Answer:
(1) (4x - 5y)(4x + 5y)
Step-by-step explanation:
Question 42
16x² - 25y²The identity to be used is : a² - b² = (a - b)(a + b)(1) (4x - 5y)(4x + 5y)Answer:
(1) (4x - 5y)(4x + 5y)
Step-by-step explanation:
Difference of Two Squares: [tex]a^2-b^2=(a-b)(a+b)[/tex]
Therefore, we can use The Difference of Two Squares to factor this expression quickly.
Given expression: [tex]16x^2-25y^2[/tex]
[tex]16=4^2 \implies 16x^2=4x \cdot 4x=(4x)^2[/tex]
[tex]25=5^2 \implies 25y^2=5y \cdot 5y=(5y)^2[/tex]
Therefore:
[tex]16x^2-25y^2=(4x)^2-(5y)^2[/tex]
Using The Difference of Two Squares:
[tex](4x)^2-(5y)^2=(4x-5y)(4x+5y)[/tex]
The side of a square is a x-3 , Find the area of the square.
Answer:
x^2 -6x + 9
Step-by-step explanation:
(x-3) (x-3) = x^2 - 6x + 9
Find the gradient of the line segment between the points (-5,-2) and (4,3).
Give your answer in its simplest form.
Answer:
5/9
Step-by-step explanation:
Solution
The gradient of the line ment when two segment given (X1, Y1) and (X2, Y1) is points
m =
[tex] \frac{y2 - y1}{x2 - x1 } [/tex]
Here two points given, (-5,-2) and (4,3)
gradient (m):
[tex] \frac{3 - ( - 2)}{4 - ( - 5)} [/tex]
Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination.
If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?
84
504
3,024
60,480
Answer:
504 combos
Step-by-step explanation:
Cannot use digits twice and last is '7'
9 digits for first place choice
8 digits for second place
7 digits for third place
only '7' for fourth place 9 x 8 x7 = 504 combos
You can use the rule of product from combinatorics to find out how many ways can the remaining digits be chosen.
The remaining digits for the given condition can be chosen in 504.
Option B: 504
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
Since 7 is already fixed and there is constraint that no two digits can be used, thus, we initially have only 10-1 = 9 digits.
For first place, we can chose 1 digit out of 9 digits in ways,
⁹C₁ = 9 ways
For second place, as one of the digit is used, thus, 1 digit out of 8 digits can be chosen in ways,
⁸C₁ = 8 ways
For third place, as two of the digits is used, only 7 digits are remaining to chose from. Thus, 1 digit out of 7 remaining digits can be chosen in ways.
⁷C₁ = 7 ways
Using product rule, we get:
Total possible number of choices for choosing digits for first, second and third position of lock with given constraints is given as
= 9 x 8 x 7
= 504 ways
Thus, The remaining digits for the given condition can be chosen in,
Option B: 504
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Can someone help me with this geometry problem
Answer:
Step-by-step explanation:
the average price of a movie ticket was $4.35 in 1996. the average price of a movie ticket was $9.16 in 2020. what was the average rate of change? if this rate continues, predict the cost of a movie ticket in 2025.
Answer:
10.16
Step-by-step explanation:
average change = 9.16 - 4.35 / 2020 - 1996 = 0.2
Cost = 9.16 + (2025 -2020) x 0.2 = 10.16
So the answer is $10.16
(√3+√7) (√3-√7) pl and me
[tex]\left( \sqrt 3 + \sqrt 7\right) \left( \sqrt 3 - \sqrt 7\right)\\\\=\left(\sqrt 3 \right)^2 - \left(\sqrt 7 \right)^2\\ \\=3-7\\\\=-4[/tex]
Answer:
- 4
Step-by-step explanation:
([tex]\sqrt{3}[/tex] + [tex]\sqrt{7}[/tex] )([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] )
each term in the second factor is multiplied by each term in the first factor.
[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) + [tex]\sqrt{7}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) ← distribute parenthesis
= 3 - [tex]\sqrt{21}[/tex] + [tex]\sqrt{21}[/tex] - 7 ← collect like terms
= - 4
A fair spinner has 12 equal sections: 4 red, 3 blue and 5 green. It is spun twice. What is the probability of getting the same colour twice?
Answer:
25/72
Step-by-step explanation:
Total outcomes :
(5 + 4 + 3)²(12)²144 outcomesP (red twice) :
16/1441/9P (blue twice) :
9/1441/16P (green twice) :
25/1445/12Adding :
1/9 + 1/16 + 5/1216/144 + 9/144 + 25/14450/14425/72Divide.
3.9 ÷ 100,000
Enter your answer as a decimal in the box.
i dont know what to do here
Answer: 0.000039
Step-by-step explanation: i us calculator
Answer:
0.000039.
Step-by-step explanation:
3.9 / 100,000
Move the decimal point 5 places to the left ( as there are 5 0's in 100,000)
filling in the zeroes as you move alomg.
So its 0.000039
What is the length of the diagonal from B to D of this rectangle? Round your answer to the nearest tenth of a metre.
Answer:
2√97
Step-by-step explanation:
BD² = BC² + DC²
⇒ BD = √BC² + DC²
= √(18)² + (8)²
= √324 + 64
= √388
Rewrite 388 as 2² · 97.
Factor 4 out of 388.
√4(97)
Rewrite 4 as 2².
√2² · 97
Pull terms out from under the radical.
2√97
The result can be shown in multiple forms.
Exact Form:
2√97
Decimal Form:
19.69771560...
Parents plan to ship some items to their child who is attending college out of town. The
student definitely needs towels, which weigh 9 pounds. The cost is $45 to ship up to 15
pounds.
a. Write and solve an inequality that represents how many pounds the parents can add
to the shipment without having to pay additional shipping costs.
b. The parents want to ship another item in addition to the towels. Which of the
following items can they send without paying extra shipping?
Item
Weight (pounds)
boots
9
tennis rackets
5
dishes
18
soccer equipment
14
1
The student decides that the tennis rackets and the towels are needed. How does
this affect the inequality in part (a)?
The inequality that represents this situation is x ≤ 6. On the other hand, the parents can ship only the tennis rackets.
What equality represents this situation?The equality that represents this situation is x ≤ 6 because the number of pounds that can be added (x) has to be 6 or less than 6.
What other item can they ship?The parents can only ship the tennis rackets because these are 5 pounds which meets the criteria of the inequality.
What happens if the student needs the towels and the tennis racket?The inequality would change to x ≤ 1 because the weight that could be added if he needs these producs changes to only 1 pound.
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Which function has the same minimum value as ? f(x) = 3x 3 f(x) = |x| 3 f(x) = –x2 3
The function that has the same minimum value as fx= 3x³ is f(x) = x + 3.
What is a function?It should be noted that a function simply means a relation or expression that involves two or more variables.
In this case, the function that has the same minimum value as the expression of 3x³ is f = x + 3.
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Answer:
B. f(x) = /x/ + 3
Step-by-step explanation:
edg 22'
Find the statement Pk + 1 for the given statement Pk
Step-by-step explanation:
k has to be replaced by k+1.
so,
4 / ((k+1)(k+1 + 3)) = 4 / ((k+1)(k+4))
I am not sure how far your teacher expects you to go with this.
just in case, I will do also the full multiplications
4 / ((k+1)(k+4)) = 4 / (k² + 4k + k + 4) = 4 / (k² + 5k + 4)
and if you need the factor to go from Pk to Pk+1 :
Pk+1 / Pk = (4/((k+1)(k+4))) / (4/(k(k+3)) =
= (4/((k+1)(k+4))) × (k(k+3))/4 =
= (k(k+3)) / ((k+1)(k+4))
Find the volume of this right triangular prism 5cm 8 cm 3 cm
Answer:
I can help, but can you label which is base, height, and length
Step-by-step explanation:
Identify the situation below as having a positive correlation, negative correlation, or no correlation.
Explain your answer.
The temperature outside and the amount of ice cream sales at an ice cream shop.
Answer:
positive correlation
Step-by-step explanation:
As the temperature increases, the ice cream sales will increase.
Since both x and y are increasing, this is a positive correlation.
which company would cost the most to serve 300 students
Answer:
Company "A"
Step-by-step explanation:
its the highest line on the graph from the 300 point.
Joe bought 3 tacos and 1 asada fry for $12.50.
Sam bought 1 taco and 2 asada fries for $13.75.
Write a system of equations that could help you
find the cost of each item.
Answer:
I am not too sure so I deeply apologize for any wrongs, but this is my thinking.
Joe bought each taco for 4 dollars, and bought an asada fry for 50 cents.
On the other hand-
Sam also bought 1 taco for 12 dollars, and bought 2 asada fries, one of them was 1 dollar, and one of them was 75 cents.
3x^2 + 14x +8 find magic x
x = -2/3 or -4
see the attachment for solution
hope it helps...!!!
If you roll a die twice what is the probability of rolling a 3 the first time and then rolling a 4 the second time? write your answer as a fraction
Answer:
Step-by-step explanation:
P(3 and 4)= 1/6×1/6
=1/36
Austin worked 28 hours last month and won $8 per hour. he was already spent $19 of your income. How much money does he have left?
Answer:
[tex]\huge\boxed{\sf \$\ 205}[/tex]
Step-by-step explanation:
Work hours = 28 hours
Earning = $8 per hour
1 hour = $8
28 hours = $8 × 28
28 hours = $224
He has earned $224 last month.
Spent = $19
Left:
= Earning - Spent
= $224 - $19
= $205
[tex]\rule[225]{225}{2}[/tex]
if there was 9/15 of leftover pizza, and jimmy ate 5/15 of the leftover pizza, how much of the original pizza did he eat
Answer:
— Work in pizza slices, assuming a dozen per pizza. If I buy 36 slices, and eat 5 slices, and Joe eats 15 slices, there should be 36 - 5 - 15 = 16 slices left.
Step-by-step explanation:
Teresa changed number shr used for her internet password every day. This is how she figured her password:A whole number that is equal to four times the fourth power of the day of the month divided by two times the square day of the month. If today id the 7th day of the month, What is teresa's password?
Using a system of equations, it is found that Teresa's password in the 7th day of the month is of 98.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The rule for her password is defined as follows: A whole number that is equal to four times the fourth power of the day of the month divided by two times the square day of the month. Hence, considering n as the day of the month, the equation is given by:
[tex]P = \frac{4n^4}{2n^2} = 2n^2[/tex]
Hence, for the 7th day, the password is given by:
P = 2 x 7² = 98.
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Mariana ha tirado 20 veces a la canasta y ha fallado la quinta parte de los tiros ¿cuantas canastas a metido?
plissssssssssssssssssssss
Veremos que de los 20 intentos, Mariana metio 16 canastas.
¿Cuantas canastas a metido Mariana?
Sabemos que ella tiro 20 veces, y sabemos que ella ha errado 1/5 de los tiros.
Entonces los otros 4/5 tiros entraron. Para obtener el numero de canastas que ha metido, debemos multiplicar la fracción por la cantidad total de tiros al aro:
C = 20*(4/5) = 16
Así, podemos concluir que Mariana ha metido 16 canastas.
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Find the nth term of this number sequence 2, 4, 6, 8, ...
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The given sequence is in Arithmetic progression, and we have to find its nth term ~
So, let's get it solved ~
First term of the sequence is :
a = 2Common difference is :
d = 6 - 4 = 4 - 2 = 2Now, if we have to write the 2nd Term with respect to first one, we can write :
2nd Term = a + (2 - 1)d = a + d = 2 + 2 = 4similarly ~
3rd Term = a + (3 - 1)d = a + 2d = 2 + 4 = 64th Term = a + (4 - 1)d = a + 3d = 2 + 6 = 8Therefore, I similar pattern ~
[tex] \qquad \sf \dashrightarrow \: nth \: term = a + (n - 1)d[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2 + (n - 1)2[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2(1 + (n - 1))[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2(1 + n - 1)[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2 n [/tex]
Feel free to ask your doubts, if you have any ~
Answer:
2nStep-by-step explanation:
from the number sequence above, each term except the first is generated by adding 2 to the term immediately preceding it.
the nth term of the sequence is usually designated Tn, and it's usually a function of n
from the number sequence
T1= 2
T2 = 2+2= 4
T3= 4+2= 6
T4= 6+2= 8
therefore, Tn= 2+2×(n-1)
= 2+2n-2
=2-2+2n= 2n
therefore, the nth term of the number sequence= 2nWhat is the solution to this equation?
log + log 3 =
log(+1)
OA I=
OB.
I=
OC
I=
D. = 1
312
NIT
13
Answer:
[tex]\textsf{B.} \quad x=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Log laws
[tex]\textsf{Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\textsf{Equality law}: \quad \textsf{if }\: \log_ax=\log_ay\:\textsf{ then }\:x=y[/tex]
Therefore:
[tex]\large \begin{aligned}\log_6 x+ \log_6 3 & =\log_6 (x+1)\\\log_6 (3x) & =\log_6 (x+1)\\3x & =x+1\\2x & =1\\x & =\dfrac{1}{2}\end{aligned}[/tex]
Which statements are true? select three options. milk was requested for 16 of the large-sized meal orders. soda was requested for 280 of the kids’ meal orders. a juice box was requested for 82 of the regular-sized meal orders. sixty-three of the orders of soda came with a regular-sized meal. a total of 124 large-sized meals were ordered.
The true statements are:
A. Milk was requested for 16 of the large-sized meal orders;D. Sixty-three of the orders of soda came with a regular-sized meal; andE. A total of 124 large-sized meals were ordered.Calculations and Parameters:Given:
Total no of meals with milk= 71Regular size meals= 55Regular sized meals with soda= 63To find the large size meals that came with milk,
71-55= 16.
Therefore, the total number of large size meals ordered was:
16+22+86 = 124.
Hence, options A, D and E are correct.
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Hi Guys. My name is ❀ ❀.
What is 3x+6 if x=5?
A. 21
B. 54
C. 1002
D. 30
Answer:
A is the answer
Step-by-step explanation:
3×5+6=15+6=21
help help help help help
Answer:
∠ T = 76°
Step-by-step explanation:
RSTU is a cyclic quadrilateral
the opposite angles of a cyclic quadrilateral sum to 180°
∠ T + ∠ R = 180°
∠ T + 104° = 180° ( subtract 104° from both sides )
∠ T = 76°
Help please
y + 4- 6(x +7)
Answer: y - 6x +46
Step-by-step explanation:
y + 4- 6(x +7)
y + 4 - 6x +42
y - 6x +46
In Debi's Girl Scout troop, of the girls have brown eyes, of the girls have blue eyes, and of the girls have hazel eyes. What fraction of the
either brown eyes or hazel eyes? [Note: Write your answer in simplest form.]
Save and Exit
Next
Subm
O
-IN
5/6 girls have either blue or brown eyes. Since 2/9=4/18
And 11/18 + 4/18 = 15/18
You can simplify 15/18 to 5/6
What are the values of a and b? a = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8
The value of a and b given that the opposite side are equal are 17 and 6 respectively
Properties of a kiteThe kite is a quadrilateral with 4 sides and the opposite side of the side are equal. If they are, then;
2a - 4 = 30
2a = 34
a = 17
Similarly
3b+6 = 24
3b = 18
b = 6
Hence the value of a and b given that the opposite side are equal are 17 and 6 respectively
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