The sum of the polynomials is \(8x^7+7x+9x^3-x+15\).
Option (C) is correct.
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also called unknowns or indeterminates) and coefficients, that involve only the operations of addition, subtraction, and multiplication, and does not involve division by a variable.
The given polynomials are
\(6x^7+9x^3-x+9\\\\2x^7+7x+6\)
Now take addition of the above polynomials, we get
\(=(6x^7+9x^3-x+9)+(2x^7+7x+6)\\\\=8x^7+9x^3+7x-x+15\)
Hence, the sum of the polynomials is \(8x^7+7x+9x^3-x+15\).
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4. Ashley and Aileen want to accumulate ₱300,000, 17 years from now, as a college fund for their baby daughter, Aria. Calculate how much they must invest now, at an interest rate of 8% compounded semi-annually, in order to have ₱300,000 in 17 years.
Hello
To solve this question, we should use the formula of compound interest and calculate the principal
\(\begin{gathered} A=p(1+\frac{r}{n})^{nt} \\ A=300000 \\ r=8\text{ \% = 0.08} \\ t=17 \\ n=2 \\ p=\text{ ?} \end{gathered}\)Let's solve for p
\(\begin{gathered} a=p(1+\frac{r}{n})^{nt} \\ 300000=p(1+\frac{0.08}{2})^{2\times17} \\ 300000=p(1+0.04)^{34} \\ 300000=p(1.04)^{34} \\ 300000=p\times3.794 \\ p=\frac{300000}{3.794} \\ p=79072.2 \end{gathered}\)From the calculation above, the principal or what they need to invest P79,072.2 now to get P300,000
What are the values of x and y that simultaneously satisfy the two linear equations graphed below? HELP PLEASE
Answer:
D
Step-by-step explanation:
x=9 and y=4 is given in the graph, this makes the answer between B and D
Since y=-⅔x+10 and y=x-5, 4=-⅔(9)+10 and 4=9-5
So the answer is D
Slope = -3; y-intercept = 2
Slope = -1; y intercept = 8
Slope = 1/4; y-intercept= 0
Slope= -5/2; y-intercept=-3
Please give me the equations for these problems
Answer:
Given Below
Step-by-step explanation:
using the formula :
y = mx + c ....where m is the slope and c is the y intercept
(a) if Slope = -3; y-intercept = 2
y = -3x + 2
(b) if Slope = -1; y intercept = 8
y = -1x + 8
y = -x + 8
(c) if Slope = 1/4; y-intercept= 0
y = x/4 + 0
y = x/4
4y = x
(d) if Slope= -5/2; y-intercept= -3
y = -5x/2 - 3
y = (-5x - 6 )/3
2y = -5x - 6
\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)
Let's solve ~
The equation of line in slope - intercept form is :
\(\qquad \sf \dashrightarrow \: y = mx + c\)
where,
m is slopec is y - interceptNow, use these values in the equation to find their respective equations ~
Question 1Slope = -3 and y-intercept = 2
\(\qquad \sf \dashrightarrow \: y = - 3x + 2\)
Question 2Slope = -1 and y intercept = 8
\(\qquad \sf \dashrightarrow \: y = - x +8 \)
Question 3Slope = 1/4 and y-intercept = 0
\(\qquad \sf \dashrightarrow \: y = \dfrac{x}{4} \)
Question 4Slope= -5/2 and y-intercept = -3
\(\qquad \sf \dashrightarrow \: y = - \dfrac{ 5}{2} x - 3\)
Find c such that (-5, -3), (10, 1), and (c, -9) lie on a line.
well, we know all three points are colinear, so the slope from the first two points is the same slope from either to the (c , -9) point, let's check the slope of the first two points given
\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{(-5)}}} \implies \cfrac{1 +3}{10 +5}\implies \cfrac{4}{15}\)
so then, the slope from say hmmmm let's use (-5 , -3), the slope from (-5 , -3) and (c , -9) must also be the same 4/15
\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{c}-\underset{x_1}{(-5)}}} \implies \hspace{5em}\cfrac{-9 +3}{c +5}~~ = ~~\stackrel{slope}{\cfrac{4}{15}}\implies \cfrac{-6}{c+5}=\cfrac{4}{15} \\\\\\ -90=4c+20\implies -110=4c\implies \cfrac{-110}{4}=c\implies -\cfrac{55}{2}=c\)
Please I’ll do anything I’m begging
Simplify each expression by using the Distributive Property and combine like terms to simplify the expression.3x+5-3x+4
The expression we have to simplify is:
\(3x+5-3x+4\)We need to combine like terms. Like terms are the ones that have the same variable, in this case the terms that contain "x". Also like terms are the independent numbers.
Thus we need to combine 3x -3x which results in 0.
Also we need to combine 5+4 which results in 9.
Thus we simplify the expression as follows:
\(3x+5-3x+4=9\)Answer: 9
Chris saved x dollars and spent half of his savings buying video games. After earning an additional $20 cutting grass, he had $60. If the equation 1/2bh represents the scenario, how much did he start with in his savings?
Answer:
80
Step-by-step explanation:
Simply reverse the steps.
In the end he has 60, before that he got 20 dollars for cutting grass, so subtract 20.
Now he has 40, which is after he spent half of his money on games, so multiply it by 2.
This is where he started, and he has 80 dollars saved.
What is the equation of the line in slope intercept form?
Answer:
y = x + 60
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 = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line
m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1
the line crosses the y- axis at (0, 60 ) ⇒ c = 60
y = x + 60 ← equation of line
Use the Pythagorean Theorem to solve for the value of x
Step-by-step explanation:
Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90 degree angle).
x² = 12² + 9² = 144 + 81 = 225
x = 15 ft
so, the first answer option is correct.
The value of hypotenuse (x) in the right angled triangle is 15ft.
Given,
Right angled triangle .
Here,
Pythagoras theorem,
c² = a² + b²
here,
c = hypotenuse
a = perpendicular
b = base
Substitute the values in the formula,
x² = 12² + 9²
x² = 144 + 81
x² = 225
x = 15 ft
Thus the length of hypotenuse is 15ft .
So, option A is correct.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the banks if you had this question before!!
An equation for the total cars and trucks for dealership A is: x + y = 164.
An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.
The number of cars that dealership A sold is: 98 cars.
The number of trucks that dealership B sold is: 66 trucks.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of cars sold.Let the variable y represent the number of trucks sold.Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;
x + y = 164.
Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;
2x + 0.5y = 229.
By solving the systems of linear equations simultaneously, we have:
2x + 0.5(164 - x) = 229
1.5x + 82 = 229
x = 98 cars.
For the y-value, we have;
2(98) + 0.5y = 229
0.5y = 229 - 196
y = 33/0.5
y = 66 trucks.
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A man gave 5/12 of his money to his son , 3/7 of the remainder to his daughter and the remaining to his wife if his wife gets rs 8700 what is the total amount
The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.
A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?
The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.
The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'
Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).
Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.
Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200
Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.
The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.
The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
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The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
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Sean is exploding a coral reef 91 feet below sea level and Liz is hiking 91 feet above sea level. Who is father away from sea level?
Answer:they are both at the same height
Step-by-step explanation: its the same exact number except one is negative and one is positive so if they are the same numbers you should be able to add it and get the number zero.
a certain bike travels 135 feet in 20 rotations of its wheels. how far will the bike travel in 45 rotations
Answer:
303.75
Step-by-step explanation:
135/20=6.75
6.75•45= 303.75
Piper has a smart phone data plan that costs $45 per month that includes 5 GB of data, but will charge an extra $25 per GB over the included amount. How much would Piper have to pay in a month where she used 5 GB over the limit? How much would Piper have to pay in a month where she used went over by xx GB?
Answer : Piper would have to pay $170 in a month if she used 5 GB over the limit and $95 in a month if she used 2 GB.
Step-by-step explanation:
45 + 25x
45 + 25(5) = 170
45 + 25(2) = 95
The length of a rectangle is shown below: (look at the picture) If the area of the rectangle to be drawn is 12 square units, where should points C and D be located if they lie vertically below the line that connects B and A, to make this rectangle? C(−2, −1), D(1, −1) C(−2, −4), D(1, −4) C(−2, −2), D(1, −2) C(−2, −5), D(1, −5)
================================================
Explanation:
The distance from B to A, or vice versa, is 3 units. You can count out the spaces between the points, or you could subtract the x coordinate values then use absolute value
|B - A| = |-2-1| = |-3| = 3
or
|A - B| = |1-(-2)| = |1+2| = |3| = 3
Whichever method you prefer, the distance between the two points is 3 units.
----------
The area of the rectangle is 12 square units, and we know one dimension of the rectangle is 3 units. The other dimension must be 12/3 = 4 units.
Point C is directly below point B. Specifically C is 4 units below B.
Start at B(-2,2) and move down 4 units to get to C(-2,-2). Then move to the right 3 units to get to D(1,-2)
Or you could start at A(1,2) and move 4 units down to get to D(1,-2) and then move 3 units to the left to get to C(-2,-2)
Answer:
Answer choice = B - C(−2, −4), D(1, −4)
in the xy plane ,the graph of f(x)=x^2 is intersected by five lines parallel to the x axis. what is the sum of the x coordinates of the points of intersection of the five lines with the graph of f
Answer:
Step-by-step explanation:that is,have them in this form:y = mx + b.Set the two equations for y equal to each other.Solve for x.This will be the x- coordinates for the point of intersection.
You are offered an investment that pays simple interest and will earn $200 interest on a $2000 investment over 5 years. What interest rate is the investment paying? A) 1.5% B) 2% C) 2.5% D) 3%
Answer:
B) 2%
Step-by-step explanation:
The simple interest formula is ...
I = Prt
Interest I is earned on principal P when it is invested at rate r for t years.
Filling in the given values, we can solve for r:
200 = 2000r(5)
200/10000 = r = 2/100 = 2%
The interest rate is 2%.
What is the distance between the points (-9 , 23) and (2 , 23) in the coordinate plane
Answer:
d=11
Step-by-step explanation:
d = √[(2 - (-9))^2 + (23 - 23)^2]
= √[(2 + 9)^2 + (0)^2]
= √[11^2 + 0^2]
= √(121 + 0)
= √121
= 11
Therefore, the distance between the points (-9, 23) and (2, 23) is 11 units.
2 * 2 * 4 * 5 * 6 * 2 * 2 * 5 * 7 * 5 = ? will mark brainliest!
Answer:
336,000
Step-by-step explanation:
2 × 2 = 4 x 4 = 16 × 5 = 80 × 6 = 480 x 2 = 960 x 2 = 1920 × 5 = 9600 x 7 = 62700 × 5 = 336,000
Factor the following:
5∙(a+3)^2-(a+3)
Answer:
(a+3)(5a+14)
Step-by-step explanation:
Factor the polynomial.
(a+3)(5a+14)
Need help with this question
Answer:
i cant see it
Step-by-step explanation:
umm
Is -16/-9 a rational number
9 is a rational number because it can be expressed as the quotient of two integers: 9 ÷ 1.
Answer:
No, the answer (1.77777777778) would be irrational.
Step-by-step explanation:
A rational number is a number that can be expressed as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333 (the threes go on forever).
So if we were to solve this problem, we would end up with 1.77777777778
-16/-9 = 1.77777777778
We can now confirm that this number is irrational based on our knowledge of rational numbers and numbers.
-----------------------------------------------------------------------------------------------------------------
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Of twice a number and another number is five the sum of two numbers is 19 find the numbers
the two numbers are -7 and 26.
Let's call the first number "x" and the second number "y".
We're given that "twice a number and another number is five", which can be translated as:
2x + y = 5
We're also given that "the sum of two numbers is 19", which can be translated as:
x + y = 19
We now have two equations with two variables. We can solve for one variable in terms of the other, and then substitute that expression into the other equation to solve for the remaining variable.
Let's solve the second equation for "x":
x + y = 19
x = 19 - y
Now we can substitute this expression for "x" into the first equation:
2x + y = 5
2(19 - y) + y = 5
38 - 2y + y = 5
38 - y = 5
y = 33
Now we can use either equation to solve for "x":
x + y = 19
x + 33 = 19
x = -14
Therefore, the two numbers are -14 and 33.
Answer: the two numbers are -7 and 26.
Step-by-step explanation:
2.
Elena has a
pet parakeet that weighs 6 when measured in one unit and
170 when measured in a different unit. Which measurement is in ounces,
and which is in grams?
170
Measurement of weight 6 is in ounces and the measurement of weight 170 is in grams.
What is measurement?
An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.
Given:
Elena has a pet parakeet that weighs 6 when measured in one unit and
170 when measured in a different unit.
We have to find the correct units from grams and ounces for these.
We know that, 1 ounce is greater than 1 gram.
1 ounce = 28.3495 grams
Multiply both sides by 6.
6 ounces = 170.097 grams
Approximate the values to the nearest whole number.
6 ounces = 170 grams
Therefore, 6 ounces = 170 grams.
Hence, measurement of weight 6 is in ounces and the measurement of weight 170 is in grams.
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will mark brainliest, 60 points
Answer:
21 C
22 B
23 169
Step-by-step explanation:
21 3m mean 3 times a certain number
22 the negative make the 4 go negative and the -5 positive
23 i did 5^2-4^2= 9
then 6^2 divided by 9+9= 13 i took the 9 from the 5^2 problem then divided it by 6^2
then 13 x 13 = 169
-6x-10=2 what is x?REMEMBER 6 IS NEGATIVE
HELLLLLPPPPPPP MEEEEEEE PLZZZZZZZZZZZ
Hurry - Please Help = 2 questions.
Answer:
3. f(3) = 16
4. h(3) = 4
Step-by-step explanation:
3.
f(x) = x² + 7
f(3) = 3² + 7
f(3) = 16
4.
h(x) = 12/x
h(3) = 12/3
h(3) = 4
The Venn diagram shows the number of customers who have purchased different types of pets from a pet store, where C represents customers who have purchased cats, D represents customers who have purchased dogs, and F represents customers who have purchased fish.
Circles C, D, and F overlap. Circle C contains 15, circle D contains 21, and circle F contains 12. The overlap of C and F contains 2, the overlap of F and D contains 0, and the overlap of D and C contains 3. The overlap of all 3 circles contains 1. Number 14 is outside of the circles.
How many people are in the set C ∩ D?
4
6
36
38
The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.
The correct answer is 4.
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.
Given information:
- Circle C (cats): 15
- Circle D (dogs): 21
- Circle F (fish): 12
- Overlap of C and F: 2
- Overlap of F and D: 0
- Overlap of D and C: 3
- Overlap of all 3 circles: 1
- Number outside of circles: 14
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.
From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.
To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.
Therefore, from the options given correct one is 4.
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Answer: 4
Step-by-step explanation:
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