Answer:
x = -1Step-by-step explanation:
[tex]4(4^x-2^x)+1=0\\\\4\bigg((2^2)^x-2^x\bigg)+1=0\qquad\text{use}\ (a^n)^m=a^{nm}\\\\4(2^{2x}-2^x)+1=0\\\\4\bigg((2^x)^2-2^x\bigg)+1=0\qquad\text{substitute}\ 2^x=t>0\\\\4(t^2-t)+1=0\qquad\text{use the distributive property}\\\\4t^2-4t+1=0\\\\4t^2-2t-2t+1=0\\\\2t(2t-1)-1(2t-1)=0\\\\(2t-1)(2t-1)=0\\\\(2t-1)^2=0\iff2t-1=0\qquad\text{add 1 to both sides}\\\\2t=1\qquad\text{divide both sides by 2}\\\\t=\dfrac{1}{2}[/tex]
[tex]\text{We're going back to substitution}\\\\t=\dfrac{1}{2}\Rightarrow2^x=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\2^x=2^{-1}\iff x=-1[/tex]
Find the distance between the points given. (0, 6) and (5, 12) √145 √61 √11
Answer:
√61
Step-by-step explanation:
Distance between 2 points (x1, y1) and (x2,y2) is given by
Distance = √ [ (x2-x1)² + (y2-y1)² ]
in our case, x1 = 0, y1 = 6, x2 = 5, y2 = 12
Distance
= √ [ (5-0)² + (12-6)² ]
= √ [ (5)² + (6)² ]
= √ 61
Answer:
√61
Step-by-step explanation:
The distance between two points is given by
d = sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt( (5-0)^2 + (12-6)^2)
=sqrt( 5^2 + 6^2)
= sqrt(25+36)
= sqrt(61)
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.
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
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]
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
7,125,000,000. What is this to the nearest billion?
Answer:
7 billion
Step-by-step explanation:
Rounding decreqases when number is under 5 and if its above (Ex, 7,685,000,000) it is rounded to 8 billion. But here, it is under 5 so it is 7 billion.
Answer:
7,000,000,000
Step-by-step explanation:
Note the Billions place value. 7 is in the billions place value. To find out if you round up or down, look at the place value directly to the right of the one you are trying to find, in this case, being the hundred million place value. The value inside the hundred million place value is a 1.
Note that the number has to be 5 or greater to round up, or else you round down. Because 1 < 5, you round down.
7,125,000,000 rounded to the nearest billion is 7,000,000,000.
~
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°
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
PLEASE HELP, ATTACHED IS THE PROBLEM
hypotenuse = 8
unknown leg = b
known leg = 4
Pythagorean theorem:
[tex]c=\sqrt{{a}^{2}+{b}^{2}}[/tex]
The answer is
[tex]8=\sqrt{{b}^{2}+{4}^{2}} [/tex]
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
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:
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.
~
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]
Which of the following is a monomial?
Answer:
[tex]20x^{11}[/tex]
Step-by-step explanation:
An expression in algebra that contains one term is called a monomial.
These include numbers, whole numbers and variables that are multiplied together.
Any number, a whole number without variables can also be monomial, like 32, 5236 etc.
So, here the monomial is [tex]20x^{11}[/tex].
Option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
As we know in the monomial there will be only one term.
Option (C) and Option (D) contains two terms so they are not monomial.
Option (B) contain fractional term.
Thus, option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.
Learn more about Polynomial here:
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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.
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:
A transformation T : (x,y) (x-5,y +3) the image of A(2,-1) is
[tex]A'=(2-5,-1+3)=(-3,2)[/tex]
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]
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.
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.
The table shows values for functions f(x) and g(2)
What is the solution to f(x) = g(x)?
Select each correct answer.
X= -2
X= -1
X= 0
X= 1
X= 2
Answer:
The solutions are x=0, x=1
Step-by-step explanation:
we know that
The solution of the equation f(x)=g(x)
are the values of x when the value of f(x) is equal to the value of g(x)
Observing the table
For x=0
f(0)=1 and g(0)=1
so
For x=0 ------> f(x)=g(x)
For x=1
f(1)=1/2 and g(1)=1/2
so
For x=1 ------> f(x)=g(x)
therefore
The solutions are x=0, x=1
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.
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
if 1/64=4^2s-1 * 16^2s+2 what is the value of s?
a) -1
b)0
c)1
D) no solution
Answer:
its A :(
Step-by-step explanation:
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 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.
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
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 ..
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:
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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.