Answer:
(a+b)² - 11(a+b) -42
Step-by-step explanation:
Thoughtfully split the expression at hand into groups, each group having two terms,
Group 1: -11b-11a
Group 2: a2+2ab
Group 3: b2-42
Pull out from each group separately :
Group 1: (a+b) (-11)
Group 2: (a+2b) (a)
Group 3: (b2-42) (1)
Looking for common sub-expressions :
Group 1: (a+b) (-11)
Group 3: (b2-42) (1)
Group 2: (a+2b) (a)
final answer:(a+b)² - 11(a+b) -42
Answer:
(a+b+3)(a+b-14)
Step-by-step explanation:
let a+b be x,
= x²-11x-42
=x²-(14-3)x-42
=x²-14x+3x-42
=x(x-14)+3(x-14)
=(x+3)(x-14))
replacing x by a+b,
=(a+b+3)(a+b-14)
JOHN RICHARDS BORROWED $875 AGAINST HIS CHARGE ACCOUNT ON SEPTEMBER
12 AND REPAID THE LOAN ON OCTOBER 14 (32 DAYS LATER). IF THE INTEREST RATE
IS 0.04273% PER DAY, HOW MUCH INTEREST DID JOHN PAY ON THE LOAN AND WHAT
AMOUNT DID HE PAY THE BANK WHEN HE REPAID THE LOAN
Using simple interest, it is found that:
John paid $12 in interest for the loan.The total amount that he paid the bank was of $887.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t units of time in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.For this problem, the parameters are given as follows:
A(0) = 875, r = 0.0004273, t = 32.
Hence the amount paid is given by:
A(32) = 875 x (1 + 0.0004273 x 32) = $887.
The amount of interest is given by:
I = 887 - 875 = $12.
More can be learned about simple interest at https://brainly.com/question/25296782
#SPJ1
Which equation does the graph represent?
Answer:
It is the second answer
Step-by-step explanation:
The standard form of an ellipse is
x^2/a^2 + y^2/b^2 or x^2/b^2 + y^2/a^2 = 1
If the x is the main axis we use the first form. If the y is the main axis we use the second form. We will use the second form.
our a is 3 and our b is 4
x^2/3^2 + y^2/4^2
Barbara runs once around the track in 3 minutes 45 seconds. Liad runs around the track in 2
minutes 30 seconds. At these rates, after 10 minutes of running, the distance Barbara has run is
what fractional part of Liad's?
Answer:
2/3rds of liad's run
Step-by-step explanation:
3 min 45s = 3 3/4 min = 15/4 min; 10/(15/4) = 8/3 laps
2min 30s = 2 1/2 min = 5/2 min; 10/(5/2) = 4 laps
(8/3)/4 = 2/3
You need to haul a load of patio bricks to a job site. Each brick weighs 4 pounds 14 ounces. Your truck can carry a 3/4 -ton load. How many bricks can your truck carry in a full load?
A.
300
B.
307
C.
362
D.
409
E.
483
Use the ANOVA analysis tool Base on the given data uploaded, will you conclude that the number of bathroom of houses is a significant factor for house price? I your answer is affirmative, then explain how the house price is influenced by the number of bathroom?
ONE HUNDRED LOTTERY TICKETS ARE SOLD FOR $5.00 EACH. ONE PRIZE OF $300
WILL BE AWARDED. STEVE PURCHASES ONE TICKET. FIND HIS EXPECTATION. SHOW ME THE WORK SO I CAN UNDERSTAND THANKS
Steve's expected win from the lottery ticket purchase is $3 because his chance of winning the $300 prize is only 1%.
How are the expected winnings of the lottery determined?The expected winnings for Steve are a function of the probability of some predictable outcomes.
In this situation, the predictable outcome is the size of the lottery prize.
The probability that Steve will win the prize is 1% (1/100), depicting his chance of winning.
Data and Calculations:Sale price per ticket = $5
Lottery prize = $300
Value of lottery prize to Steve if he wins = $295 ($300 - $5)
Probability of winning = 1% (1/100 x 100)
Expected win = $3 ($300 x 1%)
Thus, Steve's expected win is $3, which outweighs the cost of a ticket.
Learn more about expected values at https://brainly.com/question/14723169
#SPJ1
(1 point) Find y as a function of x if
y" - 12y" + 32y' = 0,
y(0) = 5, y'(0) = 2, y" (0) = 1.
0
y(x) =
if a set of test scores has a large range but a small standard deviation, describe what this means about students' performance on the test.
a. Most of students' test scores are around the mean, except that few students got scores much less than the mean.
b. Most of students' test scores are around the mean.
c. Most of students' test scores are around the mean, except for the students who got scores much greater than the mean and a few students who got scores much less than the mean.
d. Most of students' test scores are around the mean, except for the students who got scores much greater than the mean.
Answer:
C
Step-by-step explanation:
Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.
The correct option is:
b. Most of students' test scores are around the mean.
A large range indicates that there is a significant difference between the highest and lowest scores in the set.
On the other hand, a small standard deviation indicates that the data points (test scores) are clustered closely around the mean.
When the range is large but the standard deviation is small, it means that most of the students' test scores are relatively close to the mean, and there are no extreme values that are significantly far from the mean. In other words, the majority of students performed similarly on the test, with only a few outliers having scores much higher or much lower than the mean.
Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.
Learn more about standard deviation here:
brainly.com/question/23907081
#SPJ3
WILL GIVE BRAINLIEST
HELP PLEASE
Select the correct answer.
The section of paper shown in the pattern below is of a circle. It will be wrapped around a cone. The wrapper will then be painted.
What is the amount of paint needed to paint 100 of these wrappers? Round your answer to the nearest hundred.
Answer:
C
Step-by-step explanation:
Area of a 1/4 sector of a circle = 1/4 * pi r^2
Givens
100 of these quarter sectors
pi = 3.14
r = 12
Solution
You are using area because you are going to paint each one of the sectors. You must cover every cm^2 with paint.
Area = 1/4 * 3.14 * r * r
Area = 1/4 * 3.14 * 12 * 12
Area = 113.25
But there are 100 of them. so the area is
100 * Area = 11325 cm^2
Rounded to the nearest 100 hundreds = 11300 cm^2
Answer:
The answer is 11,300 cm²
Step-by-step explanation:
I got it right on edmentum jope this helps your question.
help! giving brainlest to best answer!
Answer:
C...........................
A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.
a) The slope of the secant lines are: q = 5, f(q) = 2,076: m = - 131.1, q = 10, f(q) = 1,299: m = - 106.8, q = 20, f(q) = 357: m = - 81.6, q = 25, f(q) = 84: m = - 68.1, q = 30, f(q) = 0: m = - 51.
b) The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.
How to estimate the slope of a tangent line by averaging two adjacent secant lines
In this problem we must determine the slope of several lines based on the information given by the table and using the secant line formula:
m = [f(q) - f(p)] / (q - p) (1)
If we know that a = 15 and p = 765, then the slope of the secant lines are:
q = 5, f(q) = 2,076
m = [2,076 - 765] / (5 - 15)
m = - 131.1
q = 10, f(q) = 1,299
m = [1,299 - 765] / (10 - 15)
m = - 106.8
q = 20, f(q) = 357
m = [357 - 765] / (20 - 15)
m = - 81.6
q = 25, f(q) = 84
m = [84 - 765] / (25 - 15)
m = - 68.1
q = 30, f(q) = 0
m = [0 - 765] / (30 - 15)
m = - 51
The slope of the line tangent to the curve at the point (x, y) = (15, 765) can be estimated by averaging the slopes of the closest secant lines:
m' = [(- 106.8) + (- 81.6)] / 2
m' = - 94.2
The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.
To learn more on tangent lines: https://brainly.com/question/23265136
#SPJ1
What is the value of the last digit in 3,500.45
Answer:
five-hundredths
Step-by-step explanation:
2х+чу=4 and x + 2y = 3
Since the values on both sides are equal, hence the system of equation given has no solution
Solving simultaneous equationsSimultaneous equations are equations that consists of two or more equation and unknowns.
Given the equation below
2х+4у=4
x + 2y = 3
From equation 2;
x = 3 - 2y
Substitute into equation 1
2(3-2y) + 4y = 4
Expand
6 - 4y + 4y = 4
6 = 4
Since the values on both sides are equal, hence the system of equation given has no solution
Learn more on system of equation here: https://brainly.com/question/14323743
#SPJ1
im just here to help fl vs students Select the statement that describes the expression (one fourth x 8 + 3) ÷ 5.
Add three to the quotient of one fourth and 8, then divide by 5
one fourth times the product of 8 and 3, then divide by 5
Add 3 to the product of one fourth and 8, then divide by 5
Add 3 to the sum of one fourth and 8, then divide by 5
Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which may also be given in the form of a statement. Therefore the required statement in the question is option C. Add 3 to the product of one-fourth and 8, then divide by 5.
Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which can be given in the form of a statement. When a given expression consists of both numbers and alphabets, then it forms an algebraic expression. It can also be given in the form of a statement.
Given in the question:
([tex]\frac{1}{4}[/tex] x 8 + 3) ÷ 5
This can be given in a statement form as; Add 3 to the product of one-fourth and 8, then divide by 5.
The appropriate statement that describes the given expression is: Add 3 to the product of one-fourth and 8, then divide by 5 i.e Option C.
For more clarifications on mathematical expressions, visit: https://brainly.com/question/25206494
#SPJ1
which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle
Answer:
A, C
Step-by-step explanation:
See attached image.
For the equation 2x - y = 1, if x = 0, then y = ?
Answer:
y= -1
Step-by-step explanation:
(2) (0) − y = 1
0 + − y = 1
(−y) + (0) = 1
−y = 1
Step 2: Divide both sides by -1
Y = −1
Write 2.154 × 10∧5 in decimal form.
The decimal notation for the given value in scientific notation is 215400.
How to convert from scientific to decimal notation?Very large or very small numbers are denoted in scientific notation to simplify complex calculations.
The scientific notation is represented by: a × 10ⁿ
Wher a - any number or decimal number
n - the power of 10; it is an integer number
To convert this into decimal notation,
If the value of n is positive, then the decimal point in the 'a' moves right. (OR)If the value of n is negative, then the decimal point in the 'a' moves left.Calculation:The given number is in the scientific notation,
2.154 × 10⁵
Since the power of 10 is positive, the decimal point in the number 2.154 moves towards the right. I.e,
2.154 × 10⁵ = 215400
Here power is 5. So, the decimal point moved five places to the right.
Learn more about decimal notation here:
https://brainly.com/question/14222303
#SPJ1
the tens digit of a 2 digit number is 5 greater than the units digit if you subtract twice the reverse number the result is one fourth the original
Answer:
The original number is 72.
Step-by-step explanation:
Let the number by
[A][B]
The reverse number is
[B][A]
Original number:
A = B + 5
[A][B] - 2[B][A] = [A][B]/4
10A + B - 20B - 2A = (10A + B)/4
8A - 19B = (10A + B)/4
32A - 76B = 10A + B
22A - 77B = 0
22(B + 5) - 77B = 0
22B + 110 - 77B = 0
-55B = -110
B = 2
A = B + 5 = 2 + 5 = 7
The original number is 72.
The reverse is 27.
Let's check.
"the tens digit of a 2 digit number is 5 greater than the units digit"
7 is 5 greater than 2,so 72 looks good so far.
"if you subtract twice the reverse number the result is one fourth the original"
The reverse number is 27. Twice 27 is 2 × 27 = 54.
Subtract 54 from 72: 72 - 54 = 18
18 is 1/4 of 72. It works.
Answer: the original number is 72
The ratio of Sadias age to her fathers age is 3:5. The sum of their ages is 96. What is Sadias age.
Answer:
36 years old
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
sum the parts of the ratio , 3 + 5 = 8
divide the sum of their ages by 8 to find the value of one part of the ratio
96 ÷ 8 = 12 ← value of 1 part of the ratio , then
3 parts = 3 × 12 = 36 ← Sadias age
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)
The psi that the TPMS would trigger a warning for this car is = 23.36 psi
Calculation of tire pressureThe target tire pressure of the car is = 32 psi (pounds per square inch.)
The Tire pressure monitoring systems (TPMS) warns the car below 27% of 32psi
That is , 27/100 × 32
= 864/100
= 8.64psi
Therefore, 32 - 8.64 = 23.36. When the car is below 23.36psi, TPMS would trigger a warning for this car.
Learn more about tire pressure here:
https://brainly.com/question/16039384
#SPJ1
Complete question:
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)
At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is above or below?
List the domain and range in interval notation for the following graphs listed?
The domain and range of the given graphs are as follows,
(b) Domain: x ∈ (-∞, ∞), Range: y ∈ (-∞, ∞)
(c) Domain: x ∈ [-2, ∞), Range: y ∈ [1, ∞)
Determining the Domain and Range from a Graph
The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The various output values are represented on the y-axis as the range.
Thus, in graph (b),
Since the values of the given curve extends infinitely (denoted by arrowhead of the curve) on positive as well as negative sides for both the axes, x and y, its domain and range both are (-∞, ∞).
Similarly, in graph (c),
The minimum value on x-axis or abscissa is -2 and maximum is infinity. Hence, its domain is [-2, ∞). The minimum ordinate value or y-coordinate is 1 and maximum is infinity. Thus, its range is [1, ∞).
Learn more about domain here:
https://brainly.com/question/28135761
#SPJ1
here is another one that i need help on What number represents the same amount as 8 hundreds + 10 tens + 0 ones
Answer:
810 is the number that represents the same amount.
Hope this helps :)
David rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 84 cents for each mile driven. David had to pay $250.67 when he returned the truck. For how many miles did he drive the truck?
Answer:
277 miles
Step-by-step explanation:
How many and of which kind of roots does the equation f(x)=x^3+2x^2+4x+8 have?
The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
What kind of roots does have a cubic equation?
In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.
Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.
The discriminant is described below:
Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² (1)
Where:
There are three distinct real roots for Δ > 0.Real roots with multiplicity greater than 1 for Δ = 0.A real root and two complex roots for Δ < 0.If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:
Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²
Δ = - 1024
The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
To learn more on cubic equations: https://brainly.com/question/13730904
#SPJ1
Suppose that Andrea told you that “Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me.” Is Andrea’s reasoning incorrect? If so, how can you help Andrea identify her misunderstanding?
solve x^2 + x - 12 = 0
Answer:
x₁ = -4
x₂ = 3
Step-by-step explanation:
x²+ x + 12 = 0
x = {-1±√((1²)-(4*1*-12))} / (2*1)
x = {-1±√(1+48)} / 2
x = {-1±√49} / 2
x = {-1±7} / 2
x₁ = {-1-7} / 2 = -8/2 = -4
x₂ = {-1+7} / 2 = 6/2 = 3
Check:
x₁
-4² + (-4) - 12 = 0
16 - 4 - 12 = 0
x₂
3² + 3 - 12 = 0
9 + 3 - 12 = 0
PLEASE HELP Find the value of x.
X
15
12
Answer: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
simplify 12x^6-4x^4+6x^2 over 2x^2
Answer:
6x⁴ - 2x² +3
Step-by-step explanation:
[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]
What is the next number in the following sequence 0 0 1 2 2 4 3 6 4 8 5
Answer:
10
Step-by-step explanation:
the sequence follows the rule of adding the number and then the number -1 depending on the number before it. for example, you can see in order to get from 2 to 2, it adds 0 or subtracts by 0. After that to get from 2 to 4, you add 2. After that, you subtract 1 from 2 and you subtract that number which is 1 from 4 to get 3 and so on. Following that rule, you get 10 as the next number in the sequence
Find the value of b.
Step-by-step explanation:
b + 35° = 180° ( supplementary angle )
b = 180° - 35°
b = 145°
Answer: [tex]\Large\boxed{b=145^\circ}[/tex]
Step-by-step explanation:
Given information
∡1 = 35°
∡b = ?
Total Angle = 180° (Supplementary Angle)
Derived formula from the given information
∡1 + ∡b = Total Angle
Substitute values into the given formula
(35) + b = 180
Subtract 35 on both sides
35 + b - 35 = 180 - 35
[tex]\Large\boxed{b=145^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
