SIMPLIFIED POLYNOMIALS. Combine all the similar terms of each polynomial
1. 4x + 2x - 3x
2. 10xy + 4y - 8xy + 9y
3. 6x2 + y - 8x2 + 2 + 3y
4. 14a3 - a2 + 3a2 - 16a3 + a2
5. -5pq2 + 3pq2 - p2q + pq2 - 7p2q
Answer:
1. 3x
2. 2xy+13y
3. -2x^2+4y+2
4. -2a^3+3a^2
5. -2pq^2-7p^2q
What fraction of an hour is 21 minutes in simplest form
7/20
Step-by-step explanation:
21 ÷ 3 = 7
21 - 1 = 20
7/20
Whats (c) ????????????? ????
Answer:
11
Step-by-step explanation:
yeah-ya............ right?
Check the picture below.
The question is in the photo. Answer part d
Answer
your equation in part c is wrong
Step-by-step explanation:
part c
y=mx+c
11=2m+c-----------(1)
15=3m+c----------(2)
(2)-(1)
15-11=(3m+c)-(2m+c)
4=3m-2m+c-c
m=4
substitute in (1)
2m+c=11
2*4+c=11
8+c=11
c=3
so equation should be y=4x+3
Find the distance between two points in the simplest radical form
The 2 points marked on the graph are :-
(2, 3) & (-7, -4)
Here,
=》x₁ = 2
=》y₁ = 3
=》x₂ = -7
=》y₂ = -4
Using distance formula....
√(x₂ - x₁)² + (y₂ - y₁)²
= √(-7 - 2)² + (-4 - 3)²
= √(-9)² + (-7)²
= √81 + 49
= √130 (in radical form)
= 11.4 (approx......in standard form)
♧ The distance between the 2 points is √130 units.
______
Hope it helps ⚜
A. 48 inches
B. 4 feet
Explain why length A is equivalent to length B. Use your knowledge of converting inches to feet in your answer.
Answer:
As 1 feet = 12 inches
Therefore, 4 feet = 48/12
= 4
Answer = 4 feet
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis. Given the three events, which of the following statements is true? Select all that apply.
Event A: The mother or father carries the recessive gene.
Event B: The father carries the recessive gene.
Event C: The baby is at risk for Cystic Fibrosis.
Answer:
Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis.
Given the three events, which of the following statements is true?
Select all that apply.
Event A: The mother or father carries the recessive gene.
Event B: The father carries the recessive gene.
Event C: The baby is at risk for Cystic Fibrosis.
Select all that apply:
Event A and Event B are mutually exclusive.
Event B and Event C are mutually exclusive.
Event A and Event C are not mutually exclusive.
Event A and Event C are mutually exclusive.
Event A and Event C are not mutually exclusive.
Remember that in general, A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.
In this question, note that if the mother or father carries the recessive gene for cystic fibrosis, the baby is at risk. So here, A and C are not mutually exclusive, and B and C are not mutually exclusive.
A and B are not mutually exclusive because they share an outcome: the father carrying the recessive gene.
Step-by-step explanation:
Find the equation of the line through P=(8,7) such that the triangle bounded by this line and the axes in the first quadrant has the minimal area.
The area of the triangle is given by the product of 0.5 and the distances of the x and y intercepts from the origin.
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]Reasons:
The area of the triangle, A = 0.5·x·y
Where;
x and y are the values of the line at the intercepts
The equation of the line is; (y - 7) = m·(x - 8)
At the y-intercept, x = 0, therefore;
(y - 7) = m·(0 - 8) = -8·m
At the y-intercept, y = 7 - 8·m
At the x-intercept, y = 0, therefore;
(0 - 7) = m·(0 - 8) = -8·m
At the x-intercept, -7 = m·x - 8·m
8·m - 7 = m·x
[tex]\displaystyle x = \mathbf{8 - \frac{7}{m}}[/tex]
Therefore;
[tex]\displaystyle A = 0.5 \times \left(7 - 8 \cdot m\right) \times \left(8 - \frac{7}{m} \right) = \mathbf{\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}}[/tex]
When the area is minimal, we have;
[tex]\displaystyle \frac{dA}{dm} =0 = \frac{d}{dm} \left(\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}\right) = \mathbf{-\frac{32 \cdot m^2 - 24.5}{m^2}}[/tex]
m² × 0 = 24.5 - 32·m²
[tex]\displaystyle m^2 = \frac{24.5}{32} = \frac{49}{64}[/tex]
[tex]\displaystyle m = \sqrt{\frac{49}{64}} = \frac{7}{8}[/tex]
[tex]\displaystyle m = \pm \frac{7}{8}[/tex]
The equation of the line when [tex]\displaystyle m = + \frac{7}{8}[/tex] is therefore;
(y - 7) = m·(x - 8)
[tex]\displaystyle (y - 7) = \mathbf{\frac{7}{8} \cdot (x - 8)}[/tex]
[tex]\displaystyle (y - 7) = \frac{7}{8} \cdot (x - 8) = \frac{7}{8} \cdot x - \frac{7}{8} \times 8 = \frac{7}{8} \cdot x - 7[/tex]
[tex]\displaystyle y = \frac{7}{8} \cdot x - 7 + 7 = \frac{7}{8} \cdot x[/tex]
[tex]\displaystyle y = \mathbf{\frac{7}{8} \cdot x}[/tex]
The x and y intercept of the above line are 0
When [tex]\displaystyle m = - \frac{7}{8}[/tex], we have;
[tex]\displaystyle (y - 7) = -\frac{7}{8} \cdot (x - 8) = -\frac{7}{8} \cdot x + \frac{7}{8} \times 8 = -\frac{7}{8} \cdot x + 7[/tex]
Which gives;
[tex]\displaystyle y = \frac{7}{8} \cdot x + 7 + 7 = \frac{7}{8} \cdot x + 14[/tex]
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ y = \mathbf{14 - \frac{7}{8} \cdot x}[/tex]
The equation of the line through P = (8, 7) such that the triangle bounded by the line and the axes in the first quadrant has minimal area is therefore;
[tex]\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]
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ROOM
Write an equation in function notation for each situation.
1. The admission fee to a local carnival is $8. Each ride costs
$1.50
2. Steven buys lettuce that costs $1.69/1b.
3. An amusement park charges a $6.00 parking fee plus $29.99
per person.
4. A math tutor charges $35 per hour
5. A fitness center charges a $100 initiation fee plus $40 per
month
Answer:f(x)=1.5-x + 8
Step-by-step explanation:
Can somebody please help this is honestly due tomorrow
Answer:
I am almost completely sure its 4.
Step-by-step explanation:
I dont mind brainiests by the way
Phyllis invested $50,000 in two different types of stock. The first type earned 10% and the second type earned 15%. If the profit on the 15% stock was $2,500 more than the profit on the 10% stock, how much did Phyllis invest in the 15% stock?
Answer:
$ 30,000
Step-by-step explanation:
0.15(50,000 - x) - 0.1x = 2,500
7,500 - 0.15x - 0.1x = 2,500
7,500 - 2,500 = 0.15x + 0.1x
5,000 = 0.25x
5,000/0.25 = x
x =20,000
50,000 - 20,000 = 30,000
0.15 * 30,000 = $4,500
0.1 * 20,000 = $2,000
$4,500 - $2,000 = $2,500
Find the volume of a cylinder either enter. An exact answer in terms of pie or 3.14
Answer:
Step-by-step explanation:
V = πR²h
V = π3²6
V = 54π units³
If π = 3.14, V = 169.56 units³
consider the following equation:
2x−6y=9
Determine if the given ordered pair, (2,1/2), satisfies the given equation
yes or no
Answer:
The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system. The solution is the ordered pair(s) common to all lines in the system when the lines are graphed.
Lines that cross at a point (or points) are defined as a consistent system of equations. The place(s) where they cross are the solution(s) to the system.
Parallel lines do not cross. They have the same slope and different y-intercepts. They are an example of an inconsistent system of equations. An inconsistent system of equations has no solution.
Two equations that actually are the same line have an infinite number of solutions. This is an example of a dependent system of equations.
Step-by-step explanation:
Solve the system of equations graphically.
3x + 2y = 4
−x + 3y = −5
Solution
Graph each line and determine where they cross.
The lines intersect once at (2, −1).
A graphic solution to a system of equations is only as accurate as the scale of the paper or precision of the lines. At times the point of intersection will need to be estimated on the graph. When an exact solution is necessary, the system should be solved algebraically, either by substitution or by elimination.
Substitution Method
To solve a system of equations by substitution, solve one of the equations for a variable, for example x. Then replace that variable in the other equation with the terms you deemed equal and solve for the other variable, y. The solution to the system of equations is always an ordered pair.
Example
Solve the following system of equations by substitution.
x + 3y = 18
2x + y = 11
Solution
Solve for a variable in either equation. (If possible, choose a variable that does not have a coefficient to avoid working with fractions.)
In this case, it's easiest to rewrite the first equation by solving for x.
x + 3y = 18
x = −3y + 18
Next, substitute (−3y + 18) in for x into the other equation. Solve for y.
2( 3y + 12x + y = 11
2(−3y + 18) + y = 11-------Substitute -3y + 18 in for
−6y + 36 + y = 11-------Distribute.
2(3y −5y + 36 = 11-------Combine like terms.
2(3y + 18−5y = −25-----Subtract 36 from both sides
2(3y + 18) + y = 5---- -Divide both sides by -5.
Then, substitute y = 5 into your rewritten equation to find x.
x = −3y + 18
x = −3(5) + 18
x = −15 + 18
x = 3
Identify the solution. A check using x = 3 and y = 5 in both equations will show that the solution is the ordered pair (3, 5).
Elimination Method
Another way to solve a system of equations is by using the elimination method. The aim of using the elimination method is to have one variable cancel out. The resulting sum will contain a single variable that can then be identified. Once one variable is found, it can be substituted into either of the original equations to find the other variable.
Example
Find the solution to the system of equations by using the elimination method.
x − 2y = 9
3x + 2y = 11
Solution
Add the equations.
x − 2y = 9
3x + 2y = 11
4x + 2y = 20
Isolate the variable in the new equation
4x = 20
x = 5
Substitute x = 5 into either of the original equations to find y.
x − 2y = 9
(5) − 2y = 9
−2y = 4
y = −2
Identify the ordered pair that is the solution. A check in both equations will show that (5, −2) is a solution.
It may be necessary to multiply one or both of the equations in the system by a constant in order to obtain a variable that can be eliminated by addition. For example, consider the system of equations below:
3x + 2y = 6
x − 5y = 8
Both sides of the second equation above could be multiplied by −3. Multiplying the equation by the same number on both sides does not change the value of the equation. It will result in an equation whereby the x values can be eliminated through addition.
Special Cases
In some circumstances, both variables will drop out when adding the equations. If the resulting expression is not true, then the system is inconsistent and has no solution.
4x + 6y = 13
6x + 9y = 17
3(4x + 6y = 13)
2(6x + 9y = 17)
12x + 18y = 39
12x + 18y = 34
0 = 5
The equation is false. The system has no solution.
If both variables drop out and the resulting expression is true, then the system is dependent and has infinite solutions.
6x + 15y = 24
4x + 10y = 16
2(6x + 15y = 24)
3(4x + 10y = 16)
12x + 30y = 48
12x + 30y = 48
0 = 0
The equation is true. The system has an infinite number of solutions. (Notice that both of the original equations reduce to 2x + 5y = 8. All solutions to the system lie on this line.)
What is 919,827 rounded to the nearest hundred
Answer:
919,800
Step-by-step explanation:
To round up, the tens place would have to be either 5 or higher. Since the number in the tens place is 2, which is under 5, it will stay the same.
When Li Juan's auto yard is filled to capacity with only cars, it has 60 cars. When it is filled to capacity with only vans, it has 50 vans. Which linear equation models the number of cars, c, and vans, v, that could be in Li Juan's auto yard when it is filled to capacity? А c/60 + v/50 =1 B. 60c + 50v =1 C. c/50 + v/60 =1 D. 50c + 60v =1
The linear equation that could be used to model Li Juans auto yard is c/60 + v/50 = 1
A linear equation is in the form:
y = mx + b;
where m is the rate of change, b is the initial value of y and y, x are variables.
Let c represent the number of cars and v represent the number of vans.
Hence when it is filled to capacity:
c/60 + v/50 = 1
The linear equation that could be used to model Li Juans auto yard is c/60 + v/50 = 1
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Find the number of integers between 1 and 1000 that are divisible by 12 or 15, but not by both 12 and 15.
Count the multiples of 12:
⌊1000/12⌋ = 83
(where ⌊x⌋ denotes the "floor" of x, or the largest integer that is less than or equal to x)
These are the integers
{12, 24, 36, 48, …, 996}
Count the multiples of 15:
⌊1000/15⌋ = 66
These are
{15, 30, 45, 60, …, 990}
Count the multiples of both 12 and 15; these are multiples of LCM(12, 15) = 60:
⌊1000/60⌋ = 16
These are
{60, 120, 180, 240, …, 960}
Now use the inclusion/exclusion principle to count the multiples of either 12 or 15, but not both:
83 + 66 - 2•16 = 117
Among the multiples of 12 and the multiples of 15, we count the numbers that are multiples of both 12 and 15. By subtracting the number of multiples of both (16), we get the count of integers that are either divisible by 12 or 15. We subract 16 again to remove those that are divisible by both 12 and 15.
How long would it take to earn Php 8,000 on a principal of Php 20,000 at 5% simple interest rate?
The length of time it would take the given principal to become Php 8,000 is 8 years.
The formula that would be used to determine the length of time it would take Php 20000 to accumulate an interest of Php 8000 can be determined using this formula:
Time = Interest earned / (principal x interest rate)
8000 / (20,000 x 0.05)
= 8 years
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The table gives the temperature (in °F) in five citiesſat 6 a.m. on the same day. Use the table to answer the questions.
City
Temperature
(°F)
Toronto
-16
Fairbanks
:-24
Dayton
43
San Antonio
74
Buffalo
-3
5
?
(a) By noon, the temperature in Buffalo had risen by 10 °F.
What was the temperature there
at noon
How much higher was the 6 am temperature in Toronto than in Fairbanks
Answer:
a) buffalo will be at 7
b) it will be -8
Step-by-step explanation:
a) because if u add - 3 + 10 it will equal 7
b) reason why is because if u substract -24 from - 16 it will be - 8
I took a test on the same thing thats why i kno it
Find the equation of the line L.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (8, 0) ← 2 points on the line
m = [tex]\frac{0-4}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex]
The line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of line L
someone help me on these 2 questions asap! 50 points!!
Step-by-step explanation:
earbuds
we have a 1in : 0.2in scale of drawing to reality.
0.2 = 2/10 = 1/5
so, 1in in the drawing is actually 1/5in in reality.
how long are the 4in in the drawing ?
well, 4 times the 1in thing.
4×1/5 = 4/5 = 0.8in long
again the similar triangles
similar triangles means that each pair of corresponding lines (sides, heights, ...) in the triangles follows the same scaling factor for the length.
so, what do I need to multiply the side of the large triangle with to get the corresponding side length of the small triangle ?
27 × x = 9
x = 9/27 = 1/3
and that is the scale factor.
If two events (both with probability greater than 0) are mutually exclusive, then:
Answer:
they are not independent
Step-by-step explanation:
they are not independent they would be independent if they didn't depend on each other or if the probability didn't affect the other.
5x + 5 = x + 25 what is x?
Answer:
x = 5
Step-by-step explanation:
5x + 5 = x + 25
subtract 5 from both sides
5x = x + 20
subtract x from both sides
4x = 20
divide both sides by 4
x= 20/4
x= 5
A world-famous prix fixe menu includes the following choices.
Beverage (choose one): wine, soft drink, coffee, tea, milk, juice, or cappuccino
First course (no choice): baguette, bruschetta, whole roasted garlic, and butter
Second course (choose one): quesadilla, onion soup, salad, Caesar salad, lettuce wedge, spinach salad, or romaine salad
Third course (choose one): rib eye steak, swordfish, rack of lamb, whitefish, grilled chicken, southern fried chicken, lobster, or vegetarian plate
if you choose steak, then choose one of the following: fries, mashed potatoes, creamed corn, spinach, broccoli, or grilled onions
Fourth course (choose one): chocolate cake, cinnamon tart, apple tart, pecan tart, creme brulee, mango sorbet, or chocolate tart
How many different choices are possible?
Using the fundamental counting theorem, it is found that 107,016 different choices are possible.
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, …, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the beverage, there are 7 options, hence [tex]n_1 = 7[/tex]For the first course, there are no choice, hence an arrangement of 4 options, that is, [tex]n_2 = 4! = 24[/tex]For the second course, there are 7 options, hence [tex]n_3 = 7[/tex]For the third course, there are 7 non-steak options, plus 6 steak options, hence [tex]n_4 = 13[/tex]For the fourth course, there are 7 choices, hence [tex]n_4 = 7[/tex]Then, applying the theorem:
[tex]N = 7(24)(7)(13)(7) = 107016 [/tex]
107,016 different choices are possible.
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Kathy is following a recipe for punch that calls for 3 liters
of juice. She has 3 quarts of juice. Without using an equation, does Kathy
have enough juice for the punch? Explain.
Answer:
Yes, Kathy does have enough juice.
Step-by-step explanation:
Kathy does have enough because quarts are a little bigger than liters, so the 3 quarts she has will cover the liters.
2^x+2=4081
Solve the following exponential equation
helpppp please!!!!!!!
Answer:
a
Step-by-step explanation:
a
Use the figure below to find the values of x and y
Answer:
x=68 and y = 112
Step-by-step explanation:
angles of a triangle must equal 180, so
52°+60°+x°=180
112+x=180 <-- subtract 112 to get x on one side.
x=68
To solve for y, a straight line = 180 so
68+y=180 --> just subtract 180-68
y=112
how can you determine whether two systems of equations are equivalent?
Two systems of equations are equivalent if they have they have the same solution/solutions.
Only answer this if you know the answer.
Find The nth Term of this number sequence
18, 16, 14, 12
Answer:
2
Step-by-step explanation:
18,16,14,12,10,8,6,4,2
Here's Robert's spending diary for one week. It may not look like he's spending much. Use a calculator to add up Robert's total spending for the week. Monday Tuesday Wednesday Thursday Friday Saturday Sunday Lunch $7.00 Shampoo $6.00 Lunch $7.00 Jacket $40.00 Lunch $7.00 Breakfast $4.50 Coffee $2.00 Bus $3.00 CD $14.00 Lunch $7.00 Lunch $7.00 Movie $12.00 Haircut $40.00 Total: $21.00 $13.00 $10.00 $47.00 $19.00 $44.50 $2.00 How much does Robert spend on lunch in a week, in a year? If Robert continues to buy his lunch every weekday, he will be spending /week. S weeks in a year = $ spent during the year.