Answer:
= [tex]3ab^{\frac{2}{3} }[/tex]
Step-by-step explanation:
∛(27 a³ [tex]b^{7}[/tex])
= ∛27 · ∛a³ · ∛b³ · ∛b³ · ∛b
= 3 · a · b · b ∛b
= 3ab² [tex]b^{\frac{1}{3} }[/tex]
or
= [tex]3ab^{\frac{2}{3} }[/tex]
in order to graph a linear equation in slope-interceot form, what do you need to know? what does the equation look like when the y-intercept of the line is equal to 0? what does the equation look like when it also has a slope equal to 1?
Answer:
(a) Slope and y-intercept; (b) y = mx; (c) y = x + b
Step-by-step explanation:
1. Need to know
Slope and y-intercept.
You use these numbers to calculate one other point. Then you draw a straight line between the y-intercept and the other point to get the graph.
2. y-Intercept = 0
The form of the equation is y = mx + b, where b is the y-intercept.
If the intercept is zero, b = 0, and the equation has the form
y = mx
The graph is a straight line passing through the origin.
3. Slope = 1
m represents the slope. If m = 1, the equation has the form
y = x + b
If the axes are scaled equally, the graph is a straight line that crosses the y-intercept at an angle of 45°.
The figure shows the function p(x)=[x]. Which statement about the function is not true?
A) p(0)=0
B) p(-4)=4
C) p(4)=-4
D) The domain of p(x) is all real numbers
Answer:
The option that's not true is:
C) p(4) = -4
Because if you look at that graph, you can tell, p(4) = 4 not -4.
The domain of the function p(x) = [x] is not all real numbers; it excludes integer values of x where the function is discontinuous. Statement D is not true.
The function p(x) = [x], where [x] represents the greatest integer less than or equal to x (the floor function). Let's evaluate each statement:
A) p(0) = [0] = 0. This is true.
B) p(-4) = [-4] = -4. This is true.
C) p(4) = [4] = 4. This is true.
D) The domain of p(x) is all real numbers. This statement is not true. The domain of p(x) is actually all real numbers except the points where x is an integer. At those points, there are discontinuities, and the function is undefined because the floor function jumps from one integer value to the next.
So, the statement that is not true is D) The domain of p(x) is all real numbers. The correct statement is that the domain of p(x) is all real numbers except at integer values of x.
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Which of the following is the scaling factor a of the function f(x) = 3|x|?
•-1
•-3
• 1
• 3
Answer:
Last option: 3
Step-by-step explanation:
The following are some transformations for a function f(x):
1) If [tex]a(fx)[/tex] and [tex]|a|>1[/tex], then this function is stretched vertically by a factor of "a".
2) If [tex]a(fx)[/tex] and [tex]0<|a|<1[/tex], then this function is compressed vertically by a factor of "a".
Therefore, given the function [tex]f(x) = 3|x|[/tex], we can observe that the factor "a" is:
[tex]a=3[/tex]
Then:
[tex]a>1[/tex]
This means that then this function is stretched vertically by a factor of 3.
Therefore, the scaling factor is 3.
what is the difference between the mean of each set?
a) 4
b) 5
c) 7
d) 9
NEED NOW!!! DONT NEED AN EXPLANATION I HAVE LIKE 5 MIN!!!
Which equation represents a linear function?
y – 2 = –5(x – 2)
x + 7 = –4(x + 8)
y – 3 = y(x + 4)
y + 9 = x(x – 1)
The first one. x and y only ever appear as first degree terms.
Second one, no y, third one xy isn't linear, fourth one x squared isn't linear.
Answer:
The first one: y - 2 = -5(x - 2)
Step-by-step explanation:
3. Solve the system of equations. Show your work. y = x^2-3x+4 x + y = 4
Answer: x = 2, y = 2
Step-by-step explanation:
[tex]y=x^2-3x+4\\x + y = 4\quad \implies y=4-x\\\\\underline{\text{Substitute y (in the first equation) with 4 - x:}}\\4-x=(4-x)^2-3(4-x)+4\\\\\underline{\text{Expand and distribute right-hand side:}}\\4-x=16-8x+x^2-12+3x+4\\\\\underline{\text{Simplify right-hand side:}}\\4-x=8-5x+x^2\\\\\underline{\text{Set left-hand side equal to zero (subtract 4 and add x):}}\\0=4-4x+x^2\quad \implies 0=x^2-4x+4\\\\\underline{\text{Factor and solve for x:}}\\0=(x-2)(x-2)\\0=x-2\\2=x[/tex]
Replace x with 2 in the second equation to solve for y:
x + y = 4
2 + y = 4
y = 2
If h(x) is the inverse of f(x), what is the value of h(f(x))?
OO
0 1
f(x)
Answer:
x.
Step-by-step explanation:
h(f(x) = x.
For example the inverse of f(x) = 2x is g(x) = x/2
f((gx)) 2 (x/2)
= 2x / 2
= x.
If h(x) is the inverse of f(x), then the value of h(f(x)) is:
x
Step-by-step explanation:Inverse of a function-
The inverse of a given function is a function which reverses the action of the other function.
Also, the composition of a function and it's inverse no matter in which order they are applied always gives us the identity function.
( Identity function-- Identity function is a function which when applied to some other function always retains that function )
i.e. If h(x) is the inverse of f(x) ; then we have:
[tex]h(f(x))=f(h(x))=x[/tex]
one fifth of a number plus five times that number is equal to seven times the number less 18
To solve the equation, we can use algebraic techniques to find the value of 'x'.
Explanation:To solve the equation, we can let the number be represented by 'x'. The equation can then be written as: (1/5)x + 5x = 7x - 18. Simplifying this equation gives us: (1/5)x + 5x - 7x = -18. Combining like terms, we get: (6/5)x = -18. Dividing both sides by 6/5 gives us the value of 'x'.
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Follow below steps:
The question involves solving a linear equation to find an unknown number. To solve "one fifth of a number plus five times that number is equal to seven times the number less 18", the first step is to let "x" represent the unknown number and then create an equation based on the given information.
We start by translating the words into an equation:
One fifth of a number can be written as "(1/5)x".
Five times that number is written as "5x".
Seven times the number less 18 is written as "7x - 18".
So our equation becomes "(1/5)x + 5x = 7x - 18". Simplifying, we get "(6/5)x = 7x - 18".
Combining like terms yields "(1/5)x = -18", and we solve for x to find the value of the unknown number: "x = -90".
Through this process, the student can identify the value of the number in question.
Should teens be allowed to play dangerous sports? Why or why not?
Answer:
I mean if it's there dream then why stop it? Its there life and we can't really stop that cause regardless what you say or do they're gonna find a way to do it. So I would say yes.
I am going to assume this is a poll? For our opinions?
If so then yes, I think that kids should be allowed to play dangerous sports..Football fatalities remain rare, but the game can be dangerous. That doesn't mean kids shouldn't play, same with hockey and any other
Which of the following shows the true solution to the logarithmic equation below?
log(x)+ log(x+5) = log(6x +12)
©
X=-3
x=4
X=-3 and x = 4
X=-3 and x=-4
Answer:
x = 4.
Step-by-step explanation:
log(x) + log(x+5) = log(6x +12)
log x(x +5) = log(6x + 12)
Therefore x(x + 5)= 6x +12
x^2 + 5x - 6x - 12 = 0
x^2 - x - 12 = 0
(x - 4)(x + 3) = 0
x = -3, 4.
logs of negative values do not exists so the anser is x = 4.
©
The value of x is -3 , 4 ; option C is the solution to the equation
What is an Equation ?
An equation is a mathematical statement between two algebraic expressions equated by an equal sign.
A logarithm equation is given in the question.
log(x)+ log(x+5) = log(6x +12)
The equation of Logarithm says
log (x .y) = log x + log y
From the equation
log(x)+ log(x+5) can be written as log (x(x+5))
log (x(x+5)) = log(6x +12)
We can relate this as
(x(x+5)) = 6x +12
x² + 5x = 6x +12
x² -x -12= 0
x² -4x +3x -12 = 0
x (x-4)+3(x-4) = 0
(x+3)(x-4) = 0
x = -3 , x=4
Therefore the option C is the solution to the equation
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please helpppppp me
Answer:
B. [tex] 4 \times 10^{12} [/tex]
Step-by-step explanation:
[tex] (6 \times 10^{8}) \div (1.5 \times 10^{-4}) = [/tex]
[tex] = \dfrac{6 \times 10^{8}}{1.5 \times 10^{-4}} [/tex]
[tex] = \dfrac{6}{1.5} \times \dfrac{10^{8}}{10^{-4}} [/tex]
[tex] = 4 \times 10^{8 - (-4)} [/tex]
[tex] = 4 \times 10^{12} [/tex]
The diagonal of a square is x units. What is the area of the square in terms of x? square units square units 2x square units square units
For this case we have that by definition, if we draw the diagonal of a square two rectangular triangles are formed. If the diagonal measures "x", then the Pythagorean theorem is fulfilled:
[tex]l ^ 2 + l ^ 2 = x ^ 2[/tex]
Where:
l: It's the side of the square.
[tex]2l ^ 2 = x ^ 2\\l ^ 2 = \frac {x ^ 2} {2}[/tex]
We know that the area of a square is given by:
[tex]A = l ^ 2[/tex]
So, the area is:
[tex]A = \frac {x ^ 2} {2}[/tex]
Answer:
[tex]A = \frac {x ^ 2} {2}[/tex]
Answer:
Option A: 1/2 x^2
Step-by-step explanation:
Monique has $20 available to buy some sweet corn and lima beans to make succotash. If she buys 8 lb of corn, how many pounds of lima beans can she buy
Answer:
It’s a
Step-by-step explanation:
Answer:
It's A: 4.8 lb
Step-by-step explanation:
f(x) = x2 + 5x - 1 is shifted 3 units left. The result is g(x). What is g(x)?
Answer:
g(x) = (x + 3)^2 + 5(x + 3) - 1
Step-by-step explanation:
Please use " ^ " to denote exponentiation: f(x) = x^2 + 5x - 1.
Shifting the graph of this function 3 units left results in
g(x) = (x + 3)^2 + 5(x + 3) - 1
If f(x) = 5x + 40, what is f(x) when x = –5?
First note that f(x) means the same thing as y. To solve for f(x) or y you need to plug in -5 for x and solve using the rules of PEMDAS
5(-5) + 40
-25 + 40
15
When x is -5 then y is 15
Hope this helped!
~Just a girl in love with Shawn Mendes
The graph of y= - 3x^2– 4x + 2 opens downward true or false
Answer:
True
Step-by-step explanation:
This is a parabola. The coefficient of the x^2 term is -3
Since it is negative, the parabola opens downward
Answer: False
Step-by-step explanation: A-Pexw
Which inequality is shown below ?
Answer:
b.
Step-by-step explanation:
The following two-way table shows the data for the students of two different grades in a school:
Member of Science Club Not Member of Science Club Total
Grade 7 20 2 22
Grade 8 20 8 28
Total 40 10 50
Based on the relative row frequency, the students of which grade are more likely to be members of the science club?
Grade 7
Grade 8
The students of both grades are equally likely to be members of the science club
No conclusion can be drawn about the chances of a student being a member of the science club
Answer: grade 7
Step-by-step explanation:
Grade 7: 20/22 students in club
Grade 8: 20/28 students in club
Grade 7 has higher % of students in science club
Answer:
Grade 7
Step-by-step explanation:
The relative row frequency of members of the Science Club is: Member of Science Club / Total
in Grade 7: 20/22 = 0.91.
And in Grade 8 is: 20/28 = 0.71.
Then, students of Grade 7 are more likely to be members of the science club.
How can i find the value for R
Answer:
R = 134
Step-by-step explanation:
This is a 5 sided figure. The interior angles add to (n – 2)180 where n is the number of sides
(5-2) * 180 = 540
Add up all the angles and set it equal to 540
R+ 78+109+113+106 = 540
Combine like terms
R + 406 = 540
Subtract 406 from each side
R +406-406 = 540-406
R = 134
The library is located 1.8 miles west of Callie’s house. The grocery store is located 2.4 miles south of the library. What is the length of a straight line between Callie’s house and the grocery store? Enter your answer in the box.
Check the picture below.
By using a right triangle rectangle, we will see that the distance is equal to 3 miles.
How to find the distance?You can think of the distance as the hypotenuse of a right triangle with legs that measure 1.8 miles and 2.4 miles.
Then, using the Pythagorean theorem we can write:
H^2 = (1.8 mi)^2 + (2.4 mi)^2
H = √((1.8 mi)^2 + (2.4 mi)^2) = 3mi
So the distance between Callie's house and the grocery store is 3 miles.
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Solve for x. (x - 8)(x - 8) = 0
Answer: x=8
Step-by-step explanation:
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
Set the first factor equal to 0 and solve.
x−8=0
x−8=0
Which describes the correlation shown in the scatterplot?
Answer:
None
Step-by-step explanation:
For there to be a correlation it needs to either be in a line or have equal stuff on both sides
Answer:
Option c is right
Step-by-step explanation:
Given is a scatter plot with points scattered.
We have to find from the shape the correlation coefficient
The points on the scatter plot do not support a linear correlation between the two variables.
There does not seem to be a line of fit which has minimum deviations from the line.
Hence there is no correlation is the correct answer.
From the given graph, we can say that option c is right.
Solve w = t(11 + r) for t.
Answer:
t = w/(11+r)
Step-by-step explanation:
To solve for t, we need to divide anything that t is multiplied to to get it on the other side of the equal sign.
w = t(11+r)
w/(11+r) = t
Answer:
t = w/(r + 11)
Step-by-step explanation:
Solve for t:
w = t (r + 11)
w = (r + 11) t is equivalent to (r + 11) t = w:
t (r + 11) = w
Divide both sides by r + 11:
Answer: t = w/(r + 11)
What is the following sum? Assume.. (look at picture)
ANSWER
The correct answer is B
EXPLANATION
The given sum is
[tex] \sqrt{ {x}^{2} {y}^{3} } + 2 \sqrt{ {x}^{3} {y}^{4} } + xy \sqrt{y} [/tex]
We need to remove the perfect squares.
[tex]\sqrt{ {x}^{2} \times {y}^{2} \times y } + 2 \sqrt{ {x}^{2} \times ( {y}^{2})^{2} \times x } + xy \sqrt{y} [/tex]
Let us split the radical sign for the factors to get;
[tex]\sqrt{ {x}^{2}} \times \sqrt{ {y}^{2}} \times \sqrt{y} + 2 \sqrt{ {x}^{2} } \times \sqrt{( {y}^{2})^{2}} \times \sqrt{x} + xy \sqrt{y} [/tex]
This simplifies to
[tex]xy \sqrt{y} + 2x {y}^{2} \sqrt{x} + xy \sqrt{y} [/tex]
Group similar terms to get:
[tex]xy\sqrt{y} + xy \sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]
Combine the similar terms to get:
[tex]2xy\sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]
The correct answer is B.
The sum of 26 and twice a number is 312. Find the number.
Answer:
Step-by-step explanation: 26+2c=312
Now we solve for c.
Subtract 26 on both sides giving 2c=286
So c=143
This is the equation in numbers translated (n is a number)
26 + 2n = 312
We have to find what the number (n) is. This means we must isolate n. To do this you must subtract 26 to both sides
26 - 26 + 2n = 312 - 26
0 + 2n = 286
2n = 286
To further isolate n you must divide 2 to both sides
2n/2 =286/2
n = 143
Check:
26 + 143*2 = 312
26 + 286 = 312
312 = 312
The number is 143
Hope this helped!
~Just a girl in love with Shawn Mendes
Can someone please help??
Answer:
24 + 32p = 8(3 + 4p)Step-by-step explanation:
24 = 8 · 3
32p = 8 · 4p
24 + 32p = 8 · 3 + 8 · 4p = 8 · (3 + 4p)
Find the surface area of this cube. Be sure to include the correct unit in your answer.
8 yd
8 yd
8 yd
The following dot plots shows the number of strokes golf players required at each hole .Each dot represents a different player.Order the holes from least to greatest typical number of strokes per player .
Answer:
Hole 6,7,5 is the order
Step-by-step explanation:
Final answer:
To order the holes from least to greatest typical number of strokes per player based on the dot plots, count the number of dots for each hole and arrange the holes in increasing order.
Explanation:
To order the holes from least to greatest typical number of strokes per player, we need to look at the dot plots and determine the number of players represented by each dot. We can then count the number of dots for each hole and arrange the holes in increasing order based on the number of players. The hole with the least number of strokes per player would have the fewest dots, while the hole with the greatest number of strokes per player would have the most dots.
Let's say the dot plots show the following:
Hole 1: 2 dotsHole 2: 4 dotsHole 3: 3 dotsHole 4: 1 dotHole 5: 5 dotsBased on the number of dots per hole, the order from least to greatest typical number of strokes per player would be:
Hole 4Hole 1Hole 3Hole 2Hole 5Solve for x in the equation 2x2 -5x+ 1 = 3.
Answer:
[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]
Step-by-step explanation:
[tex]2x^2-5x+1=3[/tex]
To solve for x, we make right hand side 0
Subtract 3 from both sides
Given equation becomes
[tex]2x^2-5x-2=0[/tex]
We apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=2, b=-5, c=-2
[tex]x=\frac{5+-\sqrt{5^2-4(2)(-2)}}{2(2)}[/tex]
[tex]x=\frac{5+-\sqrt{41}}{4}[/tex]
[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]
Help me please! BRAINLIEST
Answer:
1. 53 by 58 , 222 ft
2. 321000
3.1080
4. 3.5
Step-by-step explanation:
1. 23+15+15 = 53
28+15+15= 58
53+53+58+58= 222