What is the coefficient of y in the expression 1 ⋅ 4 + 7y?
Answer:
7
Step-by-step explanation:
The coefficient of a variable is simply the number it's being multiplied by or the number that is in front of it. In this case, the coefficient of y is 7.
Simplify the following Questions. (IMPORTANT NOTE!!! #'s 2 AND 7 MUST BE IN SCIENTIFIC NOTATION!!!!!) 1.) (x)²(2xy³)^5 2.) (4x10^8)^2 3.) (-h^4)^5 4.) (3xy³)²(xy)^6 5.) (p^9)^-2 6.)(5k²)³ 7.)(7x10^5)² 8.)(x)³(-x³y)² 9.)w^5(w²)^-4 10.) (2x^5)^4
Answer:
Step-by-step explanation:
Hint :
[tex](a*b)^{m}= a^{m}b^{m}\\\\\\(a^{m})^{n}=a^{mn}\\\\\\a^{m}*a^{n}=a^{m+n}\\[/tex]
[tex]1)x^{2}(2xy^{3})^{5}=x^{2}*2^{5}*x^{5}*(y^{3})^{5}\\\\\\=x^{2}*2^{5}*x^{5}*y^{3*5}\\\\=x^{2}*2^{5}*x^{5}*y^{15}\\\\=2^{5}*x^{2+5}*y^{15}\\\\=2^{5}x^{7}y^{15}[/tex]
[tex]2) (4x10^{8})^{2}=4^{2}*x^{2}*(10^{8})^{2}\\\\=16*x^{2}*10^{8*2}\\\\=1.6*10*x^{2}*10^{16}\\\\=1.6x^{2}*10^{16+1}\\\\=1.6x^{2}10^{17}[/tex]
[tex]3)(-h^{4})^{5}=(-h)^{4*5}=-h^{20}\\\\\4)(3xy^{3})^{2}(xy)^{6}=3^{2}x^{2}(y^{3})^{2}x^{6}y^{6}\\\\=9x^{2}y^{3*2}x^{6}y^{6}\\\\\\=9x^{2}y^{6}x^{6}y^{6}\\\\=9x^{2+6}y^{6+6}\\\\=9x^{8}y{12}\\\\\\[/tex]
[tex]5) (p^{9})^{-2}=p^{9*-2}=p^{-18}\\\\\\6)(5k^{2})^{3}=5^{3}(k^{2})^{3}=625k^{6}\\\\7)(7x10^{5})^{2}=7^{2}x^{2}(10^{5})^{2}\\\\=49x^{2}10^{5*2}\\\\=4.9*10^{1}x^{2}10^{10}\\\\=4.9x^{2}10^{10+1}\\\\=4.9x^{2}10^{11}[/tex]
[tex]8)x^{3}(-x^{3}y)^{2}=x^{3}*(-x^3})^{2}y^{2}\\\\\\=x^{3}*(-1)^{2}*x^{2*3}y^{2}\\\\=x^{3}*1*x^{6}y^{2}=x^{3+6}y^{2}\\\\=x^{9}y^{2}\\\\\\9)w^{5}(w^{2})^{-4}=w^{5}w^{2*-4}\\\\=w^{5}w^{-8}\\\\=w^{5-8}=w^{-3}\\\\=\frac{1}{w^{3}}\\\\\\10) (2x^{5})^{4}=2^{4}x^{5*4}\\\\=2^{4}x^{20}\\\\=16x^{20}[/tex]
the expression 12xyz-45 is a a. monomial b. binomial c. trinomial d. constant
Answer:
Hey there!
12xyz-45 is a binomial. A binomial contains two terms.
Let me know if this helps :)
cos x° = sin(3x+10°) find tan x°
Answer:
Step-by-step explanation:
we can write sin(3x+10)= cos{90-(3x+10)}
now
cosx= cos{90-(3x+10)}
eliminating cos from both sides we get
x=90-3x-10
4x=80
x=20
tan 20=0.364
it can be 40 also if we take the sin part
When two fair 6-sided dice are tossed, the numbers $a$ and $b$ are obtained. What is the probability that the two digit number $ab$ (where $a$ and $b$ are digits) and $a$ and $b$ are all divisible by 3?
=================================================
Explanation:
If either a or b (or both) are multiples of 3, then so is a*b
Consider 'a' being a multiple of 3. This means a = 3k for some integer k. Multiply both sides by b to get ab = 3k*b, and we see that 3 is a factor of ab, making ab to be a multiple of 3.
----------
There are six sides to the dice and those sides are {1,2,3,4,5,6} of which only {3,6} are multiples of 3.
If we want both dice to be multiples of 3, then the possible outcomes are
(3,3)(3,6)(6,3)(6,6)There are four outcomes. This is out of 6*6 = 36 total outcomes overall.
Dividing the values gives 4/36 = 1/9 as the probability we want
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Side note: for a roll like (a,b) = (6,3) we see that a*b = 6*3 = 18, which is a multiple of 3. The same happens with the other three (a,b) pairings mentioned above.
Will Give Brainliest. Answer ASAP please
Answer:
1) Arc length = 2πr ( Ф/360)
= 2 × 22/7 × 15 (120/360)
= 44/7 × 15 (1/3)
= 44 × 5/7
= 31.428 in
2) Arc length = 2πr ( Ф/360)
= 2 × 22/7 × 14 (90/360)
= 44/7 × 14 ( 1/4)
= 616/7 × (1/4)
= 88 (1/4)
= 22 yards
Hope it helps!!!
what is the answer to this exponent 6*6*6*6*6
Answer:
6^5 or 7776
Step-by-step explanation:
6^5 because 6 is multiplied with 6, 5 times. So, it is 6^5.
We can also simplify this number.
=> 6 x 6 x 6 x 6 x 6
=> 36 x 36 x 6
=> 36 x 216
=> 7776
is this a rhombus? see attachment
Answer: No, it is not a rhombus
Why not? This is because we do not have all four sides the same length.
DE is longer than EF, due to the opposite angles being larger. The rule is: the larger the angle, the longer the opposite side will be.
The sum of 4 consecutive even integers is 180. What are the integers? (Detailed Explanation)
Answer:
Step-by-step explanation:
Let the consecutive even numbers be 2n , (2n + 2) , (2n +4), (2n + 6)
2n + 2n+2 + 2n+4 + 2n+6 = 180
Add like terms
2n + 2n + 2n + 2n + 2 + 4 + 6 = 180
8n + 12 = 180
Subtract 12 from both sides
8n + 12 - 12 = 180 - 12
8n = 168
Divide both sides by 8
8n/8 = 168/8
n = 21
2n = 2*21 = 42
2n + 2= 2*21 +2 = 42 +2 = 44
2n +4 = 2*21 + 4 = 42 + 4 = 46
2n +6 = 2*21 + 6 = 42 + 6 = 48
The 4 consecutive even integers: 42, 44 , 46 , 48
f(2)= can someone let me know what the answer is
Answer:
-2
Step-by-step explanation:
f(2) is the value of the function when x = 2.
Look in the graph. When x = 2, the point on the graph has coordinates (2, -2).
f(2) = -2
Miguel Rodriguez borrowed $300 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.5%.
Answer:
Simple Interest = 9.75
Total Amount needed to payback = 309.75
Step-by-step explanation:
SI = P x R x T / 100
SI = Simple Interest
P = Principal
R = Rate in years
T = Time
SI = 300 x 1/2 x 6.5 /100
=> SI = 3 x 1/2 x 6.5
=> 1.5 x 6.5
=> 9.75
Total Amount needed to payback = Principal + Simple Interest
=> Total Amount needed to payback = 300 + 9.75
=> Total Amount needed to payback = 309.75
5,
5,
6,
8,
11,
What is the next number
3 is what my answer was
============================================
Explanation:
From 5 to 5, we add 0
From 5 to 6, we add 1
From 6 to 8, we add 2
From 8 to 11, we add 3
Assuming this pattern keeps up, the next term is found by adding 4.
So 11+4 = 15 is the next term.
Solve these two equations using the Addition Method (also known as the elimination method).
3/4x + 1/3y = -1/2
1/2x - 5/6y = -7/2
Answer:
(-2, 3)
Step-by-step explanation:
5/2(3/4x + 1/3y = -1/2)
1/2x - 5/6y = -7/2
15/8x + 5/6y = -5/4
19/8x = -19/4
x = -2
1/2(-2) - 5/6y = -7/2
-1 -5/6y = -7/2
-5/6y = -5/2
y = 3
Ben earns $13 per hour at Starbucks. When he works overtime, he earns time and a half. What is his regular pay for 40 hours of work?
Answer:
$520
Step-by-step explanation:
Ben earns $13 per hour of regular work
He gets for 40 hours of regular work:
$13*40 = $520Answer is $520
Describe and correct the error a student made when solving the equation 7=-4(x+7)-3+2x. What is the correct solution?
Answer:
7=-4(x+7)-3+2x
BODMAS
7=-4x-28-3+2x
7=-2x-31
7+31=-2x
x=38/2
x= -19
Which of the following does not describe a control group? O A. a group of patients given a new drug B. a group of patients given a placebo O C. a group of trees not given a new growth hormone O D. a group of students not given a new software package
Answer:
the answer = C (may be but not sure)
Answer:
The answer has to be A
Step-by-step explanation:
The trees have nothing changed about them, so they can be considered to be the control. In additon, placebo is given as a control in medical trials, so it cannot be correct. And, the students have nothing changed in D, so the answer to this question has to be A, where the patients are given a new drug.
Please help ASAP PLEASE
Jane is trying to decide between two savings account plans. Plan A offers a
quarterly compounded interest rate of 0.15%, while Plan B offers 0.5% interest
compounded annually. Which is the better plan? By how much?
Answer:
The answer is below
Step-by-step explanation:
The compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n} )^{nt}\\\\Where\ A \ is\ the\ final \ amount, P\ is\ the \ principal\ or \ initial\ amount,r\ is\ the\ rate\\n\ is\ the\ number\ of \ times\ compounded\ per\ period\ and \ t\ is\ the\ number\ of\ periods.\\[/tex]
For the same amount of principal (P) for both plan A and B:
Plan A offers a quarterly compounded interest rate of 0.15%. That is r = 0.15% = 0.0015, n = 4. Therefore:
[tex]A_a=P(1+\frac{0.0015}{4} )^{4t}\\\\A_a=P(1+0.000375)^{4t}\\\\A_a=P(1.000375)^{4t}[/tex]
Plan B offers annual compounded interest rate of 0.5%. That is r = 0.5% = 0.005, n = 1. Therefore:
[tex]A_b=P(1+\frac{0.005}{1} )^{t}\\\\A_b=P(1.005)^{t}\\\\The\ ratio\ of\ their\ interest:\\\\\frac{A_a}{A_b} =\frac{P(1.000375)^{4t}}{P(1.005)^{t}} \\\\\frac{A_a}{A_b} =\frac{(1.000375)^{4t}}{(1.005)^{t}} \\\\For\ the\ same\ time\ period\ of\ one\ year(t)=1\\\\\frac{A_a}{A_b} =\frac{(1.000375)^{4(1)}}{(1.005)^{1}} \\\\\frac{A_a}{A_b} =\frac{1.0015}{1.005} \\\\A_b=\frac{1.005A_a}{1.0015}\\ \\A_b=1.003A_b[/tex]
Plan B is the better plan, it is greater by a factor of 1.003
what is the change in each term of the sequence? 1,4,13,40,121,....
Evaluate the function. f(x) = -x2 - 6x + 12 Find f(4)
Answer:
f( 4 ) = - 28Step-by-step explanation:
f(x) = - x² - 6x + 12
To find f(4) substitute the value of x that's 4 into the expression above and solve.
That's
f( 4) = - (4)² - 6(4) + 12
= - 16 - 24 + 12
= - 40 + 12
We have the final answer as
f(4) = - 28Hope this helps you
Ben wants to buy a new car stereo and he has already saved some money. He used this inequality to represent the amount he still has to save to be able to buy the stereo, where a represents the amount still left to save. A + 212 greater-than-or-equal-to 365 If Ben saves $15 a week for the next 10 weeks, will he be able to buy the stereo and why? No, because he needs to save at least $153, and he will only save $150 over the next ten weeks. No, because he needs to save $577, and he will only save $150 more. Yes, because he has already saved $365, and the stereo cost $212. Yes, because he has already saved $212, and he will save another $150.
Answer:
No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.
Step-by-step explanation:
In case when ben wants to save $15 for a week and the total number of weeks is 10 so the total saving amount is $150. Now if the cost of a stereo is less than the total of saving amount so he is confident to purchase the stereo.
Now if the amount that required to be saved is represented by a is more than $150 so he is unable to purchase a stereo
Hence, the correct option is a.
Answer:
Step-by-step explanation:
Using the equation, A + 212 ≥ 365
No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.
20 POINTS! A book sold 39,200 copies in its first month of release. Suppose this represents 7.1% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
A video game was discounted and now costs two thirds of its original
price. If it originally cost $45, how much does it cost now?
The original price is 45.
It now costs 2/3 of 45.
[tex]\frac{2}{3} * \frac{45}{1} = \frac{90}{3}[/tex] or 30
♡ Hope this helps! ♡
❀ 0ranges ❀
Answer:
The video game will now cost $30
Step-by-step explanation:
Original price: $45
45 ÷ 3 = $15
15 x 2 = $30
Hope this helps!
Section B
1. In the adjoining figure find out perpendicular, base and
hypotenuse from the given right-angled triangle with a and
B as the reference angles. Also give your reason.
a
nto
B
С
B.
D
Answer/Step-by-step explanation:
Using α as reference angle:
Perpendicular side = BC (one of the legs that adjoins to form a right angle. It is opposite to the reference angle.)
Base side = AB (The other leg that forms a right angle with the perpendicular side at the adjoining point. It is adjacent to the reference angle)
Hypotenuse = AC (the side opposite to the right angle, 90°)
Using β as reference angle:
Perpendicular side = AB (one of the legs that adjoins to form a right angle. It is opposite to the reference angle.)
Base side = BD (The other leg that forms a right angle with the perpendicular side at the adjoining point. It is adjacent to the reference angle)
Hypotenuse = AD (the side opposite to the right angle, 90°)
Write 830,040 in expanded form with exponents.
830,040 = (8 x 105) +
(Use the operation symbols in the math palette as needed.)
Answer:
See below
Step-by-step explanation:
[tex]830040 \\ = (8 \times 100000) + (3 \times 10000) + (4 \times 10) \\ = 8 \times {10}^{5} + 3 \times {10}^{4} + 4 \times {10}^{1} \\ [/tex]
Use braces and digits to designate the set of natural numbers.
Answer:
[tex]N = \{1,2,3,4,5,6,.....\}[/tex]
Step-by-step explanation:
Required
Determine the sets of natural number
Represent this set with letter N
From definition of natural numbers, they are integer numbers starting from 1;
In other words: 1,2,3,4,5, and so on.
To represent this as a set of N, we have
[tex]N = \{1,2,3,4,5,6,.....\}[/tex]
The ..... means that the counting still continues
b)[3x-7)2 by using identities note:the 2 is a square
Answer:
9x² - 42x + 49
Step-by-step explanation:
Given
(3x - 7)² = (3x - 7)(3x - 7)
Each term in the second factor is multiplied by each term in the first factor, that is
3x(3x - 7) - 7(3x - 7) ← distribute both parenthesis
= 9x² - 21x - 21x + 49 ← collect like terms
= 9x² - 42x + 49 ← in expanded form
A bat and ball cost $1.10.
The bat costs one dollar mire than the ball.
How much does the ball cost?
Answer: Hi!
We already know that we can subtract a dollar from the total, because the bat is a dollar more than the ball. However, there's one more step! We have to divide the cost left, 10 cents, by 2 as well, because the bat is a dollar more than the ball, and if we said that the answer was a dollar, we would be wrong, because there would be 10 cents left as the cost of the ball - and if the bat was a dollar more than the ball, then the bat would be $1.10 and the total cost would be $1.20. 10 divided by 2 is 5, so the ball is 5 cents and the bat is $1.05.
Hope this helps!
5 cents
as the ball costs 5 cents the bat costs $1.05
What is the purpose of multiplying by the conjugate of a complex denominator when finding the quotient of complex numbers?
Answer: To have a real number in the denominator
Step-by-step explanation:
Ok, a quotient between two complex numbers can be written as:
[tex]\frac{A + Bi}{C+Di}[/tex]
Now, when we do these types of divisions, we multiply and divide by the same number (so in essence we are multiplying by one) that is the conjugate of the denominator.
Remember that for a complex number:
Z = A + Bi
the conjugate is = A - Bi.
Then, wen we multiply the denominator by it's conjugate, we have:
(C + Di)(C - Di) = C^2 + D*C*i - D*C*i + (D*i)*(-D*i) = C^2 + D^2
So now we have a real number in the denominator (the imaginary part of this number is equal to zero)
So the answer to the question is:
"To have a real number in the denominator"
In 1940, the average size of a privately owned farm in a particular country was 171 acres. In a recent year, the average size of a privately owned farm in the country had increased to 446 acres. What is this percent increase
Answer:
There is 160.81 % of increase.
Step-by-step explanation:
Given that,
The average size of a privately owned farm in a particular country was 171 acres.
Now, the average size of a privately owned farm in the country had increased to 446 acres.
We need to find the percent increase.
[tex]\%=\dfrac{\text{increase}}{\text{original}}\times 100\\\\\%=\dfrac{446-171}{171}\times 100\\\\\%=160.81\%[/tex]
So, there is 160.81 % of increase.
The total money earned if Lee sold four scarves at twenty dollars each.
Answer:
$80
Step-by-step explanation:
If we have four scarves, and each costs $20, we can multiply these two numbers to find the total profit made.
[tex]20\cdot4[/tex]
2 times 4 is 8, and adding a 0 to that is 80.
Hope this helped!