It is true that the value -2 is a lower bound for the zeros of the function f(x) = 4x³ - 12x² - x + 15
The polynomial as a product of linear factors is d. 2(x+2)(x+1)(x-1)
How to determine the true statement
From the question, we have the following parameters that can be used in our computation:
f(x) = 4x³ - 12x² - x + 15
Also, we have
x =-2
Calculate f(-2)
f(-2) = 4(-2)³ - 12(-2)² - (-2) + 15
f(-2) = 4 * -8 - 12 * 4 + 2 + 15
f(-2) = -32 - 48 + 2 + 15
f(-2) = -63
The above value is negative
This means that -2 is a lower bound for the zeros of the function.
Expressing the polynomial as a product of linear factors.
Here, we have
f(x) = 2x³ + 4x² - 2x - 4
Factorize in 2's
So, we have
f(x) = 2x²(x + 2) - 2(x + 2)
This can be expressed as
f(x) = (2x² - 2)(x + 2)
Factor out 2
f(x) = 2(x² - 1)(x + 2)
Express as difference of two squares
f(x) = 2(x - 1)(x + 1)(x + 2)
Hence, the polynomial as a product of linear factors is d. 2(x+2)(x+1)(x-1)
6a - 10 = 3a + 17 please explain how you got your answer
To solve the equation 6a - 10 = 3a + 17, we first move all 'a' terms to one side and constants to the other, then simplify and solve for 'a', resulting in a = 9.
The student has asked to solve the equation 6a - 10 = 3a + 17. To find the value of 'a', we need to consolidate all the 'a' terms on one side and the constants on the other side. Here's the solution step-by-step:
Subtract '3a' from both sides of the equation to get '6a - 3a - 10 = 17'.
Simplify the left side to get '3a - 10 = 17'.
Add '10' to both sides to isolate the 'a' term and get '3a = 17 + 10'.
Simplify the right side to get '3a = 27'.
Divide both sides by '3' to solve for 'a', getting 'a = 27 / 3'.
Finally, 'a = 9'.
The correct answer is a = 9.
A number cube is rolled 30 times, and a number less than five comes up 20 times. What is the experimental probability that a number GREATER than four is rolled?
A.1/20
B.2/3
C.1/10
D.1/3
Answer:
The answer is 2/3. Probably to late but i thought i might as well share!
Hope it helps haha!
Brainliest?
1. A company designs a box to package their product. The material used costs $0.112 per square foot. The box consists of a square bottom and isosceles triangles making up the sides. A net of the box is shown below.
Write an equation of the line with the given slope, m, and y-intercept left parenthesis 0 comma b right parenthesis(0,b).
Multiply or divide as indicated. Simplify your answer, if possible. (Do not express answer in exponential form.) 10/ 10^-2
Answer:
The simplified form of the provided expression is 1000.
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{10}{10^{-2}}[/tex]
Now, use the property of exponent: [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
Use the above property to solve the provided expression.
[tex]\frac{10}{10^{-2}}[/tex]
[tex]10^{1-(-2)}[/tex]
[tex]10^{1+2}[/tex]
[tex]10^3[/tex]
[tex]1000[/tex]
Thus, the simplified form of the provided expression is 1000.
−px+r=−8x−2
solve for X
Answer:
[tex]\frac{-2-r}{-p+8}[/tex].
Step-by-step explanation:
-px+r= -8x-2
-px+8x = -2-r
x(-p+8) = -2-r
x = [tex]\frac{-2-r}{-p+8}[/tex].
Would a dot plot or a histogram best represent the data presented here? Why?
Jennifer ran 4/5 of a mile on Monday. She ran 1 2/3 times as far on Tuesday. How far did she run on Tuesday?
1 4/15 miles
1 1/3 miles
2 7/15 miles
3 1/3 miles
Jennifer ran [tex]1\frac{1}{3}[/tex] miles on Tuesday.
What is multiplication?Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20.
Given that, Jennifer ran 4/5 of a mile on Monday. She ran [tex]1\frac{2}{3}[/tex] times as far on Tuesday, we need to find how far did she run on Tuesday,
Since, she ran 4/5 times mile,
And, on Tuesday she ran [tex]1\frac{2}{3}[/tex] times as far Monday,
On Tuesday she will run = 4/5 × [tex]1\frac{2}{3}[/tex]
= 4/5 × 5/3
= 4/3
= [tex]1\frac{1}{3}[/tex]
Hence, Jennifer ran [tex]1\frac{1}{3}[/tex] miles on Tuesday.
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Wallace received a 28 percent discount on an item priced at $275. What is the total price that he paid for it? cost after discount = price × (1 – discount percentage)
Answer: $198
Step-by-step explanation:
Given: The discount percentage : 28 % =0.28
The price of item = $275
The given formula for total cost of item after discount :
[tex]\text{Cost after discount = Price *(1 – Discount percentage)}[/tex]
Substitute the value of price =$275 and discount percent = 0.28 in the above formula , we get
[tex]\text{Cost after discount =}275\times(1-0.28)\\\\\Rightarrow\ \text{Cost after discount =}275\times0.72\\\\\Rightarrow\ \text{Cost after discount =}\$192[/tex]
Hence, he paid the total price of $198 for it.
In the figure, BC and AD are line segments. What is the sum of x and y?
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: BC and AD are line segments.
According to the angle sum property, the sum of interior angles of a triangle is 180°.
In triangle DOC,
[tex]\angle C+\angle COD+\angle D=180^{\circ}[/tex]
[tex]y+64^{\circ}+54^{\circ}=180^{\circ}[/tex]
[tex]y+118^{\circ}=180^{\circ}[/tex]
[tex]y=180^{\circ}-118^{\circ}[/tex]
[tex]y=62^{\circ}[/tex]
The value of y is 62°.
If two lines intersect each other then vertical opposite angles are equal.
[tex]\angle COD=\angle AOB=64^{\circ}[/tex]
In triangle AOB,
[tex]\angle A+\angle AOB+\angle B=180^{\circ}[/tex]
[tex]x+64^{\circ}+62^{\circ}=180^{\circ}[/tex]
[tex]x+126^{\circ}=180^{\circ}[/tex]
[tex]x=180^{\circ}-126^{\circ}[/tex]
[tex]x=54^{\circ}[/tex]
The value of x is 54°.
The sum of x and y is
[tex]54^{\circ}+62^{\circ}=116^{\circ}[/tex]
The sum of x and y is 116°. Therefore the correct option is 2.
Please check!
Mary has been hired as a receptionist. She is paid a flat rate of $150 each week and earns an additional $12.50 for every hour that she works. If her goal is to make $575 in one week, which equation will help Mary determine the number of hours she must work?
1/3 + 1/6 in simplest form
I need help with 8 and 9 please!!!!!
The measure of angle 1 equals 59 degrees, and the measure of angle 6 equals 72 degrees. What is the measure of angle 8?
What are families of functions and how are they useful?
What is (-1+8i)(-8+8i)
what are potential roots of p(x) = x4 + 22x2 – 16x – 12
Answer:
±1, ±2, ±3, ±4, ±6 and ±12
Step-by-step explanation:
The potential roots are obtained as following:
potential roots = factors of the constant term / factors of leading coefficient
The constant term is -12, its factors are ±1, ±2, ±3, ±4, ±6 and ±12
The leading coefficient is 1, its factors are ±1
Therefore the potential roots are ±1, ±2, ±3, ±4, ±6 and ±12
A rate that describes how much smaller or larger the scale drawing is than then real object
The scale factor is a ratio that describes the relationship between the dimensions of a scale drawing and the real object that it represents. A larger scale factor indicates a greater level of detail in the drawing, while a smaller scale factor depicts less detail and a larger area.
Explanation:The rate that describes how much smaller or larger the scale drawing is than the real object is known as the scale factor. A scale factor is a ratio that compares the dimensions of the actual object to the dimensions of a scale drawing or model. For example, a scale factor may be written as 1/200, meaning that the real object is 200 times larger than the scale drawing.
Scale can also be described using terms such as 'small' or 'large' scale. These terms relate to the level of detail a map shows; a large-scale map, with a representative fraction of 1:1,000, shows more detail and less area whereas a small-scale map, with a representative fraction of 1:1,000,000, shows less detail and more area.
Understanding these concepts is essential when interpreting maps and drawings as they communicate the level of zoom and detail. Remember, scale refers to a ratio and not the physical size of the map or drawing itself.
I don’t understand what and how to solve these
The proceeds from a saturday car wash are directly proportional to the number of cars washed. the total after 7 cars is $140. how much is raised if 60 cars are washed?
Which statement best explains how Lizabeth develops the theme in "Marigolds" that beauty can be appreciated even in the worst circumstances?
Answer:
Lizabeth remembers the poverty of her childhood hometown but also the marigolds in Miss Lottie's yard.
Explanation:
The short story "Marigolds" by Eugenia Collier is a story of a little girl's childhood experience. In the story, Lizabeth talks of how her community is impoverished, "—the brown, crumbly dust of late summer—arid, sterile dust that gets into the eyes and makes them water, gets into the throat and between the toes of bare brown feet". But despite the background image of poverty all around her, she could also remember "a brilliant splash of sunny yellow against the dust—Miss Lottie’s marigolds". Through her remembering of the marigolds amidst the poverty of her childhood hometown, Lizabeth develops the theme of beauty appreciated even in the worse circumstances.
Word problem for 24- ( 6+3)
Point V lies between points U and W on UW.
If UW = 9x – 9, what is UW in units?
5 units
6 units
30 units
36 units
Answer: The correct option is (D) 36 units.
Step-by-step explanation: Given that point V lies between points U and W on UW, where
[tex]UV=2x-4,~~VW=4x+10~~~\textup{and}~~~UW=9x-9.[/tex]
We are to find the length of UW in units.
Since point V lies on the line segment UW, so we must have
[tex]UV+VW=UW\\\\\Rightarrow (2x-4)+(4x+10)=9x-9\\\\\Rightarrow 6x+6=9x-9\\\\\Rightarrow 9x-6x=6+9\\\\\Rightarrow 3x=15\\\\\Rightarrow x=5.[/tex]
Therefore, the length of UW is
[tex]UW=9x-9=9\times5-9=45-9=36~\textup{units}.[/tex]
Thus, the length of UW is 36 units.
Option (D) is correct.
At the candy store, Sophie filled a bag with 2 2/3 kilograms of candy. 1/4 of the weight of the candy was from chocolate covered pretzels. How much did the chocolate covered pretzels in Sophie’s bag weigh?
What is the equation of a line that passes through the point (9, −3) and is parallel to the line whose equation is 2x−3y=6 ?
Enter your answer in the box
The equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]
Given:
Points the line passes through, (9, -3)
The equation of the line it is parallel to: 2x - 3y = 6
Note:
Parallel lines have the same slope valueEquation of a line in slope-intercept form is: y = mx + b. (m is slope; b is y-intercept)Point-slope form is; y - b = m(x - a)First, rewrite 2x - 3y = 6 in slope-intercept form to determine its slope.
[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{2}{3}x - 2[/tex]
The slope of 2x - 3y = 6 is therefore 2/3.Thus, the slope of the line that passes through (9, -3) is also 2/3.
Write the equation of the line in point-slope form:
Substitute m = 2/3, and (a, b) = (9, -3) into y - b = m(x - a)
Thus:[tex]y - (-3) = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}(x - 9)[/tex]
Rewrite in slope-intercept form[tex]y + 3 = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}x -\frac{2}{3}(9)\\\\y + 3 = \frac{2}{3}x - 6\\\\y = \frac{2}{3}x - 6 - 3\\\\\mathbf{y = \frac{2}{3}x - 9}[/tex]
Therefore, the equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]
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Explain how you would calculate the cost per second for the Coral Reef Fountain which costs $49.99 and has a burn time of 1 minute 35 seconds. The correct answer rounded to the nearest penny is $0.53. Show your work.
a square has an area of 25cm2 what is the length of each side?
The length of each side of the given square would be 5 cm if square has an area of 25cm².
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
What is a square?A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.
The area of a square is equal to the squared of sides or the multiplication of two sides.
We have been given a square has an area of 25 cm²
The length of one side = √( the area of a square)
The length of one side = √(25)
The length of one side = 5 cm
Therefore, the length of each side of the given square would be 5 cm.
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You earned $34,000 and your total tax due was $6,200. what was your average tax rate?
a.8%
b.10%
c.18%
d.20%
A baby elephant weighs 250 lb,
What is the elephant's weight in tons and kilograms (1 kg= 2.2 lb.)? Round to the thousandths place.
Please help me with this problem!
y =
37
39
51
y = arctan(8/10)
y = 38.65
y = 39
Answer:
Option (b) is correct.
The measure of angle y is 39°
Step-by-step explanation:
Given : A right angled triangle with some measurements.
We have to find the value of y.
Consider the given triangle,
Using trigonometric ratios,
We know tangent is the ratio of perpendicular to its base.
Mathematically written as
[tex]\tan\theta=\frac{Perpendicular}{base}[/tex]
So, for given triangle, [tex]\theta=y[/tex]
and for y, perpendicular is 8 and base is 10
Substitue, we have,
[tex]\tan y=\frac{8}{10}[/tex]
Simplify, we have,
[tex]\tan y=\frac{4}{5}[/tex]
Taking inverse of tan both side, we have,
[tex]\tan^{-1}(\tan y)=\tan^{-1}(\frac{4}{5})[/tex]
[tex]y=\tan^{-1}(\frac{8}{10})[/tex]
Simplify , we have,
[tex]y=38.65^{\circ}[/tex]
Thus, the measure of angle y is 39°