Answers
The graph and equation of a function is given.
It is required to find its y-intercept and zeros using the graph, and then finding these values algebraically.
Using the graph:
Recall that the y-intercept is the point where the graph of the function intersects the y-axis.
From the graph, notice that the graph intersects the y-axis at y=0.
Hence, the y-intercept is y=0.
Recall also that the x-intercepts or zeros is the point where the graph of the function intersects the x-axis.
From the graph, the graph intersects the x-axis at x= -1,0, and 1.5.
Hence, the zeros are x= -1,0, and 1.5.
Find these values algebraically:
To find the y-intercept algebraically, substitute x=0 into the function:
[tex]\begin{gathered} f(x)=2x^3-x^2-3x \\ \text{ Substitute }x=0\text{ into the equation:} \\ \Rightarrow f(0)=2(0)^3-0^2-3(0) \\ \Rightarrow f(0)=0 \end{gathered}[/tex]Hence, the y-intercept is y=0.
To find the zeros, substitute f(x)=0 into the function and solve for x:
[tex]\begin{gathered} 2x^3-x^2-3x=0 \\ \text{ Factor the left-hand side:} \\ \Rightarrow x(2x^2-x-3)=0 \\ \Rightarrow x(2x^2-3x+2x-3)=0 \\ \Rightarrow x[x(2x-3)+1(2x-3)]=0 \\ \Rightarrow x(x+1)(2x-3)=0 \end{gathered}[/tex]Equate each factor to 0
Related Questions
Madison says that 579.8 x 0.001 is the same as 579.8 : 10? Is she correct? Explain your answer in 3-5 sentences
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Step 1:
First, write the expression for each value
[tex]\begin{gathered} 579.8\text{ }\times\text{ 0.001 = 0.5798} \\ \\ 579.8\text{ }\times\text{ 10 = 5798} \end{gathered}[/tex]Final answer
The two are not the same because the value of 579.8 x 0.001 is less than the value of 579.8 x 10.
Finding the multiplier to give a final amount after a percentage increase or decrease
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(a) The function with which the new price can be found in terms of the original price is; New price = 0.86 × Original price
(b) New price: $34, 056
What is a function in mathematics?A function is a relationship that maps the elements of a set A to the elements of another set B, such that each element of A is mapped to only one element of the set B.
The original price of the car = $39,600
The percentage by which the price of the car is decreased = 14%
The equation that can be used to find the new price in terms of the original price is therefore;
New price = (1 - 0.14) × Original price = 0.86 × Original price
Therefore;
New price = 0.86 × Original price(b) The value of the new price is obtained by plugging in the value of the original price in the equation above, as follows;
New price = 0.86 × 39,600 = 34,056
The new price is; $34,056
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Which of the following expressions is equal to5 - 2(x + 2)?O -2x+1O 3x+6O -2x+2O 3x+2
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Given:
an expression is given as 5 - 2(x + 2)
Find:
we have to simplify the expression and find correct expression from the options, which is equal to the given expression.
Explanation:
Now
5 - 2(x + 2) = 5 - 2x - 4 = - 2x + 1
Therefore, 5 - 2(x + 2) = - 2x + 1
Do these coordinate pairs represent a function?: *{(2, 4), (2,5), (3,6), (3, 7) }
Answers
Given,
The coordinate pairs are
{(2, 4), (2,5), (3,6), (3, 7) }
Here the argument 2 returns to both 4 and 5 while 3 returns to both 6 and 7.
This violates the defination of function.
Thus the coordinate pairs doesnot represent a function.
The answer is No.
if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<14=?
Answers
According to the diagram, angles 10 and 14 are supplementary, so they sum 180°.
[tex]\begin{gathered} m\angle10+m\angle14=180 \\ 77+m\angle14=180 \\ m\angle14=180-77 \\ m\angle14=103 \end{gathered}[/tex]Hence, angle 14 measures 103°.2. The sum of the perimeters of similar quadrilaterals is 22.5 dm. Find the perimeters of the quadrilaterals if the similarity coefficient k = 1.25.
Answers
Given:
The sum of the perimeters of similar quadrilaterals is 22.5 dm. The similarity coefficient k = 1.25.
Required:
To find the perimeters of the quadrilaterals.
Explanation:
The quadrilaterals are similar and the similarity coefficient is k = 1.25.
If the quadrilateral is similar then the ratio of their corresponding sides is equal.
Let the perimeter of the one quadrilateral is x then the perimeter of the other quadrilateral will be 1.25x
Now
[tex]\begin{gathered} x+1.25x=22.5 \\ x(1+1.25)=22.5 \\ 2.25x=22.5 \\ x=\frac{22.5}{2.25} \\ x=10 \end{gathered}[/tex]Thus the perimeter of the one quadrilateral is 10dm.
The perimeter of the other quadrilateral = 1.25 x 10 = 12.5 dm
Final Answer:
Thus the perimeter of the quadrilaterals is 10dm and 12.5 dm.
Carol Wynne bought a silver tray that originally cost $150 and was advertised at 30% off. What was the sale price of the tray?The sale price was $(Type an integer or a decimal.)
Answers
The original price was $150
the discount was 30%
therefore, the final price is the following:
[tex]\begin{gathered} P_{final}=150*(1-0.3) \\ =150*0.7 \\ =105 \end{gathered}[/tex]Thus, the final price of the tray was $105
jamie needs to find the height of the parallelogram. the base is three inches long and the area is 30 square inches. what is the height. step one of 2:choose the correct formula
Answers
10 inches
Explanation:Given:
base of parallelogram = 3 in
Area pf the paralllelogram = 30 square inches
height = ?
To find the height, we apply the formula for area of parallelogram:
[tex]\begin{gathered} \text{Area of parallelogram = Base }\times\text{ height} \\ \end{gathered}[/tex][tex]\begin{gathered} 30\text{ = 3 }\times\text{ height} \\ \text{divide both sides by 3:} \\ \frac{30}{3}\text{ = }\frac{\text{3height}}{3} \\ \text{height = 10 } \\ \\ \text{The hright of parallelogram is 10 in} \end{gathered}[/tex]Factor out the greatest common factor. Simplify the factors, if possible.6x4 - 42x3 + 12x2Select the correct choice below and fill in any answer boxes in your choice.O A. 6x4 - 42x3 + 12x2 =(Type your answer in factored form.)OB. There is no common factor other than 1.ih
Answers
You have to find the greatest common factor first.
To do so, do as follows:
[tex]6x^4-42x^3+12x^2[/tex]Factors of 6 are: 1, 2, 3, 6
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The greates common factor is the greatest common factor shared by all values, in this case is 6
Now to factor it out you have to divide each term of the equation by it.
[tex](\frac{6x^4}{6})=x^4[/tex][tex](\frac{42x^3}{6})=7x^3[/tex][tex](\frac{12x^2}{6})=2x^2[/tex]The expression with the GCF factorized is then:
[tex]6(x^4-7x^3+2x^2)[/tex]What would be the equation for this line? 80 60 40 20 time in minutes 2 3 4 5 6 7 8 9 X distance in miles
Answers
the equation of the line is given as follows,
first we take points on this line
A(2,20)
and
B (4,40)
so, the equation of the line is,
[tex]y-20=\frac{40-20}{4-2}(x-2)[/tex][tex]\begin{gathered} y-20=\frac{20}{2}(x-2) \\ y-20=10x-20 \\ y=10x \end{gathered}[/tex]thus, the equation of the line is
y = 10x
it take Sarah to 1/2 AJ to make a birdhouse how much of the birdhouse will be built after 2/5 day choose the model that correctly illustrates the problem 2/5 ÷ 1/2
Answers
After 2/5 days Sarah can build 4/5 of a birdhouse.
It is given that Sarah can build birdhouses at the rate of 1/2 day per birdhouse.
Now let us use unitary method to calculate the number of birdhouses she can make in the given amount of time in a day.
Sarah takes 1/2 day to make 1 birdhouse
Sarah takes 1 day to make 1 ÷(1/2) birdhouse
Sarah takes 2/5 day to make 1÷ 1/2 × 2/5 birdhouse
Hence Sarah will make
= 1 ÷ 1/2 × 2/5
= 4/5 birdhouse
The unitary approach is a technique for solving problems that requires first figuring out how much one unit costs, then multiplying that amount to get the answer.
Therefore Sarah will take 2/5 days to make 4/5 of a birdhouse.
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A teacher receivesa monthly salary of $2800.00 What isheraunnual salary?
Answers
The year has 12 months, since the teacher receives a monthly salary of $2800, then his annual salary is:
[tex]2800\times12=33600[/tex]Answer:
$33600
Hero and Lisa are photographers they take pictures of seniors for high school yearbooks they charge a standard fee for taking the pictures there’s also a charge for each set of prints ordered so the number sets of prints determine the total cost S stand for the sets of prints ordered right the rule that describes the students total cost
Answers
Given:
We get the points (0,30), (1,31),(2,32), and (3,33) from the table.
Required:
We need to find the total cost.
Explanation:
From the point(0,30).
There is an initial cost of $30 for print.
Let s be the number of sets of prints ordered.
Let k be the additional cost for each number of sets of print
The equation of the given model is
[tex]Total\text{ cost =ks+30}[/tex]Consider the point (1,31).
Substitute total cost =31 and s=1 in the equation.
[tex]31\text{=k\lparen1\rparen+30}[/tex][tex]31\text{=k+30}[/tex]Subtract 30 from both sides.
[tex]31-30\text{=k+30-30}[/tex][tex]1\text{=k}[/tex]Substitute k =1 in the equation.
[tex]Total\text{ cost =s+30}[/tex]Consider the point (2,32).
Substitute total cost =32 and s =2 in the equation.
[tex]32\text{ =2+30}[/tex]It is true, so the equation satisfies the values in the table,
Final answer:
[tex]Total\text{ cost =s+30}[/tex]it f (x) = √ which equation describes the graphed function? y = f(-x+4)
y = -f(x+4)
y= -f(x-4) y=f(-x-4)
Answers
For the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
As given in the question,
Given equation is equal to :
f(x) = √x
Equation which help us to defined the graphed function is as follow:
From the graph we have different values of x we get,
When x = 4, x=3 x=2
a. y = f(-x +4) y = f(-x+4) y = f(-x+4)
= √-x +4 = √-3+4 = √-2+4
= √-4 +4 = 1 = 1.414
= 0
Correct. Correct Correct
b. y = -f(x+4)
= -√x+4
= -√4+4
≠ 0
Incorrect.
c. y = -f(x-4) y = -f(x-4)
= -√x-4 = -√3-4
= -√4-4 = -√-1
= 0
Correct Incorrect
d. y = f(-x-4)
= √-x-4
=√-4-4
≠0
Incorrect
Therefore, for the given equation f(x) = √x , the equation which help us defined the graphed function is given by y = f(-x +4).
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What is the measure of ZBDC?What is the measure of arc length BC?
Answers
SOLUTION
Step 1:
To find the measure of
Step 2:
The angle subtended by an arc at the centre is twice the angle subtended at the circumference. More simply, the angle at the centre is double the angle at the circumference.
Step 3:
Dividing both sides by 2, we have;
[tex]\begin{gathered} <\text{BDC = }\frac{BOC}{2}\text{ = }\frac{138}{2} \\ \\Step 4:
We are to find the measure of arc length BC;
Angle BOC is given as 138
[tex]\begin{gathered} \frac{\theta}{360}\text{ x 2 }\pi\text{ r} \\ \\ \frac{138}{360}\text{ x 2 x 3.14 x r } \\ \\ 2.407r \end{gathered}[/tex]Note: Since the value of the radius was not given so we need to express our answer in term of r.
The measure of arc length BC is 2.407r, where r is the radius.
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 timesBrooke's age. How old is Darius now?
Answers
The sum of the ages of Darius and Brooke is 78 years. 7 years ago, Darius's age was 3 times
Brooke's age. How old is Darius now?
Let
x ------> darius's age
y -----> Brooke's age
we know that
x+y=78 ------> equation A
(x-7)=3(y-7) -----> equation B
solve the sytem of equations
isolate the variable x in the equation A
x=78-y -------> equation C
substitute equation C in equation B
78-y-7=3(y-7)
slve for y
71-y=3y-21
3y+y=71+21
4y=92
y=23
Find the value of x
x=78-y
x=78-23=55
therefore
Darius now is 55 year old
whstbis the area in square inches of the shaded part of the retangle below
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The shaded area is trapezium with parallel sides as a = 10, b = 5 and height of trapezium is h = 18 in.
The formula for the area of trapezium is,
[tex]A=\frac{1}{2}\cdot(a+b)\cdot h[/tex]Determine the area of the tapezium.
[tex]\begin{gathered} A=\frac{1}{2}\cdot(10+5)\cdot18 \\ =15\cdot9 \\ =135 \end{gathered}[/tex]So area of shaded region is 135 square inch.
Drag each tile to the correct box.Arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the function thateventually has the greatest value.3x + 8+4+3x² + 63x4*
Answers
To answer the question we are going to graph the functions given:
From the graph we notice that the order will be:
[tex]\begin{gathered} 3x \\ 3x+8 \\ x^2 \\ x^2+6 \\ 4^x \\ 4^x+3 \end{gathered}[/tex]What is the exact volume of the figure?5 om12 cm(The figure is not to scale.)cm3V=(Type an exact answer in terms of A.)
Answers
Explanation
The volume of a cone is one third the area of the base multiplied by the height of the cone:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]This cone has a radius of 5cm and a height of 12cm. The volume is
[tex]\begin{gathered} V=\frac{1}{3}\pi(5\operatorname{cm})^2(12\operatorname{cm}) \\ V=\frac{1}{3}\cdot\pi\cdot5^2\cdot12\cdot cm^{2}cm \\ V=\pi\cdot\frac{1}{3}\cdot25\cdot12\operatorname{cm}^{3} \\ V=\pi\cdot\frac{300}{3}cm^{3} \end{gathered}[/tex]Answer
The volume of the figure is:
[tex]V=100\pi cm^{3}[/tex]The polynomial P(x) = 5x^3 + 2x^2- 42 has ___ local maxima and minima
Answers
SOLUTION:
Case: Local maxima and local minima
Given:
[tex]P(x)=5x^3+2x^2-42^{}[/tex]Required: To find the local maxima and minima
Method:
[tex]\begin{gathered} P(x)=5x^3+2x^2-42^{} \\ \text{ } \end{gathered}[/tex]First the find the first derivative:
[tex]\begin{gathered} P^{\prime}(x)=15x^2+4x \\ we\text{ make P'(x) = 0} \\ 15x^2+4x=\text{ 0} \\ x(15x+4)=0_{} \\ x=0\text{ or 15x+4 =0} \\ x=\text{ 0 or x= }\frac{-4}{15} \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = 0. The points are {-1, 1}.
[tex]\begin{gathered} \text{when x=-1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(-1)=15(-1)^2+4(-1) \\ P^{\prime}(-1)=15(1)^2-4 \\ P^{\prime}(-1)=15^{}-4 \\ P^{\prime}(-1)=11 \\ \text{when x= 1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(1)=15(1)^2+4(1) \\ P^{\prime}(1)=15^{}+4 \\ P^{\prime}(1)=19 \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = -4/15. The points are {-1, 0}
[tex]\begin{gathered} \text{when x= 0} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(0)=15(0)^2+4(0) \\ P^{\prime}(0)=0^{}+0 \\ P^{\prime}(0)=0^{} \end{gathered}[/tex]Final answer:
The local minima is at x= 0 while the local maxima is at x= -4/15
"A quadrilateral is a square if and only if it has fourright angles."Which of the following terms provides acounterexample for why the biconditional statement is
Answers
Given statement: A quadrilateral is a square if and only if it has four right angles
Counterexample: A quadrilateral with four right angles can be also a rectangle. Then, not all quadrilaterals with four right angles are squares.
Answer: Rectangle
Commercial agents earn 5% of the cost of each product they sell. If an agent earsn $2000 for selling a product, what was the cost of the product?
Answers
Answer: 40,000
Step-by-step explanation: 5 (the earnings) times twenty is 100 (the total cost) and if we substitute 5 for 2000, the total is 40,000.
Answer: 40,000
Step-by-step explanation:
just because
The angle of elevation to the top of a 10-story skyscraper ismeasured to be 3° from a point on the ground 2000 feet fromthe building. What is the height of the skyscraper to thenearest hundredth of a foot?
Answers
ANSWER :
The height is 104.82 feet
EXPLANATION :
The angle of elevation to the top of the building is 3 degrees from a point that is 2000 feet away from the building.
Using tangent function :
[tex]\tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}[/tex]The opposide side to the angle is H and the adjacent side is 2000 feet.
Then :
[tex]\begin{gathered} \tan3=\frac{H}{2000} \\ \\ H=2000\tan3 \\ H=104.816\sim104.82\text{ }ft \end{gathered}[/tex]What is the value of x in the triangle?a right triangle with a short leg of length x and hypotenuse of length 3 times the square root of 2A. B. C. D. E.
Answers
Solution:
Given the right triangle below:
To solve for x, we use the trigonometric ratio.
In the above triangle, the angles at A and B are equal.
Thus, we have
[tex]\begin{gathered} \angle A+\angle B+\angle C=180(su\text{m of angles in a triangle\rparen} \\ \angle A=\angle B \\ thus, \\ 2\angle\text{B+90=180} \\ \Rightarrow2\angle\text{B=180-90} \\ 2\angle\text{B=90} \\ \Rightarrow\angle\text{B=45} \end{gathered}[/tex]From trigonometric ratio,
[tex]\sin\theta\text{=}\frac{opposite}{hypotenuse}[/tex]In this case, θ is the angle at B, which is 45; opposite is AC, and hypotenuse is AB.
Thus,
[tex]\begin{gathered} \sin45=\frac{x}{3\sqrt{2}} \\ \Rightarrow x=3\sqrt{2}\times\sin45 \\ =3\sqrt{2}\times\frac{1}{\sqrt{2}} \\ =3 \end{gathered}[/tex]Hence, the value of x is
[tex]3[/tex]The correct option is B
A fuelling vehicle finished filling a plane with 12.40 tons of fuelat 10:35. If the fuelling rate is 0.20 ton of fuel per min, at whattime did the fuelling start? Give your answer in a 12-hour clockformat, such as 9:00.9:33xHmm, that wasn't the right answer. Let's give it one more try.
Answers
Manuel is planting grass seed in a rectangular lot that is 156 inches long and 228 inches wide. How wide is the deck in feet?
Answers
1 foot = 12 inches
The width of the rectangular lot = 228 inches
To change it to feet divide it by 12
The wide of the deck = 228/12 = 19 feet
The answer is 19 feet
Answer To this question so that we can move on to the next question so we can get all this homework done
Answers
y^(3)-27=9y^(2)-27y. could you please show steps
Answers
The solution to the algebraic expression is y =3
Algebraic expressionThis algebraic expression contain variable and constant along with unknow variables.
y^(3)-27=9y^(2)-27y
Add 27y to both sides
y^(3)-27 +27y =9y^(2)-27y +27y
Simplify
y^3-27 +27y =9y^2
Subtract 9y^2 from both sides
y^3-27 +27y-9y^2 =9y^2- 9y^2
y^3-27 +27y-9y^2= 0
Simplify
y^3 - 9y^2 + 27y - 27 =0
Factor by grouping y^3 - 9y^2 + 27y - 27 ; (y-3)^3
(y -3) (-y^2 + 6y -9) = 0
(y-3)^3 =0
Using the zero factor principle if ab = then a = 0 or b= 0
y-3= 0
Add 3 to both sides
y =3
Therefore, solution to the algebraic expression is y =3
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Find the values of A, B, and C in the table.Intervalfa) for a in Relation ofinterval fa) to x-axis(0, 1)f(-2)= -12below(-1, A)f(0)=Babove(A, 2)f (1.5) -0.6(2,)f(3) = 8above
Answers
From the first line of the table, it shows
[tex]f(-2)=-12[/tex]This means that
when x = -2, y = -12,
so
[tex]a=-2[/tex]Now,
Ever NL OP N 2 PN, and is the midst of MO. PALUN APON STATEMENTS REASONS: 2. Nisthe MO 1. Gren Given the following proof, what is the 5th reason? 2 MZ - OP 2. Given 3. IN EN 3. Given 2 MIN ON 4. Definition of midpoint 5 5. ALMN 2 APON SAS CPCTC SSS ASA
Answers
In this case, we have to use the SSS Postulate for the congruency of the triangles, that is, if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.
We have that all reasons are given congruent sides. The midpoint divides the segment into two equal parts, then the angles are congruent because of the reason: SSS ( SSS Postulate for congruency of triangles).