The zeros of the function f(x) = x³ + 9x² + 20x is :
0, 5 ,4
Explanation :Steps to solve quadratic equation:
Put all of the terms on one side of the equal sign and zero on the other.Factor.Set each factor to a value of zero.Each of these equations must be solved.Because they are the values of x for which f(x) = 0, the solutions of the quadratic equation ax² + bx + c = 0 correspond to the roots of the function f(x) = ax² + bx + c.Check your answer by plugging it into the original equation.
Given function,
f(x) = x³ + 9x² +20x
take x common from f(x),
=> x(x² + x - 20) = 0
=> x(x² + 5x + 4x + 20) = 0
=> x( x + 5 ) + 4 ( x +5 ) = 0
=> (x + 5) ( x + 4 ) = 0
=> x -5 = 0 or x -4 = 0
=> x = 5 and x = 4 .
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when sarah planted a tree in her yard it was 24 inches tall it grew at a rate of 2.5 inches per month the tree is now 41.5 inches tall how many months has it been since sarah planted the tree
In linear equations, 103.75 inches per month tall has it been since sarah planted the tree.
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.When an equation is given in this format, finding both intercepts is rather simple (x and y).When attempting to solve systems involving two linear equations, this form is also quite helpful.Sarah planted a tree in her yard = 24 inches tall
grew at a rate =2.5 inches per month
When tree is now 41.5 inches tall = 41 . 5 * 2.5
= 103.75
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19. Write an ordered pair for the point in Quadrant II, that is 8 units away from the point Q
(0.75 -3.25) on a coordinate plane.
An ordered pair of point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)
In this question, we need to find an ordered pair for the point in Quadrant II, that is 8 units away from the point Q(0.75 -3.25) on a coordinate plane.
If we have a coordinate point (x, y) in Quadrant ||, if the coordinate is 8 units away, the resulting coordinate will be expressed as (x - 8, y + 8)
Given the point Q(0.75, -3.25) on the coordinate the plane, if a point in Quadrant II is 8 units away from this point, the resulting point will be (0.75 - 8, -3.25 + 8) which is (-7.25, 4.25)
Therefore, an ordered pair a point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)
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You bought 6 tickets for $40 and wanted to know how many tickets you could get for $200,
you would write the following proportion:
Answer:
30
Step-by-step explanation:
200/40=5
5x6=30
therefore there are 30 tickets you could get with 400$
hope this helped
have a great day ^^
Answer:
30 tickets
Explanation:
One ticket can be represented as variable t.
Using t, we can set up an equation (proportion) using the given information:
[tex]6t = \$ 40[/tex]
Then, we can multiply both sides of the equation (proportion) by something such that the number of dollars on the right side is $200.
[tex]6t \ = \ \$ 40 \\\times 5 \ \ \ \times 5[/tex]
[tex]30t = \$ 200[/tex]
So, we can get 30 tickets for $200.
Adam is baking 4 pizzas. Each pizza is a rectangle. It takes Adam 35 minutes to bake the pizzas. He divides each pizza into the equal-size square slices shown.
Answer:
Step-by-step explanation:
Incomplete question.
Chelsy wants to buy a new pair of jeans in one store the jeans are selling for 1/5 off the original price of $70 in second store the same jeans are selling for 1/3 off the original price $81 chelsy wants to buy the cheaper pair of jeans in which store should chelsy buy the jeans and how much will they cost
iN linear equations, store 1 jeans is cheaper than store 2.
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.When an equation is given in this format, finding both intercepts is rather simple (x and y).When attempting to solve systems involving two linear equations, this form is also quite helpful.one store the jeans are selling for 1/5 off the original price of $70
$70 * 1/5 = 14
second store the same jeans are selling for 1/3 off the original price $81
$81 * 1/3 = 27
So, store 1 jeans is cheaper than store 2.
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Describe how the change affects the volume of the prism or pyramid. Multiplying the height by 3/2.
Answer:
1512 cm²
Volume is also multiplied by [tex]\dfrac{3}{2}[/tex]
Step-by-step explanation:
The volume of a pyramid is given by the expression
[tex]V = \dfrac{1}{3} l\cdot w\cdot h[/tex]
where l = base length, w = base width and h = height
The volume of this pyramid
[tex]= \dfrac{18\cdot 12\cdot 14}{3} = 1008\; cm^3[/tex]
If we multiply the height by [tex]\dfrac{3}{2}[/tex] then new height
= [tex]14 \cdot \dfrac{3}{2} = 21 cm[/tex]
New Volume [tex]= \dfrac{18\cdot 12\cdot 21}{3} = 1512\; cm^3[/tex]
[tex]\dfrac{\text{NewVolume}}{\text{Old Volume}} = \dfrac{1512}{1008} = \dfrac{3}{2}[/tex]
So volume is also multiplied by 3/2
Ariya likes to play golf. The number of times per year that she plays depends on the price of playing a round of golf, Ariya's income, and the price of other types of entertainment-in particular, the price of going to a movie instead of playing golf. The three demand schedules in the following table show how many rounds of golf per year Ariya will demand at each price per round under three different scenarios. In scenario D1, Ariya's income is $50,000 per year and movies cost $9 each. In scenario D2, Ariya's income is also $50,000 per year, but the price of seeing a movie rises to $11. And in scenario D3, Ariya's income goes up to $70,000 per year, while movies cost $11.
Scenario
Income per year
Price of movie ticket
Price of Golf
$50
$35
$20
D1
$50,000
$9
15
25
40
D2
$50,000
$11
Quantity Demanded
10
15
20
D3
$70,000
$11
15
30
50
Answer:
Using the data under D1 and D2, calculate the cross elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the cross elasticity of demand.) At $50, cross elasticity = -2.40 ± 0.05At $35, cross elasticity = -3.00 ± 0.05At $20, cross elasticity = -4.00 ± 0.05Is the cross elasticity the same at all three prices? No. Are movies and golf substitute goods, complementary goods, or independent goods? Complementary goods.b. Using the data under D2 and D3, calculate the income elasticity of demand for golf at all three prices. (To do this, apply the midpoints approach to the income elasticity of demand.) At $50, income elasticity of demand = 1.40 ± 0.05At $35, income elasticity of demand = 2.33 ± 0.05At $20, income elasticity of demand = 3.00 ± 0.05Is the income elasticity the same at all three prices? No. Is golf an inferior good? No, it is a normal good.
The required statement is given as the data tends to the normal good.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Calculate the cross elasticity of demand for golf at each of the three prices using the information under D1 and D2.
At $50, the cross elasticity is equal to -2.40 ± 0.05;
At $35, it is - 3.00± 0.05;
At $20, it is - 4.00 ±0.05.
No golf and movies complementary, independent, or alternative goods complementing products b.
Calculate the income elasticity of demand for golf at each of the three prices using the information under D2 and D3.
At $50, the income elasticity of demand is equal to 1.40±0.05
At $35, it is 2.33± 0.05
At $20, it is 3.00± 0.05
Thus, the required statement is given as the data belong to the normal good.
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What is the range of the function f(x) = |x – 5| – 3?
R: {f(x) ∈ ℝ | f(x) > 2}
R: {f(x) ∈ ℝ | f(x) < 2}
R: {f(x) ∈ ℝ | f(x) ≥ –3}
R: {f(x) ∈ ℝ | f(x) ≤ –3}
Reason:
The smallest |x-5| can get is 0 since the result of an absolute value is never negative (because it represents distance).
So the smallest f(x) = |x-5|-3 can get is 0-3 = -3
f(x) = -3 or f(x) > -3 are the only two options for the output f(x).
Condense that into [tex]f(\text{x}) \ge -3[/tex] to arrive at choice C as the final answer.
The fancy notation of f(x) ∈ ℝ translates to "f(x) is a real number".
If you were to graph this using a tool like Desmos, then notice how the lowest point occurs when y = -3
See the diagram below.
Answer:
R: {f(x) ∈ ℝ | f(x) ≥ –3}
Step-by-step explanation:
I got it right on the test.
Please help I’ll mark you as brainliest if correct!!
Answer:
14, 9, 16
Step-by-step explanation:
from 3 to 10, you add 7
from 10 to 5, you minus 5
from 5 to 12, you add 7
from 12 to 7, you minus 5
so the pattern is add 7, minus 5
7 plus 7 is 14
14 minus 5 is 9
9 plus 7 is 16
Which pair of angels are alternate exterior angles
○ <1and <2
○ <1and<7
○ <2and<7
○ <2and<5
∠2 and ∠7 are a pair of angels are alternate exterior angles .
A transversal that crosses two parallel lines results in alternate exterior angles.
They form two pairs of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal (four total angles).When a third line, a transversal, separates two lines, the expression "alternating exterior angles" is frequently used. The alternate exterior angles theorem states that pairs of alternate exterior angles are congruent if k and l are parallel. A: One of two internal angles inside the two intersecting lines, also known as an alternate internal angle. B: One of two angles with distinct vertices that are on opposite sides of a transversal at the intersection of two other lines.So from the given figure the pairs of external alternate angles are:
∠1 and ∠8
∠2 and ∠7
Hence of the given options , ∠2 and ∠7 is the required external alternate angles .
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An agency charges $100 per person for a trip to a concert if 50 people travel in a group. But for each person above the 50, the amount charged for each traveler will be reduced by $3. If x represents the number of people above the 50, write the agency's revenue R as a function of x. (Assume that x is greater than zero.)
R(x)
The revenue of the the agency is given by the function
R(x) = 5000 - 50 x - 3x² .
A function is a relationship between an independent variable and a dependent variable which defines all points on a cartesian plane which satisfies the given condition.
The set of the independent variables is called a domain and the set of the dependent variable of the function is called a range.Each data in range is related to a particular data in the domain by the function.Now in the given Agency it is given that the charge of each tourist is $100 . Now for every tourist above 50 the charge is reduced by 3 dollars.
So for x people above 50 charge will be ( 100-3 x ) for all members.
The total revenue can be measured by the function
R(x) = ( 50 + x ) ( 100 - 3x )
or , R(x) = 5000 - 150 x + 100 x - 3x²
or, R(x) = 5000 - 50 x - 3x²
Hence the revenue function is given as : R(x) = 5000 - 50 x - 3x²
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The graph of y = f (x) is given. Graph the indicated function.Graph y = f (-x) - 4
Note the - sign in the evaluation of f(x), which changes the function directly, and the term -4 indicates a displacement vertically (down), but the graph goes up because of the sign -, therefore, the only option with these conditions is option b.
The correct answer is option b.
how many 5 digit numbers can be created using the digits 2,3,4,7,8 and 9 without repeating any digits in that five digit number
Answer:
there are 720 three digit numbers that can be created from the digits provided given that no digit may be repeated.
Step-by-step explanation:
How to find the slope of a graph? 9 and 10
9. To draw the rise, you can follow these steps:
- Identify a point on the line. In this case, this can be:
[tex](-3,1)[/tex]- Draw a vertical line that rises from that point. See the picture below:
10. To draw the line that represents the run, you need to Draw a horizontal line that goes from the endpoint of the line that represents the rise and extend it until it touches the function. See the picture below:
Therefore, the answers are (See the picture):
ANSWER FAST: 4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. find the capacity 1 thumb drive and the capacity of 1 compact disk.
Capacity of 1 thumb drives = 4 gigabytes.
Capacity of 1 compact disk = 2 gigabytes.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Let capacity of a thumb dives = x
And, Capacity of a compact disk = y
Then, For first condition;
''4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes.''
We can formulate;
4x + y = 18 .... (i)
And, For second condition;
'3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes.'
We can formulate;
4x + 3y = 22 .... (ii)
Solve the equation (i) and (ii) we get;
Subtract (ii) by equation (i) we get;
2y = 4
y = 2
And, 4x + 2 = 18
4x = 16
x = 4
So, Capacity of 1 thumb drives = 4 gigabytes.
Capacity of 1 compact disk = 2 gigabytes.
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Write the sum. 54+63 as the product of a number and relatively prime addends
54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.
A prime number is a number that can be divided only by 1 and itself.
54+63 (given)
We now have to find the sum of the given numbers as the product of relatively prime numbers.
In order to find the numbers we will find first sum and then factor
Sum=54+63=117
Factors of 117 are 13 and 9
117 = 13 * 9
13 and 9 are relatively prime because the factor of 13 and 9 is 1.
Therefore, 54 + 63 = 13 * 9 is the expression obtained as the product of a number and relatively prime addends.
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Find the x intercepts of the graph of the function.
g(x)=1/4(x-6)(x-3). Hint x intercepts happen when g(x)=0.
The x intercepts of the function given in the question will be equal to x = 6 and x = 3.
A function may be defined as an entity in which for one value of input there is only one value of output. The input value is the value of x variable, or the independent variable and the output value is the value of y variable or the dependent variable. For example, f(x) = y = x + 2, in this function for the value of input x = 1 the value of output is y = 3. The x intercept of a function may be defined as the point on the graph at which the line of function crosses the x axis. For finding the x intercept the y value or the value becomes zero. We are given the function g(x) = (1/4) (x - 6) (x - 3)
Now, g(x) = 0
(1/4) (x - 6) (x - 3) = 0
=> (x - 6) (x - 3) = 0
=> x = 6 and x = 3
Therefore, x intercepts are x = 6 and x = 3.
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If the price of cord of firewood starts at $255 with a quantity supplied of 300 cords, then rises to $348 per cord, what is the new quantity supplied at this price? Assume the slope of the supply curve is 0.75. Round your answer to the nearest cord. A cord of firewood is a stack of wood 4 feet high x 8 feet long x 4 feet deep.
The new quantity supplied when the price is $348 per cord is 424.
What is the new quantity supplied?The supply curve is a graph that shows the relationship between price and quantity supplied. The supply curve has a positive slope.
The slope of the supply curve is the ratio of the change in the value of price divided by the change in the value of the quantity supplied.
Slope = change in price / change in quantity supplied
0.75 = ($348 - $255) / change in quantity supplied
0.75 = $93 / change in quantity supplied
change in quantity supplied = 93 / 0.75 = 124
The new quantity supplied = 300 + 124 = 424
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Brooklyn is trying to pick out an outfit for the first day of school. She can choose from
6 pairs of pants, 8 t-shirts, 3 sweaters or hoodies, and 5 pairs of shoes. How many
different outfits does Brooklyn have to choose from?
Answer:
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attempt 1 out of 2
Answer:
There are 16 ways in which Danny can mix and match all his outfits. You can determine this by multiplying. 4 x 2 x 2. Danny has 4 shirts. He can wear each with two different pants, so 4 x 2 giving 8 different shirt/pant combinations. Now each combination can be worn with two different pairs of shoes, so 8 x 2 giving 16 total combinations of shirt, pants and shoes.
Step-by-step explanation:
How many outfits does that make? First he has to decide on a pair of pants and he has 4 different choices. For each of those choices he has a choice of 7 ...
you would times each one for example 6 x8 6x3 6x5 and 8x6 8x3 8x5 and 3 x6 and so forth
5 is to 7 as 15 is to x.
Answer:
x = 21
Step-by-step explanation:
To get your answer, you can turn these to fractions: 5/7 = 15/x
5 * 3 = 15
7 * 3 = x
x = 21
a=3 and b=6 and c=5 what is ab+bc?
Answer:
you have the values of a, b and c
all you gotta do is just plug them in so
ab+bc is (3)(6)+(6)(5)
which equals 48.
Answer:
48
Step-by-step explanation:
since a=3, b=6 and c=5, you would replace the letters in ab+bc with their numbers, making it (3)(6)+(6)(5). then you would multiply 3 x 6 which would be 18, and 6 x 5, which would be 30, making your expression 18+30. finally you would add them together, making it 48.
5. Which of the following is a rational number that can be written as a decimal in which one or more nonzero digits repeat?
The rational number that can be written as a decimal in which one or more nonzero digits repeat is given by:
D. 5/9.
Which numbers compose the set of rational numbers?The set of rational numbers is composed by numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
For this problem, we have a focus on numbers that have repeating decimal part. The most known case is the division by 9, as when an integer that is not a multiple of 9 is divided by 9, the result is a decimal with a repeating decimal part.
To find the equivalent decimal to 5/9, we divide the numerator of 5 by the denominator of 9, hence:
5/9 = 0.55555...
The decimal digit 5 repeats infinitely, hence option D is correct.
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Heather, Ahmad, and Jim have a total of $68 in their wallets. Heather has $8 less than Jim. Ahmad has 2 times what Jim has. How much does each have?
Answer:
Step-by-step explanation:
1. Set x equal to the amount of money Jim has
Jim's money = x2. Create equations of the amount of money the other people have based on x
Heather's money = x - 8Ahmad's money = 2x3. Now, we set all of these equations as equal to 68
[tex](x)+(x-8)+(2x)=68[/tex]4. Combine the like terms, which means that the previous equation will simplify to:
[tex]4x-8=68[/tex]5. Add 8 to both sides
[tex]8+4x-8=68+8[/tex]This simplifies to: [tex]4x=76[/tex]6. Divide 76 by 4
[tex]\frac{4x}{4} =\frac{76}{4}[/tex]This equals: x = 197. Plug the value of x into the previous equations:
Jim's money: $19Heather's money: [tex]19-8=11[/tex] -> $11Ahmad's money: [tex]2*19=36[/tex] -> $36Final Answer:
Jim has $19Heather has $11Ahmad has $36Write a problem that could be solved by finding 5/8 divided by 2/5.
Answer:107/56 is the answer
At a sale, shirts were sold for $15 each. This price was 20% off their original price. What was the original price?
Answer:
The original price was 18 dollars.
Step-by-step explanation:
Givens
Final price = 15 dollars
Discount = 20%
Original Price = x
Formula
x = 15 + 20/100 15
Solution
x = 15 + 300/100 Multiply 20 * 15. Divide by 100
x = 15 + 3
x = 18
Which decimal is equivalent to39?
Answer: is 7
Step-by-step explanation: Its 7 cuz 14 weeks
I dont understand any of these functions please help on all!
1.The slope -intercept form of the function is y = 7x
2.The slope -intercept form of the function is y = x - 8
3.The slope -intercept form of the function is y = -2x +9
4.The slope -intercept form of the function is [tex]y = \frac{1}{3}x+9[/tex]
5.The slope -intercept form of the function is y = 0.5x - 1.5
6.The slope -intercept form of the function is y = 3x - 12
How is the slope -intercept form calculated?
1. The slope -intercept form of the equation of the function is y = 7x
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{0+7}{0+1} \\\\m= 7[/tex]
Substituting point (-1,-7) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
-7 = 7(-1) + c
c = 7 -7
c = 0
Substituting m and c in (1)
y = 7x
2. The slope -intercept form of the equation of the function is y = x - 8
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{-8+17}{0+9} \\\\m= \frac{9}{9} =1[/tex]
Substituting point (-9,-17) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
-17 = (-9) + c
c = -17 +9
c = -8
Substituting m and c in (1)
y = x - 8
3. The slope -intercept form of the equation of the function is y = -2x +9
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{5-9}{2-0} \\\\m= \frac{-4}{2} =-2[/tex]
Substituting point (0,9) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
9 = -2 (0) + c
c = 9
Substituting m and c in (1)
y = -2x +9
4.The slope -intercept form of the equation of the function is [tex]y = \frac{1}{3}x+9[/tex]
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{8-7}{-3+6} \\\\m= \frac{1}{3}[/tex]
Substituting point (0,9) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
9 = 1/3 (0) + c
c = 9
Substituting m and c in (1)
[tex]y = \frac{1}{3}x+9[/tex]
5. The slope -intercept form of the equation of the function is
y = 0.5x - 1.5
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{1-0.5}{5-4} \\\\m= \frac{0.5}{1}= 0.5[/tex]
Substituting point (5,1) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
1 =0.5 (5) + c
1 -2.5 = c
c = - 1.5
Substituting m and c in (1)
y = 0.5x - 1.5
6. The slope -intercept form of the equation of the function is y = 3x - 12
Slope = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m =\frac{9-3}{7-5} \\\\m= \frac{6}{2}\\\\m= 3[/tex]
Substituting point (5,3) and m in the slope-intercept form of the equation,
y = mx+ c ----(1)
3 =3(5) + c
3 -15 = c
c = - 12
Substituting m and c in (1)
y = 3x - 12
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Which fraction is in simplest form? A. 11 15 B. 12 18 C. 9 21 D. 14 24
Answer : 11 15
Reasoning : The fraction is in simplest form
9 21 is able to be simplified to 3 7,
12 18 is able to be simplified to 2 3
14 24 is able to be simplified to 7 12
How to simplify:
[tex]\frac{5}{2\sqrt{5} }[/tex]
My textbook says the answer is [tex]\frac{\sqrt{5} }{2}[/tex], but I don't know to get there.
Someone pls help
hmmm first of all, let's keep in mind that any expression multiplied by 1 is always the same expression
[tex]12\cdot 1=12\qquad 13567\cdot 1=13567\qquad spaghetti\cdot 1=spaghetti[/tex]
and so on.
now, hmm 1 can be expressed as a rational, 1/1 = 1, but but but, we can really express it as
[tex]\cfrac{9999}{9999}\implies \cfrac{7857}{7357}\implies \cfrac{\sqrt[11]{1375}}{\sqrt[11]{1375}}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{lettuce}{lettuce}\implies \text{\Huge 1}[/tex]
so let's do the so-called rationalizing of the denominator, we can also do it with the numerator btw, but we only need it for the denominator right now, by multiplying for 1 :), 1 is Da Bomb baby!!
[tex]\cfrac{5}{2\sqrt{5}}\cdot \text{\LARGE 1}\implies \cfrac{5}{2\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{5\sqrt{5}}{2\sqrt{5^2}}\implies \cfrac{5\sqrt{5}}{2(5)}\implies \cfrac{5\sqrt{5}}{10}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{5}}{2} \end{array}}[/tex]
Mr. Jackson earns $10 per hour working in an electronics store. In addition, he earns 5% commission on all of his computer sales. Last week, he worked 5 days from 9 am to 3 pm and sold $3,100 worth of computers. What was Mr. Jackson's total income for the week?