Graph the polynomial function. Note x- and y-intercepts, multiplicity, and end behavior.h(x) = (x − 1)3(x + 2)2
Answers
Given:
[tex]h\left(x\right)=\left(x-1\right)^3\left(x+2\right)^2[/tex]To graph the given polynomial function, we can plug in any values of x to find values of h(x). The graph is shown below:
We also note that the x-intercept is the point on the x-axis, while the y-intercept is the point on the y-axis. Hence,
x-intercepts: (1,0), (-2,0)
y-intercept: (0,-4)
Tt can also be noted that (x − 1) occurs 3 times while (x+2) occurs 2 times. Hence, x=1 has a multiplicity 3, while x=-2 has a multiplicity 2.
aased on the graph, the end behavior would be:
[tex]as\text{ x}\rightarrow+\infty,h(x)\rightarrow+\infty,\text{ and as x}\rightarrow-\infty,h(x)\rightarrow-\infty[/tex]
Related Questions
2(p + 19) = 8 im very confused please help
Answers
⇒2 will multiply everything in the brackets.
[tex]2(p)+2(19)=8\\2p+38=8\\[/tex]
⇒Now I will group like terms to solve for p. Note those that cross the equal sign change sign
[tex]2p=8-38\\2p=-30\\\frac{2p}{2} =\frac{-30}{2} \\p=-15[/tex]
We found that p=-15
An operation has experienced total sales of $85,000, beverage costs of $16,230, food costs of $30,167, labor costs of $22,158, rent of $4,000, and insurance of $1,000.
What is its prime cost as a percentage of total sales?
O 86.6%
19.3 %
O 13.4%
O 80.7%
Answers
Answer: 80.7%
Step-by-step explanation: COGS (beverage and food costs) = $68,555
$68,555 is 80.6529412% of $85,000 rounded to the nearest tenth is 80.7%
What is the area of a quadrilateral with vertices at (-2,-6),
(1,6), (-2,0), and (1,0)? Enter the answer in the box.
units squared
Answers
Check the picture below.
so the quadrilateral is really two triangles, each with a base of 3 and a height of 6
[tex]\stackrel{\textit{area of the two triangles}}{2\left[ \cfrac{1}{2}(\underset{b}{3})(\underset{h}{6}) \right]\implies 2(9)\implies} \text{\LARGE 18}[/tex]
COMMER MATHEMATICSGross pay with commission and salaryColumbia Mirror and Glass pays Eric Lee a $1730 monthly salary plus a 12% commission on merchandise he sells each month. Assume Eric's sales were $87,400 for last month.Calculate the following amounts:1. Amount of Commission2. Gross Pay
Answers
Answer:Explanation:
(a)$10,488
(b)$12,218.
• ric;' Monthly Salary = $1,730
,• Percentage commision = 12%
Part A
f Eric 's sales were $87,400 for last month, his amount of commission will be:
[tex]\begin{gathered} Commision=12\%\text{ of Sales} \\ =\frac{12}{100}\times87400 \\ =\$10,488 \end{gathered}[/tex]Eric's amount of commission is $10,488.
art B
Eric's gross pay will be the sum of his monthly salary and commission.
[tex]\begin{gathered} \text{Gross Pay=Salary+Commission} \\ =1730+10488 \\ =\$12,218 \end{gathered}[/tex]Eric's gross pay is $12,218.
Write the equation of the linear relationship in slope-intercept form, using decimals as needed. The equation that represents this relationship is y=
Answers
Given
Point A = (25, 98)
Point B = (55, 92)
Procedure
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
[tex]\begin{gathered} m=\frac{92-98}{55-25} \\ m=\frac{-6}{30} \\ m=-\frac{1}{5} \\ \end{gathered}[/tex]Now, what about b, the y-intercept?
[tex]\begin{gathered} b=y-mx \\ b=92+\frac{1}{5}\cdot55 \\ b=92+11 \\ b=103 \end{gathered}[/tex]The equation of the line that passes through the points
(25,98) and (55,92)
[tex]y=-\frac{1}{5}x+103[/tex]Help!
A. 8
B. 64
C. 16
D. 12
Answers
Answer:
A. 8
Step-by-step explanation:
Geometric mean= √(4×16) = √64 = 8
What is the domain of the exponential function shown below?
F(x)=2• (1/10)^x
O A. All real numbers except 2
о B. x>0
о C. x<0
O D. All real numbers
Answers
We can replace x with any real number, positive or negative. We can also plug in x = 0. There aren't any restrictions to worry about with the input.
Examples:
Plug in x = 2 to get f(2) = 2(1/10)^2 = 0.02
Plug in x = -2 to get f(-2) = 2(1/10)^(-2) = 200
Plug in x = 0 to get f(0) = 2(1/10)^(0) = 2
The domain of the given function is "All real numbers". So, option D is correct.
What is the domain of a function?The domain of a function is the set of possible values as inputs to the function. The Domain of the exponential function is the set of all real numbers represented by R.
here, we have,
Finding the domain of the given function:
The given function is f(x) = 2×
Since this function has the variable x in the exponent, this is an exponential function.
So, its inputs are of all real numbers. And the domain is {x:x ∈ R}.
Thus, option D is true.
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If one value of arctan A is 37°, find another value of arctan A in the interval [0°, 360°).
Answers
Answer:
217°
Step-by-step explanation:
the tangent ratio is positive in the first and third quadrants.
37° is the angle in the first quadrant
then the angle in the third quadrant is
180° + 37° = 217°
how many solutions does the system of equations graphed below have?A. infinite B. 0C. 2D. 1
Answers
The answer is letter B. Zero.
The solution is the point in which two lines cross, but here we observe to parallel lines, there is no intersection. So there is no solution.
Two angles of a triangle have the same measure and the third one is 21 degrees greater than the measure of each of the other two. Find the
measure of the largest angle in the triangle.
Answer: The largest angle has a measure of
degrees
Answers
Answer:
Since two angles of the triangle have the same measure, the triangle is an isosceles triangle.
Let one angle be a variable (eg: x) so we can form expressions and solve.
Let the first and second angle be x°.
Form an expression for the third angle using the information given.
Third angle = (x + 21)°
Since sum of angles in a triangle is 180°, we can form an equation.
x + x + (x + 21) = 180
Simplify and solve for x.
3x + 21 = 180
3x = 159
x = 53
Largest angle is the third angle.
Substitute x into the expression to find the value.
Third angle = 53 + 21
= 74°
Station 5
The ratio of the number of dollars Jada has to the number of dollars Kelly has is 4:7. Kelly
gives Jada $6.00. The ratio of the number of dollars Jada has to the number of dollars Kelly
has changes to 6:5. How many dollars do Jada and Kelly each have now?
Answers
The number of dollars Jada and Kelly each have now is $18 and $15.
What are ratios?Mathematicians refer to a comparison of two or more integers as a "ratio."It acts as a measuring tool to demonstrate how large or small one amount is in contrast to another. In a ratio, two quantities are compared by utilizing division. The "antecedent" in this instance is the dividend, while the "consequent" is the divisor.Given:
Ratio of the number of dollars Jada has to the number of dollars Kelly has = 4:7
Changed ratio after Kelly gives Jada $6.00 = 6:5
Let the number of dollars Jada and Kelly have be 4x and 7x.
Kelly gives Jada $6.00,
So,
Number of dollars Jada has now is $(4x + 6).
Number of dollars Kelly has now is $(7x - 6).
The ratio of the number of dollars is changed to 6:5.
⇒ [tex]\frac{4x + 6}{7x -6} = \frac{6}{5}[/tex]
⇒ 5(4x + 6) = 6(7x - 6)
⇒ 20x + 30 = 42x - 36
⇒ 42x - 20x = 30 + 36
⇒ 22x = 66
⇒ x = 3
Number of dollars Jada has now = (4x + 6) = $18
Number of dollars Kelly has now = (7x - 6) = $15
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Andy Foll is 6 times as old as Mel Kaas. Andy is 15 years older than Mel. What is Mel's age?
Answers
Answer:
9
Step-by-step explanation:
sostrict 16 4fg _d-5=9
why do you think its difficult For students to understand that the product of two negative integers is positive, and what (if anything) can be done to help Student's understand this idea?
Answers
The product of any two negative numbers is positive.
Consider a positive number to be something as a gift, and a negative number to be something you give to me.
So, let's say you get 4 laptops from me, and - 4 means you give away 4 laptops to me.
Now when you say - 4 + - 4 + - 4 + - 4 + - 4.
This means that you are giving away 4 laptops 5 times to me, so basically you have given away 20 laptops, which means I have 20 laptops and you have - 20.
Now, - 4 * - 5 means, you give away 5 laptops, for - 5 times to me. But the second number is - 4, so the receiver, that is me, is giving it back to you. Thus indirectly, you gave away 4 chocolates to yourself 5 times. Thus you have 20 laptops.
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Can someone please help me with this geometry question
Answers
Triangles 2, 4, 6, 8, 9, 10, 12, 14, and 15 are not translations of triangle 1.
What is translation?In mathematics, a translation is an up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered. There is no change in the shape because it is simply being moved from one location to another.
The object may move left at first, then right, and so forth. The object's position can change, as well as the manner in which it does so. Each point on the shape will move by the same number of units during translation.
Therefore, triangles 2, 4, 6, 8, 9, 10, 12, 14, and 15 are not translations of triangle 1.
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Identify the domain and range of y = [x] + 2.
Answers
The most appropriate choice for function, domain and range of a function will be given by
Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers
Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.
What is Function, Domain and Range of a function?
Function
A function from A to B is a rule that assigns to each element of A a unique element of B
Domain of a function
Domain of a function is the set of values for which the function is defined.
Range of a function
The set of values obtained on putting the values of the domain is called the range of a function.
Here,
Domain of [tex]y = [x] + 2[/tex]
[tex][x][/tex] is defined for all [tex]x[/tex] ∈ [tex]\mathbb{R}[/tex], the set of real numbers
Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers
[tex][x][/tex] is the greatest integer not exceeding [tex]x[/tex]
So [tex][x][/tex] [tex]+ 2[/tex] gives only integer values
So Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.
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how many 42’’ wide wall panels must be bolted together to create a 28’ wall?
Answers
From the question, we were asked that how many 42 inches wide panels must be bolted together to create a 28 feet wall.
First let's covert the two measurement to same unit.
So, lets convert 42 inches into feet.
Recall, 1 foot will give 12 inches
42 inches will be:
42/12 = 3.5 feet
Therefore, the wide wall that must be bolted together to create a 28 feet wall is:
= 28/3.5
= 8 feet.
In a class of 42 students, 25 take biology,15 take history,and 18 take biology but not history.i.Draw a Venn diagram to show the informationii.find how many students take niether history nor biology
Answers
In the class, there is a total of 42 students.
25 take biology.
15 take history.
18 take biology but not history.
There are four situations that you have to include in the Venn diagram:
"The students take only biology"
"The students take only history"
"The students take biology and history"
"The students take neither classes"
To draw the Venn diagram, you have to make one circle for each subject, i.e. one circle for biology and one for history, and label them.
Then you have to enter the similarities between both subjects, this means, where the circles overlap, you will find the students that take both subjects.
Finally, outside the circles, you will find the students that take neither subject:
Now, you have to determine how many students are included in each part of the Venn Diagram.
1) You know that 25 students take biology and that 18 take biology but not history, to determine the number of students that take both subjects, you have to calculate the difference between both values:
[tex]25-18=7[/tex]7 students take biology and history.
2) 15 students take history out of these you know that 7 take also biology. To determine the number of students that take only history, you have to calculate the difference between both values:
[tex]15-7=8[/tex]8 students take history but not biology.
3) To determine the number of students that take neither class, you have to subtract to the total number of students, those who take only biology plus those who take only history plus those who take both classes:
[tex]\begin{gathered} \text{Neither}=\text{Total-(only biology + only history + both)} \\ \text{Neither}=42-(18+7+8) \\ \text{Neither}=42-33 \\ \text{Neither}=9 \end{gathered}[/tex]9 Students of the class take neither class.
Finally, you can write each value in the corresponding part of the Venn diagram:
• Inside the green circle, you have to include the 18 students that take only biology.
,• Inside the blue circle, you have to include the 8 students that take only history.
,• Where both circles overlap, you have to include the 7 students that take both classes.
,• Outside the circles, you have to include the students that take neither.
Need to work out problem 7
Answers
Ratio of A to B = 3/4
Ratio of B to C = 12/5
Multiply the ratio of A to B by 3/3
[tex]\begin{gathered} \text{Ratio of A to B = }\frac{3}{4}\times\frac{3}{3} \\ \text{Ratio of A to B = }\frac{9}{12} \end{gathered}[/tex]Comparing the ratio of A to B and the ratio of B to C:
Ratio of A to B to C = 9 : 12 : 5
Total ratio = 9 + 12 + 5 = 26
Value of C = (5/26) x Total value
60 = (5/26) x Total value
Total value = (60 x 26)/5
Total value = 312
Value of A = (9/26) x Total value
Value of A = (9/26) x 312
Value of A = 9 x 12
Value of A = 108
Mr. Berber gives a bookmark or pencil for each book that he sells.
Each bookmark costs Mr. Berber $0.75.
• Each pencil costs Mr. Berber $0.25.
Mr. Berber sold a total of 352 books.
Of the items Mr. Berber gives with each book,
3/4
Which statements are true?
Select TWO correct answers.
were pencils and the rest were bookmarks.
Mr. Berber wants to find how much the bookmarks cost him.
Answers
Answer:
264
Step-by-step explanation:
0.75x352
8. Solve for x:
2/3 (2x - 1/2)=13
Answers
Hello! So...
We are given the following to solve:
Solve for x.
[tex]\frac{2}{3} (2x-\frac{1}{2})=13[/tex]
_______________________________________
1. Multiply both sides by 3.
[tex]3[/tex] × [tex]\frac{2}{3}(2x-\frac{1}{2})=13[/tex] × [tex]3[/tex]
_______________________________________
2. Simplify.
[tex]4x-1=39[/tex]
_______________________________________
3. Add 1 to both sides.
[tex]4x-1+1=39+1[/tex]
_______________________________________
4. Simplify.
[tex]4x=40[/tex]
_______________________________________
5. Divide both sides by 4.
[tex]\frac{4x}{4} =\frac{40}{4}[/tex]
_______________________________________
6. Simplify.
[tex]x=10[/tex]
^Hence, our solution.
__________________________________________________
Hope this helps! If you need anything else, don't hesitate to comment below and I'll see what else I can do for you. Thanks and good luck!
Teresa, Pablo, and Deon served a total of 55 orders Monday at the school cafeteria. Teresa served 9 fewer orders than Deon. Pablo served 2 times as many orders as Deon. How many orders did they each serve?
Answers
Deon served 16 orders. Pablo served 32 orders. Teresa served 7 orders.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let Deon order be x , since Teresa served 9 fewer orders than Deon. , then Teresa order is x - 9,
since Pablo served 2 times as many orders as Deon, it means Pablo's order is 2x . combining all
Deon 's orders = x
Pablo's order = 2x
Teresa 's order = x - 9
Total order = 55
Then
x + 2x + x - 9 = 55
4x - 9 = 55
4x = 55 + 9
4x = 64
x = 16
Therefore :
Deon served 16 orders
Pablo served orders = 32 orders
Teresa served 16 - 9 orders = 7 orders
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A multivitamin tablet contains
10.5 mg of calcium how much calcium does a bottle of 40 tablets contain
Answers
The bottle of 40 tablets will contain 420 milligrams of tablets.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
Given that a multivitamin tablet contains 10.5 mg of calcium and there are 40 tablets in the bottle. The total amount of the tablets in the bottles will be calculated as:-
Total tablets = 10.5 mg x 40
Total tablets = 420 mg
Therefore, a bottle of 40 tablets will contain 420 milligrams of tablets.
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The red figure is congruent to the blue figure. Describe a sequence of rigid motions between the figures.
Answers
The sequence of transformations is:
Reflection across the x-axis followed by a translation of 5 units to the left.
Which sequence of transformations will map the red figure into the blue one?We start with the red figure, the first thing we should apply is a reflection across the x-axis.
Doing this, we will see that both figures are in the same orientation, while in different positions.
At this point, we should do a translation to the left of 5 units, this will move the whole red figure 5 units to the left and that will map the red figure into the blue one.
Notice that if the transformations are applied in the other order (first the translation and then the reflection) we will get the same outcome.
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Write an expression for the amount of money (in nickels) in n dollars.
PLEASE HELP ITS DUE IN AN HOUR
Answers
Answer:
11 nickels . Are in a doldollar
Step-by-step explanation:
You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week.
Answers
The number of weeks for your friend's savings to be same as your savings does not exist
How to determine the number of weeks?The given parameters are:
Your savings account
Initial amount = $100
Weekly savings = $40
Your friend's savings account
Initial amount = $80
Weekly savings = $10
The equation that represents the amount in the account after w weeks is represented as
Amount = Initial amount + Weekly savings x Number of weeks
This gives:
You: Amount = 100 + 40x
Your friend = 80 + 10x
The above equations are linear equations
When the amounts are equal, we have
100 + 40x = 80 + 10x
This gives
30x = -20
Divide
x = -2/3
The number of weeks cannot be negative
Hence, your friend's savings will never be up to your savings
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Possible question
You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week.
When will you and your friend have the same amount?
From the choices below, choose an expression that is equivalent to the expression:
22/-4
A. (-22|-4 )
B. 22|4
C. -(22|-4)
D. -(22|4)
Answers
Answer: b
Step-by-step explanation:
Please show work
I will mark brainliest
Answers
As a result, the value of x is 20. Vertically opposite angles are formed by two straight intersecting lines that are opposite one another at a specific vertex.
What is vertical opposite angle?Vertically opposite angles are formed by two straight intersecting lines that are opposite one another at a specific vertex. Angles that are vertically opposite each other are equal. These are sometimes referred to as vertical angles.Here to find y,
∠A = ∠B ( vertically opposite angles are equal ).
5y - 8 = 42
5y = 42 +8
5y = 50
y = 10
To find ∠A,
∠ A = 5y - 8
= 5 x 10 - 8
= 50 -8
= 42°.
we know that angle on a straight line is 180°.
So , ∠A + ∠C = 180°
42 + ∠C = 180°
∠C = 180 - 42
∠ C = 138°.
Since ∠C = ∠D (vertically opposite angle ).
∠D = 138°
As a result, the value of x is 20.
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what is 2 times 5 divided by 76 and subtreacted by 12
Answers
Answer:
-11.8684210526
Step-by-step explanation:
Please answer with if the slope is positive or negative and what the slope is.
Answers
Answer:negative slope, slope=-3/5
Step-by-step explanation:
To find slope:
Rise/Run
Rise/Run: down 3 left 5 so -3/5
Which equation represents twenty-nine is one-third of the number n?
one third equals n over 29
29 equals n over 3
29 = 3n
3 = 29n
During a sleepover, Carissa played karaoke with her friends. Her song was 6 minutes long. She had already sung for 4 minutes. Which equation could be used to see how much longer she will have to sing?
x + 2 = 6
x + 4 = 10
x + 4 = 6
x − 4 = 6
Dontavious has a box of colored pencils. He uses 53 pencils and has 118 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
53 + p = 118
118 + p = 53
p − 53 = 118
p = 118 − 53
Julia has a square poster of a puppy on her bedroom wall. The width is one-fourth the length of the picture. If the width is 24 inches, write and solve an equation to determine the length.
L over 4 equals 24; L = 96 inches
4L = 24; L = 6 inches
4 + L = 24; L = 20 inches
L − 4 = 24; L = 28 inches
Answers
Answer:
1) 29 equals n over 3
2) x + 4 = 6
3) p − 53 = 118
4) L over 4 equals 24
Step-by-step explanation:
1) twenty-nine is one-third of the number n is
29 = 1/3 • n
29 = 1/3 • n/1
29 = n/3
So, the answer is 29 equals n over 3
2) The song was 6 minutes long and she has already sung 4 minutes
Let's find the equation to be used to see how much longer she will have to sing?
? + 4 = 6
x + 4 = 6
3) The equation to be used to find the pencils left according to the question is p − 53 = 118 since he has 118 pencils left out of collecting 53 pencils so the remaining pencil would be 118 - 53
Where, p is representing the pencil remaining
So, the answer is p − 53 = 118
4) I think you made a typo in this question
Correction
Julia has a square poster of a puppy on her bedroom wall. The length is one-fourth the width of the picture. If the width is 24 inches, write and solve an equation to determine the length
Answer
so the answer to this question is L over 4 equals 24
L/4 = 24
L = 24*4
L = 96
so, the length is equal to 96 inches and the equation is L over 4 equals 24