The simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]
In the given question, it is given
We know the simplification property of the division of numbers as,
Division in exponential form
[tex]\frac{a^{x} }{a^{y} }[/tex] = [tex]a^{x-y}[/tex] , and
Multiplication in exponential form
[tex]a^{x} . a^{y}[/tex] = [tex]a^{x+y}[/tex]
Similarly, we'll apply the same property to solve this question,
[tex]4^{5+3+2+3 + ( -2 -1 -2)}[/tex]
[tex]4^{5+3+2+3 - ( 2 + 1 + 2)}[/tex]
[tex]4^{13 - 5}[/tex]
[tex]4^{8}[/tex]
Hence, the simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]
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Can you please explain? I have the other options also.
Given
[tex]f(x)=\frac{1}{3}\lvert x+4\rvert-4[/tex]The graph
Inverse & Composition of Functions
1. Find the inverse of f(x) = x² + 2
Answer: √x−2,−√x−2
Step-by-step explanation:
URGENT!!!!!!!!!
Thank you to whoever solves it right!
Answer:
D
Step-by-step explanation:
The plane was at 24,000+ feet above the ground and then it ROSE (indicating an addition of feet to the original) 7,00+ feet.
Hope that helps
Please see image attached on using the diagram to name the ray
Given:
Find - Name of rays
Sol:
Ray:- In geometry, a ray can be defined as a part of a line that has a fixed starting point but no endpoint can extend infinitely in one direction. On its way to infinity, a ray may pass through more than one point.
So rays is
[tex]=\vec{AE}[/tex]13. The model represents an equation. 1 1 1 1 À AC X DOOD D0000 solue.) What value of x makes the equation true? 15.
Answer:
The equation is true when x = 2.25
Explanation:
On the left side of the equation, there are 3 triangles with value -x and 10 triangles with value 1. So, the expression for the left side of the equation is:
3*(-x) + 10*(1)
-3x + 10
For the right side, we have 5 triangles with value x and 8 triangles with value -1. So, the expression for the right side is:
5*x + 8*(-1)
5x - 8
Now, we can write the equation as:
-3x + 10 = 5x - 8
So, solving for x, we get:
-3x + 10 + 3x = 5x - 8 + 3x
10 = 8x - 8
10 + 8 = 8x - 8 + 8
18 = 8x
18/8 = x
2.25 = x
Therefore, the equation is true when x is equal to 2.25
What is the completely simplified form of the expression 2(1 - 3x) - (5x + 1)?
A) -11x + 1
B) -8x + 1
C) -11x + 3
D) -8x + 3
Answer:
A
Step-by-step explanation:
2(1-3x)-(5x+1)
=2-6x-5x-1
=1-6x-5x
=1-11x/-11x+1
Hello! I need some assistance with this homework question, pleaseQ16
we have the function
[tex]y=\sqrt[]{x}[/tex]shifted down 10 units, is the same that apply the rule
(x,y) -----> (x,y-10)
therefore
the new function is
[tex]y=\sqrt[]{x}-10[/tex]The answer is the first option
A cylinder with a radius of 1 yd and a height of 2 yd
Find the value of x in the diagram. ΔPQR ~ ΔSTU
Elsa is saving money to buy a game. So far she saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
Elsa is saving money to buy a game.
So far she saved $24, which is two-thirds of the total cost of the game.
let the cost of the game is $x
Then, two -third of the total cost = 2/3 x
Since, it is given that 24 is the two-thirds of the total cost of the game.
i.e.
[tex]\frac{2}{3}x=24[/tex]Simplify the expression for x;
[tex]\begin{gathered} \frac{2}{3}x=24 \\ \text{ Apply cross multiplication;} \\ 2x=24\times3 \\ x=\frac{24\times3}{2} \\ x=12\times3 \\ x=36 \end{gathered}[/tex]x = 36
Total cost of the game is $36
....
The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgeted for sales and research combined is 75,000,000. What is the total annual budget?
$150,000
1) In that pie chart, we can tell that the Sales and Research department combined responds to 50% (35%+15% =50%)
2) Thus, we can tell that:
[tex]\begin{gathered} 0.35x+0.15x=75000 \\ 0.5x=75000 \\ x=\frac{75000}{0.5} \\ x=150,000 \end{gathered}[/tex]So, since 50% of that budget corresponds to $75,000 we can tell that 100% (the total budget) corresponds to twice that figure, which yields 150,000
4. What is the value of x such that 5x + 2a > 2x-a?
a. x < -a
b. x > -a
C. x < a
d. x > a
Answer:
D: x > a
Step-by-step explanation:
We have 5x - 2a > 2x-a
We can rewrite this equation by subtracting 2x on both sides, which gives:
5x - 2x -2a > 2x - 2x - a,
so 3x - 2a > a
We now add 2a on both sides, which gives:
3x -2a + 2a > a + 2a, so 3x > 3a
We nog divide both sides by 3, which gives:
3x/3 > 3a/3, so x>a
The correct answer is D
A rectangular room is 4 meters longer than it is wide, and its perimeter is 24 meters. Find the dimension of the room.The length is : meters and the width is meters.
We are given the following information
Perimeter of the rectangular room = 24 meters
The rectangular room is 4 meters longer than it is wide.
Let L be the length and W be the width of the rectangular room.
[tex]L=4+W[/tex]The perimeter of a rectangular shape is given by
[tex]P=2(L+W)[/tex]Substitute P = 24 and L = 4 + W into the above equation
[tex]\begin{gathered} P=2(L+W) \\ 24=2(4+W+W) \\ 24=2(4+2W) \\ 24=8+4W \\ 24-8=4W \\ 16=4W \\ \frac{16}{4}=W \\ W=4\;m \end{gathered}[/tex]So, the width of the rectangular room is 4 meters.
[tex]\begin{gathered} L=4+W \\ L=4+4 \\ L=8\;m \end{gathered}[/tex]So, the length of the rectangular room is 8 meters.
Length = 8 meters
Width = 4 meters
Example Problem:
Suppose that perimeter is 1055 meters.
The length is 45 meters longer than the width of the rectangle.
[tex]L=45+W[/tex]Now, substitute P = 1055 and L = 45 + W into the equation for the perimeter of the rectangle.
[tex]\begin{gathered} P=2(L+W) \\ 1055=2(45+W+W) \\ 1055=2(45+2W) \\ 1055=90+4W \\ 1055-90=4W \\ 965=4W \\ W=\frac{965}{4} \\ W=241.25\;m \end{gathered}[/tex]So, the width of the rectangle is 241.25 meters.
[tex]\begin{gathered} L=45+W \\ L=45+241.25 \\ L=286.25\;m \end{gathered}[/tex]So, the length of the rectangle is 286.25 meters
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:Let r be the number of rides and g be the number of games.
2.50g + 4.00r = 52.50
r = 2g
Step-by-step explanation:
Answer:
lol no
Step-by-step explanation:
Martin eats 3/8 of a pizza. Felix eats 2/5of a pizza of
same size. Who eats more pizza? How much more pizza
does he eat?
If 3 dogs eat 4 pounds of food per day, how many dogs eat 15 pounds of food?
11 dogs will eat 15 pounds of food.
According to the question,
We have the following information:
3 dogs eat 4 pounds.
We have to find how many dogs will eat 15 pounds.
We have the following expression:
4 pounds = 3 dogs
We can treat dog as a non-living object or a product.
So, we can find the parts devoted to 1 pound:
1 pound = 3/4
Now, we have to find the same for 15 pounds:
15 pounds = (3/4)*15
15 pounds = 11.25
Now, note that the number of dogs can not be in points. So, we will round it off to form a whole number.
So, 15 pounds = 11 dogs
Hence, 15 pounds of food is enough for 11 dogs.
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following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed
Points which would fall on the line produced by the point-slope form equation y - 3=1/2(x - 7) when graphed are as follow:
c. (1,0)
d. (3, 1)
As given,
Equation of given line
y - 3=1/2(x - 7)
Points which would fall on the line produced by the point-slope form:
a.(0,1)
x=0
y-3=1/2(0-7)
⇒ y=-1/2
b.(1,-1)
x=1
y-3=1/2(1-7)
⇒y=0
c.(1,0)
x=1
y-3=1/2(1-7)
⇒y=0
Required point
d.(3,1)
x=3
y-3=1/2(3-7)
⇒y=1
Required point
Therefore, points which would fall on line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed are as follow:
c. (1,0)
d. (3, 1)
The complete question is :
Which of the following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed?
a. (0,1) b. ( 1,-1) c. (1,0) d. (3,1)
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Justin places a bet on the giants to win the superbowl. the odds are 2:3. a) Are the giants expected to win? why or why not?b) Find P(Giants win)=
To convert the odds to a probability, we can divide the odds by one plus the odds.
then, in this case we have the following:
[tex]\begin{gathered} \text{odds:} \\ 2\colon3=\frac{2}{3} \\ \Rightarrow1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]then, we have that the probability is:
[tex]\frac{\frac{2}{3}}{\frac{5}{3}}=\frac{2\cdot3}{5\cdot3}=\frac{2}{5}[/tex]thus, the probability that the Giants will win the superbowl is 2/5=0.4=40%
As we can see, we cannot expect for sure that the giants will win
determine the domain of each function yx-3x=3y-1
Domain of the given function yx-3x=3y-1 is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3}.
What is a domain?The dependent variable and the independent variable are the two types of variables used to define a function.
The domain of a function is a set of all possible values of x which is an independent variable. For example The domains of function f(x)=x² can be all real numbers.
Despite x=0, the domain of g(x)=1/x can contain any real number.
The input values to a function are referred to as domains, while the output values are referred to as the range. The data flow is as follows:
Domain → Function → Range
We are aware that the value of x is the function's domain. Therefore, the domain is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3} for the provided function.
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two trains travel at a constant speed. Train a travels 1400 miles in 5 hours and train b travels 2100 miles in 7 hours. Which train travels faster?
Christine gets $71 for working the weekend. She buys $53 in clothes and then
makes another $45 babysitting. How much does she have now?
Answer:
63 i think!
Step-by-step explanation:
71-53 is 18. 18+45 is 63!
Im so so so sorry if im wrong, have a nice day friend!: )
Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. Work out the probability that tina takes two blue counters in fraction.
Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. The probability that tina takes two blue counters in fraction is 15/72
What is the probability?Given parameters:
Bag A= 5 red + 3 blue
Bag B = 4 red + 5 blue
Hence,
Total counters in bag A = 5 +3 = 8
Total counters in bag B = 4 + 5 = 9
Now let determine the probability that she takes two blue counters
Probability = 3 /8 × 5 /9
Probability = 15 / 72
Therefore 15 / 72 is the probability that two blue was taken.
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The amount of vinegar that melody used for a recipe can be written as a whole number which could be the amount of vinegar that Melody used?A. -3.75 tspB. 1.5 tspC. 2 1/3 tspD. 12/3
Given:
The amount of vinegar that melody used for a recipe can be written as a whole number.
So, we will check the options to find which one represents a whole number
The whole number does not contain numbers after the decimal point and also the denominator will be 1
So, the answer is option D) 12/3 = 4
Hello! I need some help with this homework question, please? The question is posted in the image below. Q11
A one-to-one function means that there are no two elements in the domain of the function that corresponds to the same element in the range,
Mathematically since
[tex]\begin{gathered} x\text{ is the input or the domain, then} \\ f(x)\text{ is the output} \end{gathered}[/tex]A one-to-one follows that
[tex]\text{if }x_1\text{ and }x_2\text{ are two different inputs of a function }f,\text{ then }f(x_1)\neq f(x_2)[/tex]Bill owns land but has no access to water so he has to pay for well water from Jim.
Jim charges him $8 per month plus $0.80 per gallon.
During any given summer month, his water bill costs between $48 and $72.
Write and solve a compound inequality to determine how much water Bill is using.
Given that events A and B are independent with P(A)=0.85 and P(B) = 0.3,determine the value of P(A|B), rounding to the nearest thousandth, if necessary.
The Solution.
Given that
[tex]\begin{gathered} P(A)=0.85 \\ P(B)=0.3 \end{gathered}[/tex]The conditional probability P(A/B) is given as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]But for independent events, we have that
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence, it follows that
[tex]\begin{gathered} P(A|B)=\frac{P(A)\times P(B)}{P(B)}=P(A)=0.85\approx0.850 \\ \text{though the nearest thousandth is not necessary.} \end{gathered}[/tex]Therefore, the correct answer is 0.85 ( 0.850 if you consider it necessary)
all the odd numbers from 51 to 5001 are written what is the total number of digits used
Answer:
9404 digits
Step-by-step explanation:
The numbers written:
51, 53, 55, 57, 59, . . . 97, 99 [5*5=25 numbers; 50 digits]
101, 103, 105, . . . 997, 999 [9*50=450 numbers; 1350 digits]
1001, 1003, 1005, . . . 4997, 4999, 5001 [40*50+1=2001 numbers; 8004 digits]
Total:
50 + 1350 + 8004 = 9404 digits
find the ratio of the boxes and the circles there are 7 boxes and 10 circles
The ratio of boxes to the circles is 7: 10
8x – 12y = – 24 a. x-intercept: b. y-intercept: 10+ C. graph 9 8 7 6 5 4 13 2 -10 -9 -8 -7 -6 -5 -4 -B-2 -1 2 15 4 SI 6 8 9 10 -2 3 -6 -7 -8 9 10 Clear All Draw:
To determine the x- and y-intercepts is best to write the equation in slope-intercept form.
Given
[tex]8x-12y=-24[/tex]-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 8x-8x-12y=-8x-24 \\ -12y=-8x-24 \end{gathered}[/tex]-Divide both sides of the equal sign by -12
[tex]\begin{gathered} \frac{-12y}{-12}=\frac{-8x}{-12}-\frac{24}{-12} \\ y=\frac{2}{3}x+2 \end{gathered}[/tex]So the equation in slope-intercept form is:
[tex]y=\frac{2}{3}x+2[/tex]a) The x-intercept is the point where the line crosses the x-axis, at this point, the y-coordinate is equal to zero. To determine the x-coordinate of the intercept, you have to equal the equation to zero and calculate the corresponding value of x:
[tex]0=\frac{2}{3}x+2[/tex]-Subtract 2 to both sides of the equal sign
[tex]\begin{gathered} 0-2=\frac{2}{3}x+2-2 \\ -2=\frac{2}{3}x \end{gathered}[/tex]-Multiply both sides of the expression with the reciprocal fraction of 2/3
[tex]\begin{gathered} (-2)\frac{3}{2}=(\frac{2}{3}\cdot\frac{3}{2})x \\ -3=x \end{gathered}[/tex]The x-intercept is (-3,0)
b) The y-intercept is the point where the line crosses the y-axis, at this point, the x-coordinate is equal to zero. To determine the y-intercept, replace the equation with x=0 and calculate the corresponding value of y:
[tex]\begin{gathered} y=\frac{2}{3}x+2 \\ y=\frac{2}{3}\cdot0+2 \\ y=2 \end{gathered}[/tex]The y-intercept is (0,2)
c) To graph the line, plot both intercepts on the coordinate system and then link both points with a line:
45.6 divided by 0.03
Answer:
1,520
Step-by-step explanation: