[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\begin{cases} g(x)=8x^6\\\\ f(x)=\log_4(2x) \end{cases}\qquad \qquad \begin{array}{llll} f(~~g(x)~~)=\log_4[~2g(x)~] \\\\\\ f(~~g(x)~~)=\log_4[~2(8x^6)~] \end{array} \\\\\\ f(~~g(x)~~)=\log_4(16x^6)\implies f(~~g(x)~~)=\log_4(4^2x^6) \\\\\\ f(~~g(x)~~)=\log_4(4^2)~~ + ~~\log_4(x^6)\implies \boxed{f(~~g(x)~~)=2~~ + ~~6\log_4(x)}[/tex]
I really need help with this question
Answer:
36
Step-by-step explanation:
[tex]2(2x - 5) = 2 x+ {2}^{3} \\ 4x - 10 = 2 x + {2}^{3} \\ 4x = 2x + 8 + 10 \\ 4x = 2x + 18 \\ 4x - 2x = 18 \\ 2x = 18 \\ x = \frac{18}{2} \\ x = 9 \\ \\ 4x = 4 \times 9 = 36[/tex]
Please help! Problem is below!
Answer:
1
Step-by-step explanation:
remember that [tex]|a| = a[/tex]if a is positive or zero, and [tex]|a| = -a[/tex]if a is negative.
[tex]4-| |14|-11| = 4-|14-11| = 4-|3| = 4-3 = 1[/tex]
Select the correct answer.
In the figure, a pair of parallel lines is cut by a transversal. What kind of angle are angles A and C?
A.
corresponding angles
B.
alternate interior angles
C.
vertical angles
D.
supplementary angles
If you add 1.25 to the difference of 8.55 and 2.12, what will be the result?
Answer:
7.68
Step-by-step explanation:
8.55-2.12 is 6.43.
6.43+1.25 is 7.68
{3x + y = 5
{5x + 2y = 9
Solve using a matrix
Solution of the system of equation 3x + y = 5 , 5x + 2y = 9 using matrix is x =1 and y =2.
As given in the question,
System of equation:
3x + y = 5 ,
5x + 2y = 9
In matrix form :
[tex]\left[\begin{array}{ccc}3&1\\5&2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}5\\9\end{array}\right][/tex]
[tex]D = \left[\begin{array}{ccc}3&1\\5&2\end{array}\right][/tex]
= (3)(2) -(5)(1)
=1
[tex]D_{x} = \left[\begin{array}{ccc}5&1\\9&2\end{array}\right][/tex]
= 10 -9
= 1
[tex]D_{y} = \left[\begin{array}{ccc}3&5\\5&9\end{array}\right][/tex]
= 27 -25
= 2
[tex]x= \frac{D_{x}}{D}[/tex]
= 1
[tex]y =\frac{D_{y}}{D}[/tex]
=2
Therefore, solution of the system of equation 3x + y = 5 , 5x + 2y = 9 using matrix is x =1 and y =2.
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What is the value of f
I will give you 40 point plus Brainliest!!!
You have opened a jar of 250 toothpicks, and want to see how many pyramid levels you can make.
Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium.
Answer:
could you take a screen shot and link the graph pls?
Step-by-step explanation:
PLEASE ANSWER ASAP WILL GIVE BRAINLIEST 368 hamburgers and cheeseburgers were sold. 3x more cheeseburgers were sold than hamburgers. How many of each were sold?
Answer:
368 Hamburgers
1,104 Cheeseburgers
Step-by-step explanation:
solve the equation
-3(2x - 1)= 4x - 7
Answer:
X = 1
Step-by-step explanation:
Subtract 3 from both sides:
-6x+3-3=4x-7-3
Simplify the equation above:
-6x=4x-10
Subtract 4x from both sides:
-6x-4x=4x-10-4x
Simplify the equation above:
-10x=-10
Divide both sides by 10:
-10x/10=-10/10
Two sides of an isosceles triangle measures 20 in and 10 in. What is a possible value of the third side
please help me, include an explanation if possible!
Answer:
(10, 18)
Step-by-step explanation:
y=2x-1
*x value*
AC=2AB
2c=2(2)(5)
2c=4(5)
2c=20
c=10
*y value*
AC=2AB
3c=2(3)(9)
3c=6(9)
3c=54
c=18
HELPPP FOR BRUANLEST!!!
Answer:
2/15
Step-by-step explanation:
slow heart rate and blue eyes (2) over total (15)
2/15 doesn't simplify
Answer:
13/100 is my final answer
Step-by-step explanation:
First, in order to get blue eyes, you need to be part of 40% thats not much but not little either. Then in order to get A fast heart rate out of that, you need to be part of the 26% out of 40% and that leaves you with 13 to 14 %.
I say 13 to 14 because both the 13 and 26 % came from a decimal that went on forever but due to rounding it can be 27 gets fast heart rate with 13 percent gets slow heart rate and blue eyes or 14 gets it and 26 gets faster
Hope this helped.
A brainliest is always appreciated.
Jaden says that two triangles are congruent if their interior angles are congruent. Is Jaden correct, and why?
Yes. Congruent triangles have congruent interior angles.
Yes. If the angles of two triangles are congruent, then the triangles are similar.
No. Congruent triangles should also have corresponding congruent side lengths.
Answer:
No
Step-by-step explanation:
No. Congruent triangles should also have corresponding congruent side lengths.
Jaden is incorrect. two triangles are not congruent if their interior angles are congruent.
The correct option is C.
What are congruent triangles?Two triangles are said to be congruent if the three sides and the three angles of both the triangles are equal in any orientation.
Given, statement
two triangles are congruent if their interior angles are congruent.
Even when two triangles have all angles same,
they can still have sides of different lengths.
However, the ratio of lengths of corresponding sides will be same.
But in this case, they will be called 'similar' triangles, not congruent.
For example, in the image below, both triangles are equilateral and have all angles equal but they are not congruent.
Hence, two triangles with congruent angles are not congruent, Jaden is incorrect.
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A startled armadillo jumps straight into the air with an initial vertical velocity of 14ft / s . After how many seconds does it land on the ground? Use the equation - 16t ^ 2 + Vt + h . Round your answer to the nearest hundredth. The armadillo lands back on the ground after seconds.
Using the given equation, it is found that it lands on the ground after 0.875 seconds.
What is the equation for the projectile's height?It is given by:
[tex]h(t) = -16t^2 + vt + h[/tex]
In which:
v is the initial velocity.h is the initial height.In this problem, considering that the projectile jumps straight into the air with an initial vertical velocity of 14 ft/s, the parameters are v = 14 and h = 0, hence:
[tex]h(t) = -16t^2 + 14t[/tex]
It lands on the ground when h(t) = 0, hence:
[tex]-16t^2 + 14t = 0[/tex]
[tex]t(-16t + 14) = 0[/tex]
Then:
[tex]16t = 14[/tex]
[tex]t = \frac{14}{16}[/tex]
[tex]t = 0.875[/tex]
It lands on the ground after 0.875 seconds.
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iPad: $499 Sale: 30% off What is the new cost of the iPad?
Answer:
$349.3
Step-by-step explanation:
Discount = Original Price*Discount %/100
Discount = 499*30/100
Discount = 499*0.3
You save = $149.70
Final Price = Original Price - Discount
Final Price = 499 - 149.7
Final Price = $349.30
what is the range of 0,1,2,3,4,5,6,9
Answer: it is 9
Step-by-step explanation: if you mean calculating range as in the highest and lowest number then yes. If you mean geometric or arithmetic calculation of range then it would just be the numbers you stated.
Answer:
The median 3.5 the mean is 3.5 and the min is 0 max is 9
Step-by-step explanation:
to find the median cross out the nubers on the end if theres two ansewrs in the middle then do whatever number .5
In an n-sided polygon, two angles are right angles and each of the remaining angles is 150°. Find the value of n.
Answer: 8
Step-by-step explanation:
find the value of x trigonometry
Step-by-step explanation:
sin30° = x/14
1/2 = x/14
1/2 × 14 = x
x = 7
cos30° = y/14
squareroot3/2 = y/14
0.866 = y/14
y = 0.866 × 14
y = 12.124
Rewrite the following equation in slope-intercept form.
3x − 11y = 19
Answer:
y = 3/11(x) - 19/11
Step-by-step explanation:
Step 1: Subtract 3x from both sides.
[tex]3x-11y-3x=19-3x[/tex] [tex]-11y=-3x+19[/tex]Step 2: Divide both sides by -11.
[tex]-11y/-11=(-3x+19)/-11[/tex] [tex]y=\frac{3}{11}x-\frac{19}{11}[/tex]Therefore, the answer is y = 3/11(x) - 19/11.
(select all that apply)
1. Calculation errors when distributing 9h
2. Calculation errors when combining h^2 terms
3. Calculation errors when distributing -1
4. Calculation errors when distributing h^2
5. Calculation errors when combining h terms
The simplification of the expression (h² + 9·h - 1) × (-4·h + 3), involves the
multiplication of the terms. The error is therefore;
3. Calculating errors when distributing -1
How can the error in the calculation be found?The expansion of (h² + 9·h - 1) × (-4·h + 3), is given as follows;
(h² + 9·h - 1) × (-4·h + 3) = -4·h³ + 3·h² - 36·h² + 27·h + 4·h - 3
Which gives;
-4·h³ - 33·h² + 31·h - 3
The calculation is therefore;
[tex]\begin{array}{|c|c|c|c|}&h^2&+9 \cdot h & -1\\-4 \cdot h&-4\cdot h^3&-36\cdot h^2 &4 \cdot h\\+3& 3 \cdot h^2&27 \cdot h&3\end{array}\right][/tex]
The error is therefore, in the distribution of the -1
The correct option is;
3. Calculating errors when distributing -1
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A rectangular park has a perimeter of 374 feet and a length of 65 feet. What is the width of the park?
Answer:
122
Step-by-step explanation:
Use the formula P=2(l+W)
the length would be 65ft and the perimeter would be 374
M is the midpoint of QR. N is the midpoint of PR. Work out PM and QN in terms of a and b
Answer:
triangle in the middle but it cant explain with it
Step-by-step explanation:
In a particular country, the coins come in the denominations 1, 15 and 50 schillings. Whilst visiting this country, Peter bought a book for his wife, Rachel, paying with several (more than 2) coins. He paid with the minimum number of coins needed to make that amount.
His change contained one more coin than the handful of coins with which he paid, but again it was the minimum number of coins needed to make that amount.
What are the eight lowest possible prices for the book?
What is the lowest price of the book where the coins Peter pays with is a sensible set of coins to have handed over?
Answer:
Step-by-step explanation:
Depending on the tools available to your 11y.o., it's a typical question for linear inequalities.
Where a,b,c are the # of 1,15,50 coins given by the buyer, and d,e,f the # of coins given back by the seller.
1×a + 15×b + 50×c > 1×d + 15×e + 50×f
a+b+c+1>=d+e+f
a+b+c >=2
Now, there are other clues in the text :
If the seller gives back money, then you didn't pay with 1's, otherwise, it means you overpay and you could have given fewer coins. So a=0.
Similarly, the seller cannot give you back a coin of 50, otherwise, you could have given fewer coins as the buyer. So f=0.
So that gives :
15×b + 50×c > 1×d + 15×e
b+c+1>=d+e
b+c >=2
From that point on, there is only a handful of scenarios to test.
find the midpoint between the two points (-11,-14) and (-40,22)
Answer:
Mid = ( -51 / 2 ), 4
Step-by-step explanation:
Mid = ( x1 + x2, y1 + y2 )
/ /
2 2
Mid = ( -11 + (-40)), (-14 + 22 )
/ /
2 2
Mid = ( -51 ), ( 8 )
/ /
2 2
Mid = ( -51 / 2 ), ( 4 )
I hope this helps!
Solve the equation for y.
8x – 9y = 11
A. y = −9/8x − 9/11
B. y = −8x − 11
C. y = 8/9x − 11/9
D. y = 9/8x + 11/8
Step-by-step explanation:
8x - 9y = 11
8x = 9y + 11
8x - 11 = 9y
y = 8x/9 - 11/9
so, C is correct
Please help me. Picture below
Answer:
1. Median is 79 (in)
(78+80/2 => gives halfway point)
2. 7 (in)
(IQR is UQ - LQ => that is 82 - 75)
3. LQ is 75 (in)
4. Maximum height is 84 (in)
(the largest value or the tallest you could be)
I've included units - pretend they don't exist.
Hope this helps!
Which graph represents the equation y= -1/2x -3 ?
The graph that represents the equation y = -1/2x -3 is B
What is a graph?A graph is a series of points, discrete or continuous, forming a curve or a straight line, each of which represents a value of a given function.
Graphs could be positive, or negative.
When the increase in y results to an increase, in x then the graph is said to be positive graph while and increase in y leads to a decrease in x is called negative graph.
From the equation, y = -x/2 -3
If x = 0, then the y-intercept is -3 which is below the x -axis.
Also, if x = 2, y will be -4, if x = 4, y = -5
These shows that as x increases y- decrease, making it a negative graph which slopes from left to right passing through the y-axis at x = -3 which is graph B
In conclusion the graph that represents the given equation is B
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2x-4=x+1 giải phương trình
PLEASE EXPLAIN HOW TO DO THIS
Answer:
B) 243 km^3
Step-by-step explanation:
The formula for volume is Length x width x height, so we must find those values. By looking at the shape, the length is 9 km, width is 9 km, and height is 3 km, and after substituting these values in the equation, we get 9 km x 9 km x 3 km. When multiplied, it equals to 243 km^3, so the answer for the volume of the solid is B) 243 km^3.
Hope this helped somewhat! :P