[tex]f(x) = -2x^5 +x^3 -7x \\\\-f(x) =-(-2x^5 +x^3 -7x) = 2x^5 -x^3 +7x = x(2x^4 - x^2 +7)\\\\f(-x) = -2(-x)^5 + (-x)^3 -7(-x) = 2x^5 -x^3 +7x = x(2x^4 -x^2 +7) \\\\\\\text{Hence,} ~ -f(x)=f(-x)[/tex]
Jim swam 8 laps on Tuesday, 19 laps on Wednesday, 30 laps on Thursday, and 41 laps on Friday. What kind of sequence is this? both neither arithmetic geometric
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
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 ⚜
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
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.
1. “Zoe and Toria are going into business. They need 80,000 to start the business. Their investment is 3:5, respectively.
a. What's Zoe & Ares individual investment amounts?
b. What percent did each person invest?
9514 1404 393
Answer:
a. Z: 30,000; T: 50,000
b. Z: 37.5%; T: 62.5%
Step-by-step explanation:
a. The "ratio units" add up to 3+5 = 8, so we can find the investment amounts by multiplying the ratio by 10,000
Z : T = 3 : 5 = 30,000 : 50,000
Zoe invested 30,000Toria invested 50,000__
b. Zoe's investment amount is 3/8 of the total, or ...
3/8 × 100% = 37.5%
Toria's percentage is the rest of it:
100% -37.5% = 62.5%
Zoe invested 37.5% of the total; Toria invested 62.5% of the total.
In physics, the equation PV = nRT is called the ideal gas law. It is used to approximate the behavior of many gases under different conditions.
P, V, and T represent pressure, volume, and temperature, n represents the number of moles of gas, and R is a constant for the ideal gas. Which equation is solved for T?
A: PV/R = nT
B: PV/nR = T
C: T= PV - nR
D: PVnR = T
Answer:
Option B
Step-by-step explanation:
[tex]PV = nRT\\\rule{150}{0.5}\\\rightarrow \frac{PV = nRT}{nR}\\\\\rightarrow \boxed{\frac{PV}{nR} = T}[/tex]
Hope this helps.
The equation for T will be;
⇒ T = PV/nR
Where, P, V, and T represent pressure, volume, and temperature, n represents the number of moles of gas, and R is a constant for the ideal gas.
Option B is true.
What is Linear equation?
When in an equation the highest power of variable is one then its called Linear equation.
Given that;
The equation for the ideal gas law is,
PV = nRT
Where, P, V, and T represent pressure, volume, and temperature,
n represents the number of moles of gas, and R is a constant for the ideal gas.
Now,
Solve the equation for T as;
PV = nRT
Divide both side by 'nR' we fet;
PV/nR = nRT/nR
PV/nR = T
T = PV/nR
Thus, The equation for T will be;
⇒ T = PV/nR
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Simplify the linear expression.
−23a+18−16a−34
Answer:
-39a - 16 is not the answer, it's -5/6a - 5/8
Step-by-step explanation:
Took the test and got it incorrect.
Answer:
-5/6a - 5/8
Step-by-step explanation:
There is a massive difference between -2/3a & -23a.
Same goes for 1/8 & 18, -1/6a & -16a, and -3/4 & -34.
My earlier answer, -39a - 16, IS correct for the question you wrote. What was incorrect was the question.
It is important to write the question properly because
−23a+18−16a−34
and
−2/3a+1/8−1/6a−3/4
will have very different answers.
In conclusion, make sure you write your question correctly. It's unfair to others genuinely trying to help who then are blamed for supplying the "wrong answer" by others who also copied and pasted from their school work.
If you had written, −2/3a+1/8−1/6a−3/4, then the answer would be -5/6a - 5/8.
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:
2^x+2=4081
Solve the following exponential equation
Solve the system, or show that it has no solution.
10x + 4y = 14
15x + 6y = 21
Answer:
Step-by-step explanation:
(6)10x + 4y = 14(6)
4(15x + 6y) = 21(4)
60x + 24y = 84
60x + 24y = 84
It has infinite, as if this were to be graphed the lines would overlap.
Which expression is equivalent to this polynomial expression?
(5ry2 + 3x2 – 7) + (3.272 – 142 + 3y2 + 4)
Answer:
Step-by-step explanation:
the answer is . (5xy² + 3x² - 7) + (3x²y² - xy² + 3y² + 4). hope this helps
A line has a slope of –8 and includes the points (5,–3) and (4,z). What is the value of z?
Find x intercept
(0, 24) (4,0)
Answer:
bt.ly/d97sjdu8 there is your answer!
Step-by-step explanation:
Answer:
x-intercept is 0
Step-by-step explanation:
(0, 24) (4,0)
(x, y)
0/4=0
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
The number of fish in a lake decreased by 15% between last year and this year. This year, there were 51 fish in the lake. What was the population last year? Consider creating a tape diagram, to help you make sense of the situation.
Answer:
234
Step-by-step explanation:
the d of c e rt rt egr yr oigj rethoy ejtheruot utheoig eoigh eoijg oeijrg ioetjg eroitj e eiotj ertioj wet df fv 1q3r 2396 e059i58 the end oej etejg rtyehrThe answer to your question is 7.65.
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
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.
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
Whats (c) ????????????? ????
Answer:
11
Step-by-step explanation:
yeah-ya............ right?
Check the picture below.
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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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.)
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:
Multiplying polynomials
Steps are in the attachment.
________
Hope it helps :)) ⚜
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.
helpppp please!!!!!!!
Answer:
a
Step-by-step explanation:
a
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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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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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.
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