Answer:
Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Actually 1 and x both are polynomials. Therefore 1/x is already a quotient of polynomials.
Two polynomial expressions whose quotient, when simplified, is 1/x
x+1/x^2+x
Take the common of the denominator
x+1/x(x+1)
x+1 will be cancelled out by x+1
1/x
1/x is not a polynomial, so polynomials are not closed under division.
Polynomials are closed under addition, subtraction and multiplication. Addition and multiplication are associative and commutative.
There is an additive identity which is 0.
There is a multiplicative identity which is 1....
Polynomial expressions involve variables, coefficients, and exponents, combined by addition, subtraction, and multiplication. They are not closed under division, as shown by the quotient 1/x, which is not a polynomial. However, polynomials are closed under addition, subtraction, and multiplication.
Explanation:A polynomial expression is a mathematical expression that can involve variables, coefficients, and exponents, that are combined using addition, subtraction, and multiplication operations. For your question, we can consider two polynomial expressions: x and 1. The quotient of these two expressions is 1/x.
However, 1/x is not a polynomial expression, because it involves division by a variable. This shows that polynomial expressions are not closed under division.
In contrast, polynomials are closed under the operations of addition, subtraction, and multiplication. For example, if we add, subtract or multiply any two polynomials we will always get another polynomial.
These operations do not generate any new type of expressions outside the realm of polynomials, unlike division, which can produce non-polynomial results, such as rational expressions.
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A right triangle in which one acute angle is a reference angle for a 115 degree angle in standard position intersects the unit circle at (-0.423, 0.906). What is the approximate value of cos 115 degree?
Answer:
[tex]\cos (115\degree)=-0.423[/tex]
Step-by-step explanation:
The parametric equations of a circle is
[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]
The radius of the unit circle is 1 unit.
This implies that any point on the unit circle is represented by:
[tex]x=\cos \theta[/tex] and [tex]y=\sin \theta[/tex]
where [tex]\theta[/tex] is the angle in standard position,
From the question, the given angle in standard position is [tex]115\degree[/tex].
This angle intersects the unit circle at [tex]x=-0.423[/tex]
But [tex]x=\cos \theta[/tex]
We substitute [tex]\theta=115\degree[/tex] and [tex]x=-0.423[/tex]
This implies that: [tex]\cos (115\degree)=-0.423[/tex]
Scientists released 10 birds into a new habitat in year 0. Each year, there were
three times as many birds as the year before. How many birds were there
after x years? Write a function to represent this scenario.
To model the bird population that triples each year starting with 10 birds, an exponential growth function is used: f(x) = 10 × 3^x, where x is the number of years.
Explanation:To create a function that represents the scenario of birds increasing threefold each year, we need to use an exponential growth model.
The initial population of birds is 10 and then it triples every year.
Therefore, the function that describes the number of birds after x years would be:
f(x) = 10 × 3^x
Here, f(x) represents the number of birds after x years, 10 is the initial number of birds released into the habitat, and 3^x indicates that the population is growing three times each year for x years.
Final answer:
The number of birds after x years can be calculated using the exponential function B(x) = 10 × 3^x, representing the initial population of 10 birds tripling every year.
Explanation:
The scenario describes a population of birds in a new habitat growing exponentially each year. The initial population of birds is 10 (in year 0), and the population triples every year thereafter. To represent this situation mathematically, we can use an exponential function.
To find the number of birds after x years, we can use the following function:
B(x) = 10 × 3^x
Where:
B(x) is the number of birds after x years
10 is the initial number of birds
3 is the growth factor, as the population is tripling each year
x is the number of years since the birds were first released into the habitat
This equation models exponential growth and gives us the predicted population of the birds for any given year x.
the solution to 2x+8>10 is x<1
true or false
Answer:
false
Step-by-step explanation:
correct me if this is wrong, but it's actually x>1
Answer:
false.
Step-by-step explanation:
Given : 2x+8>10.
To find : the solution to 2x+8>10 is x<1 true or false.
Solution : We have given that
2x+8>10.
On subtracting both sides by 8
2x > 10 -8.
2x > 2
On dividing both sides by 2
x > 1
So, given statement false .
Therefore, false.
what is the value of 4r^2-8 when r=3?
Answer:
28
Step-by-step explanation:
So this means to replace the r you see in 4r^2-8 with 3.
Let's do that:
4(3)^2-8
Now to simplify this just use pemdas or a calculator:
4(9)-8 since 3^2 means 3*3=9
36-8
28
Answer:
28.
Step-by-step explanation:
Put r =- 3 and work it out:
That would be 4(3)^2 - 8
= 4 * 9 - 8
= 36 - 8
= 28.
What is the x-coordinate of the vertex of the parabola whose equation is y = 3x^2 + 12x + 5?
Answer:
(-2,-7)
Step-by-step explanation:
Answer:
x= -2
Step-by-step explanation:
-b/2a = x
-(12)/2(2) = x
-12/6 = x
-2 = x
a rectangular field has an area of 1,764m^2. the width of the field is 13m more then the length. what is the perimeter of the field?
Answer:
170 m
Step-by-step explanation:
Area of a rectangle is width times length:
A = WL
Given:
A = 1764
W = L + 13
Substitute:
1764 = (L + 13) L
1764 = L² + 13L
0 = L² + 13L − 1764
0 = (L + 49) (L − 36)
L + 49 = 0, L − 36 = 0
L = -49, L = 36
Since length can't be negative, L = 36 m.
So the width is W = L + 13 = 49 m.
Perimeter of a rectangle is twice the width plus twice the length.
P = 2W + 2L
P = 2(49) + 2(36)
P = 170 m
The perimeter is 170 meters.
How do I solve two step equations?
1. 3x+5=-16
Answer:
x = - 7
Step-by-step explanation:
Given
3x + 5 = - 16 ( subtract 5 from both sides )
3x = - 21 ( divide both sides by 3 )
x = - 7
Two-step equations can get more difficult the higher the numbers get, but they're not too hard! ;)
To solve 3x+5=-16:
First subtract 5 from each side
Now its 3x=-21
Next divide 3 from each side
You get x=-7!
Always check your work! To check your work plug your answer "-7" into x.
So it looks like this: 3(-7)+5=-16 then distribute and solve!
You'll get -16=-16, that means its correct/true!
The perimeter of a rectangle is 230 feet. The short sides are each 30 feet long, but the lengths of the long sides are unknown. Which equation represents this situation?
30+2a=230
2(30)+2a=230
2(30)a=230
30a=230
Answer:
b
Step-by-step explanation:
because perimeter of rectangle is 2(l+b)
For this case we have that by definition, the perimeter of a rectangle is given by:
[tex]P = 2a + 2b[/tex]
Where:
a: It is the length of the rectangle
b: It is the width of the rectangle
We have as data that:
[tex]P = 230 \ ft\\b = 30 \ ft[/tex]
Then, replacing we have:
[tex]230 = 2a + 2 (30)[/tex]
Answer:
Option B
what is the formula of (x^3 + y^3) as a factorized form?
Answer:
see explanation
Step-by-step explanation:
x³ + y³ ← is a sum of cubes and factors as
(x + y)(x² - xy + y²) ← in factored form
Which values of a,b and c represent the answer in simplest form
[tex]1 \frac{3}{4}[/tex]
Fractional division is fractional multiplication with the second fraction the reciprocal of itself. This means the problem can be written as [tex]\frac{7}{9}*\frac{9}{4}[/tex]. Fractional multiplication results in the multiplication of the numerators and denominators---in this case, [tex]\frac{7}{4}=1\frac{3}{4}[/tex]
Answer:
Option B) a = 1, b = 3, c = 4
Step-by-step explanation:
We are given the following information in the question:
We are given an expression:
[tex]\displaystyle\frac{7}{9} \div \frac{4}{9} = a\frac{b}{c}[/tex]
The solving of the above expression can be done in the following manner:
[tex]\displaystyle\frac{7}{9} \div \frac{4}{9}\\\\\frac{7}{9}\times \frac{9}{4}\\\\\frac{7}{4} =\frac{(4\times 1) + 3}{4}= 1\frac{3}{4}[/tex]
Comparing the right side of the expression, we have,
[tex]a\displaystyle\frac{b}{c} = 1\frac{3}{4}[/tex]
Comparing, we get,
a = 1, b = 3, c = 4
Option B) s the correct option.
Suppose you multiplied the cereal box dimensions in a different order:
V = (x)(4x+3)(4x)
First, (X)(4x+3) =
DONE
[tex]\bf V=(x)(4x+3)(4x)\implies \cfrac{V}{4x}=(x)(4x+3)[/tex]
Answer:
[tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]
Step-by-step explanation:
Given : Expression [tex]V = (x)(4x+3)(4x)[/tex]
To find : Suppose you multiplied the cereal box dimensions in a different order ?
Solution :
The given expression is the product of three numbers,
[tex]V = (x)(4x+3)(4x)[/tex]
First we multiply first two terms,
[tex](x)(4x+3)=4x^2+3x[/tex]
Substitute back,
[tex]V = (4x^2+3x)(4x)[/tex]
Then multiply the left terms,
[tex]V =16x^2+12x[/tex]
Therefore, [tex]V=(x)(4x+3)(4x)=16x^2+12x[/tex]
Which equation represents the line that passes through (–6, 7) and (–3, 6)?
y = –x + 9
y = –x + 5
y = –3x – 11y
y = –3x + 25
Answer:
The equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5
Step-by-step explanation:
The equation of line for point=slope form is
y-y₁ = m(x-x₁)
Finding Slope m:
m= y₂-y₁/x₂-x₁
here y₂= 6,y₁= 7,x₂= -3,x₁= -6
m = 6-7/-3-(-6)
m = -1/-3+6
m = -1/3
The slope m = -1/3 and considering point (-6,7) the equation is:
y-y₁ = m(x-x₁)
y-7 = (-1/3)(x-(-6))
y-7 = -1/3(x+6)
y-7 = -1/3x -2
y = -1/3x-2+7
y = -1/3x + 5
So, the equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5
x² + 2x – 1 = 0 in English words.
Answer:
x squared plus two times x minus one = zero.
Step-by-step explanation:
(This is a Quadratic equation in the variable x).
Answer:
One less than the sum of square of a number and twice the number is 0
Step-by-step explanation:
[tex]x^2+ 2x - 1 = 0[/tex]
x represents any number. x^2 represents square of a number
2x represents twice the number
[tex]x^2+2x[/tex] can be written as sum of square of a number and twice the number
[tex]x^2+2x-1[/tex]
One less than the sum of square of a number and twice the number
[tex]x^2+2x-1=0[/tex]
One less than the sum of square of a number and twice the number is 0
Is the line that passes through the points A(0,1) and B(2,5) parallel to the line that passes through the
points C(0,7) and D(4,15)?
Find the slope of AB
The slope of AB
Answer:
Yes the lines are indeed parallel. The slope of AB is 2
Step-by-step explanation:
the measure of XYZ is 296 what is the measure of XZW the tangent chord angle
Answer:
D. 148°
Step-by-step explanation:
Theorem: The measure of the angle formed by a tangent and a chord is equal to one-half the measure of the intercepted arc.
In your diagram, XZ is the chord, WZ is the tangent, and XYZ is the intercepted arc.
Per the theorem,
mXZW = ½ mXYZ = ½ × 296° = 148°
The measure of the tangent chord angle is 148°.
Answer: D: 148 is correct
Step-by-step explanation: apx :)
girardo is using the model below to solve the equation 3x+1=4x+(-4)
Answer:
x = 5Step-by-step explanation:
[tex]3x+1=4x+(-4)\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\3x-4x+1=4x-4x-4\\\\-x+1=-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=-4-1\\\\-x=-5\qquad\text{change the signs}\\\\x=5[/tex]
Answer:
The answer is B. In step one he should have added 3 negative x-tiles to both sides.
Step-by-step explanation:
Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).
Answer:
5x - 2y = -4Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
Te formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
===========================================
We have two points: (2, -3) and (4, 2). Substitute:
[tex]m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]
[tex]y-(-3)=\dfrac{5}{2}(x-2)\\\\y+3=\dfrac{5}{2}(x-2)[/tex]
Convert it to the standard form [tex]Ax+By=C[/tex]:
[tex]y+3=\dfrac{5}{2}(x-2)[/tex] multiply both sides by 2
[tex]2y+6=5(x+2)[/tex] use the coordinates of the point
[tex]2y+6=5x+10[/tex] subtract 6 from both sides
[tex]2y=5x+4[/tex] subtract 5x from both sides
[tex]-5x+2y=4[/tex] change the signs
[tex]5x-2y=-4[/tex]
solve the equation above
Answer:
½ = x
Step-by-step explanation:
As discussed in one of my You-Tube videos on Exponential Rules, aᵐ\ⁿ, any base to the half power is the SAME AS taking the exponential denominator of that power, and setting that to the square root of the base, leaving the exponential numerator on the outside:
25¹\² = √25
25 = a [Base]
1 = m [Exponential Numerator]
2 = n [Exponential Denominator]
As you can see, it is unnecessary to put the two because by definition, any vacant root is automatically assumed as the square root, and 1, which is the exponential numerator, is on the outside, which again is unnecessary because 5¹ is 5.
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Len needs $135.75 for a television. How many weeks will it take her to save enough money to buy a television? Equation: t = 25 + 8.25w
Answer:
14 weeks
Step-by-step explanation:
t = 25 + 8.25w
Len needs 135.75
135.75 = 25 + 8.25w
Subtract 25 from each side
135.75-25 = 25-25 + 8.25w
110.75 = 8.25w
Divide each side by 8.25
110.75/8.25 = 8.25w/8.25
13.42424 = w
Since we need at least 135.75, it will take Len a little more than 13 weeks, so it will take Len 14 weeks to have enough money
Answer:
14 weeks
Step-by-step explanation:
It will take 14 weeks for Len to save enough money to buy a television.
t = 25 + 8.25w
135.75 = 25 + 8.25w
Hope this helps!
How many seconds are in 240 minutes?
1 minute = 60 seconds
240 minute = 240 × 60 = 14400 seconds
240 minute = 14400 secondsThe lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth. 10.2 inches 24.0 inches 28.2 inches 30.0 inches
Answer:
10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
[tex]a=12\ in, b=15\ in[/tex]
Applying the Pythagoras Theorem
Find the length of the hypotenuse
[tex]c^{2}=a^{2} +b^{2}[/tex]
substitute
[tex]c^{2}=12^{2} +15^{2}[/tex]
[tex]c^{2}=369[/tex]
[tex]c=19.2\ in[/tex]
Second case
The given lengths are one leg and the hypotenuse
so
[tex]a=12\ in, c=15\ in[/tex]
Applying the Pythagoras Theorem
Find the length of the other leg
[tex]b^{2}=c^{2} - a^{2}[/tex]
substitute
[tex]b^{2}=15^{2} - 12^{2}[/tex]
[tex]b^{2}=81[/tex]
[tex]b=9\ in[/tex]
Find the difference between the two possible lengths of the third side of the triangle
so
[tex]19.2-9=10.2\ in[/tex]
Answer:
10.2
Step-by-step explanation:
is a pimp ting
help me i need this please
Answer:
B.
Step-by-step explanation:
P(something not happening)+P(something happening)=1 or 100%.
So if we have
P(something not happening)+40%=100%
Then the P(something not happening)=60% since 60%+40%=100%.
Yes I was using the event="something not happening" as the complement of something happening.
In fancy notation, some people might write:
[tex]P(A)+P(A')=1[/tex]
or
[tex]P(A)+P(A^c)=1[/tex]
(02.01 LC)
Is the following relation a function?
x y
1 4
−1 −2
3 10
5 16
Yes
No
Yes or no?
Yes. You should add commas next time to make it easier to read.
Answer:
Yes this is a function..
Step-by-step explanation:
We have to see the inputs and outputs for the function.
Here x represents input and y represents output.
For a relation to be a function there should be no repition in domain or input of the function i.e. every element in domain should be unique.
The domain for given relation is:
{1,-1,3,5}
All the inputs are only once mapped to the output so this relation is a function ..
Find the length of the segment indicated.
Answer: The length of the indicated segment is 14.45 units.
Step-by-step explanation: We are given to find the length of the indicated segment.
From the figure, we note that
A chord is bisected by the radius of the circle that makes a right-angled triangle with hypotenuse measuring 16.1 units and the other two sides measures x units and 7.1 units.
Using Pythagoras theorem, we get
[tex]x^2+7.1^2=16.1^2\\\\\Rightarrow x^2+50.41=259.21\\\\\Rightarrow x^2=259.21-50.41\\\\\Rightarrow x^2=208.8\\\\\Rightarrow x=\pm\sqrt{208.8}\\\\\Rightarrow x=\pm14.45.[/tex]
Since x is the length of side of a triangle, so we get
x = 14.45.
Thus, the length of the indicated segment is 14.45 units.
Choose the equation that represents a line that passes through points (−1, 2) and (3, 1). A)4x − y = −6 B)x + 4y = 7 C)x − 4y = −9 D)4x + y = 2
Answer:
B.
Step-by-step explanation:
I think I'm going to go with the plug in method here.
If you get the same value on both sides, then the point is contained on the line.
A)
4x-y=-6
Test (-1,2): 4(-1)-2=-6
4(-1)-2=-6
-4-2=-6
-6=-6
True; the equation holds for (-1,2).
Test (3,1): 4(3)-1=-6
4(3)-1=-6
12-1=-6
11=-6
False; the equation doesn't hold for (3,1).
A isn't the right choice.
B)
x+4y=7
Test (-1,2): -1+4(2)=7
-1+4(2)=7
-1+8=7
7=7
True, the equation holds for (-1,2).
Test (3,1): 3+4(1)=7
3+4(1)=7
3+4=7
7=7
True, the equation holds for (3,1).
Since the equation held for both (-1,2) and (3,1) then B is the right answer.
-------------------Let's also go ahead and find the equation another way:
(3,1) and (1,-2) are points on your line.
I'm going to write an equation for these points in slope-intercept form first which is y=mx+b where m is slope and b is y-intercept.
I will then rearrange into standard form like your choices are in.
m=slope=rise/run.
To find this, I like to line up the points and subtract and then put 2nd difference over 1st difference.
Like so:
(-1,2)
-(3,1)
---------
-4 1
The slope is 1/-4 or -1/4.
So the equation so far is y=-1/4 x+b since m=-1/4.
Now to find b, I'm going to use y=-1/4 x +b along with one of the given points on the line like (x,y)=(-1,2).
y=-1/4 x+b
2=-1/4 (-1)+b
2=1/4+b
Subtract 1/4 on both sides:
2-1/4=b
7/4=b
So the equation of the line is y=-1/4 x +7/4.
Now the goal is to write in ax+by=c form where a,b,c are integers.
Multiply both sides of y= -1/4 x +7/4 by 4 giving you:
4y=-1x+7
Add 1x on both sides:
1x+4y=7
or
x+4y=7 since 1x=x
So x+4y=7 is the answer if you prefer this way. Well anyway you prefer, this is the correct standard form for this line.
The equation of line that passes through points (-1, 2) and (3, 1) will be
x + 4y = 7
Option B is true.
What is Equation of line?
The equation of line with slope m and y intercept at point b is given as;
y = mx + b
Given that;
The points on the line are (-1, 2) and (3, 1).
Since, The equation of line will be;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁)/ (x₂ - x₁) is slope of the line.
And, (x₁, y₁) is the point on the line.
Thus, Slope = (1 - 2) / (3 - (-1))
= (-1)/4
= -1/4
So, The equation of line with slope -1/4 and point (-1, 2) will be;
y - 2 = -1/4 (x - (-1))
4 (y - 2) = - 1(x + 1)
4y - 8 = -x - 1
x + 4y = 8 - 1
x + 4y = 7
So, The equation of line that passes through points (-1, 2) and (3, 1) will be
x + 4y = 7
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Jayne is studying urban planning and finds that her town is decreasing in population by 3%
each year. The population of her town is changing by a constant rate.
True
False
Answer:
True
Step-by-step explanation:
Let, [tex]P_0[/tex] be the initial population,
Given,
The population is decreasing by 3% each year,
Thus, the population after t years would be,
[tex]P=P_0 (1-\frac{3}{100})^t[/tex]
[tex]\implies P=P_0(1+\frac{-3}{100})^t[/tex]
Since, if a population is changing by a constant rate then the population after t years is,
[tex]P=P_0(1+\frac{r}{100})^t[/tex]
Where, r is the rate of changing per period.
Hence, in the given situation the population is changing by the constant rate.
Given that f(x) = x2 – 7x – 1, g(x) = 2x – 3, and h(x) = 4x – 5 find each function.
(f + g)(x)
options:
A) x2 – 5x – 4
B) x2 – 11x + 4
C) x2 – 3x – 6
D) x2 – 5x – 6
Answer:
A)
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
now plug in the expressions of f(x) and g(x) :
(f+g)(x) = [tex]x^{2} -7x-1 + 2x-3[/tex]
we combine like terms we get :
(f+g)(x) = [tex]x^{2} -7x+2x -1-3[/tex]
we simplify we get :
(f+g)(x)=[tex]x^{2} -5x-4[/tex]
so the answer is A)
Answer:a
Step-by-step explanation:
cos155° = _____ -cos25° cos 55° cos(-25)°
Answer:
- cos 25°
Step-by-step explanation:
Cosine function is one of the trigonometric functions. Cosine function is regarded as an even function, which means that f(-x) = f(x). Also, cosine function is positive in the first quadrant and the last quadrant and negative in the second quadrant and the third quadrant. 155° lies in the second quadrant since 155° is smaller than 180°. Therefore, the basic angle or the reference angle of 155° is 180° - 155° = 25°. We know that cos 155° will be negative because it lies in the second quadrant and cos 25° will be positive because it lies in the first quadrant. Since cos 55° is positive, and cos (-25°) = cos 25° by the even function property, therefore option 2 and option 3 are incorrect since cos 155° is negative. Therefore, option 1 is the correct answer i.e. cos 155° = - cos 25°!!!
Answer:
- [tex]cos25^{o}[/tex]
Step-by-step explanation:
Hope This Helps!!!
When the polynomial in P(x) is divided by (x + a), the remainder equals P(a)
Answer:
This is a false statement:
Step-by-step explanation:
According to Remainder Theorem dividing the polynomial by some linear factor x + a, where a is just some number. As a result of the long polynomial division, you end up with some polynomial answer q(x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r(x).
P(x)= (x+/-a) q(x)+r(x)
P(x)=(x+a) q(x)+r(x). Note that for x=-a
P(-a)=(-a+a) q(-a)+r(-a)= 0* q(-a)+ r(-a)
P(-a)=r(-a)
It means that P(-a) is the remainder not P(a)
Thus the given statement is false....
Which statement is true about the diagram
(Picture is added)
Answer:
3
Step-by-step explanation: