Match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
Screenshot of the tiles below
(Please help)
The We have given that the pairs of values of f(x) and g(x) with the corresponding values of h(x) s given below.
(x^2-9)/(x-3)
x^2-4x+3/x-3
x^2+4x-5/x-1
x^2-16/x-4
We have to match the pairs of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).
What is the function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
1)f(x)/g(x)=(x^2-9)/(x-3)=x+3
2)f(x)/g(x)=x^2-4x+3/x-3=x+1
3)f(x)/g(x)=x^2+4x-5/x-1=x+5
4)f(x)/g(x)=x^2-16/x-4=x+4
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PLEASE HELP!!! Evaluate Show your work.
Answer:
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
Step-by-step explanation:
Given: [tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Simplify the expression.
[tex]\Rightarrow \sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Distribute [tex]\sqrt{7x}[/tex] over parentheses
[tex]\Rightarrow \sqrt{7x}\cdot\sqrt{x}-\sqrt{7x}\cdot7\sqrt{7}[/tex]
[tex]\Rightarrow \sqrt{7x^2}-7\sqrt{7^2x}[/tex]
square term take out from square root
[tex]\Rightarrow x\sqrt{7}-7\cdot 7\sqrt{x}[/tex]
[tex]\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
what are the roots of the polynomial equation x3-7x=6x-12? Use a graphing calculator and a system of equations.
The roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a polynomial equation:
x³ - 7x = 6x - 12
[tex]\rm x^3-7x+12=6x[/tex]
x³ - 13x + 2 = 0
(x - 1)(x -3)(x + 4) = 0
x = 1, 3, -4
Thus, the roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.
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Which of the following equations describes the graph shown?
A.) y = x+2
B.) y = -x - 2
C.) y = x - 2
D.) y = -x + 2
Answer: The correct option is (D) y = -x + 2.
Step-by-step explanation: We are to select the correct equation that describes the given graph.
We can see that the graph is a straight line passing through the points (0, 2) and (1, 1).
So, the slope of the line will be
[tex]m=\dfrac{2-1}{0-1}=-1.[/tex]
Therefore, the equation of the line with slope m = -1 and passing through the point (0, 2) is given by
[tex]y-2=m(x-0)\\\\\Rightarrow y-2=-1\times x\\\\\Rightarrow y-2=-x\\\\\Rightarrow y=-x+2.[/tex]
Hence, the equation that describes the graph is y = -x + 2.
Thus, (D) is the correct option.
A hyperbola centered at the origin has a vertex at (3, 0) and a focus of the hyperbola is located at (9, 0). What are the equations of the directrices?
x = ±
To find the equations of the directrices for a hyperbola centered at the origin with a vertex at (3, 0) and a focus at (9, 0), we use the formula x = ±a/e. The hyperbola's directrices are x = ± 1.
Explanation:The student asked about the equations of the directrices for a hyperbola that is centered at the origin, with a vertex at (3, 0) and a focus at (9, 0). A hyperbola has two directrices, and each is a line that is perpendicular to the transverse axis and equidistant from the center as the foci are, but on the opposite side. The equation of a directrix can be found using the formula x = ±a/e, where 'a' is the distance from the center to the vertex and 'e' is the eccentricity, which is the ratio of the distance from the center to a focus (c) over 'a'.
In this case, the hyperbola is aligned along the x-axis. Given a vertex at (3, 0), it implies that 'a' is equal to 3. Since the focus is at (9, 0), it suggests 'c' is equal to 9. The eccentricity 'e' can be found by e = c/a, which is 9/3 = 3. Using the directrix formula x = ±a/e, the two directrices of the hyperbola would be x = ±(3/3), which simplifies to x = ± 1.
During a recent snowstorm in red hook ny Jaime notice that there were 4 inches of snow on the ground at 3:00p.m and there were 6 inches of snow on the ground at 7:00p.m. If she were to graph these data what does the slope of the line connecting these two point represent in the context of this problem
what is the degree of 12x^4-8x+4x^2-3
Answer:
The degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.
Step-by-step explanation:
The given polynomial is [tex]12x^4-8x+4x^2-3[/tex]
This polynomial is of one variable which is x. Hence, the degree of the polynomial is the highest exponent.
For the given polynomial, the highest exponent is 4.
Therefore, the degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.
Find the missing factor x(y+6)-5(y+6)( ) (y+6)
We are given the equation:
x (y + 6) – 5 (y + 6) ---> 1
We are to look for the missing factor in the equation: (_) (y + 6) from the given values.
Knowing the rules of the polynomial multiplicity, we can have an idea that the given equation can also be written in the form of:
(x – 5) (y + 6) ---> 2
wherein the whole factor (y + 6) was simply distributed to the values in the factor (x – 5). To prove that equations 1 and 2 are equal:
x (y + 6) – 5 (y + 6) = (x – 5) (y + 6)
Expanding:
x y + 6 x - 5 y – 30 = x y + 6 x – 5 y – 30 (EQUAL!)
Therefore our missing factor is:
(x – 5)
Find all solutions to the equation in the interval [0, 2π). cos 2x - cos x = 0
Answer:
The other answer is correct here except it is missing the answer 4pi/3
other wise its correct. The answers are 0, 2pi/3, and 4pi/3
Step-by-step explanation:
see previous answer
I NEEED HELPOPOP!!!!
PLEASE ASSIT ME FOR TWO MATH QUESTIONS
Margie and four friends are eating lunch at a restaurant. The total bill is $52.50 before tax and tip. Margie has a coupon good for $10off their total purchase. If sales tax of 6 percent is collected on the discount amount, what is the total cost after tax?
A baseball team has won 13 out of 18 games they played this session. How many additional games must the team win in a row to raise its winning percentage to 80%?
A) 7
B) 14
C) 5
D) 24
Find the prime factors of each of the following numbers. a. 25 b. 38 c. 36 d. 285 e. 650 f. 1,740
Answer:
The prime factors are:
a. 5 and 5 (5 × 5 = 25)
b. 2 and 19 (2 × 19 = 38)
c. 2, 2, 3, and 3 (2 × 2 × 3 × 3 = 36)
d. 3, 5, and 19 (3 × 5× 19 = 285)
e. 2, 5, 5, and 13 (2 × 5 × 5 × 13 = 650)
f. 2, 2, 3, 5, and 29 (2 × 2 × 3 × 5 × 29 = 1,740)
Step-by-step explanation:
straight from Penn
What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?
Which polynomial is a perfect square trinomial?
A. 36x²-18x-9
B. 4a²-28a-49
C. 25b²-40b+16
D. 4x²-6x+9
what level of measurement is qualitative? Nominal? Ordinal? Interval? Or ration?
What is the polygon being rotated to create the brown quilt block pattern?
Answer with explanation:
The pre image which is in blue color is parallelogram.
There are four blue parallelograms here,congruent to each other,each one of them when rotated by certain angle ,gives parallelogram in brown color.
When we rotate a polygon,after rotation neither the shape nor the size of polygon changes.The two shapes are congruent to each other.
→The Polygon being rotated to create the brown quilt block pattern is
Option C: Parallelogram
Determine the distance between a(-1, 2,3) and b(4,-5, 6) to the nearest tenth
If 35% of a natural area is to be developed, leaving 500 acres untouched, how many acres are to be developed?
Answer:
Area to be developed = 269.23 acres
Step-by-step explanation:
Let there is A acres natural area to be developed.
If 35% of A acres is developed then untouched area will be (100 - 35 = 65%)
Now it has been given in the question that 65% of A (untouched area) = 500 acres
[tex]A.\frac{65}{100}=500[/tex]
[tex]A=\frac{500}{0.65}=769.23[/tex]
So area of the natural field = 769.23 acres
Now 35% of the natural area which is to be developed = A×35%
[tex]=769.23.\frac{35}{100}=(769.23)(.35)=269.23[/tex]
Area of the natural area to be developed is 269.23 acres
The number of acres that are to be developed is 269 acres.
Number of acresUsing this formula
Number of acres=(Number of acres untouched/(100%-Percentage of natural area)×Percentage of natural area
Let plug in the formula
Number of acres=500 acres/(100%-35%)×35%
Number of acres=(500 acres/65%)×35%
Number of acres=769.23×35%
Number of acres=269 acres
Inconclusion the number of acres that are to be developed is 269 acres.
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Help Please!!!!!!
f(x)=5x^2+9x−4
g(x)=−8x^2−3x−4
Find (f+g)(x)
My Options Are...:
a. 3x^2+6x−8
b. −3x^3+6x^2−8x
c. −3x^4+6x^2−8
d. −3x^2+6x−8
What is the equation of a line that has a slope of -5 and passes through the point (0, 2)?
If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
m∠A = 15° and m∠C = 35°
m∠A + m∠B = 155°
m∠A + m∠C = 60°
m∠A = 20° and m∠C = 30°.
Solve 152x = 36. Round to the nearest ten-thousandth.
A. 0.6616
B. 2.6466
C. 1.7509
D. 1.9091
Since no one was getting the the answer that is on the assignment I plugged the problem into an algebra calculator, and got A 0.6616
the square has a radius of 3 square root 2 what is the apothem?
The apothem of the square is equal to half the length of a side of the square, which can be calculated by doubling the radius. In this case, the apothem is 3√2.
Explanation:The apothem of a square is a line segment drawn from the center of the square to any side of the square, perpendicular to that side. The apothem is equal to half the length of a side of the square.
Given that the square has a radius of 3√2, we can determine the length of a side of the square by doubling the radius. So, the length of a side is 2 * 3√2 = 6√2.
Therefore, the apothem of the square is half the length of a side, which is (6√2)/2 = 3√2.
Fill in the missing term in the equation. x/x^2-4x+4-x/x^2-3x+2=?/(x-2)^2(x-1)
Answer:
The missing term is x.
Step-by-step explanation:
Given expression is,
[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}------(1)[/tex]
Since, [tex]x^2-4x+4=(x)^2-2\times (2x)+(2)^2[/tex]
[tex]\implies x^2-4x+4=(x-2)^2------(2)[/tex] ( (a-b)² = a² - 2ab + b² )
Now, [tex]x^2-3x+2=x^2-2x-x+2[/tex] ( By middle term splitting )
[tex]=x(x-2)-1(x-2)[/tex]
[tex]\implies x^2-3x+2=(x-1)(x-2)------(3)[/tex]
From equation (1), (2) and (3),
[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}=\frac{x}{(x-2)^2}-\frac{x}{(x-2)(x-1)}[/tex]
[tex]=\frac{x(x-1)-x(x-2)}{(x-2)^2(x-1)}[/tex]
[tex]=\frac{x(x-1-x+2)}{(x-2)^2(x-1)}[/tex]
[tex]=\frac{x(1)}{(x-2)^2(x-1)}[/tex]
[tex]=\frac{x}{(x-2)^2(x-1)}[/tex]
Hence, the missing term in the equation is x.
He nine ring wraiths want to fly from barad-dur to rivendell. rivendell is directly north of barad-dur. the dark tower reports that the wind is coming from the west at 68 miles per hour. in order to travel in a straight line, the ring wraiths decide to head northwest. at what speed should they fly (omit units)?
This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).
Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:
sin θ = opposite side / hypotenuse
sin 45 = 68 miles per hr / flight
flight = 68 miles per hr / sin 45
flight = 96.17 miles per hr
What is the value of 35+20/5-4*7
11
49
245
35
Hellllpp :)
Write cos 53 degrees in terms of sine.
The value of cos 53 degrees in terms of sine is,
⇒ sin 37 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
⇒ cos 53 degree
Hence, We can change it into sine as;
⇒ cos 53 degree
⇒ sin (90 - 53)
⇒ sin 37 degree
Thus, The value of cos 53 degrees in terms of sine is,
⇒ sin 37 degree
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In the triangle below, determine the value of a.
PLEASE HELP ASAP 20 POINTS PLUS BRAINIEST!
Find the greatest possible error for each measurement.
3 ft
a.
1 ft
b.
1/2 ft
c.
1/4 c
d.
1/6 c
the greatest possible error when measuring in feet is 1/2 foot
answer is B