Answer:12+27= 39.
Step-by-step explanation: You would do 6x4 first due to PEMDAS. Then you would do 24 divided by 2 which is 12. Then, you add it to 3 to the power of 3, which is 39. The simplified equation would be be 12+27.
A right triangle with vertices P(-3,9) Q(-3,5) R(-7,5) is reflected on the y-axis then the image is rotated 180 degrees about the origin. What are new coordinates of the right triangle?
We could start by drawing the triangle we are given. However, it would be better to draw the triangle after the y-axis reflection. To calculate the y-axis reflection, we first think as follows
We see that the reflected point is at the same height as the original point. This means that the y coordinate should remain the same. So, the only thing that changed is the x coordinate. This suggests that, to calculate the reflection about the y-axis, we simply multiply by -1 the first coordinate. So, after the reflection we get the points
P'(-3*(-1),9)=(3,9)
Q'(-3*(-1),5)=(3,5)
R'(-7*(-1),5) =(7,5)
Now, if we plot this points we get
So, if we rotate this 180° we would get the following
So the new points after rotating 180°, would be
P''(-3,-9)
Q''(-3,-5)
R''(-7,-5)
How do I graph this?
Answer:
See below
Step-by-step explanation:
Write the integer that represents the opposite of the opposite. A temperature rise of 15 degrees Fahrenheit
The given number is 15, which express degrees Fahrenheit.
The opposite of the opposite means the negative of the negative because an opposite number refers to multiply by -1.
[tex]-(-15)[/tex]Hence, the opposite of the opposite of 15 is -(-15).If UV = 9 and WX = 14, what is the length of the diameter of circle X?
Given:
[tex]UV=9\text{ ; WX=14}[/tex][tex]\begin{gathered} UW=2(UV) \\ UW=2(9) \\ UW=18 \end{gathered}[/tex][tex]\text{Diameter of the circle X}=2(UW+WX)[/tex][tex]\text{Diameter of the circle X}=2(18+14)[/tex][tex]\text{Diameter of the circle X}=2(32)[/tex][tex]\text{Diameter of the circle X}=64[/tex]Given the following geometric sequence, find the common ratio.33,99,297,891,2673,…Give your answer as a reduced fraction, if necessary.
SOLUTION:
From the given geometric sequence gives
The common ratio. reduce
[tex]r=\frac{99}{33},r=\frac{297}{99},r=\frac{891}{297}[/tex]Simplifying this gives
[tex]r=3[/tex]Therefore the common ratio is r=3
find the equation of the line:
parallel to the x-axis passing through the point (-3;4)
Answer:
y=4
Step-by-step explanation:
Since any two parallel lines have the same slope we know the slope of the unknown line is 0 (its from the slope of y=0(x)+0 which is also 0).
Also since the unknown line goes through (3,4), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
y−y
1
=m(x−x
1
) where m is the slope and (x
1
,y
1
) is the given point.
Now substituting the values:
y−4=0(x−3)
⇒y−4=0
⇒y=4
Hence, the equation of the line is y=4.
in a student election, sam received 20% more votes then john.If 99 people voted for them altogether, how many votes did john receive?
Let's call the votes John recieved x
If Sam recieved 20% more votes than John, it means that the total votes Sam recieved are 1.20x
We know that the total amount of votes add up to 99. Thereby,
[tex]\begin{gathered} x+1.20x=99\rightarrow2.20x=99\rightarrow x=\frac{99}{2.20} \\ \rightarrow x=45 \end{gathered}[/tex]Thereby, John recieved 45 votes in total
use the first five terms of the exponential series of e^x and a calculator to approximate e^0.2 to the nearest hundredth
Solution:
Using the Maclaurin series;
[tex]e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}+...[/tex]Thus;
[tex]\begin{gathered} x=0.2; \\ \\ e^{0.2}=1+(0.2)+\frac{(0.2)^2}{2!}+\frac{(0.2)^3}{3!}+\frac{(0.2)^4}{4!} \\ \\ e^{0.2}\approx1.22 \\ \end{gathered}[/tex]ANSWER: 1.22
To compare two values, first convert the values to the same ____
To compare two values, first convert the values to the same measuring unit.
What is a measuring unit?
The definition of a unit of measurement is a certain magnitude of a quantity that has been defined and acknowledged by law or convention and is used as a standard for measuring other quantities of the same kind.
Any other quantity of that sort can be expressed as a multiple of the unit of measurement. For instance, a length is a physical quantity. Measurement is the process of identifying a number that accurately captures the amount of anything.
A measuring unit is a recognized quantity that is used to represent a physical quantity. Let's examine a few of the common units for measuring physical quantities.
Given that, to compare the values
If we want to compare two values first we have to convert it in same measuring unit.
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There are 17 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers
finish first through fifth?
This can be solved using permutations
What are permutations?
A permutation of a set in mathematics is a loosely defined organization of its members into a sequence or linear order, or, if the set is already sorted, a rearranging of its elements. The act or process of shifting the linear order of an ordered set is often referred to as "permutation." Permutations are distinct from combinations, which are random picks of certain members of a collection. For example, there are six permutations of the set 1, 2, 3 represented as tuples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 1, 2). (3, 2, 1). Permutations include anagrams of words with various letters.
No. of ways using permutation = ¹⁷P₅ = 742560
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Write a recursive formula and an explicit formula for the following arithmetic sequence.
-5, 1, 7, 13, 19, ...
A recursive formula is a₁ = a₁ = ₁
(Simplify your answers.)
The recursive formula is aₙ₊₁ = aₙ + 6 and the explicit formula is aₙ = -5 + (n-1)6 for the given sequence.
What is the recursive formula of an arithmetic sequence?The recursive formula to find the nth term of an arithmetic sequence is:
aₙ = aₙ₋₁ + d for n ≥ 2
where aₙ is the nth term of an A.P.
In arithmetic, sequence d represents the common difference.
Where aₙ is the nth term of the sequence and a₁ is the first term
Given the sequence -5, 1, 7, 13, 19, ...
The first term (a₁) = -5
a₂ = 1
a₃ = 7
a₄ = 13
a₅ = 19
The common difference (d) = a₅ - a₄= a₄ - a₃= a₃ - a₂ = 6
So, aₙ₊₁ - aₙ = 6
aₙ₊₁ = aₙ + 6
The explicit formula of the given sequence is given by,
aₙ = a₁ + (n-1)d
aₙ = -5 + (n-1)6
Hence, the recursive formula is aₙ₊₁ = aₙ + 6 and the explicit formula is aₙ = -5 + (n-1)6 for the given sequence.
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2)Point C is reflected across a b such that in maps and to point D. Point C and D are then connected to form CD. Which of the following must be true? A)CD bisects ABB)AB=CD C)CD is parallel to ABD) CD is perpendicular to AB
Point C is reflected across a line AB such that it maps to point D.
Points C and D are then connected to form a line CD.
Let us draw a figure to better understand the problem
As you can see from the above figure,
We have reflected the point C across the line AB and the reflected point is mapped to point D.
Then we connected the point C to point D using the red color to form line CD.
The line CD is perpendicular to line AB.
All other options depend on the exact scenario which means they may or may not be true.
But we can be sure about option D that it must always be true.
Therefore, option D is the correct answer.
what is the measure of ZXY in the figure below
we get that
[tex]5x+3x=180\rightarrow8x=180\rightarrow x=\frac{180}{8}=22.5[/tex]so the angle ZXY is:
[tex]\angle ZXY=3\cdot22.5=67.5^{\circ}[/tex]2x - 8 = 6 what is the equation
Answer:
Step-by-step explanation:
x = 7
determine the pattern then write the decimal to complete the decimal grid 0.34 0.65
0.7768
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Although part of your question is missing, the complete question is "determine the pattern then write the decimal to complete the decimal grid 0.34 0.65 as shown in a grid".
The decimals in given pattern is 0.23, 0.24, 0.25, 0.34, 0.43, 0.44, 0.45, 0.54 , 0.63, 0.64, 0.65.
In the decimal grid, there are 5 horizontal rows and 3 vertical columns. In each row, the next element increases by 0.01 and In each column, the next element increases by 0.10.
So in the first row, the elements are 0.23, 0.24, 0.25
The given element below that is given as 0.34
The elements in the next row are 0.43, 0.44, 0.45
The element in the fourth row is 0.54
The elements of the last row are 0.63 and 0.65
Hence, completing the pattern missing elements are 0.23, 0.24, 0.25, 0.43, 0.44, 0.45, 0.54 and 0.63
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2. In the 1936 US presidential election polls, the Literary Digest held a poll that forecast that Alfred E. Landon would defeat Franklin Delano Roosevelt by 57% to 43%. They had used lists of telephone and automobile owners to select their sample. George Gallup, using a much smaller sample (300,01 rather than 2,000,000) , predicted Roosevelt would win, and he was right. What went wrong with the Literary Digest poll?
Explanation
We can infer that the Literary Digest poll was wrong because it was biased.
We are told that the poll used lists of telephone and automobile owners to select their sample which doesn't give a full representation of all those who will vote in the election.
So we can infer that the problem with the Literary Digest poll is that it was Biased
Evaluate the logarithmic expression.log464
Answer:
3
Explanation:
Given the logarithmic expression:
[tex]\log_464[/tex]First, express 64 as a power of 4:
[tex]\log_44^3[/tex]Next, apply the power law of logarithms:
[tex]\begin{gathered} \log a^n=n\log a \\ \implies\log_44^3=3\log_44 \end{gathered}[/tex]Finally, by the unity law:
[tex]\begin{gathered} \log_aa=1 \\ \implies3\;\log_44=3\times1=3 \end{gathered}[/tex]The result of the evaluation is 3.
R !!! CR Algebra 1 B (GP) 21-22 / 8:Radical Expressions and Equations 10 8 2 10-8 -6 -4 -20 2 6 10 -2 -6 00 10 Match the graph with its function by translating the graph of y = Vx. 6. O y=√x+2 O y = √x-2 O y=√x+2 O y=√x-2 ј е co) a Search the web and Windows
This is the graph of the parent function:
[tex]y=\sqrt[]{x}[/tex]But translated 2 units up. Therefore, the equation of this graph is given by:
[tex]y=\sqrt[]{x}+2[/tex]What is a composite number? Options: A number.A number with multiple factors.A number that divides into itself without leaving a remainder.
A composite number is a positive integer that has more than two factors, for example, 4, it can be expressed as 2x2=4 and 1x4=4.
Then, the answer is a number with multiple factors
100 people were asked if they liked Math, Science, or Social Studies. Everyone answered thatthey liked at least one.56 like Math43 like Science35 like Social Studies18 like Math and Science10 like Science and Social Studies12 like Math and Social Studies6 like all three subjects
SOLUTION
Venn Diagram for the problem is shown below
Now from the Venn Diagram the number at the center of the intersection of all three circles is 6. This represents the number of students that liked all three subjects.
Number that liked Math and Science is 18, So number that liked "Math and Science only", will be 18 (all the people that like Math and Science) minus 6 (numbers that liked all three subjects). This becomes 12.
This was how 4 (numbers that liked science and social studies
What is the word for added and subtracted parts of an expression
The term is the word that is used to represent the added and subtracted parts of an expression.
What is a term in an addition and subtraction?When one is writing a mathematical expression, they would have to make use of numbers, variables as well as symbols in the equation that is being written.
The operators that are written are seen to be connected through the use of symbols of multiplication, addition or otherwise.
The parts of the expression that are known to be fully connected to the addition as well as the subtraction is what is referred to as terms.
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I need the answers please SHOW WORK
The solution to each equation involving absolute values:
k = 8 ∨ k = - 8 k = 7 ∨ k = - 7 a = 6 ∨ a = - 10 n = 5 / 2 ∨ n = - 5 / 2 m = - 4 ∨ m = 22 x = - 4 ∨ x = 34 / 5 x = 9 ∨ x = - 16 a = - 12 / 5 ∨ a = 6 / 5How to solve equations involving absolute values
In this exercise we have eight cases of equations involving absolute values. The definition of absolute value is:
|x| = a, where x = a, for x ≥ 0 and - x = a, for x < a.
Now we proceed to resolve on each case:
Case 1
|k| = 8
k = 8 ∨ - k = 8
k = 8 ∨ k = - 8
Case 2
|x| = 7
k = 7 ∨ - k = 7
k = 7 ∨ k = - 7
Case 3
|a + 2| = 8
a + 2 = 8 ∨ - a - 2 = 8
a = 6 ∨ a = - 10
Case 4
|8 · n| / 10 = 2
|8 · n| = 20
8 · n = 20 ∨ - 8 · n = 20
n = 20 / 8 ∨ n = - 20 / 8
n = 10 / 4 ∨ n = - 10 / 4
n = 5 / 2 ∨ n = - 5 / 2
Case 5
|- m + 9| = 13
- m + 9 = 13 ∨ m - 9 = 13
m = - 4 ∨ m = 22
Case 6
|7 - 5 · x| = 27
7 - 5 · x = 27 ∨ - 7 + 5 · x = 27
5 · x = - 20 ∨ 5 · x = 34
x = - 4 ∨ x = 34 / 5
Case 7
|2 · x + 7| / 5 = 5
|2 · x + 7| = 25
2 · x + 7 = 25 ∨ - 2 · x - 7 = 25
2 · x = 18 ∨ 2 · x = - 32
x = 9 ∨ x = - 16
Case 8
|- 3 - 5 · a| / 9 = 1
|- 3 - 5 · a| = 9
- 3 - 5 · a = 9 ∨ 3 + 5 · a = 9
5 · a = - 12 ∨ 5 · a = 6
a = - 12 / 5 ∨ a = 6 / 5
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Which set of fractions is ordered from greatest to least? 11/12, 7/10, 5/6 11/12 7/10
Answer:
11/12 11/12 7/10 7/10 5/6
Step-by-step explanation:
I did smallest to largest. still answer your question so 5/6 is the greatest (it's bigger) and 11/12 is the least (it's the smallest) think of it like a cookie would you rather have 11/12 of a cookie or 5/6 of a cookie which is the bigger piece? the bigger piece is the greater number.
Find AB if (-9,2) and B(5,-4)
Given:
A(-9, 2) and B(5, -4)
Here,
(x1, y1) ==> (-9, 2)
(x2, y2) ==> (5, -4)
To find AB, use the distance formula below:
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which two numbers which have an absolute value that is greater than the absolute value of 4 1/4
a) -4
b) -5
c) 3
d) 2
e) 6
Answer: b) and a)
Step-by-step explanation:
Cause absolute value is the opposite of the number
Between what values of X is there a slight decrease?
Amanda has scored 24,22,27,23 and 30 points in her five basketball games so far. How many points does she need to score in her next game so that her average (mean) is 25 points per game?
To answer this question, we need to remember that the mean of a data is the sum of the data divided by the total number of elements that represent this data.
Therefore, if we need to find the sixth value for which the average (mean) per game is 25 points, we can proceed as follows:
[tex]\frac{24+22+27+23+30+x}{6}=25[/tex]Now, to find the value, x, we need to follow the next steps:
1. Add the values in the numerator of the fraction:
[tex]\frac{126+x}{6}=25[/tex]2. Multiply both sides by 6:
[tex]\begin{gathered} \frac{6\left(126+x\right?}{6}=6\left(25\right? \\ \frac{6}{6}\left(126+x\right?=150 \\ 126+x=150 \end{gathered}[/tex]3. Finally, subtract 126 from both sides of the equation:
[tex]\begin{gathered} 126-126+x=150-126 \\ x=24 \end{gathered}[/tex]Therefore, the value she needs is 24 points.
And we can check this value as follows:
[tex]\frac{24+22+27+23+30+24}{6}=\frac{150}{6}=25[/tex]Therefore, in summary, we have that Amanda needs to score 24 points in the next game so that her average is 25 points per game.
Create a linear equation that satisfies conditions.Type your equation in the form y = mx + b if a value is not an integer then type it in as a decimal rounded to the nearest hundredth.
Solution
Part a
For the first part we have two points (2,4) and (4,10)
We can find the slope like this:
[tex]m=\frac{10-4}{4-2}=\frac{6}{2}=3[/tex]And then the intercept would be:
4= 3*2 +b
b= 4-6= -2
Then the answer is:
y= 3x -2
Part b
f(-4)=18 and f(4) =2
The slope is:
[tex]m=\frac{18-2}{-4-4}=-2[/tex]
2= -2*4 +b
b= 2+8=10
y= -2x+10
Part c
x intercept at (-5,0) and the y intercept (0,4)
[tex]m=\frac{4-0}{0+5}=\frac{4}{5}[/tex]And using the y intercept we have:
4= 4/5*0 +b
b= 4
y= 4/5x +4
A sculptor is planning to order a rectangular of composite stone to sculpt a lion. The sculptor anticipated that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lions body, have a height of 3.5 feet. The composite stone weighs 40 pounds per cubic foot. To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue
In order to sculpt the lion, the scupltor must have, at least, a rectangular composite that has the maximum dimensions of the final sculpture.
Thereby,
[tex]5ft\cdot2ft\cdot3.5ft=35ft^3[/tex]The rectangular composite would need to have a volume of 35 cubic feet.
Now, let's use a rule of three to calculate the weight of the composite, since we're given its density:
This way,
[tex]x=\frac{35\cdot40}{1}\rightarrow1400lbs[/tex]We can conclude that the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue is 1400 lbs
Tarik starts his morning walk at 7:00 am, his distance, in miles to the nearby grocery store after x hours is F(x) = 3|x - 0.5| 7:15 am Tarik is {blank} away from the store?
Tarik is 0.75 miles away from the store.
How to calculate the value?It should be noted that based on the information given, the expression has been given for the hours used.
In this case, the minutes used was:
= 7.15am - 7.00am
= 15 minutes
This will be changed to hour
15 minutes = 15/60 = 0.25 hour.
The expression given is:
= 3(x - 0.5)
where x = hours used 0.25
= 3(x - 0.5)
= 3(0.25 - 0.5)
= 3(-0.25)
= -0.75
He is 0.75 miles away.
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