Remark
Answer: The second one. The second step removes the brackets on the right. It uses the distributive property which puts back the common factor that was taken out of the two terms 6x and 24. Quite often the distributive property is useful when presenting a problem to be solved.
The associative property is more of an order thing and that is very useful sometimes as well what it says is that if you have three numbers a + b + c the order which you combine things does not matter.
For example 3 + 4 + 5 could be combined as 3 + 4 = 7; 7 + 5 = 12 or 3 + 5 = 8, 8 + 4 = 12.
The associative property is useful when adding fractions.
What is the greatest integer k such that 2k is a factor of 67!?
67!/2 = k = 18 235 555 459 094 342 644 124 929 548 302 732 213 583 817 657 024 762 296 850 814 250 133 981 218 471 936 000 000 000 000 000
about 1.82×10⁹⁴
Answer:
k=64
Step-by-step explanation:
To find out the greatest integer such that 2^{k}is a factor if 67!
We divide the quotients by 2 and then finally add all the quotients.
67/2 = 33.5 --------> 33
33/2 = 16.5 ---------> 16
16/2 = 8 --------> 8
8/2= 4 ---------> 4
4/2 = 2--------> 2
2/2 = 1 ----------> 1
k= 33+16+8+4+2+1
= 64
Hence, 64 is the greatest integer such that 2^{k} is a factor of 67!.
Using the diagram on the right, find the length of GT and TA.
GT = 13 and TA = 3
Triangles GRT and GEA are similar and so the ratios of corresponding sides are equal
[tex]\frac{16}{16-x}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )
8(16 - x) = 80
128 - 8x = 80
- 8x = - 48 ⇒ x = 3 = TA
16 - x = 16 - 3 = GT
Answer: GT = 13 and TA = 3
Triangles GRT and GEA are similar and so the ratios of corresponding sides are equal
= ( cross- multiply )
8(16 - x) = 80
128 - 8x = 80
- 8x = - 48 ⇒ x = 3 = TA
16 - x = 16 - 3 = GT
TA = 6 and GT = 10 ( arithmetic !!)
Step-by-step explanation:
When rolling a fair number cube with numbers 1 through 6, what is the probability of rolling a number greater than 2?
A.) 1/2
B.) 1/4
C.) 2/3
D.) 5/6
You are asking for the proportion of numbers 1–6 that are greater than 2. The ones greater than 2 are 3, 4, 5, 6. There are 4 of them, out of the 6 possible numbers. Since the cube is fair, all numbers have equal probability. This means the probability of an outcome greater than 2 is
... 4/6 = 2/3
The appropriat choice is ...
... C.) 2/3
Am i right geometry below
I believe so. :) correct me if i'm wrong.
What is the y-coordinate of A'? (picture included)
y- coordinate 0f A' = 2
note that the coordinates of A(1, 2 ) and the centre of dilatation (4, 2) both have the same y- coordinate 2
This means they are both on the horizontal line y = 2
and so the y- coordinate of A' will also be 2
Answer both please man. Or sorry you'll get a 1 star rating. THanks for answering guys!
For the first one,
x = 10.
For the second one,
x = 12
x = [tex]\frac{60}{9}[/tex] and x = [tex]\frac{45}{8}[/tex]
Since in both cases the figures are similar then the ratios of corresponding sides are equal
[tex]\frac{x}{15}[/tex] = [tex]\frac{4}{9}[/tex] ( cross- multiply )
9x = 60 ( divide both sides by 9 )
x = [tex]\frac{60}{9}[/tex]
and [tex]\frac{x}{5}[/tex] = [tex]\frac{9}{8}[/tex]
8x = 45 ( divide both sides by 8 )
x = [tex]\frac{45}{8}[/tex]
Solve using synthetic division. (x^3 − 2x^2 − 5x + 6) ÷ (x − 1)
1 | 1 - 2 - 5 6
1 - 1 - 6 0
quotient = x² - x - 6 = (x - 3 )( x + 2 )
lm is the angle biesector of nlk and nlk=72,what is klm
∠KLM = 36°
the angle bisector divides ∠NLK into 2 equal angles
∠NLK = ∠NLM + ∠KLM
since ∠NLK = 72° then ∠NLM = ∠KLM = 36°
!!!! I need help with numbers 1 and 9 please !!!!!
(1)
given [tex]\frac{j}{6}[/tex] = [tex]\frac{9}{10}[/tex] ( cross- multiply )
10j = 54 ( divide both sides by 10 )
j = [tex]\frac{54}{10}[/tex] = [tex]\frac{27}{5}[/tex] ← in simplest form
(9)
let h be the hours worked daily , then
3h = 20 [tex]\frac{2}{3}[/tex] = [tex]\frac{62}{3}[/tex] ( divide both sides by 3 )
h = [tex]\frac{62}{3}[/tex] ÷ 3
= [tex]\frac{62}{3}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{62}{9}[/tex] = 6 [tex]\frac{8}{9}[/tex]
She worked 6 [tex]\frac{8}{9}[/tex] hours each day
Which pair of angles shares ray A.F as a common side? DAF and DAB EAF and CAE BAF and EAD BAF and FAD
Look for the adjacent letters A.F or F.A in the names of the pair of angles.
The appropriate choice is ...
... BAF and FAD
Answer:
BAF and FAD
Step-by-step explanation:
In order for an angle to have A.F as a side, it must have the letters A.F or FA in its name.
In DAF, the angle is made of rays AD and A.F. In DAB, the angle is made up of rays AD and AB. This is not the correct pair.
In EAF, the angle is made of rays AE and A.F. In CAE, the angle is made up of rays AC and AE. This is not the correct pair.
In BAF, the angle is made of rays AB and A.F. In EAD, the angle is made up of rays AE and AD. This is not the correct pair.
In BAF, the angle is made up of rays AB and A.F. In FAD, the angle is made up of rays A.F and AD. This is the correct pair.
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B. PLEASE HELP ITS DUE TODAY!!!
X= amount of rides
Y=total price (33.50)
Equation: 0.75(18) + X = 33.50
13.50+ X=33.50
-13.50 -13.50
X=20.00
Admission=20.00
Answer:
Part a) [tex]x=18\ tickets[/tex], [tex]y=\$33.50[/tex]
Part b) [tex]y=0.75x+20[/tex]
Step-by-step explanation:
Let
x------> the number of ride tickets.
k-----> constant that represent the cost for festival admission
y----> the total cost
we know that
[tex]y=0.75x+k[/tex]
we have that
[tex]x=18\ tickets[/tex]
[tex]y=\$33.50[/tex]
substitute the values
[tex]33.50=0.75(18)+k[/tex]
solve for k
[tex]k=33.50-0.75(18)[/tex]
[tex]k=\$20[/tex]
The linear equation to calculate the cost for anyone who only pays for festival admission and rides is equal to
[tex]y=0.75x+20[/tex]
You have also set up a card game in which a player picks a card from a standard deck of 52 cards. The player wins if these two events occur together: E1, in which the card drawn is a black card, and E2, in which the card drawn is a numbered card, 2 through 10.What is the probability of getting a black card and a numbered card? Calculate the probabilities P(E1) and P(E2) as fractions.
First, let's count:
there are 26 possible outcomes for E1 (black card)
there are 4x9 = 36 possible outcomes for E2, to pick a numbered card (any color)
there are 2x9 =18 possible outcomes for E1 (black) AND E2 (numbered, spade + clower)
the probability of E1 AND E2 is the ratio of the count of possible outcomes for E1 + E2 and the count of all possible outcomes (52 choices to pick a card from the deck):
P(E1 and E2) = 18/52 (34.6%)
And as asked:
P(E1) = 26/52 = 1/2 (50%)
P(E2) = 36/52 = 9/13 (69.2%)
[tex]n (S) = 5\\ n (E_1) = 2 x 13 = 26\\P (E_1) \frac{n (E_1)}{n (S)} = \frac {26}{52} = \frac{1}{2} \\\\ n (E_2) 4 x 9 = 36\\P (E_2)\frac{n (E_2)}{n (S)}=\frac{36}{52}= \frac{9}{13}[/tex]
EDMENTUM / PLATO ANSWER!!!!!!!!
CAN JUST WRITE:
[tex]P (E_1) \frac{n (E_1)}{n (S)} = \frac {26}{52} = \frac{1}{2}[/tex] = (50%)
[tex]P (E_2)\frac{n (E_2)}{n (S)}=\frac{36}{52}= \frac{9}{13}[/tex] = (69.2%) :)))))
Solve x -2/3(3x - 4) + 3x = 5/6 is x -19/6, 11/6, 21/6, 29/6
Answer:
x=-11/12
Step-by-step explanation:
Given an equation for x
x -2/3(3x - 4) + 3x = 5/6
We are asked to find the value of x.
We use equation rules to solve
To get rid of denominator in fraction, let us multiply the whole equation by 6.
6x-4(3x-4) +18x = 5
Simplify:
-6x+18x+16 =5
12x = 5-16 = -11
x = -11/12
Answer:
- 11/6
Step-by-step explanation:
A theater can seat 550 people. The number of rows is 3 less than the number of seats in each row. How many rows of seats are there?
The number of rows will be a divisor of 550 such that the quotient is 3 more.
... 550 = 1×550 = 2×275 ≈ 5×110 = 10×55 = 11×50 = 22×25
Factors 22 and 25 differ by 3.
The number of rows of seats is 22.
_____
The number of seats in a row is 25.
The theater has 22 rows of seats. To find this, we solve the equation x(x - 3) = 550, where x is the number of seats per row, leading to x = 25 seats per row and 22 rows after subtracting 3.
To find out how many rows of seats are in the theater with a seating capacity of 550, where the number of rows is 3 less than the number of seats in each row, we can set up an equation to solve for the number of rows. Let the number of seats per row be represented by x, and the number of rows will then be x - 3. Since the total number of seats in the theater is the product of the number of rows and the number of seats per row, we have the equation x(x - 3) = 550.
Now, we will factor this quadratic equation to find the value of x.:
x² - 3x - 550 = 0
Factoring this, we find that it breaks down into (x - 25)(x + 22) = 0. We can then find the value of x by setting each factor equal to zero:
x - 25 = 0: x = 25x + 22 = 0: x = -22 (negative values are not feasible for number of seats)We ignore the negative solution since we cannot have a negative number of seats. Hence, there are 25 seats in each row. To find the number of rows, we subtract 3 from the number of seats per row: 25 - 3 = 22 rows.
Therefore, the theater has 22 rows of seats.
A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand X aspirin. How many doctors use brand X aspirin? (Hint: Solve for X)
Show your work
2000 times 0.60 = 1200 doctors
3/5=0.6
x= 2000* 3/5
x=2000*0.6
x=1200
so... 1200 doctors use brand X aspirin.
I’m literally begging u for help, I need help with the last question in the pic I’m
Jeremy is opening a savings account earning simple interest. he plans to deposit his $50 birthday money and leave the account alone until he goes to college. he will earn $5 per year in interest.
I just need help with the last question plzzzz
If the second coordinate of the ordered pair represents the dollar amount in Jeremy's savings account, then adding 10 to it means that $10 has been added to Jeremy's account.
−4x + 3y = 15, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 40km/hr.
26.25 hours = 26 hours 15 minutes
substitute y = 40 into the equation and solve for x
- 4x + 120 = 15 ( subtract 120 from both sides )
- 4x = - 105 ( divide both sides by - 4 )
x = 26.25 hours = 26 hours 15 minutes
Melissa put her cat, Herman, on a diet and kept track of his weight. At the end of 4 weeks, she recorded Herman's weight change as −4 1/2 ounces. She noticed that he had lost the same amount of weight each week. What is Herman's weight change each week of the diet? Enter your answer in the box.
-103
if he lost the same weight each week that means -412 (the weight he lost) ÷ 4 (number of weeks) = -103 (amount of weight lost in one week)
Answer: -1 1/8
Step-by-step explanation: When you have a problem like this, you have to divide.
So you turn the improper fraction into a mixed number which (4 1/2 turns into 9/2) and then you do KCF (Keep Change Flip). So you keep the 9/8, change division into multiplication, and since we are going to put the four over a 1 like this 4/1, we need to change it into 1/4. Then you multiply across. 9x1=9 and 2x4=8 so it would be 9/8. But it's an improper fraction right? So you do long division, and you get -1 1/8.
WILL GIVE BRAINLIEST ANSWER PLEASE HELP In a theater there are 12 seats on the first row and 16 seats in the second row. the number of seats in a row continues to increase by 4 with each additional row
a. write and iterative (explicit rule to model the sequence formed by the number of seats in each row. Show your work
b. use the rule to determine which row has 60 seats. Show your work
(a) [tex]a_{n}[/tex] = 4n + 8
(b) row 13 has 60 seats
(a)
the sequence of seats is an arithmetic sequence whose n th term is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
where [tex]a_{1}[/tex] is the first term and d the common difference
here the sequence is 12, 16, ....
with [tex]a_{1}[/tex] = 12 and d = 16 - 12 = 4, thus
[tex]a_{n}[/tex] = 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8
(b)
calculate the number of rows n when 60 seats
solve 4n + 8 = 60 ( subtract 8 from both sides )
4n = 52 ( divide both sides by 4 )
n = 13 ← number of rows
BRAINLIEST!!
A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
• When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $80.
• When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $100.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A) (2, 12)
B) (4, 24)
C) (12, 2)
D) (24, 4)
Set up the equations:
2x+3y=80
1x + 4y = 100
solve for x and y:
1x + 4y = 100
x = 100-4y
plug into first equation
2(100-4y)+3y=80
200-8y+3y=80
y=120/5=24
x = 100-4y=100-96=4
So the charges are (x,y)=(4,24)
So the correct answer (B)
What is the value of x?
A.)62°
B.) 46°
C.) 56°
D.) 134°
The sum of the interior angles in a triangle is 180°. To find the value of x, you must subtract 47 and 71 from 180.
180-47-71=x
x=62
The answer is A. 62°
The subscription to a popular magazine decreased from $66 per year to $52.80 per year. What is the percent of decrease for the magazine's subscription?
Final answer:
The percent of decrease for the magazine's subscription is 20%.
Explanation:
To find the percent of decrease for the magazine's subscription, we need to calculate the difference between the original price and the new price, and then divide it by the original price.
The decrease in price is $66 - $52.80 = $13.20.
The percent of decrease is ($13.20 / $66) * 100% = 20%.
Locating Zeros of Polynomial Functions:
Determine the zeros to the nearest tenth
A graph shows zeros near -1.449 and +3.449. These suggest that one factor is the quadratic (x -1)² -6. That makes the other quadratic factor be (x -0.5)² +0.75. So, the complete factorization in integers is
... f(x) = (x² -2x -5)(x² -x +1)
The two real roots are near ...
... d. -1.4, 3.4
Megan is going on a long distance road trip. She drives for 13 miles before being able to travel at a constant speed using cruise control. The equation used to find her total distance traveled is shown below.
y = 59x + 13
If y is the total number of miles driven, and x is the number of hours driven after reaching 13 miles, which statement best describes the rate of change in the distance traveled?
A. For every 13 hours, she will drive 72 miles.
B. For every two hours, she will drive 59 miles.
C. For every hour, she will drive 59 miles.
D. For every hour, she will drive 72 miles.
The rate of change of y (miles traveled) with respect to x (time in hours) is 59, the coefficient of x. The appropriate choice is ...
... C. For every hour, she will drive 59 miles.
The equation y = 59x + 13 shows that Megan's rate of change in distance traveled is 59 miles for every hour driven at cruise control, after the first 13 miles. So, the correct answer is C. For every hour, she will drive 59 miles.
The equation y = 59x + 13 represents Megan's total distance traveled after driving the first 13 miles without cruise control. The variable y stands for the total number of miles driven, and x represents the number of hours driven at a constant speed using cruise control. To identify the rate of change in the distance traveled, we look at the coefficient of x in the equation, which is 59. This coefficient indicates how many miles are added to the initial 13 miles for every hour of driving at cruise control. Therefore, for every hour, Megan will drive 59 miles after the initial 13 miles are accounted for. It is important to note that the initial 13 miles are a fixed distance and do not change with time. Thus, the correct statement describing the rate of change in the distance traveled is C. For every hour, she will drive 59 miles after the first 13 miles.
A box contains 8 books. It is 1/6 full. If the box were completely full, how many books would be in the box? A) 14 books B) 48 books C) 16 books D) 24 books
Let x equal the number of books in the box.
x* 1/6 = 8
Multiply each side by 6
x=48 books
The correct answer is B) 48 books.
To determine how many books a completely full box would hold, we need to consider the information given:
The box contains 8 books and it is 1/6 full. To find out how many books would be in the box if it were completely full, we need to set up a proportion:
[tex]\(\frac{8}{\frac{1}{6}} = \frac{8 imes 6}{1} = 48\)[/tex]
This means the box can hold 48 books when full.
So, the correct answer is:
B) 48 books
Jimmy ran with the speed of m miles per hour. How far did he run in t minutes?
Answer:
Jimmy run in t minute = [tex]\frac{m*t}{60}[/tex] miles.
Step-by-step explanation:
Given : Jimmy ran with the speed of m miles per hour.
To find : How far did he run in t minutes.
Solution : We have given
Speed = m miles per hour .
Speed = [tex]\frac{Distance}{time}[/tex].
We can say in 1 hour Jimmy ran =m miles.
1 hour = 60 minute .
Jimmy ran in 60 minute = m miles .
Jimmy run in 1 minute = [tex]\frac{m}{60}[/tex] miles.
Jimmy run in t minute = [tex]\frac{m}{60}* t[/tex] miles.
Jimmy run in t minute = [tex]\frac{m*t}{60}[/tex] miles.
Therefore, Jimmy run in t minute = [tex]\frac{m*t}{60}[/tex] miles.
The distance covered by Jimmy after t minutes is
[tex]m \: \times ( \frac{t}{60} )[/tex]
Recall :
Distance = Speed × Time
Speed = m miles per hour
Time = t minutes
Converting t to hours :
Recall :
1 hour = 60 minutes
t minutes = t/60 hours
Multiplying Jimmy's speed by the number of minutes run
Distance covered :
[tex]m \: \times ( \frac{t}{60} )[/tex]
Learn more : https://brainly.com/question/11236233
Lars bought 3 jars of marbles. Each jar has 42 marbles, of which 13 are red. Lars can use the calculation below to find the total number of red marbles. 3×(13×42) How can Lars simplify the calculation using only the associative property of multiplication? Drag and drop the appropriate number or expression into each box. 13342 (3×13) (13×42) ×
I had a test and this was one of the questions and the answer it said was (3x1/3) x 42 so you dont have to figure it out. hope this helps anyone who needs it. :)
Andrew solved the following inequality, and his work is shown below:
−4(x + 8) + 25 ≤ −2 + 1(x − 50)
−4x − 32 + 25 ≤ −2 + 1x − 50
−4x − 7 ≤ 1x − 52
−5x ≤ −45
x ≤ 9
What mistake did Andrew make in solving the inequality? (2 points)
He subtracted 1x from both sides when he should have added 4x.
When dividing by −5, he did not change the ≤ to ≥.
He added 7 to both sides when he should have added 52.
He did not make a mistake.
Try this option:
rule: if to make a dividing by negative number (<0), the inequatlity sign must be changed to opposite.
According the rule described above, the correct answer is
'When dividing by -5, he did not change the ≤ to ≥'.
When dividing by - 5 he did not change ≤ to ≥
His calculations are correct down to the line - 5x ≤ 9
When dividing or multiplying by a negative quantity the inequality symbol must be reversed, thus
- 5x ≤ 9 ( divide both sides by - 5 )
x ≥ 9 ← inequality symbol reversed
Approximate the data using the line y = 0.25x + 3. Find the data point that has the residual with the greatest absolute value. Give that data point and its associated residual. Data point: (20, 6); Residual = -2.00 Data point: (15, 5); Residual = 6.75 Data point: (5, 3); Residual = -1.25 Data point: (10, 10); Residual = 4.50
Solution: We are given data points and associated residuals:
Data Point Residual Absolute value(Residual)
(20,6) -2.00 2.00
(15,5) 6.75 6.75
(5,3) -1.25 1.25
(10,10) 4.50 4.50
From the above absolute value(Residual) column, we clearly see the data point (15,5) has the residual with greatest absolute value of 6.75.
Therefore, the data point and its associated residual is:
(15,5) and 6.75
Answer:
Data Point: (10,10); Residual = 4.50
the number, 19/7, is _____ number
options:
A. an irrational
B. a rational
The number, 19/7, is B. a rational number
Rational numbers are numbers that can be written as a fraction.
In this case, 19/7 is already a fraction
~Rise Above the Ordinary