Hello!
3(x + 2) - 4x = 8 <=>
<=> 3x + 6 - 4x = 8 <=>
<=> -x + 6 = 8 <=>
<=> -x = 8 - 6 <=>
<=> -x = 2 <=>
<=> x = -2
Good luck! :)
Is the proportion 28/16 = 14/8 correct
Answer:
yes
Step-by-step explanation:
its correct because divide by 2/ 28/16=14/8
maybe
The polynomial 3x² + mx? - nx - 10 has a factor of (x - 1). When divided by x + 2, the remainder is 36. What are
the values of m and n?
Answer:
[tex]m = 12[/tex]
[tex]n =3[/tex]
Step-by-step explanation:
Given
[tex]P(x) = x^3 + mx^2 - nx - 10[/tex]
Required
The values of m and n
For x - 1;
we have:
[tex]x - 1 = 0[/tex]
[tex]x=1[/tex]
So:
[tex]P(1) = (1)^3 + m*(1)^2 - n*(1) - 10[/tex]
[tex]P(1) = 1 + m*1 - n*1 - 10[/tex]
[tex]P(1) = 1 + m - n - 10[/tex]
Collect like terms
[tex]P(1) = m - n + 1 - 10[/tex]
[tex]P(1) = m - n -9[/tex]
Because x - 1 divides the polynomial, then P(1) = 0;
So, we have:
[tex]m - n -9 = 0[/tex]
Add 9 to both sides
[tex]m - n = 9[/tex] --- (1)
For x + 2;
we have:
[tex]x + 2 = 0[/tex]
[tex]x = -2[/tex]
So:
[tex]P(-2) = (-2)^3 + m*(-2)^2 - n*(-2) - 10[/tex]
[tex]P(-2) = -8 + 4m + 2n - 10[/tex]
Collect like terms
[tex]P(-2) = 4m + 2n - 10 - 8[/tex]
[tex]P(-2) = 4m + 2n - 18[/tex]
x + 2 leaves a remainder of 36, means that P(-2) = 36;
So, we have:
[tex]4m + 2n - 18 = 36[/tex]
Collect like terms
[tex]4m + 2n = 36+18[/tex]
[tex]4m + 2n = 54[/tex]
Divide through by 2
[tex]2m + n=27[/tex] --- (2)
Add (1) and (2)
[tex]m + 2m - n + n = 9 +27[/tex]
[tex]3m =36[/tex]
Divide by 3
[tex]m = 12[/tex]
Substitute [tex]m = 12[/tex] in (1)
[tex]m - n =9[/tex]
Make n the subject
[tex]n = m - 9[/tex]
[tex]n = 12 - 9[/tex]
[tex]n =3[/tex]
CHECK MY ANSWERS PLEASE
____
The sequence is geometric:
3, 13, 23, 33,...
True
False***
_____________________
The sequence is geometric:
5, -25, 125, -625,...
True***
False
Step-by-step explanation:
For a geometric sequence,
[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]
1. The sequence is :
3, 13, 23, 33,...
[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]
It is not geometric. It is false
2. The sequence is :
5, -25, 125, -625
[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]
So, the sequence is geometric as the common ratio is same. It is true.
Given the function
Calculate the following values:
f( - 1) =
f(0)
f(2)=
-1 is less than 0, so you use the first equation:
3(-1) +2 = -3+2 = -1
f(-1) = -1
For 0 use the 2nd equation:
3(0) + 4 = 0+4 = 4
f(0) = 4
For 2 use the 2nd equation:
3(2) + 4 = 6+4 = 10
f(2) = 10
If a woman makes $32,000 a year receives a cost of living increase 2.2% what will her new salary be?
Answer:
$32 704
Step-by-step explanation:
(102.2÷100) × 32 000 = $32 704
4g+r=2r-2x
I need someone’s help if you can help me
Answer:
4g+2x=r
Step-by-step explanation:
4g+r=2r-2x
collecting like terms
4g+2x=2r-r
4g+2x=r
Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the equation. Plot the point _______, move _______ unit(s) down, and _______ unit(s) over to find the next point on the line.
A. (–2, 4), one, three
B. (4, –2), one, three
C. (2, 4), one, three
D.(4, –2), three, one
Answer:
A. (–2, 4), one, three
Step-by-step explanation:
For a linear equation:
y = a*x + b
the point-slope form is:
(y - y₁) = m*(x - x₁)
Where we know that this line has the slope m, and passes through the point (x₁, y₁)
In this case, the equation:
(y + 2) = –1/3(x – 4)
is already in the point-slope form.
here we have:
y₁ = -2
x₁ = 4
then the point is (-2, 4)
m = -(1/3)
m = -1/3 means that when we move 3 units to the right, we need to move one unit down. (or the inverse, we can move one unit down and 3 to the right)
So, to complete the statement we have:
plot the point (-2, 4), move one unit down, and three units over to find the next point on the line.
The correct option is A.
Find the value of x in each case:
What is the HCF of 1280 and 630
Given:
The two numbers are 1280 and 630.
To find:
The HCF of the given numbers.
Solution:
First write the given numbers in prime factorization form.
[tex]1280=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 5[/tex]
[tex]630=2\cdot 3\cdot 3\cdot 5\cdot 7[/tex]
Now the product of all the common prime factors is known as the HCF of 1280 and 630.
[tex]HCF=2\cdot 5[/tex]
[tex]HCF=10[/tex]
Therefore, the HCF of 1280 and 630 is 10.
ayúdenme por favor, es de matemática.
Answer:welcome to brainly
Step-by-step explanation:
Hello there! My name is agenthammerx, a Master Answerer and Engagement Team Member here on Brainly. I am here to welcome you to the site! Thank you for taking initiative to check out Brainly and for posting your first question! The Brainly Community welcomes you. If you have any questions regarding anything about the site, please don’t hesitate to reach out to me! I will try my best to help you and answer your question or check out our help center at https://faq.brainly.com/
help i’ll give brainliest please hurry
The number of diners at a restaurant each day is recorded and a daily average is calculated every month (assume 30 days in a month). The number of diners each day has a mean of 107 and a standard deviation of 60, but does not necessarily follow a normal distribution.The probability that a daily average over a given month is greater than x is 2.5%. Calculate x. You may find standard normal table useful. Give your answer to 3 decimal places.x =
Answer:
x = 128.472
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The number of diners each day has a mean of 107 and a standard deviation of 60.
This means that [tex]\mu = 107, \sigma = 60[/tex]
Distribution of the daily average:
Over a month of 30 days, so [tex]n = 30, s = \frac{60}{\sqrt{30}} = 10.955[/tex]
The probability that a daily average over a given month is greater than x is 2.5%. Calculate x.
This is X when Z has a p-value of 1 - 0.025 = 0.975, so X when Z = 1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.96 = \frac{X - 107}{10.955}[/tex]
[tex]X - 107 = 1.96*10.955[/tex]
[tex]X = 128.472[/tex]
So x = 128.472
Solve (x + 3)2 + (x + 3) – 2 = 0.
9514 1404 393
Answer:
x = -5 or x = -2
Step-by-step explanation:
Factoring, we have ...
((x +3 +2)((x +3) -1)) = 0
(x +5)(x +2) = 0
x = -5 or x = -2 . . . . . . . . values that make the factors zero
If the fixed cost is 9000 per year. Variable costs are estimated to be Tk. 60.75 / item. The firm wants to break even if 80 items are sold per year. What should be the unit price of the item?
9514 1404 393
Answer:
Tk 173.25
Step-by-step explanation:
The firm will break even if its cost is equal to its revenue. That is, the price of each item sold must equal the cost of producing it. To cover the fixed cost, a share of it must be added to each of the items sold. Then the break-even price for 80 items is ...
price = variable cost + share of fixed cost
price = Tk 60.75 +9000/80 = Tk 60.75 +112.50 = Tk 173.25
List all factors of the number 52. SHOW ALL WORK!!!
Answer:
Factors of number 52
Factors of 52: 1, 2, 4, 13, 26 and 52.
Negative Factors of 52: -1, -2, -4, -13, -26 and -52.
Prime Factors of 52: 2, 13.
Prime Factorization of 52: 2 × 2 × 13 = 22 × 13.
Sum of Factors of 52: 98.
Write 2 1/4 as a decimal
Hey there!
2 1/4
= 2 * 4 + 1 / 4
= 8 + 1 / 4
= 9 / 4
= 9 ÷ 4
= 2.25
Therefore, your answer is: 2.25
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The sum of 4 consecutive integers is 122. What is the third number in this sequence?
Answer:
31
Step-by-step explanation:
Let the smallest integer be x.
Since the 4 integers are consecutive (they come right after the other),
2nd integer= x +1
3rd integer= x +1 +1= x +2
4th integer= x +2 +1= x +3
Sum of the integers= 122
x +x +1 +x +2 +x +3= 122
4x +6= 122
4x= 122 -6
4x= 116
x= 116 ÷4
x= 29
3rd number
= 29 +2
= 31
Use the expression 9(7 + 2x) to answer the following:
Part A: Describe the two factors in this expression. (4 points)
Part B: How many terms are in each factor of this expression? (4 points)
Part C: What is the coefficient of the variable term? (2 points)
Step-by-step explanation:
Part A:
The two factors in 9(7+2x) are 9 and 7+2x
Part B:
First term: 9
Second term: 7+2x
Part C:
9(7+2x)
Open bracket
63+18x
The coefficient is 18x
A. The two factors are 9 and (7+2x).
B. In first factor, only one term and in second factor , two terms i.e. 7 and 2x are present.
C. The coefficient of the variable term is 18.
Algebraic expression:Given expression is;
[tex]9(7+2x)[/tex]
In given expression, there are two factors fist is 9 and second one is [tex](7+2x)[/tex]
In first factor, only one term and in second factor , two terms i.e. 7 and 2x are present.
To find the coefficient of variable term, we have to to expand given expression.
[tex]9(7+2x)=63+18x[/tex]
The coefficient of the variable term is 18.
Learn more about the algebraic expression:
https://brainly.com/question/4344214
one particular ice cream parlor has 28 different flavors available. How many ice cream cups are possible if you order 4 scoops? this is a combination
Answer:
20,475 cream cups are possible.
Step-by-step explanation:
The order in which the flavors are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
4 cups from a set of 28.
So
[tex]C_{28,4} = \frac{28!}{4!24!} = 20475[/tex]
20,475 cream cups are possible.
helppp
True or false: f(x) represents a function.
The scale of a map is 1/8 inch=10 miles. If two cities are 3 inches apart on the map how many miles are they from each other
SOMEONE HELP ASAP PLES NO EXPLANATOIN NEEDED PLS LEAVE UR ANSWER AS TEXT (SOME TIMES I CAN'T SEE IMAGES) THANK YOU SO MUCH!!!
Answer:
i cant see the image
Step-by-step explanation:
Sam thinks of a 4 digit number. The digit in the one’s place is 3 less than the digit in the ten’s place and digit in thousand’s place is 5 less than the digit in hundred’s place. The value of the hundred’s place is 800. The digit in ten’s place is the greatest even number. What is the number Sam is thinking of?
9514 1404 393
Answer:
3885
Step-by-step explanation:
The hundreds digit is 8, and the thousands digit is 5 less, so is 3.
The tens digit is 8 (the largest even digit), and the ones digit is 3 less, so is 5.
The number is ...
3885
How is solving for speed similar to solving for time?
O They both require that two numbers be added.
O They both require that two numbers be subtracted
O They both involve writing a rate.
O They both use the same units of measure.
Answer:
third one
Step-by-step explanation:
Which angle is an adjacent interior angle?
Triangle L M N. Angle L is 1, angle M is 2, angle N is 3. Side M N extends to form angle 4.
1
2
3
4
Step-by-step explanation:
Triangle LNM is an adjecent interior angle
Answer:
I think it's C
Step-by-step explanation:
Let me know if it's incorrect.
Amy has 2$, Jack has 3 times as much as Amy. Catherine has twice as much as Jack. How much does Catherine have?
Answer: 12 dollars
Step-by-step explanation:
2x3x2=12
Easy math
I WILL MARK BRAINLIEST:))
Please translate this expression into a verbal expression 4(5j+2+j). (5 points)
PLEASE HELP WILL MARK BRAINLIEST
Answer:
AB
Step-by-step explanation:
From the question given above, we were told that triangle ABC is similar to triangle PTG.
Since both triangles are similar, the following assumptions hold:
PG / AC = PT / AB = TG / BC
Comparing the equation above with those given in the question, the missing part of the equation is AB
Some number times 7 is equal to the number increased by 9
Answer:
.
Step-by-step explanation:
.
Cell Phone Service
Cellular phone service is available for $31 per month for 666 minutes. What is the
monthly cost per minute? Round your answer to the nearest tenth of a cent.
The cost for the phone service is
cents per minute.
9514 1404 393
Answer:
4.7¢/min
Step-by-step explanation:
To find the cost in cents per minute, divide the cost in cents by the number of minutes.
$31.00/(666 min) = (3100¢)/(666 min) ≈ 4.7¢/min
