use the graph of f at the right to complete each of the parts (a) through (h)
Answers
Answers:
a. The domain of f is ]-∞ , ∞[
b. The range of f is [-4 , ∞[
c. f(1) = 5
d. The vales of x for which f(x) is -3 are 7 and 9
e. The points at which the graph crosses the x-axis are (6,0) and (10,0)
f. The point where the graph of f crosses the y-axis is (0,5)
g. The values of x for which f(x) < 0 are ]6 , 10[
h. f(-7) is positive
Explanation:
Part a:
The domain of the function refers to all the possible x-values that can be used as an input for this function.
Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.
In interval notation, this is written as:
Domain = ]-∞ , ∞[
Part b:
The range of the function refers to all the possible y-values that can be used as an output for the function.
From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.
This means that the range of the function starts from -4 (included) and extends to positive infinity.
In interval notation, this is written as:
R = [-4 , ∞[
Part c:
f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.
From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.
Doing this, we will find that the value of y at x=1 is 5
Therefore:
f(1) = 5
Part d:
f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3
To get the value of x, we go y=-3 and move horizontally till we intersect the graph.
Doing this, we will find that the value of y is -3 at x = 7 and x = 9
Part e:
The points where the graph crosses the x-axis are the points that have y-value equal to 0
Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)
Part f:
The point where the graph crosses the y-axis is the point that has x-value equal to 0
Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)
Part g:
f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)
Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)
In interval notation, this is written as ]6 , 10[
Part h:
f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7
From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞
This means that, at x=-7, the value of y is 5 which is a positive value
Hope this helps :)
Related Questions
find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an approximation for pi.
Answers
Answer:
2794 m^2
Step-by-step explanation:
Area of Triangle - Area of Circle
1/2bh - piR^2
4050 - 1256
= 2794
The approximate area of the shaded region is, 2794 m²
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given a right triangle with a circle cut out of it,
Area of circle = π*Radius²
Area of triangle = 1/2*base*height
Area of circle = π*20² = 1256 m²
Area of triangle = 1/2*90*90 = 4050 m²
Area of the shaded region = Area of triangle - Area of circle
Area of the shaded region = 4050 - 1256 = 2794 m²
Hence, The approximate area of the shaded region is, 2794 m²
For more references on Area, click;
https://brainly.com/question/27683633
#SPJ2
Fast forward a few years...and suppose you need to get your car repaired. You see the ads above. Your father, who knows a bit about cars, says it will probably take 3 hours to fix your car. How do you determine where you should take your car to get it repaired?1. Write an equation for each repair shop to represent the total cost of the car repair as a function of the number of hours worked.Let x = number of hours worked Let y = total cost to you
Answers
Mikes repair shop $100 service charge plus $65 per hour Amys auto repair $40 service charge plus $80 per hour write an equation for each repair shop to represent the total cost of a car repair as a function of the number of hours worked let C = total cost to you let h = number of hours worked. Suppose you need to get the dent in your car repaired you see the ads above in the newspaper your father who knows a bit about cars said it would take no more than 3 hours for the repair person to fix your car how do you determine where you should take your car to get it repaired
-Mike Cost:: M(3) = 100 +65*3 = $295
-Amy Cost:: A(3) = 40 + 80*3 = $280
------------------------------------------------------------
-Mike charges 100 dollars service charge plus 65 dollars per hour.
-Amy charges 40 dollars service charge plus 80 dollars per hour.
-The cost to repair from mike is 100 + 65 * x.
-The cost to repair from amy is 40 + 80 * x.
------------------------------------------------------------
Let x = 3 and you get:
The cost to repair from mike is 100 + 65 * 3 = 295 dollars.
The cost to repaid from amy is 40 + 80 * 3 = 280 dollars.
As long as the time to repair is 3 hours or less, the cost to repair will be cheaper from Amy.
What is an equation of the line that passes through the points (7,-6)(3,-6)
Answers
Answer:
Step-by-step explanation:
Since both points have their y coordinate as -6, and this is a line,
Then your answer would be y = -6
M - 2 3/4 = 6 1/2 what does the m equal
Answers
Answer:
Step-by-step explanation:
6 1/2 + 2 3/4=M
M=9 1/4
J. Reexamine the sequence 20, 14, 8, 2, ... from the problem
term of the sequence.
-- from the problem above. Write an equation for the nth
Answers
Answer:
The n th of the given sequence is [tex]t_{n} = 26-6 n[/tex]
Step-by-step explanation:
Step 1 :-
Given sequence is 20,14,8,2,.......this sequence in arithmetic progression but this sequence is decreasing sequence.
given first term is 20 and difference is[tex]d = second term- first term = 14-20=-6[/tex]
now the nth term of given sequence is
by using formula [tex]t_{n}=a+(n-1)d[/tex]
[tex]t_{n}= 20+(n-1)(-6)[/tex]
[tex]t_{n}= 20-6 n+6[/tex]
final answer:-
[tex]t_{n} = 26-6 n[/tex]
verification:-
[tex]t_{n} = 26-6 n[/tex]
put n=1 we get first term is 20
put n=2 we get second term is 14
put n=3 we get third term is 8
put n=4 we get fourth term is 2
so the n th term of sequence is
[tex]t_{n} = 26-6 n[/tex]
A video game system costs $185 and one video game costs $14.95. You can spend no more than $280 on the system and games. set up and solve an inequality to calculate the maximum number of games you can purchase
Answers
Answer:
Therefore the maximum number of video games that we can purchase
is 6.
Step-by-step explanation:
i) Let us say the number of video game system we can buy that costs $185
is x and the number of video games of cost $14.95 is y.
ii) The total amount we can spend on the purchase of the video game
system is $280.
iii) Now with the amount of $280 mentioned in ii) we can see that the
number of game systems that can be bought is 1.
Therefore x = 1.
Therefore the equation we can write to equate the number of video
games and video game system is given by $185 + $14.95 × y ≤ 280
Therefore 14.95 × y ≤ 280 - 185 = 95
Therefore y ≤ 95 ÷ 14.95 = 6.355
Therefore the maximum number of video games that we can purchase
is 6.
What is the values of x and y?
(5x) + (9y)
Answers
Answer:
x=5 y=9
Step-by-step explanation:
hope this helps :) have a nice day :) :) :)
the graph of f(x)=|x| is reflected across the x-axis, moved 2 units to the right and 7 units down. What is the function?
Answers
The transformed function after reflecting f(x)=|x| across the x-axis, moving it 2 units to the right, and 7 units down is f(x)=-|x-2|-7.
Explanation:The original function is f(x)=|x|.
When the graph of the function is reflected across the x-axis, it changes the sign of the output or y-coordinate.
Thus, the absolute value function becomes f(x)=-|x|.
When this function is moved 2 units to the right, it results in a shift in the coordinate of x within the function, thus becoming f(x)=-|x-2|.
Lastly, when the function is moved 7 units down, 7 is subtracted from the function, resulting in the final equation of f(x)=-|x-2|-7.
Learn more about Function Transformations here:https://brainly.com/question/26896273
#SPJ1
F(x)=2x+6
G(x)=-5x-9
Find the product of f and g.
A.-10x^2-54
B.-10x^2-48x-54
C.-10x^2-12x-54
D.-10x^2+48x-54
Answers
Answer:
Step-by-step explanation:
F(x) = 2x + 6
G(x) = - 5x - 9
product of F and G .....the product is the result of multiplication
(2x + 6)(-5x - 9) =
-10x^2 - 18x - 30x - 54 =
-10x^2 - 48x - 54 <====
The answer should be b . hopes this helps
Five times a number , subtracted from ten , is triple the number . Find the number.
Answers
The value of the variable number x will be 1.25.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Let x be the number. Then the Five times a number is written as 5x. Then the expression will be
⇒ 10 - 5x
The triple number is written as 3x. Then the equation is given below.
10 - 5x = 3x
Simplify the equation, then we have
10 = 3x + 5x
10 = 8x
x = 10 / 8
x = 1.25
The value of the variable number x will be 1.25.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Final answer:
The algebraic equation set up from the problem 10 - 5x = 3x leads us to find that x = 1.25. Thus, the number in question is 1.25.
Explanation:
The question describes an algebraic problem where we are trying to find a particular number. According to the problem, five times this number, when subtracted from ten, equals three times the number. To find the number, we set up the equation based on the given information:
10 - 5x = 3x
Where x is the number we are trying to find. Now, we will solve for x:
Add 5x to both sides of the equation to get all x terms on one side:
10 = 3x + 5x
Combine like terms on the right side:
10 = 8x
Divide both sides by 8 to solve for x:
x = 10/8
Simplify the fraction:
x = 1.25
So, the number we were seeking is 1.25.
What’s the slope of y=-7x+5
Answers
Answer:
m=-7
Step-by-step explanation:
The slope intercept form is y=mx+b.
So, the variable that represents slope is x.
If your plug your equation in, -7 would be the slope.
What is the length of the radius, r?
Answers
Answer:
18 cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ← r is the radius
Given
C = 36π, then
2πr = 36π ( divide both sides by 2π )
r = [tex]\frac{36\pi }{2\pi }[/tex] = 18
Suppose we want to choose 2 objects, without replacement from the objects pencil, eraser and desk
Answers
The question is about finding the number of ways to choose 2 items without replacement from a set of 3 items using combinatorics, and there are 3 different ways to do so.
The question deals with the concept of combinations in probability and combinatorics. When choosing 2 objects from a set of 3 items (a pencil, an eraser, and a desk) without replacement, we can use the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose.
In this case, we have 3 items and we want to choose 2, so we plug the values into the formula to get the number of combinations without replacement.
Using the combination formula, C(3, 2) = 3! / (2! × (3-2)!) = 3.
Therefore, there are 3 different ways to choose 2 objects from the set of a pencil, an eraser, and a desk.
Solve by factoring:
4x² - 8x=0
Answers
Answer:
Step-by-step explanation:
4x² - 8x= 0
4x(x -2) = 0
: 4x = 0 or x - 2 = 0
4x = 0
Dividing by 4
x = 0/4
x = 0
And
x - 2 = 0
x = 2
2 litre 450 ml mustard oil was used from a can of 5 litre in a month. How much is left? For how many months in all can it be used?
Answers
Answer:
Step-by-step explanation:
1 liter = 1000 ml....so 2 liters and 450 ml = (2* 1000) + 450) = 2450 ml
5 liters = (5 * 1000) = 5000 ml
5000 ml - 2450 ml = 2550 ml or 2 liters and 550 ml <== this is how much is left
so he used 2450 ml in 1 month....and he has 5000 ml
5000/2450 ≈ 2.04 months <=== it will be all used up
Answer:
Step-by-step explanation:
1 litre = 1000 ml
5 liter = 5 * 1000 = 5000 ml
2 liter 450 ml = 2 liter + 450 ml = 2000 ml + 450 ml = 2450 ml
Oil left = 5000 - 2450 = 2550 ml
2550 - 2450 = 100 ml
4 liter 900ml is used in two months and 100 ml will be left over
An outfielder throws a ball vertically upward with a velocity of 30 meters per second. Its distance from the ground after t seconds is approximately equal to 30t - 5t² meters. How many seconds will it take the ball to reach its maximum distance from the ground?
15
6
1.5
3
Answers
Answer:
12
Step-by-step explanation:
I calbvkjy
The answer is 3 :)
Have a nice day!
PLEASEEE HELPPP ASAPP! THANK YOU LOTS!! <3 (7TH GRADE MATH)
btw January: -5/8 and July: 6 5/8
Answers
Answer:
Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= -3.4 cm)
Step-by-step explanation:
i) change in water level over the course of 9 months =
[tex]- \frac{5}{8} - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6\frac{5}{8} - 3.2 + 0.3[/tex]
= [tex]-0.625 - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6.625 - 3.2 + 0.3[/tex]
= -3.4
Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= - 3.4 cm)
Hank has eight action figures this is 12 less than the quotient of 60 and the number figures palo has
Answers
Answer:
6
Step-by-step explanation:
hold up hold up so you are saying 60 less than what quotient I'm guessing 68 divided by 12 so the answer would be 6
Need to show my work
Answers
Answer:
[tex]\large\boxed{x=\dfrac{5}{4},\ y=\dfrac{15}{16}}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=\dfrac{3}{4}x&(1)\\\dfrac{5}{2}x+2y=5&(2)\end{array}\right\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\\dfrac{5}{2}x+2\left(\dfrac{3}{4}x\right)=5\\\\\dfrac{5}{2}x+\dfrac{3}{2}x=5\\\\\dfrac{5+3}{2}x=5\\\\\dfrac{8}{2}x=5\\\\4x=5\qquad\text{divide both sides by 4}\\\\x=\dfrac{5}{4}[/tex]
[tex]\text{Put the value of}\ x\ \text{to (1)}\\\\y=\dfrac{3}{4}\cdot\dfrac{5}{4}\\\\y=\dfrac{15}{16}[/tex]
Answer:
Step-by-step explanation:
y = 3x/4 .........(1)
5x/2 + 2y = 5 .......(2)
Putting (1) into (2)
5x/2 + 2(3x/4) = 5
5x/2 + 3x/2 = 5
Multiply each term by 2
5x + 3x = 10
8x = 10
x = 10/8
x = 5/4
x = 1 1/4
And y = 3x/4
y = 3(5/4) ÷ 4
y = 15/4 ÷ 4
y = 15/(4×4)
y = 15/16
Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola. x^2 + 2y^2 = 2
Answers
This is an equation representing the ellipse
Explanation:
The general equation for an ellipse is [tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex] so, when you simplify it according to the characteristics of a and b, you would end up in the similar form of the equation givenwhere a represents half the length of the major axis and b represents half the length of the minor axis. The easiest method to identify, look at whether both the variables are squared, and also the coefficient of x and y should be positive but different.What is the value of x?
Enter your answer in the box.
°
Answers
Answer:
x = 111
Step-by-step explanation:
Sum of interior angles= (n-2)*180= (7-2)*180 = 5*180 = 900
x + 139 + 121 + 125 + 126 + 158 + 120 = 900
x + 789 = 900
x = 900 - 789 = 111
x = 111
what is n/8=11/5 solve for n
Answers
Answer:
n = 17.6
Step-by-step explanation:
Cross-multiply and you have:
5 * n = 11 * 8
5n = 88
n = 88/5 = 17.6
how do u compare rate of change and slope help plz
Answers
Step-by-step explanation:
The slope is described by the the initial and final value of one quantity over the difference between the initial and final of the other
Rate: for points on a Cartesian plane,(x1, y1) and (x2, y2)
the slope, m= (y2 - y1)/(x2 - x1)
The rate of change on the other hand is mostly refers to how much a quantity is changing with time i.e the rate of change of y from y1 to y2 can be expressed as
rate = (y2 - y1)/(t2 - t1)...where t1 and t2 are the various time in y1 and y2 respectively...
what is the slope of (1,2) and (4,11)
Answers
Answer:
slope = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, 11)
m = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3
Answer:
3
Step-by-step explanation:
y2 - y1/ X2 - X1
11 - 2/ 4-1
9/3
= 3
Anita's mother hosted a party. The table shows the costs. Use associative property to write two equivalent expressions that could be used to find the total amount spent. TABLE ITEM:cake COST: $12 ITEM: hot dogs and hamburgers COST:$24 ITEM:drinks COST: $6
Answers
Using the associative property of addition, two equivalent expressions to find the total cost are: (1) ($12 + $24) + $6 and (2) $12 + ($24 + $6). Both expressions will yield the same result due to the associative property.
The question involves using the associative property of addition to find equivalent expressions for the total cost of items bought for Anita's mother's party. The total costs given are for three items: cake ($12), hot dogs and hamburgers ($24), and drinks ($6). To demonstrate the associative property, we can group the costs in different ways before adding them.
The first expression could group the cost of the cake and hot dogs and hamburgers together, then add the cost of drinks: ($12 + $24) + $6.The second expression could group the cost of hot dogs and hamburgers and drinks together, then add the cost of the cake: $12 + ($24 + $6).Both expressions will yield the same total cost when calculated, which shows the associative property of addition in action.
For which value of x is the equation 3x + x = 2x + 24 true?
A) 3
B) 4
C) 6
D) 12
do you guys know the answer?
Answers
Answer:
D) 12
Step-by-step explanation:
3x+x=2x+24
4x=2x+24
4x-2x=24
2x=24
x=24/2
x=12
Pls help me x+4=__+24 I don’t know the answer pls I really need this 200 points I give you
Answers
Answer:
x-20
Step-by-step explanation:
x+4=y+24
x=y+24-4
x=y+20
y=x-20
Find the two missing terms of the sequence and determine if the sequence is arithmetic, geometric, or neither.
3, 1, -1, -3, __, __
Answers
The sequence is arithmetic.
if k is a constant, what is the value of k such that the polynomial k^2x^3 - 6kz+9 is
divisible by x-1?
Answers
The value of k that makes the polynomial k^2x^3 - 6kz + 9 divisible by x-1 is 3. This is found using the Remainder Theorem and substituting x=1 into the polynomial and solving the resulting equation.
Explanation:The question asks for the value of k such that the polynomial k2x3 - 6kz + 9 is divisible by x-1. To find the value of k, we use the Remainder Theorem, which states: if a polynomial f(x) is divisible by x-c, then f(c) = 0.
Applying this theorem, we set x=1 and solve for k:
Therefore, the value of k that makes the polynomial divisible by x-1 is 3.
Find the value of x. Round your answer to the nearest tenth.
A.) 52.6
B.) 52.9
C.) 6.2
D.) 6.5
Answers
Answer:
Option A: 12.5
Step-by-step explanation:
We use trigonometric ratios on this right angled triangle.
[tex]$ cos \hspace{1mm} \theta = \frac{adj}{hyp} $[/tex]
we get:
[tex]$ cos \hspace{1mm} 28^{\circ} = \frac{11}{x} $[/tex]
Also cos 28° = 0.88
Therefore, x = [tex]$ \frac{11}{0.88} $[/tex]
[tex]$ = \frac{100}{8} =\textbf{12.5} $[/tex]
OPTION A is the answer.