Solve the equation. f(x)=g(x) by graphing. f(x) = l x +5 l g(x) = 2x + 2 Select all possible solutions: No Solutions x=3 x=0 X=-1
Answers
As you can observe in the graph below, the given functions intercept at one point.
Hence, there is a unique solution and it's x = 3.
Related Questions
[tex]4(2 \times - 1) \ \textless \ (4 \times - 3)[/tex]That is the Math problem
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What is the coordinate point location of the y-intercept of the graph below?
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The y-intercept is located at the coordinate (0, 4) as shown below. Y-intercept is the point where a line or a graph crosses the y-axis.
please help :(Find the coordinates of the midpoint of HXH(4 1/2, -4 1/4) , X(2 3/4, -2 1/4)
Answers
To find the coordinates of the midpoint of HX, we would apply the midpoint formula which is expressed as
[tex]\text{Midpoint = }\lbrack\frac{(x1\text{ + x2)}}{2},\text{ }\frac{(y1\text{ + y2)}}{2}\rbrack[/tex]From the information given,
[tex]\begin{gathered} x1\text{ = 4}\frac{1}{2}\text{ = 4.5, x2 = 2}\frac{3}{4}=\text{ 2.75} \\ y1\text{ = -4}\frac{1}{2}=-4.5,\text{ }y2=-2\frac{1}{4}=\text{ - 2.25} \\ \text{Midpoint = }\lbrack\frac{(4.5\text{ + 2.75)}}{2},\text{ }\frac{(-4.5\text{ - 2.25)}}{2}\rbrack \\ \text{Midpoint = (3.625, - 3.375)} \end{gathered}[/tex]A study shows that 28% of the population has high blood pressure. The study also shows that 86% of those who do not have high blood pressure exercise at least 90 minutes per week, while 32% of those with high blood pressure exercise at least 90 minutes per week. Which of the following relative frequency tables could the study provide?
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The study can provide relative frequency table 2 (starting from the top)
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. The word per cent means per 100. It is denoted by the symbol “%”.
The total percentage of two or more ratios in a thesame entity is 100. For example, In a population, 28% has HBP (high blood pressure)
This means that number of those that do not have HBP will be 100 - 28 = 72%
86% of those who did not have HBP exercise at least 90 minute per week i.e
86% of no HBP ,exercise >or = 90 = (86/100) × 72 = 62%( nearest whole number)
Those that do exercise <90 minute per week = 72-62= 10%
32% of those with HBP exercise at least 90 minute( >or = 90 minutes) =( 32\100) × 28= 9%( nearest whole number)
Those with HBP and exercise <90= 28- 9= 19%
Therefore Table 2 starting from the top clearly shows this data.
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Which ordered pair is a solution tothe system of inequalities shown?
Answers
We want to know which ordered pair is a solution of the system of inequalities shown:
[tex]\begin{cases}x-4y\ge0 \\ x-y<-1\end{cases}[/tex]For doing so, we will try to solve both inequalities for one variable, in this case, we will use y.
On the first equation:
[tex]\begin{gathered} x-4y\ge0 \\ x\ge4y \\ y\le\frac{x}{4} \end{gathered}[/tex]On the second equation:
[tex]\begin{gathered} x-y<-1 \\ x+1-y<0 \\ x+1And joining those two results we get:[tex]x+1Now we check each of the ordered pairs, if they hold the condition above:For (0, 2)
We have that x=0, and y=2. Thus,
[tex]\begin{gathered} x+1=1 \\ \frac{x}{4}=0 \\ \text{And as }2>0,\text{ (0, 2) is NOT a solution of the system.} \end{gathered}[/tex]For (-3, 8)
In this case, x=-3 and y=8.
[tex]\begin{gathered} x+1=-2 \\ \frac{x}{4}=-\frac{3}{4} \\ \text{As }8>-\frac{3}{4},\text{ this means that (-3, 8) is NOT a solution of the system.} \end{gathered}[/tex]For (2,5)
In this case, x=2 and y=5.
[tex]\begin{gathered} x+1=3 \\ \frac{x}{4}=\frac{2}{4}=\frac{1}{2} \\ \text{As }5>\frac{1}{2}\text{ this means that (2, 5) is NOT a solution of the system.} \end{gathered}[/tex]For (-7, -4)
In this case, x=-7 and y=-4.
[tex]\begin{gathered} x+1=-6 \\ \frac{x}{4}=-\frac{7}{4} \\ \text{As }-6<-4\le-\frac{7}{4},\text{ (-7, -4) is a SOLUTION of the system.} \end{gathered}[/tex]For (6, -1)
We have that x=6 and y=-1.
[tex]\begin{gathered} x+1=7 \\ \frac{x}{4}=\frac{6}{4}=\frac{3}{2} \\ \text{As }7>-1,\text{ (6, -1) is NOT a solution of the system. } \end{gathered}[/tex]Thus, the ordered pair which is a solution of the system is (-7, -4).Which of the following systems of equations is an example of one where elimination is the best method?A) {y=27x+11 {3x−4y=−24 B) {4x+5y=20 {−4x+6y=24 C) {y=13x+15 {2x−2y=18 D) {x = 11 {y = -8
Answers
Answer:
Explanation:
When solving a system of equations, the elimination method is best used when the system is given in such a way that the coefficients of one variable can be eliminated by addition or subtraction.
Of the given system of equations, the example of where elimination is the best method is:
[tex]\begin{gathered} 4x+5y=20 \\ -4x+6y=24 \end{gathered}[/tex]In this example, we see that the variable 'x' can be directly eliminated by adding the two equations.
The correct option is B.
please help me I dont understand A number is less than or equal to - 7 or greater than 12.
Answers
To translate the sentence as an inequality, we have:
[tex]x\leq-7,x>12[/tex]Since the number is less or equal ( < = ) we use this symbol to represent it as inequality, and greater than using the symbol ( > ).
Then, we can answer the question as:
x < = -7 or x > 12.
0896. Calculate the atomic mass of copper if copper-63 is 69.17% abundant and copper-65 is30.83% abundant.
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The atomic mass of the copper is
[tex]63\times69.17\text{ \% + 65}\times30.83\text{ \%}[/tex]solve the above expression
[tex]63\times\frac{69.17}{100}+65\times\frac{30.83}{100}[/tex][tex]63\times\frac{6917}{10000}+65\times\frac{3083}{10000}[/tex][tex]46.35+20.03=66.38[/tex]So the atomic weight of the mixture is 66.36 .
Ji min's grandmother asked him to pick up some ginger on his way home .He knows that she wants to get 2 meals(4oz/ meal)out of it and it costs $2.99 per root. how much will he spend if each root is approximately 6 oz?
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Since 1 meal is equivalent to 4oz, then 2 meals are equivalent to 8oz (4*2=8).
Now, one root (6oz) cost $2.99 and we need 8oz, then Ji-min must buy 2 roots because he cant buy parts of the root, that is
[tex]2.99\cdot2=5.98[/tex]that is, Jim will spend $5.98 approximately.
what digit is in the
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Let:
Mp = Marked price = $310
r = Rate of discount = 20% = 0.2
D = Discount
Sp = Sale price
The discount will be given by:
[tex]\begin{gathered} D=r\cdot Mp \\ D=0.2\cdot310 \\ D=62 \end{gathered}[/tex]And the sale price will be:
[tex]\begin{gathered} Sp=Mp-D \\ Sp=310-62 \\ Sp=248 \end{gathered}[/tex]How many radians are equal to 360 degrees 2 2pi 1 Pi
Answers
Answer:
2pi
Explanation:
By definition, 360 degrees are equal to 2π radians.
This follows from the fact that the circumference of a circle is 2π times the radius. Therefore, if radius = 1, then
circumference = 2π
Since the circumference is the distance around a circle, and degrees are the "angular distance " around the circle, these two quantities can be related.
So if you think of the circle in terms of the circumference, a circle measures 2π. If you think in terms of degrees, a circle measures 360 degrees.
Therefore, we say
360 degrees = 2π (radians)
Points that lie on the same line are called: a) opposite rays b) coplanar and non-collinear c) non-collinear and non-coplanar d) collin ear and coplanar
Answers
Given:
Points that lie on the same line.
Opposite rays
WHAT IS THE CHEAPEST UNIT RATE??? 10 donuts for 13.00 or 1 dozen donuts for 12.00
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Step 1: Let's review the information provided to us to answer the question correctly:
• Option 1: 10 donuts for 13.00
,• Option 2: 1 dozen donuts for 12.00
Step 2: Let's calculate the price of a donut in each option, as follows:
• One donut Option 1 = 13/10 = 1.30, this means the price of an individual donut is $ 1.30
,• One donut Option 2 = 12/12 = 1, this means the price of an individual donut is $ 1
Step 3: Twitch Beast 8 will decide what is the cheapest unit rate based on the calculations we did on Step 2
Translate to system Grandpa and Grandma are treating their family to the movies. Matineetickets cost $4 per child and $4 per adult. Evening tickets cost $6 per childand $8 per adult. They plan on spending no more than $80 on the matineetickets and no more than $100 on the evening tickets.
Answers
Answer:
4x + 4y ≤ 80
6x + 8y ≤ 100
Explanation:
Let's define x as the number of children and y as the number of adults.
For Matinee tickets, they spend $4 per child and $4 per adult, so if the total is no more than 80, we get:
4x + 4y ≤ 80
In the same way, they spend $6 per child and $8 per adult on the evening tickets, so
6x + 8y ≤ 100
Therefore, the system is
4x + 4y ≤ 80
6x + 8y ≤ 100
Question 125 ptsA raffle sells 1000 tickets at $5 per ticket. The possible prizes are given below. Find the expectedvalue of each ticket (from the perspective of the person buying the ticket). Include signs in youranswer as appropriate.1 ticket wins $10005 tickets win $10010 tickets win $20
Answers
The answer is $0.5
Explanation:
⇒ Total amount of tickets sold = 1000 x $5 = $5000
⇒ Expected value E(X) =∑X.P(x)
⇒ 1 x (1000/5000) + 5 x (100/5000) + 10 x (20/1000)
= 0.2 + 0.1 + 0.2
= $0.5
Determine the x-intercept for 3x + 2y = 14.A) (7,0) B) (0,7) C) (14/3,0) D) (0,14/3)
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By definition, when the line intersects the x-axis, the value of "y" is:
[tex]y=0[/tex]Knowing this, you can substitute that value of "y" into ithe equation given in the exercise:
[tex]\begin{gathered} 3x+2y=14 \\ 3x+2(0)=14 \end{gathered}[/tex]Now you must solve for the variable "x" in order to find the x-intercept. This is:
[tex]\begin{gathered} 3x+0=14 \\ 3x=14 \\ x=\frac{14}{3} \end{gathered}[/tex]Then, you get this point:
[tex](\frac{14}{3},0)[/tex]The answer is: Option C.
if AC equals x + 3 and DB equals 3x - 19 find a CFA E equals 3x + 3 + E C equals 5x - 15 find a c d equals 50x - 7 + 80 equals 4x + 9 find DB
Answers
2) If DB = 27 the we can replace that:
[tex]27=3x-19[/tex]and we can solve for x
[tex]\begin{gathered} 3x=27-19 \\ 3x=8 \\ x=\frac{8}{3} \end{gathered}[/tex]now we can replace x in the equation for AC:
[tex]\begin{gathered} AC=x+3 \\ AC=\frac{8}{3}+3 \\ AC=\frac{8}{3}+\frac{9}{3} \\ AC=\frac{17}{3} \end{gathered}[/tex]3) we have that:
[tex]\begin{gathered} AE=3x+3 \\ EC=5x-15 \end{gathered}[/tex]So the segment AC will be the sum of the segments:
[tex]\begin{gathered} AC=AE+EC \\ AC=3x+3+5x-15 \\ AC=8x-12 \end{gathered}[/tex]and we also know that
[tex]\begin{gathered} x=\frac{8}{3} \\ \text{then} \\ AC=\frac{64}{3}-\frac{36}{3} \\ AC=\frac{28}{3} \end{gathered}[/tex]3) we have that:
[tex]\begin{gathered} DE=6x-7 \\ AE=4x+6 \end{gathered}[/tex]Consider the complex number 2 = V17 (cos(104°) + i sin(104°)).Plot z in the complex plane below.If necessary, round the point's coordinates to the nearest integer.Im5+4+3+2+1 +ReA+-5+-4-3-2-112345-1+-2-3 +-4+-5 +
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Recall that to plot a point in the complex plane we have to know its real part and its imaginary part.
The real part of the given number is
[tex]\sqrt[]{17}\cos 104^{\circ},[/tex]and its imaginary part is
[tex]\sqrt[]{17}\sin 104^{\circ}.[/tex]Simplifying the above expressions, and rounding to the nearest integer we get that:
[tex]\begin{gathered} \operatorname{Re}(z)=-1, \\ \operatorname{Im}(z)=4. \end{gathered}[/tex]Therefore, the point has coordinates (-1,4).
Answer:
Suppose that the functions f and g are defined as follows. f(x)= x-6/x+5 g(x)= x/x+5. find f/g. Then, give its domain using an interval or union of intervals. simplify your answers.
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STEP 1:
To find f/g we divide f(x) by g(x)
[tex]\frac{f}{g}=\frac{\frac{x-6}{x+5}}{\frac{x}{x+5}}\text{ = }\frac{x-6}{x+5}\text{ }\times\text{ }\frac{x+5}{x}\text{ =}\frac{x-6}{x}[/tex]Therefore the value of f/g is
[tex]\frac{f}{g}=\frac{x-6}{x}[/tex]STEP 2:
Also, the domain is the set of all possible x-values which will make the function "work", and will output real values.
The domain of this function is
[tex]-\inftyThis implies that the function would exist for all values of x except when x=0The above domain can also be represented as :
[tex](-\infty,0)\text{ and (0,}\infty)[/tex]Determine the period
I hate acellus
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Answer:
my answer i got is y=2x+9
Answer:
5
Step-by-step explanation:
They are asking for the Period. The Period goes from one peak to the next (or from any point to the next matching point). To me it looks like that value is 5 for this graph.
Two segments of Parallelogram ABCD are shown below.  Which coordinate pair BEST represents the location of Point D, the fourth vertex of Parallelogram ABCD? A. (6, 1) B. (7, 0) C. (8,2) D. (7,1)
Answers
Given coordinates of A(2,-1), B(1,3), C(6,5)
Let the coordinates of D(x,y)
Let join AC and BD:
SO by mid point rule:
Coordinates of midpoint by AC are:
[tex](\frac{2+6}{2},\text{ }\frac{-1+5}{2})\rightarrow(4,2)[/tex]And the midpoint of BD are same as AC:
[tex]\begin{gathered} \frac{1+x}{2}=4 \\ 1+x=8 \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{3+y}{2}=2 \\ 3+y=4 \\ y=4-3 \\ y=1 \end{gathered}[/tex]hence the coordinates of D are (7,1)
Option D is correct.
flying against the wind, an airplane travels 7840 kilometers in 8 hours. flying with the wind, the same plane travels 5280 kilometers in 4 hours. what is the rate of the plane in still air and what is the rate of the wind?
Answers
The rate of the plane in still air is 1150km/hr and the rate of the plane in the wind is 170km/hr.
Explanations:The formula for calculating distance is expressed as:
[tex]\begin{gathered} dis\tan ce=\text{speed}\times\text{time} \\ d=st \end{gathered}[/tex]Let the rate of the plane in still air be "x"
Let the rate of the plane in the wind be "y"
if flying against the wind, an airplane travels 7840 kilometers in 8 hours, then;
8 (x - y) = 7840
x - y = 980 ........................ 1
If flying with the wind, the same plane travels 5280 kilometers in 4 hours
4 (x + y) = 5280
x + y = 1,320 ......................2
Add both equations:
x + x = 980 + 1320
2x = 2,300
x = 2300/2
x = 1150 km/hr
Substract x = 1150km/hr into equation 1.
x - y = 1320
1150 + y = 1320
y = 1320 - 1150
y = 170km/hr
Hence the rate of the plane in still air is 1150km/hr and the rate of the plane in the wind is 170km/hr
Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2)? Responses The graph of g(x) is the graph of f(x) translated 2 units right. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units right. The graph of g(x) is the graph of f(x) translated 2 units down. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units down. The graph of g(x) is the graph of f(x) translated 2 units up. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units up. The graph of g(x) is the graph of f(x) translated 2 units left.
Answers
The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2) so option (D) is correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
If a function f(x) is transformed by funciton g(x) as shown,
g(x) = f(x+a)
For a>0, then the graph of f(x) shifts left by "a" unit, while if a<0, then the graph of f(x) shifts right side by "a"units.
As per the given function,
g(x) = f(x + 2)
Since 2 > 0 therefore the function will shift 2 units left.
Hence "The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2)".
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need help with this answer in a quick and clear response
Answers
ANSWER
Yes
EXPLANATION
The system of inequalities shows that y is greater than or equal to the first line and less than or equal to the second line. This means that any point on both lines is a solution to the system.
Hence, the intersection of the boundary lines is part of the solution.
How is this wrong can someone explain, and what is the correct answer
Answers
Answer:
Step-by-step explanation:
find and classify the global extrema of the following function
f(x)=(x-2)^2+5
compute the critical points of (x-2)^2+5
to find all critical points, first compute f(x)
f(x)=2(x-2)
solving 2(x-2)=0 yields x=2
x=2
f(x) exists everyhere
2(x-2) exists everyhere
the only critical point of (x-2)^2+5 is at x=2
x=2
the domain of (x-2)^2+ 5 is R
the endpints of R are x = -∞ and ∞
Evalute (x-2)^2+5 at x = -∞, 2 and ∞
the open endpoints of the domain are marked in gray
x () f(x)
-∞ ∞
2 5
∞ ∞
the largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
the open endpoints of the domain are marked in gray
x () f(x) extrema type
-∞ ∞ global max
2 5 global min
∞ ∞ global max
remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved
x () f(x) () extrema type
2 5 global min
f(x) = (x-2)^2+5 has one global minimum
Answer:
f(x) has a global minimum at x = 2
Answer:
Step-by-step explanation:
A parabola that passes through the point (8, 28) has vertex (-2, 8). Its line of symmetry is parallel to the y-
axis.
Find equation of the parabola: y =
When x 18, what is the value of y:
What is the average rate of change between x = -2 and x = 18:
Answers
The equation of the parabola is y = 1/5( x + 2 )² + 8.
When x = 18 the value of y is 88 and the average rate of change between x = - 2 and x = 18 is 4.
The general equation of the parabola is given as:
y = a(x – h)² + k where ( h, k ) is the vertex of the parabola.
We have, the vertex as ( - 2, 8 ) and the parabola passes through ( 8, 28 ).
Then,
y = a(x – h)² + k
28 = a( 8 - (-2) )² + 8
28 = a(10)² + 8
28 - 8 = a(10)²
100a = 20
a = 20/100 = 1/5
Therefore, the equation of the parabola will be:
y = a(x – h)² + k
y = 1/5( x + 2 )² + 8
Now, when x = 18:
y = 1/5( x + 2 )² + 8
y = 1/5( 18 + 2 )² + 8
y = 1/5( 20 )² + 8
y = 80 + 8 = 88
Now, the change between x = - 2 and x = 18:
Then,
y = f(18) = y = 1/5( 18 + 2 )² + 8 = 1/5(20)² + 8 = 88
And;
y = f( - 2) = 1/5( -2 + 2 )² + 8 = 1/5(0)² + 8 = 8
Therefore the average rate of change between x = - 2 and x = 18 will be:
= [ f(18) - f(-2) / ( 18 - (-2) ) ]
= ( 88 - 8 ) / 20
= 80/20
= 4
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the score on the right is a scaled copy of the square on the left identify the scale factor express your answer in the simplest form
Answers
Answer
Scale factor = 3.5
Explanation
Scale factor expresses how much the copy/image of the original figure is bigger or smaller than the original figure.
If the scale factor is more than 1, then the image is an enlargement of the original figure.
But if the scale factor is less than 1, then the image is a reduction of the original figure.
Mathematically,
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Length of a side of the image or scaled copy = 56
Corresponding length of that side on the original figure = 16
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Scale factor = (56/16) = (7/2) = 3.5
Hope this Helps!!!
Answer
Scale factor = 3.5
Explanation
Scale factor expresses how much the copy/image of the original figure is bigger or smaller than the original figure.
If the scale factor is more than 1, then the image is an enlargement of the original figure.
But if the scale factor is less than 1, then the image is a reduction of the original figure.
Mathematically,
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Length of a side of the image or scaled copy = 56
Corresponding length of that side on the original figure = 16
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Scale factor = (56/16) = (7/2) = 3.5
Hope this Helps!!!
I need an quadratic equation with -3 and 6 for this assignment
Answers
If a quadratic equation has solutions
[tex]x=a,x=b[/tex]Then
[tex]x-a=0\text{ and x-b=0}[/tex]Furthermore, the quadratic can be written as
[tex]\begin{gathered} y=(x-a)(x-b) \\ where,y=0 \end{gathered}[/tex]Therefore,
[tex](x-a)(x-b)=0[/tex]Given:
[tex]a=-3,b=6[/tex]Hence,
[tex]\begin{gathered} (x--3)(x-6)=0 \\ (x+3)(x-6)=0 \end{gathered}[/tex]Simplify
[tex]\begin{gathered} x(x-6)+3(x-6)=0 \\ x^2-6x+3x-18=0 \\ x^2-3x-18=0 \end{gathered}[/tex]Hence, the quadratic equation is
[tex]x^{2}-3x-18=0[/tex]find the average rate of change on the interval (SHOW ALL WORK)
Answers
First, evaluate the function at the ends of the interval:
[tex]\begin{gathered} g(x)=x^3-2x \\ g(-1)=(-1)^3-2(-1) \\ g(-1)=-1^{}+2 \\ g(-1)=1 \end{gathered}[/tex][tex]\begin{gathered} g(x)=x^3-2x \\ g(2)=2^3-2(2) \\ g(2)=8-4 \\ g(2)=4 \end{gathered}[/tex]Now, the average rate of change will be
[tex]\begin{gathered} \text{Average rate of change }=\frac{g(2)-g(-1)}{2-(-1)} \\ \text{Average rate of change }=\frac{4-1}{2-(-1)} \\ \text{Average rate of change }=\frac{3}{2+1} \\ \text{Average rate of change }=\frac{3}{3} \\ \text{Average rate of change }=1 \end{gathered}[/tex]event a is the event that randomly selected students from your school is make event b is the event that randomly selected students from your school owns a bicycle which of the following do we know for certain correctly represents the probability of selecting a male students or selecting a student who owns a bicycle
Answers
The or probability in the context of this problem is represented as follows:
P(A U B).
Or probabilityThe or probability between two events A and B is the probability that at least one of the events happen.
The symbol of the or probability is given as follows:
U
In the context of this problem, the events are given as follows:
Event A: a randomly selected student is male.Event B: a randomly selected student owns a bike.Hence the probability of selecting a male students or selecting a student who owns a bicycle is represented as follows:
P(A or B) = P(A U B).
The other options are as follows:
P(A ∩ B): both male and own bike, representing the intersection operation of the events.P(A): male.P(B): own bike.Missing informationThe complete problem is given by the image at the end of the answer.
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