I. Simplify the following fully:
1.1 (2x-1)(x^(2)-3x+1)
= 2x^(3) - 6x^(2) + 2x - x^(2) + 3x - 1
= 2x^(3) - 7x^(2) + 5x - 1
1.2 12(2x+3)(5-x)
= 12(-2x^(2) + 7x + 15)
= -24x^(2) + 84x + 180
1.3 (x^(3)-1)/((x+2)+x(x+2))+(x-1)/(2x+4)
= (x^(3)-1)/(x^(2)+3x+2)+(x-1)/(2(x+2))
= (x-1)(x^(2)+x+1)/(x+2)(x+1)+(x-1)/(2(x+2))
= (2(x-1)(x^(2)+x+1)+(x-1)(x+1))/(2(x+2)(x+1))
= (2x^(3)+x^(2)-x-1+x^(2)-1)/(2(x+2)(x+1))
= (2x^(3)+2x^(2)-x-2)/(2(x+2)(x+1))
1.4 (3)/(x^(2)-9)+(2)/((x-3)^(2))
= (3)/((x+3)(x-3))+(2)/((x-3)^(2))
= (3(x-3)+2(x+3))/(x+3)(x-3)^(2)
= (3x-9+2x+6)/(x+3)(x-3)^(2)
= (5x-3)/(x+3)(x-3)^(2)
2. Factorise:
2.1 6x^(2)+7x-20
= (2x-4)(3x+5)
2.2 x^(3)+x^(2)-x-1
= (x+1)(x^(2)-1)
= (x+1)(x+1)(x-1)
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Vinne Two weeks ago, the cost to fly from to was 210$. Now the cost is 300$. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Step-by-step explanation:
for % questions always find 100% and/or 1%.
everything else can be easily calculated out of these 2.
the original price of $210 = 100%, as we want to know how many % the new price is different from that.
100% = $210
1% = 100%/100 = 210/100 = $2.10
the new price is $300.
the difference is 300 - 210 = $90
how many % are $90 compared to the original price ?
well, as many as the times 2.1 (1%) fits into 90 :
90/2.1 = 42.85714286...%
that increase from $210 to $300 was 42.85714286...%.
an additional $50 baggage fee ?
we have to add this to the $300 and get $350 as new price.
that difference is now 350 - 210 = $140.
how many % are $140 compared to the original price ?
140/2.1 = 66.66666666...%
that increase from $210 to $350 was 66.66666666...%.
Allister’s father is 120% of Allister’s height. If his father measures 180 cm, then how many centimeters tall is Allister? help plsss
Answer:
Step-by-step explanation:
216
38 dollars less than charlie earned.in variables
Answer:
x = c - 38
Step-by-step explanation:
Jason earns $232.50 per week as the manager at Big Bucks Department Store. He is single and claimed
1 allowance last year. How much more will be deducted from his weekly check if he claims no
allowances?
If Jason claims no allowances this year, $17 more will be deducted from his weekly check for taxes compared to last year when he claimed one allowance.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
The amount of money deducted from Jason's paycheck for taxes depends on the number of allowances he claims.
Claiming more allowances reduces the amount of taxes withheld from his paycheck while claiming fewer allowances increases it.
If Jason claimed 1 allowance last year, his employer would have withheld taxes from his paycheck based on that information.
If he claims no allowances this year, more taxes will be withheld.
To calculate how much more will be deducted from his weekly check if he claims no allowances, we need to know his tax bracket and the amount of taxes that will be withheld for each allowance.
Assuming Jason is paid on a weekly basis, we can use the IRS tax withholding tables for 2021 to estimate the additional amount of taxes that will be withheld if he claims no allowances.
Using these tables, we find that for a single person earning $232.50 per week, claiming no allowances would result in an additional withholding of $17 per week.
Therefore, claiming no allowances would result in an additional withholding of $17 per week.
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x + sin x, if x < 0
F(x) = { 2, if x=0
2/(1+x^2), if x > 0
a) Determine if f is continous from the left at x =0
b) Determine if f is continous from the right at x =0
c) Determine if f is continous at f = 0
"f " is continuous at x = 0.
a) To determine if f is continuous from the left at x = 0, we need to evaluate the limit of f(x) as x approaches 0 from the left. This means we need to use the first piece of the function, x + sin x, since this is the piece that applies when x < 0:
lim(x->0-) f(x) = lim(x->0-) (x + sin x) = 0 + sin 0 = 0
Since the limit exists and is equal to the value of the function at x = 0 (which is 2), f is continuous from the left at x = 0.
b) To determine if f is continuous from the right at x = 0, we need to evaluate the limit of f(x) as x approaches 0 from the right. This means we need to use the third piece of the function, 2/(1+x^2), since this is the piece that applies when x > 0:
lim(x->0+) f(x) = lim(x->0+) (2/(1+x^2)) = 2/(1+0^2) = 2
Since the limit exists and is equal to the value of the function at x = 0 (which is 2), f is continuous from the right at x = 0.
c) To determine if f is continuous at x = 0, we need to make sure that the limits from the left and right both exist and are equal to each other and to the value of the function at x = 0. We already found that the limits from the left and right are both equal to 2, which is also the value of the function at x = 0. Therefore, f is continuous at x = 0.
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Assume we can move the hour and minute hands on a clock freely. Find the measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1. (Note: There are 360° in a circle. Use the measure of the angle that is less than or equal to 180°.)
The measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1 is 144°.
To find the measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1, we need to calculate the difference between the two positions on the clock.
Each hour on the clock represents (360°/12) = 30°, and each minute represents (360°/60) = 6°.
Therefore, the hour hand at 5 represents 150° (5 x 30°) and the minute hand at 1 represents 6° (1 x 6°). The difference between the two positions is 144° (150° - 6°).
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Write a formula for the given measure. Tell what each variable represents. Identify which variable depends on which in the formula.
1. The perimeter of a rectangle with the length of 4 meters.
2. The area of a triangle with a base length of 10 feet.
HELP! i dont know what to do pls help
Help
Answer number 9 algebra 2
Show work
The time can be obtained from 1/0.042 * ln (p(t)/1000)
What is an exponential function?
An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is a variable. The base a is usually a number greater than 1, although it can be any positive number.
Exponential functions have a distinctive characteristic that sets them apart from other types of functions: the value of the function increases or decreases exponentially as the value of x increases or decreases. In other words, the rate of change of the function is proportional to its current value, which results in a rapid growth or decay.
We have that;
p(t) = 1000e^0.042t
p(t)/1000 = e^0.042t
ln (p(t)/1000) = 0.042t
t = 1/0.042 * ln (p(t)/1000)
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Math question 6 help
20 points pls quick and mark brainly
American Eagle Outfitters is advertising 30% off all merchandise.
14A. Zoe wants to buy a sweater that originally costs $40. How much will she save if she buys it on sale? Show your work or explain in words how did you get the answer.
Answer:
Zoe will save 30% of the original cost of the sweater, which is $40. To calculate the amount saved, we must multiply 30% by the original cost of the sweater, which gives us 0.30 x $40 = $12. Therefore, Zoe will save $12 on the sweater with the 30% discount
Step-by-step explanation:
Answer:
She will save $12.00
Step-by-step explanation:
.3 x 40 = 12
30% as a decimal is .3.
The cost of the sweater on sale would be
.7 x 40 = 28
If we take 30% off, we are leaving 70% on.
28 + 12 = 40 the original cost.
Helping in the name of Jesus.
Determine y when x = 18 if y = 20/3 when x = 30
x = 18 ...... y = 20/3
x = 30 ..... y = ?
____________
[tex]y = \dfrac{30 \cdot 20}{3 \cdot 18} = \dfrac{100}{9}[/tex]
B Solve the following showing all steps \( 5 \quad \log _{2}(32)=x \) \( 6 \log _{2}(x-4)+\log _{2}(x)=5 \)
To solve this problem, use logarithmic properties to combine the two equations into one.
First, use the product rule to combine the two equations:
$\log_2(32) + \log_2(x-4) + \log_2(x) = 5$
Then use the power rule to combine the last two terms:
$\log_2(32) + \log_2(x^2 - 4x) = 5$
Finally, use the quotient rule to separate the terms:
$\log_2\frac{32}{x^2 - 4x} = 5$
To solve for $x$, take the inverse logarithm of both sides:
$\frac{32}{x^2 - 4x} = 2^5$
Expand and simplify the left side to get a quadratic equation:
$x^2 - 4x - 32 = 0$
Solve the quadratic equation using the quadratic formula:
$x = \frac{4 \pm \sqrt{4^2 + 4(32)}}{2}$
$x = \frac{4 \pm \sqrt{136}}{2}$
$x = 4 \pm \sqrt{17}$
Therefore, the solutions are:
$x = 4 + \sqrt{17}$
$x = 4 - \sqrt{17}$
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Malcolm is finding the solutions of this quadratic equation by factoring
3r²-24x=-45
Which of these is a correctly factored equation that can be used to find the solutions?
O 3(2-15)(x+1)=0
O 3(x-3)(x-5)=0
○ (3x - 5)(+9) = 0
O (3-3)(r-15) = 0
In a case whereby Malcolm is finding the solutions of this quadratic equation by factoring 3x²-24x=-45, the correctly factored equation that can be used to find the solutions is 3(x-3)(x-5)=0
How can the solution be found?The given equation is 3x²-24x=-45
The equation can be re written as;
3x²-24x=-45
3x²-24x+45 = 0
Then we can divide by 3 and have
x²-8x + 12= 0
thene if we factorize we have
x= 5, x= 3
Therefore, option B is correct. which is 3(x-3)(x-5)=0
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Find all values of m for which the equation has two complex (non-real ) solutions.
The answer of values of m for which the equation has two complex (non-real) solutions are all values greater than 1/8. In other words, m > 1/8
To find all values of m for which the equation has two complex (non-real) solutions, we need to use the discriminant of the quadratic formula.
The discriminant is the part of the quadratic formula under the square root: b²-4ac. If the discriminant is less than 0, then the equation will have two complex (non-real) solutions.
So, let's start by setting the discriminant to be less than 0:
b²-4ac < 0
Now, let's plug in the values from the equation into the discriminant. The equation is in the form ax²+bx+c=0, so we can plug in the values for a, b, and c:
(1)²-4(m)(2) < 0
Simplify:
1-8m < 0
Subtract 1 from both sides:
-8m < -1
Divide both sides by -8:
m > 1/8
So, the values of m for which the equation has two complex (non-real) solutions are all values greater than 1/8. In other words, m > 1/8.
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Knowledge Check Questio Calculate the distance between the points C=(-7,6) and E=(-2,2)
The distance between the points C=(-7,6) and E=(-2,2) is 6.4 units.
To calculate the distance between two points, we use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are C=(-7,6) and E=(-2,2), so we can plug in the values into the formula:
d = √((-2 - (-7))^2 + (2 - 6)^2)
d = √((5)^2 + (-4)^2)
d = √(25 + 16)
d = √(41)
d = 6.4
Therefore, the distance between the points C=(-7,6) and E=(-2,2) is 6.4 units.
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The rational expression (20n^(2)-180)/(4n^(2)+36n+72) is not defined for any values of n for which the denominator equals zero. Find the values of n for which the denominator equals zero.
The final values of n for which the denominator equals zero are n = -3 and n = -6.
The rational expression [tex](20n^2-180)/(4n^2+36n+72)[/tex]is not defined for any values of n for which the denominator equals zero. To find the values of n for which the denominator equals zero, we need to solve the equation [tex]4n^2+36n+72 = 0.[/tex]
First, we can simplify the equation by dividing all terms by 4:
[tex]n^2+9n+18 = 0[/tex]
Next, we can use the quadratic formula to find the values of n:
n = [tex](-9 ± √(9^2-4(1)(18)))/(2(1))[/tex]
n = (-9 ± √(81-72))/2
n = (-9 ± √9)/2
n = (-9 ± 3)/2
The two values of n are:
n = (-9 + 3)/2 = -6/2 = -3
n = (-9 - 3)/2 = -12/2 = -6
So the values of n for which the denominator equals zero are n = -3 and n = -6.
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Phil spent $21 of his $115 pocket money on eating out for one meal. What percent of Phil's pocket money did he spend on eating out for one meal? Round your answer to the nearest hundredth.
Phil spent 18.26% of his pocket money on eating out for one meal.
How do you calculate the percentage difference between two values?The following is the formula for calculating the percentage difference between two values:
100% of ((new value - old value) old value)
In order to describe the change as a percentage, this formula calculates the difference between the new and old values, divides that difference by the old value, and multiplies the result by 100.
Given that, Phil spent $21 of his $115 pocket money.
Thus,
$21 ÷ $115 × 100% = 18.26%
Hence, Phil spent 18.26% of his pocket money on eating out for one meal.
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f(2)=5_(2^(2))+3_(2+1)
Given this function, what is the output
The value of Function f(x) = 5x²+ 3x + 1 at x=2 is 27.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
Given:
We have the Function as
f(x) = 5x²+ 3x + 1
Now, we have to find value of function at x= 2 so
f(x) = 5x²+ 3x + 1
f(2) = 5(2)²+ 3(2) + 1
f(2) = 5(4)+ 6 + 1
f(2) = 20 + 7
f(2)= 27
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H i there what is the answer for this
Answer:
t = 56 degree
Step-by-step explanation:
A triangle is 180 degrees.
The angle on the right is a vertical angle to the 34-degree angle, meaning their angles are equal.
We know two angles; one is 90 degrees, and the other is 34 degrees. To find the angle t, we take
180 - 90 - 34 = 56 degree
So, t = 56 degree
if point a is at (6,2 on coordinate plane and point B is located at (-4,2) what is the distance between the two points
explain please
Answer: 10
Step-by-step explanation:
Since both points have the same y value, we just need to find the change of x, which would be the distance of the points.
Reading the points from left to right on an imaginary graph, point B would come first as it has the lesser x value.
To find the change of x subtract the x value of the second point from the first, so...
6 - (-4) = 10
The change of x = 10
The distance between the points is 10
Hope this helps!
Test the hypothesis that a majority of the population of soft drink consumers prefer pepsi over coke. Use alpha=.10 (define the population parameter in H0)
Test the hypothesis that a majority of the population of soft drink consumers prefer pepsi over coke. Use alpha=.10 (define the population parameter in H0)
H0:
Ha:
Test statistic:
Rejection Region:
Obtain the P value:
Conclusion:
a)z-score
b)z-score > 1.64
c)comparing the z-score to a z-table
d)a majority of the population of soft drink consumers prefer Pepsi over Coke.
To test the hypothesis that a majority of the population of soft drink consumers prefer Pepsi over Coke, we will use a significance level of α = .10.
H0: The proportion of soft drink consumers who prefer Pepsi is ≤ 0.5.
Ha: The proportion of soft drink consumers who prefer Pepsi is > 0.5.
Test statistic: z-score
Rejection Region: z-score > 1.64
We will obtain the P value by comparing the z-score to a z-table.
Conclusion: Based on the P value, if it is less than or equal to the significance level of 0.10, then we reject the null hypothesis. We can conclude that there is sufficient evidence to suggest that a majority of the population of soft drink consumers prefer Pepsi over Coke.
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Give an example of:
1. A vector space V, and a (non-empty) subset of V that is closed under addition but not under scalar multiplication.
2. A vector space V and a (non-empty) subset of V that is closed under scalar multiplication but not under addition.
1). W is closed under addition.
W is not closed under scalar multiplication
2. W is not closed under addition
W is closed under scalar multiplication
1. Let V be the vector space of all 2x2 matrices with real entries. Consider the subset W of V consisting of matrices of the form:
| a b |
| 0 c |
where a, b, and c are real numbers. Note that W is non-empty, since the matrix |0 0| is in W.
|0 0|
Now, let A and B be any two matrices in W, so that A has the form:
| a1 b1 |
| 0 c1 |
and B has the form:
| a2 b2 |
| 0 c2 |
Then the sum of A and B has the form:
| a1+a2 b1+b2 |
| 0 c1+c2 |
which is clearly also in W. Therefore, W is closed under addition.
However, W is not closed under scalar multiplication. Let A be any matrix in W, so that A has the form:
| a b |
| 0 c |
where a, b, and c are real numbers. Then, if we multiply A by a non-real scalar k = xi (where x is a real number and i is the imaginary unit), we get:
kA = xi * | a b | = | xia xib |
| 0 c | | 0 xc |
which is not in W, since the entry in the (1,2) position is non-zero. Therefore, W is not closed under scalar multiplication.
2. Let V be the vector space of all polynomials with real coefficients. Consider the subset W of V consisting of all polynomials of degree at most 2.
Note that W is non-empty, since the polynomial p(x) = 0 is in W.
Now, let c be any real scalar, and let p(x) be any polynomial in W.
Then cp(x) is a polynomial of degree at most 2, since multiplying a polynomial of degree at most 2 by a scalar does not change its degree. Therefore, W is closed under scalar multiplication.
However, W is not closed under addition. Let p(x) and q(x) be any two polynomials in W of degree at most 2. Then the sum p(x) + q(x) may have degree greater than 2, and hence may not be in W. For example, if p(x) = x^2 + 2x + 1 and q(x) = -x^2 + x - 1, then p(x) + q(x) = 3x, which is not in W. Therefore, W is not closed under addition.
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Problem: Suppose you start a business assembling and selling
scooters. It costs you $1500 for tools and equipment to get started,
and the materials for each scooter cost $200 for each scooter. Your
scooters sell for $300. (a) Write and solve a system of equations
representing the total cost and revenue of your business. (b)
Describe what the solution means in terms of the situation. (c) Give
an example of a reasonable number of scooters you could assembly
and sell in order to make a profit and find the profit you will make for
that number of scooters.
a) Tοtal cοst C(x) = 200x + 1500
Revenue cοst R(x) = 300x
What is equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.
Let x be the number οf scοοters.
It cοsts yοu $1500 fοr tοοls and equipment tο get started, and the materials cοst $200 fοr each scοοter.
Here fixed cοst = $1500 and variable cοst = $200
We knοw that cοst functiοn = variable cοst per unit + fixed cοst
Cοst functiοn :
C(x) = 200x+1500
Yοur scοοter sell fοr $300
Revenue functiοn :
R(x) = 300x
(b) The sοlutiοn means
When yοu start a business assembling initial cοst is $1500 fοr tοοls and equipment.
The material cοst will increase $200 fοr each number οf scοοter increases.
The revenue will increase $300 fοr each number οf scοοter increases.
c) Let us take number οf scοοters x=50
Then cοst C(50)=200*50+1500 = 10000+1500=$11500
Revenue Cοst R(50)=300*50=$15000
Then prοfit = Revenue- cοst = 15000-11500 = $3500.
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Irons is trying to lay out the bases for a game of kickball such that the infield is a square as shown. She would like bases to be 25 feet apart. She first placed home base and then places first and third base 25 feet from home base
How far to the nearest tenth of a foot should first base and third base be from each other justify.
The answer of the given question based on the Irons is trying to lay out the bases for a game of kickball such that the infield is a square the answer is first base and third base should be about 35.4 feet apart.
What is Pythagorean theorem?The Pythagorean theorem is fundamental concept in geometry that relates to three sides of right triangle. It states that in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of the squares of lengths of other two sides.
We can use the Pythagorean theorem to find this distance.
Let's call the distance between home base and first base "a". We know that the distance between home base and third base is also "a", because the infield is a square. We also know that the distance between home base and second base (which is the hypotenuse of the right triangle formed by home base, first base, and second base) is 25 feet.
Using the Pythagorean theorem, we can solve for "a":
a² + 25² = a² + a²
2a² = 25²
a² = (25²)/2
a = sqrt((25²)/2) ≈ 17.7 feet
So the distance between first base and third base should be approximately 35.4 feet (2a). Rounding to the nearest tenth of a foot, this is 35.4 feet. Therefore, first base and third base should be about 35.4 feet apart.
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Find the slope of the line through the points (-2, -8) and (8, -8)
Answer:
The two points given are (-2, -8) and (8, -8), which lie on a horizontal line. Since the line is horizontal, the slope is zero.
To see this, we can use the formula for the slope of a line between two points:
slope = (y2 - y1)/(x2 - x1)
Substituting the coordinates of the two given points, we get:
slope = (-8 - (-8))/(8 - (-2)) = 0
Therefore, the slope of the line through the points (-2, -8) and (8, -8) is 0.
Step-by-step explanation:
Answer: d = √(Δy2 + Δx2) = √(02 + 102) = √100 = 10
Step-by-step explanation:
A company makes wax candles in the shape of a rectangular prism. Each candle is 5 inches long, 4 inches wide, and 7 inches tall. How much wax will they need to make 420 candles?
The company will need 58,800 cubic inches of wax to make 420 candles.
How much wax will they need to make 420 candles?To calculate the amount of wax required to make 420 candles,
We need to first calculate the volume of wax required to make one candle,Then multiply that by the total number of candles to find the total amount of wax required.The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.
So, we have
V = 5 in x 4 in x 7 in = 140 cubic inches
To find the total amount of wax required to make 420 candles,
We have
Total amount of wax = 140 cubic inches/candle x 420 candles
= 58,800 cubic inches
Hence, the company needs 58,800 cubic inches
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There are 120 coins made up of Php 5 and Php 10 amounting to Php 950. How many of each kind of coin are there?
To solve this problem, we can use a system of equations.
Let's call the number of Php 5 coins x and the number of Php 10 coins y. The first equation will represent the total number of coins: x + y = 120. The second equation will represent the total amount of money: 5x + 10y = 950. Now we can use the elimination method to solve for one of the variables. Let's multiply the first equation by -10 and then add the two equations together:
-10x - 10y = -1200
5x + 10y = 950
-----------------
-5x = -250
Divide both sides by -5 to get x:
x = 50. Now we can plug this value back into the first equation to solve for y:
50 + y = 120
y = 70
So there are 50 Php 5 coins and 70 Php 10 coins.
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I NEED HELP AND FAST
Answer:
-1 ⇒ -6
0 ⇒ -2
1 ⇒ 2
2⇒6
Step-by-step explanation:
The playground at a park is shaped like a trapezoid. The dimensions of the playground are shown in the diagram.
What is the area of the playground in square feet?
A.3,120 feet2
B.1,768 feet2
C.1,560 feet2
D.3,536 feet2
Answer:
To find the area of the trapezoid-shaped playground, we need to use the formula:
Area = (1/2) × (base1 + base2) × height
In the given diagram, the length of the top base is 24 feet, the length of the bottom base is 48 feet, and the height is 52 feet.
So, the area of the playground is:
Area = (1/2) × (24 + 48) × 52
= (1/2) × 72 × 52
= 1,872 square feet
Therefore, the area of the playground is 1,872 square feet.
The closest option to this answer is option B, which is 1,768 square feet. However, the correct answer is actually 1,872 square feet.