Answer:
[tex]3ab^2\sqrt[3]{b}[/tex]
if the problem was [tex]\sqrt[3]{27a^3b^7}[/tex].
Step-by-step explanation:
Correct me if I'm wrong by I think you are writing [tex]\sqrt[3]{27a^3b^7}[/tex].
[tex]\sqrt[3]{27a^3b^7}[/tex]
I'm first going to look at this as 3 separate problems and then put it altogether in the end.
Problem 1: [tex]\sqrt[3]{27}=(3)[/tex] since [tex](3)^3=27[/tex].
Problem 2:[tex]\sqrt[3]{a^3}=(a)[/tex] since [tex](a)^3=a^3[/tex]
Problem 3: [tex]\sqrt[3]{b^7}[/tex]. This problem is a little harder because [tex]b^7[/tex]is not a perfect cubes like the others were. But [tex]b^7[/tex] does contain a factor that is a perfect cube. That perfect cube is [tex]b^6[/tex] so rewrite [tex]b^7[/tex] as [tex]b^6 \cdot b^1[/tex] or [tex]b^6 \cdot b[/tex].
So problem 3 becomes [tex]\sqrt[3]{b^6 \cdot b}=\sqrt[3]{b^6}\cdot \sqrt[3]{b}=b^2 \cdot \sqrt[3]{b}[/tex]. The [tex]b^2[/tex] came from this [tex](b^2)^3=b^6[/tex].
Anyways let's put it altogether:
[tex]3ab^2\sqrt[3]{b}[/tex]
The graph of the function f(x) is shown below.
What is x when f(x)=0?
-1.8
-1.2
0
5
Answer:
a -1.8
Step-by-step explanation:
f(x)=y=0
when y = 0, x=-1.8
Answer:
A. [tex]-1.8[/tex]
Step-by-step explanation:
We have been graph of a function. We are asked to find the value of x, when [tex]f(x)=0[/tex].
We know that [tex]f(x)=0[/tex] stands for x-intercept. [tex]f(x)[/tex] stands for value of y. We know that y is zero on x-axis.
Upon looking at our given graph, we can see that our function has only one x-intercept that is at point [tex](-1.8,0)[/tex].
This means that [tex]f(-1.8)=0[/tex], therefore, the value of x is [tex]-1.8[/tex] and option A is the correct choice.
find the inverse -4
a. -1/4
b. 1/4
c. 4
d. -4
Answer:
c. 4
Step-by-step explanation:
To find the inverse of a number, x, then you end up getting -x.
x = -4
- ( -4 ) = 4
For this case we must find the inverse of the following number:
-4
By definition we have that the inverse of a number multiplied by the number gives us 1 as a result.
Let "x" be the inverse of -4, then:
[tex]x (-4) = 1\\-4x = 1\\x = - \frac {1} {4}[/tex]
So, the inverse of -4 is[tex]- \frac {1} {4}[/tex]
Answer:
[tex]- \frac {1} {4}[/tex]
f(x) = 2x - 1
g(x) = 7x -12
what is h(x)=f(x)+g(x)?
A) h(x)=9x-13
B) h(x)=9x-12
C) h(x)=-5x+11
D) h(x)=5x-13
Answer:
A) h(x)=9x-13
Step-by-step explanation:
f(x) = 2x - 1
g(x) = 7x -12
Add them together
f(x) = 2x - 1
g(x) = 7x -12
-------------------------
f(x)+g(x) = 9x-13
h(x) = 9x-13
Answer:
A
Step-by-step explanation:
I took the test
Solve for x. 2x2 − 4x = 0
Answer:
x = 2
Step-by-step explanation:
From my understanding, this question is
2x² - 4x = 0
Step 1: Take x as common
2x² - 4x = 0
x(2x - 4) = 0
2x - 4 = 0/x
2x - 4 = 0
Step 2: Solve to find x
2x - 4 = 0
2x = 4
x = 4/2
x = 2
Therefore, the value of x after solving is x = 2
!!
Answer:
[tex]x = 0[/tex] and [tex]x = 2[/tex]
Step-by-step explanation:
We have the following quadratic equation
[tex]2x^2 - 4x = 0[/tex]
Take 2x as a common factor
[tex]2x(x - 2) = 0[/tex]
Note that equality is met when either factor equals zero.
That is to say:
[tex]2x = 0[/tex] → [tex]x = 0[/tex]
[tex](x-2) = 0[/tex] → [tex]x = 2[/tex]
Finally the solutions of the equation are:
[tex]x = 0[/tex] and [tex]x = 2[/tex]
7. Identify the period for the trigonometric function: f (t) = 3cot(t).
Answer:
π
Step-by-step explanation:
recall that for a cotangent function
f(x) = cot (bx) + k
the period is simply π / | b |
in our case b = 1, hence | b | = 1
therefore the period is simply π / 1 = π
take a look at the following figure if angle B measures 78°, and is the measure of BDC?
a. 204 degree
b. 156 degree
c. 39 degree
d. 78 degree
Answer:
Option a. 204 degree
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The semi-inscribed angle is half that of the arc it comprises.
so
∠B=(1/2)[arc BC]
substitute
78°=(1/2)[arc BC]
arc BC=156°
Remember that
arc BC+arc BCD=360°
arc BCD=360°-156°=204°
Which equation involves a prime quadratic and cannot be solved by factoring?
A. x2-x-6=0
B. x2 + 5x -4 = 0
C. x2 + 6x + 9 = 0
D. x2 + 3x-4=0
Answer:
B x^2 + 5x − 4 = 0
Step-by-step explanation:
PLATO
A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to the one-way fare, 100 passengers will find other means of transportation. Let x represent the number of $1.00 increases in ticket price. Choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000. Then, use the inequality to select all the correct statements.
options:
1.The maximum profit the company can make is $4,125.00.
2.The price of a one-way ticket that will maximize revenue is $7.50.
3.The maximum profit the company can make is $15,625.00.
4.The price of a one-way ticket that will maximize revenue is $12.50.
Answer:
number 2
Step-by-step explanation:
Total number of riders that ride on carpool daily = 2000
Total Cost of one way ticket = $ 5.00
Total Amount earned if 2000 passengers rides daily on carpool = 2000 × 5
= $10,000
If fare increases by $ 1.00
New fare = $5 + $1
= $6
Number of passengers riding on carpool = 2,000 - 100 = 1,900
If 1,900 passengers rides on carpool daily , total amount earned ,if cost of each ticket is $ 6 = 1900 × $6 = $11400
As we have to find the inequality which represents the values of x that would allow the carpool service to have revenue of at least $12,000.
For $ 1 increase in fare = (2,000 - 1 × 100) passengers
For $ x increase in fare, number of passengers = 2,000 - 100·x
= (2,000 - 100·x) passengers
New fare = 5 + x
New Fare × Final Number of passengers ≥ 12,000
(5+x)·(2,000 - 100 x) ≥ 12,000
5 (2,000 - 100 x) + x(2,000 - 100 x) ≥ 12,000
10,000 - 500 x + 2,000 x - 100 x² ≥ 12,000
100 - 5 x + 20 x - x² ≥ 120
- x² + 15 x +100 - 120 ≥ 0
-x² + 15 x -20 ≥ 0
x² - 15 x + 20 ≤ 0
⇒ x = 1.495
x ≥ $ 1.495, that is if we increase the fare by this amount or more than this the revenue will be at least 12,000 or more .
Also, f'(x) = 0 gives x = 7.5
⇒ The price of a one-way ticket that will maximize revenue is $7.50
+3 + 3x2 – 2X-6
is this a prime polynomial
Answer:
see explanation
Step-by-step explanation:
This is not a prime polynomial as it can be factored into polynomials of lower degree.
Given
x³ + 3x² - 2x - 6 ( factor the first/second and third/fourth terms )
= x²(x + 3) - 2(x + 3) ← factor out (x + 3) from each term
= (x + 3)(x² - 2) ←can be reduced further as a difference of squares
= (x + 3)(x - [tex]\sqrt{2}[/tex] )(x + [tex]\sqrt{2}[/tex] )
If statement q is angles ABC and QRT are vertical angles then ~q is angles ABC and QRT are congruent
True or false?
Answer:
true
Step-by-step explanation:
vertical angles are congruent
The vertex form of the equation of a parabola is y=6(x-2)2-8. What is the standard form of the equation?
The answer is D!!!
y=6x^2-24x+16
Answer:
Option 4 - [tex]y=6x^2-24x+16[/tex]
Step-by-step explanation:
Given : The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]
To find : What is the standard form of the equation?
Solution :
The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]
We solve the equation to get standard form,
[tex]y=6(x^2-2^2-2(x)(2))-8[/tex]
[tex]y=6(x^2+4-4x)-8[/tex]
[tex]y=6x^2+24-24x-8[/tex]
[tex]y=6x^2-24x+16[/tex]
The standard form of the equation is [tex]y=6x^2-24x+16[/tex]
Therefore, Option 4 is correct.
Fill in the other coordinate line y=7/2x+6:(8,)
Answer:
The other coordinate for the given equation is 34.
Step-by-step explanation:
We are given the following equation and we are to fin the value of the y coordinate given that the value of the x coordinate is [tex] 8 [/tex]:
[tex] y = \frac { 7 } { 2 x + 6 } [/tex]
Substituting the given value of x in the above equation to find y:
[tex]y = \frac { 7 } { 2 } ( 8 ) + 6 [/tex]
y = 34
(8, 34)
What is the solution to the equation 1/2x + 3 = 2/3x + 1
Answer:
x=12
Step-by-step explanation:
1/2x + 3 = 2/3x + 1
Subtract 1 from each side
1/2x + 3-1 = 2/3x + 1-1
1/2x +2 = 2/3 x
Subtract 1/2 x from each side
1/2x -1/2x+ 2 = 2/3x -1/2x
2 = 2/3x -1/2x
Get a common denominator of 6 2/3 = 4/6 and 1/2 = 3/6
2 = 4/6x - 3/6x
2 = 1/6 x
Multiply each side by 6 to isolate x
2*6 = 1/6x *6
12 =x
Answer:
x=12
Step-by-step explanation:
If f(x) = -4x^ - 6x - 1 and g(x) = -x2 - 5x + 3, find (f - g)(x).
O
A. (f - g)(x) = -3x2 - 11x + 2
O B. (f - g)(x) = 5x2 + x + 2
O C. (f – 9)(x) = -3x2 - x - 4
O D. (f - g)(x) = 3x2+x+4
Answer:
O C. (f – g)(x) = -3x^2 - x - 4
Step-by-step explanation:
I will assume that f(x) is -4x^2- 6x - 1
f(x) = -4x^2 - 6x - 1
g(x) = -x2 - 5x + 3
(f - g)(x)= -4x^2 - 6x - 1 - (-x2 - 5x + 3)
Distribute the minus sign
(f - g)(x)= -4x^2 - 6x - 1 +x2 + 5x - 3
Combine like terms
(f - g)(x)= -3x^2 - 1x - 4
What value of x will make this proportion true 14/x=1/2?
Answer:
x = 28
Step-by-step explanation:
Given
[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
x = 14 × 2 = 28
Answer:
x = 7
Step-by-step explanation:
14 / x = 1 / 2
14 / x = 0.5
14 = x(0.5)
14 / 0.5 = x
7 = x
Hope this helps!
A hot tub is 75 percent full with 600 gallons
of water. How many gallons of water are in
the hot tub when it's half full?
Answer:
When the hot tub is half full, there are 400 gallons of water in it.
Step-by-step explanation:
If 75% or 3/4 of the hot tub is 600 gallons and you need to find 50% or 1/2. Divide 600 by 3 to get 200 then simply multiply by 2 to get 400.
When the hot tub is half full, it would contain 400 gallons of water.
To find out how many gallons are in the hot tub when it's half full, calculate the total capacity of the hot tub using the information that 75% equals 600 gallons. Then, take 50% of that total capacity to find that when the hot tub is half full, it contains 400 gallons.
If a hot tub is 75 percent full with 600 gallons of water, that means the hot tub's total capacity when it's 100% full is larger than 600 gallons. To find out how many gallons are in the hot tub when it's half full, we must first determine the hot tub's total capacity. We can set up a proportion to find the total capacity (T) since 75% of T is 600 gallons.
75% of T = 600 gallons
0.75 imes T = 600 gallons
Now, to find the total capacity (T), divide both sides by 0.75:
T = 600 gallons / 0.75
T = 800 gallons
So, the hot tub's total capacity is 800 gallons. To find the amount of water when the hot tub is half full, simply take 50% of the total capacity:
50% of 800 gallons = 0.5 imes 800 gallons
50% of 800 gallons = 400 gallons
Therefore, when the hot tub is half full, it would contain 400 gallons of water.
The equation tan^2 x+1=sec^2 x is an identity true or false
Answer:
tan²x + 1 = sec²x is identity
Step-by-step explanation:
* Lets explain how to find this identity
∵ sin²x + cos²x = 1 ⇒ identity
- Divide both sides by cos²x
∵ sin x ÷ cos x = tan x
∴ sin²x ÷ cos²x = tan²x
- Lets find the second term
∵ cos²x ÷ cos²x = 1
- Remember that the inverse of cos x is sec x
∵ sec x = 1/cos x
∴ sec²x = 1/cos²x
- Lets write the equation
∴ tan²x + 1 = 1/cos²x
∵ 1/cos²x = sec²x
∴ than²x + 1 = sec²x
- So we use the first identity sin²x + cos²x = 1 to prove that
tan²x + 1 = sec²x
∴ tan²x + 1 = sec²x is identity
Simplify the expression given below.
1|2x^2-4x-2/x
Answer:
[tex]\large\boxed{D.\ \dfrac{-4x+9}{2x(x-2)}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{2x^2-4x}-\dfrac{2}{x}=\dfrac{1}{2x(x-2)}-\dfrac{2}{x}=\dfrac{1}{2x(x-2)}-\dfrac{(2)(2)(x-2)}{2x(x-2)}\\\\=\dfrac{1-4(x-2)}{2x(x-2)}\qquad\text{use the distributive property}\\\\=\dfrac{1-4x+8}{2x(x-2)}=\dfrac{-4x+9}{2x(x-2)}[/tex]
Answer:
The correct option is D.
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{1}{2x^2-4x}-\frac{2}{x}[/tex]
Now take the LCM of the denominator and solve the above expression as shown:
[tex]\frac{x-2(2x^2-4x)}{x(2x^2-4x)}[/tex]
[tex]\frac{x-4x^2+8x}{x(2x^2-4x)}[/tex]
[tex]\frac{9x-4x^2}{x(2x^2-4x)}[/tex]
Cancel out the x as it is common in numerator and denominator.
[tex]\frac{9-4x}{2x^2-4x}[/tex]
[tex]\frac{-4x+9}{2x(x-2)}[/tex]
Hence, the correct option is D.
The product of two numbers is 30. If one of the numbers is 15/, what is the other number?
Answer:
The other number is 2 if the given number is 15.
Step-by-step explanation:
One of the numbers is 15, correct?
Let the other number be x.
15 × x = 30
x = 30/15
x = 2.
Let's check:
15 × 2 = 30.
30 = 30.
Correct!
The other number whose product with 15 yields 30 is; 2.
According to the question;
The product of two number is 30.Additionally, one of the numbers is 15.Let the other number be X.
As such; the product of x and 15 is 30.
Therefore;
15x = 30x = 30/15x = 2.Therefore, The other number whose product with 15 yields 30 is; 2.
Read more:
https://brainly.com/question/18589599
Given that ABC ~ DEF, if EF = 7.5 what is the length of ?
6.5
6
5
5.5
Answer:
5
Step-by-step explanation:
The triangles have a 2:3 ratio given by the heights of the triangles. We can assume the sides of the triangles must always form a 2:3 ratio with the sides. 5:7.5 forms 2:3 ratio if you divide 5/7.5. This equals .67, just as 2/3 does.
If a 4x16 rectangle has the same area as a square what is the length of a side of the square
The area of the rectangle is 4 x 16 = 64 square units.
Because the sides of a square are all the same, to find the length of the side, take the square root of the area:
Side length = √64
Side = 8
Which graph most likely shows a system of equations with no solutions
Answer: C
Step-by-step explanation
I got 100% on edge
How do you divide 85 by 41 with remainder
Answer:
2 remainder 3.
Step-by-step explanation:
Well 2 * 41 = 82 so the quotient is 2 and the remainder is 85-82 = 3.
41 ) 85 ( 2
- 82
3.
[tex]\huge{\boxed{2,\ remainder\ 3}}[/tex]
Explanation:First, find how many times [tex]41[/tex] can fit into [tex]85[/tex].
[tex]41*1=41[/tex]
[tex]41*2=82[/tex]
[tex]41*3=123[/tex] is greater than [tex]85[/tex], so we need to go back down to [tex]41*2=82[/tex].
Now, subtract [tex]85-82[/tex] to get a remainder of [tex]3[/tex].
Vladimir says that the equation of the line that passes through points above Robyn says that the line passes through the points above Who is correct?
Answer:
Both are correct
Step-by-step explanation:
The Line has the following equation: y= 1+4/5 x
So we need to know which points: (-5,-3) and (10,9), (-10,-7). (-15, -11) are part of the line
For instances, lest start by evaluating (-15,-11) in y=1+4/5 x
this leaves us to the following operation: -11=1+4/5 * (-15)
-11=1-4*3 resulting in a equality -11=-11, this point does belong to the line
Repeat the above for all of the remaining points and you will get the same conclusion, that is we Vladimir and Robyn are correct.
What is the area of Figure ABCD?
Answer:
66 in^2.
Step-by-step explanation:
We can use the formula for the area of a trapezoid:
Area = (h/2) (a + b) where h = the height and a and b are the lengths of the opposite parallel lines.
so the Area of ABCD = (6/2)*(10 + 12)
= 3 * 22
= 66 in^2.
For this case we have that the area of the figure is given by the sum of the area of a rectangle plus the area of a triangle.
By definition, the area of a reactangle is given by:
[tex]A = a * b[/tex]
Where:
a, b:they are the sides of the rectangle.
According to the figure we have:
[tex]a = 10\\b = 6[/tex]
Substituting we have:
[tex]A = 10 * 6\\A = 60[/tex]
Thus, the area of the rectangle is [tex]60in ^ 2[/tex]
On the other hand, the area of a triangle is given by:
[tex]A = \frac {b * h} {2}[/tex]
Where:
b is the base and h is the height of the triangle.
According to the figure we have to:
[tex]b = 12-10 = 2\\h = 6[/tex]
Substituting in the formula:
[tex]A = \frac {2 * 6} {2} = \frac {12} {2} = 6[/tex]
Thus, the area of the rectangle is[tex]6in ^ 2[/tex]
Then, the total area of the figure is:
[tex]A_ {T} = 60in ^ 2 +6in ^ 2 = 66 \ in ^ 2[/tex]
Answer:
[tex]66 \ in ^ 2[/tex]
What colleges don’t require on campus housing?
Answer:
1. University of Wisconsin–Madison
2. New York University
3. Purdue University
4. Texas A&M University
5. Auburn University
6. University of California, Davis
7. College of Charleston
Step-by-step explanation:
These schools don't require you to live on campus.
Some colleges, such as community colleges and online universities, do not require on-campus housing, offering students the flexibility of living off-campus or at home while studying.
Colleges that do not require on-campus housing:
Some colleges that typically do not require on-campus housing include community colleges and online universities.
Community colleges often allow students to live at home to keep costs down, catering to both young people and adults who prefer living at home while studying.
Online universities provide education entirely through online platforms, allowing students to study from their own locations without the need for on-campus housing.
i cant figure it out 3+2x=5+4x. x=?
Answer:
x=-1
Step-by-step explanation:
3+2x=5+4x
Subtract 2x from each side
3+2x-2x=5+4x-2x
3 = 5x+2x
Subtract 5 from each side
3-5 =5-5+2x
-2 =2x
Divide each side by 2
-2/2 = 2x/2
-1 =x
Which of the following numbers is rational?
A -9
B 5/8
C 0
D All Of Above
Answer:
D All Of Above
Step-by-step explanation:
Any number that is the ratio of two integers, a repeating decimal fraction, or a value you can write completely without using symbols such as π or √2 is a rational number. All the numbers shown are complete in a finite number of digits, so are rational.
All the provided options (-9, 5/8, and 0) are rational numbers because they can all be expressed as a ratio of two integers or as whole numbers. Hence, the correct answer is 'All of the Above.'
A rational number is one that can be expressed as the ratio of two integers (where the denominator is not zero) or as a whole number. Therefore, -9 (which is a whole number), 5/8 (which is a fraction with both numerator and denominator as integers), and 0 (which can be expressed as 0/1) are all rational numbers. Thus, All of the Above are rational numbers.
The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.
If x represents the smallest integer, then which of the following equations could be used to solve the problem?
Ox= 2x + 6
Ox= 2x + 3
2x + 2 = x + 4
Answer:
x=2x+6 is the equation that to solve for the smallest.
The three numbers are -6, -4 , and -2.
Step-by-step explanation:
Let x be the smallest of three consecutive even integers.
The next even integer would then have to be x+2 (because x+1 is odd if x is even).
The third one in this sequence would have to be x+4 (because x+3 is odd if x is even).
We are given the first of these numbers equals the sum of the second and third.
So we have x=(x+2)+(x+4).
Combine like terms on right hand side:
x=x+x+2+4
Simplify the combining:
x=2x+6
Subtract 2x on both sides:
x-2x=6
Simplify left hand side:
-x=6
Multiply both sides by -1:
x=-6
If x=-6, then the three mentioned numbers are:
x=-6
x+2=-6+2=-4
x+4=-6+4=-2
The three numbers are -6, -4 , and -2.
Select the two values of x that are roots of this equation.
2x-5=-3x^2
A. x= 3
B. X=1
C. x=-5/3
D. x=-1/2
Answer:
[tex]\large\boxed{B.\ x=1,\ C.\ x=-\dfrac{5}{3}}[/tex]
Step-by-step explanation:
[tex]2x-5=-3x^2\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2+2x-5=0\\\\3x^2+5x-3x-5=0\\\\x(3x+5)-1(3x+5)=0\\\\(3x+5)(x-1)=0\iff3x+5=0\ \vee\ x-1=0\\\\3x+5=0\qquad\text{subtract 5 from both sides}\\3x=-5\qquad\text{divide both sides by 3}\\x=-\dfrac{5}{3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]