Which is the graph of f(x) = (x + 3)(x - 2)?
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4 6
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2
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4
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1-2
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Answers
Answer: It should look something like this.
Step-by-step explanation:
The graph of f(x) = (x + 3)(x - 2) is a parabolic function that is the product of two linear factors, (x + 3) and (x - 2).
The graph is given below.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To understand the graph, we can begin by considering the x-intercepts, which are the points where the graph crosses the x-axis.
These occur where the value of f(x) is zero, which happens when either
x + 3 = 0 or x - 2 = 0.
So the x-intercepts are x = -3 and x = 2.
Next, we can consider the leading coefficient, which is 1 in this case.
Since the leading coefficient is positive, the parabola opens upward.
We can also find the vertex of the parabola by completing the square.
We have:
f(x) = x² + x(-2 + 3) - 2(-3)
f(x) = x² + x + 6
Now we can rewrite this in vertex form:
f(x) = (x + 1/2)² + 23/4
So the vertex is (-1/2, 23/4), which is a minimum point on the graph.
Thus,
We can sketch the graph of f(x) = (x + 3)(x - 2) as an upward-opening parabola that crosses the x-axis at -3 and 2 and has a minimum point at (-1/2, 23/4).
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Related Questions
A cylindrical container is packaged inside a prism-shaped box. the box has a volume of 96 cubic units. if the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? round the answer to two decimal places. a. 20.60 cubic units b. 37.77 cubic units c. 51.27 cubic units d. 75.40 cubic units
Answers
Volume is a three-dimensional scalar quantity. The volume of the empty space is 20.602 units³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the volume of the prism, the box is 96 units³ and the diameter of the cylindrical container is 4 units(Radius=2 units), while the height of the cylinder is 6 units. Therefore, The volume of the empty space is,
The volume of the empty space
= Volume of prism - Volume of the cylindrical container
= 96 units³ - (π×2²×6) units³
= 96 units³ - 75.398 units³
= 20.602 units³
Hence, the volume of the empty space is 20.602 units³.
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Factorise completely 12 x³y - 18 xy²
Answers
Answer:
6xy(2x²-3y)
Step-by-step explanation:
factorized completely
An mp3 player was reduced from $229.99 to $129.99. find the percent reduction in price. round the answer to the nearest tenth of a percent, if necessary.
Answers
Answer:
43.4%
Step-by-step explanation:
229.99 - 129.99
= 100
The percent reduction is:
100/229.99 * 100
=43.4%
Which point is one fourth of the way between point A and point B on the line segment AB shown on the coordinate plane below?
Answers
The coordinate of the point between point A and point B on the line segment AB is [tex](\frac 92, -\frac{19}4)[/tex]
How to determine the point?The points are given as:
A = (4,-5)
B = (6,-4)
m : n = 1 : 3
The coordinate of the point is then calculated using:
[tex]P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)[/tex]
So, we have:
[tex]P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)[/tex]
Evaluate the sum of product
[tex]P = \frac{1}{4}(18, -19)[/tex]
Evaluate the product
[tex]P = (\frac 92, -\frac{19}4)[/tex]
Hence, the coordinate of the point is [tex](\frac 92, -\frac{19}4)[/tex]
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I dive to 17 metres for 47 minutes. after a 30 minute surface interval i do a second dive to 17 metres. losing track of time, i notice my bottom time is now 25 minutes. according to the general rules, what should i do
Answers
If your bottom time is 25 minutes, general rules recommend that you ascend immediately to 15 feet then remain there for 8 minutes. You should then go to the surface and not dive for 6 hours.
What do general rules on diving say about a 25 minute bottom time?The recommended bottom time is 24 minutes which means that staying there for 25 minutes will have exceeded this recommendation.
You should immediately ascend to 15 feet or 5 meters, and then wait there for 8 minutes. Then return to the surface and avoid diving for the next 6 hours.
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55 POINTS!!!!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!! PLS HELP ASAP!!!!!!!!!!
Danielle is trying to solve the equation [tex]8^x=\frac{1}{64}[/tex] Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answers
Answer:
[tex]x=-2\\[/tex]
Step-by-step explanation:
[tex]8^x=\frac{1}{64}\\xlog8=log\frac{1}{64}\\x=\frac{log\frac{1}{64}}{\log8}\\x=-2[/tex]
First we write the equation given
Next we take the log of both sides. This turns [tex]x[/tex] into a normal term instead of an exponent, but turns [tex]8[/tex] and [tex]64[/tex] into the log version of themselves.
Next we can divide both sides by [tex]log8[/tex] to isolate [tex]x[/tex].
This gives us our answer of [tex]\boxed{-2}[/tex]
Help!! Also the questions says “Which of the following shows JUST a variable?”
Answers
Variables are letters that represent unknown numbers
It can be any letter if the alphabet (a,b,c,d…..)
The others are what we call an (expression )which is basically when we put variables with other numbers
what is the distance from (7,0)- (-5,5)
Answers
Answer:
[tex]\frac{5}{-12}[/tex]
Step-by-step explanation:
If you use the formula [tex]m = \frac{y2 - y1} {x2 - x1}[/tex] with x1 being 7, y1 being 0, -5 being x2 and 5 being y2, then you can subtract. 5(y2) minus 0(y1) is 5, and -5(x2) minus 7(x1) is -12. The formula would look like this: [tex]m = \frac{5 - 0}{-5 - 7} \frac{5}{-12}[/tex].
(tip: you need to do rise over run, aka y over x, shown as [tex]\frac{y}{x}[/tex] or [tex]\frac{rise}{run}[/tex])
I hope I helped you answer your question, and helped better understand it as well
how can i find area of abd triangle. .............
Answers
Answer:
6 square units
Step-by-step explanation:
The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.
__
anglesAny right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.
Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.
segmentsThe fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.
The tangent ratio is ...
Tan = Opposite/Adjacent
Applying that to angle β, we have
tan(β) = OD/AD [eqn 1]
tan(β) = BC/AC [eqn 2]
These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.
areaEquation [eqn 1] tells us ...
AD = OD/tan(β)
Equation [eqn 2] tells us ...
BC = AC·tan(β)
The area of ΔADB is ...
Area = 1/2bh
Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))
Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel
The length of AC is given as 6, and we know OD = 2, so the area is ...
Area = 1/2(2)(6) = 6
The area of triangle ADB is 6 square units.
Which of the following is the equation of the function below? y=2sec (x+pi/6)+2 y=sec2(x+pi/6)]+2 y=sec[2(x+2)] + pi/6 y=2sec(x+2) + pi/6
Answers
The equation of the function is y = sec(2(x + π/6)) + 2
How to determine the equation of the function?From the graph, we have the following parameters:
Local maximum = 3Local minimum = 1Period = 2Phase shift = π/6A secant function is represented as:
y = A sec(b(x + c)) + d
Where:
A = 0.5 * (max - min) = 0.5 * (3 - 1) = 1
b = Period = 2
c = Phase shift = π/6
d = 0.5 * (max + min) = 0.5 * (3 + 1) = 2
So, we have:
y = 1 * sec(2(x + π/6)) + 2
Evaluate
y = sec(2(x + π/6)) + 2
Hence, the equation of the function is y = sec(2(x + π/6)) + 2
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Answer
The answer is B on Edgenuit
Step-by-step explanation:
Desmos
The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was
Day 8.
(a) Determine C(5), C(6), and C(7). Explain how you determined these amounts.
(b) Estimate C(1), C(2), and C(3). Explain how you determined these amounts.
(c) The stage manager said that the amount of money taken out of the account each day between Day 8
and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4.
Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could
you show the stage manager was incorrect?
Answers
Answer:
The answer is c, hope this helps
Step-by-step explanation:
find the altitude of a kite where 120 feet of string makes a 64 degree angle to the ground
Answers
Answer:
107.86 to 2 d.p.
Step-by-step explanation:
makes a triangle. 120 feet is the hypotenuse.
we want to find the opposite so we will use sine.
sin(x) = opp/hyp which means opp = sin(x)hyp.
opp = sin(64)120
opp = 107.86 to 2d.p.
In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. the students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. for one student, it lands tails side up six times. the student will construct a 90% confidence interval for the true proportion of tails up. are the conditions for inference met?
Answers
Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.
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Question Progress
Work out the value of 4° x 16°
Answers
Answer:
20°0°0 is the correct answerI will choose brainlyist and 20 POINTS
Answers
Answer:
They are all non triangles, but I'm not in your math class, so I don't know.
Step-by-step explanation:
The slope of a line is 7/8 The y-intercept of the same line is 4
Complete the slope-intercept form equation
Answers
Answer:
y = -7/8x + 4
Step-by-step explanation:
Slope-intercept form :
y = mx + b
m = slopeb = y-interceptHence, the equation formed is :
y = -7/8x + 4Which is the equation of the line passing through (0,4) and (8,0)?
Answers
Answer:
[tex]\sf y = -\dfrac{1}{2} x +4[/tex]
Find slope (m):
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m): \dfrac{0-4}{4-0} = -\dfrac{1}{2}[/tex]
Now, find equation:
[tex]\sf y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex]
[tex]\rightarrow \sf y - 4 = -\dfrac{1}{2} (x - 0)[/tex]
[tex]\rightarrow \sf y = -\dfrac{1}{2} x +4[/tex]
Slope of (-9,-2) and (-9,-6)
Answers
Answer:
Slope is undefined.
Step-by-step explanation:
What is the length of the diagonal from vertex J to vertex L in the quadrilateral below?
Answers
Answer: 6.7 units for the diagonal from J to L
Step-by-step explanation:
you can use the Pythagorean theorem to find the diagonal (hypotenuse)
a^2 + b^2 = c^2
by counting units from M to J you have a length of 3 for the "a" value
by counting units from M to L you have a length of 6 for the "b" value
3^2 + 6^2 = c^2
9 + 36 = c^2
45 = c^2
take square root of both sides
6.7 = c
the diagonal is 6.7 units
Find perimeter of this square with sides of length 5 cm
Answers
Answer:
P = 20 cm
Step-by-step explanation:
the perimeter (P) is the sum of the 4 sides (s) of the square
the sides of a square are congruent , then
P = 4s = 4 × 5 = 20 cm
Quadrilateral ABCD has the following coordinates: A(-6,3) B(-4,5) C(-1,6) and D(-3,2) and
maps onto A"B"C"D". It will undergo transformations that will consist of a reflection over
the y-axis followed by a translation. Point D" is shown plotted in the plane after the
transformation.
A) Write the translation rule that maps point D' to point D".
B) Write the coordinates of point A"
Answers
The translation rule that maps point D' to D" is (x + 3, y) and the coordinate of point A" is (9,3)
How to determine the translation rule?The coordinates are given as:
A(-6,3) B(-4,5) C(-1,6) and D(-3,2)
When reflected across the y-axis, the transformation rule is:
(x,y) -> (-x,y)
So, we have:
A' = (6,3)
D' = (3,2)
Point D" on the grid is (6,2).
This means that the translation rule that maps both point is (x + 3, y)
The coordinates of point AIn (a), we have:
A' = (6,3)
Using the translation rule (x + 3, y), we have:
A" = (6 + 3,3)
A" = (9,3)
Hence, the coordinate of point A" is (9,3)
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Select the expression that’s is equivalent to (x-1)^2
Answers
Answer:
(x-1)^2
=x^2 - 2x + 1
Step-by-step explanation:
hope this helps
I need to know how to solve this
Answers
Answer:
K=-6/11
Step-by-step explanation:
3(k/3+4-2k)=3(-9k)
K+12-6k=-27k
12-5k=-27k
12=-22k
K=-6/11
The diagram shows a regular polygon.
x
What is the value of x?
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Answers
Answer:
To find the value of x, use the formula
(n-2) x 180, where n is the number of sides.
In this case, we have a TRIangle, which has THREE sides.
So, n=3
(3-2) x 180
1 x 180
180
If the total sum of the angles is 180, then the measure of one angle would be 180 divided by 3, which is 60.
Let me know if this helps, or if you got any more questions
Choose the expression that represents a linear expression.
6x + 6
O-6x² +8x-9
O8x3 + 9x² - 10x + 11
07x4-8x³+9x² - 10x + 11
Question 3(Multiple Choice Worth 1 points)
(06.01 LC)
Answers
Answer:
6x+6
Step-by-step explanation:
a linear expression has no power attached to the x (the unknown)
A rectangle is 21 meters long and 11 meters wide. what is the perimeter of this rectangle?
Answers
Step-by-step explanation:
the perimeter is simply the distance you would have to walk when going around the whole object once.
so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.
so, the perimeter of a rectangle is
2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m
Solve for x. Round to the nearest tenth. 34° 90% (Figure is not necessarily drawn to scale) O x 3.1 0x 2.7 x=2 C= 5.9
Answers
Answer:
x=2.7
Step-by-step explanation:
tan34 = x/4
x = 4tan34 = 2.7
Points a and b lie on a circle centered at point o. if oa = 5 and what is the area of sector aob? use the value π = 3.14, and choose the closest answer. a. 19.6 square units b. 39.3 square units c. 7.85 square units d. 15.7 square units
Answers
The area of sector AOB whose radius OA 5 units is 19.6 sq. units.
What is the Sector?A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.
Here, Radius of Circle = 5 units
length of arc AB / circumference = 1/4
So, Area of Sector AOB = one fourth of area of circle
= 1/4 X π X r²
= 0.25 X 3.14 X 5²
= 0.25 X 3.14 X 25
= 19.625 sq. units
Thus, the area of sector AOB whose radius OA 5 units is 19.6 sq. units.
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Answer:
19.6
Step-by-step explanation:
The volume of air in a balloon is represented by the function v(r)=4/3 pi ^3, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.
Answers
A dog eats 3 cans of dog food in 12 days. Write an equation to represent th
proportional relationship. Then find k, the constant of proportionality.
Let c =
Let d =
Equation:
= k•
k=-
Answers
The equation to represent the proportional relationship is c = 0.25d
How to determine the equation?Let c = the number of cans
Let d = the number of days
So, we have:
c = kd
Where k represents the constant of proportionality.
From the given parameters, we have:
3 = 12k
Divide both sides by 12
k = 0.25
Substitute k = 0.25 in c = kd
c = 0.25d
Hence, the equation to represent the proportional relationship is c = 0.25d
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