Which is equivalent to 5√1,215^x?
A)243x
B)1,215^1/5x
C)1,215^1/5x
D)243^1/x
Answer:
Option C is correct
The expression [tex](1215)^{\frac{1}{5}x}[/tex] is equivalent to [tex]\sqrt[5]{1215^x}[/tex]
Step-by-step explanation:
Simplify the radical Expression: [tex]\sqrt[5]{1215^x}[/tex]
A radical expression can be written by using the exponents and also using the following procedure:
[tex]\sqrt[n]{x} = x^{\frac{1}{n}}[/tex]
when x be non-negative then n can be any index
when x is negative, then n can be odd.
The following radical expression can be written as:
[tex]\sqrt[5]{1215^x} = (1215^x)^{\frac{1}{5}}[/tex] = [tex](1215)^{\frac{1}{5}x}[/tex]
Therefore, the expression [tex](1215)^{\frac{1}{5}x}[/tex] is equivalent to [tex]\sqrt[5]{1215^x}[/tex]
Consider the trinomial x2 – 9x + 18. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?
The required pair of number are -3 and -6
The factored form of the trinomial is (x-3) and (x-6)
The standard form of a quadratic equation is expressed as:
[tex]ax^2+bx+c=0[/tex]
Given the expression [tex]x^2 - 9x + 18.[/tex]
[tex]a=1\\b=-9\\c=18[/tex]
We are to get two values that we must add to get b, and that we will multiply that will give c.
The given values are -6 and -3
Check:
[tex]-6+(-3)=-6-3=-9\\-6(-3) = 18[/tex]
Factorize the trinomial
[tex]x^2-9x+18\\x^2-6x-3x+18\\x(x-6)-3(x-6)\\(x-3)(x-6)[/tex]
Hence the factored form of the trinomial is (x-3) and (x-6).
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Can someone please answer this for me I'm begging
The top of a cliff overlooking the ocean is 250 feet above sea level. The sea floor at the foot of the cliff is 40 feet below sea level. A rock falls off the cliff and drops toe the sea floor. What number represents the change in elevation of the rock.
The change in elevation of the rock is 290 feet.
Explanation:The change in elevation of the rock can be calculated by finding the difference in height between the top of the cliff and the sea floor.
Given that the top of the cliff is 250 feet above sea level and the sea floor is 40 feet below sea level, we can calculate the change in elevation by subtracting the elevation of the sea floor from the elevation of the top of the cliff.
The change in elevation is therefore 250 feet - (-40 feet), which simplifies to 250 feet + 40 feet = 290 feet. So, the number that represents the change in elevation of the rock is 290 feet.
WILL GIVE A BRAINLIEST IF UR RIGHT!!
Evaluate f(–2) in the given function below.
f(x)= 3x-3 if -5 ≤ x < 3 x+4 if 3 ≤ x ≤ 12
A.
–6
B.
–3
C.
2
D.
–9
Describe the relationship between the segments made when secant lines intersect outside a circle. Use the following image as reference.
The price of a community pool membership has a one-time sign-up fee and a monthly fee. The price can be modeled by the function y = 20x + 50, where x is the number of months.
What is the slope, and what does it represent?
Answer:
The answer is 20 and it represents the monthly fee.
Step-by-step explanation:
How many years will it take $1,000 invested at 7% interest to earn $280?
A game is biased such that the choices A-J have the following probabilities of winning: A 5% B 10% C 15% D 5% E 5% F 25% G 10% H 10% I 10% J 5% If you chose the letters D and H for 20 turns, how many times are you most likely to win? 1 2 3 4 5
Since we have chosen 2 letters, then the total probability of winning the game is the sum of the probabilities of each letter. Therefore:
Total probability of winning = Probability of D + Probability of H
Total probability of winning = 5% + 10%
Total probability of winning = 15%
Since we are playing the game for 20 turns, therefore out of those 20 games, we will win 15% of the time. So:
15% = 0.15
Winning times = 0.15 * 20
Winning times = 3
Therefore we have a chance or probability to win at least 3 games out of 20 turns.
Answer:
C: 3
Step-by-step explanation:
HELP PLEASE!!! (I will give brainliest to the first one to answer)
Your friend lives exactly 3 miles south of your house. That means the distance between your houses is negative three (-3) miles. Answer yes or no and explain your answer.
The statement that "the distance between your houses is negative three (-3) miles" is correct.
What is a cartesian coordinate?A Cartesian coordinate system on a plane is a coordinate system in which each point is uniquely specified by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicularly oriented lines measured in the same unit of length.
If we assume that your house is the origin of a graph, and each unit square on the graph is equal to 1 square mile. Therefore, if your friend's house is exactly south of your house then it will be on the y-axis that too in the negative direction.
Therefore, the statement that "the distance between your houses is negative three (-3) miles" is correct.
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What is the peremeter of this polygon? (With picture)
a scale model of a school building is 5 inches tall. If the building is 100 feet tall, find the scale of the model
Answer with Step-by-step explanation:
A scale model of a school building is 5 inches tall.
Actual size of the school building is 100 feet.
1 feet=12 inches
100 feet=12×100 inches
= 1200 inches
5 inch is representing 1200 inches
1 inch represents 1200/5 inches
1 inch represents 240 inches
or 1 inch represents 12×20 inch
or 1 inch represents 20 feet
Scale of the model is:
1 inch represents 240 inches
1 inch represents 20 feet
Which graph shows a triangle and its reflection image over the x-axis?
A. first picture
B. 2nd picture
C. picture 3
D. picture 4
A. is wrong
Answer-
In picture 4, the triangle is reflected over x axis.
Solution-
While reflecting a point over x axis, (x, y) → (x, -y) rule is followed.
Only the sign of y-coordinate is changed, keeping x-coordinate intact.
In the first picture, though the image is reflected, but it is reflected over y axis.
In the second picture, the image is first reflected over y axis, then it is translated 1 unit down.
We rotating a point 90° clockwise, (x, y) → (y. -x) rule is followed.
In the third picture, the triangle is rotated 90° clockwise and then translated 1 unit to right.
But, in case of the fourth picture, the figure is reflected over x axis. Only the y coordinates sign are changed, all the x coordinates are same as before.
what is the average rate of change for this quadratic function please help
A cell phone company orders 500 new phones from a manufacturer. If the probability of a phone being defective is 2.6%, predict how many of the phones are likely to be defective. Round to the nearest whole number.
A.)16 phones
B.)11 phones
C.)13 phones
D.)130 phones
(03.05 LC)
What is the volume of a cone (in cubic inches) with a radius of 3 inches and a height of 6 inches?
Use 3.14 for π. Round your answer to the nearest hundredth.
18.84 cubic inches
28.26 cubic inches
56.52 cubic inches
169.56 cubic inches
The volume of the cone is 56.52 cubic inches.
What is a cone?Having a flat base and a smooth tapering tip or vertex, a cone is a three-dimensional geometric object.
Given, the radius of the cone is 3 inches and the height of the cone is 6 inches.
The volume of a cone is given by,
V=(1/3)πr²h
V = (1/3) × 3.14 × 3² ×6
V = 56.52 cubic inches
Hence, the volume of the cone is 56.52 cubic inches.
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A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6 find the toal area of the pyramid
For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e?
e ≥ 50 or e ≤ 100
e > 50 or e < 100
50 < e < 100
50 ≤ e ≤ 100
Answer:
The answer is D.
Step-by-step explanation:
We know this because it is an "and" problem because it is numbers in between, not outside.
We also know it is "no less" or "no more" than 50 or 100. so we use a less than and equal too. Not just a less than sign.
Really hoped this helped, kind of in a test right now so just giving a brief way of how to figure this stuff out.
Continue and have fun learning!
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 18 1 3 7 4 6.5 6.4 4.3
NY 14 1 4.5 8.5 4 5.5 6.1 3.2
Which of the choices below best describes how to measure the center of this data?
- Both centers are best described with the mean.
-Both centers are best described with the median.
- The Rome data center is best described by the mean. The New York data center is best described by the median.
-The Rome data center is best described by the median. The New York data center is best described by the mean.
Final answer:
For Rome, both the mean and the median are almost identical, suggesting a well-balanced data set and either can be used to describe the center. For New York, the median might be a better measure if the data are skewed or contain outliers, but more information would be needed to make a definitive judgment.
Explanation:
When considering the best measure to describe the center of a data set, we should look at the presence of outliers and the distribution of the data. The mean is the numerical average and is sensitive to extreme values, while the median is the middle value that splits the data set in half and is less affected by outliers.
For Rome, the mean is 6.4 and the median is 6.5, which are very close to each other, indicating that the data is likely symmetric without extreme outliers. Thus, in Rome's case, either the mean or the median could serve as a good measure of center. On the other hand, New York's mean is 6.1 and the median is 5.5, suggesting slightly skewed data or the presence of outliers. However, without more data points or visual representation, it's difficult to determine which is more representative solely based on these summary statistics.
Considering the provided values and common statistical practice, the centers can potentially be described as follows:
The Rome data center can be best described by either the mean or the median as they are similar.
The New York data center might be best described by the median if outliers or skewness are present.
Find the area of the figure. PLEASE HELP
find area of larger figure
then subtract area of cut out
larger figure 40 *36 = 1440 square yards
cut out = 20 *10 = 200 square yards
1440-200 = 1240 square yards total
What would you do to isolate the variable in the equation below, using only one step? x + 5 = -12 Select one: a. Add 5 to both sides of the equation. b. Subtract 5 from both sides of the equation. c. Add 12 to both sides of the equation. d. Subtract 12 from both sides of the equation.
To isolate the variable in x + 5 = -12, subtract 5 from both sides of the equation. This leads to the equation x = -12 - 5.
Explanation:In order to isolate the variable x in the equation x + 5 = -12, you should subtract 5 from both sides of the equation. This gives us the equation in a simplified form that allows us to determine the value of x. The idea here is to cancel out the +5 on the left side by subtracting 5 from both sides, resulting in x = -12 - 5. Hence, the answer is option b.
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Match the sets of points representing one-to-one functions with the sets of points representing their inverse functions.
Tiles
h = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
g = {(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)}
f = {(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)}
i = {(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)}
Pairs
Sets of Points Representing Inverse Functions Sets of Points Representing Functions
h-1 = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
arrowBoth
i -1 = {(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)}
arrowBoth
g-1 = {(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)}
arrowBoth
f -1 = {(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)}
arrowBoth
NextReset
Each pair has the inverse points corresponding to the points in the original set.
To match the sets of points representing one-to-one functions with the sets of points representing their inverse functions, we need to find the pairs where each point in one set corresponds to the inverse point in the other set.
Here are the matches:
1. Set of Points Representing Function: [tex]\( h = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( h^{-1} = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]
2. Set of Points Representing Function: [tex]\( g = \{(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( g^{-1} = \{(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)\} \)[/tex]
3. Set of Points Representing Function: [tex]\( f = \{(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( f^{-1} = \{(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)\} \)[/tex]
4. Set of Points Representing Function: [tex]\( i = \{(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( i^{-1} = \{(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)\} \)[/tex]
Each pair has the inverse points corresponding to the points in the original set.
Are theses right ? Or are some wrong please let me know wrong and right ones
Boating across a river, the current moves you downstream. Instead of going directly across the river, the boat moves at a 10 degree angle. If the river is 420 feet across, how far downstream will you end up?
To solve this problem, we use the tan function. The distance across the river is the adjacent side, the distance drownstream is the opposite side while the direction of the boat is the hypotenuse.
tan θ = opposite side / adjacent side
tan 10 = opposite side / 420 ft
opposite side = 74.06 ft
Therefore the boat will move about 74 ft downstream.
Why is it difficult to measure circumference accurately? answers?
One of either the circumference or distance across is not rational. If you have a bit of string precisely 1 inch long and you make it into an idealize circle, the distance across of that circle will be an irrational value. You could try to measure it, however regardless of how precisely you measured it, it would in any case not be very sufficiently precise. So, you can never know precisely what the diameter is just by measuring.
What's more, on the off chance that you took that string and made a width with it, the circumference would be irrational and you could never have the capacity to measure the circumference precisely enough. Whatever you quantified would be close however not correct.
the area of Juan's garden after he adds a border x feet wide is equal to (3+2x)(6+2x) which polynomial represents the area of Juan's garden?
A. 4x^4+30x+18
B. 4x^2+22x+27
C. 4x^2+18x+18
D. 4x^2+6x+18
Find the missing value. Show your work
(GEOMETRY, PLEASE HELP!!)
Which of the following is a solution of x2 + 5x = −2?
5 plus or minus the square root of 33 divided by two.
5 plus or minus the square root of 17 divided by two
negative 5 plus or minus the square root of 33 divided by two.
negative 5 plus or minus the square root of 17 divided by two.
Answer:
negative 5 plus or minus the square root of 17 divided by two: [tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
Step-by-step explanation:
We have the equation
[tex]x^2+5x=-2[/tex]
[tex]x^2+5x+2=0[/tex].
To solve it, we are going to use the general formula. This formula is used to find the solutions of quadratic equations.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a is the coefficient of [tex]x^2[/tex], in this case a=1, b is the coefficient of x, in this case b=5 and c is the independent term, in this case c=2.
[tex]x=\frac{-5\pm\sqrt{5^2-4(1)(2)}}{2(1)}[/tex]
[tex]x=\frac{-5\pm\sqrt{25-8}}{2}[/tex]
[tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
If at least one independent variable is between-groups and at least one is within-groups, the design is referred to as:
A variable is an object that you are trying to measure. It has two types; independent and dependent variable. An independent variable is a variable that is not affected by other variables. A dependent variable on the other hand is a variable that depends on the other variables. Suppose you want to know the quality of sleep of the students in their academic performance. The quality of sleep is the independent variable and the academic performance is the dependent variable. There are also controlled variables in an experiment. A controlled experiment is an experimental setup designed to test the hypotheses. It has one or more conditions (independent variables) and measures (dependent variables). It is necessary to change more than one variable, but all of the experimental conditions will be controlled so that only the variables being examined change and the amount or way of change is measured.
PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?
3y − x = −6
4y − x = 44
3y + x = −6
4y + x = 44
3y − 3x = −6
4y − 4x = 44
3y + 3x = −6
4y + 4x = 44
The system of equations are 3y − x = −6 and 4y − x = 4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
One third x − 2 = one fourth x + 11
1/3x - 2 = 1/4x + 11
Now let us take y as 1/3x - 2
y= 1/3x - 2
3y=x-6
Subtract x on both sides
3y-x=-6
and Let us consider the right side equation
y=1/4x + 11
4y=x+44
Subtract x on both sides
4y-x=44
Hence, the system of equations are 3y − x = −6 and 4y − x = 44
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