Which equation justifies why 7^1/3 = 3 square root 7?
Answer:
c
Step-by-step explanation:
I took the test and got it right
The correct equation that justifies why seven to the one-third power equals the cube root of seven is option C: [tex](7^{(1/3)})^3[/tex]=[tex]7^{(1/3 * 3)[/tex]=7.
C. Seven to the one-third power all raised to the third power equals seven to the one-third times three power equals seven.
Let's break down the steps:
Seven to the one-third power all raised to the third power:
[tex](7^{(1/3)})^3[/tex]
Using the property of exponents [tex](a^{(m*n)} = (a^m)^n)[/tex] to simplify:
[tex]7^{(1/3 * 3)[/tex]
The exponent 1/3 multiplied by 3 is equal to 1:
[tex]7^1[/tex]
Any number raised to the power of 1 is itself, so:
7
This justifies that [tex]7^{(1/3)[/tex] raised to the power of 3 is equal to 7.
Therefore, [tex]7^{(1/3)[/tex] is equal to the cube root of 7.
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Write P(x) = x^3 + x^2 − 17x + 15 as a product of two factors, using x − 3 as one factor.
A. (x − 3)(x^2 + x − 17)
B.(x − 3)(x^2 + 4x − 17)
C.(x − 3)(x^2 – 4x − 5)
D.(x − 3)(x^2 + 4x − 5)
Answer:
D. (x-3)(x^2 + 4x - 5)
Step-by-step explanation:
P(x) = x³ + x² - 17x + 15 can be written as (x - 3) (x² + 4x - 5) as a product of two factors.
What is Polynomials?Polynomials are expressions in algebra which consist of variables, constants and exponents combined using the basic operations in mathematics like addition, subtraction, multiplication and division.
Polynomials can be classified as monomials, binomials and trinomials depending on the degree of the variables as 1, 2 and 3 respectively.
The given polynomial is P(x) = x³ + x² - 17x + 15.
We already have x - 3 is the factor of this polynomial.
To get the other factor which is a binomial, we have to divide the given polynomial with x - 3.
On dividing, we get x² + 4x - 5 as the quotient and remainder equals zero.
So x² + 4x - 5 is the other factor of the given polynomial.
Hence, the polynomial P(x) = x³ + x² - 17x + 15 can be written as (x - 3) (x² + 4x - 5) as a product of two factors.
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Enter the x coordinate of the solution to this system of equations.
- 2x + y = 5
– 5x + y = – 4
Answer:
x = 3
Step-by-step explanation:
Given the 2 equations
- 2x + y = 5 → (1)
- 5x + y = - 4 → (2)
Multiply (2) by - 1 then add to (1) to eliminate y
5x - y = 4 → (3)
Add (1) and (3) term by term to eliminate y
3x = 9 ( divide both sides by 3 )
x = 3
(just the first question) pls help my work is due tonight i will give brainliest
The value of a collectible coin can be represented by the equation y = 2 x + 9.74, where x represents the number of years that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the value of the coin when Consuello originally purchased it? $4.87 $7.74 $9.74 $19.48
Answer:
you would multiply 2 * 4.87 and then add that to 9.74 and then you do that to everyone and then one of them will get you your answer and I am not sure about the answer but I think its b
Step-by-step explanation:
Answer:
The value of the coin when Consuelo originally purchased it is $9.74 ⇒ C
Step-by-step explanation:
The form of the linear equation is;
y = m x + b, where
m is the slope of the line (The rate)
b is the y-intercept (initial amount, value y at x = 0)
∵ The value of a collectible coin can be represented by the equation
y = 2 x + 9.74
→ Compare it with the form of the linear equation above
∴ m = 2
∴ b = 9.74
∵ x represents the number of years that Consuelo has owned the coin
∵ y represents the total value, in dollars, of the coin
→ That means the value of y at x = 0 is the value of the coin when
Consuelo originally purchased it
∵ b represents the value of y at x = 0
∵ b = 9.74
∴ The value of the coin when Consuelo originally purchased it is $9.74
Does anyone knows how to solve this?
Answer:
This is the answer do it fast. Ok
Answer:
see explanation
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - 8x + 13 ← is in standard form
with a = 1 and b = - 8 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{-8}{2}[/tex] = 4
Substitute x = 4 into the equation for corresponding value of y
y = 4² - 8(4) + 13 = 16 - 32 + 13 = - 3
Vertex = (4, - 3 )
The axis of symmetry is a vertical line passing through the vertex with equation
x = 4 ← equation of axis of symmetry
To determine direction of opening
• If a > 0 then graph opens up
• If a < 0 then graph opens down
Here a = 1, thus graph opens up
What type of triangle is this?
A. Right
B. Equilateral
C. Isosceles
D. Scalene
Answer:
It's an Equilateral triangle
Step-by-step explanation:
This is because of the fact that all of its sides are equal
Answer:
Equilateral Triangle
Step-by-step explanation:
All sides are equal (60 degrees) so it is an equilateral triangle
the mean of a,b,c,and d is 9 and the mean of a,b,c,d,e and f is 12. find the mean of e and f
Answer:
mean of e + f = 18
Step-by-step explanation:
(a + b + c + d)/4 = 9 Multiply by 4
a + b + c + d = 9 * 4 = 36
(a + b + c + d + e + f ) / 6 = 12
but a + b + c + d = 36
(36 + e + f)/6 = 12 Multiply by 6
36 + e + f = 72 Subtract 36 from both sides
e + f = 36 Divide by 2 to find the mean.
(e + f)/2 = 36/2
mean of e + f = 18
Josh runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Answer:
6 / 55 = x / 44
44*6/55= x
x = 4.8 miles
Step-by-step explanation:
Given g(x) = -
—x – 2, find g(-3).
Answer:
1
Step-by-step explanation:
negative times negative is positive so that would make it 3-2 which is 1.
Find the amount to be paid at the end of 6 months on rupee 1800 at 8% per annum compounded quarterly. Plz give me with all the steps and ill mark uh as brainliest
Answer:
The amount to be paid is rupee 1872.72
Step-by-step explanation:
Compound Interest
It occurs when interest in the next period is earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
The initial amount is P=1800 at r=8% = 0.08 during t=6 months (t=0.5 years) compounded quarterly. There are 4 quarters in a year, thus n=4.
Calculating A:
[tex]\displaystyle A=1800\left(1+{\frac {0.08}{4}}\right)^{4*0.5}[/tex]
[tex]\displaystyle A=1800(1.02)^{2}[/tex]
A = 1872.72
The amount to be paid is rupee 1872.72
In a candy mix there are 4 green bars for every 3 red bars. How many red bars are there if there are 200 green bars? A. 150 red bar's B. 199 red bars c.201 red bars d. 267 red bars
Step-by-step explanation:
4 green bars to 3 red bars
=> 200 green bars to 3 * (200/4) = 150 red bars.
There are 150 red bars. (A)
Answer:
Step-by-step explanation:
A - 150 is the a answer
4 green bars for every 3 red bars, take 3 red bars as one bucket so total we have 200/4 buckets which is 50
now 1 bucket has 3 green bars so total we have 3* 50 buckets which is 150
Lola gets two 20-minute breaks at work each day. She works 5 days a week. How much time does she spend on break each week?
Group of answer choices
Answer:
200 minutes / 3 hours & 20 minutes.
Step-by-step explanation:
This is quite simple.
First, since we know that Lola takes two 20 minute breaks at work each day, let's multiply 20 and 2.
20 × 2 = 40
This means she is on break for a total of 40 minutes each day.
Finally, let's take that 40 and multiply it by 5.
40 × 5 = 200
This means she spend 200 minutes (3 hours & 20 mins) on break each week.
Please help!!! ASAP!
the following box plot shows the number of hours students have spent of math this week. what information can you get from this?
a. the median number of hours spent on Math was about 2.9
b. the mean number of hours spent on Math was about 3.4
c. No students spent less than 2.27 hours on Math
d. All students spent between 2.27 and 4.54 hours on math
Answer:
A. the median number of hours spent on Math was about 2.9
Step-by-step explanation:
The least number of hours was 0 and the greatest was 11.35. The IQR is between 2.27 and 4.54.
The median number of hours spent on Math was about 2.9. Therefore, option A is the correct answer.
The given box plot shows the number of hours students have spent on math this week.
How to find the median in the box plot?The far left of the chart (at the end of the left “whisker”) is the minimum (the smallest number in the set) and the far right is the maximum (the largest number in the set). Finally, the median is represented by a vertical bar in the centre of the box.
Here, in the given box plot we can see the least number of hours was 0 and the greatest was 11.35. The IQR is between 2.27 and 4.54.
The vertical line represents the median, which is 2.9.
Therefore, option A is the correct answer.
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There are 5 roses in a vase of 11 flowers,the rest are daisies
what is the ratio of roses to daisies
A roofing contractor has 29 bundles of roofing shingles that he needs to carry up a ladder and put onto a roof he carries two bundles at a time how many bundles are still on the ground after his seventh trip up the ladder
Answer:
15 bundles of roofing shingles
Step-by-step explanation:
Total bundles of roofing shingles = 29
He carries two bundles at a time
How many bundles are still on the ground after his seventh trip up the ladder?
First trip = 2 bundles of roofing shingles
Second trip = 2 bundles of roofing shingles
Third trip = 2 bundles of roofing shingles
Fourth trip = 2 bundles of roofing shingles
Fifth trip = 2 bundles of roofing shingles
Sixth trip = 2 bundles of roofing shingles
Seventh trip = 2 bundles of roofing shingles
Total bundles of roofing shingles carried in 7 trips = 2 + 2 + 2 + 2 + 2 + 2 + 2
= 14 bundles of roofing shingles
Bundles still on ground after 7 trips = Total bundles of roofing shingles - Total bundles of roofing shingles carried in 7 trips
= 29 - 14
= 15 bundles of roofing shingles
In the notation "s(X) = ...," what does "s(x)" represent?
A.
The value of s(x) depends on the value of x, since s is a function of x.
B.
The value found when sis multiplied by the value x.
С.
There is not enough information to answer this question.
D.
The value of x depends on the value of s(x), since x is a function of s.
Answer: Choice A) The value of s(x) depends on the value of x, since s is a function of x.
The outer letter s tells us what the function's name is. It's the dependent variable and it might be handy to tie it to the y variable. The x is the independent variable. It changes freely without relying on what s happens to be.
Answer: A. The value of s(x) depends on the value of x, since s is a function of x.
Step-by-step explanation: s(x) is the output of the function when a given value of x is calculated according the operations in the function.
Identify the initial amount and the growth rate of the following:
Y = 250 (1+0.2)
Answer:
y = 300
Step-by-step explanation:
y = 250 (1+0.2)
First add the 1 and 0.2
y=250(1.2)
multiply 250 with 1.2
y = 300
:)
please please please help!! i’ll mark the brainliest and give 15 points!!!!
9514 1404 393
Answer:
-108
Step-by-step explanation:
About the easiest way to do this for small values of n is to compute each of the terms using the given recurrence relation.
[tex]a_1=4\\\\a_2=-3a_1=-3(4)=-12\\\\a_3=-3a_2=-3(-12)=36\\\\a_4=-3a_3=-3(36)=-108\\\\\boxed{a_4=-108}[/tex]
_____
Alternate solution
You recognize that the recurrence relation describes a geometric sequence with a first term of 4 and a common ratio of -3. The n-th term of a geometric sequence is ...
[tex]a_n=a_1\cdot r^{n-1} \qquad\text{for first term $a_1$ and common ratio $r$}[/tex]
Then the 4th term will be ...
[tex]a_4=4\cdot(-3)^{4-1}=4\cdot(-27)=-108[/tex]
2) A big league pitching coach tries to limit his pitchers to 110
pitches per game. If the pitcher has already thrown 52
pitches, write and solve an inequality to find how many more
pitches he can throw before reaching the limit.
Answer:
x<58 the< with line under the pitcher can throw 58 or less pitches
Step-by-step explanation:
Passes through (8,8) and (10,9)
Plz help need answer ASAP
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
Assuming you require the equation of the line.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 8) and (x₂, y₂ ) = (10, 9)
m = [tex]\frac{9-8}{10-8}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 8) , then
8 = 4 + c ⇒ c = 8 - 4 = 4
y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
A carton contains 1.92 liters of milk. There are 8 servings in the carton. How many liters of milk are in each serving? A. 0.14 B. 0.19 C. 0.24 D. 0.29
Answer:
C. 0.24
Step-by-step explanation:
A carton contains 1.92 liters of milk. There are 8 servings in the carton. How many liters of milk are in each serving? A. 0.14 B. 0.19 C. 0.24 D. 0.29
From the above question:
8 servings = 1.92 liters of milk
1 serving = x liters
Cross Multiply
8 × x liters = 1 × 1.92 liters
x liters = 1.92 liters/8
x liters = 0.24 liters
There are 0.24 liters of milk, in 1 serving
Answer:
0.24
Step-by-step explanation:
grams of fish
number of calories
1000
2001
Enter the missing values in the boxes below.
b=0
Answer:
♂️ but if you know please answer
Answer:
12344567891011121314151617181920
Step-by-step explanation:
12344567891011121314151617181920
For the month of march, Kasey plans to vacuum her floor every fourth day and clean her bathroom every seventh day if she begins this march 1, on what day of the month will she do both jobs?
Answer: March 28
Step-by-step explanation:
Solve for this by checking for the lowest common multiple of 7 and 4.
Multiples of 7: 7, 14, 21, 28, 35
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32
Lowest is 28 so on March 28th she both will vacuum her floor and clean her bathroom.
Please help!!!!
Tom, Lisa, and Jane are competing in a cooking competition. They all used different amounts of sugar from a can containing 4 pounds of sugar. Tom used 13% of the total sugar in the can. Lisa used 0.6 pounds of the total sugar in the can. Jane used 0.12 of the total sugar in the can. Who used the greatest amount of sugar from the can? Show your work and explain your answer in words.
Answer:
13 x 4
100
= 0.52 so tom used the most
Step-by-step explanation:
HELP I NEED THOS FASSTTTT A
What is the domain of the function?
Answer:
A
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
domain -are all values of x
c -because x can take any value except 1
heeelp will give brainliest
X varies directly with y. If x is 24 when y is 36, find x when y is 132.
equation:_________
x=_________
Step-by-step explanation:
x = ky, where k is a real constant.
When y = 36, x = 24.
=> (24) = k(36), k = 2/3.
Hence x = (2/3)y.
When y = 132, x = (2/3)(132) = 88.
Answer:
see explanation
Step-by-step explanation:
Given x varies directly with y then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 24 when y = 36, then
36 = 24k ( divide both sides by 24 )
1.5 = k
y = 1.5x ← equation of variation
When y = 132, then
132 = 1.5x ( divide both sides by 1.5 )
x = 88
Sam had 75 pollywog pralines. He wanted to put them in bags of 3. How many bags
will he need?
12
25
3
30
Answer:
sam will take the 75 pollywog pralines and divide them into the three bags
75÷3 =25