Answer: [tex]\frac{2a\sqrt{c}}{3}[/tex]
Step-by-step explanation:
Remember that:
[tex]\sqrt[n]{a^n}=a[/tex][tex]\sqrt{ab}=(\sqrt{a})(\sqrt{b})[/tex][tex](\sqrt{a})^2=a[/tex]The product of powers property establishes that: [tex](a^m)(a^n)=a^{(m+n)}[/tex]Given the expression [tex]\frac{6(\sqrt{a^3b^2c^4})}{9b\sqrt{ac^3} }[/tex]
You know that:
[tex]a^3=a^2*a\\c^3=c^2*c[/tex]
Then, you must rewrite the expression and simplify:
[tex]\frac{6\sqrt{a^2ab^2c^4}}{9b\sqrt{ac^2c} }=\frac{6abc^2\sqrt{a}}{9bc\sqrt{ac}}=\frac{2ac\sqrt{a}}{3(\sqrt{a})(\sqrt{c})}=\frac{2ac}{3\sqrt{c}}[/tex]
Multiply the numerator and the denominator by [tex]\sqrt{c}[/tex]:
[tex]\frac{(2ac)\sqrt{c})}{(3\sqrt{c})(\sqrt{c})}=\frac{2ac\sqrt{c}}{3(\sqrt{c})^2}=\frac{2ac\sqrt{c}}{3c}=\frac{2a\sqrt{c}}{3}[/tex]
What is the domain of the square root function graphed below?
Answer: all real numbers
Step-by-step explanation: the domain for any function is always , all real numbers or in other words, negative infinity to positive infinity.
Answer:
c. x >= 0
Step-by-step explanation:
Helppp????? Answer????
Answer:
No. of sweets Sue has = (18-x) -5
No. of sweets Tony has = (18+x)/2
Step-by-step explanation:
Sue has sweets = 18
Tony has sweets = 18
Sue give Tony sweets = x
Sweets left for Sue = 18 - x
Sweets for Tony = 18 + x
Sue eats 5 sweets = (18-x) -5
Tony eat half of his sweets = (18 +x)/2
No. of sweets Sue has = (18-x) -5
No. of sweets Tony has = (18+x)/2
Find the area of a triangle which has a base of 22cm and a height of 16cm
The area of the triangle will176 because 22×16 you will 352 s you just need to divide that by two and you get 176 so you your total area for the triangle is 176 and don’t forget put as square
Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
[tex]\frac{(x+5)(x-3)}{(x+5)(x+1)}[/tex]
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
Using the continuity concept, it is found that the function with both a removable and a non-removable discontinuity is:
[tex]f(x) = \frac{(x - 1)(x - 2)}{(x - 1)(x - 3)}[/tex]
----------------------------------------------
Continuity:
A function is not continuous at points that are outside it's domain.
If the point outside the domain can be factored, it is removable.If the point outside the domain cannot be factored, it is non-removable.----------------------------------------------
An example can be taken considering a function as follows:
[tex]f(x) = \frac{(x - 1)(x - 2)}{(x - a)(x - b)}[/tex]
If a = 1, the term with [tex]x - 1[/tex] in the denominator can be factored with the term with [tex]x - 1[/tex] in the numerator, and this the function will have a removable discontinuity.Now, if for example, b = 3, the term with [tex]x - 3[/tex] cannot be factored, and thus, the function will have a non-removable discontinuity.The function is:
[tex]f(x) = \frac{(x - 1)(x - 2)}{(x - 1)(x - 3)}[/tex]
A similar example is given at https://brainly.com/question/23496517
Let f(x) = 3x2 - 6x + 2. Find f(-2).
A) 20
B) 22
C) 24
D) 26
Answer:
D) 26
Step-by-step explanation:
f(x) = 3x^2 - 6x + 2
Let x = -2
f(-2) = 3(-2)^2 - 6(-2) + 2
=3(4) +12+2
= 12 +12+2
=26
For this case we have a function of the form [tex]y = f (x).[/tex]
Where:
[tex]f (x) = 3x ^ 2-6x + 2.[/tex]
We must find the value of the function when [tex]x = -2.[/tex]
Substituting we have:
[tex]f (-2) = 3 (-2) ^ 2-6 (-2) +2\\f (-2) = 3 * 4 + 12 + 2\\f (-2) = 12 + 12 + 2\\f (-2) = 26[/tex]
Thus, the value of the function is 26.
Answer:
26
Option D
Given ax^+bx+c=2(1.2x+0.3)(x-0.5)+(0.5x^+2.5x-1.3). What are the values of a,b, and c?
For this case we must find the values a, b, c:
[tex]2 (1.2x + 0.3) (x-0.5) + (0.5x ^ 2 + 2.5x-1.3) =\\(2.4x + 0.6) (x-0.5) + (0.5x ^ 2 + 2.5x-1.3) =[/tex]
We apply distributive property:
[tex](2.4x ^ 2-1.2x + 0.6x-0.3) + (0.5x ^ 2 + 2.5x-1.3) =\\(2.4x ^ 2-0.6x-0.3) + (0.5x ^ 2 + 2.5x-1.3) =[/tex]
We finish the term:
[tex]2.9x ^ 2 + 1.9x-1.6[/tex]
Answer:[tex]a = 2.9\\b = 1.9\\c = -1.6[/tex]
50 points!
For which rational expression is -5 an excluded value of x?
A) x-5/6
B) x+5/6
C) 6/x-5
D) 6/x+5
Answer:
D
Step-by-step explanation:
An excluded value is any value of x that makes the denominator of the rational expression zero as this would make the expression undefined.
Consider expression D
[tex]\frac{6}{x+5}[/tex]
This will be undefined when
x + 5 = 0 ⇒ x = - 5 ← excluded value → D
Answer:
D) 6/x+5
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
In this example, we will use D
x + 5 = 0 ⇒ x = - 5 ( Excluded value )
How can we define appropriate quantities for the purpose of descriptive modeling?
Answer:
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays
Step-by-step explanation:
You've assigned your math class a set of word problems. One of the questions ends with, "How many people voted for candidate Jones?" Fingers fly over calculators as your students try to determine the correct answer. After a minute or two, Tommy raises his hand and announces his answer: 4,602.28
Everything inside of you wants to scream, "Are you out of your mind, Tommy boy? A closer answer would be 4 because at least it would be possible! How on earth could a candidate receive 28 hundredths of a vote?"
Okay, breathe. Poor Tommy has made the kind of error that drives math teachers like you to the brink of insanity. He's given an answer that makes absolutely no sense.
Whatever else math is or isn't, it is always logical. Answers should always make sense. Math frequently relies on general knowledge—concepts that we assume are known by everyone over the age of about seven—along with a healthy dose of common sense (not you, Thomas Paine).
The problem, of course, is that people have a tendency to ignore both common sense and the knowledge that they possess. Particularly when calculators are involved, there's the tendency to run with the answer you're given. That ignores one very basic principle: the calculator answers the question you ask, not the one you intended to ask.
This was just an example of Descriptive Modeling
Thank you for asking this question
please choose me as brainiest Answer to support me
We can define appropriate quantities for the purpose of descriptive modeling on the basis of evaluation,analyse,understanding and selecting appropriate measurement units to solve problems.
Defining appropriate quantities for the purpose of descriptive modeling
Suppose we are analysing a data of two sports academy for training of players.
[tex]$$\begin{table}[]\begin{tabular}{llll}Academy & Coaches & Players & Equipment \\Academy A & 4 & 50& 70\%\\Academy B & 3 & 45& 80\% \end{tabular}\end{table}$$[/tex]
If we calculate performance of two academy on the basis of no. Of players per coach then Academy B is best.
If we calculate Academy performance by calculating percentage of equipment per player then Academy A is best.
Here we are evaluating the performance of two sports academy by understanding the problem and analysing the given data by using the appropriate units.
So from the above data we can say that evaluation,analyse,understanding and selection of appropriate measurement units is important for appropriate quantities for the purpose of descriptive modeling.
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Two angles are supplementary (add up to 180 degrees). The measure of one angle is ten more than the other. Find the measure of each angle.
Answer:
85° and 95°
Step-by-step explanation:
So, one angle is x, the other angle is x + 10. Using this, you can form an equation.
x + x + 10 = 180
Now, solve the equation.
2x + 10 = 180
2x = 170
x = 85
So, one angle is 85 while the other angle is 95.
85 + 95 = 180,
so we know that our answer is correct.
Answer:
85,95
Step-by-step explanation:
find the surface area of the rectangular prism
4x2x3
Answer:
52
Step-by-step explanation:
Answer:
64 in²
Step-by-step explanation:
Please, include the units of measurement:
"rectangular prism 4 in by 2 in by 3 in."
One side is 4 by 2 in², or 8 in²; another is 4 by 3 in², or 12 in², and the third side is 3 by 4 in², or 12 in². We have 2 of each side, so the total surface area is
A = 2(8 in² + 12 in² + 12 in²) = 2(32 in²), or 64 in²
If f(x) =x/2+8, what is f(x) when x=10 ?
A) 4
B)9
C)13
D)36
I did the math and got the answer c -13
The answer would be option C, 13
Math 3: First question on the attached file
Step-by-step explanation:
cos 330°=cos ( 360 -30)
In fourth quad the value of cos A is positive .
All angles when subtracted by multiple of 180° or (π) the function remain same
cos (30°)=√3/2
Also-
Cos(330)=Cos(360–30)
since Cos(360-x)=cos(x) where x is in degree
Cos(330)=Cos(30)= √ 3 /2 ~ 0.866
Answer:
Answer:
cos ( 330 º ) = √ 3 /2
Explanation:
Remember that
cos ( a − b ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b )
and that
330 º = 360 º − 30 º , so
cos ( 330 º ) = cos ( 360 º − 30 º ) = cos ( 360 º ) cos ( 30 º ) + sin ( 360 º ) sin ( 30 º )
The cosine, sine, tangent and secant of 360º equal the cosine, sine, tangent and secant of 0º respectively. We know that
sin 0 º is 0, and that cos 0 º = 1 so
cos ( 330 º ) = 1 ⋅ cos ( 30 º ) + 0 ⋅ sin ( 30 º )
cos ( 330 º ) = √ 3 /2
Hope This Helps! Have A Nice Day!!
The answer is A right?
Answer:
C. 42
Step-by-step explanation:
PEMDAS
1. Parentheses: (4 + 2) = 6
6² + 3 • 2
2. Exponents: 6² = 36
36 + 3 • 2
3. Multiplication/Division: 3 • 2 = 6
36 + 6
4. Addition/Subtraction: 36 + 6 = 42
42
A. A frog is climbing out of a well that is 8 feet deep. The frog can climb 4 feet per
hour but then it rests for an hour, during which it slips back 2 feet. How long will
it take for the frog to get out of the well?
B. What if the well was 40 feet deep, the frog climbs 6 feet per hour, and it slips back
1 foot while resting?
Answer:
A: 5 hrs. B: 14 hrs. and 40 min.
Step-by-step explanation:
too long to explain.
In the first scenario, the frog takes 4 hours to get out of the 8-feet deep well. In the second scenario, it takes the frog 8 hours to get out of the 40-feet deep well.
Explanation:The question is about calculated frog’s movement to get out of a well involving both climbing rate and slip-back rate during rest which brings us into the realm of simple arithmetic and mental math. Let's take each case one at a time.
A. 8 Feet Deep Well
The frog climbs 4 feet per hour but then slips back 2 feet. Therefore, effectively, the frog climbs only 2 feet per hour (4-2=2). After 3 hours, the frog would have climbed 6 feet (3*2=6). In the fourth hour, the frog would climb another 4 feet reaching a total of 10 feet, but since the well is only 8 feet deep, he would have already climbed out. Therefore, it would take the frog 4 hours to climb out of the well.
B. 40 Feet Deep Well
The frog climbs 6 feet per hour and slips back 1 foot, therefore effectively climbs 5 feet per hour (6-1=5). After 7 hours, the frog would have climbed 35 feet (7*5=35). In the eighth hour, the frog would climb additional 6 feet, reaching a total of 41 feet. Again, considering the well is only 40 feet deep, he would have climbed out at this point. So, it would take 8 hours for the frog to climb out of a 40 feet deep well.
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Which point on the number line below represents a number that is less than -2.5 but greater than -7.5?
Point R
Point S
Point T
Point V
HELP ASAP
Answer:
S
Step-by-step explanation:
Answer:
S is the answer
Step-by-step explanation:
The figure shows a blueprint of a dining room, kitchen, and living room. Each square has a side length of 1/4 inch. Tile costs $7 per square foot. What is the cost of the tile for the kitchen?
The cost of the tile for the kitchen is $___
Answer:
The cost of the tile for the kitchen is $1,680
Step-by-step explanation:
step 1
we know that
The scale drawing is [tex]\frac{1}{16}\frac{in}{ft}[/tex]
The dimensions of the kitchen in the blueprint are
L=3(1/4)=3/4 in
W=5(1/4)=5/4 in
step 2
Find the actual dimensions of the kitchen
Divide the dimensions of the kitchen in the blueprint by the scale drawing
L=(3/4)/(1/16)=12 ft
W=(5/4)/(1/16)=20 ft
The area is equal to
A=(12)(20)=240 ft²
step 3
Find the cost of the tile for the kitchen
7(240)=$1,680
Answer:
Cost of the tiles for the kitchen is $1680
Step-by-step explanation:
From the figure attached,
Dimensions of the kitchen = 5 small squares by 3 small squares
Since 1 small square = [tex]\frac{1}{4}[/tex] inch
So the dimensions of the kitchen in inches = [tex]\frac{5}{4}[/tex] inches by [tex]\frac{3}{4}[/tex] inches
Map Scale has been given as
1 inch = 16 ft
Therefore actual dimensions of the kitchen will be
[tex]\frac{5}{4}\times 16[/tex] ft by [tex]\frac{3}{4}\times 16[/tex] ft
= 20 ft by 12 ft
Area of the kitchen = 20×12
= 240 ft²
Per square feet tile cost = $7
So the cost of tiling 240 ft² will be = 240 × 7
= $1680
Therefore, cost of the tiles for the kitchen is $1680
What is the area of this figure ?
The area of the figure which is composed of a rectangle and a square is 76 km²
What is the area of the composite figure?The figure in the image is composed of a rectangle and a square.
The area of a rectangle = length × width
The area of a square = length²
To determine the area of the figure, we add the area of the rectangle and the area of the square.
Area of the figure = ( length × width ) + ( length² )
Plug in the given dimensions:
Area of the figure = ( 9 km × 8km ) + ( 2 km )²
Simplifying; we get:
Area of the figure = 72 km² + 4 km²
Area of the figure = 76 km²
Therefore, the area of the composite figure measures 76 km².
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passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to ?
A.
5x − 3y = 0
B.
-x + 3y = 0
C.
-5x − 3y = 0
D.
3x + 5y = 0
E.
-3x + 5y = 0
ANSWER
[tex]- 5x - 3y = 0[/tex]
EXPLANATION
The line that passes through the origin has equation of the form:
y=mx
Where m is the slope.
Since the line is parallel to the line through A(-3, 0) and B(-6, 5), they have the same slope.
The slope is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{5 - 0}{ - 6 - - 3} = - \frac{5}{3} [/tex]
Hence the required equation is:
[tex]y = - \frac{5}{3} x[/tex]
Multiply through by 3,
[tex]3y = - 5x[/tex]
In standard form, the equation is
[tex] - 5x - 3y = 0[/tex]
Answer:
The answer is C. -5x - 3y = 0
The side of a square measures 3mn2? What is the area of the square if x = -2 and y = 2?
Answer:
ur cute
Step-by-step explanation:
Which is a counterexample for the conditional statement shown?
If two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function.
The points have the same x-coordinate value.
The points have the same y-coordinate value.
The points follow the rule (x, y) (–x, –y).
The points follow the rule (x, y) (–y, –x).
Answer: First Option
The points have the same x-coordinate value.
Step-by-step explanation:
By definition, a relation is considered a function if and only if for each input value x there exists only one output value y.
So, the only way that the line that connects two points in the coordinate plane is not a function, is that these two points have the same coordinate for x.
For example, suppose you have the points (2, 5) and (2, 8) and draw a line that connects these two points.
The line will be parallel to the y axis.
Note that the value of x is the same x = 2. But when x = 2 then y = 5 and y = 8.
There are two output values (y = 8, y = 5) for the same input value x = 2.
In fact all the vertical lines parallel to the y-axis have infinite output values "y" for a single input value x. Therefore, they can not be defined as a function.
Then the correct option is:
The points have the same x-coordinate value.
What is the benefit of using expressions in math?
Answer:
To help you understand the problem with out actually doing the work, you are just writing it out.
Step-by-step explanation:
Answer:
The benefits of using expressions in math is to know what you are supposed to be using to solve your problem. Expression area good use too also for word problems!!
Step-by-step explanation:
Plz mark Brainlist!!!
The grass in jamie's yard grew 16 centimeters in 10 days.It was growing at a constant rate. How many days did it take the the grass to grow 1 centimeter?,How many centimeter did the grass grow in 1 day?
Answer:
1.6 cm
0.625 day
Step-by-step explanation:
We are given that the grass in Jamie's yard grew 16 cm in 10 days.
It was growing at constant rate.
We have to find number of days taken by the grass to grow 1 cm and how many cm grass grow in one day.
In 10 days , grass grow=16 cm
In 1 day, grass grow=[tex]\frac{16}{10}=1.6 cm[/tex]
Grass takes time to grow 16 cm=10 days
Grass takes time to grow 1 cm=[tex]\frac{10}{16}[/tex]=0.625 days
Hence, the grass grow 1 cm in 0.625 days and the grass grow 1.6 cm in one day.
To find the number of days it took for the grass to grow 1 centimeter, divide the number of days by cm of growth. This equals 0.625 days. To find how many centimeters the grass grew in a day, divide the total growth by the total number of days. This equals 1.6 centimeters per day.
Explanation:The problem states that the grass in Jamie's yard grew 16 centimeters in 10 days at a constant rate. We can set up two equal ratios to find out how many days it took for the grass to grow 1 centimeter and how many centimeters it grew in 1 day.
Firstly, to determine the number of days it took for the grass to grow 1 centimeter, you can divide the number of days (10) by the number of centimeters (16). This gives us 10/16 = 0.625 days for the grass to grow 1 centimeter. Secondly, to determine how many centimeters the grass grew in 1 day, you would divide the total growth (16 centimeters) by the total number of days (10). This results in 16/10 = 1.6 centimeters of growth per day. Learn more about Ratio and Proportion here:
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Find m< ABC (4x+2) (7x-19)
Answer:
<ABC = 30°
Step-by-step explanation:
Vertical angles are equal
So
4x+2 = 7x - 19
-7x + 4x = -19 - 2
-3x = -21
x = 7
<ABC = 4(7) + 2 = 28 + 2 = 30
<ABC = 30°
The table shows the results of a survey on the preferred flavor of ice cream. Based on this survey, what is the probability that an adult prefers chocolate ice cream? A) 55 52 B) 55 54 C) 55 107 D) 55 119
Answer:
C)
55
107
Step-by-step explanation
i took the usa test prep
Using it's concept, it is found that the probability that an adult prefers chocolate ice cream is given by:
D. 55/119.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there is a total of 55 + 54 + 10 = 119 adults, and of those, 55 prefer chocolte ice cream, hence the probability is given by:
p = 55/119.
Thus option D is correct.
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What is 3 2/3 + 5 11/24?!
[tex]\text{Hey there!}[/tex]
[tex]\text{What is 3}\frac{2}{3}\ + 5\frac{11}{24}[/tex]
[tex]\text{3}\frac{2}{3}\rightarrow 3\times3=9\rightarrow9+2=11\rightarrow\ \rightarrow\frac{11}{3}[/tex]
[tex]5\frac{11}{24}\rightarrow5\times24=120\rightarrow120+11=131\rightarrow\ \rightarrow\frac{131}{24}[/tex]
[tex]\text{Your problem becomes:}\frac{11}{3}+\frac{131}{24}[/tex]
[tex]\text{Solve that}\uparrow\text{and your should come up to}\rightarrow[/tex] [tex]\frac{73}{8}\ or\ 9\frac{1}{8}[/tex]
[tex]\boxed{\boxed{\bf{Answer:\frac{73}{8}\ or \ 9\frac{1}{8}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Help me.. ASAP just number 10 pls
use the bar graph to find the experimental probability of the event
10 ~ Spinning A 3
I hope this helps!~ I tried
Honestly I feel like it is 10.
what is the surface area of this square pyramid
Answer:
33 ft²Step-by-step explanation:
We have
the square with side s = 3ft
four triangles with base b = 3ft and height h = 4ft
The formula of an area of a square:
[tex]A=s^2[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_{\square}=3^2=9\ ft^2[/tex]
[tex]A_{\triangle}=\dfrac{(3)(4)}{2}=\dfrac{12}{2}=6\ ft^2[/tex]
The Surface Area:
[tex]S.A.=A_{\square}+4A_{\triangle}\\\\S.A.=9+(4)(6)=9+24=33\ ft^2[/tex]
Answer:
33 ft&²
Step-by-step explanation:
multiply 4x3x3 = 36 and put half of 6, then it is 33 33ft²
In a 2-card hand, what is the probability of holding 2 kings?
A pack of cards has 52 cards, 4 of which are kings, so the probability of the first card being a king is (4/52). Since you have already chosen a card, there are only 51 cards left to choose from in the entire deck (the first card is not counted anymore because it has already been pulled from the deck), and since the card you chose was a king, you are left with only 3 more kings, meaning that the probability of the second card being a king is (3/51). Since we are interested in both happening simultaneously, we must multiply the probability of the first by the probability of the second: (4/52) • (3/51), which leaves us with: * 12/2,652 or 0.0045249 *
To find the probability of holding 2 kings in a 2-card hand, you need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, there are 6 favorable outcomes out of 1,326 possible outcomes, resulting in a probability of approximately 0.0045 or 0.45%.
Explanation:To find the probability of holding 2 kings in a 2-card hand, we first need to determine the total number of possible 2-card hands that can be dealt from a standard 52-card deck. The number of combinations of choosing 2 cards from 52 is given by the formula C(52, 2) = 52! / (2! * (52-2)!) = 1,326.
Next, we need to determine the number of favorable outcomes, which is the number of ways to choose 2 kings from the 4 kings in the deck. This can be calculated as C(4, 2) = 4! / (2! * (4-2)!) = 6.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: P(2 kings) = 6/1,326 ≈ 0.0045 or 0.45%.
Rolling probability of 2
The answer is 25%
If you roll 20 times in total and you land on two 5 times 5/20 = .25
Hope this helps!
Which set of ordered pairs is a function?
Answer:
The second set is a function as none of the x values repeat.
Step-by-step explanation:
In order for a set of ordered pairs to be a function, they must only have one range value for each domain value.
In other words, an x value cannot occur twice.
Within the first set, the value x=2 is repeated 5 times. This means that it is not a function
Within the third set, the value x=1 is repeated twice and x=4 is repeated twice, This means that it is not a function
Within the fourth set, the value x=1 is repeated twice and x=2 is repeated twice, this means that this is not a function
The second set is a function as none of the x values repeat.
Answer:
the second one is a function
Step-by-step explanation: