The quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,
f(x) = (-x² - 2x + 3)/3
Given, an equation having
x-intercepts: (-3,0) and (1,0). Also, y-intercept: (0,1)
Now, as we know that the equation is quadratic then, it is clear that the equation will be in the given form :
f(x) = ax² + bx + c
Now, using the given points,
x-intercepts: (-3,0) and (1,0) and y-intercept: (0,1)
we get,
0 = 9a - 3b + c
0 = a + b + c
1 = c
Now, using the value of c, we get
9a - 3b = -1
a + b = -1
On solving the equations, we get
9a - 3b = -1
3a + 3b = -3
On adding both the equations we get,
12a = -4
a = -1/3
Now, using the value of a, we get
-3 - 3b = -1
-2 = 3b
b = -2/3
So, the quadratic equation, be
f(x) = -x²/3 - 2x/3 + 1
On simplifying, we get
f(x) = (-x² - 2x + 3)/3
Hence, the quadratic equation for the given points x-intercepts: (-3,0) and (1,0). y-intercept: (0,1) is,
f(x) = (-x² - 2x + 3)/3
Learn more about Quadratic Equations here https://brainly.com/question/27179040
#SPJ1
5. * 20 points Rotate 180° about the origin. 3 Y 4 5 3
In order to rotate these point 180° about the origin, we just need to change the signal of all coordinates.
So we have that:
[tex]\begin{gathered} X(-1,3)\to X^{\prime}(1,-3) \\ W(-2,5)\to W^{\prime}(2,-5) \\ V(-5,5)\to V^{\prime}(5,-5) \\ T(-4,3)\to T^{\prime}(4,-3) \end{gathered}[/tex]Looking at the options, the correct one is c. (the third one).
Susan monitors the number of strep infections reported in a certain neighborhood in a given week.The recent numbers are shown in this table:WeekNumber of People020126234344According to her reports, the reported infections are growing at a rate of 30%.If the number of infections continues to grow exponentially, what will the number of infections bein week 10?
SOLUTION
The formula for growth rate is given below;
[tex]y=a(1+r)^x[/tex]Where;
y = number of infections,
a = initial number of infections (20),
r = rate (30% or 0.3) and
x = the week to find (10)
[tex]\begin{gathered} y=a(1+r)^x \\ y=20(1+0.3)^{10} \\ y\text{ = 20 (13.7858)} \\ y\text{ = 275.72} \end{gathered}[/tex]The number of infections in week 10 will be 276.
D=2730 mi t=9.75 h find r
In order to calculate the rate r (in this case, the speed), we can use the following formula:
[tex]\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ d=r\cdot t \end{gathered}[/tex]So, using the values of d = 2730 and t = 9.75, we have:
[tex]\begin{gathered} 2730=r\cdot9.75 \\ r=\frac{2730}{9.75} \\ r=280 \end{gathered}[/tex]So the value of r is equal to 280 miles per hour.
Tracey paid $145 for an item that was originally priced at $550. What percent of the original price did Tracey pay?
Tracey paid $145 for an item that was originally priced at $550. What percent of the original price did Tracey pay?
we know that
$550 represent 100%
so
Applying proportion
100/550=x/145
solve for x
x=(100/550)*145
x=26.36%Rotation of 270° (x,y) or (a,b) becomes
A totation of 270º will chncge the sign of the x and y coordinate so the condinates will change:
[tex]\begin{gathered} (x,y)\to(-x,-y) \\ (a,b)\to(-a,-b) \end{gathered}[/tex]-4x-2y = -6a. y = -2x + 3b. y = 2x-3C. y = 2x + 3d. y = -2x - 3
What is the domain of h?y7h---7 6 5 4 3 276+5+4+3+21++ +++++1 2 3 4 5 6 72+-3+-4+-5 .-6+-7
The domain of a function is the set of all possible x-values.
In this case, the function h(x) is discrete, then the domain is the set of x-values where h(x) is defined, that is,
Domain: {-2, -1, 1, 5, 6}
You Try! As an Equation Example B: A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet. Find the dimensions of the rectangle. Write an equation to model this problem and solve it in the sketch area below. 市里。 Entrega
Let the width be w and the length be l
Since the width is 5ft less than the length,
then
w=l-5
The area of the rectangle is 126 square feet
Then
l times w = 126
therefore
l(l-5) = 126
[tex]\begin{gathered} \Rightarrow l^2-5l=126 \\ \Rightarrow l^2-5l-126=0 \end{gathered}[/tex]Factorising the equation, we have:
[tex]\begin{gathered} l^2+9l-14l-126=0 \\ \Rightarrow(l+9)(l-14)=0 \\ \Rightarrow l=-9\text{ or 14} \end{gathered}[/tex]Since l cannot be negative
then the only correct option is l=14
Since w = l - 5
then
w = 14 - 5 = 9
Therefore the length is 14ft and the width is 9ft
can you please solve this problem then tell me what was wrong with the answer
Given:
[tex]64^{\circ\text{ }}and\text{ }x^{\circ}[/tex]Sum of the angles of Same side interior angles is 180 degree.
[tex]\begin{gathered} 64+x=180 \\ x=180-64 \\ x=116^{\circ} \end{gathered}[/tex]Elena is conduction a study about the effects of toxins in the water on the hormones of fish. Elena surveys 350 male fish in a river and finds that 150 of the male fish have egg cells growing inside them. According to Elena’s survey, what is the ratio of male fish with egg cells to male cells in the river?
Answer:
3:7
Explanation:
We know that Elena surveys 350 male fish in a river.
Out of these 350 fish, 150 have egg cells growing inside them.
Therefore,
male fish with egg cells: male fish in the river = 150: 350
The next step is to write this ratio as a fraction and simplify it.
Writing the ratio as a fraction gives
[tex]\frac{150}{350}[/tex]dividing both the numerator and the denominator by 50 gives
[tex]\frac{150\div50}{350\div50}[/tex][tex]=\frac{3}{7}[/tex]Hence, the ratio of the male fish with egg cells to total male fish in the river is 3:7.
The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 69?
Given:
The box-and-whisker plot below represents some data set.
As shown:
The median = 65
The value of Q1 = 61
The value of Q3 = 69
The percentage of the data values that are greater than 69 will be the percentage of the data that are greater than Q3
So, the answer will be 25%
Harry took a loan from the bank.D represents Harry's remaining debit (In dollars) after t months.D = -200t + 9000
D = His remaining debt in dollars
t = number of months
[tex]\begin{gathered} D=-200t+9000 \\ D=9000-200t \end{gathered}[/tex]The size of the loan will be $9000 . From the equation you can notice the product of 200 and t is always subtracted at t months from the amount he borrowed($9000)
12. One year ago the median price for a home was $342,000. Now the current median price for a home is $215,000. What was the percent decrease in the median price of a home over the last year? Give your answer to at least one decimal place.%
One year ago the median price for a home was $342,000. Now the current median price for a home is $215,000. What was the percent decrease in the median price of a home over the last year? Give your answer to at least one decimal place.
In this problem
$342,000 ------> represents 100%
so
Applying proportion
Find out how much percentage represents the difference (342,000-215,000=127,000)
100/342,000=x/127,000
solve for x
x=(100/342,000)*127,000
x=37.1%A credit union client deposits $2,700 in an account earning 6% interest, compounded annually. What will the balance of the account be at the end of 31 years?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Balance ≈ $________ after 31 years.
Answer:
Balance ≈ $7,722 after 31 years
Step-by-step explanation:
multiply your deposit by your interestMultiply by how longAdd your base deposit to the interestEx.
2, 700(0.06) =$162.
162(31)= $5,022.
5,022 + 2,700 = $7,722.
If 3 girls can decorate 2 holiday cards in 1.5 minutes, how many holiday cards can 6 girls decorate in 1 hour if they work at the same speed?
Notice that 2*3=6.
On the other hand, according to the question, 3 girls can decorate a total of
[tex]\begin{gathered} \frac{60}{1.5}=40 \\ \Rightarrow40\cdot2=80 \end{gathered}[/tex]80 holiday cards in one hour. Therefore, 6 girls can decorate 2*80=160 holiday cards in the same amount of time.
The answer is 160 holiday cards per hour
if the great circle circumference of a sphere is 16 pi yards, find its surface area.
Next, find the surface area.
[tex]\begin{gathered} \text{Surface area = 4}\pi r^2 \\ \text{ = 4}\pi\text{ }\times8^2 \\ \text{ = 4}\pi\text{ x 64} \\ \text{ = 256}\pi yd^2 \end{gathered}[/tex]Analyze the data in the line plot "attached "Use the data to construct a line plot.Number of students in a classroom:22, 28, 31, 33, 28, 29, 31, 28, 29, 32, 27, 18, 29, 31, 30, 31, 32, 27, 29, 33
Answer:
Most classrooms have between 29-31 students.
Step-by-step explanation:
To construct a line plot, create a number line that includes all the numbers or values in the data set. Then place an x over each data value on the number line, if a value occurs more than one place x's as necessary:
For the following exercise, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptotes of the function. use that information to sketch graph.
Answer:
The expression is given below as
[tex]a(x)=\frac{x^2+2x-3}{x^2-1}[/tex]The horizontal intercepts will be at y=0
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ \frac{x^2+2x-3}{x^2-1}=0 \\ x^2+2x-3=0 \\ x^2+3x-x-3=0 \\ x(x+3)-1(x+3)=0 \\ (x-1)(x+3)=0 \\ x-1=0,x+3=0 \\ x=1,x=-3 \end{gathered}[/tex][tex]\begin{gathered} x^2-1=0 \\ x^2=1 \\ x=\pm1 \\ x=1,x=-1 \end{gathered}[/tex]Hence,
The horizontal intercepts is at x = -3
The vertical intercept is at x=0
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ y=\frac{0^2+2(0)-3}{0^2-1} \\ y=\frac{-3}{-1} \\ y=3 \end{gathered}[/tex]Hence,
The vertical intercept is at y=3
A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ a(x)=\frac{(x-1)(x+3)}{(x-1)(x+1)_{}} \\ \text{hence, the vertical aymspote will be at} \\ x+1=0 \\ x=-1 \end{gathered}[/tex]Hence,
The vertical asymptotes is at x= -1
The horizontal asymptotes will be calculated using the image below
[tex]\begin{gathered} a(x)=\frac{x^2+2x-3}{x^2-1} \\ a=1,b=1,n=m=1 \\ y=\frac{a}{b} \\ y=\frac{1}{1} \\ y=1 \end{gathered}[/tex]Hence,Do you have any questions about the steps to solve your question?
The horizontal asymptotes is y=1
The graph is represented below as
The table summarizes results from 977 pedestrian deaths that were caused by automobile accidents.Pedestrian DeathsDriverPedestrian Intoxicated?Intoxicated?YesNoYes4885No260584If one of the pedestrian deaths is randomly selected, find the probability that neither the pedestrian nor the driver wasintoxicated. Please enter a decimal to 4 places.Probability
We are asked to find the probability that neither the pedestrian nor the driver was intoxicated.
Probability is given by
P = number of desired outcomes/total number of outcomes
From the given table we know that
Total number of pedestrian deaths = 977
The desired outcomes are
Driver intoxicated = No and Pedestrian intoxicated = No (584)
So the probability is
P = 584/977
P = 0.5977
Therefore, the probability that neither the pedestrian nor the driver was intoxicated is 0.5977
The equation of the line of best fit is y= 25x+7.5. What does the y-intercept represent?
y= 25x+7.5
The general equation of a line is given as
y = mx + c
where m is the slope and c is the y-intercept
Comparing with the equation
the y intercept is 7.5
Charlotte is making pies for her whole family. So far, she has made 5.04 pounds
worth of pie, and has 7 people to feed, including herself. How much does each
person get if Charlotte is finished making pies?
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more
people to feed, how much pie will each person get from Charlotte's 5.04
pounds?
Step-by-step explanation:
Charlotte is making pies for her whole family. So far, she has made 5.04 pounds worth of pie, and has 7 people to feed, including herself. How much does each person get if Charlotte is finished making pies?
5.04 / 7 = 0.72 pounds per person
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more people to feed, how much pie will each person get from Charlotte's 5.04 pounds?
7 + 2 = 9 people now
5.04 / 9 = 0.56 pounds per person
7. Simplify28120.51 +423) + (222 +7.51).
Answer: 581.5i + 140.64
Explanation:
574i + 118.44 + 22.2 +7.5i
grouping the terms yield
574i + 7.5i + 118.44 + 22.2
⇒
???????????????????
The domain is the set of all possible inputs that would satify the function while the range is the set of possible output values
Looking at the given graph,
Domain = ( - infinity, 4)
Range = (- 5, 2)
The volume of this cone is 53,851 cubic yards. What is the height of this cone? Use pi = 3.14 and round your answer to the nearest hundredth.
Volume of a cone = 1/3 π r^2 h
Where:
r= radius = 35 yd
h= height
π = 3.14
Replacing with the values given:
53,851 = 1/3 (3.14) 35^2 h
Solve for h
53,851 / (1/3 (3.14) 35^2)= h
h= 42
Can you please help me out with a question
As you can see in the given figure, there are two intersecting chords inside the circle.
Recall that the "Intersecting Chords Theorem" is given by
[tex]AE\cdot EC=BE\cdot DE[/tex]For the given case, we have
AE = 7
BE = 6
EC = 9
Let us substitute these values into the above equation and solve for DE
[tex]\begin{gathered} AE\cdot EC=BE\cdot DE \\ 7\cdot9=6\cdot DE \\ 63=6\cdot DE \\ \frac{63}{6}=DE \\ 10.5=DE \\ DE=10.5 \end{gathered}[/tex]Therefore, the length of DE is 10.5 units.
Show that (fof-1) (x)=x and (F-1 of)(x) = x for the following pair of functions.f(x) = 5-4x, f'(x) =5-754Show that (fof-1)(x) = x.(fof- ')(x) = 0Write the expression for the composition.= x(Do not simplify. Type an exact answer, using radicals as needed.)
To obtain the expression for the composition of the function of the inverse function of x, the following steps are necessary:
Step 1: Write out the expression for the function of x and the inverse function of x, as below:
[tex]\begin{gathered} f(x)=\sqrt[5]{5-4x} \\ ^{}f^{-1}(x)=\frac{5-x^5}{4} \end{gathered}[/tex]Step 2: Write out the expression for the composition of the function of the inverse function of x, as below:
[tex](f^{-1}Of))(x)=^{}\frac{5-(\sqrt[5]{5-4x})^5}{4}[/tex]Thus, the above is how the expression for the composition of the function of the inverse function of x is to be written out
i need help with this problem Find rate of change.
Step 1:
First, pick two points where the line intercept with both the horizontal and the vertical axis.
( 0 , 300 ) and (
Can you please help me with the answers, I don’t need the work I just need the answer please
Given that
The angles of the triangle are
30, 60 and 90
Consider the sine law formula
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Let A=30, B=60, and C=90, and substitute these values in the sine law, we get
[tex]\frac{a}{\sin 30^o}=\frac{b}{\sin 60^o}=\frac{c}{\sin 90^o}[/tex][tex]\frac{a}{\frac{1}{2}}^{}=\frac{b}{\frac{\sqrt[]{3}}{2}}=\frac{c}{1}[/tex]The ratio of the legs a and b is
[tex]\frac{a}{b}=\frac{\frac{1}{2}}{\frac{\sqrt[]{3}}{2}}=\frac{1}{2}\times\frac{2}{\sqrt[]{3}}=\frac{1}{\sqrt[]{3}}[/tex][tex]1\colon\sqrt[]{3}[/tex]The ratio of the legs b and c is
[tex]\frac{b}{c}=\frac{\frac{\sqrt[]{3}}{2}}{1}=\frac{\sqrt[]{3}}{2}[/tex][tex]\sqrt[]{3}\colon2[/tex]The ratio of the legs a and c is
[tex]\frac{a}{c}=\frac{\frac{1}{2}}{1}=\frac{1}{2}[/tex][tex]1\colon2[/tex]Hence the answer is
[tex]1\colon\sqrt[]{3}[/tex]Option C is correct.
PLEASE HELP ME !!!!!!!!
Find and describe the error in the following problem
Answer:
When multiplying the bottom equation, they did not multiply 4y by -2, but instead by 2.
The function shown by the graph is non-differentiable at x = 4. Why?
A. It has a vertical tangent line at x = 4.
B. It has a jump discontinuity at x = 4.
C. It has a corner at x = 4.
D. It has a vertical asymptote at x = 4.
Answer: In photo below
You're Welcome :)
The reason for the function being non-differentiable at x = 4 is given as follows:
C. It has a corner at x = 4.
What are the conditions for differentiability at a point?A function is differentiable at a point x = a if:
The function is continuous at x = a.The first derivative of the function is continuous at x = a.The continuity of a function at a point x = a is defined as follows:
Same lateral limits.Lateral limits are equal to the numeric value, that is, equal to f(a).Analyzing the graphed function at point x = 4, we have that:
The function is continuous, as the lateral limits are equal to the numeric value.The first derivative of the function is not continuous.The reason for the first derivative being not continuous is that:
To the left of x = 4, the function is increasing, hence it has a positive derivative.To the right of x = 4, the function is constant, hence it has a derivative of zero.Due to the different lateral limits, the first derivative is not continuous and then the function is not differentiable, thus option c is correct.
More can be learned about differentiable functions at brainly.com/question/27864122
#SPJ1