Answer:
1/4
Step-by-step explanation:
y varies directly as x means you should translate this as y=kx.
y varies indirectly as x means you should translate this as y=k/x.
Anyways we had directly, so the equation is of the form y=kx for any point (x,y) where k is the constant.
We are given y=kx and that this equation should satisfy (x,y)=(8,2).
So let's plug in 8 for x and 2 for y giving us
2=k*8
Divide both sides by 8:
2/8=k
Simplify:
1/4=k
So k is a constant, that constant, the never changing number, for the point (x,y) is 1/4.
That means the equation is y=1/4 *x. The 1/4 is the constant of variation, also called the constant of proportionality.
The constant of variation, in this case, is found to be 1/4 using the formula y = kx.
The constant of variation in this case is 1/4.
Given that y varies directly as x and y = 2 when x = 8, we can use the formula y = kx to find the constant of variation.
By substituting the values y = 2 and x = 8 into the formula, we get 2 = k * 8, which simplifies to k = 1/4.
6,382
The value of an eight
worth 100 times the
value of the eight in
the number above.
Answer:
8000
Step-by-step explanation:
The value of 8 in this number is 80, so you multiply that by to get 8000.
I am joyous to assist you.
7. David bought two types of cards. He bought x type of cards that cost $4 andy
type of cards that cost $2. There are a total of 22 cards and they have a total cost of
$26. If he bought 5 of the $4 type of cards, how many of the $2 cards did he buy?
cards
Answer:
Step-by-step explanation:
x + y = 22
22 cards = 26
5(4) +y(2) = 26
20+2y = 26
20-20 +2y = 26-20
2y =6
2y/2 = 6/2
y = 3
andy bought 3 cards
David bought 5 of the $4 cards and 17 of the $2 cards. By setting up and solving the equations, we determined the number of each type of card he purchased.
To solve this problem, we set up two key equations based on the given information.
Let x be the number of $4 cards and y be the number of $2 cards.
The equations are:
Total cards: x + y = 22Total cost: 4x + 2y = 26We know that David bought 5 of the $4 cards.
Therefore, x = 5.
Substituting x into the first equation:
5 + y = 22
y = 22 - 5
y = 17
So, David bought 17 of the $2 cards.
given the function f(x)=-2x^2+3x+10 find f(1) and f(3) choose the statement that is true concerning these two values
the value of f(1) us the same as the value of f(3)
the value of f(1) cannot be comparEd to the value of f(3)
the value of f(1) is larger than the value of f(3)
the value of f(1) is smaller than the value of f(3)
We found the values of the function f(x) at points 1 and 3 and compared them. It's found that the value of f(1) is significantly larger than the value of f(3), hence the third statement is true.
Explanation:To answer your question, we need to substitute 1 and 3 into the function f(x)=-2x^2+3x+10, respectively. So:
For f(1), we get -2*1^2 + 3*1 + 10 = -2 + 3 + 10 = 11.
For f(3), we get -2*3^2 + 3*3 + 10 = -18 + 9 + 10 = 1.
Therefore, we can clearly see that the value of f(1) is larger than the value of f(3), meaning the third statement is true.
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Decide if the following scenario involves a permutation or combination. Then find the number of possibilities. The student body of 165 students wants to elect 3 representatives
Answer:
735,130.
Step-by-step explanation:
The order of election of the 3 representatives does not matter so it is a combination.
The number of possible combinations
= 165! / 162! 3!
= (165 * 164 * 163) / (3*2*1)
= 735,130.
Final answer:
The scenario of electing 3 representatives from a student body of 165 students involves combinations since the order of selection does not matter. Using the combination formula, there are 4,598,340 possible ways to choose the representatives.
Explanation:
The scenario described involves electing 3 representatives from a student body of 165 students. In this context, we are dealing with combinations, not permutations, because the order of selection does not matter; it only matters who is chosen, not in which order they are elected.
To calculate the number of possible combinations of 165 students taken 3 at a time, we can use the combination formula:
C(n, k) = n! / [k!(n - k)!]
where:
n = total number of items,k = number of items to choose,! indicates a factorial, which is the product of all positive integers up to that number.Therefore, the number of possibilities is:
C(165, 3) = 165! / [3!(165 - 3)!]
Calculating this gives us:
165! / (3! * 162!) = (165 * 164 * 163) / (3 * 2 * 1) = 4,598,340 combinations.
Which coordinates will best represent point A'?
A. (-2, 5)
B. (4, -3)
C. (-2, -3)
D. (4, 5)
Answer: OPTION A.
Step-by-step explanation:
You know that the rule that will be used for the translation of the figure ABC is:
[tex](x,y)[/tex]→[tex](x-3,\ y+4)[/tex]
You can observe in the figure that the coordinates of the point A is this:
[tex]A(1,1)[/tex]
Then, in order to find the coordinates that will best represent point A', you need to subtract 3 from the x-coordinate of the point A and add 4 to the y-coordinate of the point A:
[tex]A'(1-3,\ 1+4)\\\\A'(-2,5)[/tex]
Answer:
A. (-2,5)
Step-by-step explanation:
The figure ABC is translated to A'B'C' by the rule (x-3, y+4)
The Image of the triangle will therefore be as follows:
A' (1-3,1+4)
B'(2-3,5+5)
C'(3-3,2+5)
The vertices will thus be A'(-2,5), B'(-1,10) and C'(0,7)
Thus the correct answer will be A. (-2,5)
What is the product of the binomials below?
(2x +5)(4x +4)
A. 9x2 +28x + 20
B. 8x2 +28x+9
C. 8x1 +28x+20
D. 9x2 +28x+9
Answer:
The correct answer is 8x^2+28x+20.
Step-by-step explanation:
(2x+5)(4x+4)
Multiply the first bracket with each element of second bracket:
=4x(2x+5)+4(2x+5)
=8x^2+20x+8x+20
Now solve the like terms:
=8x^2+28x+20
Thus the correct answer is 8x^2+28x+20....
x^y=y^x find derivitive
Answer:
[tex]y'=\frac{y^2-xy\ln(y)}{x^2-xy\ln(x)}[/tex]
Step-by-step explanation:
Take natural log of both sides first.
[tex]x^y=y^x[/tex]
[tex]\ln(x^y)=\ln(y^x)[/tex]
Taking the natural log of both sides allows you to bring down the powers.
[tex]y\ln(x)=x\ln(y)[/tex]
I'm going to differentiate both sides using the power rule.
[tex](y)'(\ln(x))+(\ln(x))'y=(x)'(\ln(y))+(\ln(y))'x[/tex]
Now recall (ln(x))'=(x)'/x=1/x while (ln(y))'=(y)'/y=y'/y.
[tex]y'(\ln(x))+\frac{1}{x}y=1(\ln(y))+\frac{y'}{y}x[/tex]
Simplifying a bit:
[tex]y' \ln(x)+\frac{y}{x}=\ln(y)+\frac{y'}{y}x[/tex]
Now going to gather my terms with y' on one side while gathering other terms without y' on the opposing side.
Subtracting y'ln(x) and ln(y) on both sides gives:
[tex]\frac{y}{x}-\ln(y)=-y'\ln(x)+\frac{y'}{y}x[/tex]
Now I'm going to factor out the y' on the right hand side:
[tex]\frac{y}{x}-\ln(y)=(-\ln(x)+\frac{x}{y})y'[/tex]
Now we get to get y' by itself by dividing both sides by (-ln(x)+x/y):
[tex]\frac{\frac{y}{x}-\ln(y)}{-\ln(x)+\frac{x}{y}}=y'[/tex]
Now this looks nasty to write mini-fractions inside a bigger fraction.
So we are going to multiply top and bottom by xy giving us:
[tex]\frac{y^2-yx\ln(y)}{-xy\ln(x)+x^2}=y'[/tex]
[tex]y'=\frac{y^2-xy\ln(y)}{x^2-xy\ln(x)}[/tex]
The derivative of the implicit function [tex]x^y = y^x[/tex] is [tex]\[\frac{dy}{dx} = \frac{\ln(y) - \frac{y}{x}}{\ln(x) - \frac{x}{y}}\][/tex].
To find the derivative of the implicit function defined by [tex]\( x^y = y^x \),[/tex] follow these steps:
Take the natural logarithm of both sides to simplify the expression:[tex]\ln(x^y) = \ln(y^x)[/tex]
Using logarithm properties, this becomes:y ln(x) = x ln(y)
Differentiate both sides with respect to x. Use implicit differentiation where y is considered a function of x:
For the left side, differentiate y ln(x):[tex]\[ \frac{d}{dx}[y \ln(x)] = \frac{dy}{dx} \ln(x) + y \cdot \frac{1}{x} \][/tex]
For the right side, differentiate x ln(y):[tex]\[ \frac{d}{dx}[x \ln(y)] = \ln(y) + x \cdot \frac{1}{y} \cdot \frac{dy}{dx} \][/tex]
Set the derivatives equal to each other:[tex]\[ \frac{dy}{dx} \ln(x) + \frac{y}{x} = \ln(y) + \frac{x}{y} \cdot \frac{dy}{dx} \][/tex]
Solve for [tex]\( \frac{dy}{dx} \):[/tex]
Rearrange terms involving [tex]\( \frac{dy}{dx} \):[/tex][tex]\[ \frac{dy}{dx} \ln(x) - \frac{x}{y} \cdot \frac{dy}{dx} = \ln(y) - \frac{y}{x} \][/tex]
Factor out [tex]\( \frac{dy}{dx} \):[/tex][tex]\[ \frac{dy}{dx} \left(\ln(x) - \frac{x}{y}\right) = \ln(y) - \frac{y}{x} \][/tex]
Finally, solve for [tex]\( \frac{dy}{dx} \):[/tex][tex]\[ \frac{dy}{dx} = \frac{\ln(y) - \frac{y}{x}}{\ln(x) - \frac{x}{y}} \][/tex]
1
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the expressions with their simplified versions.
Answer:
[tex]4\sqrt{2}.\sqrt{2} = 8\\3\sqrt{7}-2\sqrt{7} =\sqrt{7}\\\frac{\sqrt{7}}{2\sqrt{7}} = \frac{1}{2}\\2\sqrt{5}.2\sqrt{5} = 20[/tex]
Step-by-step explanation:
[tex]4\sqrt{2}.\sqrt{2}\\=4 . (\sqrt{2})^2\\=4*2\\=8\\\\3\sqrt{7}-2\sqrt{7}\\As\ the\ square\ root\ is\ same\ in\ both\ terms\\= (3-2)\sqrt{7}\\=\sqrt{7}\\\\\frac{\sqrt{7}}{2\sqrt{7}} \\The\ square\ roots\ will\ be\ cancelled\\= \frac{1}{2}\\ \\2\sqrt{5}.2\sqrt{5}\\=(2*2)(\sqrt{5})^2\\=4*5\\=20[/tex]
Answer:
Below we present each expression with its simplest form.
[tex]4\sqrt{2} \sqrt{2}=4(2)=8[/tex]
[tex]3\sqrt{7} -2\sqrt{7}=(3-2)\sqrt{7} = \sqrt{7}[/tex]
[tex]\frac{\sqrt{7} }{2\sqrt{7} } =\frac{1}{2}[/tex]
[tex]2\sqrt{5} 2\sqrt{5}=4(5)=20[/tex]
So, the first expression matches with 8.
The second expression matches with the square root of seven.
The third expression matches with one-half.
The fourth expression matches with 20.
2. Let f(x) = -2x - 7 and g(x) = -4x + 6. Find(gof)(-5).
[tex](g\circ f)(x)=-4(-2x-7)+6=8x+28+6=8x+34\\\\(g\circ f)(-5)=8\cdot(-5)+34=-6[/tex]
what is the input-output table for the function f(x) = 3x^2-x+4
Answer:
Step-by-step explanation:
The input-output table can be made by putting value of x and finding the value of f(x)
f(x) = 3x^2-x+4
f(0) = 3(0)^2-0+4 = 0-0+4 = 4
f(1) = 3(1)^2-1+4 = 3-1+4 = 2+4 =6
f(2) = 3(2)^2-2+4 = 3(4)-2+4 = 12-2+4 = 10+4 = 14
f(3) = 3(3)^2-3+4 = 3(9)-3+4 = 27-3+4 = 24+4 = 28
So put value of x and find f(x) and fill the input-output table.
x f(x)
0 4
1 6
2 14
3 28
A system of linear equations contains two equations with negative reciprocal
slopes. Select all of the correct statements.
O
O
A. The system will have two solutions.
O
B. The system will have one solution.
O c. The system may have no solution.
D. The system may have infinitely many solutions.
The system of equation will have one solution.
The correct answer is an option (B)
What is a system of equation ?It is a collection of one or more linear equation involving the same variable.
For given question,
Two equations have negative reciprocal slope .
Which means if one equation have slope = m
then slope of other equation will be = -1/m
This means, both the lines are perpendicular to each other , hence both the lines must be intersecting each other at one point.
In system of equation , the solution of the two equation is the point where they intersect .
Since, both the lines are intersecting at one point . Hence, it will have only one solution.
Therefore, the correct answer is an option b) the system will have one solution
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The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years
Answer:607.81
Step-by-step explanation:that’s what I got believe me on this one guys
The value of the collector's item after 4 years is $607.75.
Given :
Item is purchased for $500.
Value increases at a rate of 5% per year.
Solution :
We know that the exponential growth function is
[tex]y = a(1+r)^x[/tex]
where,
a = $500
r = 0.05
x = 4
The value of the item after 4 years is,
[tex]= 500(1+0.05)^4[/tex]
[tex]= 500\times(1.05)^4[/tex]
[tex]= 607.75[/tex]
The value of the item after 4 years is $607.75.
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How could 1.75 metres be written as a fraction?
Answer:
1 3/4 meters
Step-by-step explanation:
1.75 = 1 3/4 [think of it as since 3 quarters equals 75 cents, and 4 quarters equals 100 cents or a dollar.]
So, 1 3/4 meters
If EFGH is a parallelogram, then ________
Answer:
A parallelogram is a quadrilateral whose opposite sides are parallel and equal, opposite angles are equal, the sum of the interior angles is 360 degrees. Therefore, the parallelogram EFGH might be a rhombus.
Step-by-step explanation:
Answer:
then it might be a rhombus
Step-by-step explanation:
which rule represents the translation of hexagon D'E'F'G'H'I' ?
A. (x, y) -> (x - 8, y - 7)
B. (x, y) -> (x - 7, x - 8)
C. (x, y) -> (x - 4, x - 5)
D. (x, y) -> (x - 5, y - 4)
Answer:
C (X,Y)->(X-4,×-5) I would say bro
What is the following product? 3sqrt4 * sqrt3
Answer:
[tex]6\sqrt{3}[/tex]
Step-by-step explanation:
We need to find the product of [tex]3\sqrt{4} \sqrt{3}[/tex]
We know that:
[tex]3\sqrt{4} \sqrt{3}[/tex] ⇒ [tex]3\sqrt{12}[/tex] ⇒[tex]6\sqrt{3}[/tex]
Therefore, the product is [tex]6\sqrt{3}[/tex]
The product of 3sqrt4 and sqrt3 can be calculated as 6sqrt3. This result is obtained by multiplying 3 by the square root of 4, which is 2, giving you 6, and then multiplying that by the square root of 3.
Explanation:The product of 3sqrt4 and sqrt3 can be calculated following the rules of multiplication for square roots. Firstly, sqrt4 is 2. Therefore, 3sqrt4 is 3*2, which equals 6. Secondly, you multiply this result by sqrt3 to get the final product:
6 * sqrt3Therefore, your final product is 6sqrt3.Learn more about Multiplication of Square Roots here:https://brainly.com/question/29279167
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The school football team had 43 new players and 13 returning players, if the coach put them in groups of 8. how many groups were there?
Answer: There were 7 groups.
Step-by-step explanation:
43 + 13 = 56
56/8 = 7
Answer: 7 groups.
Step-by-step explanation: Add the new and the only players.
43+13=56
Divide this number by 8.
56/8=7
There are 7 groups.
Charles wants to find out if the students in foreign language classes spend more time in class speaking in English or in the
foreign language they are studying Charles first gets class lists of all students taking foreign language classes. He then
chooses 10 students from each different language class to survey. Which best explains why the sample he chose may not b
a representative sample?
Is this app good
Step-by-step explanation:
hvvvbgdddtunnfdyjvhjk
Graph of f(x) = 2(3)^x?
Please and Thank You
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=2(3)^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value (y-intercept)
b is the base
r is the rate of change
b=(1+r)
In this problem
a=2
b=3
1+r=3
r=3-1=2
r=200%
using a graphing tool
The graph in the attached figure
Which of the following is equivalent to the radical expression below?
For this case we must indicate an expression equivalent to:
[tex]\sqrt {10x ^ 7}[/tex]
By definition of properties of powers and roots we have that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, we can rewrite the expression as:
[tex]10 ^ {\frac {1} {2}} * x ^ {\frac {7} {2}}[/tex]
Answer:
OPTION A
What are the solutions of 4x2-x+9=0
For this case we must find the solutions of the following equation:
[tex]4x ^ 2-x + 9 = 0[/tex]
We apply the cudratic formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 4\\b = -1\\c = 9[/tex]
Substituting:
[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (4) (9)}} {2 (4)}\\x = \frac {1 \pm \sqrt {1-144}} {8}\\x = \frac {1 \pm \sqrt {-143}} {8}[/tex]
Thus, the complex roots are:
[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]
Answer:
[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]
3. A catering service paid $520 for 10 center pieces and 60 glasses. The guest list grew, requiring an
additional 2 centerpieces and 36 glasses at a cost of $152. Follow the steps outlined below in order
to use a system of equations to find the cost of each centerpiece and each glass.
a. Name your variables.
Let x = the cost of a single centerpiece.
Let y = the cost of a single glass
b. Fill in the table.
First Bill- cost of centerpieces-cost of glasses-total cost
Second Bill-cost of centerpieces-cost of glasses-total cost
c. Write a system of equations to represent both orders.
10x+60y=520.
2x+30y=152
d. Solve the system using any preferred method.
e. Interpret your answer to part d using a complete sentence.
Need help asap!! Whats the answer
Answer:
The correct answer is option B. 11√2
Step-by-step explanation:
From the figure we can see two isosceles right angled triangle.
Therefore the sides are in the ratio 1 : 1 : √2
It is given that equal sides of the triangle is 11 units
So we can write, 11 : 11 : x = 1 : 1 : √2
x = 11√2
Therefore the value of x = 11√2
The correct answer is option B. 11√2
A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and
jacks. Two cards are chosen from the deck at random.
Which expression represents the probability of drawing a king and a queen?
522
669)
522
GP,3GP)
522
(CGC)
522
Answer:
A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and jacks. Two cards are chosen from the deck at random.
Which expression represents the probability of drawing a king and a queen?
StartFraction (4 P 1) (3 P 1) Over 52 P 2 EndFraction
StartFraction (4 C 1) (3 C 1) Over 52 C 2 EndFraction
StartFraction (4 P 1) (4 P 1) Over 52 P 2 EndFraction
StartFraction (4 C 1) (4 C 1) Over 52 C 2 EndFraction
it is D
Step-by-step explanation:
The probability of drawing a king and a queen is 1/169.
Given,
A standard deck of 52 playing cards contains four of each numbered card 2–10 and four each of aces, kings, queens, and jacks.
Two cards are chosen from the deck at random.
We need to find which expression represents the probability of drawing a king and a queen.
What is a combination?A combination is used when we want to determine the number of possible arrangements in a collection of items where the order of the selection does not matter.
The formula is given by:
[tex]^nC_r[/tex] = n! / r! ( n-r)!
We have,
52 playing cards
4 kings and 4 queens.
This means we have
The probability of drawing a king and a queen is:
= probability of drawing a king x probability of drawing a queen
= ^4C_1 / ^52C_1 x ^4C_1 / ^52C_1
= 4 / 52 x 4 / 52
= 1/13 x 1/13
= 1/169
Thus the probability of drawing a king and a queen is 1/169.
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Find two equivalent expressions for the opposite of the polynomial -x^2+50x-9
Equivalent expressions are expressions of equal values.
[tex]\mathbf{x^2 - 50x + 9}[/tex] and [tex]\mathbf{ -(-x^2 + 50x - 9)}[/tex] are equivalent expressions for the opposite of [tex]\mathbf{-x^2 + 50x - 9}[/tex]
The expression is given as:
[tex]\mathbf{f(x) = -x^2 + 50x - 9}[/tex]
To calculate the opposite, we simply negate the signs of the expression.
So, we have:
[tex]\mathbf{-f(x) = -(-x^2 + 50x - 9)}[/tex]
Expand
[tex]\mathbf{-f(x) = x^2 - 50x + 9}[/tex]
The above highlights mean that:
[tex]\mathbf{x^2 - 50x + 9}[/tex] and [tex]\mathbf{ -(-x^2 + 50x - 9)}[/tex] are equivalent expressions for the opposite of [tex]\mathbf{-x^2 + 50x - 9}[/tex]
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Final answer:
To find equivalent expressions for the opposite of the polynomial [tex]-x^2+50x-9[/tex], we change the signs of all terms to get [tex]x^2-50x+9[/tex]. Equivalent expressions may be generated by distributing a factor such as [tex](-1)(-x^2+50x-9)[/tex], but the polynomial does not factor nicely over the integers for other simplifications.
Explanation:
To find two equivalent expressions for the opposite of the polynomial [tex]-x^2+50x-9[/tex], we start by taking the opposite of the given polynomial. The opposite (or negative) of a polynomial consists of changing the sign of each term. Therefore, the opposite of the given polynomial is [tex]x^2 - 50x + 9.[/tex]
An equivalent expression can be obtained by factoring, if possible, or by using other algebraic manipulations. However, in this case, [tex]x^2 - 50x + 9[/tex] does not factor nicely over the integers. To get an equivalent expression, we can express it in different forms, such as:
Distributing a factor: [tex](-1)(-x^2 + 50x - 9)[/tex]Factoring by grouping (though not applicable to this specific polynomial)Another way to express an equivalent polynomial is to add and subtract the same value within the expression, which maintains its equality.
a child lies on the ground and looks up at the top of a 14-ft tree nearby. the child is 7 ft away from the tree. what is the angle if elevation from the child to the top of th tree? round to the nearest whole degree.
Answer:
63°
Step-by-step explanation:
From the diagram, the angle of elevation from the child to the top of the tree can be calculated using the tangent ratio.
Recall SOH-CAH-TOA from your Trigonometry class.
The tangent is opposite over adjacent.
[tex] \tan(A) = \frac{14}{7} [/tex]
[tex]A = \tan^{ - 1} ( 2)[/tex]
[tex]A = 63.43 \degree[/tex]
The angle of elevation is 63° to the nearest degree.
write two linear functions, f(x) and g(x). For example, f(x)= 3x-7 and g(x)= -2x+5. Then see whether f(x) - (-g(x)) is equivalent to f(x) + g(x).
Answer:
the two expressions are equivalent.
Step-by-step explanation:
We know that f(x)= 3x-7 and g(x)= -2x+5, therefore:
f(x) - (-g(x)) = 3x-7 - ( +2x-5) = 3x - 7 - 2x + 5 = x -2
f(x) + g(x) = 3x-7 -2x + 5 = x - 2
Therefore, f(x) - (-g(x)) is equivalent to f(x) + g(x).
Another way to check that the two expressions are equivalent is by solving the parenthesis:
f(x) - (-g(x)) → f(x) + g(x)
Therefore, the two expressions are equivalent.
0.45x - 0.2(x - 5) = 0.25
Answer:
[tex]\boxed{\bold{x=-3}}[/tex]
Explanation:
Multiply Both Sides By 100
[tex]\bold{0.45x\cdot \:100-0.2\left(x-5\right)\cdot \:100=0.25\cdot \:100}[/tex]
Refine
[tex]\bold{45x-20\left(x-5\right)=25}[/tex]
Expand [tex]\bold{-20\left(x-5\right): \ -20x+100}[/tex]
= [tex]\bold{45x-20x+100=25}[/tex]
Add Similar Elements: [tex]\bold{\:45x-20x=25x}[/tex]
= [tex]\bold{25x+100=25}[/tex]
Subtract 100 From Both Sides
[tex]\bold{25x+100-100=25-100}[/tex]
Simplify
[tex]\bold{25x=-75}[/tex]
Divide Both Sides By 25
[tex]\bold{\frac{25x}{25}=\frac{-75}{25}}[/tex]
Simplify
[tex]\bold{x=-3}[/tex]
Mordancy.
What is the first term of the quotient of the following division problem? (x3 – 1) ÷ (x + 2)
Answer:
x^2
Step-by-step explanation:
given:
x^3-1/x+2
As the denominator is linear function and the highest power in numerator is x^3
So the first term in quotient is going to be x^2 to cancel first term of numerator i.e x^3!
Answer:
x^2
Step-by-step explanation:
given:
x^3-1/x+2
As the denominator is linear function and the highest power in numerator is x^3
So the first term in quotient is going to be x^2 to cancel first term of numerator i.e x^3!
Factor the expression.
3x3 + 3x2 + x + 1
(x + 3)(3x2 – 1)
(x + 1)(3x2 + 1)
3x2(x + 1)
x(3x2 + x + 1)
Answer:
(x + 1) (3 x^2 + 1)
Step-by-step explanation:
Factor the following:
3 x^3 + 3 x^2 + x + 1
Factor terms by grouping. 3 x^3 + 3 x^2 + x + 1 = (3 x^3 + 3 x^2) + (x + 1) = 3 x^2 (x + 1) + (x + 1):
3 x^2 (x + 1) + (x + 1)
Factor x + 1 from 3 x^2 (x + 1) + (x + 1):
Answer: (x + 1) (3 x^2 + 1)
Answer:
(x + 1) (3 x^2 + 1)
Step-by-step explanation: