The length of rectangle is (x - 5).
We are given-
Area of rectangle = [tex]x^{3} - 5x^{2} + 3x - 15[/tex]
Width of rectangle = [tex]x^{2} + 3[/tex]
Using the formula, the length will be calculated by rewriting the formula as -
Length = Area/width
Keep the values in formula to find the length of rectangle.
Length = [tex]\frac{x^{3} - 5x^{2} + 3x - 15}{x^{2} + 3}[/tex]
In numerator, separating the common values and rewriting the equation -
Length = [tex]\frac{x^{2} (x - 5) +3 (x - 5)}{x^{2} + 3}[/tex]
Rewriting the equation to for ease of solving to find the length of rectangle -
Length = [tex]\frac{(x^{2} +3)(x - 5)}{(x^{2} +3)}[/tex]
Cancelling [tex](x^{2} + 3)[/tex] as it is common in both numerator and denominator. Now, we will get the value of length of rectangle.
Length = (x - 5)
Hence, the length of rectangle is (x - 5).
The complete question is -
The area of a rectangle is [tex]x^{3} - 5x^{2} + 3x - 15[/tex], and the width of the rectangle is [tex]x^{2} + 3[/tex]. If area = length × width, what is the length of the rectangle? x + 5 x – 15 x + 15 x – 5
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se polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. find the following sums without using a calculator or a formula
The sums of series using Polya's four-step problem-solving strategy in (a), (b) and (c) are 79800, 150975, and 1560 respectively.
(a) Let S = 1 + 2 + 3 + … + 398 + 399Write the series in reverse order and then add both series.S = 1 + 2 + 3 + … + 398 + 399S = 399 + 398 + … + 2 + 12S = 400 + 400 + … + 400 + 4002S = 400 x 399S = (400 X 399 ) / 2 = 200x399 = 79800(b) Let S = 1 + 2 + 3 + … + 548 + 549Write the series in reverse order and then add both series.S = 549 + 548 + … + 2 + 12S = 550 + 550 + … + 550 + 5502S = 550 x 549S = (550x549 ) / 2 = 275x549 = 150975(c) Let S = 2 + 4 + 6 + 8 + … + 72 + 74 + 76 + 78Write the series in reverse order and then add both series.S = 2 + 4 + 6 + … + 72 + 74 + 76 + 78S = 78 + 76 + 74 + … + 6 + 4 + 22S = 80 + 80 + … + 80 + 802S = 80 x 39S = (80 X 39 ) / 2 = 40 x 39 = 1560a sequence is, more or less speaking, a description of the operation of adding infinitely many quantities, one after the opposite, to a given starting quantity. The examine of series is a chief part of calculus and its generalization, mathematical evaluation. series are utilized in maximum areas of mathematics, even for reading finite structures (which includes in combinatorics) thru producing features.
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Find a quadratic function that includes the set of values below
(0,8) (2,10) (3,1)
The quadratic function is defined as follows:
- 2 / 3 x² + 7 / 3 x + 8
How to find quadratic function?The quadratic function has the following sets of values below:
(0,8) (2,10) (3,1).
The quadratic function is represented as follows:
f(x) = ax² + bx + c
using (0,8)
8 = a(0)² + b(0) + c
8 = c
Therefore, using (2, 10)(3 , 1).
f(x) = ax² + bx + c
10 = a(2)² + b(2) + 8
10 - 8 = 4a + 2b
2 = 4a + 2b
1 = 2a + b
1 = a(3)² + b(3) + 8
1 = 9a + 3b
Hence, combine the equations,
2a + b = 1
9a + 3b = 1
multiply equation(i) by 3
6a + 3b = 3
9a + 3b = 1
3a = - 2
a = - 2 / 3
Therefore,
9a + 3b = 1
9(- 2 / 3) + 3b = 1
-6 + 3b = 1
3b = 7
b = 7 / 3
Therefore, the quadratic function is defined as follows:
- 2 / 3 x² + 7 / 3 x + 8
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What is the value of y when x=-3
Answer:
when x=-3 then from the graph the value of y is -2
1. Write the following sentence using mathematical symbols.
Twice x, plus 10, is the same as - 5.
The sentence can be represented as 2x+10=-5, with x = -7.5
Given that twice the value of x plus 10 is equals to -5
Mathematical symbols are used to perform various operations. The symbols make it easier to refer Mathematical quantities. It is interesting to note that Mathematics is completely based on numbers and symbols. The math symbols not only refer to different quantities but also represent the relationship between two quantities. All mathematical symbols are mainly used to perform mathematical operations under various concepts.
• Helps in denoting quantities
• Establishes relationships between quantities
• Helps to identify the type of operation
2(x)+10=-5
2(x)=-15
x=-15/2
x=-7.5
Hence, The sentence can be represented as 2x+10=-5, with x = -7.5
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Identify the range of the function y=-3x+6 when the domain is {-1,2,4}
A. {-6,0,9}
B. {-9}
C. {3,-12,-18}
D. {-3,12}
E. {-6,9}
Answer:
A. {-6,0,9} but in order of domain it's {9,0,-6}
Step-by-step explanation:
There's two ways of finding the range;
Way #1: The traditional method
In the traditional method you substitute x for all the numbers in the domain When substituting you replace x and solve it like a regular equation (so for example for -3(-1) + 6 = 9 so y=9 when x equals to 2 or f(-1)= 9) to find yAfter substituting your y-values or the range (in order from least to greatest in domain or x-values) is {9,0,-6}Way #2: The graphing calculator method
Using a graphing calculator you use the table function Turn on the calculator press the button "Y=" place the function -3x+6 Hit "2nd" then "Graph" to get the tableLook at your x-functions to find your domain and next to these domains are your y-values those y-values that correlate to your domain are the ranges which are {9,0,-6}Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?
(
,
)
The ordered pair for the greatest amount he can buy is (3.2, 12)
How to find the greatest cost of gas?He has $12 to put gas in his car. The gas costs $3.75 per gallon.
Therefore,
x = number of gallons of gasy = total cost of the gas.Hence, the total amount he has to spend is 12 dollars.
Therefore,
y = 3.75x
where
y = 12 dollars
Therefore,
12 = 3.75x
divide both sides by 3.75
12 / 3.75 = 3.75x / 3.75
x = 3.2
Therefore, the ordered pair for the greatest amount he can buy is (3.2, 12)
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Write 10 algebraic expressions and then solve them!
(This is kinda easy and also I'll make brainliest answer to someone who answered correctly,clear and detailed!)
Answer: done
x + 3 = 0
subtract 3 on both sides
x = -3
x +4 = -3
subtract 4 on both sides
x = -7
3x = 0
divide 3 on both sides
x = 0
5x = 2
divide 5 on both sides
x = 2/5
x - 4 = 0
add 4 on both sides
x = 4
5x - 4 = 0
add 4 on both sides then divide both sides by 5
x = 4/5
2x + 4 = 5
subtract both sides by 4 then divide both sides by 2
x = 1/2
2x^2 = 9
square root both sides then divide both sides by 2
x = 3/2
5x - 1 = 2
add both sides by 1 then divide both sides by 5
x = 3/5
x + 3 = 65
subtract both sides by 3
x = 62
*First to answer rightfully will get brainliest. NO LINKS are allowed. Thank you.
Please help with the following question:
You just got back from a trip to
Florida for the school break and
you still have $225 in U.S.
currency. Today, the bank rate is
C$1.04 for US$1. How much in
Canadian funds will you get for
your U.S. currency?
NEED HELP ASAP!! PLEASE HELP ME SOLVE THIS AND SHOW YOUR WORK! EXTRA POINTS IF YOU FOLLOW THE INSTRUCTIONS GIVEN.
Hello and Good Morning/Afternoon
Let's take this problem step-by-step:
The sum of all angles in a triangle is equal to 180 degrees:
[tex]\hookrightarrow x + 120 +20 = 180\\\hookrightarrow x + 140 = 180\\\hookrightarrow x =180-140=40[/tex]
∠y and ∠x are on a flat line ⇒ total angle measured between is 180°
[tex]\hookrightarrow x + y = 180\\\hookrightarrow 40 + y = 180\\\hookrightarrow y = 180-40=140[/tex]
Answer: y = 140°
Hope that helps!
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3x^2-13xy+4y^2 how do I solve this
10 divided by a 100 is equals to what
Answer:
10/100= 0.1
100/10= 10
Step-by-step explanation:
Find the absolute value equation
How do i solve
|3x-9|= 1x + 1
Answer:
Step-by-step explanation:
The points G and H, 19m apart are on the same side of a tree. The angles of elevation of the top T, of the tree from G and H on the horizontal ground with the foot of the tree are 430 and 38° respectively. (1). Illustrate the information in a diagram. (i). Find, correct to one decimal place, the height of the tree.
Using relations in a right triangle, it is found that
The height of the tree is of 91.6 meters.
The graph for this problem is given at the end of the answer.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.From the diagram graphed, we can build two relations involving the tangent of the angles, as follows:
From the smaller right triangle:
tan(43º) = h/x
0.9325 = h/x
x = (1/0.9325)h.
x = 1.0724h (we want to find h, hence we write x as a function of h).
From the larger right triangle:
tan(38º) = h/(x + 19).
tan(38º) = h/(1.0724h + 19).
0.7813 = h/(1.0724h + 19).
Applying cross multiplication:
h = 0.7813(1.0724h + 19).
h = 0.8379h + 14.8447.
0.1621h = 14.8447
h = 14.8447/0.1621
h = 91.6 meters.
The height of the tree is of 91.6 meters.
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Guys i need help
Transform the following rational equation into quadratic equation please help me i need it asap
Answer:
y=
Step-by-step explanation:
Which expression is equivalent to fraction numerator 9 minus 4 i over denominator negative 3 plus 8 i end fraction?
Expression -4/-9 equals fraction numerator 9 minus 4 in math.
Fraction definition:
In mathematics, a fraction is a unit that represents a part or element of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.It has two negative numbers, hence the result will be the same because of the rule, which is why it is equivalent (minus times minus is equal to zero)
4/9= -4/-9
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I need help. somebodysolve this. i think the answer is 8
(2x +20)y X=10 y=5
Answer:
If there is divide sign between (2x+20) and y, then the answer is 8 but if there's multiplication sign between (2x+20) and y, then the answer is 200.
HELLLPPPPP
45 POINTS!!!!!!
Calculate the percent increase or decrease between the starting and ending quantities below. Round your answer to one decimal place. (There’s 5 questions to answer)
1- Start:3 end: 10
2- start:9 end:20
3-start:100 end: 85
4- start: 45 end:20
5-start: 30 end: 60
1 - there will be increase of 233.33 % , 2 - there will be increase of 122.22 % , 3 - there will be decrease of 15 % , 4 - there will be decrease of 55.56 % , 5 - there will be increase of 100%
WHAT IS PERCENTAGE ?% is a relative number that is used to represent hundredths of any quantity. Since one percent (1%) equals one tenth of something, 100 percent denotes the entire amount, and 200 percent denotes twice the amount mentioned percentage.
CALCULATION1 - Start : 3 end : 10
formula for finding percentage increase is = [tex]\frac{end - start }{start } * 100[/tex]
so substituting value in the formula ;
that is equal to = [tex]\frac{10-3}{3} * 100[/tex]
= [tex]\frac{7}{3} * 100[/tex]
= 233.33% increase
2 - Start : 9 End : 20
directly substituting the values in the above mentioned formula
= [tex]\frac{20-9}{9} * 100[/tex]
= [tex]\frac{11}{9} * 100[/tex]
= 122.22% increase
3 - Start : 100 end : 85
plugging in the values = [tex]\frac{85-100}{100}*100[/tex]
= [tex]\frac{-15}{100} * 100[/tex]
= -15% i.e. decrease of 15%
4 - Start : 45 end : 20
putting in the values = [tex]\frac{20-45}{45} * 100[/tex]
= [tex]\frac{-25}{45}*100[/tex]
= -55.56% i.e. decrease of 55.56 %
5 - Start : 30 end : 60
putting in the values = [tex]\frac{60-30}{30}* 100[/tex]
= [tex]\frac{30}{30} * 100[/tex]
= 100% increase
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Martin scores 10% of the points in a game if this represents 10 point how many points were scored in total
Answer:
10 OR 100. Read the explanation for details.
Step-by-step explanation:
If Martin scored 10%, and this represents 10 points, that means that martin scored 10 points. If he is talking about ALL the points in total then there are 100 points because 10% is 1/10, and if each 1/10th is 10 points, if you multiply that by 10 you get
100.
Benjamin's credit card has an APR of 19%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. His credit card record for the last 7 months is shown in the table
below.
End of
month
2
3
5
6
7
Previous
balance
$0.00
$2400.00
$2390.00
$2380.04
$2370.12
$2360.25
$2350.41
New
charges
$2400.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
Payment Finance
received
charges
$0.00
$0.00
OA. $59.38
OB. $47.01
OC. $285.01
OD. $225.64
$48.00
$47.80
$47.60
$47.40
$47.20
$47.01
$38.00
$37.84
$37.68
$37.53
$37.37
$37.21
Principal
paid
$0.00
$10.00
$9.96
$9.92
$9.88
$9.83
$9.79
New
balance
$2400.00
$2390.00
$2380.04
$2370.12
$2360 25
$2350.41
$2340.62
What is the total amount that Benjamin has made in payments over the 7
months?
If Benjamin's credit card has an APR of 19%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. the total amount that Benjamin has made in payments over the 7 months is: $285.01.
Total amount made in paymentTo determine the total amount that Benjamin has made in payments over the 7 months we would need to add up or sum up all the Payment Finance received charges for the first six months.
Now let calculate the total amount that Benjamin made in payment.
Hence,
Total amount made in payment=$48.00+$47.80+$47.60+$47.40+$47.20+$47.01
Total amount made in payment =$285.01
Therefore if Benjamin's credit card has an APR of 19%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. the total amount that Benjamin has made in payments over the 7 months is: $285.01.
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A basketball player plays 1, 481 minutes the first year of his career, 2, 683 minutes the second year of his career, and 3, 316
minutes the third year of his career. How many minutes has he played in three years
Which is a reasonable first step that can be used to solve the equation 2 (x + 6) = 3 (x minus 4) + 5?
Group of answer choices
Distribute 2 to (x + 6) and 3 to (x – 4).
Apply the subtraction property of equality to move the 6 from the left side of the equation to the right side.
Combine like terms, 3 and 5, on the right side of the equation.
Distribute 2 to x on the left side of the equation and 3 to x on the right side of the equation.
Answer:
x = 19
Step-by-step explanation:
I think you are on the right track. Below is the way I would approach it:
1. Expland the brackets
2. Collect like terms
3. Make x the subject
Let me know if you want the working out. Hope this helps.
The world's supply of helium is finite. There are approximately 35 billion cubic meters of helium on Earth, and every year humans consume about 210 million cubic meters of it. Let stand for the volume (in millions of cubic meters) of helium remaining, and stand for the number of years since 2018. Which of the following linear equations could model the decreasing supply of helium
The equation which correctly models the decreasing supply of helium as described in the task content is; y = 35 - 0.21x.
Which equation correct models the decreasing supply of helium?It follows from the task content that the equation which correctly models the decreasing supply of helium according to the description is to be determined.
Let, y = amount of helium remaining.
Let x = no of years since 2018.
First, one must convert 210 million to billion cubic feets as follows;
210 million = (210/1000) billion.
= 0.21 billion cubic meters per year.
The number above represents the rate of change of the linear model, otherwise termed the slope.
On this note, since the starting deposit of helium in 2018 was; 35 billion.
This insinuates that the y-coordinate of the y-intercept of the required model is; 35.
Hence, the required decreasing Linear model for the supply of helium is;
y = 35 - 0.21x.
The equation above follows from the slope-intercept form of a linear equation.
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05.05
The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Determine P(2 tails).
12.5%
37.5%
50%
75%
The value of P(2 tails) is 37.5%, the correct option is B.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
The sample space= {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Now,
The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, where H represents heads and T represents tails.
To determine P(2 tails), we need to count the number of outcomes in which there are 2 tails, and divide that by the total number of outcomes:
Number of outcomes with 2 tails: There are three outcomes with 2 tails: TTH, THT, and HTT.
Total number of outcomes: There are eight outcomes in total.
P(2 tails) = number of outcomes with 2 tails / total number of outcomes = 3/8 = 0.375, which is equivalent to 37.5%.
Therefore, the probability the answer will be 37.5%.
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up
A water tap is leaking at the rate of 25 mL every 20 seconds. How many litres of
water are wasted each day?
[3 marks]
Answer: 108 liters
Step-by-step explanation: There are 86,400 seconds in a 24-hour day. If 25 mL leak every 20 seconds, divide 86,400 by 20 (4,320), then multiply by 25 (108,000). There is 1,000 mL for every liter, so divide 108,000 by 1,000, and you will get 108 liters.
On a coordinate plane, point P is at (negative 4, 3). a. (–4, 3) b. (–3, 4) c. (3, –4) d. (4, –3) Group of answer choices
option (A) ( - 4 , 3 ) is the correct option to represent the coordinate of point P at ( negative 4, 3 ).
We are given the coordinate of the point as:
(negative 4, 3)
the negative means a minus ( - ) sign.
So, the coordinate of point P can also be written as:
( - 4 , 3 )
So, we get that:
Option (A) ( - 4 , 3 ) is the correct option.
Therefore, we get that, option (A) ( - 4 , 3 ) is the correct option to represent the coordinate of point P at ( negative 4, 3 ).
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Determine the values of y in the equation y2 = 121.
y = ±60.5
y = ±11
y = 60.5
y = 11
Answer:
y = ± 11
Step-by-step explanation:
y² = 121 ( take square root of both sides )
[tex]\sqrt{y^2}[/tex] = ± [tex]\sqrt{121}[/tex]
y = ± 11
You are solving a measurement problem where the numbers 4.0286 × 109 and 3.1 × 10−4 are divided. How many significant digits should the quotient have?
The quotient will have 2 significant figures.
The digits in the number , that contribute to the degree of accuracy can be defined as Significant Figures.
For Example ; 2.096 has 4 significant Figures
0.069 has 2 significant figures.
Rule Of Significant for Multiplication & Division :
Rule says in multiplication or division , the final result should retain as many significant figures as there are in the original number with the least significant figures.
In the given question
4.0286 × 10⁹ = 5 significant figures
3.1 × 10⁻⁴ = 2 significant figures
The quotient on dividing the numbers is 1.2995 x 10¹³ will have 2 significant figures as the least significant from 5 and 2 is 2.
Therefore , the quotient will have 2 significant figures.
The given question is incomplete , the complete question is
You are solving a measurement problem where the numbers 4.0286×10⁹ and 3.1×10⁻⁴ are divided. How many significant digits should the quotient have?
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graph: y + 2 = 2 (x + 3)
Muse synthetic division to find the quotient and remainder when 3x^4 +19x^3+22x^2-6x+4 is divided by x+2
Answer: 3x^3 +13x^2 -4x +2 +0/(x+2)
Step-by-step explanation:
-2: 3 19 22 -6 4=
-6 -26 8 -4
3 13 -4 2 0 ==> 3x^3 +13x^2 -4x +2 +0/(x+2)
Quotient: 3x^3 +13x^2 -4x +2
Remainder: 0
one of the interier angles of a triangle equals 30, and one of the exterier angles equals to 40. Find the remaining interier angles
Answer:110degrees
Step-by-step explanation:
the angles of the inside of a triangle always add up to 180
180-30-40=a
a is unknown angle
180-30-40=110