Answers
Answer:
[tex](f-g)(x)=x^2-6x+5[/tex] dom: (-∞,∞)
[tex](\frac{f}{g})(x)=x-7+\frac{7}{x+2}[/tex] dom: (–∞,–2)u(–2,∞)
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)=(x^2-5x+7)-(x+2)[/tex] *distribute the negative sign into (x+2)!
[tex]x^2-5x+7-x-2\\x^2-6x+5[/tex]
a parabola (anything that begins with [tex]x^2[/tex]) will have a domain of (-∞,∞) or all real numbers!!
[tex](\frac{f}{g} )(x)= \frac{x^2-5x+7}{x+2}[/tex] use synthetic division to divide (the attached picture)
domain: Because the graph is not continuous, you have to write the domains on both sides of the asymptote which is (-∞,-2)u(-2,∞)
synthetic division:
1. take the divisor (x+2) and solve for x. x= –2 this goes in the top left corner
2. write the numbers AND their signs on the top row. if there is no number and just the variable (like [tex]x^2[/tex] ) just write 1.
3. the first number gets pulled down
4. multiply -2 by 1 and subtract it from –5. (-5-2= -7)
multiply -2 by -7 and add that to the next number in the top row which is -7. (-7 + 14=7)
5. the first number in the bottom row of numbers is the first number in the answer but with one less exponent than the dividend. **write 1 as x**
6. the last number in the bottom row, if it is not 0, is a remainder. write it as that number over the divisor. in this case the remainder is 7. so write it as [tex]\frac{7}{x+2}[/tex]
Related Questions
Help please having trouble solving these two problems
Answers
Answer:
First function:
Zeros = 6 and -6. Y-intercept = (0,72). X-intercepts = (6,0) and (-6,0).
Second function:
Zeros = 3 and -3. Y-intercept = (0, -27). X-intercepts: (3, 0) and (-3, 0).
Step-by-step explanation:
The zeros are x-intercept numbers.
The y-intercept can be found when the function is in standard form. Plug in 0 for x, then solve.
Hope this helps!
Answer:
1. x₁ = 6, x₂ = -6
2. x₁ = 3, x₂ = -3
Step-by-step explanation:
Given functions:
[tex]1)\ f(x) = -2(x-6)(x+6)[/tex]
[tex]2)\ f(x)=(x-3)(3x+9)[/tex]
..................................................................................................................................................
Zero Product Property: If m • n = 0, then m = 0 or n = 0.
Standard Form of a Quadratic: ax² + bx + c = 0.
..................................................................................................................................................
1. f(x) = -2(x - 6)(x + 6)
Step 1: Set the function to zero.
[tex]\implies 0 = -2(x-6)(x+6)[/tex]
Step 2: Divide both sides of equation by [tex]-2[/tex].
[tex]\implies \dfrac{0}{-2} = \dfrac{-2(x-6)(x+6)}{-2}[/tex]
[tex]\implies 0=(x-6)(x+6)[/tex]
Step 3: Apply the Zero Product Property.
[tex]x_1 \implies x-6=0[/tex]
[tex]x_2 \implies x+6=0[/tex]
Step 4: Solve for x in both equations.
[tex]x-6+6=0+6 \implies \boxed{x_1 = 6}[/tex]
[tex]x+6-6=0-6 \implies \boxed{x_1 = -6}[/tex]
The zeros (x-intercepts) of this function are: [tex]x_1=6,\ x_2=-6[/tex].
.................................................................................................................................................
2. f(x) = (x - 3)(3x + 9)
Step 1: Set the function to zero.
[tex]\implies 0 = (x - 3)(3x + 9)[/tex]
Step 2: Apply the Zero Product Property.
[tex]x_1 \implies x-3=0[/tex]
[tex]x_2 \implies 3x + 9=0[/tex]
Step 3: Solve for x in both equations.
[tex]x-3+3=0+3 \implies \boxed{x_1 = 3}[/tex]
[tex]3x=-9 \implies \dfrac{3x}{3}=\dfrac{-9}{3} \implies \boxed{x_1 = -3}[/tex]
The zeros (x-intercepts) of this function are: [tex]x_1=3,\ x_2=-3[/tex].
..................................................................................................................................................
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The solution to the system of equations shown is (2, 0).
3x − 2y = 6
x + 4y = 2
When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14
.
Which system of equations will also have a solution of (2, 0)?
Answers
Answer:
7x = 14
x + 4y = 2
Step-by-step explanation:
3x − 2y = 6
x + 4y = 2
6x - 4y = 12
x + 4y = 2
-----------------------
7x = 14 Replace the first equation with this one.
Suppose you have 5 riders and 5 horses, and you want to pair them off so that every rider is assigned one horse (and no horse is assigned two riders). How many ways can you do this?
Answers
There are 120 ways in which 5 riders and 5 horses can be arranged.
We have,
5 riders and 5 horses,
Now,
We know that,
Now,
Using the arrangement formula of Permutation,
i.e.
The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],
So,
For n = 5,
And,
r = 5
As we have,
n = r,
So,
Now,
Using the above-mentioned formula of arrangement,
i.e.
The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],
Now,
Substituting values,
We get,
[tex]^5N_5 = \frac{5!}{(5-5)!}[/tex]
We get,
The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,
So,
There are 120 ways to arrange horses for riders.
Hence we can say that there are 120 ways in which 5 riders and 5 horses can be arranged.
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Can someone help with this problem please.
A sheet of paper, 12 inches by 18 inches, is folded so that 2 opposite corners touch, as shown in the figures below. What is the area, in square inches, of the shaded triangle formed as the result of the overlap. (Please look at the picture!)
Answers
The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²
Calculation of the equilateral triangleAfter folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.
An equilateral triangle is a type of triangle where by all the three sides are equal.
To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.
Using the formula for the area of an equilateral triangle,
A = √¾ a²
a= 12 inches
A = √¾ ×12²
A = 62.35 inches ²
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Answer:
Its 78!!!!
Solution:
1/2(12 * 18 - 5 * 12) = 78
A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft. Josh decides to make the house addition smaller, and he changes the scale of the drawing to 1 in. = 1.1 ft.
What is the change in the scale factor from the old scale to the new scale?
Answers
The change in the scale factor from the old scale to the new scale is 3.
What is the change in the scale factor?A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension.
The change in the scale factor = larger scale / smaller scale
3.3 / 1.1 = 3
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PLEASE HELP I GIVE 95 POINTS
Answers
3^x is positive, and the y-in. is 1.
3^0 = 1
Process of elimination.
Determine the area of the figure.
Answers
Answer: 3x - 6 (in^2)
Step-by-step explanation:
base * height / 2
=
3 ( 2x - 4) / 2 (in^2)
= 3x - 6 (in^2)
Answer: 3x-6 in^2
Step-by-step explanation:
There is no way to figure out what x is without additional information, so you have to leave the answer in this form
Question 5 of 15
What would be the best first step in solving this system
x²-3x + 2y = -4
y = 3x + 2
Answers
Now you can equate it with second one to get x
Answer:
Substitute y = 3x + 2 into x² - 3x + 2y = -4
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x^2-3x+2y=-4\\y=3x+2\end{cases}[/tex]
Since y is already isolated in the second equation, the best first step would be to substitute the second equation into the first equation, then solve for x.
Substitute equation 2 into equation 1:
[tex]\implies x^2-3x+2(3x+2)=-4[/tex]
Expand the brackets and simplify so that the equation equals zero:
[tex]\implies x^2-3x+6x+4=-4[/tex]
[tex]\implies x^2+3x+4+4=0[/tex]
[tex]\implies x^2+3x+8=0[/tex]
Now use the Quadratic Formula to solve for x.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Define the variables:
[tex]\implies a=1, \quad b=3, \quad c=8[/tex]
Substitute the values into the formula and solve for x:
[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(8)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{-23}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{-1 \cdot 23}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{-1}\sqrt{23}}{2}[/tex]
Remember that [tex]i^2=-1[/tex]
[tex]\implies x=\dfrac{-3 \pm i\sqrt{23}}{2}[/tex]
Therefore, the solutions to the system of equations are:
[tex]x=\dfrac{-3 + i\sqrt{23}}{2}, \quad \dfrac{-3 - i\sqrt{23}}{2}[/tex]
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Question 1
Which equation represents the relationship shown in the table
at the right?
Answers
Answer:
Option (4)
Step-by-step explanation:
When x = 0, y = -3.
Eliminate Option 1.Also, the slope is
[tex]\frac{-1-(-3)}{1-0}=2[/tex]
So, the equation is y = 2x - 3.
how do you graph y=12/x
Answers
Answer: [tex]\frac{12}{x}[/tex] is an asymptote
Step-by-step explanation:
Apply a table, and plug in values of x into the equation. For example f(2)=[tex]\frac{12}{2} =6[/tex]. That's one of the points on the graph that we just found (2,6)
which of the following points could be added to the graph f(x)=-|x+3| to keep the graph a function?
a.(0.3) b.(-3,-6)
c. both a and b d. none of the above
Answers
None of the points could be added to the graph f(x)=-|x+3| to keep the graph a function
How to determine the point?The equation of the function is given as:
f(x) = - |x + 3|
The points are given as:
(0, 3) and (-3, -6)
When x = 0, we have:
f(0) = - |0 + 3|
f(0) = -3 --- different y value from (0, 3)
When x = -3, we have:
f(-3) = - |-3 + 3|
f(-3) = 0 --- different y value from (-3, -6)
This means that the x values point to different y values (this does not represent a function)
Hence, none of the points could be added to the graph f(x)=-|x+3| to keep the graph a function
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PLS HELPPP!!!! Look at pic
Answers
The correct option regarding whether the equation x² = y² is a function is:
No, since if you solve the equation for x, then [tex]x = \pm y[/tex]
What is needed for a relation to represent a function?In a function, each value of x can be associated with only one value of y.
In this problem, the equation is:
[tex]x^2 = y^2[/tex]
Then:
[tex]x = \pm \sqrt{y^2}[/tex]
[tex]x = \pm \sqrt{y}[/tex]
x is associated with two values, [tex]-\sqrt{y}[/tex] and [tex]\sqrt{y}[/tex], hence it is not a function.
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A map's numerical coordinates are in kilometres. Town A is at (16.3, 2.9) and town B is at
(4.5, 6.3). A road is to be constructed on a direct line between the two towns. Each town is
responsible for the construction up to the mid-point at a cost of $150 000 for each kilometre.
Determine the cost for each town.
Answers
Answer:
$92,250 per town
Step-by-step explanation:
See attached image.
The two towns may be connected with a straight line, the road, that can be made into the hypotenuse of a right triangle. The twio sides are calculated from the coordinates and shown in the image. Then use the phythagorean theorem to calculate the hypotenuse. The towns are 12.3 km apart. The total road cost would be:
($150,000/km)(12.3 km) = $1,845,000, or $92,250 per town.
Irene knows her blood type is A, but William does not know his blood type. However, William knows that his mother and father both had blood type B. Irene and William's first child is a boy with type O blood. Based on this information, William's blood type could be
Answers
Based on this information, William's blood type could be either B or O.
What is Segregation of alleles?
Allele pairs (several features of the same gene) are segregated during meiosis so that they can be transferred selectively to different gametes.During meiosis, maternal and paternal alleles separate.What is genotype vs phenotype ?
Genotype: An organism's genetic makeup. Phenotype. physical characteristic that arises within an organism as a result of its genotype. Probability law.Genotype - the set of alleles that make up an organism.How does genotype influence phenotype ?
The alleles you have for a specific gene or collection of genes are referred to as your genotype. The physical attribute itself, or phenotype, can be affected by both genotype and environmental variables.Learn more about Genotype
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Complete the sentence using the following formula. Enter your answer using digits.
area
The length of a rectangle can be found using the following formula: length width
The length of a rectangle that has a width of 2.5 cm and an area of 20.5 cm² is __ cm.
Answers
Answer: 8.2 cm
Step-by-step explanation:
Area of a rectangle = l x w
[tex]A= 25 cm^{2}[/tex]
[tex]l= ?[/tex]
[tex]w= 2.5 cm[/tex]
[tex]25cm^{2} = l(2.5cm)[/tex]
Rearrange the equation to get Length by itself[tex]\frac{25cm^{2} }{2.5cm}= l[/tex]
[tex]8.2 cm=l[/tex]
Write the expanded expression in expanded form using the definition of an exponent.
2wz^2?
Answers
The expanded form of the given expression is 2 × w × z × z
Writing an expressionFrom the question, we are to determine the expanded form of the given expression
The given expression is
2wz²
To write an expression in an expanded form, we will write the expression as a repeated multiplication in the simplest way possible.
To do this, we will first expand the index in the given expression.
The index in the given expression is z²
Thus, we get
z² = z × z
Now, we will include the remaining individual terms in the expression and write them as product.
That is,
2wz² = 2 × w × z × z
Hence, the expanded form of the given expression is 2 × w × z × z
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In 2015, around ____ percent of the world’s population had an internet connections.
Answers
"The average speed of a vehicle and the distance it covers in a period " Is this a direct proportion
Answers
Answer:
Yes
Step-by-step explanation:
As the Average speed increases, the amount of distance covered will increase. As the average speed decreases, the amount of distance traveled will decrease as well over a certain period.
Convert 10000 seconds in to the number of equivalent hours minutes and seconds
Answers
Answer:
2 hours 46 minutes and 40 seconds
Step-by-step explanation:
First we divide by 60 to find how many minutes are in 10000 seconds :
10000÷60 = 166 minutes with remainder 40 seconds
If 166 minutes and 40 seconds is 100000 seconds then we change 166 minutes into hours and minutes :
We do this by dividing 166 by 60 :
166 ÷ 60 :
2 hours Remainder 46 minutes
So our final answer is :
2 hours 46 minutes and 40 seconds
Hope this helped and have a good day
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answers
Answer: [tex]\triangle RQP \sim \triangle VPW[/tex]
Step-by-step explanation:
By the corresponding angles theorem, [tex]\angle RPQ \cong \angle VWP[/tex] and [tex]\angle RQP \cong \angle VPW[/tex].
Therefore, [tex]\triangle RQP \sim \triangle VPW[/tex] by AA.
Please explain the answer before, and also help with number line!
Answers
The solution to the given inequality is x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
Number line and inequalityGiven the inequality expression as shown
6x + 6 < -30
Subtract 6 from both sides
6x < -30 - 6
6x < -36
Divide through by 6
x < -36/6
x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
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What is the
y-intercept
of this line?
Answers
Answer: (0, 3)
Step-by-step explanation:
The y-intercept of the line is where the line intercepts the y-axis. In other words, the coordinate value of the line when x is 0.
Answer: (3, 0)
Step-by-step explanation:
y-intercept = y=a number and x=0
So, y=3, x=0.
(3, 0)
I need to find the equation of the line
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line
Answer:
y = 3x + 3
Step-by-step explanation:
See attached image.
Determine the measure of
Answers
Answer:
M: 74.579° = 74°34'43" = 1.30164
O: 49.421° = 49°25'17" = 0.86256 rad
Lola has collected 935 buttons. what is the number of buttons rounded to the nearest ten?
Answers
Answer:
940
Step-by-step explanation:
Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940
if the length of a rectangle is decreased by 2cm and the width is increased by 6 cm the result will be a square the area of this square will be 64 cm^2 greater than the area of a rectangle find the area
Answers
The area of the rectangle is 105 square cm
How to determine the rectangle area?Represent the dimensions of the rectangle with x and y
So, the length of the square would be:
Length = x - 2
Width = y + 6
The areas are then calculated as:
Rectangle = xy
Square = (x -2)(y + 6)
The relationship between the areas is:
(x -2)(y + 6) = 64 + xy
Expand
xy + 6x - 2y - 12 = 64 + xy
This gives
6x - 2y - 12 = 64
Add 12 to both sides
6x - 2y= 76
Divide through by 2
3x - y = 38
By trial by error, we have:
x = 15 and y = 7
The rectangle area is then calculated as:
Rectangle = xy
This gives
Rectangle = 15 * 7
Evaluate
Rectangle = 105
Hence, the area of the rectangle is 105 square cm
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Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?
15x – 15 = 15x – 24
15x – 5 = 15x – 24
39x – 45 = 15x – 24
39x – 15 = 15x – 24
Answers
The equivalent equation of the given equation is 39x - 45 = 15x - 24.
Hence, option C) is the correct answer.
What is the equivalent of the given equation?Given the equation; 3[x + 3(4x – 5)] = 15x – 24
We expand and collect like terms
3[x + 3(4x – 5)] = 15x – 24
3( x + 12x - 15 ) = 15x - 24
3x + 36x - 45 = 15x - 24
We add the like terms on both sides
39x - 45 = 15x - 24
Therefore the equivalent equation of the given equation is 39x - 45 = 15x - 24.
Hence, option C) is the correct answer.
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There are 752 cal in 8 ounces of a certain ice cream how many calories are there in 2 pounds
Answers
752 calories * 4 = 3008 calories in 2 pounds of ice cream.
Again pls help out!
Answers
Answer:
okay so I think its, horizontal shift right 2 and a vertical shift down 1
Step-by-step explanation:
so x says + 2 so right 2 and y says -y so down 1..?
I'm kinda rusty tho so yeah
A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid m. what is the shape of the cross section?
Answers
The cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.
If the peak of the rectangular pyramid is directly above the center of the base, it creates a perpendicular to the base, indicating the height of the pyramid. This type of rectangular pyramid is known as the right rectangular pyramid.
A rectangle is a quadrilateral, that is a closed figure with 4 line segments, with all four interior angles at 90°.
When we slice a right rectangular pyramid vertically down at the red line by a plane, not passing through the vertex, of the pyramid will be a dilated image of its base.
A dilated image is an enlarged or diminished image of the preimage, similar with all angles.
Thus, the cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.
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For complete question, refer to the attachment.
Answer:trapozoid
Step-by-step explanation: