Which best describes the graph of the cubic function f(x) = x^3 +x^2 +x +1?
A. x increases, y increases along the entire graph.
B. As x increases, y increases, decreases, and then increases again.
C. As x increases, y decreases, increases and then decreases again.
D. As x increases, y decrease along the entire graph.
Answers
Answer:
A.
Step-by-step explanation:
Now since the degree is odd (3 in this case) and the leading coefficient is positive (1), then the end behavior is going to be:
for left-end behavior, it is down
for right-end behavior, it is up
We are going to definitely have some increasing action going on because it goes from down to up reading from left to right.
Let's graph it in our ti-84's or whatever you have.
This is a very rough graph but you can see it is just increasing on the entire domain. This means reading the graph from left to right, there is only rise.
I can give you an answer with calculus in it if you prefer.
Related Questions
what is the slope of the line passing through the points (-5,9) and (2,-12)
Answers
Answer:
-3
Step-by-step explanation:
To find the slope of a line given two points, we use:
[tex]\frac{y_2-y_1}{x_2-x_1} \text{ when the points } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are on the line }[/tex].
Or you could line up the points vertically and subtract the points vertically, then put 2nd difference over 1st difference.
That looks like this:
( 2 , -12)
-( -5 , 9 )
----------------
7 -21
So the slope is -21/7 which gives you -3.
The temperature of a liquid increases the same amount over time. At the end of the first day, its temperature was 47 f and at the end of the third day, it was 51f The following line represents this situation. But the graph has some missing parts.
Answers
Answer:
It increases by 2 degrees every day
Step-by-step explanation:
51-47=4 4/2 equal 2
3. Write an equation in point-slope form for the line through the given point with the given slope.
(4, -6); m = 3/5
A. Y-4=3/5x (x+6)
B. Y+6=3/5(x-4)
C. Y+6=3/5x-4
D. Y-6=3/5(x+4)
Answers
Answer:
B
Step-by-step explanation:
recall that point-slope form of a linear equation is expressed as follows
y - y1 = m (x - x1)
where m = slope and (x1, y1) is the coordinate of any point on the line
so, here we have m = (3/5), x1 = 4 and y1 = -6
substitute these into the formula
y - (-6) = (3/5) (x - 4)
y + 6 = (3/5) (x - 4)----> answer
Answer:
[tex]\boxed{\text{B. }y + 6 =\dfrac{3}{5}(x - 4)}[/tex]
Step-by-step explanation:
The point-slope formula for a straight line is
[tex]y - y_{1} = m(x - x_{1})[/tex]
x₁ = 4; y₁ = -6; m = ⅗
Substitute the values
[tex]\begin{array}{rcl}y - (-6) & = & \dfrac{3}{5}(x - 4)\\\\y + 6 & = & \dfrac{3}{5}(x - 4)\\\\\end{array}\\\text{The equation for the line is $\boxed{\mathbf{y + 6 =\dfrac{3}{5}(x - 4)}}$}[/tex]
The figure shows the graph of the equation with slope ⅗ passing through (4,-6).
Rachel is going to calculate the following expression: 3.32/1.66+18.4. She calculates the expression as it is written and then writes down the answer rounded to the nearest whole number. She then calculates it again, but rounds each of the 3 numbers in the expression to the nearest integer, and then performs the division and addition. She writes this answer down next to the answer she got before. What is the positive difference between the 2 answers she got?
Answers
Answer:
the answer is 0.5 lol
for questions 5-6 the functions are
f(x)=5x^2+3
g(x)=x^2-7
Answers
Answer:
see explanation
Step-by-step explanation:
Note that
(f + g)(x) = f(x) + g(x) and
(f - g)(x) = f(x) - g(x)
5
f(x) + g(x)
= 5x² + 3 + x² - 7 = 6x² - 4
6
f(x) - g(x) = 5x² + 3 - (x² - 7) ← distribute parenthesis
= 5x² + 3 - x² +7 ← collect like terms
= 4x² + 10
7
f(x) + g(x) = [tex]4^{x}[/tex] + 3x + 2x - 5 = [tex]4^{x}[/tex] + 5x - 5
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? A] The test contains 4 three-point questions and 20 five-point questions. B]The test contains 10 three-point questions and 14 five-point questions. C]The test contains 14 three-point questions and 10 five-point questions. D]The test contains 20 three-point questions and 8 five-point questions.
Answers
Answer:
B. The test contains 10 three-point questions and 14 five-point questions.
Step-by-step explanation:
Let us first find the solution to the system of equations.
x+y= 24
3x+5y= 100
We use substitution method.
x=24-y
Replacing the value of x in the second equation.
3(24-y)+5y=100
Then solve for y.
72-3y+5y=100
2y=100-72
2y=28
y=14
To find x let us replace the value of y in x=24-y
x=24-14
x=10
This means that the test has 14 five-point questions and 10 three point questions.
Solve for k k/2 + 1/2 = 3
Answers
k/2+1/2=3
Move +1/2 to the other side. Sign changes from +1/2 to -1/2
k/2+1/2-1/2=3-1/2
k/2=3-1/2
Find the common denominator for 3 and -1/2.
Common denominator is 2
k/2=3(2)-1/2
k/2= 6/2-1/2
k/2=5/2
Multiply k/2 with 2. Multiply 2 with 5/2
k/2 (2/1)=2(5/2)
Cross out 2 and 2. Divide by 2. Cross out 2 and 2 for 5/2(2). Divide by 2
k=5
{(1,2), (-2,3), (1,3), (-2,2)} is what type of relation?
A. one-to-many
B. many-to-many
C. one-to-one
D. many-to-one
Answers
Answer:
B. Many-to-many
Step-by-step explanation:
We have the following ordered pairs:
(1,2)(-2,3)(1,3)(-2,2)First let's define the following concepts:
One-to-one: A function is said to be one-to-one if every y value has exactly one x value mapped onto it.Many-to-one: If there are y values that have more than one x value mapped onto them.One-to-many: If there are x values that have more than one y value mapped onto them. (NOT A FUNCTION)Many-to-many: If there are x values that have more than one y value mapped onto them and at the same time, there are y values that have more than one x value mapped onto them (NOT A FUNCTION)From all the ordered pairs, we find that the points (1,2) and (1,3) have the same x-value for diferent y-values. Also we find that the points (1,2) and (-2, 2) have different x-values for the same y-value.
Therefore, the ordered pairs DO NOT belong to a function and can be considered MANY-TO MANY.
The given relation is a many-to-one relationship.
The given relation {(1,2), (-2,3), (1,3), (-2,2)} is an example of a many-to-one relationship. In a many-to-one relation, multiple elements in the domain map to a single element in the range. Each x-value has a unique y-value.
Which statement best describes triangles UWW and
XYZ?
Answers
Answer:
Similar but not congruent
Step-by-step explanation:
For them to be congruent, they have to have same everything but not necessarily the same orientation. They are not congruent because their corresponding sides aren't the same measurement.
You can tell if two triangles are similar if each pair of corresponding are congruent.
They will also have corresponding sides are proportional.
That is 50/40=60/48=40/32 in this case? Well does it? It does, because each one of them is equal to 1.25.
Answer:
The correct answer is second option
They are similar, but not congruent
Step-by-step explanation:
From the given diagram we can see two triangles.
ΔUVW and ΔXYZ
m<X = m<U,
m<Y = m<V and
m<Z = m<W
Therefore two triangles are similar
The sides of these two triangles are not congruent, therefore these two triangles are not congruent.
The correct answer is second option
They are similar, but not congruent
Simplify remove all the perfect squares from inside the square root 45
Answers
Answer:
3[tex]\sqrt5}[/tex]
The square root of 45 can be simplified by removing perfect square factors. In this case, the number 9 is a perfect square factor of 45, resulting in the simplification √45 to 3√5.
Explanation:To simplify the square root of 45 by removing perfect squares, we first need to identify the factors of 45 that are perfect squares. In this case, the number 9 is a factor of 45 and is a perfect square. Therefore, we can simplify √45 to √9*5 or 3√5. Simplifying square roots is a basic principle of Mathematics one should know as it is often applied in various middle school, high school, and even college math problems.
Learn more about Simplifying Square Roots here:https://brainly.com/question/1441039
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Multiply. Express your answer in simplest form. 9 1/6 × 1 1/11
Answers
Answer:
10
Step-by-step explanation:
First convert the fractions.
9 1/6 to 55/6 and 1 1/11 to 12/11
With these fractions, you can cross out 11 and 6.
55 times 12 5 × 2
6 11 1 × 1
This equals 10/1 or 10
Final answer:
To multiply 9 1/6 by 1 1/11, first convert them to improper fractions, 55/6 and 12/11 respectively. Multiply the numerators together to get 660, and the denominators together to get 66. Simplify by dividing both by their greatest common divisor, which is 66, to get the simplest form, which is 10.
Explanation:
The question asks to multiply 9 1/6 by 1 1/11 and express the answer in simplest form. First, we will convert these mixed numbers to improper fractions. For the first number, 9 1/6, we multiply the whole number part by the denominator of the fractional part and add the numerator: (9 × 6) + 1 = 54 + 1 = 55, thus we get 55/6. For the second number, 1 1/11, we follow the same process: (1 × 11) + 1 = 11 + 1 = 12, resulting in 12/11.
Next, we multiply the resulting improper fractions. The numerators are multiplied together, and the denominators are multiplied together yielding 55 × 12 over 6 × 11 which equals 660/66. Simplifying by common factors, we notice that both the numerator and denominator have a common factor of 66. Dividing the numerator and denominator by 66 gives us the simplest form, which is 10/1 or simply 10.
What is the mean of the following numbers: 5, 7, 4, 4, 5, 4, 6?
35
5
4
6
Answers
Answer: 5
Step-by-step explanation: First, add all of the given numbers.
5+7+4+4+5+4+6=35
Next, divide 35 by the number of given numbers, which is 7.
35/7 = 5
The mean is 5.
What type of function is represented by the table of values below?
8
12
16
20
Answers
Answer:
To be precise, I think it's a pattern question, where you have to add 4 to each number. I'm not very sure though.
find the equivalent expression using the same bases (46 x 59)^6
Answers
Answer:
46^6 x 59^6
Step-by-step explanation:
For properties (axb)^y has the equivalent expression of a^y x b^y
Then, (46x59)^6 can be written as 46^6 x 59^6
Answer: [tex]46^6* 59^6[/tex]
Step-by-step explanation:
Given the expression [tex](46* 59)^6[/tex], in order to find an equivalent expression using the same bases, you need to remember the following:
[tex](a*b)^n=a^n*b^n[/tex]
So, you can observe that, in this case:
[tex]a=46\\b=59\\n=6[/tex]
Therefore, substituting values, you get the following equivalent expression:
[tex](46* 59)^6=46^6* 59^6[/tex]
which decimal is equivalent to forty and seventy six thousands ? a.40.076 b 40.76 C 47.006 D 47.06
Answers
Answer:
A. 40.076
Step-by-step explanation:
Because B is forty and seventy six hundredths. C is forty-seven and six thousandths. D is forty-seven and six hundredths.
Seventy-six thousandths is written as .076, making the final answer 40.076.
The decimal equivalent to forty and seventy six thousandths is 40.076. This is because seventy-six is in the thousandths place after the decimal point.
The decimal equivalent to forty and seventy six thousandths is 40.076. To write this out, you place the decimal point after the whole number forty, then you need to ensure that seventy-six is in the thousandths place. When writing decimal numbers, the first place to the right of the decimal is the tenths place, the second is the hundredths place, and the third is the thousandths place. Therefore, seventy-six thousandths is written as .076, making the final answer 40.076.
Dakota believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation y = 3.9 − 0.3x.
Identify and interpret the slope in this scenario.
a. The slope is −3.9. Starting at 0.3, the GPA will decrease by 3.9 for every text sent in class.
b. The slope is 3.9. Starting at 0.3, the GPA will increase by 3.9 for every text sent in class.
c. The slope is 0.3. Starting at 3.9, the GPA will increase by 0.3 for every text sent in class.
d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Answers
Answer:
d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Step-by-step explanation:
You can write the equation is the slope intercept form of y=mx+c
where m is the slope and c in the y-axis intercept
write the equation as;
y=mx+c
y= -0.3x+3.9
Here , you have a negative slope which means the GPA will reduce by 0.3 for every text sent in class.
See attached graph to visualize the y-intercept point
Answer:
The correct option is d.
Step-by-step explanation:
The given equation of best fit line is
[tex]y=3.9-0.3x[/tex] .... (1)
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept or initial value.
From (1) and (2), we get
[tex]m=-0.3[/tex]
[tex]b=3.9[/tex]
It means the slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Therefore the correct option is d.
A savings account was opened with an initial deposit and never touched again. An account that does not meet the minimum
balance requirement is charged a service fee.
Assuming the account was open with an initial deposit below the minimum amount, the current account balance, B, is equal to the
product of the initial deposit, I, and the quantity of the difference of 1 and the monthly service fee, f, raised to the power of n, the
number of months since the account was open.
If an initial deposit of $2,586,00 is made to the account with a monthly service fee of 2% what will be the value of B after
19 months? Round to the nearest cent.
A.
$1,797.62
B. $1,603.32
C. $1,761.67
D. $3,767.31
Answers
Whitch expression is equivlent to the expression
7(3x-2) + 4(x+5)
Answers
Answer:
[tex]\large\boxed{7(3x-2)+4(x+5)=25x+6}[/tex]
Step-by-step explanation:
[tex]7(3x-2)+4(x+5)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(7)(3x)+(7)(-2)+(4)(x)+(4)(5)\\\\=21x-14+4x+20\qquad\text{combine like terms}\\\\=(21x+4x)+(-14+20)\\\\=25x+6[/tex]
Answer:
[tex]\Huge \boxed{25x+6}[/tex]
Step-by-step explanation:
[tex]\large \textnormal{Distributive property}[/tex], [tex]\large \textnormal{A(B+C)=AB+AC}[/tex].
[tex]\displaystyle 7(3x-2)=21x-14[/tex]
[tex]\displaystyle 21x-14+4(x+5)[/tex]
[tex]\displaystyle 4(x+5)=4x,5\times 4=20, 4x+20[/tex]
[tex]\Large\textnormal{Solve to find the answer.}[/tex]
[tex]\displaystyle 21x-14+4x+20=25x+6[/tex]
[tex]\Large \textnormal{Correct answer is \boxed{25x+6}.}[/tex]
Square root of 4/(7-3i)+(2+5i)
Answers
you can do it ans is above
(7z^3+42z^2-15z+1)- (36z^2+12z-21)
Answers
Answer:
7z^3+6z^2-27z+22
Step-by-step explanation:
The given question is of subtraction:
So,
(7z^3+42z^2-15z+1)- (36z^2+12z-21)
=7z^3+42z^2-15z+1-36z^2-12z+21
Combining alike terms to simplify
=7z^3+42z^2-36z^2-15z-12z+1+21
=7z^3+6z^2-27z+22
So the answer in simplified form is:
7z^3+6z^2-27z+22 ..
Answer:
7z³ + 6z² - 27z + 22
Step-by-step explanation:
It is given an expression in variable z,
(7z³ + 42z² - 15z + 1) - (36z² + 12z - 21)
To find the simplified form
(7z³ + 42z² - 15z + 1) - (36z² + 12z - 21)
= (7z³ + 42z² - 15z + 1 - 36z² - 12z + 21)
= 7z³ + 42z² - 36z² - 15z -12z + 1 + 21
= 7z³ + 6z² - 27z + 22
Therefore the simplified expression is = 7z³ + 6z² - 27z + 22
how many 1/4s fit in 1/2
Answers
Answer:
2
Step-by-step explanation:
1/4+1/4=1/2
F(x)=3x+1 and g(x)= x^2-6 find (f•g)(x)
Answers
Answer:
Step-by-step explanation:
It never occurred to me that the closed circle meant multiplication. The most common symbol for multiplication here is *. If that is what is meant (closed circle = multiplication) then my answer is wrong.
f(x) = 3x + 1
g(x) = x^2 - 6
f(x)(g(x)) = (3x + 1)(x^2 - 6)
f(x)(g(x)) = 3x^3 - 18x + x^2 + 6 or more properly
f(x)(g(x)) = 3x^3 + x^2 - 18x - 6
[tex](f\cdot g)(x)=(3x+1)(x^2-6)=3x^3-18x+x^2-6=3x^3+x^2-18x-6[/tex]
Which term describes how the two sides of this figure are related?
O
A. Induction
O
B. Deduction
O
C. Symmetry
O
D. Scientific method
Answers
Answer:
The answer is A - symmetry.
None of the other options really have bearing in relation to the question.
Hope this helps.
Step-by-step explanation:
The given image shows the symmetry of a shape. Both the divided sides are equal halves of the shape. Therefore, option C, symmetry is correct option.
What is symmetry of a figure ?Symmetry is a property of a figure that describes how it looks the same after being transformed in a certain way. In other words, a figure is said to have symmetry if it can be divided into parts that are mirror images or identical to each other.
There are different types of symmetry, such as :reflection symmetry, rotational symmetry, translational symmetry etc.
Symmetry is an important concept in many areas of mathematics and science, such as geometry, crystallography, physics, and chemistry. It is also a fundamental aspect of beauty and aesthetics in art, architecture, and design.
The given figure can be divided into two equal halves. Hence, the two sides are in symmetry. Thus, option C is correct.
Find more on symmetry :
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Your complete question is attached below:
Wendy is paid $12 per hour and plans to work between 30 and 35 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.
weekly pay; hours worked; 30 to 35 hours; $360 to $420
hours worked; weekly pay; 30 to 35 hours; $0 to $420
hours worked; weekly pay; 30 to 35 hours; $360 to $420
weekly pay; hours worked; $360 to $420; 30 to 35 hours;
Answers
Answer:
See below.
Step-by-step explanation:
The independent variable is the number of hours worked and the dependent variable is the weekly pay.
The domain is 30 to 35.
The range is $360 to $420.
Which of the following is the correct notation for the complex number
Answers
Answer:
1-4i
Step-by-step explanation:
[tex]i=\sqrt{-1}[/tex]
We have [tex]1-\sqrt{-16}[/tex].
Let's look at the [tex]\sqrt{-16}[/tex] part.
Since it has a negative inside the square root, it is imaginary. This is our imaginary unit [tex]i=\sqrt{-1}[/tex].
So [tex]\sqrt{-16}[/tex]
[tex]=\sqrt{16} i [/tex]
[tex]=4i[/tex]
So [tex]1-\sqrt{-16}=1-4i[/tex]
Which of the following inequalities matches the graph?
[tex]x \leqslant 0[/tex]
[tex]x \geqslant 0[/tex]
[tex]y \leqslant 0[/tex]
[tex]y \geqslant 0[/tex]
which one is it 1,2,3,or the 4 one
Answers
Answer:
[tex]\large\boxed{x\leq0}[/tex]
Step-by-step explanation:
x ≤ 0 - the region below the line x = 0 (x axis)
x ≥ 0 - the region above the line x = 0 (x axis)
y ≤ 0 - the region on the left of the line y = 0 (y axis)
y ≥ 0 - the region on the right side of the line y = 0 (y axis)
all region with lines (axes)
We have the region below the x axis (x = 0).
Need some help ya plz
Answers
Answer:
C. (-5, 3)
Step-by-step explanation:
Point C is currently (5,3).
If it is reflected over the y-axis, that means while the y-coordinate stays the same, the x- coordinate is negative of what is was before.
C is the only answer that keeps the y-coordinate constant, so just by looking at that, we can say that the answer is C.
Answer:
C
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y )
Hence
C(5, 3 ) → C'(- 5, 3 ) → C
What is the approximate radius of a sphere whose volume is 1349 cm?
Answers
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=1349 \end{cases}\implies 1349=\cfrac{4\pi r^3}{3}\implies 4047=4\pi r^3 \\\\\\ \cfrac{4047}{4\pi }=r^3\implies \sqrt[3]{\cfrac{4047}{4\pi }}=r\implies 6.85\approx r[/tex]
The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants
Answers
Answer:
13
Step-by-step explanation:
If you look at where $5 crosses the line of best fit, you see it between 12 and 14 ounces. The answer is 13.
Answer:
13 oz
Step-by-step explanation:
The blue line here is the trend line of the function between cost and size.
The trend line is the linear equation approximation of the function
So, for predicting the size when $5 is paid we need to take the corresponding x axis value and the corresponding y axis value on the trend line.
Hence, the Size of frozen yogurt is between 12 and 14 oz which means the size is 13 oz.
What is the surface area of the figure?
314 in.2
792 in.2
628 in.2
546 in.2
Answers
Answer:
628 n.2 is the correct answer