Choose the correct graph to fit the inequality.
x ^2 - y^ 2 <9
Answer:
It is the second one
⇒The given inequality is
x²-y²<9
[tex]\frac{x^2}{3^2}-\frac{y^2}{3^2}<1[/tex]
⇒The general equation of Hyperbola is
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
→The curve will cut the x axis at (3,0) and (-3,0).
So, the given function matches with the curve of Hyperbola.
⇒When the points are from [-3,3] , the function will satisfy the given Inequality.That is if you take , points prescribed in the given interval the function will satisfy the inequality.
⇒Graph B
Suppose the number of items you can deliver in a day is a random variable with some unknown distribution with a mean = 35 and a standard deviation of 8. What is the probability a random sample of 36 days would have a mean between 32.6 and 34.6?
Answer:
P = 0.3462
Step-by-step explanation:
See attached photo for work.
We have a sample mean of 35, a sample standard deviation of 8, and a sample size of 36.
You need to see that the probability of the number of items you can deliver in a day is between 32.6 and 34.6.
The answer is 0.3462, so there's about a 34.62% chance that you will deliver an average of 32.6 to 34.6 packages per day.
The probability a random sample of 36 days would have a mean between 32.6 and 34.6 is 0.3462
What is probability?The chance of happening of an event is called probability.Probability is always less then 1 What is mean?Mean is actually the average of all the observations.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean
What is z-score?A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
How to find the probability of the random sample?According to the problem,
Mean = 35Standard Deviation = 8Sample = 36Here we need to find P(32.6 < x < 34.6)
Firstly we should find the z-score of 32.6 and 34.6[tex]z_{32.6}[/tex] = [tex]\frac{32.6-35}{\frac{8}{\sqrt{36} } }[/tex] = - 1.80
[tex]z_{34.6} = \frac{34.6-35}{\frac{8}{\sqrt{36} } }[/tex] = -0.30
∴ P(32.6 < x < 34.6) = P ( -1.80 < z < -0.30)
= P(z< -0.30) - P(z < -1.80)
= 0.3821 - 0.0359 = 0.3462
∴ The required probability is 0.3462
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Two boats leave an island at the same time. One of the boats travels 12 miles east and then 16 miles north. The second boat travels 24 miles south and then 18 miles west. Use the pythagorean theorem to find the distance between the boats.
Answer:
The distance between the boats is [tex]50\ mi[/tex]
Step-by-step explanation:
we know that
The Pythagoras Theorem states that
In a right triangle
[tex]c^{2}=a^{2}+b^{2}[/tex]
where
c is the hypotenuse
a and b are the legs
In this problem
Let
c ----> the distance between the boats
a -----> the horizontal distance between the boats
b -----> the vertical distance between the boats
[tex]a=12+18=30\ mi[/tex]
[tex]b=16+24=40\ mi[/tex]
substitute the values
[tex]c^{2}=30^{2}+40^{2}[/tex]
[tex]c^{2}=2,500[/tex]
[tex]c=50\ mi[/tex]
Final Answer:
The distance between the two boats is 50 miles.
Explanation:
To find the distance between the two boats after they have traveled, we need to determine the final position of each boat relative to the island, and then use the Pythagorean theorem to find the distance between these two positions. Let's go through the calculations step-by-step:
Step 1: Determine the final position of each boat relative to the island.
- Boat 1 travels 12 miles east and then 16 miles north. Let’s define east as the positive x-direction and north as the positive y-direction. So, the final coordinates of Boat 1 relative to the island are (12, 16).
- Boat 2 travels 24 miles south and then 18 miles west. Let’s define south as the negative y-direction and west as the negative x-direction. So, the final coordinates of Boat 2 relative to the island are (-18, -24).
Step 2: Determine the differences in the x and y coordinates between Boat 1 and Boat 2.
- The difference in x-coordinates dx is the x-coordinate of Boat 1 minus the x-coordinate of Boat 2:
[tex]\( dx = 12 - (-18) = 12 + 18 = 30 \)[/tex] miles.
- The difference in y-coordinates dy is the y-coordinate of Boat 1 minus the y-coordinate of Boat 2:
[tex]\( dy = 16 - (-24) = 16 + 24 = 40 \)[/tex] miles.
Step 3: Use the Pythagorean theorem to calculate the distance between the two boats.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse c (the side opposite the right angle) is equal to the sum of the squares of the other two sides a and b:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Here, dx and dy can be considered the lengths of the sides of a right triangle, and the distance between the boats d is the hypotenuse of this triangle. So:
[tex]\[ d = \sqrt{dx^2 + dy^2} \\\\\[ d = \sqrt{30^2 + 40^2} \\\\\[ d = \sqrt{900 + 1600} \\\\\[ d = \sqrt{2500} \\\\\[ d = 50 \][/tex]
Therefore, the distance between the two boats is 50 miles.
Condense the following logs into a single log:
[tex]8log_{g} x+5log_{g} y[/tex]
[tex]8log_{5} x+\frac{3}{4} log_{5} y-5log_{5} z[/tex]
QUESTION 1
The given logarithm is
[tex]8\log_g(x)+5\log_g(y)[/tex]
We apply the power rule of logarithms; [tex]n\log_a(m)=\log_(m^n)[/tex]
[tex]=\log_g(x^8)+\log_g(y^5)[/tex]
We now apply the product rule of logarithm;
[tex]\log_a(m)+\log_a(n)=\log_a(mn)[/tex]
[tex]=\log_g(x^8y^5)[/tex]
QUESTION 2
The given logarithm is
[tex]8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)[/tex]
We apply the power rule of logarithm to get;
[tex]=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)[/tex]
We apply the product to obtain;
[tex]=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)[/tex]
We apply the quotient rule; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex]
[tex]=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})[/tex]
[tex]=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})[/tex]
please help me!!
i need this ASAP
[tex]f(3)= \sqrt[3]{ \frac{x}{ - 7x + 1} } \: \: \: \: \: \\[/tex]
Answer:
f(3) = (-∛150)/10
Step-by-step explanation:
Put 3 where x is and evaluate. If you don't want the decimal, you can rationalize the denominator to get an exact form.
f(3) = ∛(3/(-7·3+1)) = ∛(-3/20)
= -∛(3·50/(20·50)) = (-∛150)/10 ≈ -0.5313292845913...
_____
Multiplying numerator and denominator by 50 makes the denominator 1000, a perfect cube.
A bag contains 6 red jelly beans, 4 green jelly beans, and 4blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?
The probability of picking a green jelly bean with the first pick is 4/14 = 2/7, because there are 14 jelly bean in total (6 red + 4 green + 4 blue) and 4 of them are green.
If you pick a green jelly bean at the beginning, you have 13 jelly beans remaining, of which 6 are red. So, the probability of picking a red jelly bean is now 6/13.
You want these two events to happen one after the other, to be more precise you want to pick a green jelly bean with the first pick AND a red jelly bean with the second pick. We know the probabilities of the two events, so we have to multiply them to get the probability of them happening both:
[tex]\dfrac{2}{7}\cdot\dfrac{6}{13}=\dfrac{12}{91}[/tex]
3 1/2 times 4 2/3 without simplest form
Answer:
12 2/6
Three times four is 12.
two times one is 2.
two times three is 6.
Answer:
3 1/2 x 4 2/3 = 98/6
*This is without simplest form*
In simplest form:
3 1/2 x 4 2/3 = 16 1/3
help idk "There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete
there are 13 small dogs that compete
Please answer this multiple choice question!
==========================
Explanation:
Triangle PQC is congruent to triangle RQC. We can prove this through use of the hypotenuse leg theorem (HL theorem). Note that PC = RC are congruent radii, and also note that CQ = CQ through the reflexive theorem. We have a pair of hypotenuses and a pair of legs for the right triangles.
Then through CPCTC (corresponding parts of congruent triangles are congruent), we know that the pieces PQ and QR are congruent. For now, let's just call them x. They must add to PR which is 12, so,
PQ + QR = PR ..... segment addition postulate
x + x = 12
2x = 12
x = 6 ..... divide both sides by 2
QR = 6
This shows that if you have a radius perpendicular to a chord of a circle, then the radius will bisect this chord. Bisect means to cut in half.
Step-by-step Answer:
There is a theorem in geometry that states that a perpendicular (CQ) to any chord (PR) bisects the chord. This means that PQ=RQ=6cm.
5x + 3y = -2 3x + 2y = -1 Solve the system of equations. A) (-1, 1) B) (1, -1) C) (-1, -2) D) ( 1 3 , 1)
Answer:
Here is what i can do i can not exactly tell you the answer but I can help you understand to find the answer because were here to help each other but telling each other the answers is not the key because on an real test you cant use Brainly .com to help you find the answer because they need to see what you know not the internet.
Step-by-step explanation:
The correct option is A) (-1, 1)
Step-by-step explanation:See the image
a person reaching out to the edge of a building edge of a building ledge 85 feet off the ground flicks a twig up and off the ledge with an initial upward velocity of 11 feet per second. what is the maximum height of the twig? when will the twig hit the ground?
Final answer:
The maximum height of the twig is approximately 0.570 meters. The twig will hit the ground approximately 0.683 seconds after being flicked up.
Explanation:
To find the maximum height of the twig, we can use the kinematic equation for vertical motion. The equation is given by:
h = v0y2 / (2g)
Where:
h is the maximum height
v0y is the initial vertical velocity
g is the acceleration due to gravity (approximately 9.8 m/s2)
Plugging in the values, we have:
h = (11 ft/s)2 / (2 * 9.8 m/s2)
Converting the initial velocity from feet per second to meters per second:
11 ft/s * 0.3048 m/ft = 3.35 m/s
Substituting the values into the equation:
h = (3.35) / (2 * 9.8)
Simplifying the equation:
h = 0.570 m
Therefore, the maximum height of the twig is approximately 0.570 meters.
To find when the twig will hit the ground, we can use the equation for time in vertical motion:
t = 2 * v0y / g
Plugging in the values, we have:
t = 2 * 3.35 m/s / 9.8 m/s2
Simplifying the equation:
t = 0.683 s
Therefore, the twig will hit the ground approximately 0.683 seconds after being flicked up.
A chemist needs 30mL of a 12% acid solution for an experiment. The lab has available a 10% solution and a 25% solution. How many milliliters of the 10% solution and how many milliliters of the 25% solution should the chemist mix to make the 12% solution?
parts of 10% soln, x
parts of 25% soln, y
total soln, x+y =30
{x(0.1) + y(0.25)}/(x + y) = 0.12...eqn 1
x + y = 30...eqn 2
from eqn 2...=》 x = 30-y
subst for x in eqn 1...
=》 {(30-y)(0.1) + y(0.25)}/ 30-y+y = 0.12
=》 (3-.1y+.25y)/30 =0.12
=》 3+.15y = 3.6
=》 .15y = .6
=》 y =4
using x = 30 - y = 26
ans
26ml of 10% soln
4ml of 25% soln
Using a system of equations to represent the scenario, 26mL of 10% solution and 4mL of 25% solution would be required.
Let ;
Amount of 10% solution = a Amount of 25% solution = ba + b = 30 - - - - (1)0.1a + 0.25b = (0.12 × 30)0.1a + 0.25b = 3.6 - - - (2)From (1)
a = 30 - b - - - (3)Substitute (3) into (2)
0.1(30 - b) + 0.25b = 3.6
3 - 0.1b + 0.25b = 3.6
0.15b = 0.6
b = 0.6/0.15
b = 4
From (3) :
a = 30 - 4
a = 26
Hence, 26mL of 10% solution and 4mL of 25% solution would be required.
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Work parentheses from inside out, and don't forget to multiply/divide together, left to right, and then do the same for add/subtract.
Answer:
This is correct PEMDAS
Step-by-step explanation:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
given the following sets.
A = {0, 1, 2, 3}
B = {a, b, c, d}
C = {0, a, 2, b}
find B u C
a. {0, 1, 2, 3}
b. {a, b, c, d}
c. {0, a, 2, b}
d. empty set
e. {a, b, c, d, 0, 2}
Answer:
[tex]\large\boxed{e.\ \{a,\ b,\ c,\ d,\ 0,\ 2\}}[/tex]
Step-by-step explanation:
[tex]\text{The union (denoted by}\ \cup\ \text{) of a collection of sets is the set of all elements of the sets. }\\\\A=\{0,\ 1,\ 2,\ 3\}\\\\B=\{a,\ b,\ c,\ d\}\\\\C=\{0,\ a,\ 2,\ b\}\\\\B\ \cup\ C=\{a,\ b,\ c,\ d,\ 0,\ 2\}[/tex]
Please help me. I need help with this
See the attached picture:
Factor x^3 -4x^2 -3x +18 =0
Given that 4 is a zero
A (x-2) (x-3) (x+3)=0
B (x-2) (x-3)^2 =0
C (x-2) (x- sqrt 3)(x+ sqrt 3) =0
D (x-2) (x-3)^2 =0
Answer:
none of the above
Step-by-step explanation:
A graphing calculator shows the zeros to be x=-2, and a double zero at x=3. Hence the factorization is ...
(x +2)(x -3)^2 = 0
The premise that 4 is a zero is incorrect, and none of the answer choices include (x+2) as a factor. The problem is unworkable as written here.
Collin is buying dirt to fill a garden bed that is a 9ft by 16ft rectangle. If he wants to fill it to a depth of 4 inches, how many cubic yards of dirt does he need? If dirt costs $25 per yard cubed, how much will the project cost?
Answer:
Cubic yards of dirt needed for project = [tex]1\frac{7}{9}[/tex] cubic yards
Cost of Project = About $44.44
Step-by-step explanation:
To find number of cubic yards of dirt needed, we need to find the volume.
Rectangular Prism Volume = length * width * depth
Note: Length is 9ft, width is 16ft, depth is 4 inches. We need to change depth to ft. So 4 inches = [tex]\frac{1}{3}[/tex] feet.
Now finding the volume (in cubic ft) = [tex]9*16*\frac{1}{3}=48[/tex]
We know 3 feet is 1 yard. To convert cubic feet to cubic yards, we have to divide it by (3)^3 = 27. Hence:
[tex]\frac{48}{27}=\frac{16}{9}[/tex] cubic yards
* Since dirt is $25 per cubic yard, to find cost, we multiply 25 by 16/9. Hence
Cost of Project = 25 * 16/9 = 400/9 = $44.44
Collin needs to buy 1.76 cubic yards of dirt to fill his 9ft by 16ft garden bed to a depth of 4 inches, and the total cost for the dirt will be $44.
Explanation:To calculate the cubic yards of dirt Collin needs for his 9ft by 16ft garden bed at a depth of 4 inches, we must first convert the dimensions to consistent units and then find the volume. One yard is equivalent to 3 feet, so the bed has dimensions of 3 yards by 5.33 yards (since 9ft / 3 = 3 yards and 16ft / 3 ≈ 5.33 yards). The depth must also be converted from inches to yards: 4 inches is equal to 4/36 or approximately 0.11 yards (because there are 36 inches in a yard).
Now we'll calculate the volume in cubic yards: 3 yards * 5.33 yards * 0.11 yards = 1.76 cubic yards. Next, to find the total cost, we multiply the volume by the cost per cubic yard: 1.76 * $25 = $44. So, Collin will need to pay $44 to fill his garden bed with dirt.
Here are some of the conversions and calculations used:
9ft / 3ft per yard = 3 yards (Length)16ft / 3ft per yard = 5.33 yards (Width)4 inches * (1 yard / 36 inches) = 0.11 yards (Depth)Volume of dirt needed = Length * Width * DepthTotal cost = Volume * $25 per yard cubedLearn more about Volume of Dirt Needed here:https://brainly.com/question/30037972
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The amount in an account with a beginning balance of 3000 and interest compounded continuously at an annual rate of 5.5% can be modeled by the equation A=3000^5.5t
Answer:
Step-by-step explanation:false
Identify the range of the function shown in the graph.
Answer:
A
All real numbers
Step-by-step explanation:
Given in the question a graph
To find the range of graph
The range is the set of possible output values, which are shown on the y-axis.
We can see in the graph that for negative values of x it have positive values, zero and negative values of y.
The graph extends vertically from (-∞,∞), along the y axis. So the range of the function shown in the graph is (-∞,∞).
Hence, it is concluded that range is All real numbers
Mary mixies white paint and blue paint in the ratios 2:3. She makes a total of 20 litres of paint. How much more blue paint does she needs to add to the mixture so the ratios of white paint to the blue paint become 1:7?
Answer:
44 liters
Step-by-step explanation:
It is 44 liters !!!!!
A florist has 40 tulips 32 roses 60 daisies and 50 petunias.Draw a line from each comparison to match it to the correct ratio
Answer:
Need to see the choices
Step-by-step explanation:
One letter is selected from the word "probability." What is the probability that a "b" or "i" is chosen?
4/11
4/9
5/11
3/11
Answer:
The correct answer option is 4/11
Step-by-step explanation:
We know that the word 'probability' has 11 alphabets.
We are to find to find the probability of getting a 'b' or an 'i' from this word.
Probability of getting a b = [tex]\frac{2}{11}[/tex] (since there are 2 b's in probability)
Probability of getting an i = [tex]\frac{2}{11}[/tex] (since there are 2 i's in probability)
Probability of getting 'b' or 'i' = [tex]\frac{2}{11} + \frac{2}{11} = \frac{4}{11}[/tex]
Which sets of measurements could be the interior angle measures of a triangle?
Select each correct answer.
Question 2 options:
10°, 10°, 160°
15°, 75°, 90°
20°, 80°, 100°
35°, 35°, 105°
60°, 60°, 60°
The sum of all the three interior angles of a triangle are 180 degrees. This does not depend on the positioning of the three sides. The sides can be positioned in any way, but the sum must be 180 degrees.
So, the best possible sets of measurements that could be the interior angle measures of a triangle are : 15°, 75°, 90° And 60°, 60°, 60°
The sets of measurements that could represent the interior angles of a triangle are those whose angles add up to exactly 180°. The valid options provided are 10°, 10°, 160°; 15°, 75°, 90°; 35°, 35°, 105°; and the equilateral set of 60°, 60°, 60°.
Explanation:The question pertains to the interior angles of a triangle. According to the Triangle Sum Theorem, the interior angles of a triangle always add up to 180°. Therefore, to determine which sets of measurements could represent the interior angles of a triangle, we must check if the sum of the given angles is equal to 180°.
10°, 10°, 160°: The sum is 180°, so this could represent the interior angles of a triangle.15°, 75°, 90°: The sum is also 180°, making this a valid set of interior angles for a triangle.20°, 80°, 100°: The sum exceeds 180°, therefore, these cannot be the interior angles of a real triangle in Euclidean geometry.35°, 35°, 105°: Once again, the sum is 180°, indicating these could be the angles of a triangle.60°, 60°, 60°: The angles add up to 180°, and this set describes an equilateral triangle where all angles are equal.From the options given, the sets of measurements that represent the interior angles of a triangle are:
10°, 10°, 160°15°, 75°, 90°35°, 35°, 105°60°, 60°, 60°
P=−4b ^2+6b−9
Q=7b ^2−2b−5
P − Q =
Answer is :−11b^2+8b−4
Answer:
see explanation
Step-by-step explanation:
P - Q
= - 4b² + 6b - 9 - ( 7b² - 2b - 5) ← distribute by - 1
= - 4b² + 6b - 9 - 7b² + 2b + 5 ← collect like terms
= - 11b² + 8b - 4
Answer:
[tex]\large\boxed{P-Q=-11b^2+8b-4}[/tex]
Step-by-step explanation:
[tex]P=-4b^2+6b-9\\Q=7b^2-2b-5\\\\P-Q=(-4b^2+6b-9)-(7b^2-2b-5)\\P-Q=-4b^2+6b-9-7b^2-(-2b)-(-5)\\P-Q=-4b^2+6b-9-7b^2+2b+5\qquad\text{combine like terms}\\P-Q=(-4b^2-7b^2)+(6b+2b)+(-9+5)\\P-Q=-11b^2+8b-4[/tex]
Find the area of a rectangle with a length of 27 8 inches and a width of 1 2 inch.
3336_____________________________
The owner of a large manufacturing plant pays the base rate of $11.24 per $100 in wages paid for workers’ compensation insurance. The payroll for September is $179,805. What is the month’s premium for the workers’ compensation insurance?
A $20, 210.08
B $23,459.19
C $19,357.21
D $18,650.93
Answer:
Answer is B
Step-by-step explanation:
To find the workers' compensation insurance premium, multiply the payroll for September ($179,805) by the base rate converted to decimal (0.1124), resulting in a premium of $20,210.08 (Option A).
The question involves calculating the premium for workers' compensation insurance based on the total payroll for the month of September. To determine the monthly premium, we need to apply the base rate to the total payroll amount. The base rate is given as $11.24 per $100 in wages paid. We can calculate the premium with the following steps:
Convert the base rate to a decimal by dividing by 100. This will give us 0.1124.
Multiply the total payroll amount ($179,805) by the decimal base rate (0.1124) to get the premium amount.
Let's perform the calculation:
$179,805 * 0.1124 = $20,210.08
Therefore, the correct option is:
A) $20,210.08
The length of a rectangle is x and the width is 2x-8. If the area of the rectangle is 234 yd^2, find the value of x.
Answer:
x = 13
Step-by-step explanation:
The area of a rectangle is found by A = l*w. Since the length here is x and the width is 2x - 8, substitute these values and A = 234 to solve for x.
[tex]A = l*w\\234 = x(2x-8)\\234 = 2x^2 - 8x[/tex]
To solve for x, move 234 to the other side by subtraction. Then remove the common factor between all three terms of 2. Factor and solve.
[tex]2x^2 - 8x - 234 = 0 \\2(x^2 - 4x - 117) = 0\\2(x - 13)(x+9) = 0\\[/tex]
Set each factor equal to 0 and solve.
x - 13 = 0 so x = 13
x + 9 = 0 so x = -9
Since x is a side length and length/distance cannot be negative, then x = 13 is the length of the rectangle.
Blocks numbered 0-9 are placed in a box and a black is randomly picked the probability of picking an odd prime number is
Answer:
Step-by-step explanation:
[tex]B_n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\\B_p = 2, 3, 5, 7\\B_{o_p} = 3, 5, 7\\[/tex]
There are 3 odd primes, namely : 3, 5, 7
The total amount of blocks is 9
The odds of picking and odd prime is [tex]\frac{3}{9} \cdot 100\% = 33,(3)\%[/tex]
[tex]f(x) - \frac{x^{2}-4 }{x^{4} +x^{3} -4x^{2}-4 }[/tex]
What is the:
Domain:
V.A:
RootsL
Y-Int:
H.A:
Holes:
O.A:
Also, graph it.
a) The given function is
[tex]f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}[/tex]
The domain refers to all values of x for which the function is defined.
The function is defined for
[tex]x^4+x^3-4x^2-4\ne0[/tex]
This implies that;
[tex]x\ne -2.69,x\ne 1.83[/tex]
b) The vertical asymptotes are x-values that makes the function undefined.
To find the vertical asymptote, equate the denominator to zero and solve for x.
[tex]x^4+x^3-4x^2-4=0[/tex]
This implies that;
[tex]x= -2.69,x=1.83[/tex]
c) The roots are the x-intercepts of the graph.
To find the roots, we equate the function to zero and solve for x.
[tex]\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]
[tex]\Rightarrow x^2-4=0[/tex]
[tex]x^2=4[/tex]
[tex]x=\pm \sqrt{4}[/tex]
[tex]x=\pm2[/tex]
The roots are [tex]x=-2,x=2[/tex]
d) The y-intercept is where the graph touches the y-axis.
To find the y-inter, we substitute;
[tex]x=0[/tex] into the function
[tex]f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}[/tex]
[tex]f(0)=\frac{-4}{-4}=1[/tex]
e) to find the horizontal asypmtote, we take limit to infinity
[tex]lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]
The horizontal asymtote is [tex]y=0[/tex]
f) The greatest common divisor of both the numerator and the denominator is 1.
There is no common factor of the numerator and the denominator which is at least a linear factor.
Therefore the function has no holes.
g) The given function is a proper rational function.
There is no oblique asymptote.
See attachment for graph.
Please help me out if possible!!!!
Answer:
∠PST = 45°
Step-by-step explanation:
The diagonals of a square bisect the angles
∠SPQ = 90° ⇒ ∠SPT = 45°