Answer:
log₄ 10 = log₁₀ 10 / log₁₀ 4
Step-by-step explanation:
Taking the x to be a power then;
[tex]4^x +2 =12[/tex]
[tex]4^x = 12-2[/tex]
[tex]4^x=10[/tex]
Introduce log on both sides
x log 4= log 10
x= log 10/log 4
log₄ 10 = log₁₀ 10 / log₁₀ 4
Answer: x = log₄(3/4) = -0.207
Step-by-step explanation:
when you have the equation:
n^x = b
whe have that:
Logₙ(b) = x
in this case we have the equation:
4^(x+2) = 12
(4^x)*(4^2) = 12
16*4^x = 12
4^x = 12/16 = 3/4
x = log₄(3/4) = -0.207
three of the 15 people in the Latin club are chosen at random to wear togas to school to promote the club. What is the probability that Joseph, Heldi, and Katy are chosen
The probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that three of the 15 people in the Latin club are chosen at random to wear togas to school to promote the club. Therefore, the number of ways 3 people can be chosen out of 15 is,
Number of ways to choose 3 people = ¹⁵C₃ = 455
Now, the number of ways Joseph, Heidi, and Katy can be chosen in only one way. Therefore, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is,
Probability = 1 /455 = 0.002197
Hence, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.
Learn more about Probability:
https://brainly.com/question/795909
#SPJ2
What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0? units
Answer:
2
Step-by-step explanation:
Center: (−4,3)
Radius: 2
Answer:
radius = 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
Given
x² + y² + 8x - 6y + 21 = 0
Use the method of completing the square to obtain standard form
Collect the x- terms and y- terms together and subtract 21 from both sides
x² + 8x + y² - 6y = - 21
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(4)x + 16 + y² + 2(- 3)y + 9 = - 21 + 16 + 9
(x + 4)² + (y - 3)² = 4 ← in standard form
with centre (- 4, 3) and radius = [tex]\sqrt{4}[/tex] = 2
Given: AB= 4
AD= 6
Which points are in the exterior of both circles?
E and G
H and F
H and G
Answer:
A
Step-by-step explanation:
The answer would be E and G. Points E and G are both OUTSIDE both circles
Hope this helped!
~Just a girl in love with Shawn Mendes
Find the decimal equivalent of 6/9
Answer:
0.66666666666666666 ( goes on forever )
Step-by-step explanation:
This simplifies to 2/3, which is known to be 0.666666666666 and so on.
Answer:
0.66666667
Step-by-step explanation:
The numbers just keep going on and on and on, but the 7 in the number stops it.
The model represents x2 – 9x + 14. Which is a factor of x2 – 9x + 14?
Answer:
(x-2)(x-7)
Step-by-step explanation:
x2 – 9x + 14 = x² - 2x - 7x + 14
= x(x-2) - 7(x-2)
= (x-2)(x-7)
Answer:
Factor of x² – 9x + 14 is:
(x-2)(x-7)
Step-by-step explanation:
We have to find the factors of:
x² – 9x + 14
On splitting the middle term, we get
x² -7x -2x +14
which could also be written as:
x(x-7)-2(x-7)
which is equivalent to:
(x-2)(x-7)
Hence, Factor of x² – 9x + 14 is:
(x-2)(x-7)
Find the length of each side of the polygon for the given perimeter
Answer:
choice number 2) 10 in, 18.5 in 31.5 in
Step-by-step explanation:
we collect and evaluate the like terms.like terms means the ones that can be evaluated. like 2y and 7y are like terms. they either can be added or subtracted to get an answer . 7y-2y =5y. but you cant subtrac or add 7y with 5 because they are not like terms.
2y +1 + 7y + 3y + 5 = 60
(2y+7y+3y)+(1+5) = 60
12y + 6 = 60
The 6 crosses the equal sign to the other side because of like terms.And becomes a minus
12y = 60 - 6
12y = 54
y = 4.5
so,
2y +1= 2 x 4.5 + 1 =10
7y = 7 x 4.5 = 31.5
3y + 5= 3 x 4.5 + 5 =18.5
Answer is 10 in, 18.5 in, 31.5 in
If you need any clarification or more explanation pls do mention at the comment section so that i can help more thx
Hope this helps and if it does pls mark as branliest answer thx
If n2 = 1/16, then n could be which of the following?
-8
-1/4
1/4
[tex]n^2=\dfrac{1}{16}\\\\n=-\dfrac{1}{4} \vee n=\dfrac{1}{4}[/tex]
In your last 14 basketball games, you attempted 65 free throws and made 47. Find the experimental probability that you make a free throw. Write the probability as a percent, to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
% = (sucesses / attempts) * 100
% = (47/65) * 100
% = 0.723 * 100
% = 72.3 %
Answer: 72.3%
Step-by-step explanation:
Given statements : The number of basketball games = 14
The number of free throws attempted = 65
The number of made = 47
Now, the experimental probability that you make a free throw is given by :-
[tex]\dfrac{\text{47}}{65}=0.72307\approx0.723[/tex]
In percent , [tex]0.723\times100=72.3\%[/tex]
Hence, the experimental probability that you make a free throw =72.3%
The triangles to the right are congruent. Which of the following statements must be true
Answer:
It is the last one, bc=df
The true statement is one that derives from the condition that ΔABC and
ΔDEF are congruent.
Response:
The statement that must be true is; ∠A ≅ ∠DHow can the true statement be found?Given that the tringles are congruent, we have;
The length of the corresponding sides are equal
Similarly, the measure of the corresponding are equal
The side [tex]\mathbf{\overline{AC}}[/tex] ≅ Side [tex]\overline{DE}[/tex]
Side [tex]\mathbf{\overline{AB}}[/tex] ≅ Side [tex]\overline{EF}[/tex]
Which gives;
∠A ≅ ∠D
Given that ΔABC ≅ ΔDEF, we have;
Side [tex]\mathbf{\overline{BC}}[/tex] ≅ Side [tex]\overline{DF}[/tex]
Which gives;
∠C ≅ ∠F
Therefore;
∠B ≅ ∠D
The correct option is therefore; ∠A ≅ ∠DLearn more about congruent triangles here:
https://brainly.com/question/23309852
Rewrite this radicand as two factors, one of which is a perfect square. √60
Answer:
√4 * √15.
Step-by-step explanation:
√60
=√(4 * 15)
= √4 * √15
Answer:
our answer is [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form
as [tex]2*\sqrt{15}[/tex]
Step-by-step explanation:
[tex]\sqrt{60}[/tex]
We need to solve the above expression
Factors of 60:
1X60, 2X30, 3X20, 4X15, 5X12, 6X10
We need two factors one of which is perfect square
From the above factors only 4X15 full fills our condition as 4 is a perfect square
[tex]\sqrt{60}\\ =\sqrt{4 * 15}\\ We\,\,know\,\, \sqrt{a*b}= \sqrt{a}*\sqrt{b}\\ =\sqrt{4}*\sqrt{15}\\[/tex]
Solving, we get
[tex]2*\sqrt{15}[/tex]
So, our answer is [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form
as [tex]2*\sqrt{15}[/tex]
Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?
Answer:
20000*(0.85)^x
Step-by-step explanation:
Answer:
The function f(x) representing the value of car after x years is given by
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
Step-by-step explanation:
Since value of car depreciates by 15% each year
Value of car after 1 year
[tex]f(1)=value of new car \times(1-\frac{15}{100})[/tex]
=>[tex]f(1)=\$ 20,000\times(1-\frac{15}{100})[/tex]
Value of car after 2 year
[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})^{2}[/tex]
Value of car after 3 year
[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})^{3}[/tex]
Similarly value of car after x years is
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
Which is a correct first step in solving 5- 2x < 8x - 3?
Answer:
Isolating the x.
Step-by-step explanation:
The first step to solving this problem is to isolate the variable, x.
To do so, subtract 8x and 5 from both sides.
Step #1)
5 - 2x < 8x - 3
5 (-5) - 2x (-8x) < 8x (-8x) - 3 (-5)
-2x - 8x < -3 - 5
-10x < -8
~
Answer:
x>4/5
Step-by-step explanation:
Subtract by 5 from both sides of equation.
5-2x-5<8x-3-5
Simplify.
-2x<8x-8
Subtract by 8x from both sides of equation.
-2x-8x<8x-8-8x
Simplify.
-10x<-8
Multiply by -1 from both sides of equation.
(-10x)(-1)>(-8)(-1)
Simplify.
10x>8
Divide by 10 from both sides of equation.
10x/10>8/10
Simplify, to find the answer.
8/10=4/5
x>4/5 is the correct answer.
I hope this helps you, and have a wonderful day!
Choose the Domain & Range of the Relation shown in the graph:
Domain: -1, 0, 1, 2, 3
Range: -3, -1, 0, 3
Domain: -3, -1, 0, 3
Range: -3, -1, 0, 3
Domain: -3, -1, 0, 3
Range: -1, 0, 1, 2, 3
Domain: 3, 1, 0, 3
Range: -1, 0, 1, 2, 3
Answer:
C) Domain: -3, -1, 0, 3
Range: -1, 0, 1, 2, 3
Step-by-step explanation:
Domain is using x values
Range is using y values
Will mark Brainlist
Which variable expression represents the following word phrase?
four times the sum of five and a number
4.5+n
4n + 5
4(5 + n)
n. 5+4
Answer:
The correct option is C) 4(5 + n).
Step-by-step explanation:
Consider the provided phrase.
Four times the sum of five and a number
Let the number is n and the sum of five and a number can be written as:
[tex]n+5[/tex]
Thus, four times the sum of five and a number can be written as:
[tex]4(n+5)[/tex]
Hence, the required expression is [tex]4(n+5)[/tex]
Therefore, the correct option is C) 4(5 + n).
Find the cube root of x^54.
hope this helps. goodluck
(Do not use spaces. Use to represent exponents. Example 2^3 is 22.)
Answer: y=6^x-3
It is a exponent form of graph, so first:
y=a^x-b
When b=0, the asymptote is y=0 but as the asymptote given is y=-3, b=-3
Second:
the y value increases 6, when x changes 0 to 1, so a=6
A flock of 200 birds were flying south for the winter. Every day, the amount of birds in the flock increased by an average of 4%.
The amount of birds in the flock, b, can be represented by an exponential function, where d represents the number of days since the 200 birds started. What is the equation of this exponential function?
b = 1.04 · 200d
Answer:
[tex]b=200(1.04)^{d}[/tex]
Step-by-step explanation:
we know that
The exponential function is of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
In this problem we have
a=200 birds
b=100%+4%=104%=104/100=1.04
substitute
[tex]y=200(1.04)^{x}[/tex]
Let change of variables
[tex]b=200(1.04)^{d}[/tex]
where
b is the amount of birds in the flock
d is the number of days since the 200 birds started
if f(x)= 3x+6 which of the following is the inverse of f(x)
Answer:
f(x)^-1 = 1/3x - 2
Step-by-step explanation:
Replace f(x) with y and solve:
y = 3x + 6
Swap x and y
x = 3y + 6
Now isolate y
x/3 = 3y/3 + 6/3
1/3 x = y + 2
1/3 x - 2 = y + 2 - 2
y = 1/3x - 2 or f(x)^-1 = 1/3x - 2
For this case we have the following function:
[tex]f (x) = 3x + 6[/tex]
We must find the inverse of the function, then:
Replace f (x) with y:[tex]y = 3x + 6[/tex]
We exchange the variables:
[tex]x = 3y + 6[/tex]
We solve for "y":
Subtracting 6 on both sides of the equation:
[tex]x-6 = 3y[/tex]
Dividing between 3 on both sides of the equation:
[tex]y = \frac {x} {3} - \frac {6} {3}\\y = \frac {x} {3} -2[/tex]
We change y by [tex]f ^ {- 1} (x)[/tex], and finally we have:
[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]
ANswer:
[tex]f ^ {- 1} (x) = \frac {x} {3} -2[/tex]
Please answer the question from the picture above:)
Answer:
It's the red figure. This is because it is rotated 180 degrees.
Step-by-step explanation:
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
help Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
[tex]\bf f(x)=\stackrel{\stackrel{m}{\downarrow }}{4} x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \begin{array}{ccll} x&g(x)\\ \cline{1-2} 2&5\\4&7\\6&9 \end{array}~\hfill \begin{array}{llll} (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-5}{6-2}\implies \cfrac{4}{4}\implies \stackrel{\stackrel{m}{\downarrow }}{1} \end{array}[/tex]
well, clearly 4 > 1.
Answer:
f(x) has a greater slope.
Step-by-step explanation:
The slope of a function in the form of y=Mx+C is represented by the letter M, so the slope in the function F(x) =4.
Now when you have a function but you only have a table to evaluate it, to calculate the slope you have the next formula:
[tex]m=\frac{y^{2}- y^{1}}{x^{2} -x^{1} }[/tex]
You just have to pick two points from the table to use in the formula, we´ll use (4,7) as our point 1 and
(6,9) as our point 2.
This means that:
[tex]x^{1}=4[/tex] [tex]y^{1}=7[/tex]
[tex]x^{2}=6[/tex] [tex]y^{2}=9[/tex]
Now you just put it into the formula:
[tex]m=\frac{9-7}{6-4}[/tex]
[tex]m=\frac{2}{2}[/tex]
[tex]m=1[/tex]
Now that you have both slopes, you can see that the slope of g(x)=1 and the slope of f(x)=4, and you can see that f(x) has a greater slope thatn g(x).
Find the circumference of the circle. Round your answer to two decimal places, if necessary.
what two values of x are roots of this equation x^2+2x-5=0
Answer:
x = 1 + √6
x = 1 - √6
The two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]
From the question,
We are to determine the values of x that are roots to the quadratic equation x² +2x -5=0
Using the quadratic formula
[tex]x= \frac{-b \pm \sqrt{b^{2} -4ac} }{2a}[/tex]
From the given equation x² +2x -5=0
[tex]a = 1, \ b = 2, \ and \ c=-5[/tex]
Putting the values into the equation, we get
[tex]x= \frac{-(2) \pm \sqrt{(2)^{2} -4(1)(-5)} }{2(1)}[/tex]
This becomes
[tex]x= \frac{-2 \pm \sqrt{4 --20} }{2}[/tex]
[tex]x= \frac{-2 \pm \sqrt{4+20} }{2}[/tex]
[tex]x= \frac{-2 \pm \sqrt{24} }{2}[/tex]
Then,
[tex]x= \frac{-2 \pm 2\sqrt{6} }{2}[/tex]
∴ [tex]x= -1 \pm \sqrt{6}[/tex]
[tex]x= -1 + \sqrt{6} \ OR \ x= -1 - \sqrt{6}[/tex]
Hence, the two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]
Learn more here: https://brainly.com/question/17256836
A square sign has an area of approximately 158 feet .What is the approximate length of one side of the sign?
Answer:
12.5698 (approximately 12.5, rounding to the nearest half)
Step-by-step explanation:
The area of a square is represented by the following equation:
[tex]A=a^2[/tex]
Whereas "a" represents the length of any one of the sides.
Since all sides of a square are equal in length, we can reverse engineer this formula to find the length of one side.
[tex]158=a^2[/tex]
Simply take the square root of both sides and you will have your answer.
[tex]12.5698=a[/tex]
To determine the length of one side of a square sign with an area of 158 feet, calculate the square root of the area which is approximately 12.57 feet.
A square sign has an area of approximately 158 feet. To find the length of one side of the sign, you need to calculate the square root of the area:
Side length = √(Area)
Side length = √(158) = 12.57 feet
solve the system of linear equations separate the x- and y- values with a comma. -13x = -54 - 20y and -10x= 60 + 20y
[tex]\bf \begin{cases} -13x=-54-20y\\ -10x=60+20y \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{-13x=-54-20y}\implies -13x+20y=-54\implies \boxed{20y}=13x-54 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 2nd equation}}{-10x=60+\left( \boxed{13x-54} \right)}\implies -10x=6+13x\implies -10x-6=13x[/tex]
[tex]\bf -6=23x\implies \blacktriangleright -\cfrac{6}{23}=x \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{-13\left( -\cfrac{6}{23} \right)=-54-20y}\implies \cfrac{78}{23}=-54-20y[/tex]
[tex]\bf \stackrel{\textit{multipying both sides by }\stackrel{LCD}{23}}{23\left( \cfrac{78}{23} \right)=23(-54-20y)}\implies 78=-1242-460y\implies 1320=-460y \\\\\\ \cfrac{1320}{-460}=y\implies \blacktriangleright -\cfrac{66}{23}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( -\frac{6}{23}~,~-\frac{66}{23} \right)~\hfill[/tex]
If the sum of n terms of a G.P series is 225, the common ratio is 2 and the last term
(nth term) is 128.
Answer:
Step-by-step explanation:
what is the finance charge?
Answer:
n = 8.
Step-by-step explanation:
I am assuming that the sum is 255.
The last term is 128 and the common ratio is 2 so we can work backwards until we reach a sum of 255.
Term n = 128 so the previous term must be 128/2 = 64.
So following this pattern we have:
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
So we see that n = 8.
find missing term w+9/6=12
Answer: The missing term for W is 10.5.
Step-by-step explanation:
W + 9/6 = 12
W +9/6 - 9/6 = 12- 9/6
W = 12 - 1.5
W = 10.5
Write a formula to help Jaheed determine the
number of cartons of juice he needs to
buy to make the punch.
Let's let
n = number of cartons of juice
m = number of liters in each carton
Enter the correct answer.
Answer:
n=m(x)
Step-by-step explanation:
n is the dependent variable m is the independent variable.
how many cartons, depends on how many liters are in a carton.
how many he needs to buy= the amount in carton× how ever much is in his recipe
for example
if they're are let's say 1.5 liters per carton than m=1.5. and if he needs 15 liters than n= 15
than the equation is
[tex]15 = 1.5 \times x[/tex]
x is how many cartons he needs to buy
solve for x by dividing both sides of the equation by 1.5
[tex]15 \div 1.5 = x[/tex]
and x=10 in this scenario
how to find a slope of a line on a graph
Answer:
change of y/ change of x
Step-by-step explanation:
The equation has no solution.
A. 13y + 2 - 2y = 10y + 3 - y
B. 9(3y +7) - 2 = 3(-9y + 9)
C. 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
D. 5(2.2y + 3.4) = 5(y - 2) + 6y
Option D which simplifies to 11y +17 = 11y -10 has no solution since the left and right sides of the equations aren't equal after simplifying.
Explanation:We are tasked with determining which equation has no solution among the given options: A) 13y + 2 - 2y = 10y + 3 - y, B) 9(3y +7) - 2 = 3(-9y + 9), C) 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1 and D) 5(2.2y + 3.4) = 5(y - 2) + 6y. The equation without a solution will be the one in which the variables cancel out and the remaining numbers are not equal.
Solving the equations, starting with A, by combining like terms, we have 11y + 2 = 9y + 3, this eventually gives us y = 0.5. Option B, simplifying gives us 27y + 63 = -27y + 27, therefore y = -1.33. For C, we simplify to 34.5y + 3.1 = 34.5y - 5.1. Because both sides of the equation have equal coefficients for y, this results in 34.5y = 34.5y, which holds true for any value of y. Hence, the equation has infinitely many solutions. Option D simplifies to 11y +17 = 11y -10. Here, we see that 11y = 11y is true, however, the constants are not equal (i.e. 17 does not equal -10). Thus, option D is the equation with no solution.
Learn more about No Solution Equation here:https://brainly.com/question/14603452
#SPJ3
for each figure, find the missing side lengths. leave your answer as radicals in simplest form.
Answer:
4
Step-by-step explanation:
I'm not sure what question you are asking about but the one you had answer is incorrect.
You are given the long side which is 2sqrt(3).
Compare this to xsqrt(3) and hopefully you see x is 2 and is the short side.
The hypotenuse is twice the short side measurement so 2(2)=4.
Answer: 4
Answer:
Step-by-step explanation:
48
This is a 30-60-90 triangle, and we are given the [tex]x[/tex] value for the triangle, which makes it easier.
The hypotenuse for a 30-60-90 triangle will always be [tex]2x[/tex], while the adjacent side for a 30-60-90 triangle will always be [tex]x*\sqrt{3}[/tex].
So the hypotenuse is 14, and the adjacent side is [tex]7*\sqrt{3}[/tex]/
49
This is also a 30-60-90 triangle, and we can use the rules explained above.
The x value is [tex]5*\sqrt{3}[/tex] so the hypotenuse is [tex]10*\sqrt{3}[/tex] and the adjacent side is 15.
51
This is also a 30-60-90 triangle, and the root three value is [tex]2*\sqrt{3}[/tex], making the x value 2 and the hypotenuse 4.
52
This is a 45-45-90 triangle, and the same side value is [tex]4*\sqrt{2}[/tex].
This means that the adjacent side is also [tex]4*\sqrt{2}[/tex] and the hypotenuse is 8.