Answer:
P(2)=0 then x-2 is a factor of P(x)
Step-by-step explanation:
To see if (x-2) is a factor just plug in 2 for x into the polynomial expression.
2(2)^3-3(2)^2-17(2)+30
2(8)-3(4)-34+30
16-12-34+30
4-34+30
-30+30
0
Since P(2)=0 then x-2 is a factor
Explain how to write an equation that represents this scenario
Answer:
1 ticket equals to $2.50. Since x number of tickets are sold, the total amount raised will be $2.50 multiply by x, which is 2.5x. Since y represents the total amount of money raised, 2.5x equals to y
Write an equation in standard form for the circle?
Answer:
(x - 3)² + (y - 5)² = 64Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
Look at the picture.
We have
center at (3, 5) → h = 3 anf k = 5
radius r = 8
Substitute:
[tex](x-3)^2+(y-5)^2=8^2\\\\(x-3)^2+(y-5)^2=64[/tex]
which of the following values of X is not in the domain of f(x)=x+3/x-7
The value of x that is not in the domain is x = 7.
which of the following values of X is not in the domain of f(x)?
Remember that in math we can't divide by zero, so any value that makes the denominator equal to zero can't be in the domain.
Here the rational function is:
f(x) = (x + 3)/(x - 7)
When x = 7, the denominator becomes zero, so x = 7 is not in the domain.
Help me please algebra 2 PLEASSEEEEE!!!
Answer:
29.74 degrees.
Step-by-step explanation:
Tan(theta) = opposite / adjcent.
opposite = 8
adjacent = 14
Tan(theta) = 8/14
Tan(theta) = 0.5714
theta = tan^-1(0.5714)
theta = 29.74 degrees
what is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83
Answer:
35
Step-by-step explanation:
We know that the general formula for arithmetic sequence is
a_n=a_0+(n-1)d
Using the general formula, we can make equations for 6th term and 9th term
a_6=a_0+(6-1)d
a_6=a_0+5d
101=a_0+5d Eqn 1
For 9th term
a_9=a_0+(9-1)d
a_9=a_0+8d
83=a_0+5d Eqn 2
Subtracting equation 2 from equation 1
101-83=a_0+5d-(a_0+8d)
18=a_0+5d-a_0-8d
18=-3d
d= -6
Putting d=-6 in Eqn 1, we get:
101=a_0+5(-6)
101=a_0-30
a_0=101+30
a_0=131
Now that we have values of a_0, and d we can find the 17th term
a_17=a_0+(17-1)d
=131+(16)(-6)
=131-96
=35
So the 17th term is 35 ..
Nine less than the product of 2 and number is equal to 7
Answer:
x = 8
Step-by-step explanation:
Step 1: Write an equation
2x - 9 = 7
Step 2: Use the Addition Property of Equality
2x = 16
Step 3: Use the Division Property of Equality
x = 8
Answer:
number = 8
Step-by-step explanation:
Let "number" = x. Set the equation.
"product of 2 and number" = 2(x)
"nine less" = -9
"equal to 7" = "= 7"
2x - 9 = 7
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 9 to both sides.
2x - 9 (+9) = 7 (+9)
2x = 7 (+9)
2x = 16
Divide 2 from both sides.
(2x)/2 = (16)/2
x = 16/2
x = 8
8 is your answer.
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Which shows how to find the value of this expression when X=-2 and Y = 5?
(3x3y=272
31-216
(-2)4
21954
Answer:
Option 1 is correct
Step-by-step explanation:
Given expression is:
[tex](3x^3y^{-2})^2\\[/tex]
Putting the values
[tex]= [3 (-2)^3 (5)^{-2}]^2\\We\ have\ to\ make\ the\ powers\ positive\\= [{\frac{3(-2)^3}{5^{2}} }]^2\\= \frac{[{3(-2)^3}]^2}{(5^2)^2} \\Applying\ outer\ power\\= \frac{3^2(-2)^6}{5^4} \\[/tex]
Hence option one is correct ..
The map below shows the location of 3 houses where you had to do lawn work today. Your truck gets 8 miles per gallon of gasoline, so you chose the shortest route from your house to the jobs and then back home, as shown below. If gas costs $1.52 per gallon, what was the total cost of the gas that you used today?
Answer:
$3.80
Step-by-step explanation:
We are given a graph showing the location of 3 houses where you had to do lawn work today, with the distances from your house.
Given that one truck gets 8 miles per gallon of gasoline and gas costs $1.52 per gallon, we are to find the total cost of the gas used.
Total distance = 7 + 3 + 4 + 6 = 20 miles
Gallons of gas used = 20 / 8 = 2.5
Total cost of gas used = 2.5 * 1.52 = $3.80
Two lines perpendicular to the same plane are?
• A. coinciding lines
• B. equivalent
• C. parallel lines
• D. congruent lines
us
Answer:
C. parallel lines
Explanation:
If two straight lines be at right angles to the same plane, the straight lines would be parallel.
Which country was an ally of the United States durning World War II
Answer:
United Kingdom , France, Soviet Union , and China
Step-by-step explanation:
United Kingdom , France, Soviet Union , and China was an ally of the United States durning World War II.
The composition of a function and its inverse is always __________.
Answer:
Answer:
X
The given statement is true.
Step-by-step explanation:
An inverse function can be defined as a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x.
Examples are x+2 and x-2
WE get f(x) = x+2
Apply g(x) = g(f(x))=g(x+2)
=x+2-2=x
Thus by applying composiiton g f or fg in any order we get the answer as x
THis is the property of any inverse function
Step-by-step explanation:
Answer:
X
Step-by-step explanation:
It was corrected on E2020.
Jayne is studying urban planning and finds that her town is decreasing in population by 3% each year. The population of her town is changing by a constant rate.True or False?
Rewrite the rational exponent as a radical expression. 3 to the 2 over 3 power, to the 1 over 6 power
Pleaseeeeee Helppppp ;)
Answer:
the ninth root of 3
Step-by-step explanation:
3 to the 2 over 3 power, to the 1 over 6 power rewritten as a radical expression is ''the ninth root of 3''.
Hope this helps!
Answer:
kk
Step-by-step explanation:
What is the square root of a^3 and b^4 expressed in simplified form?
Answer:
(a)(b²)√a
Step-by-step explanation:
√(a³b⁴)
Root both variables. Note that pairs of the same variables can be brought out of the root.
√(a³) = √(a * a * a) = a√a
√(b⁴) = √(b * b * b * b) = b²
(a)(b²)√a is your answer.
I know the answer I got is wrong help.
Answer:
∠2 = 18°
Step-by-step explanation:
∠WXZ = ∠1 + ∠2 ← substitute ∠1 = 3∠2
∠WXZ = 3∠2 + ∠2, that is
72 = 4∠2 ( divide both sides by 4 )
18 = ∠2, that is
∠2 = 18°
first operation to solve 2x + 3 = 11
Answer:
subtract 3 from both sides
Step-by-step explanation:
Given
2x + 3 = 11 ( subtract 3 from both sides )
2x = 8 ( divide both sides by 2 )
x = 4
Which logarithmic equation is equivalent to the exponential equation below? e^a=55
(You will receive 34 points)
Answer:
The answer is B.
e^a=55
Taking log on both sides,
lne^a = ln 55
a lne= ln55
a= ln55.
The value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).
What is Logarithm?
A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
What is the value of [tex]e^a = 55[/tex]?We solve the value of this expression using the basic logarithm,
[tex]\rm{log_ab=c[/tex]
Similarly,
[tex]\rm{log_e55=a[/tex]
we know that the log base of exponent is natural log, therefore,
[tex]\rm ln\ 55=a[/tex]
Therefore, the value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).
Learn more about Logarithm:
https://brainly.com/question/163125
What is 77543 rounded to the nearest hundred
[tex]77500[/tex]
Step-by-step explanation:In this case, the digit in the hundredths place is a [tex]5[/tex]. We need to take a look at the next digit to the right, which is a [tex]4[/tex].
Since it is [tex]4[/tex] or less, we can simply replace the [tex]4[/tex] and the rest of the digits to the right with [tex]0[/tex]s to round it.
If the [tex]4[/tex] was [tex]5[/tex] or more, we would round the [tex]5[/tex] up to [tex]6[/tex] and replace the remaining digits to the right with [tex]0[/tex]s.
Answer:
77500
Step-by-step explanation:
To round something to the nearest hundred, we first look to the 10s digit. It is 4. Since 4 is less than 5, then we keep the same hundreds place. So we get 77500.
According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 - 33x2 – 12x + 20.
Which is an actual root of f(x)?
a) -5/2
b) -2
c) 1
d) 10/3
Answer:
a) -5/2.
Step-by-step explanation:
Try substituting (-5/2) into f(x):
6(-5/2)^4 + 5(-5/2)^3 - 33(-5/2)^2 - 12(-5/2) + 20
= 234.375 + -78.125 - 206.25 + 30 + 20
= 0.
So it is -5/2.
Answer:
a) [tex]x= -5/2[/tex]
Step-by-step explanation:
We substitute in the function the values given in the options to confirm whether they are roots or not
a) [tex]x= -5/2[/tex]
the function will be:
[tex]f(-\frac{5}{2} )=6(-\frac{5}{2} )^4 + 5(-\frac{5}{2} )^3-33(-\frac{5}{2} )^2-12(-\frac{5}{2})+20[/tex]
simplifying:
[tex]f(-\frac{5}{2} )=6(\frac{625}{16} )-5(\frac{125}{8} )-33(\frac{25}{4} )+30+20[/tex]
[tex]f(-\frac{5}{2} )=234.375-78.125-206.25+50\\f(-\frac{5}{2} )=0\\\\[/tex]
since the function when [tex]x= -5/2[/tex] is equal to zero, this is an actual root of f(x).
Graph y = √x + 2 and y = 3x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation √x + 2 = 3x. Then, find the solutions using an algebraic method.
Answer:
x = 1
Step-by-step explanation:
The graph is shown below. The solution is x = 1.
___
√x +2 = 3x . . . . given
√x = 3x -2 . . . . . subtract 2
x = 9x^2 -12x +4 . . . . square both sides
9x^2 -13x +4 = 0 . . . . subtract x to put in standard form
(x -1)(9x -4) = 0 . . . . . factor the quadratic
x = 1 . . . or . . . x = 4/9 . . . . values of x that make the factors zero
The "solution" x = 4/9 is extraneous, in that it does not satisfy the equation. It would correspond to the intersection of the line with the negative branch of the square root function. That is, it does satisfy -√x +2 = 3x.
The solution is x=1.
Can someone plz give me the answer for this question?
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = [tex]e^{2x}[/tex] - 4
let f(x) = y
y = [tex]e^{2x}[/tex] - 4
Switch x and y and solve for y, that is
x = [tex]e^{2y}[/tex] - 4 ( add 4 to both sides )
x + 4 = [tex]e^{2y}[/tex]
Take the ln of both sides
ln(x + 4) = ln [tex]e^{2y}[/tex] = 2y [tex]ln_{e}[/tex] = 2y
Divide both sides by 2
y = [tex]\frac{ln(x+4)}{2}[/tex], that is
[tex]f^{-1}[/tex] (x) = [tex]\frac{ln(x+4)}{2}[/tex]
Study the products shown. Is there a pattern? (x + 3)2 = x2 + 6x + 9 (x + 4)2 = x2 + 8x + 16 (x + 5)2 = x2 + 10x + 25 (x + 6)2 = x2 + 12x + 36
Answer:
Yes,a similar formula is used to find all the products
Step-by-step explanation:
The formula applied in this case is;
(a+b)²= (a+b) (a+b)= a(a+b)+b(a+b) = a²+ab+ab+b²= a²+2ab+b²
In the first one;
[tex](x+3)^2= (x+3) (x+3) = x(x+3)+3(x+3) = x^2 +3x+3x+9 = x^2 +6x +9[/tex]
In the second one;
[tex](x+4)^2 = (x+4) (x+4) = x(x+4)+ 4(x+4) = x^2 +4x+4x+16 = x^2 +8x+16[/tex]
⇒This is the same for the third and fourth product.
Answer:
3rd option is right
Step-by-step explanation:
CAN YOU PLEASE HEP ME WITH THIS ONE THIS IS TIMED PLEASE! Amy has 35 tiles of the same shape and size in a box. The colors of and amounts of the tiles are shown below:
12 red tiles
8 yellow tiles
15 pink tiles
Without looking in the box, Amy takes out a tile at random. She then replaces the tile and takes out another tile from the box. What is the probability that Amy takes out a yellow tile in both draws?
8 over 35 multiplied by 7 over 34 equal 56 over 1190
8 over 35 multiplied by 8 over 35 equal 64 over 1225
8 over 35 plus 7 over 34 equal 517 over 1190
8 over 35 plus 8 over 35 equal 560 over 1225
Answer:
B) 8 over 35 plus 8 over 35 equal 64 over 1225
Step-by-step explanation:
There are 8 yellow tiles out of 35 tiles.
Its not A because she replaces.
Its not C or D because you would only add when it says and
Answer:
8 over 35 multiplied by 8 over 35 equal 64 over 1225
Step-by-step explanation:
I got it right on my test. Give the other person brainliest.
What is the area of the kite?
Answer:
= 135 m²
Step-by-step explanation:
First we divide the kite into 2 isosceles triangles
The bigger triangle has base angles = 45°
We can use these angle as follows to find the common base of the two triangles.
Cos 45=adjacent/9√2
Adj=9√2×cos 45
=9
common base =9×2=18
We can use the angle 45° above to find the height of the bigger triangle.
Tan 45°=opposite/adjacent
Opposite = adjacent×Tan 45
=9 tan 45=9
Area =1/2BH+1/2Bh where B is the common base H is the height of the big triangle, h represents the height of the smaller triangle.
A=1//2× 18 × 9 +1/2× 18 × 6
= 135 m²
PLEASE HELP AS FAST AS POSSIBLE PLEASE
Find the product of (-8y2 + 3) and (-4y - 3).
A) 32y3 + 24y2 - 12y - 9
B) -32y3 - 24y2 + 12y - 9
C) 12y3 - 12y - 9
D) -8y2 - 4y - 9
Answer:
A) 32y³ + 24y² - 12y - 9
Step-by-step explanation:
(-8y² + 3)(-4y - 3) = (-8y² x -4y) + (-8y² x -3) + (3 x -4y) + (3 x -3)
= 32y³ + 24y² - 12y - 9
The product of [tex]-8y^2+3[/tex] and [tex]-4y-3[/tex] is:
[tex]32y^3+24y^2-12y-9[/tex]
Step-by-step explanation:We are asked to find the product of the two expressions which are given by:
[tex]-8y^2+3[/tex] and [tex]-4y-3[/tex]
i.e.
we are asked to find the product of a quadratic and a linear polynomial.
We are asked to find the result of:
[tex](-8y^2+3)\cdot (-4y-3)[/tex]
Hence, on using the distributive property we have:
[tex]-8y^2(-4y-3)+3(-4y-3)\\\\=-8y^2\times -4y-8y^2\times (-3)+3\times (-4y)+3\times (-3)\\\\i.e.\\\\=32y^3+24y^2-12y-9[/tex]
The correct answer is: Option: A
Find the factored form of
-7y - y2 = 0
Answer:
-y(7+y) =0
Step-by-step explanation:
-7y - y^2 = 0
Factor out a -y
-y(7+y) =0
Using the zero product property
-y =0 and 7+y =0
y=0 7-7+y = 0-7
y=0 y = -7
Find the slope of the line through (3, 7) and (–1, 4)
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Slope = change in y ÷ change in x
The line passes through (3,7) and (-1,4)
Slope = [tex]\frac{7 - 4}{3 - -1}[/tex] = [tex]\frac{3}{4}[/tex]
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
According to the data we have the following points:
[tex](x_ {1}, y_ {1}): (- 1,4)\\(x_ {2}, y_ {2}) :( 3,7)[/tex]
Substituting we have:
[tex]m = \frac {7-4} {3 - (- 1)} = \frac {3} {3 + 1} = \frac {3} {4}[/tex]
Thus, the slope of the line is [tex]\frac {3} {4}[/tex]
Answer:
[tex]\frac {3} {4}[/tex]
A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the number of adults. The number of female students was half the number of male students. If the total number of people who went on the trip is 82, find the numbers of male students and female students. The number of male students is . The number of female students is .
Answer:
see below
m = males = 50
e = females = 25
a = adults = 7
Step-by-step explanation:
Givens
Let the adults = a
let the males students = m
lef the female students = e
Equations
a + m + e = 82
m = 7*a + 1
e = 1/2 * (7a + 1)
Solution
a + 7a + 1 + 1/2(7a + 1) = 82 Remove the brackets on the left.
a + 7a + 1 + 3.5*a + 1/2 = 82 Combine the like terms on the left.
11.5a + 1.5 = 82 Subtract 1.5 from both sides.
11.5a + 1.5 - 1.5 = 82 - 1.5 Combine
11.5a = 80.5 Divide by 11.5
a = 80.5/11.5
a = 7
The number of adults = 7
===============================
m = 7a + 1
m = 7*7 + 1
m = 50
===============================
e = 1/2 m
e = 1/2 * 50
e = 25
Which quadratic inequality does the graph below represent?
NEED TO KNOW BEFORE 14 MINUTES PLZ!!!!
If you look at the graph, the line crosses the y axis at (0,3).
That means you can eliminate the inequality that shows the y intercept as -3 (which is the 3rd option)
Also the inequality has to have y ≤ .... so that the correct part of the graph is shaded. This elimates all of the inequalities that has y ≥ ... ( which is the 2nd and 4th option)
This leaves you with only the first inequality left:
y ≤ 2x² - 8x + 3
-----------------------------------------------------------------------
Answer
y ≤ 2x² - 8x + 3
What is an imaginary number
Answer:
An imaginary number is a number that does not exist pretty much. It is usually written as "i", and, when squared = -1. However, you cannot root -1 to get a number, so i is the term that is given to be the answer.
Note:
i² = -1
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