For this case we have the following function given:
[tex]f(x)=7-4x[/tex]We also know that the domain is given by:
[tex]D=\left\lbrace -2,0,\frac{3}{4}\right\rbrace [/tex]and in order to find the range we need to use the domain given:
[tex]f(-2)=7-4(-2)=7+8=15[/tex][tex]f(0)=7-(4\cdot0)=7[/tex][tex]f(\frac{3}{4})=7-4\cdot\frac{3}{4}=7-3=4[/tex]So then the range for this case would be given by:
[tex]R=\left\lbrace 15,7,4\right\rbrace [/tex]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.
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)
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
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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please help with this problem.no explanation needed, I am just looking for an answer
we have that
the answer is Breakfastin 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
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.
Please help me with this Homework .
$2000 are invested in a bank account at an interest rate of 10 percent per year.
Find the amount in the bank after 9 years if interest is compounded annually.
Answer:
1,800 im not sure tho
Step-by-step explanation:
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 transformations have been made from the parent graph f(x) = log x to get f(x) = log(x - 2)? OA. 2 units in the x direction B. -2 units in the x direction C.-2 units in the y direction D. 2 units in the y direction Reset Selection Next
Given:
The function f(x) = log(x) and f(x) = log(x - 2).
Required:
What transformtaion have been made from parent function?
Explanation:
The graph of the function,
The graph of f(x) = log(x - 2) shifted to 2 units in the x - direction.
Answer:
Option A is correct.
Match each equation with an equivalent equation. Some of the answer choices are not used.
3x+5=4x+8
3(x+5)=4x+8
3x+4x=8-5
The equivalent equations in the given choices are : 3x+5=4x+8 and 3x+4x=8-5.
What are equivalent equations?
Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
The equations that are equivalent are :
3x+5=4x+8 and 3x+4x=8-5
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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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If x = 10, y = 5, and z = 11, what is the tangent ratio for g½2/110/115/11
Recall that by definition, in a right triangle:
[tex]tan\theta=\frac{oppposite\text{ leg}}{adjacent\text{ leg}}.[/tex]In the given triangle, if we consider angle g, we get:
[tex]tan(g)=\frac{x}{y}.[/tex]Substituting x=10, and y=5, we get:
[tex]tan(g)=\frac{10}{5}=\frac{2}{1}.[/tex]Answer: [tex]\frac{2}{1}.[/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
What is the equation of the line that passes through the point (5,-5) and has a slope of -1/2
Answer: y= -1/2x - 2.5
Step-by-step explanation:
Slope: y= mx+ b
m being the slope
b being the y intercept
You're given the slope, so you substitute m for -1/2
y=mx+b
y = -1/2x + b
You have the coordinates (5, -5) which you can substitute (the line passes through that point.)
-5 = -1/2(5) + b
-5 = -2.5 + b
+2.5 +2.5
-2.5= b
y= -1/2x + 2.5
Check:
-5 = -1/2(5) - 2.5
-5 = -2.5 - 2.5
-5 = -5
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
In which set(s) of numbers would you find the number49integerO rational numberOreal numberO natural numberwhole numberO irrational number
Rational numbers, Real numbers, Natural numbers, whole number
Explanation:[tex]49\text{ can also be written as }\frac{49}{1}[/tex]Rational numbers can be written as a fraction. 49 can be written as a fraction
Real numbers consists of natural numbers, whole umbers, integers and rational numbers.
Since it is already a rational number, then it is also a real number
Natural numbers are counting numbers from 1 to positive infinity. 49 is between 1 to positive infinity.
Hence, it is a natural number
whole numbers start from 0 to positive infinity. 49 is between 0 to positive infinity.
Hence, it is a whole number
Irrational numbers cannot be written in the form of fraction. SInce 49 can be written as fraction, it is not an irrational number
Hence, the set(s) of numbers would you find the number 49 are Rational numbers, Real numbers, Natural numbers, whole number
I need the answer ASAP
Answer:
I'm pretty sure it's the last on but I could be wrong
Step-by-step explanation:
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
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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. 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.
Large drinks cost $2.75 each and medium drinks cost $2.15 each. A restaurant sold 52 drinks yesterday and took in a total of $131.60. How many medium drinks did they sell?
To solve this type of question we need to form 2 equations of 2 variables and solve them to find the 2 variables
Let x is the number of the large drinks and y is the number of the medium drinks
Since the restaurant sold 52 drinks, then
[tex]x+y=52\rightarrow(1)[/tex]Since the cost of the large drink is $2.75 each, then
The cost of the large drinks is 2.75(x)
Since the cost of the medium drink is $2.15 each, then
The cost of the medium drinks is 2.15(y)
Since the total cost of them is $131.60, then
Add 2.75(x) and 2.15(y) and equate the sum by 131.60
[tex]\begin{gathered} 2.75(x)+2.15(y)=131.60 \\ 2.75x+2.15y=131.60\rightarrow(2) \end{gathered}[/tex]Now we have a system of equations to solve it
Multiply equation (1) by -2.75 to make x equal in values of the two equations and different in signs to eliminate it
[tex]\begin{gathered} (-2.75)x+(-2.75)y=(-2.75)(52) \\ -2.75x-2.75y=-143\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} 2.75x+2.15y+(-2.75x)+(-2.75y)=131.60+(-143) \\ (2.75x-2.75x)+(2.15y-2.75y)=131.6-143 \\ 0-0.6y=-11.4 \\ -0.6y=-11.4 \end{gathered}[/tex]Divide both sides by -0.6
[tex]\begin{gathered} \frac{-0.6y}{-0.6}=\frac{-11.4}{-0.6} \\ y=19 \end{gathered}[/tex]They sold 19 medium drinks yesterday
suppose that the function V = 40x to the 2nd -500× + 5000 describes the value of a car from 1960 to 2012. What year did the car have the least value? (x = 0 is 1960)
We have the next function
[tex]V=40x^2-500x+5000[/tex]In 1960, x=0
[tex]V=5000[/tex]In 1965, x=5
[tex]V=3500[/tex]In 1966, x=6
[tex]V=3440[/tex]In 1967, x=7
[tex]V=3460[/tex]In 1968, x=8
[tex]V=3560[/tex]As we can see the year with the least value is 1966
A recipe book shows measurement conversions for pints to cups. It shows that 1.5 pints equals 3 cups and 2.5 pints equals 5 cups.
Write an equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups.
p equals 3 over 1.5 times n
n equals 1.5 over 3 times p
p = 0.5n
n = 0.5p
The equation that t shows the proportional relationship between pints and cups is p = 3 over 1.5 times n
What is the equation?The mathematical operation that would be used to determine the equation is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
In order to determine the proportional relationship, divide the measurement for cups by the measurement for pints.
p = 3 / 1.5n
p = 2n
p = 5 / 2.5
p = 2
This means that one pint represents two cups.
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A 5-ounce bottle of glue costs $2.85. What is the unit price?
Answer:
$0.57 per ounce
Step-by-step explanation:
2.85/5 = 0.57
Answer:
Step-by-step explanation:
First, set up an equation: $2.85/5 oz.
Next, divide both the numerator and denominator by 5. NOTE: do them one at a time.
2.85/5=$0.57
5/5=1
So, the unit rate is $0.57/oz.
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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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
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
The Scooter Company manufactures and sells electric scooters. Each scooter cost $200 to produce, and the company has a fixed cost of $1,500. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
The total profit of the company is represented by the equation -2x^2-600x-1500
Cost of each scooter = $200
Fixed cost of each scooter = $1500
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The coefficient of x2 must be a non-zero term (a 0) in order for an equation to meet the definition of a quadratic equation.
Function of revenue R(x) = 400x -2x^2
Let x represent each electric scooter sold
The total cost of the scooter = Fixed cost + variable cost number of scooters sold
= 1500 + 200x
Profit = Revenue - Cost
= 400x - 2x^2 - 1500 + 200x
= 600x - 2x^2 -1500
-2x^2 - 600x -1500
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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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