The graph of f(x) is a parabola with "arms up"
The vertex of the parabola is (0,-3)
Then we can know all the problem ask us:
increasing: (-3, infinity)
decreasing: (minus infinty, -3)
DNE maximum, beacuase it's arbitrarily large.
The minimum is the vertex: minimum of -3 at x = 0
The domain is all real numbers
The range is [-3, infinity)
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To know the shape of a parabola you want to look 2 things. The standar formula of a parabola is:
[tex]f(x)=ax^2+b[/tex]We focus on a and b. Always will be a squared x, but a and b vary. a lot
A tell us if the parabola has it's arms up or down. If is positive, has arms up. If it's negative, arms down.
Also, this isn't something "strictly mathematical" but can tel you is the parabola is thin or fat.
Now b tells us what happends when x=0. If b is positive, the vertex will be "rised up". If b is negative, the vertex will be "pulled down"
When you get relatively confident, you can watch a and b, and based on their sign and how big they are, you can make a really good idea how the graphic is.
All the information the problem ask, you can get it by those numbers.
To know how wide is a parabola, you need to look at a. Let's supose a = 100. This is a very big number, si if I plug in an x, the function will square it and multiply it by 100 right? Then the function will be very thin. For an x very low, the function will be very great. Example: f(x)=100x^2 if I put x = 1 then I have to square it, and multipli it by 100: 1^2*100=100
Now let's copare this with an smaller a. Suppose a =2. Then if I plug x = 1 I get:
[tex]2x^2\text{ at x =1 }\Rightarrow f(1)=2\cdot1^2=2[/tex]For the same value of x, the first function is 100 and the second 2
hello, in the picture you can see a graph and my teacher said that the domain and range would be all real numbers possible. could you please help me because I don't understand why.
The domain is all the values of the independent variable (in this case, x) for which the function is defined.
In this case, as it is indicated with the arrows in both ends, the function continues for greater and smaller values of x.
As there is no indication that for some value or interval of x the function is not defined (a discontinuity, for example), then it is assumed that the function domain is all the real values.
Example function:
We have the function y=1/(x-2)
We can look if there is some value of x that makes the function not defined.
The only value of x where f(x) is not defined is x=2. When x approximates to 2, the value of the function gets bigger or smaller whether we are approaching from the right or from the left.
Then, the function is not defined for x=2. So, the domain of f(x) is all the real numbers different from x=2.
The domain is, by default, all the real numbers, but we have to exclude all the values of x (or intervals, in some cases like the square roots) for which f(x) is not defined.
Select the correct choice below and, if necessary, fill in the answer box within your choice
x² - 20x + 100
Find two numbers, such that its sum gives -20 and its product gives 100
If such numbers exist, this implies that the polynomial is NOT prime
The two numbers are: -10 and -10
Replace the coefficient of x with the two numbers
x² - 10x -10x + 100
x(x-10) - 10(x - 10)
(x-10)(x-10)
(x-10)²
Therefore, the correct option is A.
x² - 20x + 100 = (x-10)²
Which of the following expressions is equivalent to 2^4x − 5? the quantity 8 to the power of x end quantity over 10 the quantity 4 to the power of x end quantity over 5 the quantity 16 to the power of x end quantity over 32 the quantity 1 to the power of x end quantity over 32
The equivalent expression for the given exponent equation is 16^x/32
Given,
The exponent equation; 2^4x - 5
We have to find the expressions which is equivalent to 2^4x - 5
Exponential equations are inverse of logarithmic equations.
This can also be expressed as;
2^(4x-5) = 2^4x/2^5
2^4x-5 =16^x/2^5
2^4x-4 = 16^x/32
Hence the equivalent expression is 16^x/32
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Answer:it's not 4^x/5
Step-by-step explanation:
20. Write the slope-intercept form of the line described in the followingPerpendicular to -2+3y=-15and passing through (2, -8)
The equation of a line in Slope-Intercept form is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
Solve for "y" from the equation given in the exercise in order to write it in Slope-Intercept form:
[tex]\begin{gathered} -2+3y=-15 \\ 3y=-15+2 \\ y=-\frac{13}{2} \end{gathered}[/tex]You can notice that the equation has this form:
[tex]y=b[/tex]Where "b" is the y-intercept.
Then, it's a horizontal line, which means that its slope is:
[tex]m=0[/tex]Since it is a horizontal line, the lines perpendicular to that line is a vertical line, whose slope is undefined and whose equation is:
[tex]x=k[/tex]Where "k" is the x-intercept.
Knowing that the x-coordinate of any point on a vertical line is always the same, and knowing that this line passes through this point:
[tex]\mleft(2,-8\mright)[/tex]You can determine that the equation of the line is:
[tex]x=2[/tex]find x..in a right triangle ️ with a height of 10 and hypotenuse of 19
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c= hypotenuse (the longest side) = 19
a & b = the other 2 legs of the triangle
Replacing:
19^2 = 10^2 + x^2
Solve for x
361 = 100 + x^2
361 - 100 = x^2
261 = x^2
√261 =x
x= 16.16
Identify the function rule from the values in the table.
we are given a table of inputs and ouputs of a function. We notice that each output is obtained by multiplying the input by -4:
[tex]\begin{gathered} (-2)(-4)=8 \\ (0)(-4)=0 \\ (1)(-4)=-4 \\ (3)(-4)=-12 \end{gathered}[/tex]Therefore, the right answer is A.
3. The number line below represents the solution to which inequality of he 0 1 2 3 4 5 6 7 8 9 10
let x be the money daniel has. So we get that
[tex]x\ge72+15\rightarrow x\ge87[/tex]Daniel has at least $87
points E,D and H are the midpoints of the sides of TUV, UV=100,TV=126,and HD=100, find HE.
Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:
[tex]\begin{gathered} \frac{VD}{VU}=\frac{HD}{TU} \\ \end{gathered}[/tex]Since D is the midpoint of VU, VD=50
[tex]\begin{gathered} \frac{50}{100}=\frac{100}{TU} \\ 50\times TU=100\times100 \\ TU=200 \end{gathered}[/tex]then
[tex]\begin{gathered} \frac{HE}{UV}=\frac{HD}{TU} \\ \frac{HE}{100}=\frac{100}{200} \\ HE=\frac{100}{200}\times100 \\ HE=50 \end{gathered}[/tex]Find the length of the segment indicated. Round to the nearest tenth if necessary. Note: One segment of each triangle is a tangent line
Given
A circle with a tangent drawn to it forming one side of a triangle
Required
we need to find the diameter of the circle
Explanation
clearly it is a right angled triangle as radius through point of contact is perpendicular to the tangent. let the lenght of missing side be d
Therefore
[tex]d^2+12^2=20^2[/tex]or
[tex]d^2=400-144[/tex]or
[tex]d^2=256[/tex]or d=16
1. Which of the following is NOT a linear function? (1 point ) Oy=* -2 x x Оy - 5 ya 0 2. 3*- y = 4 3.
hello
to solve this question we need to know or understand the standard form of a linear equation
the standard form of a linear equation is given as
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]from the options given in the question, only option D does not corresponds with the standard form of a linear equation
[tex]undefined[/tex]A diesel train left Abuja and traveled west. One hour later a freight train left traveling 50 mph faster in an effort to catch up to it. After three hours of freight train finally caught up. Find the diesel train’s average speed.
The speed at which diesel train was moving is = 150mph
In the above question, it is given that,
Let the speed of the diesel train which left Abuja be x mph
then, speed of freight train which is moving 50 mph faster than diesel train = (50 + x)mph
Further, the freight train finally caught up the diesel train after three hours
So time taken by freight train = 3 hours
While time taken by diesel train would 1 hour more than freight train as its moving slower = 3 + 1 = 4 hours
Now, it is given that both the trains finally catch up, it means the distance travelled by both the trains would be equal
We know that,
Speed = [tex]\frac{Distance}{Time}[/tex]
Distance = Speed x Time
Distance travelled by Diesel train = distance travelled by Freight train
4x = 3(50 + x)
4x = 150 + 3x
x = 150 mph
Hence, the speed at which diesel train was moving is = 150mph
While, the speed at which freight train was moving is = (150 + x)mph = (150 + 50)= 200mph
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Mrs. Williams estimates that she will spend $65 onschool supplies. She actually spends $73. What is thepercent error? Round to the nearest tenth ifnecessary.
We can calculate the percent error as the absolute difference between the predicted value ($65) and the actual value ($73) divided by the actual value and multiplied by 100%.
This can be written as:
[tex]e=\frac{|p-a|}{a}\cdot100\%=\frac{|65-73|}{73}\cdot100\%=\frac{8}{73}\cdot100\%\approx11.0\%[/tex]Answer: the percent error is approximately 11.0%
20 P1: a For two events, A and B.P(B) -0.5, P(AB) -0.4 andPAB) = 0.4.Calculatei PAB)ii P(A)ili P(AUB)iv P(AB)(8 marks)b Determine, with a reason, whetherevents A and B are independent ornot.(2 marks)probabilityStatistics and
We have two events A and B.
We know that:
P(B) = 0.5
P(A|B) = 0.4
P(A∩B') = 0.4
i) We have to calculate P(A∩B).
We can relate P(A∩B) with the other probabilities knowing that:
[tex](A\cap B)\cup(A\cap B^{\prime})=A[/tex]So we can write:
[tex]P(A\cap B)+P(A\cap B^{\prime})=P(A)[/tex]We know P(A∩B') but we don't know P(A), so this approach is not useful in this case.
We can try with the conditional probability relating P(A∩B) as:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, we can use this to calculate P(A∩B) as:
[tex]\begin{gathered} P(A\cap B)=P(A|B)P(B) \\ P(A\cap B)=0.4*0.5 \\ P(A\cap B)=0.2 \end{gathered}[/tex]ii) We have to calculate P(A) now.
We can use the first equation we derive to calculate it:
[tex]\begin{gathered} P(A)=P(A\cap B)+P(A\cap B^{\prime}) \\ P(A)=0.2+0.4 \\ P(A)=0.6 \end{gathered}[/tex]iii) We have to calculate P(A∪B).
We can use the expression:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=0.6+0.4-0.2 \\ P(A\cup B)=0.8 \end{gathered}[/tex]iv. We can now calculate P(A|B') as:
[tex]\begin{gathered} P(A)=P(A|B)+P(A|B^{\prime}) \\ P(A|B^{\prime})=P(A)-P(A|B) \\ P(A|B^{\prime})=0.6-0.4 \\ P(A|B^{\prime})=0.2 \end{gathered}[/tex]b) We now have to find if A and B are independent events.
To do that we have to verify this conditions:
[tex]\begin{gathered} 1)P(A|B)=P(A) \\ 2)P(B|A)=P(B) \\ 3)P(A\cap B)=P(A)*P(B) \end{gathered}[/tex]We can check for the first condition, as we already know the value:
[tex]\begin{gathered} P(A|B)=0.4 \\ P(A)=0.6 \\ =>P(A|B)P(A) \end{gathered}[/tex]Then, the events are not independent.
Answer:
i) P(A∩B) = 0.2
ii) P(A) = 0.6
iii) P(A∪B) = 0.8
iv) P(A|B') = 0.2
b) The events are not independent.
quien me puede ayudar a resolver estos ejercicios porfa de ecuaciones
3x^2 -5x +1 =0
Aplica la formula cuadrática:
[tex]\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]Donde:
a = 3
b= -5
c= 1
Reemplazando:
[tex]\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot3\cdot1}}{2\cdot3}[/tex][tex]\frac{5\pm\sqrt[]{25-12}}{6}[/tex][tex]\frac{5\pm\sqrt[]{13}}{6}[/tex]Positivo:
(5+√13) /6 = 1.43
NEgativo:
(5-√13) /6 = 0.23
the table below shows the attendance and revenue at theme parks in the us
Let
y ------> the year
x ----> revenue
so
Plot the given ordered pairs
see the attached figure
(please wait a minute to plot the points)
In the graph the x-coordinate 0 represent year 1990
Find out the equation of the line
take two points
(1990, 5.7) and (2006, 11.5)
Find the slope m
m=(11.5-5.7)/(2006-1990)
m=5.8/16
m=0.3625
Find the equation of the line in slope intercept form
y=mx+b
we have
m=0.3625
point (1990, 5.7)
substitute and solve for b
5.7=(0.3625)(1990)+b
b=-715.675
therefore
y=0.3625x-715.675What is 120 percent of 118?
120 percent of 118 is expressed mathematically as;
120% of 118
120/100 * 118
= 12/10 * 118
= 6/5 * 118
= 708/5
= 141.6%
Hence 120 percent of 118 is 141.6%
Find the slope of every line that is parallel to the graph of the equation
1. Are these ratios equivalent? 8:7 and 4:2
EXPLANATION
The answer is no, because 8:7 and 4:2 are different relationships.
Can you Convert 840 inches to cm. Use unit analysis to convert the rate.
we know that
1 in=2.54 cm
so
840 in
Applying proportion
1/2.54=840/x
x=(840*2.54)/1
x=2,133.6 cm
answer is
2,133.6 cmApplying unit rate or unit analysiswe have
2.54 cm/in
Multiply by 840 in
2.54*(840)=2,133.6 cm40/
Writing a equation of a circle centers at the origin
ANSWER
[tex]x^2+y^2=100[/tex]EXPLANATION
The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = the center of the circle
r = radius of the circle (i.e. distance from any point on its circumference to the center of the circle)
The center of the circle is the origin, that is:
[tex](h,k)=(0,0)[/tex]To find the radius, apply the formula for distance between two points:
[tex]r=\sqrt[]{(x_1-h)^2+(y_1-k)^2_{}}[/tex]where (x1, y1) is the point the circle passes through
Hence, the radius is:
[tex]\begin{gathered} r=\sqrt[]{(0-0)^2+(-10-0)^2}=\sqrt[]{0+(-10)^2} \\ r=\sqrt[]{100} \\ r=10 \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(10)^2 \\ \Rightarrow x^2+y^2=100 \end{gathered}[/tex]F(x) = -3x,x<0 4,x=0 x^2, x>0 given the piece wide functions shown below select all of the statements that are true
The correct statements regarding the numeric values of the piece-wise function are given as follows:
B. f(3) = 9.
D. f(2) = 4.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
A piece-wise function means that the definition of the input is different based on the input of the function. In this problem, all the numeric values we are calculating are for positive numbers, hence the definition of the function is given by:
f(x) = x².
Then the numeric values of the function are given as follows:
f(1) = 1² = 1.f(2) = 2² = 4.f(3) = 3² = 9.f(4) = 4² = 16.Meaning that options B and D are correct.
Missing informationThe options are given by the image at the end of the answer.
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Add or subtract. Simplify. Change the answers to mixed numbers, if possible.
Answer:
[tex]\begin{gathered} \frac{1}{8} \\ \\ \text{LCD = 8} \end{gathered}[/tex]Explanation:
Here, we start by finding the lowest common denominator
From what we have, the lowest common denominator is the lowest common multiple of both denominators which is equal to 8
We divide the first denominator by this and multiply the result by its numerator. We take the same step for the second denominator
Mathematically, we have it that:
[tex]\frac{11-10}{8}\text{ = }\frac{1}{8}[/tex]The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011 $5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020)..
The given data plot will look thus:
a) Building a model using just the 1999 and 2019 years:
[tex]\begin{gathered} 1999\rightarrow0\rightarrow2196 \\ 2019\rightarrow20\rightarrow7186 \\ \text{Havng} \\ x_1=0,y_1=2196 \\ x_2=20,y_2=7186 \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{The model will be:} \\ P_t=249.5t+2196 \end{gathered}[/tex]b) The cost of insurance in 2030
[tex]\begin{gathered} P_t=249.5t+2196 \\ t=2030-1999=31 \\ \text{The cost of insurance in 2030 therefore will be:} \\ =249.5(31)+2196 \\ =7734.5+2196 \\ =\text{ \$9930.5} \end{gathered}[/tex]c) When do we expect the cost to reach $12,000
[tex]\begin{gathered} P_t=249.5t+2196 \\ 12,000=249.5t+2196 \\ 12000-2196=249.5t \\ 9804=249.5t \\ \frac{9804}{249.5}=\frac{249.5t}{249.5} \\ 39.2946=t \\ Since\text{ t = year -1999} \\ 39.2946+1999=\text{year} \\ 2038.2946=\text{year} \\ Since\text{ we are to give our answer as an exact year} \\ \text{The year will be }2039. \end{gathered}[/tex]Which sequence of transformations will map AABC onto AA' B'C'?A- reflection and translationB- rotation and reflectionC- translation and dilation D- dilation and rotation
For the given problem, we can observe that the image is bigger than the original diagram.
We can also observe that the image is rotated counterclockwise.
Hence, the sequence of transformation that maps triangle ABC onto triangle A'B'C' is a dilation and a rotation.
Answer: Option D
alex was late on his property tax payment to the county. he owed $6,915 and paid the tax 9 months late. the county charges a penalty of 5% simple interest. find the amount of the penalty. (round to the nearest cent as needed)
We have to use the simple interest formula.
[tex]A=P(1+rt)[/tex]Replacing the given information, we have.
[tex]\begin{gathered} A=6,915(1+0.05\cdot\frac{9}{12}) \\ A=6,915(1.0375) \\ A=7,174.31 \end{gathered}[/tex]The final amount is $7,174.31, where the penalty is $259.31.Hunter has $300 in a savings account. The interest rate is 8%, compounded annually.To the nearest cent, how much will he have in 3 years?
EXPLANATION
If Hunter has $300 in savings and the interest rate is 8%, compounded annualy, we can apply the following equation:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where, P=Principal=300, r=rate (in decimal form) = 8/100 = 0.08, n=number of compounded times = 1 and t = time = 3
Substituting terms:
[tex]A=300\cdot(1+\frac{0.08}{1})^{1\cdot3}[/tex]Adding numbers:
[tex]A=300\cdot(1.08)^3[/tex]Computing the powers:
[tex]A=300\cdot1.26[/tex]Multiplying numbers:
[tex]A=378[/tex]In conclusion, there will be 378.00 in three years
This graph shows the solution to which inequality?3.2)(-3,-5)O A. ys fx-2B. vfx-2O c. vfx-2OD. yzfx-2
First, find the equation of the line, given that the points (3,2) and (-3,-6) belong to that line. To do so, use the slope formula and then substitute the value of the slope and the coordinates of a point on the slope-point formula of a line:
[tex]y=m(x-x_0)+y_0[/tex]The slope of the line, is:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{(2)-(-6)}{(3)-(-3)} \\ =\frac{2+6}{3+3} \\ =\frac{8}{6} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the equation of a line (using the point (3,2)) is:
[tex]\begin{gathered} y=\frac{4}{3}(x-3)+2 \\ =\frac{4}{3}x-\frac{4}{3}\times3+2 \\ =\frac{4}{3}x-4+2 \\ =\frac{4}{3}x-2 \end{gathered}[/tex]Since the colored region on the coordinate plane is placed above the line
y=(4/3)x-2, then the equation of the inequality is:}
[tex]undefined[/tex]This is Calculus 1 Problem! MUST SHOW ALL THE JUSTIFICATION!!!
Given: A surveyor standing 50 feet from the base of a large tree measures the angle of elevation to the top of the tree as 75.8 degrees.
Required: To determine how accurately the angle must be measured if the percent error in estimating the tree's height is less than 5%.
Explanation: To estimate the angle, we will use the trigonometric ratio
[tex]tanx=\frac{h}{50}\text{ ...\lparen1\rparen}[/tex]where h is the tree's height, and x is the angle of elevation to the top of the tree.
Hence we get
[tex]\begin{gathered} h=50\cdot(tan75.8\degree) \\ h=197.59\text{ feet} \end{gathered}[/tex]Now differentiating equation 1, we get
[tex]sec^2xdx=\frac{1}{50}dh[/tex]We can write the above equation as:
[tex]sec^2x\cdot\frac{xdx}{x}=\frac{h}{50}\cdot\frac{dh}{h}\text{ ...\lparen2\rparen}[/tex]Also, it is given that the error in estimating the tree's height is less than 5%.
So
[tex]\frac{dh}{h}=0.05[/tex]Also, we need to convert the angle x in radians:
[tex]x=1.32296\text{ rad}[/tex]Putting these values in equation (2) gives:
[tex]\frac{dx}{x}=\frac{197.59}{50}\cdot\frac{cos^2(1.32296)}{1.32296}\cdot0.05[/tex]Solving the above equation gives:
[tex]\begin{gathered} \frac{dx}{x}=3.9518\cdot0.04548551012\cdot0.05 \\ =0.008987\text{ radians} \end{gathered}[/tex]Let
[tex]d\theta\text{ be the error in estimating the angle.}[/tex]Then,
[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]Final Answer:
[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]The function, f. is drawn on the accompanying set of axes. On the same set of axes, sketch the graph of f-?, the inverse of f
We are given the following graph:
The inverse of the graph is shown below:
second number when the list is sorted from greatest to least
5.2% = 0.052
1/7 = 0.14
-11/5 = -2.2
From the greatest to least:
[tex]0.14>0.052>-0.8>-2.2[/tex]The second number is: 5.2%
Answer:
5.2%