Answer:
The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1
Step-by-step explanation:
* Lets revise how to identify the type of the conic
- Rewrite the equation in the general form,
Ax² + Bxy + Cy² + Dx + Ey + F = 0
- Identify the values of A and C from the general form.
- If A and C are nonzero, have the same sign, and are not equal
to each other, then the graph is an ellipse.
- If A and C are equal and nonzero and have the same sign, then
the graph is a circle
- If A and C are nonzero and have opposite signs, and are not equal
then the graph is a hyperbola.
- If either A or C is zero, then the graph is a parabola
* Now lets solve the problem
The equation is 4x² + 2y² - 8x + 16y - 52 = 0
∴ A = 4 and C = 2 ⇒ same sign and different values
∴ The equation is ellipse
* The standard form of the ellipse is
(x - h)²/a² + (y - k)²/b² = 1
- Lets try to make this form from the general form
- Group terms that contain the same variable, and move the
constant to the opposite side of the equation
∴ (4x² - 8x) + (2y² + 16y) = 52
- Factorize the coefficients of the squared terms
∴ 4(x² - 2x) + 2(y² + 8y) = 52
- Complete the square for x and y
# To make completing square
- Divide the coefficient of x (or y) by 2 and then square the answer
- Add and subtract this square number and form the bracket of
the completing the square
# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1
∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4
- Rewrite as perfect squares ⇒ 4(x -1)² - 4
# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16
∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32
- Rewrite as perfect squares ⇒ 2(y + 4)² - 32
∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52
∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52
∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88
∴ (x - 1)²/22 + (y + 4)²/44 = 1
Three cities, A, B, and C, are located so that city A is due east of city B. If city C is located 35° west of north from city B and is 100 miles from city A and 70 miles from city B, how far is city A from city B?
Answer:
41.776756 miles
Step-by-step explanation:
Using trigonometry and the Law of Cosines, we find that the distance between city A and city B is approximately 122.47 miles.
The question involves using trigonometry to solve for distances between points in a coordinate system, which represents cities in this context. To determine how far city A is from city B given that city C is 35° west of north from city B and specific distances from cities A and B, we can set up a right-angled triangle between the cities.
First, we calculate the angle formed at city B using the information provided about city C's angle. Since city C is 35° west of north and city A is due east of city B, the angle between cities A, B, and C is 180° - 35° = 145°.
We now have a triangle with cities A, B, and C forming the vertices and the following information: side BC (70 miles), side CA (100 miles), and angle BAC (145°). We can solve for the distance between city A and B using the Law of Cosines:
c² = a² + b² - 2ab×cos(C), where c is the side opposite the angle C and a and b are the other two sides.
The distance between cities A and B (side c) is therefore calculated as:
c = √(70² + 100² - 2×70×100×cos(145°))
After calculation, we find that the distance between city A and city B is approximately 122.47 miles.
A delivery man earns $350 per week. He also earns 15% commission on any sales he makes. The function E(s) = 350+0.15s relates his sales, s, to his total weekly earnings, E(s). What were his sales, in dollars, the week he earned $432.50?
Answer:
$550
Step-by-step explanation:
You need the equation E(s) = 350 + 0.15s, where E(s) represent his total weekly earnings.
If he earned $432.50 this means E(s) = 432.50 and you can write it as:
350 + 0.15s = 432.50 and this is the equation we need to solve
You need to substract 350 on both sides of the equation
350 - 350 +0.15 s = 432.50 - 350
And we get
0.15s = 82.5
Then we divide both sides of the equation by 0.15
0.15s/0.15 = 82.5/0.15
And we get s = 550.
Let D = {x| x is a student} be the domain, and let ƒ(x) = “date of birth” be the possible function. Determine if the relation is an example of a function.
It is.
The function is just another way of saying to transfer something from domain A to domain B.
[tex]f(x)=y:A\longrightarrow B; x\in A, y\in B[/tex]
Now your function states:
[tex]D=\{x\} \\
f(x)=y: D\longrightarrow E; x\in D, y\in E[/tex]
According to the general equation for conditional probability, if (image attached)
A. 2/3
B. 1/3
C. 1/6
D/ 5/6
Answer:
Option B
[tex]P(A|B') = \frac{1}{3}[/tex]
Step-by-step explanation:
If B 'is the complement of B then [tex]P(B') = P({\displaystyle {\overline {B}}})=1-P(B) = \frac{2}{3}[/tex]
In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:
[tex]P(A|B') = \frac{P(A\ and\ B)}{P(B')}[/tex]
Then if [tex]P(A\ and\ B) = \frac{2}{9}[/tex] and [tex]P(B') = \frac{2}{3}[/tex]
[tex]P(A|B') = \frac{\frac{2}{9}}{\frac{2}{3}}\\\\P(A|B') = \frac{1}{3}[/tex]
Answer:
The correct answer option is B. 1/3.
Step-by-step explanation:
We are given that P (A ∩ B') = 2/9 and P (B') = 1/3 and we are to find P (A | B').
We also know that the formula of conditional probability is given by:
P (A | B') = P (A ∩ B') / P (B)
So substituting the given values in the formula above to get the value of P (A | B'):
P (A | B') = [tex] \frac { \frac { 2 } { 9 } } { \frac { 1 } { 3 } } = \frac { 2 } { 9 } \times \frac { 3 } { 1 } [/tex] = 1/3
Katie has a job planting shrubs beside the highway. She needs to plant 500 shrubs in a week. So far, She has planted this many: Monday 84 Tuesday 92 Wednesday 87 Thursday 104 How many shrubs does Katie need to plant on Friday?
ANSWER: Katie Must Plant 133 Shrubs On Friday.
First, We Know That Katie Needs To Plant 500 Shrubs In A Week. So Then, We Add Up 104+87+92+84 And When We Add Those Numbers Up, We Get How Many Shrubs She Has Planted On Monday Tuesday Wednesday And Thursday. To Find Out How Many Plants She Needs To Plant On Friday, Subtract 367 From 500 And You Get 133.
QUICK!
what is the probability that George will draw a blue marble from a container that contains 6 red, 4 blue, 3 yellow and 5 green marbles?
1/3
1/6
2/9
5/18
Answer is 2/9.
You have 18 marbles in total. You also have 4 blue marbles. 4/18 divided by 2 is 2/9. Therefore 2/9 is the correct answer.
Your answer is C) 2/9
Hope this helps chu fellow kpop fan XD
☆ Dont forget to mark brainliest ☆
Use the graphs of f(x) = 2
x
and g(x) = 1
-3-x
to determine the solutions to f(x) = g(x).
Answer:
A
Step-by-step explanation:
The solution to f(x) = g(x) occurs where the two graphs cross. That's at the point (-2, -1).
Answer A.
To find where f(x) = g(x), set the two functions equal to each other and solve for 'x'. After some mathematical simplification and operations on both sides of the equation, we find that the solution is x = -1/9.
Explanation:In mathematics, to find the solution for f(x) = g(x), you need to set the two equations equal to each other and solve for x. Here, we have f(x) = 2x and g(x) = 1/-3-x. Setting these two equations equal gives 2x = 1/-3-x.
To solve this equation, first, let's simplify the right hand side by multiplying both sides by -1 to make it easier to solve. Now the equation is -2x = 1/3+x.
Subtracting 'x' from both sides of the equation gives -3x = 1/3. Divide by -3 to solve for x so, x = -1/9. So, the solution for the equation f(x) = g(x) is x = -1/9.
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50 POINTS!!!
Find the area of the segment of circle C shown in the diagram above.
Answer:
B. 9.76 u²
Step-by-step explanation:
First calculate the area of the 60° wedge of the circle by calculating the area of the full circle and multiplying it by a fraction of 60°/360°:
[tex]A_{ABC}=\frac{60}{360}*\pi *r^{2}\\A_{ABC}=\frac{60}{360}*\pi *(6\sqrt{3})^{2}\\A_{ABC}=56.54[/tex]
Now calculate the the area of the white triangle in the wedge, by using a base length of [tex]3\sqrt{2}[/tex], and height:
[tex]h=\sqrt{(6\sqrt{3})^{2}-(3\sqrt{3})^{2}} \\h=9[/tex]
[tex]A_{TRI}=\frac{1}{2}*9*6\sqrt{3} \\A_{TRI}=27\sqrt{3} \\A_{TRI}=46.78[/tex]
Find the area of the red segment:
[tex]A_{ABC} -A_{TRI}\\=56.54-46.78\\=9.76[/tex]
LMN = QPR
What is the value of x in degrees?
Answer:
x = 72 degrees
Step-by-step explanation:
If triangle LMN = triangle QPR, that means:
- angle L (x) equals angle Q
- angle M equals angle P
- angle N equals angle R
We know angle Q equals 72 degrees and we know angle Q equals angle L. Since angle L is the "x" we are looking for, we know that x = 72 degrees.
Jackie can 150 meters
every minute. She is
training for a track
meet. She ran 500
meters during a warm
up. Write a function
that represents how
many meters Jackie
can runs in total at any
given minute. Then
determine how many
meters she runs after
12 minutes
Answer:
1800 meters
Step-by-step explanation:
The function is for every minute represented by X 150 meters is completed...or
x(150m)
To find 12 minutes you replace the x with 12
12(150m)=1800 meters
The function that represents how many meters Jackie can run is: 'y = 150*x + 500'. After 12 minutes, Jackie can run 2300 meters.
Explanation:The problem is basically describing a linear relationship between the minutes Jackie trains and the total distance she covers. The function can be represented by the equation: y = mx + c. In this context, 'y' represents the total distance run, 'm' represents the speed (150 meters/minute), 'x' represents time (minutes), and 'c' is the initial distance covered (500 meters).
So the function will be: y = 150*x + 500.
To find out how much Jackie run after 12 minutes, substitute 12 for 'x' in the equation: y = 150*12 + 500. After doing the calculations, we see that Jackie can run 2300 meters in 12 minutes.
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What would be the maximum value of the function for the graph shown if we consider the graph to be a cosine function of the form y = a cos (x - c)?
0
2
-4
-2
Answer:
2
Step-by-step explanation:
The maximum value is the amplitude. Looking at graph, it would be the highest point in the graph.
Each unit of the graph is 2 units, hence the maximum value, clearly looking at the graph, would be y = 2. Also the minimum value is y = -2.
So, the maximum value is 2
Triangle ABC is congruent to triangle DEF .
Which statement must be true about the triangles?
BC = DE
m∠A=m∠D
m∠B=m∠F
AC = EF
Answer:
[tex]\boxed{m\angle A = m\angle D}\\[/tex]
Step-by-step explanation:
When you use a congruence statement, you must line up the corresponding parts of the triangles.
BC = DE is wrong, because BC = EF.
[tex]\boxed{m \angle A = m \angle D}[/tex] is correct.
m∠B = m∠F is wrong, because m∠B = m∠E.
AC = EF is wrong, because AC = DF
Triangle ABC is congruent to triangle DEF.m∠A=m∠D must be true about the triangles. Option B is correct.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
Triangle DEF and triangle ABC are congruent. The following assertion concerning triangles must be true:
m∠A=m∠D
Hence, statement B is correct.
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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The lengths of trout in a lake are normally distributed with a mean of 30 inches and a standard deviation of 4.5 inches.
Enter the z-score of a trout with a length of 28.2 inches.
Answer:
z = -0.4.
Step-by-step explanation:
Here's the formula for finding the z-score (a.k.a. standardized normal variable) of one measurement [tex]x[/tex] of a normal random variable [tex]X \sim N(\mu,\; \sigma^{2})[/tex]:
[tex]\displaystyle z = \frac{x-\mu}{\sigma}[/tex],
where
[tex]z[/tex] is the z-score of this measurement, [tex]x[/tex] is the value of this measurement, [tex]\mu[/tex] is the mean of the random normal variable, and[tex]\sigma[/tex] is the standard deviation (the square root of variance) of the random normal variable.Let the length of a trout in this lake be [tex]X[/tex] inches.
[tex]X \sim N(30, \; 4.5^{2})[/tex].
[tex]\mu = 30[/tex], and[tex]\sigma = 4.5[/tex].For this measurement, [tex]x = 28.2[/tex]. Apply the formula to get the z-score:
[tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{28.2 - 30}{4.5} = -0.4[/tex].
What is the area of the figure?
What is the area of the figure?
Answer:
the answer 43.5 units²
Step-by-step explanation:
i took this in school and remember it hope it helped
1. The area of the figure is 42 units².
2. The area of the figure is 38 units²
The area of a figure is the extent of its 2D space, quantifying the region it occupies.
It's calculated using specific formulas based on the figure's geometric properties, such as length, width, and shape.
1. The figure can be splitted into 3
Area1 = 1/2bh
= 1/2 × 7 × 2
= 7units²
Area 2 = l × w
= 7 × 4 = 28 units²
Area 3 = 1/2bh
= 1/2 × 7 × 2
= 7 units²
Area of figure = 28+7+7
= 42 units²
2. The shape can be divided into a trapezoid and two equal triangles
area of Trapezoid = 1/2(a+b)h
= 1/2 ( 3+5)8
= 8 × 4
= 32 units²
area of triangle = 1/2bh
= 1/2 × 3 × 4
= 6 units²
area of the figure = 32 + 6
= 38 units²
Express the quotient in simplest form
i believe the answer is a
Answer:
answer : D
Step-by-step explanation:
What is mCE?
A.9
B.9.6
C.10
D.9.4
Answer:
B
Step-by-step explanation:
Triangle ABD and triangle ACE are similar. So we can write a proportion:
AB / BD = AC / CE
5 / 4 = 12 / CE
CE = 9.6
The measure of side CE will be 9.6. Then the correct option is B.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle ΔABD and triangle ΔACE are similar. Then we have
AB / AC = BD / CE
5 / 12 = 4 / CE
CE = 9.6
Then the measure of side CE will be 9.6.
Then the correct option is B.
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If a=22.3 and B=47°18’ find c (picture provided)
Answer:
d. 32.9
Step-by-step explanation:
To find c, we'll use the Law of Sines that says:
[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]
And we'll isolate a to get:
[tex]c = \frac{sin(C) * a}{sin(A)}[/tex]
We first need to find A, which is easy. The sum of the interior angles of a triangle is 180 degrees... and we already have 2 of them, so:
A = 180 - 90 - 47.3 = 42.7
(converted 47°18' to 47.3)
Then we will plug-in the information we already have
[tex]c = \frac{sin(90) * 22.3}{sin(42.7)} = 32.88[/tex]
So, let's round it to 32.9 to match the answer number D.
Answer:
D, 32.9
Step-by-step explanation:
The total cost of 5 boxes of pasta is $13.00. There are 12 ounces of pasta in each box. Each box of pasta costs the same amount. What is the maximum number of boxes that can be purchased with $65.00?
Answer: 25 boxes of pasta
Step-by-step explanation:
$13 / 5 = $2.60
$65 / $2.60 = 25
Find the perimeter of this figure to the nearest tenth. Use 3.1 to approximate
Since the diameter and height of both shapes are the same, we know that the equation to solve for the semi circle is:
πr = 3.1*8 = 24.8
16 + 20 = 36
36 + 24.8 = 60.8
The perimeter of the shape is 60.8 ft
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Remember to be mindful of the signs when adding and subtracting. The answer is:11w^4-5w^2z^2-4z^4
Three ships are at sea: the Admiral, the Barstow, and the Cauldrew. The crew on the Admiral can see both the Barstow and the Cauldrew. They measure the angle between the line of sight to the Barstow and the line of sight to the Cauldrew as 31°. They radio the Barstow and by comparing known landmarks, find that the distance between the Admiral and the Barstow is 402 meters. The Barstow reports that an angle of 70° is found between their line of sight to the Admiral and their line of sight to the Cauldrew. To the nearest meter, what is the distance between the Barstow and the Cauldrew?
38 meters
211 meters
220 meters
133 meters
Answer:
I am very disappointed in you. I give you extra credit to try and help your grade and you cheat? Please come and see me tomorrow about what you are doing.
Step-by-step explanation:
Answer:
211 meters
Step-by-step explanation:
Let A represents the Admiral, B represents the Barstow and C represents the Cauldrew.
According to the question,
AB = 402,
∠B = 70°,
∠A = 31°,
∵ ∠B + ∠A + ∠C = 180° ⇒ 70° + 31° + ∠C = 180° ⇒ ∠C = 180° - 101° = 79°
By the law of sine,
[tex]\frac{sin C}{AB}=\frac{sin A}{ BC}[/tex]
By substituting the values,
[tex]\frac{sin 79^{\circ}}{402}=\frac{sin 31^{\circ}}{BC}[/tex]
By cross multiplication,
[tex]BC\times sin 79^{\circ} = 402\times sin 31^{\circ}[/tex]
[tex]\implies BC = \frac{ 402\times sin 31^{\circ}}{sin 79^{\circ}}=210.92050995\approx 211[/tex]
Hence, the distance between the Barstow and the Cauldrew is 211 meters ( approx )
Second option is correct.
If 5 + x = 12, and you add -5 to the left side of the equation, what should you add to the right side of the equation?
Answer: You must subtract 5 from 12.
Step-by-step explanation:
When solving a one step equation such as this one where you are trying to find x, you must subtract 5 from both sides of the equation. You have to subtract because there is a plus sign: 5 + x = 12
If instead there was a minus sign, you would ADD 5 to both sides. Since it is a plus sign, subtract 5 from 5 and from 12. You then get 7. X=7.
Hope this helped :)
Answer: -5
Step-by-step explanation:
5 + x = 12
-5 -5
________
x = 7
Which can be multiplied?
Answer:
B) BD
Step-by-step explanation:
The number of columns of the first matrix (2nd dimension) must match the number of rows of the second matrix (1st dimension). When you write the dimensions together, the two middle numbers must be the same.
AB ⇒ (3x2) × (3x5) . . . . 2 ≠ 3, so cannot be multiplied
BD ⇒ (3x5) × (5x7) . . . . 5 = 5, so can be multiplied
CD ⇒ (2x3) × (5x7) . . . . 3 ≠ 5, so cannot be multiplied
DD ⇒ (3x5) × (3x5) . . . . 3 ≠ 5, so cannot be multiplied
What shape is the cross section formed by the intersection of a cone and a plane parallel to the base of the cone?
The intersection of a cone and a plane parallel to its base is a circle. This is due to the concept of 'conic sections' that determine the shape based on the angle and position of the plane's intersection with the cone.
Explanation:The cross section formed by the intersection of a cone and a plane parallel to the base of the cone is a circle. This shape is one of the conic sections, which also include the ellipse, parabola, and hyperbola. These shapes are formed depending on the angle and position at which a plane intersects with a cone.
A circle is formed when the cutting plane is parallel to the base of the cone. If the plane was at an angle, other shapes like an ellipse, parabola or hyperbola would be obtained. The word 'conic sections' comes from this geometric principle of intersecting a cone with a plane.
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Please Help!!! What is the true solution to the equation below? 2log3(6x)-log3(4x)=2log3(x+2)
Answer:
x = 1 and x = 4
Step-by-step explanation:
A graph of the given equation, after rewriting to make the solutions be zeros of the function, shows the solutions to be x = 1 and x = 4.
You can take the antilog and solve the quadratic:
log3((6x)^2/(4x)) = log3((x+2)^2) . . . . consolidate the logs
9x = (x +2)^2 . . . . simplify and take the antilog
0 = x^2 -5x +4 . . . subtract 9x
0 = (x -4)(x -1) . . . . factor
Solutions are x = 1 and x = 4. (These values make the factors zero.)
Answer:
c on edge
Step-by-step explanation:
HELPPPP What is the volume of the square pyramid? Use Pythagorean’s Theorem to find the height of the pyramid
Answer: 4,111.7 mm³
Step-by-step explanation:
You need to use this formula to calculate the volume of the square pyramid:
[tex]V=\frac{s^2h}{3}[/tex]
Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.
Find the height with the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.
You can identify in the figure that:
[tex]a=26mm\\\\b=\frac{23mm}{2}=11.5mm\\\\c=h[/tex]
Then, you can find the height:
[tex](26mm)^2=(11.5mm)^2+h^2\\\\h=\sqrt{(26mm)^2-(11.5mm)^2}\\\\h=23.318mm[/tex]
Then, knowing that:
[tex]s=23mm\\h=23.318mm[/tex]
You can calculate the volume:
[tex]V=\frac{(23mm)^2(23.318mm)}{3}=4,111.7mm^3[/tex]
A firework is thrown from the top of a hill. The distance, in feet, between the rock and the ground x seconds after it's set off is given by h(t)=-8^2t + 48t + 56. What is the height of the hill where the rocket is set off?
so you first at the two numbers then you at the number to go out with a second then you keep doing that until you get into you don't have no more to answer so thank you
Staci has seven more cats than Taylor. Write an expression that illustrates how many cats Staci has.Use x to represents the number of cats that Taylor has.
Answer: x+7
Step-by-step explanation:
Taylor has x number of cats. Because we do not know how many cats they have combined, or the number of cats Taylor has, we can only simplify it to x+7. Therefore, x+7= the number of Staci's cats. Hope that helps! :)
PLEASE HELP BRAINLY AND MAX POINTS!!!
You bought a car that was 25,500 dollars and the value depreciates by 4.5% each year. How much would the car be worth after 5 years? Be sure to give the equation and the answer.
Answer:
19,262.5
Step-by-step explanation:
If the car decreases by 4.5% eah year for 5 years-
4.5 x 5 = 22.5%
So after 5 years, the car would be 22.5% cheaper.
22.5% of 25,000 is multiplication-
.225 x 25,000 = 19,262.5
hope this helps!
The probability that a fair coin tossed 10 times will land heads up on all ten tosses is 1 out of ____.
A.)2
B.)10
C.)210
Answer:
10
Step-by-step explanation:
because tossed 10 times so it would be 1 out of 10
Answer:
The answer is B
Step-by-step explanation: