Answer: [tex]12x^3-25x^2+9[/tex]
Step-by-step explanation:
Given expression: [tex](4x-3)(3x^2-4x-3)[/tex]
To simplify the above expression we apply the distributive property [ (b+c)a=ba+ca, where a,b, c be any expression] we get ,
[tex](4x-3)(3x^2-4x-3)\\\\=4x(3x^2-4x-3)-3(3x^2-4x-3)\\\\=12x^{1+2}-16x^{1+1}-12x-9x^2+12x+9.......\text{[by law of exponents]}\\\\=12x^{3}-16x^{2}-12x-9x^2+12x+9\\\\\text{Combing like terms, we get}\\\\=12x^3-(16+9)x^2-12x+12x+9\\\\=12x^3-25x^2+9[/tex]
Answer:
[tex]12x^{3}-25x^{2}+9[/tex]
Step-by-step explanation:
1. Write down the equation:
[tex](4x-3)(3x^{2}-4x-3)[/tex]
2. Multiply the first term on the left parenthesis by each term on the right parenthesis:
[tex]4x*3x^{2}=12x^{3}[/tex]
[tex]4x*(-4x)=-16x^{2}[/tex]
[tex]4x*(-3)=-12x[/tex]
3. Multiply the second term on the left parenthesis by each term on the right parenthesis:
[tex]-3*(3x^{2})=-9x^{2}[/tex]
[tex]-3*(-4x)=12x[/tex]
[tex]-3*(-3)=9[/tex]
4. Add up all the terms:
[tex]12x^{3}-16x^{2}-12x-9x^{2}+12x+9[/tex]
Simplify:
[tex]12x^{3}-25x^{2}+9[/tex]
What is 666 divided by 22?
Answer:
30.27272727272727 and repeating.
Step-by-step explanation:
James is no longer able to feel the same effect from his drug of choice with his regular dose; he needs to increase the amount of the drug to feel the desired effect this demonstrates this demonstrates
a.withdrawal
b. tolerance
c. adjustment
d. intolerance
Find the area of a parallelogram with sides of 12 inches and 8 inches if one of the angles is 120
degrees
Answer:
48√3 sq. in.
Step-by-step explanation:
I know this is correct bc I just had this question and this was the correct answer
{4x+3y=6
{2x -5y=16
Which of the following points is the solution to the system?
What is 3 6/10 simplified?
a girl has a coloring book with 60 pages in it. she uses 5 pages every 3 days. How many days will it take her to finish the coloring book?
In the diagram, P1P2 and Q1Q2are the perpendicular bisectors of AB¯¯¯¯¯ and BC¯¯¯¯¯, respectively. A1A2 and B1B2 are the angle bisectors of ∠A and ∠B, respectively. What is the center of the circumscribed circle of ΔABC?
a. p
b. q
c. r
d. s
Five cards are randomly selected without replacement from a standard deck of 52 playing cards. what is the probability of getting 5 hearts? round your answer to four decimal places
The probability of getting 5 hearts from the deck of cards is 0.0962.
We need to find the probability of getting 5 hearts.
What is in a 52 deck of cards?A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suite contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
P(E)=Number of favourable outcomes/Total number of outcomes.
Now, P(E)=5/52=0.0962
Therefore, the probability of getting 5 hearts from the deck of cards is 0.0962.
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Corresponding angles lie on the same side of a transversal?
SELECT ONE:
TRUE
FALSE
The range of the function f(x)=x+5 is (7,9). What is the function's domain?
Is it
(2,4)
(-2,-4)
(12,14)
(-12,-14)
(0,5)
What is 528−−√+63−−√528+63 in simplest radical form?
Answer: [tex]13\sqrt{7}[/tex]
Step-by-step explanation:
In the simple radical form there are no square root is remain to find.
Since, the given expression,
[tex]5\sqrt{28} + \sqrt{63}[/tex]
[tex]5\sqrt{4\times 7} + \sqrt{9\times 7}[/tex]
[tex]5\sqrt{4} \times \sqrt{7} + \sqrt{9}\times \sqrt{7}[/tex]
[tex]5\times 2 \times \sqrt{7} + 3\times \sqrt{7}[/tex]
[tex]10 \sqrt{7} + 3\sqrt{7}[/tex]
[tex](10 + 3)\sqrt{7}[/tex]
[tex]13\sqrt{7}[/tex]
Since, we do not need to find further square root of 7.
Thus, the required radical form of [tex]5\sqrt{28} + \sqrt{63}[/tex] is [tex]13\sqrt{7}[/tex].
Answer:
[tex]13\sqrt{7}[/tex]
Step-by-step explanation:
[tex]5\sqrt{28} +\sqrt{63}[/tex]
To simplify the given expression we simplify each radical
[tex]5\sqrt{28} = 5\sqrt{4*7} = 5*2\sqrt{7} =10\sqrt{7}[/tex]
[tex]\sqrt{63} = \sqrt{9*7} =3\sqrt{7}[/tex]
[tex]5\sqrt{28} +\sqrt{63}[/tex]
[tex]10\sqrt{7}+3\sqrt{7}[/tex]
[tex]13\sqrt{7}[/tex]
When it is 2 hours after 2 o'clock, then it is 4 o'clock (2 + 2 = 4). When it is 10 hours after 10 o'clock, then it is 8 o'clock. In this kind of "clock arithmetic," 10 + 10 = 8.
When a clock time gets bigger than 12, you subtract 12 and take the answer as the actual clock time. For example, if you subtract 12 from 20, the answer is 8, so 20 o'clock is really 8 o'clock.
Brad has a certain medication that he needs to take every 5 hours without fail, starting at 1 o'clock on a certain day. The sequence of clock times that he takes his pills is 1, 6, 11, 4, 9, ...
What is the clock time when Brad takes his 16th pill?
The two interior angles that are not adjacent to an exterior angle are called ________.
remote exterior angles
remote interior angles
alternate exterior angles
corresponding angles
Answer: Second option is correct.
Step-by-step explanation:
The two interior angles that are not adjacent to an exterior angle are called "Remote interior angles"
As remote interior angles are those interior angles that are inside the are inside the triangle but opposite to the exterior angles.
Hence, Second option is correct.
The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) is ...?
The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) is -3/4.
Explanation:The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) can be found using the concept of implicit differentiation. To find the slope, we need to differentiate the equation with respect to x and then substitute the coordinates (2, -1) into the resulting equation. Let's solve it step by step.
First, we differentiate the equation implicitly with respect to x:
2y * dy/dx + 3(xy + 1)^2 * (y + x * dy/dx) = 0
Next, we substitute the values x = 2 and y = -1 into the equation:
2(-1) * dy/dx + 3(2(-1) + 1)^2 * (-1 + 2 * dy/dx) = 0
Simplifying the equation:
-2dy/dx - 3 * 1 * (-1 + 2dy/dx) = 0
-2dy/dx + 3 + 6dy/dx = 0
Combining like terms:
4dy/dx = -3
Finally, solving for dy/dx, we get:
dy/dx = -3/4
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The slope of the tangent line to the curve at the point \((2, -1)\) is:
[tex]\[\boxed{\frac{3}{4}}\][/tex]
To find the slope of the tangent line to the curve given by the equation [tex]\( y^2 + (xy + 1)^3 = 0 \)[/tex] at the point [tex]\( (2, -1) \)[/tex], we need to use implicit differentiation.
Given the curve:
[tex]\[y^2 + (xy + 1)^3 = 0\][/tex]
We differentiate both sides with respect to x . Using the chain rule and implicit differentiation, we get:
[tex]\[\frac{d}{dx} [y^2] + \frac{d}{dx} [(xy + 1)^3] = 0\][/tex]
First, differentiate [tex]\( y^2 \):[/tex]
[tex]\[\frac{d}{dx} [y^2] = 2y \frac{dy}{dx}\][/tex]
Next, differentiate [tex]\( (xy + 1)^3 \)[/tex] using the chain rule:
[tex]\[\frac{d}{dx} [(xy + 1)^3] = 3(xy + 1)^2 \cdot \frac{d}{dx} [xy + 1]\]\[= 3(xy + 1)^2 \cdot (y + x \frac{dy}{dx})\][/tex]
Putting it all together, we get:
[tex]\[2y \frac{dy}{dx} + 3(xy + 1)^2 (y + x \frac{dy}{dx}) = 0\][/tex]
Now, substitute [tex]\( x = 2 \) and \( y = -1 \)[/tex] into the equation:
[tex]\[2(-1) \frac{dy}{dx} + 3((2)(-1) + 1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\]\[-2 \frac{dy}{dx} + 3(-2 + 1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\][/tex]
[tex]\[-2 \frac{dy}{dx} + 3(-1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\]\[-2 \frac{dy}{dx} + 3(1) \left( -1 + 2 \frac{dy}{dx} \right) = 0\][/tex]
[tex]\[-2 \frac{dy}{dx} + 3(-1 + 2 \frac{dy}{dx}) = 0\]\[-2 \frac{dy}{dx} + 3(-1 + 2 \frac{dy}{dx}) = 0\][/tex]
[tex]\[-2 \frac{dy}{dx} + 3(-1) + 6 \frac{dy}{dx} = 0\][/tex]
[tex]\[-2 \frac{dy}{dx} - 3 + 6 \frac{dy}{dx} = 0\][/tex]
[tex]\[4 \frac{dy}{dx} - 3 = 0\][/tex]
[tex]\[4 \frac{dy}{dx} = 3\][/tex]
[tex]\[\frac{dy}{dx} = \frac{3}{4}\][/tex]
So, the slope of the tangent line to the curve at the point \((2, -1)\) is:
[tex]\[\boxed{\frac{3}{4}}\][/tex]
Ava was making muffins. she used 1 1/3 tsp of cinnamon and 1/2 tsp of nutmeg. how many teaspoons of spice did ava use?
If Tucson's average rainfall is 12 1/4 and Yumas is 2 3/5 inches, how much more rain, on an average does Tucson get? ...?
Answer:
[tex]9\frac{13}{20}\text{ inches}[/tex]
Step-by-step explanation:
Given,
Tucson's average rainfall = [tex]12\frac{1}{4}\text{ inches}=\frac{49}{4}\text{ inches}[/tex]
Also, Yumas's average rainfall = [tex]2\frac{3}{5}\text{ inches}=\frac{13}{5}\text{ inches}[/tex]
Difference between Tucson's average rainfall and Yumas's average rainfall
[tex]=\frac{49}{4}-\frac{13}{5}[/tex]
[tex]=\frac{245-52}{20}[/tex]
[tex]=\frac{193}{20}[/tex]
[tex]=9\frac{13}{20}[/tex]
Hence, Tucson gets [tex]9\frac{13}{20}[/tex] inches more rainfall.
3 is 1 percent of what amount
The value of the solution is, 3 is 1 percent of 300.
We have to give that,
To find the amount for 1 percent is 3.
Let us assume that,
3 is 1 percent of x.
Hence, It can be written as,
3 = 1% of x
Solve for x,
3 = 1/100 × x
3 × 100 = x
x = 300
Therefore, 3 is 1 percent of 300.
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Triangle ABC is similar to triangle DEF.
What is the scale factor of triangle DEF to triangle ABC?
Triangle A B C and triangle D E F are drawn. Side A B is labeled 9. Side A C is labeled 12. Side D E is labeled 3. Side D F is labeled x.
3
1/3
4
1/4
Triangle ABC is similar to triangle DEF.
What is the scale factor of triangle DEF to triangle ABC?
Triangle A B C and triangle D E F are drawn. Side A B is labeled 9. Side A C is labeled 12. Side D E is labeled 3. Side D F is labeled x.
3
1/3
4
1/4
what is 26.100??
...?
Which expression is equivalent to 7(xy)
7x+y
7x-y
x(7y)
xy/7
Answer: [tex]x(7y)[/tex]
Step-by-step explanation:
The given expression: [tex]7(xy)[/tex]
i.e. a product of 7 and xy.
The operation used here: Multiplication.
Commutative property of multiplication :-
[tex]a\times b=b\times a[/tex] for any numbers a and b.
Associative property of multiplication :-
[tex]a\times(b\times c)=(a\times b\times c)[/tex] for any numbers a , band c.
Now, [tex]7(xy)=(7x)y[/tex] [Associative property of multiplication]
[tex]=(x7)y[/tex] [Commutative property of multiplication]
[tex]=x(7y)[/tex] [Associative property of multiplication]
The ratio of trumpet players to tuba players at a high school is 5:2 Which statement is true?
A.2/5 of the total tuba and trumpet players are tuba players.
B.The number of trumpet players is 2.5 times the number of tuba players.
C.There are 2 trumpet players for every 5 tuba players.
D.If there are a total of 100 trumpet and tuba players, 52 of them are tuba players.
The correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.
Let's analyze each statement and determine which one is true:
A. "2/5 of the total tuba and trumpet players are tuba players."
To find out if this statement is true, we need to determine what portion of the total number of players are tuba players. Since the ratio of trumpet players to tuba players is 5:2, for every 5 + 2 = 7 players, 2 are tuba players. So, the proportion of tuba players is 2/7, not 2/5. Therefore, Statement A is false.
B. "The number of trumpet players is 2.5 times the number of tuba players."
According to the given ratio, for every 5 trumpet players, there are 2 tuba players. Thus, the number of trumpet players is indeed 2.5 times the number of tuba players. Therefore, Statement B is true.
C. "There are 2 trumpet players for every 5 tuba players."
This statement matches the given ratio, so it is true. However, it doesn't provide any additional information beyond what's already given in the initial problem.
D. "If there are a total of 100 trumpet and tuba players, 52 of them are tuba players."
To verify this statement, we can calculate the number of tuba players using the given ratio. Since the total ratio parts is 5 (trumpet) + 2 (tuba) = 7, and the total number of players is 100, we can find the number of tuba players as (2/7) * 100 = 28. Thus, Statement D is false.
Therefore, the correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.
Forty-six and seven thousandths in decimal form
Stella graphs the equation y=13x – 2y=13x – 2 .
Select all statements about Stella's graph that are true.
The graph is a straight line.
The line passes through the origin.
The line passes through the point (0, –2)(0, –2) .
The slope of the line is 3.
The y-intercept of the line is 2.
Verify the identity.
tan^5x = tan^3xsec^2x -tan^3x
Use the remainder theorem to determine whether x - 2 is a factor of
f(x) = x^3 + 3x^2 - x - 18
A) Yes, x - 2 is a factor of f(x) because f(2) = 0
B) No, x - 2 is not a factor of f(x) because f(2) = 0
C) Yes, x - 2 is a factor of f(x) because f(-2) = -12
D) No, x - 2 is not a factor of f(x) because f(-2) = -12
lizzy is tiling the kitchen floor for the first time. she had a tough time at first and placed only 5 tiles the first day. she started to go faster, and by the end of day 4 she had places 35 tiles. she worked at a steady rate after the first day. use an equation in point slope form to determine how many days lizzy took place all of 100 tiles needed to finish the floor
Answer:
10.5 days
Step-by-step explanation:
Point slope form
y-5=10(x-1)
Substitute for y
100-5=10(x-1)
Distribute the 10
100-5=10x-10
Combine like terms
95=10x-10
Add ten to both sides
105=10x
Divide by 10
X = 10.5
How much money will Rachel have in her account in ten years
Proportion is ________________
Proportion is a mathematical concept that describes the relationship between two or more quantities. It is often represented using ratios and can be used to solve for unknown values, scale measurements, and interpret data.
Explanation:Proportion is a mathematical concept that describes the relationship between two or more numbers or quantities. It is a way of expressing that one quantity is equal to another quantity, or that one quantity is a fraction or multiple of another quantity. Proportions can be represented using ratios, which compare the relative sizes of different quantities.
For example, if we have two ratios, such as 1:2 and 3:6, we can determine if they are proportional by cross-multiplying and checking if the products are equal. In this case, 1 × 6 = 2 × 3, so the ratios are proportional.
Proportions are used in many different areas of mathematics, such as solving for unknown values, scaling up or down, and interpreting data. They are also used in real-world applications, such as finding the missing side length of a similar triangle or calculating the unit price of a product.
TRUE OR FALSE! If a quadratic equation can be factored and each factor contains only real numbers then there can not be an imaginary solution.
The first step in solving 7/8 = 3x - 5/11 is to subtract 5/11 from both sides of the equation.
True
False
Answer:
false
Step-by-step explanation:
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