Answer: C, 217
Step-by-step explanation:
Use the function f(x) = 4x2 + 8x − 5 to answer the questions.
Part A: Completely factor f(x).
Part B: What are the x-intercepts of the graph of f(x)? Show your work.
Part C: Describe the end behavior of the graph of f(x). Explain.
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.
a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).
b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.
c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.
d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.
How to graph the quadratic function?The quadratic function for this problem is defined as follows:
f(x) = 4x² + 8x - 5.
Hence the coefficients are given as follows:
a = 4, b = 8, c = -5.
The discriminant is given as follows:
D = 8² - 4 x 4 x (-5)
D = 144.
Hence the x-intercepts are given as follows:
x = (-8 + square root (144))/8 = 0.5.x = (-8 - square root (144))/8 = -2.5.Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:
f(x) = 4(x - 0.5)(x + 2.5).
As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.
The y-intercept is given as follows:
f(0) = 4(0)² + 8(0) - 5
f(0) = -5.
The coordinates of the vertex are given as follows:
x = -b/2a = -8/8 = -1.y = -D/4a = -144/16 = -9.More can be learned about quadratic functions at https://brainly.com/question/24737967
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The probability that a student studied is 0.85. The probability that a student will not pass, given that the student studied is 0.10.
a) Find the probability that a student will study and will pass.
b) Suppose that the probability that a student will either study or pass is 0.8. Find the probability that a student will pass.
a) The probability that a student will study and will pass is 0.765.
b) The probability that a student will pass is 0.715.
What is probability?
Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.
Define some events -
A: A student studies.
B: A student will pass.
Given that P(A)=0.85 and
P(B|A)=1-P([tex]\bar{B}[/tex]|A)
=1-0.10
=0.90
a) P(a student will study and will Pass)= P(A∩B)
= P(A)·P(B|A)
= 0.85×0.90
= 0.765
b) Given that P( student will either study or pass), the probability is -
=P(A∪B)= 0.8 then P(a student will pass)
=P(B)
It is known that P(A∪B)= P(A)+P(B)-P(A∩B)
Then P(B)=P(A∪B) -P(A) +P(A∩B)
=0.8-0.85 + 0.765
=0.715
Therefore, the probabilities are 0.765 and 0.715.
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11. One side of a kite is 2 cm less than 2 times the length of another. If the perimeter is 38 cm, find the length of each side of the kite. (show work)
Answer:
Step-by-step explanation:
good
Given that,
Perimeter of kite - 38 cm
Let "x" be the one side of kite
Both of the top sides are equal
Therefore, other side = x
One side of a kite is 2 cm less than 2 times the length of another
Therefore,
One of bottom side = 2x - 2
Bottom sides are also equal
Thus, other bottom side = 2x - 5
We know that,
Perimeter = sum of all sides
38 = x + x + 2x - 2 + 2x - 2
38 = 6x - 4
6x = 38 + 4
6x = 42
x = [tex]\frac{42}{6}[/tex]
x = 7
Thus length of each side of kite is:
x = 7
2x - 2 = 2(7) - 2 = 14 - 2 = 12
Thus length of each side of kite is 7 cm , 7 cm , 12cm , 12cm
Please Brainliest
CANN SOEMOEN PLS HELP ME PLS. I DONT KNOW WHAT TO DO AND THIS IS ALREADY A WEEK LATE.
Answer:
y = 72 and x = 36
Step-by-step explanation:
So firstly, the outside angle is 108, right? And the total of all angles in a triangle is 180 degrees. So:
180 - 108 = 72
Then the other angle, angle x, is also 72 degrees. That's because they are supplementary angles.
Now that we know x = 72 degrees. To find the y angle, you add 72 and 72 together. Which is 144.
Then you do 180 - 144. Which is 36. So, x = 72 and y = 36
I hope it helped you!
A large green jar of candy contains red, green, and yellow candy. The probability of pulling a red candy out of the jar is 1/4. The probability of pulling a green candy out of the jar is 5/8. What is the probobility of randomly pulling a yellow candy out of the jar
Answer:
1/8
Step-by-step explanation:
total probability = 1
total probability = probability of red + probability of green + probability of yellow
1 = 1/4 + 5/8 + yellow
we want to find a common denominator
in this case, we know 4 * 2 = 8, so we can multiply 1/4 by 2/2 = 1 to get
1/4 * 2/2 = 2/8
1 = 2/8 + 5/8 + yellow
1 = 7/8 + yellow
subtract 7/8 from both sides to isolate yellow
1 = 8/8
1 - 7/8 = 8/8 - 7/8 = 1/8 = yellow
Factor the quadratic expression
4a²+27a+18
The factors of given quadratic expression are (4a+3) and (a+6).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given quadratic expression is 4a²+27a+18.
By splitting middle term method, we get
4a²+3a+24a+18
= a(4a+3)+6(4a+3)
= (4a+3)(a+6)
Therefore, the factors of given quadratic expression are (4a+3) and (a+6).
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Which statement best describes a line graph?
A. It shows a line that connects a series of data
points.
B. It shows a line passing through scattered data points.
C. It shows data as proportions of a whole.
D. It shows the locations of errors in data.
Answer:
A
Explanation:
A line graph is a unique type of graph which is used in statistical application which represents the change in a quantity with respect to another quantity.
The price of different flavors of chocolates varies which can be represented, these variation is plotted in a two-dimensional XY plane.
If the relation include two measures can be presented by using a straight line in a graph called as linear graphs or a linear graph.
There are different types of the line graph, Simple Line Graph refers to Only one line is plotted on the graph, Multiple Line Graph where More than one line plotted on the same set of axes.
Compound Line Graph refers to the information can be divided into two or more types of data and this line graph is called a compound line graph which can be drawn to show the component.
What is the value of a if 2 is a zero of the polynomial 4x² 2x 5a?
The value of a is [tex]-\frac{12}{5}[/tex] if 2 is a zero of the polynomial [tex]$4 x^2-2 x+5 a$[/tex].
As per the given data, the polynomial is p(x) = [tex]$4 x^2-2 x+5 a$[/tex]
The polynomial is zero polynomial if x is 2
The places where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (0).
Replace x with 2 we get
Therefore [tex]4(2)^2-2(2)+5 \mathrm{a}=0[/tex]
[tex]\Rightarrow[/tex] 4 (4) - 2 (2)+5 (a) = 0
[tex]& \Rightarrow[/tex] 16 - 4 + 5 (a) = 0
[tex]& \Rightarrow[/tex] 12 + 5 (a) = 0
Add -12 on both sides we get
12 + 5 (a) - 12 = 0 - 12
5 (a) = -12
Divided by 5 into both sides we get
a = [tex]-\frac{12}{5}[/tex]
Therefore the value of a is [tex]-\frac{12}{5}[/tex]
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Graph the system on equation . Y-2x+5=0 and y+ 4x-1=0
The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.
Let's write the terms in the order x, y therefore,
y - 2x + 5 = 0
- 2x + y = - 5.
2x - y = 5.
And
y + 4x + 1 = 0.
4x + y = - 1.
The graph of the system of equations is attached in the image.
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Solve the simultaneous equations
xy=-16
y=x+8
Answer:
x = 4, y = 12
Step-by-step explanation:
xy = -16
y = x + 8
substitute y = x + 8 into xy = -16
x(x + 8) = -16
x^2 +8x + 16 = 0
x = 4
sub x = 4 into y = x + 8
y = 4 + 8
y = 12
If QS is the ANGLE bisector, solve for x
Question setup: x over 18 = 45 over 20
Solving for x in the angle bisector which resulted to the proportion x over 18 = 45 over 20 results to x = 40.5
What are angle bisectors as used in geometry?In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.
By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
The division from angle bisectors gave rise to the proportion which is given by
x / 18 = 45 / 20
cross multiplying
x = 18 * 45 / 20
x = 40.5
hence x is solved to get 40.5
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need help on both these , preciate it .
Therefore ,we can conclude from answering the offered question that the region of the circle, triangle, and square is where the darkest area is. A=210-123 = 87 square units
Triangle - what is it?A triangle is a polygon since it has three sides plus three vertices. It is one of the basic geometric forms. An illustration of a triangle with the sides A, B, and C is Triangle ABC. A distinct plane or triangle in Geometrical are discovered when the three aspects are not collinear. Three sides & three corners define a triangle as a polygon. The triangle's corners are defined as the locations where three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
The total of the circle, triangle, and square's surface areas.
The region of the darkish area is comprised of the areas of the Circle, Triangle, and Square.
=>A = 210 – 123 = 87 square units
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How to know if an equation is factorable using discriminate
On solving the provided question we can say that - here in equation we have [tex]y = 160+ 2 *t= > y = 160 + 2X 30 = > y= 160+ 60 = > y = 220 pounds[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]
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30PTS 30PTS don’t explain just answer.
Answer:
y = 90°
Step-by-step explanation:
Problem 2
Use each of the numbers 4, 40, and 4000 once to make true statements.
The correct numbers to complete the statements given are 40, 400, and 4000.
What does this question require you to do?This question requires you to complete a statement with a given number (40, 400 or 4000) to make the statement true by dividing the number by 40.1. To find the correct order the numbers must be place using division, let's find out the results of each of these divisions:
40 / 40.1 = 0.997400 / 40.1 = 9.974000 / 40.1 = 99.7Based on the above, it can be concluded:
40 / 40.1 = is much less than 1400 / 40.1 = is close to 14000 / 40.1 = is much greater than 1Based on this, the complete statements are:
The value of 400 ÷40.01 is close to 1The value of 40 ÷40.01 is much less than 1.The value of 4000÷40.01 is much greater than 1.Note: This question is incomplete; here is the complete question:
Use each of the numbers 4, 40, and 4000 once to make true statements.The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is close to 1
The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much less than 1.
The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much greater than 1.
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Which of the following lists of ordered pairs is a function?
Answer:
C is a function
Step-by-step explanation:
for a relation to be a function each value of x must map to exactly one unique value of y
A
2 → 5 and 2 → 2 ← not a function
B
- 1 → 6 and - 1 → 7 ← not a function
C
all values of x map to exactly one unique y ← function
D
3 → 1 and 3 → 2 ← not a function
A child pushes a toy car with a force of 5. 25 N a distance of 6. 5 m. The car rolls for a total distance of 32 m. How much work is done on the toy car? Need formula and the way the work is done, ASAP
The work done on the toy car is 164.4 J.
The formula for work is:
Work = force * distance
In this case, given that:
Force = 5.2 N
Distance = 32 m
So, the work is:
Work = force * distance
Work = 5.2 * 32
Work = 166.4 J
Hence, the work done is 164.4 J.
What is work vs force?Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.
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A
70°
B
E
30
What angle relationship describes angles CBE and DEB?
[tex]\angle CBE[/tex] and [tex]\angle DEB[/tex] are same-side interior angles.
URGENT!!
Which of the following lists is in order from least to greatest?
Answer:
It's B, -2, v/5 4, and 3².
What type of data collection might be best to study how voters might decide an upcoming ballot issue
Observational data collection might be best to study how voters might decide an upcoming ballot issue.
What kinds of information is observed?The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).
The observational study method is what?In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.
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There were 9 pieces of paper. Some of them were cut into 3 pieces. As a result, there
are now 15 pieces of paper. How many pieces of paper were cut?
6=3
6÷3
2 is the required answer for this question
Which of the options below are the terms of the expression 5x² + 9x + 6? Choose all of the correct answers. 5x 9x 6 X x² 5 5x² 9
The terms of the expression are 5x², 9x and 6
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.
They are also known to be made up of arithmetic operation, such as;
DivisionAdditionParenthesesMultiplicationSubtractionBracket, etcIt is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.
They can be regrouped by the addition of their coefficients. Like terms are those that has the same variables to the same powers or coefficients.
The types are;
5x², 9x and 6
Thus, they are 5x², 9x and 6
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Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale
the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale is 4√5
What is altitude Class 9?
The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.
In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.
Let's call it x
According to Euclidean theorem x^2 = 5×16
x^2= 80 and
x = 4√5
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The table shows the approximate area
in square miles of the largest and smallest
states in the United States. What is the
difference between the areas in
square miles?
State
Area (mi?)
873
Alaska
Rhode Island
392
The difference between the areas is 481 square miles.
Given information:
Alaska is 873 sq miles in size, as well as Rhode Island, is 392 sq miles in total.
To determine the difference between the areas in square miles, the following calculation must be performed: subtract Alaska from Rhode Island square miles then we get:
Let X be the total difference:
873 - 392 = X
481 = X
Therefore, the difference in the areas in square miles is 481.
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A=?cm
What is the correct answer?
Answer:
A = 80 cm²
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 4 and h = 2 , then
A = 4 × 2 = 8 cm²
there are a total of 10 tiles required ( 5 black and 5 white ) , then total area is
A = 10 × 8 cm² = 80 cm²
What is the ratio for cos?
The ratio for cos (cosine) of angle θ is: cos(θ) = adjacent side of θ / hypotenuse
We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of given angle to the hypotenuse.
In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:
cos(θ) = adjacent side of θ / hypotenuse
Consider following right triangle PQR with angle PQR = 90 degrees
Here, PR is the hypotenuse.
Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.
By definition of cosine of angle θ,
cos(θ) = adjacent side of θ / hypotenuse
cos(θ) = QR / PR
And by definition of cosine of angle α,
cos(α) = adjacent side of α / hypotenuse
cos(α) = PQ / PR
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An ancient human tribe had a hierarchical system where there existed one chief with $2$ supporting chiefs (supporting chief A and supporting chief B), each of whom had $2$ equal, inferior officers. If the tribe at one point had $10$ members, what is the number of different ways to choose the leadership of the tribe? That is, in how many ways can we choose a chief, $2$ supporting chiefs, and two inferior officers reporting to each supporting chief?
The number of different ways is 7560 ways
How to determine the number of different waysFrom the question, we have the following parameters that can be used in our computation:
Chiefs = 1
Supporting chiefs = 2
Members = 10
Inferior officers = 2
There are 10 members.
So, the number of ways to select a chief is 10
Now, there are 9 members left
The number of ways to select a supporting chief is then represented as
Supporting chief = ⁹C₂
Now, there are 7 members left
The number of ways to select an inferior officer is then represented as
Inferior officers = ⁷C₂
So, the total number of ways is
Ways = 10 * ⁹C₂ * ⁷C₂
Evaluate
Ways = 7560
Hence, the number of ways is 7560
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Solve for 2 |v+2|-41=-9
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution"
Answer:
[tex]v=-18,14[/tex]
Step-by-step explanation:
[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]
A family buy a new minivan for $45,000 and makes a down payment of $12,000. The monthly payment factor is 0.202764. Calculate the monthly payment
The family's monthly payment for their new minivan is $6,664.52
How to calculate the monthly payment?To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.
Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:
Monthly Payment = Financed Amount * Monthly Payment Factor
So in this case:
Monthly Payment = $33,000 * 0.202764 = $6,664.52
Therefore, the family's monthly payment for their new minivan is $6,664.52
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Can you help me with this
The graph of the given equation y=2x+1 is attached below.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
The equation y=2x+1 gives the following information:
The slope is 2
The line intercepts is 1 on the y axis
First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.
By using my slope we know that (1,3) and (-1,-1).
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