Answer:
(a-b)^2 = a²-2ab+b²
Step-by-step explanation:
(a-b)^2 is not a^2 - b^2.
(a-b)²= (a-b)(a-b)
= a(a-b)-b(a-b)
=a²-ab-ba+b²
=a²-ab-ab+b²
=a²-2ab+b²
Solve this inequality. -9x - 3 > 51 A. x -392 C. x -6
Answer:
The answer is option C.
Step-by-step explanation:
- 9x - 3 > 51
Group like terms
- 9x > 51 + 3
- 9x > 54
Divide both sides by -9
x < - 6
Hope this helps you
Given StartFraction (x minus 2) squared Over 25 EndFraction + StartFraction (y + 3) squared Over 4 EndFraction less-than 1, which point lies in the solution set?
All points that satisfy this Inequality will lie in the solution set.
Given that Start Fraction (x minus 2) squared Over 25 End Fraction + Start Fraction (y + 3) squared Over 4 End Fraction less-than 1, we need to find out which point lies in the solution set.
So, let's analyze the given inequality. We haveStartFraction (x minus 2) squared Over 25 EndFraction + StartFraction (y + 3) squared Over 4 EndFraction less-than 1Since the first term is a fraction with the denominator of 25, it will be maximum when the numerator is minimum. Similarly, the second term will be maximum when the numerator is minimum. Therefore, the given inequality will be maximum when x = 2 and y = -3.
Now, we can substitute these values into the inequality to find out the maximum value of the left side of the inequality. We haveStart Fraction (2 minus 2) squared Over 25 EndFraction + StartFraction (-3 + 3) squared Over 4 EndFraction = 0 + 0 = 0Since this value is less than 1,
all points that are close enough to (2, -3) will be a part of the solution set. In other words, all points whose distance from (2, -3) is less than the distance from (2, -3) to the point on the ellipse that is farthest from it, will be a part of the solution set.
Now, we need to find out the farthest point from (2, -3) on the ellipse.
We know that the ellipse has semi-major and semi-minor axes of lengths 5 and 2 respectively. Therefore, the farthest point from (2, -3) will be the point on the ellipse that lies on the major axis and is farthest from (2, -3).
This point will be (2, -3 + 2) = (2, -1). Therefore, the distance between (2, -3) and (2, -1) will be the maximum distance between (2, -3) and any point on the ellipse. We have d = |-3 - (-1)| = 2.
Therefore, the solution set will contain all points whose distance from (2, -3) is less than 2. In other words, the solution set will be a circle with center at (2, -3) and radius of 2.
We can write the equation of this circle as (x - 2)² + (y + 3)² < 4.
Therefore, all points that satisfy this inequality will lie in the solution set.
For example, the point (2, -2) satisfies this inequality, and therefore lies in the solution set.
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To determine which point lies in the solution set of the given inequality, we need to compare the value of the left side of the inequality to 1. If the left side is less than 1, the point lies in the solution set. If it equals or is greater than 1, it does not.
Explanation:To determine which point lies in the solution set of the given inequality, we need to compare the value of the left side of the inequality to 1. Let's start by rearranging the inequality:
(x - 2)^2/25 + (y + 3)^2/4 < 1
If the left side of the inequality is less than 1, then the point (x, y) lies in the solution set. If the left side equals 1 or is greater than 1, then the point is not in the solution set. To visually represent the solution set, we can graph the equation of an ellipse.
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AABC is similar to AADE. Enter the congruence statements that must be true.
The congruence statements that must be true are
Answer:
A is congruent to A, B is congruent to D, and C is congruent to E
Step-by-step explanation:
If ABC is congruent to ADE, then that means both triangles angles are congruent in the order they are given in.
(Hopefully you can comprehend what I just explained lol-)
how would i anwser this? help pls!
Answer:
Step-by-step explanation:
To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.
For example:
y=-2/3(-6)=7
-2/3x6=-4
-4+7=3
(-6,3)
You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.
To get the x value, you need to fill in the y in the equation y=-2/3x+7
for example:
5=-2/3x+7
-2=-2/3x
3=x
(3,5)
y=-2/3x+7
y=-2/3(15)+7
y=-10+7
y=-3
(15,-3)
y=-2/3x+7
15=-2/3x+7
8=-2/3x
-12=x
(-12,15)
please i need help:/
Answer:
92
Step-by-step explanation:
for each sale, the number of tokens increases by a pattern from 1 sale to 2, the tokens increase by 7. next by 9. next by 11. if this pattern continues, by eaight sales the number of tokens will be 92 tokens
5 -41 tokens
6 - 56 tokens
7 - 73 tokens
8 - 92 tokens
this is my best guess at the problem, if you aren\t working with sequences then this is probably wrong
When keith had 5 years left in college, he took out a student loan for $14,342. The student loan has an annual interest rate of 2.7%. Keith graduated 5 years after acquiring the loan and began repaying the loan immediately upon graduation What was his subsided monthly payment
Keith's subsidized monthly payment upon graduation would be approximately $135.65.
Keith took out a student loan for $14,342 with an annual interest rate of 2.7%. He had 5 years left in college before he began repaying the loan. To find his subsidized monthly payment, we need to first calculate the total amount he owes after 5 years and then divide that by the number of months in the repayment period.
1. Convert the annual interest rate to a decimal: 2.7% ÷ 100 = 0.027
2. Calculate the interest for one year: $14,342 × 0.027 = $387.234
3. Calculate the total interest for 5 years: $387.234 × 5 = $1,936.17
4. Add the interest to the principal amount: $14,342 + $1,936.17 = $16,278.17
5. Assume a standard repayment period of 10 years (120 months) after graduation.
6. Divide the total amount owed by the number of months in the repayment period: $16,278.17 ÷ 120 = $135.65
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(Diversifying Portfolios MC)
worth points)
Name of Stock Symbol High Low Close
Stock A
105.19 103.25 103.38
Stock B
145.18 143.28 144.05
A
B
Last year, an investor purchase
difference in overall loss or ga
O The difference in overall gain is $207.00.
O The difference in overall loss is $207.00.
O The difference in overall loss is $200.70.
O The difference in overall gain is $200.70.
shares of stock A at $90 per share and 75 shares of stock B at $145 per share. What is the
ween selling at the current day's high price or low price?
The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.
To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.
Stock A:
High price = $105.19
Low price = $103.25
Close price = $103.38
Stock B:
High price = $145.18
Low price = $143.28
Close price = $144.05
The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.
To calculate the selling prices, we need to multiply the number of shares by the respective selling price.
Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50
Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50
Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50
Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00
Now, let's calculate the difference in overall gain or loss:
Difference in overall gain = Selling price at the high price - Selling price at the low price
= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)
= $16,148.00 - $15,908.50
= $239.50
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what’s the nth term of -5,-4,-1,4,11,20,31
Answer:
The nth term is n + odd numbers
Thank you and please rate me as brainliest as it will help me to level up
-
1) The difference quotient for f(x)=√x at the point (16, 4) is
a) 16 + h 16
h
b) √4 + h - √16
h
c) √4 + h - 16
h
d) √16 + h - 4
h
Difference quotient for f(x) = √x at (16,4) is √16+h - 4 / h
Difference quotient is mathematical operation used to solve derivation of function by using following formula :
difference quotient = \(\frac{f(x+ h) - f(x) }{h}\)
For the function f(x) = √x at point (16,4)
f(x +h) = \(\sqrt{x+h}\)
putting value in formula
difference quotient = \(\frac{\sqrt{x+h} -\sqrt{x} }{h}\)
now , putting x = 16 ,
difference quotient = √16+h - √16 / h
taking square root of 16 ,
= √16+h - 4 / h
So, the required Difference quotient for the function at (16,4) is √16+h - 4 / h
option (d) is correct
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Evaluate the expression, given functions f , and g :
f(x) =7x−4
g(x) =11−x2
3f(1)−4g(−2)=
Number
The solution of the function 3f(1) - 4g(-2) is -19.
How to solve functions?The functions can be solved as follows;
f(x) = 7x - 4
g(x) = 11 - x²
Therefore, let's solve the composite function as follows:
A composite function is generally a function that is written inside another function.
Hence,
3f(1) - 4g(-2) = ?
f(1) = 7(1) - 4 = 7 - 4 = 3
g(-2) = 11 - (-2)² = 11 - 4 = 7
Therefore,
3f(1) - 4g(-2) = 3(3) - 4(7) = 9 - 28 = -19
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Maureen has a Jump rope that is 62 inches long nancys jump rope is 10 inches longer how long is nancys jump rope?
Answer: 6 feet long
Step-by-step explanation:
1ft. = 12 in
62 inches = 5 feet and 2 inches
Break down 62 into 60 and 2
60 divided by 12 = 5 (12x5=60)
60in. = 5ft.
2in. = 2in.
5ft. and 2in.
10in.= 10in.
Add the inches
10in. + 2 in. = 12 in.
12in.= 1ft.
5ft. + 1ft. = 6ft.
Answer: Nancy’s rope is 6ft. long
Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100
Answer: C
she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week. About how many gallons of milk does the class drink in 10 weeks? Round your answer to the nearest tenth of a gallon if needed.
262.5 gallons of milk does the class drink in 10 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week.
as, we know that
1 pint= 0.125 Galloon
So, 210 pints milk = 210 x 0.125 = 26.25 Galloon
Then, In 10 weeks amount of milk drink
= 26.25 x 10
= 262.5 Gallon
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Which of the following calculations described in the following statements require that you use the addition rule?
A)Calculate the probability of black offspring from the cross AaBb × AaBb,when B is the symbol for the black allele.
B)Calculate the probability of children with both cystic fibrosis and polydactyly when parents are each heterozygous for both genes.
C)Calculate the probability of each of four children having cystic fibrosis if the parents are both heterozygous.
D)Calculate the probability of a child having only sickle-cell anemia or cystic fibrosis if each parent is each heterozygous for both traits.
If probability each parent is heterozygous for both features, determine the likelihood that a child will only have cystic fibrosis or sickle-cell anaemia.
P(Sickle-cell Anemia)
= 0.25
P(Cystic Fibrosis)
= 0.25
P(Sickle-cell Anemia or Cystic Fibrosis) = P(Sickle-cell Anemia) + P(Cystic Fibrosis)
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.25 + 0.25
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.5
The likelihood that a child will have either cystic fibrosis or sickle-cell anaemia is 0.5 or 50%. This is because both parents are heterozygous for both features. This means that each parent has a 25% chance of passing on either one of the conditions to their child. The probability of having either one of the conditions is the sum of the individual probabilities, which is 0.25 + 0.25 = 0.5 or 50%.
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What is the slope of the line that passes through the coordinate points: (0,3)
and (5, 96)?
Answer:
93/5
Step-by-step explanation:
What transformations were applied to ABCD to obtain A'B'C'D?
Answer:
Step-by-step explanation:
The answer is B; 90°
Option C is the correct transformation to transform ABCD to A'B'C'D'.
What are rotation and translation?Rotation involves moving an object about a fixed point. Each point on the object describes a circular path with the center, the center of rotation.
Translation involves moving an object such that only one of the three cartesian coordinates changes during the transformation.
here, we have,
Rotation
Rotate the square ABCD counterclockwise about the origin. Sides AD and BC of square ABCD will become parallel to the sides A'D' and B'C' respectively of the square A'B'C'D'. The square ABCD is, thus, oriented the same way as the square A'B'C'D'.
Vertical Translation
After the rotation, the side AB is 1 unit above the y-axis, which is the same as that of the square A'B'C'D'. So, the vertical position of the square ABCD is the same as that of the square A'B'C'D'.
Horizontal Translation
The side AD of the square ABCD is 5 units to the left of the x-axis. The side A'D' of the square A'B'C'D' is 8 units to the left of the x-axis. So, translate the square ABCD to the left by 3 units to coincide with the position of A'B'C'D'.
Thus, to obtain A'B'C'D' from ABCD first rotate it by 90° counterclockwise then, translate it to the left by 3 units.
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what is a Pythagoras theorem
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
What is mathematical representation of Pythagoras theorem?From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;
C² = a²+b²
Where:
'C' represents the hypotenuse which is the longest part of the triangle and is always diagonal connecting the two other points.'a' represents the perpendicular length that forms the angle 90° of the right angle triangle.'b' represents the base of the triangle.Learn more about Pythagorean formula here:
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Solve each system of equations algebraically. For each one, explain what the solution (or lack thereof) tells you
about the graph of the system.
Solve A and B
PLEASE HELP ASAP!!!
Answer:
a: no solutions
b: (2, 3)
Step-by-step explanation:
a:
In both equations, the slope of x is the same, but the y-intercept is not, which means they are parallel. Therefore, this system of equations has no solutions.
b:
Since both of the equations are equal to y, we can set them equal to each other:
\(\frac{1}{2}x^2+1= 2x-1\\x^2 + 2 = 4x - 2\\x^2-4x+4=0\)
We can solve by factoring (by finding a number that multiplies to 4 and adds up to -4):
(x-2)^2 = 0
x = 2
Now, to find y, plug-in x to any of the equations:
y = 2*2-1 = 3
Therefore, the solution to this system of equation is (2, 3)
I hope this helped.
multiply -x^2(x^2+5x-8)
Answer:
\(-x^4-5x^3+8x^2\)
Step-by-step explanation:
\(\left(-x^2\right)x^2+\left(-x^2\right)\cdot \:5x+\left(-x^2\right)\left(-8\right)\\-x^2x^2-5x^2x+8x^2\\-x^4-5x^3+8x^2\)
Answer: −x4−5x3+8x2
Step-by-step explanation:
What time is it in iowa when the sun goes down in new york at 5:20 pm est?
PLEASE HELP ANSWER!
There are 108 major sources of pollen in state A. These pollen sources are categorized as grasses, weeds, and treesIf the number of weeds is 7 less than thrice the number of grasses, and the number of trees is 3 more than thrice the number of grasses, find the number of grasses, weeds, and trees that are major pollen sources.
The number of grasses is 17, the number of weeds is 3 × 17 - 7 = 42, and the number of trees is 3 × 17 + 3 = 56.
What are pollens?Pollen is a fine powdery substance consisting of microscopic grains that are produced by the male reproductive organs of seed plants.
Let's call the number of grasses "G".
The number of weeds is 3G - 7.
The number of trees is 3G + 3.
The total number of sources is G + (3G - 7) + (3G + 3) = 108.
Combining like terms, we get 7G = 118.
Dividing both sides by 7, we find G = 17.
Therefore, the number of grasses is 17, the number of weeds is 3 * 17 - 7 = 42, and the number of trees is 3 × 17 + 3 = 56.
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it takes a boat 3 hours to down a river from point A to point b and 5 hoursto travel up the river from B to A how long would it take the same boat to go to a to b in still water
Answer:
3 3/4 hr
Step-by-step explanation:
I had an 'aha moment' while I was out on a starlit run...(Check out the night sky just after sunset.(Northern hemisphere)...Venus and Jupiter are very near each other and BRIGHT....add the moon and Mars for almost a straight line !)
the time it takes up stream = 5 hours = distance / (r-s)
so d = 5 (r-s)
downstream = 3 hours = distance/ (r+s)
so d = 3(r+s)
Equate these two definitions of d
5r- 5s = 3r+ 3s
2r = 8s
r = 4 s so set a distance say 15 miles
then r = 4 and s = 1 to get 5 hrs and 3 hrs
if d = 15 and r = 4 the time for still water travel = 15/4 = 3 3/4 hrs
As another example say r = 6 then s = 6/4 then d = 22.5
22.5 / 6 = 3 3/4 hrs <===== same answer
So distance is NOT required to answer this question!
(7u)/(u-9) find the equivalent rationale expression
\( \frac{7u}{u - 9} = \frac{7u - 63 + 63}{u - 9} = \frac{7(u - 9) + 63}{u - 9} \)
\(= \frac{7(u - 9) }{u - 9} + \frac{63}{u - 9} \)
\( = 7 + \frac{63}{u - 9} = 7\frac{63}{u - 9} \)
Answer:.......
Ok done. Thank to me :>
Which of the following expressions represents 3 less than 5 times a number
A) 5n - 3
B) 5 - 35
C) 3n - 5
D) 3 - 5
Answer:
A)
Step-by-step explanation:
The correct expression which represents ''3 less than 5 times a number'' would be,
A) 5n - 3
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that,
A mathematical expression is,
''3 less than 5 times a number''
Let us assume that,
A number = x
Hence, the expression to represent ''3 less than 5 times a number'' is,
⇒ (5 × n) - 3
⇒ 5n - 3
So, the correct option is,
A) 5n - 3
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What is the surface area of the cylinder with height 3 cm and radius 2 cm? Round your answer to the nearest thousandth.
Work Shown:
r = 2 = radius
h = 3 = height
SA = surface area of the cylinder
SA = 2*pi*r^2 + 2*pi*r*h
SA = 2*pi*2^2 + 2*pi*2*3
SA = 8pi + 12pi
SA = 20pi ....... exact surface area
SA = 20*3.1415926535898
SA = 62.831853071796
SA = 62.832 ....... approximate surface area
Ivy wants to see 20 birds on her hike. So far, she has seen 8. How many more birds does she need to see.
Answer:
12
Step-by-step explanation:
20-8=12
Is the relation shown in the table below a function? (type in yes or no)
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
What is the absolute value of l -32 l?
Represent the following sentence as an algebraic expression, where “a number” is the letter x1 is subtracted from a number
Let:
x = Unknown number
We need to subtract 1 from the unknown number, therefore:
\(x-1\)Answer:
x - 1