Answer:
(15, 20)
Explanation:
If the point (10,20) belongs to the graph of f(x), a function that satisfies this point for example could be:
[tex]f(x)=2x[/tex]When x is replaced with x-5, we have:
[tex]\begin{gathered} f(x-5)=2(x-5) \\ =2x-10 \end{gathered}[/tex]Therefore, when x=15
[tex]\begin{gathered} f(x-5)=2(15)-10 \\ =30-10 \\ =20 \end{gathered}[/tex]A point that belongs to the graph of y = f(x-5) is (15, 20).
13. Name the legs.
a. AB & BC
b. AC & BC
c: BC & AC
Legs are mentioned below.
Define triangles.A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A triangle's side is one of its legs. The term "leg" for a right triangle typically refers to a side other than the one across from the right angle (which is termed the hypotenuse). The word catheti also refers to legs.
Given,
a) AB and BC
AB = height
BC = base
b) AC and BC
AC = hypotenuse
c) BC and AC
BC = Base
AC = hypotenuse
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PLEASE ANSWER FAST
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
Annot a traperakthe of this Be sure to include the correct unit in your answer
To find the area of the trapezoid, we will use the formula below:
[tex]A=\frac{a+b}{2}h[/tex]where a and b are the base and h is the height.
From the diagram given, a=7 , b=17 and h = 5.
Substitute the values into the formula and evaluate.
That is;
[tex]A=\frac{7+17}{2}\times5[/tex][tex]=\frac{24}{2}\times5[/tex][tex]=12\times5[/tex][tex]=60[/tex]Hence, the area of the trapezoid is 60 yd².
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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Between what values of X is there a slight decrease?
When I was 2 my sister was twice my ag Now I'm 40, how old is my sister...
Answer:
Let you be "x"
and your sister be "y"
when you are 2 your sister is twice your
x=2 y=4
so your sister is 2 year older than you
now you're 40 so your sister would be
Step-by-step explanation:
When I was 2 my sister was twice my ag Now I'm 40 then my sister age is 80.
\
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
When I was 2 years my sister was twice of my age.
Let us consider the ages by using a equation like this
x/y------>X represents my age/ y represents my sister age
x/y ----->2/4=40/a
a is the age of sister when i was 40.
Now let us solve 2/4=40/a
One by two equal to forty by a.
Apply cross multiplication
2a=160
Divide both sides by 2
a=80
Hence, if I'm 40, my sister is 80 years old.
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Find the constant of proportionality, then write an equation relating x and yy is directly proportional to x, and y = 81 when x = 9
When x=9, y=81.
To find the proportionality constant take the ratio of y/x.
[tex]\begin{gathered} \frac{y}{x}=\frac{81}{9} \\ =9 \end{gathered}[/tex]Thus, the proportionality constant is 9.
The relation between y and x can be determined as,
[tex]\begin{gathered} \frac{y}{x}=constant \\ \frac{y}{x}=9 \\ y=9x \end{gathered}[/tex]Thus, the required relationship between x and y is y=9x.
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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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.
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]. Imagine that you wanted to test the effects of driving at different speeds on the gas mileage of your car. To find out, you drove a distance of 100 miles at many different rates of speed. During your first trip. you drove at exactly 55 miles per hour and calculated that your gas mileage was 20 miles per gallon. During your next trips, you either decreased or increased your rate of speed. Study the graph below from your trips and see if you can identify a control as well as the independent and dependent variables. Explain which axes the dependent and independent variables should be on. Also, what can you conclude from this experiment? How might your car get better gas mileage?
We are asked to study a graph of car performance and give details about the dependent and independent variables. Here is the graph in question:
Our control point is: the info given: 55 miles per gallon gave 20 mi/gallon gas usage. We see clearly that point on the graph, located at (55, 20) on the red line.
Therefore, the gas performance, is the quantity we are studying and it is the "DEPENDENT" variable. As such, it should be graphed on the veritical axis as it is on the graph provided.
The INDEPENDENT variable is the speed we are trying (in the first case the 55 mph (miles per hour) . This variable is what is plotted on the horiontal axis.
Given the shape of the graph: we see it as a line decreasing as we go at higher speeds, the better performance (more miles per gallon) will be obtained as we reduce the speed (going towards 45 miles per hour or even less). Notice that at the beginning of the horizontal axis (for about a 35 mph speed) we see the maximum height of the line at around 27 miles per gallon. So to answer the last question: We could get better gas mileage if we reduce the travelling speed at 35 miles per hour.
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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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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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
2x - 8 = 6 what is the equation
Answer:
Step-by-step explanation:
x = 7
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
How do I graph this?
Answer:
See below
Step-by-step explanation:
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
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.
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
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.
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
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]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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Solve: (2,1); m=undefined. Answer has to be in slope intercept form, so y=mx+b. SHOW ALL WORK SO I CAN HAVE A BETTER UNDERSTANDING :)
The equation of the line is x = 2
How to determine the line equation?The slope of the line is given as
Slope = Undefined
This can be rewritten as
m = Undefined
The point on the line is also given as
(x, y) = (2, 1)
For a line with an undefined slope, it means that:
The line is a vertical line
The equations of all vertical lines are represented as
x = x₁
In this case,
(x₁, y₁) = (2, 1)
Remove the y-coordinate
x₁ = 2
Substitute x₁ = 2 in the equation x = x₁
So, we have
x = 2
Hence, the line has an equation of x = 2
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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]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 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)
What is the slope of the line passing through the points (-3, 4) and (4, -1)?
The slope of the line passing through the given points is equal to -5/7.
What is a slope?A slope is also known as gradient and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (-1 - 4)/(4 - (-3))
Slope = -5/(4 + 3)
Slope = -5/7
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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
