Use the function f(x) = 4x2 − 7x − 15 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.
Answers
a) The factored function is given as follows: f(x) = 4(x + 1.25)(x - 3).
b) The x-intercepts are given as follows: x = -1.25 and x = 3.
c) The end behavior is given as follows: Due to the positive leading coefficient, the function increases to left and right.
d) The graph of the function is given by the image presented at the end of the answer.
How to graph the function?The quadratic function for this problem is defined as follows:
f(x) = 4x² - 7x - 15.
The coefficients are given as follows:
a = 4, b = -7, c = -15.
Inserting these coefficients into a quadratic function calculator, the roots, which are the x-intercepts, are given as follows:
x = -1.25 and x = 3.
Considering the leading coefficient of 4 and the linear factors of the function, the factored function is given as follows:
f(x) = 4(x + 1.25)(x - 3).
The x-coordinate of the vertex is given as follows:
x = -b/2a = 7/8.
Hence the coordinates of the vertex are:
(7/8, f(7/8)).
Then the graph is made considering:
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Related Questions
AABC is an isosceles triangle. AB is the longest side with
length 9x+3, BC = 4x+6 and CA = 3x+9. Find AB.
Answers
Answer:
30
Step-by-step explanation:
Since ABC is isosceles, BC = CA.
4x + 6 = 3x + 9x = 3So, AB = 9(3)+3 = 30.
Gabrielle is baking large batches of brownies and cookies to share with her friends and family. Among other ingredients, her brownie recipe calls for 1 cup of sugar and 2 eggs and her cookie recipe calls for 3 cups of sugar and 2 eggs. Gabrielle has 20 eggs and 21 cups of sugar, and she would like to know how many batches of brownies and cookies she can bake without getting more of these ingredients. Part A Question Which system of inequalities can model Gabrielle’s situation, where x represents batches of brownies and y represents batches of cookies?
Answers
The system of inequalities can model Gabrielle’s situation is;
x + 2y ≤ 20
x + 2y ≤ 203x + 2y ≤ 21
InequalityIt follows from the task content, that the inequalities which can be used to model Gabrielle's situation be determined.
By setting variables as follows;
batches of brownies = x batches of cookies = yBrownie:
Sugar = 1 cup
Eggs = 2
Cookie:
Sugar = 3 cups
Eggs = 2
x + 2y ≤ 20
x + 2y ≤ 203x + 2y ≤ 21
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2x⁴ - 4-7x - 38x²/x - 4
Answers
Answer:
2x⁴-45x-8
Step-by-step explanation:
can someone please help me
answer choices:
A - sin(0°)
B - cos(0°)
C - sin(180°)
D - cos(180°)
E - sin(270°)
F - cos(270°)
Answers
Answer:
B
Step-by-step explanation:
Cos(0)=1
since the diagram shows x as (1,0)
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
Answers
The surface area of the composite figure shown in the figure attached is 233.6 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²
The surface area of the composite figure shown in the figure attached is 233.6 cm²
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what scale factor can be applied to Cone 1 to make Cone 2?
Answers
The scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
What are scale factors?This are constants that is used to enlarge of diminish a given figure of sides of a figure
We can determine the scale factor by finding the ratio of the similar sides of two figures, From the given cones, the ratio of their radius can determine the scale factor that is applied to Cone 1 to make Cone 2
From the given figure;
scale factor = radius of cone 2/radius of cone 1
Given the following parameters
radius of cone 2 = 2 ft
radius of cone 1 = 2.5ft
Substitute
scale factor = 2/2.5
scale factor = 0.8
Hence the scale factor that can be applied to Cone 1 to make Cone 2 is 0.8
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When given an inverse variation, how do you find k?
Answers
Considering an inverse proportional relationship, you find k taking a point (x,y), and multiplying the values of x and y.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For an inverse relationship, the function is:
[tex]y = \frac{k}{x}[/tex].
Then:
k = xy.
Which means that to find k, you take a point (x,y), and multiply the values of x and y.
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Find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
Answers
The least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
A number (A) is divisible by another number (K) when the division of A by K, leaves a remainder of 0.
In the question, we are asked to find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
Now, we need to know that the multiples of 225 end with 00, 25, 50, and 75.
So, to have a multiple with digits 0, 1, and 2, we need the last digits to be 00.
The smallest multiple of 225, ending with 00 is 225*4 = 900.
So, we need to have the least multiple of 900, with digits 0, 1, and 2.
We know that a multiple of 9, has a sum of its digit as 9.
The smallest multiple of 9, with digits 1, and 2, will be 12222.
Adding the last 00 to this, we get the least multiple as 1,222,200.
Thus, the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
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If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
Answers
Answer:
Step-by-step explanation:
If Sam has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have
What is the shape of the graph of the function?
h(t)=0.6\cdot 3.2^th(t)=0.6⋅3.2
t
Answers
The graph of a function f exists the set of all points in the plane of the form (x, f(x)).
What is the graph of a function?
The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could even describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists as a special case of the graph of an equation.
Given: [tex]h(t)=0.6\cdot 3.2^t[/tex]
Substitute the values in the function, we get
t = -2, h(t) = 0.05859375
t = -1, h(t) = 0.1875
t = 0, h(t) = 0.6
t = 1, h(t) = 1.92
t = 2, h(t) = 6.144
t = 3, h(t) = 19.6608
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ANSWER THIS QUESTION FIRST=BRANIEST
Answers
Answer:
18
Step-by-step explanation:
first we divide both parties by 5 making it so that 1/6 =3 and then we multiply by 6 to make it 6/6 = 18
Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).
Answers
Answer: The function is even because [tex]f(x)=f(-x)[/tex].
Step-by-step explanation:
[tex]f(x)=3x^4 \\\\f(-x)=3(-x)^4 = 3x^4\\\\\therefore f(x)=f(-x)[/tex]
So, the function is even.
Write an equation of the line point(2,-1) and parallel passing through y=3x-5 write in slope-intercept form
Answers
Answer:
y = 3x - 7
Step-by-step explanation:
Since the lines are parallel, the slopes will be the same. In this case 3. Now we have to find the y-intercept. We will use the slope (3), the x (2) and y (-1) to help us do this. We get the x and the y from the ordered pair given(2,-1).
y = mx + b
-1 = 3(2) + b Plug in what you know
-1 = 6 + b Subtract 6 from both sides
-7 = b
Now we can write the equation
y = 3x -7
In a bag of 10 marbles, there are 4 blue, 3 red, 2 green,
and 1 yellow. What is the probability that you draw one
marble that is green, DO NOT replace it, and draw another
marble that is yellow?
1
30
O b. 139
OC. 15
45
a.
O d. 7/19
2
Answers
Answer: 1/45
Step-by-step explanation: 10 total marbles. 4 are blue 3 are red 2 are green and 1 is yellow. The chance of drawing a green is 2/10 or 1/5. Then there are only 9 marbles left in the bag. So the chance of a yellow marble is 1/9. 1/5 x 1/9 = 1/45.
Please help me fast
What is the equation of this graph
Answers
Answer-4,5
Step-by-step explanation:
PLEASE HELP FAST!
A figure has rotational symmetry if a rotation of 180°
or less produces an image that fits exactly on the original figure. Select each degree of rotation that shows the figure below has rotational symmetry.
30 °
45 °
60 °
90 °
120 °
135 °
150 °
180 °
Answers
Answer:180 °
Step-by-step explanation:
Answer:
90 degrees
Step-by-step explanation:
The only numbers that are possible to be divided into 180 are these: 30, 45, 60, 90, & 180.
Now to figure out if this figure is symmetrical. It is. Why? Because you can put at least one line through each triangle. 8 in total but 180 cannot be divided by 8. So you could maybe split it in half. 180/4= 45
45x2= 90
Easy: Since there are now, two halves, since it is split up, it could be possible that the answer could be 90. Because 180/2 halves= 90.
The answer is 90
The ratio of boys to girls who play soccer in Mr. Fraser’s class is 14:6. If there were 400students in the school, how many boys would likely play soccer?
Answers
Answer:
280
Step-by-step explanation:
Set up a ratio to solve.
Mr. Fraser's class has 20 soccer playing students, and 14 are boys.
14/20 = x/400
Cross multiply. 20x= 5600
Divide by 20 to solve
x= 280
The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school?
Answers
Using the mean concept, the average collection for a student in this school was of $16.13.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
The number of students is given as follows:
82 + 74 + 96 + 99 = 351.
The sum is:
82 x 26.75 + 74 x 12.25 + 96 x 15.50 + 99 x 10.85 = $5662.15
Hence the mean is:
M = $5662.15/351 = $16.13.
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15. If 3x + 10 = 3y - 2(y + 4), what is the value of y in terms of x? (A) x + 18 (B) 3x+6 (C) 3x + 14 (D) 3x + 18
Answers
Answer:
3x + 18
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 18 = y
Answer:
D, 3x + 18.
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 10 = y - 8
y = 3x + 10 + 8
y = 3x + 18.
Which equation is the inverse of Y equals 9X Square -4
Answers
[tex]y = 9x {}^{2} - 4 \\ flip \: x \: and \: y \\ x =9 (y ) {}^{2} - 4 \\ solve \: for \: the \: inverse \: of \: y \\ x + 4 = 9(y ) {}^{2} \\ y {} {}^{2} = \frac{x + 4}{9} \\ you \: can \: split \: it \: into \: two[/tex]
[tex]y {}^{(1)} = \sqrt{ \frac{x + 4}{9} } \\ y {}^{(2)} = - \sqrt{ \frac{x + 4}{9} } [/tex]
a big water tank contained 200 litres of water. during the day, 88 l 580 ml of water was used and 200 ml leaked. how much water was left in the water tank?
Answers
The quantity of water left in the tank as described in the task content is; 111 l 220ml.
What is the amount of water left in the tank?The tank described in the task content initially contains 200 liters, in which case, 1 liter corresponds to 1000ml.
Hence, when 88l 580ml was used, the remaining quantity of water is; 200l - (88l 580ml) = 111 l 420ml.
And finally, since 200 ml leaked, the quantity of water left is; 111l 220ml.
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Please help and explain how to solve
Answers
Answer:
$ 7.52
Step-by-step explanation:
Find charge per minute
59 - 23 min = 36 minutes cost 16.32 - 10.56 = $ 5.76
or $5.76 / 36 min = 16 cents per min
from 59 to 78 = 19 more minutes x .16/min = $ 3.04
so from 59 to 78 will leave 10.56 - 3.04 = $7.52
If the term of arthematic progression decrease in magnitude then common difference must be
Answers
We can say that if the term of arithmetic progression decrease in magnitude then the common difference must be negative.
An arithmetic progression is a sequence where every term is a sum of the previous term and a common difference.
If we suppose the first term of an arithmetic progression to be a, and the common difference to be d, then the arithmetic progression goes like this:
The first term, a₁ = a,
Second term, a₂ = a₁ + d = a + d,
Third term, a₃ = a₂ + d = a + 2d,
Fourth term, a₄ = a₃ + d = a + 3d, and it goes so on up to,
The n-th term, aₙ = aₙ₋₁ + d = a + (n - 1)d.
In the question, we are asked if the term of arithmetic progression decrease in magnitude then what can we say about the common difference.
As the magnitude of the term decreases, we can show that as:
The n-th term < The first term,
or, aₙ < a₁,
or, a + (n - 1)d < a,
or, a + (n - 1)d - a < a - a {Subtracting a from both sides},
or, (n - 1)d < 0.
Since, n > 1, (n - 1) > 0, thus we get the common difference, d < 0, that is, the common difference is negative.
Thus, we can say that if the term of arithmetic progression decrease in magnitude then the common difference must be negative.
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La siguiente tabla muestra el saldo de las tres cuentas bancarias de Dmitri.
Ahorros........$573.73
Retiro............$294.43
Cheques --$435.24
Ayuda a Dmitri a ordenar sus cuentas de menor a mayor valor absoluto del saldo.
Answers
Las cuentas de Dmitri de menor a mayor se ordenan: retiro, cheques y ahorros.
¿Cómo organizar las cuentas bancarias de Dmitri?Para organizar las cuentas bancarias de Dmitri de menor a mayor debemos observar cuidadosamente los valores de cada una. Adicionalmente para organizarlas por valor absoluto nos fijamos únicamente en el número sin tener en cuenta el símbolo, en ese caso el valor de cheques pierde su símbolo negativo.
Entonces las cuentas quedarían organizadas así:
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Need help in this pls
Answers
Answer:
6
Step-by-step explanation:
The arc length is (2)(pi)(27)(40/360)=6pi.
So, k=6.
If the ratio of areas of two similar solids is 25:36, what is the linear ratio.
Answers
Answer: Hi here go your answer is
25 divides by 36 is 0.69444 or 0.69
Step-by-step explanation:
Find the zeros of: [tex]f(x)=-\frac{1}{1500} (x^3+10x^2-275x-1500)[/tex], and the use them to find all of the linear factors of the polynomial function
Answers
The function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the graph of the function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.
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What is the value of -3/2÷-7/2?
Answers
The value of the given division operation is 3/7
Division operationFrom the question, we are to determine the quotient of the given division operation
The given division operation is
-3/2÷-7/2
[tex]\frac{-3}{2} \div \frac{-7}{2}[/tex]
[tex]=\frac{-3}{2} \times \frac{2}{-7}[/tex]
[tex]=\frac{-3}{-7}[/tex]
[tex]=\frac{3}{7}[/tex]
Hence, the value of the given division operation is 3/7
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Complete the following table:
Answers
Minimum value of -16 occurs at x = 1
Axis of symmetry: x = 1
Zero’s: -3 and 5
Direction of opening: up (positive)
Y-intercept: -15
If u are 13, and ur birthday is 21 of october, how old will you be in 2050?
Answers
Answer:
41 years old
Step-by-step explanation:
2050-2022=28 years
13years old +28years = 41 years old (sorry if wrong)
Answer: Based on today's date of 7/19/2022, you will be 41 until October 21, 2050. On October 21, 2050 you will turn 42. You were born in 2008
Step-by-step explanation: