal places =1.129
A warranty identification number for a certain product consists of a letter of the alphabet followed by four-digit number. How many possible identification numbers are there if the first digit of the four-digit number must be nonzero?,
At breakfast, restaurant charges $2 for the first cup of orange juice and then $1 for each refill which graph represents this situation
It would be 2 + 1x. The y intercept is 2, and every unit, you would multiply those numbers together. For example, if the x axis is 6, then you would do 2 + 6 which is 8 on the y axis and etc.
Answer:
its D
Step-by-step explanation:
A yoga membership costs $16 and an additional $7 per class. Write a linear equation modeling the cost of a yoga membership.
y = 16x + 7
y = 7x + 16
y = 23x + 7
y = 23x + 16,
The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x2, which of the following could be the equation of G(x)?
A. G(x) = 4x2
B. G(x) = -1/4x2
C. G(x) = -4x2
D. G(x) = 1/4x2
Answer:
The correct option is C.
Step-by-step explanation:
The given function is
[tex]F(x)=x^2[/tex]
The transformation of the function is defined as
[tex]G(x)=kF(x)[/tex]
If k>1, then the graph of function F(x) stretched vertically and If 0<k<1, then the graph of function F(x) compressed vertically.
It is given that the graph of F(x) can be stretched vertically, it means the value of k must be greater than 1.
The graph of F(x) is flipped over the x-axis, so the function G(x) is equal to the negative of k times of F(x).
[tex]G(x)=-kF(x)[/tex]
Where must be greater than 1.
In option 3, G(x) is equal to the negative of 4 times of F(x). Only in this option, there is negative relation between F(x) and g(x) with k>1.
[tex]G(x)=-4F(x)[/tex]
Therefore the correct option is C.
what are the answers to all of these questions?
fourteen less than three fourths of a number is negative eight
the sum of two number is 10. the difference between the numbers is 4. what are the two numbers.
A poker hand consist of 5 cards?
a.find the total number of possible five card poker card hands.
b.find the number of ways in which one can king can be selected? c)find the number of ways in which four aces can be selected .
d.find the number of ways of getting four aces and one king.
In poker probability calculations, there are 2,598,960 possible five-card hands, various specific hand combinations such as those containing a king or four aces have their own probability, which can be determined using the formulas for combinations.
Calculations for Poker Probabilities
The subject of probability in a poker hand involves various combinations and permutations. Here's how the calculations are made:
Total number of five-card poker hands: The total number is calculated using combinations, as the order in which cards are drawn does not matter. This is given by the combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of available cards (52), and r is the number of cards drawn (5). Thus, there are 52! / (5!(52-5)!)= 2,598,960 possible hands.
Number of ways one king can be selected: There are four kings in a deck, so there are C(52, 5) - C(48, 5) ways to choose a hand with at least one king, as you subtract the number of hands without any kings from the total number of hands.
Number of ways four aces can be selected: There is only one way to choose all four aces, and then there are 48 remaining cards to choose the fifth card from, which gives 48 combinations.
Number of ways of getting four aces and one king: There are four kings to choose from and one specific combination of aces, so there are 4 ways to have a hand with four aces and one king.
Set operations including cardinality of power sets and listing the elements of a power set and finding the number of subsets of a given size. let u = {-1, 0, 1, 2, 3, 4, 6} , a = {-1, 1, 2, 3, 4} and b = {0, 2, 4, 6}. find
a.a u b,
b.a ∩ b,
c.b – a,
d.the power set of b and its cardinality
The union of A and B is {-1, 0, 1, 2, 3, 4, 6}, the intersection is {2, 4}, and the difference B - A is {0, 6}. The power set of B contains 16 subsets.
Set Operations: Union, Intersection, Difference, and Power Sets
Let's solve the given problems step by step:
a. The union of sets A and B (A ∪ B)
A ∪ B represents all unique elements that are in either set A or set B.
Given: A = {-1, 1, 2, 3, 4} and B = {0, 2, 4, 6}
A ∪ B = {-1, 0, 1, 2, 3, 4, 6}
b. The intersection of sets A and B (A ∩ B)
A ∩ B represents all elements that are present in both sets A and B.
A ∩ B = {2, 4}
c. The difference of sets B and A (B - A)
B - A represents all elements that are in set B but not in set A.
B - A = {0, 6}
d. The power set of B and its cardinality
The power set of a set is the set of all its subsets, including the empty set and the set itself. If a set has n elements, its power set will contain 2^n subsets.
B = {0, 2, 4, 6}
The power set of B is: { {}, {0}, {2}, {4}, {6}, {0, 2}, {0, 4}, {0, 6}, {2, 4}, {2, 6}, {4, 6}, {0, 2, 4}, {0, 2, 6}, {0, 4, 6}, {2, 4, 6}, {0, 2, 4, 6} }
The cardinality of the power set of B is 2^4 = 16.
In summary:
A ∪ B = {-1, 0, 1, 2, 3, 4, 6}
A ∩ B = {2, 4}
B - A = {0, 6}
The power set of B has 16 elements.
What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –(x – 6) and passes through the point (−2, −2)?
hElP!
A carpenter designs two cabinets: one in the shape of an oblique rectangular prism and one in the shape of a right rectangular prism. The volume of each cabinet is 4,608 cubic inches. The oblique rectangular prism is 48 inches tall and has an edge length of 64 inches. The right rectangular prism has a height of 48 inches. Which statements about the cabinets are true? CHECK ALL THAT APPLY
a. The cabinets have the same base area.
b.The base area of the oblique prism is smaller than the base area of the right prism.
c.The cabinets may have the same base dimensions.
(MORE DOWN BELOW),
Answer:
A- The cabinets have the same base area.
C- The cabinets may have the same base dimensions.
D- The cabinets may have different base dimensions
Step-by-step explanation:
Answer:
A. C. D.
Step-by-step explanation:
You and your friend are standing back-to-back. Your friend runs 10 feet forward and then 8 feet right. At the same time, you run 11 feet forward and then 12 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?
What is the measure of ∠ABD?
27°
54°
114°
124°
we know that
An exterior angle is equal to the sum of the two non adjacent angles
so
In this problem
[tex](4n+6)\°=2n\°+60\°[/tex]
Solve for n
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](4n-2n)\°=(60-6)\°[/tex]
Combine like terms
[tex]2n\°=54\°[/tex]
[tex]n=27\°[/tex]
Find the measure of angle ABD
∠ABD=[tex](4n+6)\°[/tex]
Substitute the value of n
∠ABD=[tex](4*27+6)\°=114\°[/tex]
therefore
the answer is the option
[tex]114\°[/tex]
Answer:
the answer is 114
Step-by-step explanation:
hope i helped all of you guys and girls
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Help please asap
1. The area of a rectangular carpet is given by the trinomial 5x^2 - 3x - 14. What are the possible dimensions of the carpet? Use factoring.
A. (5x + 7) and (-x - 2)
B. (5x + 7) and (x - 2)
C. (5x - 7) and (x - 2)
D. (5x - 7) and (x + 2)
2. The area of a rectangular barnyard is given by the trinomial 6x^2 + 7x – 20. What are the possible dimensions of the barnyard? Use factoring
A. 2x - 5 and 3x + 4
B. -2x - 5 and -3x + 4
C. 2x + 5 and 3x - 4
D. 2x - 5 and 3x - 4
The possible dimensions for the rectangular carpet with an area represented by the trinomial 5x^2 - 3x - 14 are (5x + 7) and (x - 2). For the barnyard with area 6x^2 + 7x - 20, the dimensions are (2x - 5) and (3x + 4).
To find the possible dimensions of the rectangular carpet with area 5x^2 - 3x - 14, we need to factor the trinomial. Factoring the trinomial, it is evident that we need two numbers whose product is -70 (5 * -14) and whose sum is -3. Factoring the trinomial we get (5x + 7)(x - 2), so the possible dimensions of the carpet are (5x + 7) and (x - 2), which corresponds to option B.
Similarly, to determine the dimensions of a barnyard with area 6x^2 + 7x - 20, we again factor the trinomial. We are looking for two numbers that multiply to -120 (6 * -20) and add up to 7. Factoring yields (2x - 5)(3x + 4), so the possible dimensions of the barnyard are (2x - 5) and (3x + 4), which corresponds to option A.
Exponential Growth/Decay Function
Hint/Tip:
Remember, the basic general exponential function form is: y = Abx In detail, b is written as (1-r) where r is the rate of growth or decay, so our detailed formula is: y = A(1-r)x
Always work with the rate as a decimal number, not as percentage. If the rate is given as percent (%), you will need to divide it by 100 to have the decimal form.
The value of a car is $21,500. It loses 12% of its value every year.
(a) Write a function that represents the value y (in dollars) of the car after x years.
(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
point j has coordinate (-2,8) and point r has coordinates (-7,-3. find the coordinate of point A that partition line segment JR in the ratio of 5:2
In triangle XYZ, the length of side XY is 24 mm and the length of side YZ is 34 mm. Which of the following could be the length side XZ?
A. 8 mm
B. 63 mm
C. 42 mm
D. 60 mm