The function y = (x2 + 1)(x2 + 2) has how many x-intercepts? options:a) 0 b) 1 c) 2 d) 3
Answers
We must find the number of x-intercepts present in the function:
\(y=(x^2+1)(x^2+2)\)The x-intercepts are the points where the graph of the function intercepts the x-axis which implies that y=0 at those points. Then the number of x-intercepts is equal to the number of solutions of the equation y=0:
\(0=(x^2+1)(x^2+2)\)We have that the product of two expressions is equal to 0. This means that the solutions to this equation are also the solutions to the two equations given by equalizing each term to 0:
\(\begin{gathered} x^2+1=0 \\ x^2+2=0 \end{gathered}\)We can substract 1 from both sides of the first equation and 2 from both sides of the second equation:
\(\begin{gathered} x^2+1-1=0-1\rightarrow x^2=-1 \\ x^2+2-2=0-2\rightarrow x^2=-2 \end{gathered}\)As you can see in both equation the square of x is a negative number. This is false for any real value of x which means that the original equation has no real solutions. Therefore the value of y is never 0 and the function has no x-intercepts.
AnswerThen the answer is option a).
Related Questions
15 POINTS :)
Solve the inequality.
-3x+4<25
Answers
Answer:
x > -7
Step-by-step explanation:
-3x + 4 < 25
-3x + 4 - 4 < 25 - 4
-3x < 21
-3x/-3 < 21/-3
x > -7
May i have brainliest? :)
Solve for the rate (as a %). Round to the nearest tenth of a percent when necessary. What is the rate if the base is 366 and the portion is 50?
Answers
Answer:
\(\Huge \boxed{\text{13.66$\%$}}\)
Step-by-step explanation:
To find the rate, we need to use the following formula:
\(\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}\)
Where "Portion" is the part of the whole and "Base" is the whole.
Now, let's plug in the given values:
\(\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}\)
Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).
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From a batch of 13 students who had appeared in an examination, 4 students
were failed. The marks of passed students were 43, 57, 45, 61, 75, 64,53,50 and
40. Calculate median marks of all students.
Answers
Answer:
37 7/13
Step-by-step explanation:
there are 13 students
total marks of students is488
therefore we are finding the median
=488/13
=37 7/13
Find the product
5/8 of 24
A. 8
B.15
C.11
D.9
Answers
Answer:
15
Step-by-step explanation:
The lengths of the sides of a triangle are 3 , 4 , 5 Classify the triangle as acute, right, or obtuse.
Answers
What is the volume of a cylinder with base radius 2 and height 5?
Answers
Answer:
20 pi (sign)
Step-by-step explanation:
khan answer trust me bro
All else being equal, a study with which of the following error ranges would be
the most reliable?
A. +12 percentage points
B. 117 percentage points
C. +2 percentage points
D. 17 percentage points
Answers
In ΔXYZ, y = 500 inches, � m∠Y=117° and � m∠Z=10°. Find the length of z, to the nearest inch.
Answers
The length of z in the triangle is 97 inches.
How to find the side of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the side z of the triangle XYZ using sine law as follows:
a / sin A = b / sin B = c / sin C
Hence,
500 / sin 117 = z / sin 10
cross multiply
500 sin 10 = z sin 117
divide both sides by sin 117
z = 500 sin 10 / sin 117
z = 86.8240888335 / 0.89100652418
z = 97.4410774411
Therefore,
z = 97 inches
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When you graph y ≥ 2x - 5, what part of the half-plane you will shade?
Correct answer= all my points and brainlist wrong= report and take back my points
Answers
The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.
What is graph of inequality?The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
In the given problem, the inequality presented is;
y ≥ 2x - 5
To graph this, we would use a graphing calculator to find the boundary lines and plane.
In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.
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I NEED THIS ANSWER NOW PLS I'LL GIVE YOU 30 POINTS IF YOU ANSWER IN THE NEXT COUPLE OF SECONDS
What is the sign of the product (3)(−25)(7)(−24)?
Positive, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is positive
Positive, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is positive
Negative, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is negative
Negative, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is negative
Answers
Answer:
A. Positive, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is positive
1. Find the area of the composite figure below. Make sure you show your work neatly for full
credit.
(3.5)
18 in.
18 in.
9 in.
36 in.
18 in.
Answers
The calculated area of the composite figure is 85 cm².
How to calculate the the area of the composite figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure (see attachment)
Where, we have
Rectangle:
Area = length × width.
Therefore, the area of the rectangle is 10 cm × 6 cm = 60 cm².
Triangle:
Area = (1/2) × base × height.
Therefore, the area of the triangle is (1/2) × 5 cm × 10 cm = 25 cm².
To find the total area of the composite figure, we add the areas of the rectangle and the triangle:
Total Area = Area of Rectangle + Area of Triangle
= 60 cm² + 25 cm²
= 85 cm².
Therefore, the area of the composite figure is 85 cm².
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1/4(d-3)=-15 solve for d
Answers
i hope it is helpful for you
What is the answer to this question? Need help.
Answers
Answer:
\(4x^2 + 12x + 9\)
Step-by-step explanation:
an exponent of \(^2\) means that the equation is being multiplied by itself 2 times
\((2x + 3)^2 = (2x + 3)(2x+3)\)
\(4x^2 + 6x + 6x + 9\)
\(4x^2 + 12x + 9\)
A shed in the shape of a rectangular prism has a volume of 910 cubic feet. The length of the dumpster is 7 feet less than twice the width w, and the height is 3 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the shed in feet. Your answer should be in the form of a polynomial equals a constant. Provide your answer below:
Answers
2w³ - 13w² + 21w = 910 is the equation, in terms of w, that could be used to find the dimensions of the shed in feet.
What does volume mean in plain terms?
The capacity of a solid shape is determined using volume, a three-dimensional quantity.
The volume of a closed figure is used to determine how much space it can fill in three dimensions.
Volume = 910 cubic feet
as per question
l = 2wc- 7 .................1
h = w - 3 .....................2
from 1 , 2 and 3
v = 910
lwh = 910
(2w - 7)w ( w - 3 ) = 910
( 2w² - 7w ) ( w - 3 ) = 910
2w³ - 6w² - 7w² + 21w = 910
2w³ - 13w² + 21w = 910
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The exponential regression equation y=307.60(1.11)^x models the dollar value of a retirement fund after x years. Which is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made. ?
A. $310
B. $580
C. $1,880
D. $2,050
Answers
Answer:
B. $580
Step-by-step explanation:
Value of the retirement fund after x years:
The value of the retirement fund after x years is given by the following function:
\(y(x) = 307.6(1.11)^x\)
Which is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made?
This is y(6). So
\(y(6) = 307.6(1.11)^6 = 575.34\)
Close to $580, and thus, the correct answer is given by option B.
Answer:
B. $580 is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made.
Thus it is little close to answer because actual answer is $575.34.
will report anybody who gives a link!
3,947 ÷ 45 = (?) R (?)
Answers
Answer:
87.7(1)
=
87 Remainder 32
In a factory a test run over 400 computer chips resulted in 8 defective one how many possible out comes are there
Answers
Answer:
392
Step-by-step explanation:
A person picking apples stand on a ladder 3.0 m above the ground. He throws them into
a basket 2.0 m away. How fast must the person throw the apple in order for it to land in
the basket?
Answers
/\t = 0.7825
/\ is a triangle
2.0m = V_x (0.7825)
V_x = 2.56 m/s
(V_x subscript x)
Determine the number of ways in which a jury of 6 men and 6 women can be selected from a group of 11 men and 14 women.
Answers
Answer:
1387386 ways.
Step-by-step explanation:
This is solved using the combination rule
C(n, r) = nCr = n!/r! (n - r)!
The number of ways in which a jury of 6 men and 6 women can be selected from a group of 11 men and 14 women is calculated as:
11C6 × 14C6
= 11/6! (11 - 6)! × 14/6!(14-6)!
= 11/6! × 5! × 14!/6! × 8!
= 462 × 3,003
= 1387386 ways.
URGENT!!!! Find the y-intercept of the line that passes through the points (-3, 7) and (3, −9).
Answers
Answer:
\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)
\(7 = - \frac{8}{3} ( - 3) + b\)
\(7 = 8 + b\)
\(b = - 1\)
\(y = - \frac{8}{3} x - 1\)
The y-intercept is -1.
Please answer these 3 questions
Answers
The Volume of the box is 12 cubic unit.
We have,
Height = 1 unit
Width = 2 unit
Length = 6 unit
So, Volume of box
= l w h
= 1 x 2 x 6
= 12 cubic unit
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Solve for x
-2x + 7 = 25
Answers
Answer:
-9
Step-by-step explanation:
Step 1:
-2x + 7 = 25
Step 2:
-2x = 18
Step 3:
-18 = 2x
Answer:
-9
Hope This Helps :)
Answer: -9
Step-by-step explanation: hope this helped ❤️
The area of the triangle below is 2/5 square meters. What is the length of the base Express your answer as a fraction in simplest form.
3/5 m is the height
Answers
Let's set the base of the triangle to x.
(x* 3/5) / 2= 2/5
Now just solve
x*3/5=4/5
x=4/3
The base has length 4/3
Hope it helped!
The length of the base is 4/3 meters.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The area of a triangle is given by the formula:
A = (1/2)bh
where A is the area, b is the base length, and h is the height.
We are given that the area of the triangle is 2/5 square meters and the height is 3/5 meters.
Plugging these values into the formula, we get:
2/5 = (1/2)bh
b = (2/5) / [(1/2)(3/5)]
b = (2/5) / (3/10)
b = (2/5) * (10/3)
b = 4/3
Therefore,
The length of the base is 4/3 meters.
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Which reason justifies the second statement in the proof below?
Given: parallelogram L E N S and parallelogram N G T H
Prove: Angle L is congruent to angle T.
A. In a parallelogram, consecutive angles are supplementary.
B. Alternate Interior Angles Theorem
C. In a parallelogram, opposite angles are congruent.
D. Corresponding Angles Postulate
SOMEONE PLEASE HELP!
Answers
The reason that justifies the second statement "Angle L is congruent to angle T" is:
In a parallelogram, opposite angles are congruent.
Option C is the correct answer.
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
Parallelogram LENS and parallelogram NGTH
Now,
Parallelogram LENS:
∠L = ∠N _____(1)
Opposite angles are equal.
Parallelogram NGTH:
∠N = ∠T ______(2)
Opposite angles are equal.
Now,
∠ENS = ∠GNH
Vertical angles are equal.
So,
From (1) and (2).
∠L = ∠T
Angle L is congruent to angle T
Thus,
Angle L is congruent to angle T
[ In a parallelogram, opposite angles are congruent ].
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wing Lines Parallel
Solve for x to make A||B.
B
3x
A
X = = [?]
7x
Enter
![wing Lines ParallelSolve for x to make A||B.B3xAX = = [?]7xEnter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/VmxS6tS378ZStBa0f3rTt1tnUYdgZ1Qq.png)
Answers
If line A is parallel to line B then the value of x is 18.
Given that a line A is parallel to line B
We have to find the value of x
3x+7x=180
Combine the like terms
10x=180
Divide both sides by 10
value x=18
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A researcher is investigating the relationship between the length, in centimeters, and weight, in grams, of pineapples. The researcher will select a random sample of 15 pineapples from grocery stores in a region and construct a 95% confidence interval for the slope of the population regression line, where length is the explanatory variable and weight is the response variable. When computing a confidence interval for the slope of the population regression line, which of the following is not a condition that must be checked?
A. The true relationship between length and weight is linear.
B. The standard deviation for weight does not vary with length.
C. The values of weight are approximately normally distributed at each value of length.
D. The sum of the residuals is zero.
E. The observations are independent.
Answers
Answer:
D. The sum of the residuals is zero.
Step-by-step explanation:
The relation between length and weight of pineapples is observed. The observation should be independent and the values must be normally distributed in order to find the confidence interval for slope of population regression line.
Southside High School found that 80% of last year's sold-out plays occurred
during weekend performances. Based on this information, the drama teacher
decided to add another performance time on Saturday. This decision is a
result of
OA. describing data
OB. making an inference
OC. creating involvement
D. collecting data
Answers
Answer:
B. making an inference.
Step-by-step explanation:
The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.
What is the probability of randomly selecting a month of the year and not getting a month that has fewer than 30 days
Answers
Answer
11 out of 12
11/12
Step-by-step explanation:
What is the answer help
Answers
Answer: 162°
Step-by-step explanation:
To find the answer to this question, we need to find what 45% of 360 degrees (a circle) is.
First, a percent divided by 100 becomes a decimal.
45% / 100 = 0.45
Next, "of" means multiplication in mathematics.
0.45 * 360 = 162
The central angle will be 162°.
I need help with my math
Answers
The Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)The graph provided suggests the use of the points (3,-3) and (5,-3). The slope is:
\(\displaystyle m=\frac{-3+3}{5-3}=\frac{0}{2}=0\)The slope of the line is 0. It corresponds to a horizontal line