Please help me with this question:Graph the function F(x) = x^2 + 4x - 12 on the coordinate plane by finding the important points below.Be sure to show all steps in your calculations.(a)What are the x-intercepts?(b)What is the y-intercept?(c)What is the maximum or minimum value?(d)Use the points to graph the function.
Answers
Given the function:
[tex]f(x)=x^2+4x-12[/tex]Let's graph the function.
Let's find the following:
• (a). x-intercepts:
The x-intercepts are the points the function crosses the x-axis.
To find the x-intercepts substitute 0 for f(x) and solve for x.
[tex]\begin{gathered} 0=x^2+4x-12 \\ \\ x^2+4x-12=0 \end{gathered}[/tex]Factor the left side using AC method.
Find a pair of numbers whose sum is 4 and product is -12.
We have:
6 and -2
Hence, we have
[tex]\begin{gathered} (x+6)(x-2)=0 \\ \\ \end{gathered}[/tex]Equate the individual factors to zero and solve for x.
[tex]\begin{gathered} x+6=0 \\ Subtract\text{ 6 frm both sides:} \\ x+6-6=0-6 \\ x=-6 \\ \\ \\ x-2=0 \\ Add\text{ 2 to both sides:} \\ x-2+2=0+2 \\ x=2 \end{gathered}[/tex]Therefore, the x-intercepts are:
x = -6 and 2
In point form, the x-intercepts are:
(x, y) ==> (-6, 0) and (2, 0)
• (b). The y-intercept.
The y-intercept is the point the function crosses the y-axis.
Substitute 0 for x and solve f(0) to find the y-intercept:
[tex]\begin{gathered} f(0)=0^2+4(0)-12 \\ \\ f(0)=-12 \end{gathered}[/tex]Therefore, the y-intercept is:
y = -12
In point form, the y-intercept is:
(x, y) ==> (0, -12)
• (c). What is the maximum or minimum value?
Since the leading coefficient is positive the graph will have a minimum value.
To find the point where it is minimum, apply the formula:
[tex]x=-\frac{b}{2a}[/tex]Where:
b = 4
a = 1
Thus, we have:
[tex]\begin{gathered} x=-\frac{4}{2(1)} \\ \\ x=-\frac{4}{2} \\ \\ x=-2 \end{gathered}[/tex]To find the minimum values, substitute -2 for x and solve for f(-2):
[tex]\begin{gathered} f(-2)=(-2)^2+4(-2)-12 \\ \\ f(-2)=4-8-12 \\ \\ f(-2)=-16 \end{gathered}[/tex]Therefore, the minimum value is at:
y = -16
Using the point form, we have the minimum point:
(x, y) ==> (-2, -16).
• (d). Use the points to plot the graph.
We have the points:
(x, y) ==> (-6, 0), (2, 0), (0, -12), (-2, -16)
Plotting the graph using the points, we have:
Related Questions
how much time has elapse? 3:00 A.M to 7:14 A.M
Answers
To know how much time has elapsed from 3:00 A.M. to 7:14 A.M., we subtract the hours with the hours and the minutes with the minutes,
[tex]\begin{gathered} \text{Hours,} \\ 7h-3h=4h \\ \text{ Minutes,} \\ 14\min -0\min =14\min \end{gathered}[/tex]So, the time that has elapsed is 4 hours 14 minutes.
A transformation is a nonrigid transformation if it does not preserve what? Can you name anonrigid transformation? What is the rule for the nonrigid transformation?Nonrigid transformationRule (x,y) →
Answers
A transformation is nonrigid transformation if it does not preserve the structure of the original object.
An example of a nonrigid transformation is the dilation, and its general rule is:
[tex]D_k(x,y)=(kx,ky)[/tex]where 'k' is the scale factor
Q1 6.6QUESTION 1IF YOU CANT DO QUESTION 1 DO 2 OR 3THANK YOU
Answers
The area is 115
Find the area of the triangle specified below.
a = 9 meters, b=4 meters, c = 6 meters
A = square meters
(Round to the nearest integer as needed.)
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The answer will be 9.562m² using a triangle.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The perimeter will be P = sum of all three side.
s = p/2 = 9.5
Side a = 9 meters, b=4 meters, c = 6 meters
A = [tex]\sqrt{(s)(s-a)(s-b)(s-c)}\\=\sqrt{(9.5)(9.5-9)(9.5-4)(9.5-6)}\\[/tex]
A = 9.562m²
Hence the Area of the triangle is 9.562m².
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Airline pilots were asked to take a 2% cut in their salaries. They currently make $125,000. What will their new salaries be after the cut has been made?
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The new salaries of Airline pilots is $122500.
Given that the current salary of a Airline pilot is $125000.
They are asked 2% cut in their salaries.
So the cut amount is = 125000*(2/100) = $2500
Hence their new salaries will be = $125000-$2500 = $122500.
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The expression 5a + 3c can be used to find the cost of a adults and c children to attend the school play. What is the cost of 4 adults and 9 children to attend the school play?
Answers
The expression 5a + 3c can be used to find the cost of a adults and c children to attend the school play, so we have a expression as a function of the number of adults a and the number of children c. Therefore:
[tex]C(a,c)=5a+3c[/tex]What is the cost of 4 adults and 9 children to attend the school play?
[tex]\begin{gathered} a=4 \\ c=9 \\ C(4,9)=5(4)+3(9) \\ C(4,9)=20+27 \\ C(4,9)=47 \end{gathered}[/tex]$47
I need help please I'll send the rest after we meet
Answers
A line passes through (5,3) with a slope of 3/5,
[tex]y=mx[/tex]where m = slope
[tex]\begin{gathered} y=mx \\ y=\frac{3}{5}x \end{gathered}[/tex]Therefore the points for the graph are:
[tex]\begin{gathered} \lbrack0,0\rbrack \\ \lbrack15,9\rbrack \\ \lbrack10,6\rbrack \\ \lbrack7,4\rbrack \end{gathered}[/tex]Find the midpoint M of the line segment joining the points C=(8,7) and D= (4,-5)
Answers
Explanation
We are told to find the midpoint of the line segment. To do so, we will use the formula:
[tex]midpoint=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}[/tex]In our case
[tex]\begin{gathered} x_1=8,y_1=7 \\ x_2=4,y_2=-5 \end{gathered}[/tex]Substituting the values above
[tex]\begin{gathered} Midpoint=\frac{8+4}{2},\frac{7-5}{2} \\ \\ Midpoint=\frac{12}{2},\frac{2}{2} \\ \\ Midpoint=(6,1) \end{gathered}[/tex]Thus, the midpoint is (6,1)
Explain when 'p or q' is true. Select all that apply.A. 'p or q' is true when both p and q are false.B. 'p or q' is true when p is true and q is false.C. 'p or q' is true when p is false and q is true.D. 'p or q' is true when both p and q are true.
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SOLUTION
From the truth-table of logic, (p or q) is true either if:
- p is true and q is false
- q is true and p is false
- both p is true and q is true.
Hence these 3 statements must p satisfied for (p or q) to be true.
So, looking at the options, B, C and D are correct
Hence the answer is B, C and D
Gene bought a living room suite for P85,000. He agreed to pay in 5 months at 12% simple interest rate. How much will he pay for the furniture?
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Given the cost of the room 85000.
Rate of interest 12%
time =5 months=5/12 year
IN 5 months he will pay as interest
[tex]85000\times\frac{12}{100}\times\frac{5}{12}=4250[/tex]In total, he will pay
[tex]85000+4250=89250[/tex]Deb's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 34 sodas in all, 50% of which were regular. How many regular sodas did the diner serve?
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We can set this equation up by saying: 34 x .50
If we plug this into a calculator we get:
17 regular sodas served by the diner
After crossing a bridge, Brian drives at a constant speed. The graph below shows the distance (in miles) versus the time since he crossed the bridge (in FUse the graph to answer the questions.1140100Distance (miles)5020Time (hours)OR(a) How much does the distance increase for each hoursince Brian crossed the bridaeExplanation Check2022 McGraw Hill LLC. All Rights Reserved. Terms of UsePrivacy Cer2Tyne here to search
Answers
EXPLANATION
Since Brian drives at a constant speed, in order to get the rate, we need to compute the slope, by applying the slope equation, as shown as follows:
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x_1,y_1)=(20,100) (x_2,y_2)= (50,140)
Plugging in the terms into the slope equation:
[tex]\text{Slope}=\frac{140-100}{50-20}=\frac{4}{3}[/tex]In conclusion, the distance will increase by 4 miles per hour.
Are the triangles below congruent?If so, write a congruence statement and say why
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Answer:
123(8)67/#;#--#442627!* aopqppwiue
Congruent means, “In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.”
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.y³ - 2y² - 9y + 18/y² + y - 6Rational expression in lowest terms:Variable restrictions for the original expression: y
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ANSWER
[tex]\begin{gathered} \text{ Rational expression in lowest terms: }y-3 \\ \\ \text{ Variable restrictions for the original expression: }y\ne2,-3 \end{gathered}[/tex]EXPLANATION
We want to reduce the rational expression to the lowest terms:
[tex]\frac{y^3-2y^2-9y+18}{y^2+y-6}[/tex]First, let us factor the denominator of the expression:
[tex]\begin{gathered} y^2+y-6 \\ \\ y^2+3y-2y-6 \\ \\ y(y+3)-2(y+3) \\ \\ (y-2)(y+3) \end{gathered}[/tex]Now, we can test if the factors in the denominator are also the factors in the numerator.
To do this for (y - 2), substitute y = 2 in the numerator. If it is equal to 0, then, it is a factor:
[tex]\begin{gathered} (2)^3-2(2)^2-9(2)+18 \\ \\ 8-8-18+18 \\ \\ 0 \end{gathered}[/tex]Since it is equal to 0, (y - 2) is a factor. Now, let us divide the numerator by (y -2):
We have simplified the numerator and now, we can factorize by the difference of two squares:
[tex]\begin{gathered} y^2-9 \\ \\ y^2-3^2 \\ \\ (y-3)(y+3) \end{gathered}[/tex]Therefore, the simplified expression is:
[tex]\frac{(y-2)(y-3)(y+3)}{(y-2)(y+3)}[/tex]Simplify further by dividing common terms. The expression becomes:
[tex]y-3[/tex]That is the rational expression in the lowest terms.
To find the variable restrictions, set the denominator of the original expression to 0 and solve for y:
[tex]\begin{gathered} y^2+y-6=0 \\ \\ y^2+3y-2y-6=0 \\ \\ y(y+3)-2(y+3)=0 \\ \\ (y-2)(y+3)=0 \\ \\ y=2,\text{ }y=-3 \end{gathered}[/tex]Those are the variable restrictions for the original expression.
Graph the system and find the vertices (corners of the darkest shaded area, where the lines intersect) of the region.f(x) = 2x-3f(x) 3XS-2(0, -3). (2.0), (0,0)(-2, 3), (-2,-6), (4,3)(0, -3), (-2,3), (4,3)(3,-2).(-2,-6), (3, 4)
Answers
We are given the following system of inequalities:
[tex]\begin{gathered} f(x)\ge\frac{3}{2}x-3 \\ f(x)\le3 \\ x\le-2 \end{gathered}[/tex]We are told to plot the graphs and find the coordinate of the vertices.
In order to find the vertices we need to plot each inequality.
Plot 1:
[tex]f(x)\ge\frac{3}{2}x-3[/tex]In order to plot this inequality, we simply choose two points because a line can be created with only two points.
The way to choose these two points, is to set x = 0 and find f(x) and set f(x) = 0 and find x. These would help us find the y-intercept and x-intercept respectively.
Let us perform this operation:
[tex]\begin{gathered} f(x)\ge\frac{3}{2}x-3 \\ \text{set x = 0} \\ f(x)\ge\frac{3}{2}(0)-3 \\ f(x)\ge-3 \\ \\ \text{set f(x)=0} \\ 0\ge\frac{3}{2}x-3 \\ \text{add 3 to both sides} \\ 3\ge\frac{3}{2}x \\ \therefore3\times\frac{2}{3}\ge x \\ \\ x\le2 \end{gathered}[/tex]From the above, we just need to plot (0, -3) and (2, 0) to find the inequality plot.
We can see the forbidden region. This is the region that does not conform to the inequalities.
Next, we move to the next system of inequality.
Plot 2:
[tex]f(x)\le3[/tex]Here, we just draw the line f(x) = 3 and then shade the forbidden region as well.
The forbidden region here is above the line because that is the region where f(x) is greater than 3, hence we shade it off.
Finally, the last inequality:
[tex]x\le-2[/tex]Plot 3:
We simply plot the line x = -2 and then shade the forbidden region
After plotting all three, we shall have the following:
j
The points V1, V2, and V3 where the lines meet are the coordinates of the vertices.
A picture of the vertices is attached below:
Thus, the vertices are (-2, 3), (4, 3) and (-2, -6)
The final answer is Option 2
how to solve y=2x+3 y=2x+1
Answers
how to solve y=2x+3
y=2x+1
In this problem, we have two parallel lines with different y-intercept, ( two different parallel lines) so the lines don't intersect
That means------> the system has no solution
Using a graphing tool
see the attached figure
please wait a minute
Remember that, when solving a system by graphing, the solution is the intersection point. in this problem, the system has no solution , because the lines don't intersect
AB||CD, BE=DE, AE=CE, andAB=CD. Can we conclude thatthe two triangles are congruent?YesNo
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The answer is YES
Because their three sides are of equal lenght
Find the exact length of the floor clearance, using metres.
Answers
the length of the floor clearance is 2.8 m
Explanationas we have 2 similar triangles ( ABC and AED) we can set a proportion
Step 1
a)let
[tex]ratio=\frac{vertical\text{ side}}{horizontal\text{ side}}[/tex]so
for triangle ABC ( divide the given measure by 100 to obtain meters)
[tex]ratio_1=\frac{0.30\text{ m}}{0.40\text{ m}}=\frac{3}{4}[/tex]and
for triangle AED
let
[tex]ratio_2=\frac{2.1}{floor\text{ clearance}}[/tex]Step 2
as the ratio is the same, set the proportion
[tex]\begin{gathered} ratio_1=ratio_2 \\ \frac{3}{4}=\frac{2.1}{floor\text{ clerance}} \\ solve\text{ for floor clearance} \\ floor\text{ }cleareance=\frac{2.1*4}{3} \\ floor\text{ }cleareance=2.8\text{ m} \end{gathered}[/tex]therefore, the length of the floor clearance is 2.8 m
I hope this helps you
Usain Bolt ran the 2012 Olympic 100m race and 9.63 seconds if he runs at this rate on a road with a speed limit of 25 miles per hour how will his speed compared to the speed limit justify your answer 25 meter equals 40234 m a h r
Answers
Let's calculate his velocity:
v = d/t
v = 100m/9.63s = 10.38m/s
The speed limit of the road is 25mi/h
Let's make a conversion:
[tex]\frac{25mi}{h}\times\frac{1609.34m}{1mi}\times\frac{1h}{3600s}=\text{ 11.18m/s}[/tex]Therefore, we can conclude, that the speed limit is greater than the velocity of Usain Bolt, since:
11.18m/s > 10.38m/s
A carpenter has a plank 8 1/5 feet long. How many feet should be cut off to make a plank 5 7/8 feet long?
Answers
Answer:
2 13/40 feet or 2.325 ft
Explanation:
The length of the plank = 8⅕ feet
To determine many feet should be cut off, subtract 5⅞ feet from 8⅕ feet.
[tex]8\frac{1}{5}-5\frac{7}{8}[/tex]Step 1: Convert both fractions to improper fractions.
[tex]=\frac{41}{5}-\frac{47}{8}[/tex]Step 2: Find the lowest common multiple of the denominators 8 and 5.
[tex]\begin{gathered} =\frac{41(8)-47(5)}{40} \\ =\frac{328-235}{40} \\ =\frac{93}{40} \\ =2\frac{13}{40}\text{ feet} \end{gathered}[/tex]2 13/40 feet of the plank should be cut off.
Find the length of the arc, S, on the circle of radius are intercepted by central angle zero. Express the arc length in terms of X. Then round your answer to two decimal places. Radius, our equals 8 inches; central angle, zero equals 135°. First convert the degree measure into radians. Then use the formula S equals 0R, where S is the arc length zero is the measure of the central angle in radians and are is the radius of the circle
Answers
The length of an arc subtended by a central angle and 2 radii is
[tex]S=r\theta[/tex]Where:
r is the radius
Cita is the central angle in radian
Since the radius of the circle is 8 inches, then
[tex]r=8[/tex]Since the arc is subtended by a central angle of 135 degrees, then
[tex]\begin{gathered} \theta=135\times\frac{\pi}{180} \\ \theta=\frac{3}{4}\pi \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} S=8\times\frac{3}{4}\pi \\ S=6\pi \end{gathered}[/tex]The length of the arc is 6pi
We will find it in 2 decimal places
[tex]\begin{gathered} S=6\pi \\ S=18.85 \end{gathered}[/tex]The length of the arc is 18.85 inches
Find each angle measure in the figure. (x + 30) The angle measures are and : Use the equation to justify your answer. x + (x +30) + 2x =(can you write the answers on the picture please)
Answers
x = 50º
x +30º = 80º
2x = 100º
1) Since in any triangle the Sum of the interior angles is equal to 180º, we can write for this triangle:
x + 2x + x +30 = 180º Combine like terms
3x +30 = 180 Subtract 30 from both sides
3x = 150
x = 150/3
x= 50
2) So the angles are:
x = 50º
x +30º = 80º
2x = 100º
3) And the answer is 50º, 80º, and 100º
1. Write an equation for a polynomial with the following properties: it has even degree, it has at least 2 terms, and, as the inputs getlarger and larger in either the negative or positive directions, the outputs get larger and larger in the negative direction.
Answers
the polynomial must be even, so we chose x²
it has at least 2 terms, then we add 1 to the previous item, we get: x² + 1
to get outputs larger and larger in the negative direction, we have to multiply the previous item by -1 to get: -x² - 1
This function has a graph like the next one:
Then, -x² - 1 satisfies all the features needed
Using the values from the graph, compute the values for the terms given in the problem. Percentage of Market Value of Car (solid line) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0 Maintenance and Repair Costs as Percentage of Car's Value (dashed line) Ist yr. 2nd yr: 3rd yr. 4th yr. 5th yr. 6th yr. 7th yr. 8th yr. 9th yr. 10th yr. Age of car = 5 years. Original cost = $16,995. The current market value is $ O 13,596.00 0 3,399.00 5,098.50 11,896.50
Answers
We can use the graph to find the percentage of the value that correspond to a 5-year-old car in respect to its original value.
For a car that is 5 years old, its value is 20% of the original value.
If the original value is $16,995, we can calculate its actual value multypling its original price by the proportion of value that we have taken from the graph:
[tex]V=0.2\cdot16,995=3,399[/tex]Answer: the current market value is $3,399.
In the figure, RS is 24 units long. What is the length of WV ?
Answers
using,
RS/ST = WV/VT
Where,
RS = 24
ST = 2x + 11
WV
Translate this phrase into an algebraic expression.64 less than twice Greg's heightUse the variable g to represent Greg's height.A+ローロ園×園.x & S?
Answers
Answer
64 < 2g
Explanation
Let Greg's height be g
We need to express in equation form,
64 less than twice Greg's height
Greg's height = g
Twice Greg's height = 2g
64 less than twice Greg's height = 64 < 2g
Hope this Helps!!!
Use the model A = Pe^rt to determine the average rate of return under continuous compounding. Round to thenearest tenth of a percent. Avoid rounding in intermediate steps.
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Given
[tex]\begin{gathered} P=\$10,000 \\ A=\$14,296.88 \\ t=4 \\ \text{Find }r \end{gathered}[/tex][tex]\begin{gathered} A=Pe^{rt} \\ \text{Solve for }r \\ \frac{A}{P}=\frac{Pe^{rt}}{P} \\ \frac{A}{P}=\frac{\cancel{P}e^{rt}}{\cancel{P}} \\ e^{rt}=\frac{A}{P} \\ \ln e^{rt}=\ln \mleft(\frac{A}{P}\mright) \\ rt=\ln \mleft(\frac{A}{P}\mright) \\ r=\frac{\ln \mleft(\frac{A}{P}\mright)}{t} \\ \\ \text{Substitute the following values} \\ r=\frac{\ln \mleft(\frac{14296.88}{10000}\mright)}{4} \\ r=0.089364\rightarrow8.9364\% \\ \\ \text{Round to tenth of a percent} \\ r=8.9\% \end{gathered}[/tex]Therefore, the average rate of return under continous compounding is approximately 8.9%.
Evaluate your answers as a fraction in simplest form [tex]( \frac{1}{3} ) {4} [/tex]
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A fraction in simplest form is 1/81.
[tex]\left(\frac{1}{3}\right)^4[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]=\frac{1^4}{3^4}[/tex]
[tex]$$\begin{aligned}&1^4=1 \\&=\frac{1}{3^4}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}&3^4=81 \\&=\frac{1}{81}\end{aligned}$$[/tex]
A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator. A suitable fraction has a numerator that is less than the denominator.
In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by 14. Fractions make it easier to distribute and judge numbers and speed up calculations.
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Determine the slope of the line represented by the equation: -5x - 7y = -9DO NOT USE 1 AS THE DENOMINATOR!
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ANSWER
[tex]-\frac{5}{7}[/tex]EXPLANATION
We want to find the slope of the given line:
[tex]-5x-7y=-9[/tex]First, put the line in the slope-intercept form:
[tex]y=mx+b[/tex]where m = slope; b = y-intercept
Therefore, we have that:
[tex]\begin{gathered} -7y=5x-9 \\ \Rightarrow y=-\frac{5}{7}x+\frac{9}{7} \end{gathered}[/tex]From the equation above, we see that the slope of the line is:
[tex]-\frac{5}{7}[/tex]Samantha likes to run at least 5 miles each day. She plans a new course: from home to the park is 1 1/3 miles, from the park to the library is 2 2/5 miles, and from the park to home is 2/3 mile. Will Samantha run at least 5 miles on this new course? Use only estimation to decide. Then explain if you are confident in your estimate or if you need to find an actual sum. Show your work.