5/16, 3/8, 7/16, 1/2
All you sre doing is adding 1/16 to each term then reducing it.
1/16 + 1/16 = 2/16
2/16 = 1/8
2/16 + 1/16 = 3/16
etc.
heres the simplest explanation:
all they are doing is counting and reducing
Reduce
1/16. 1/16
2/16. 1/8
3/16. 3/16
4/16. 1/4
5/16. 5/16
6/16. 3/8
7/16. 7/16
8/16. 1/2
Answer:
The sequence has a common difference of 1/16, which means to get the next term, we need to add 1/16 to the previous term.
The next four terms would be:
9/32 (1/4 - 1/16)
5/16 (1/4 + 1/16)
11/32 (5/16 + 1/16)
3/8 (11/32 + 1/16)
So the full sequence is: 1/16, 1/8, 3/16, 1/4, 9/32, 5/16, 11/32, 3/8, ...
100 Points!!! Algebra question, only looking for answer to last two. Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Photo attached. Thank you!
1) y = -3x and y = -3x + 2: inconsistent system of equations.
2) y = x - 5 and -2x + 2y = - 10: consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.
Explain about the consistent and inconsistent system of equations?If there is at least one solution, an equation system is considered consistent. If there is no solution, a system is inconsistent.If one equation is a multiple of the other in a pair of equations that have two variables, both equations are dependant. Every point in dependent systems is a potential solution, giving them an endless number of solutions.The given equation are:
The graph for each system of equations is plotted.
1) y = -3x and y = -3x + 2
From the graph 1 it is shown that the lines for the each equation form the parallel lines.
Thus, system of equations are inconsistent.
2) y = x - 5 and -2x + 2y = - 10
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
Know more about the inconsistent system of equations
https://brainly.com/question/19282045
#SPJ1
let f(x)=x+2 and g(x)=2x2 + 1
look at picture
The values of x such that f(x) = x + 2 and g(x) = 2^x + 1 if f(x = g(x) are x =0 and x = 1
Calculating the values of xGiven that
f(x) = x + 2
g(x) = 2^x + 1
To find x when f(x) = g(x), we need to set the two expressions equal to each other and solve for x:
f(x) = g(x)
x + 2 = 2^x + 1
Subtracting 1 from both sides:
x + 1 = 2^x
We can solve for x by using trial and error or by using numerical methods.
One solution to this equation is x = 1.
To see why, we can plug x = 1 into both sides of the equation:
x + 1 = 2^x
1 + 1 = 2^1
2 = 2
Another solution is x = 0
0 + 1 = 2^0
0 + 1 = 1
1 = 1
Hence, the solutions are x = 0 and x = 1
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
The ships kitchen stocks 1 3/5 quarts of ice cream for every 1/4 cake. There are 10 cakes in the kitchen. How many quarts of ice cream are there?
Please explain if you really really know the answer
Therefore , the solution of the given problem of unitary method comes out to be the pantry has 16 quarts of ice cream.
What is an unitary method?The goal can be achieved by making use of what has expression learned to date, utilizing this global access, and incorporating all crucial elements from previous changeable study that employed a specific technique. It is going to be equation possible to get in touch with the entity again if the expected claim result actually happens, or both crucial processes will surely miss the statement. A Rs ($1.21) redeemable fee may be needed for fifty pens.
Here,
Finding the overall quantity of cake in the kitchen is a good place to start. If there are 10 pastries, each measuring 1/4 inch, then there will be:
=> 10 desserts divided by 1/4 each equals the total cake.
=> Cake total equals 10/4 cakes.
=> 2.5 pastries altogether
=> 1 3/5 pints of ice cream for every 1/4 cake.
=> 8 and a half pints of ice cream per 1/4 cake
To determine the total amount of ice cream, we can multiply the ice cream per cake by the total number of cakes:
=> Total ice cream equals the sum of the cakes' ice cream.
=> Total ice cream = (8/5 quarts per 1/4 cake) * (10/4 cakes)
=> Total ice cream = 16 quarts
Consequently, the pantry has 16 quarts of ice cream.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Subway 80
Bicycle 20
Car Service 30
Bus 16
Walk 54
Which of the following circle graphs correctly represents the data in the table?
Option A is correct. The circle graph or pie chart have five parts as 5 ways of transportation labeled Subway 40%, bicycle 10%, car service 15%, bus 8%, and walk 27%
How to create a pie chart with all percentages of transportation?Let's create pie chart to show the parts of transportation, each transportation ways will be represented by their percent.
Total number of visitors from various transportation = 80 + 20 + 30 + 54 + 16 = 200
Percentage of ways of transportation for each type:
Subway: %
Bicycle: %
Car Service: %
Bus: %
Walk: %
So, the correct pie chart of different ways of transportation will have five parts named as Subway 40%, bicycle 10%, car service 15%, bus 8%, and walk 27%.
To know more about pie chart, visit:
brainly.com/question/9979761
#SPJ1
Find the rule x = 8 y = 10 x = 9 y = 12
The equation of the rule that relates x and y is y = 2x - 6.
What is the equation's rule?Anything on one side of the equals sign in a calculation must equal anything on the other side of the equals sign. So long as we maintain the balance on both sides of the equals symbol, we can do whatever we want to an equation.
We can create a system of equations using the provided values (8, 10) and (9, 12) in order to determine the rule that connects x and y. One approach is as follows:
The slope of the line connecting the two locations can be determined first:
m = (y2 - y1)/(x2 - x1) = (12 - 10)/(9 - 8) = 2/1 = 2
The point-slope version of the equation of a line can then be used, using either of the two points:
y - y1 = m(x - x1)
For example, using the first point (8, 10):
y - 10 = 2(x - 8)
Simplifying:
y - 10 = 2x - 16
y = 2x - 6
To know more about equation visit:-
https://brainly.com/question/29538993
#SPJ9
a package contains 6 blue, 4 red, and 5 yellow gumballs. You randomly choose a gumball from the bag, and you do not replace it. Then you randomly choose another gumball. What is the propobility of both gumballs not being red?
The probability of both gumballs not being red is 11/21.
What is the probability?
The probability of the first gumball not being red is:
P(first gumball not red) = P(blue) + P(yellow)
= (6/15) + (5/15)
= 11/15
After removing the first gumball, there are 14 gumballs left in the bag. The probability of the second gumball not being red depends on what color the first gumball was.
Case 1: The first gumball was blue
If the first gumball was blue, there are 5 blue, 4 red, and 5 yellow gumballs left in the bag. The probability of the second gumball not being red is:
P(second gumball not red | first gumball was blue) = P(blue or yellow)
= P(blue) + P(yellow)
= (5/14) + (5/14)
= 5/7
Case 2: The first gumball was yellow
If the first gumball was yellow, there are 6 blue, 4 red, and 4 yellow gumballs left in the bag. The probability of the second gumball not being red is:
P(second gumball not red | first gumball was yellow) = P(blue or yellow)
= P(blue) + P(yellow)
= (6/14) + (4/14)
= 5/7
The probability of both gumballs not being red is the product of the probabilities of each event:
P(both gumballs not red) = P(first gumball not red) * P(second gumball not red | first gumball not red)
P(both gumballs not red) = (11/15) * (5/7)
P(both gumballs not red) = 55/105
P(both gumballs not red) = 11/21
Therefore, the probability of both gumballs not being red is 11/21.
To know more about probability, visit:
https://brainly.com/question/11234923
#SPJ1
20 points answer for brainlist
Multiply, Final answer needs to be in Standard Form.
−5m (−2m + m^2 − 4m^3 + 9)
Answer:
Using the distributive property, we can multiply -5m by each term inside the parentheses:
-5m(-2m + m^2 - 4m^3 + 9) = (-5m)(-2m) + (-5m)(m^2) + (-5m)(-4m^3) + (-5m)(9)
Simplifying each term:
= 10m^2 - 5m^3 + 20m^4 - 45m
The terms are arranged in descending powers of m, so this is already in standard form. Therefore, the final answer is:
20m^4 - 5m^3 + 10m^2 - 45m.
Factor by substitution: (3y−2)2−(3y−2)−2.
The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²
How to factor Polynomial by substitution?Factoring polynomials simply means separating a polynomial into its component polynomials.
Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.
We have the equation:
(3y - 2)² - (3y - 2)⁻²
Let 3y - 2 be denoted by S and as such we have:
S² - S⁻²
= S² - 1/S²
Using the denominator as factor, we have:
= (S⁴ - 1)/S²
Plugging 3y - 2 for S gives us:
((3y - 2)⁴ - 1)/(3y - 2)²
Read more about Polynomial at: https://brainly.com/question/17517586
#SPJ1
Number 5 Please look at image
The solutions to the quadratic equations are as follows
4a. The rocket was launched from an initial height of 10 meters.
b. The maximum height of the rocket was 55 meters.
c. The rocket reaches its maximum height at 3 seconds
d. the rocket is in the air for t = 6.316 seconds
5. when the horizontal distance is 1 foot, the height of the balloon is 8.875 feet
b. when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet.
How do we solve the quadratic equation?The function is a quadratic equation, and here is how we solve each problem;
a. The initial height of the rocket is the value of h when t=0. So we substitute t=0 into the equation to find:
h = -5(0)² + 30(0) + 10 = 10 meters
b. & c. The maximum height of a projectile launched upward occurs at the vertex of the parabola represented by the quadratic function. For a quadratic function in the form y = ax² + bx + c, the time at which the maximum (or minimum) occurs is -b/2a. In this case, a = -5 and b = 30. So:
t = -b/2a = -30 / (2×-5) = 3 seconds
So, the rocket reaches its maximum height at t=3 seconds. We can find this maximum height by substituting t=3 into the equation:
h = -5(3)² + 30(3) + 10 = -5×9 + 90 + 10 = 45 meters
The rocket is in the air from the time it was launched until it hits the ground. The time when it hits the ground is when h = 0. So we can set the equation to 0 and solve for t:
0 = -5t² + 30t + 10
This is a quadratic equation and can be solved using the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a)
Let's calculate the roots:
t = [-30 ± √((30)² - 4×-5×10)] / (2×-5)
= [-30 ± √(900 + 200)] / -10
= [-30 ± √(1100)] / -10
= 6.316 or -0.32
5. a. To find the height of the balloon when d=1, we substitute d=1 into the equation:
h = -1/8(1)²+ 4(1) + 5 = -1/8 + 4 + 5 = 8.875 feet
b. To determine whether the balloon hits your enemy, we need to see if the balloon's height (h) is above ground level (h > 0) when d=33. So, we substitute d=33 into the equation:
h = -1/8(33)² + 4(33) + 5
h = -1/8×1089 + 132 + 5
h = -136.125 + 132 + 5
h = 0.875 feet
when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet. This means the balloon is above ground level and therefore would indeed hit your nemesis standing 33 feet away.
Find more exercises on quadratic equations;
https://brainly.com/question/26090334
#SPJ1
What is the scale factor, k, if D (k, o)(3,5) = (7.41, 12.35)
A. 2.47
B. 7.35
C. 4.41
D. 1.35
When D (k, o) (3,5) = (7.41, 12.35), then the scale factor k is 2.47. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
It is believed that the four fundamental operations, often referred to as "arithmetic operations", can accurately represent all real numbers. Division, multiplication, addition, and subtraction are followed by the mathematical operations quotient, product, sum, and difference.
We are given that D is (k, o) (3,5) = (7.41, 12.35).
This can be represented as
⇒ (3k,5o) = (7.41, 12.35)
So,
⇒ 3k = 7.41
⇒ k = 2.47 (Using the division operation)
Hence, when D (k, o) (3,5) = (7.41, 12.35), then the scale factor k is 2.47.
Learn more about arithmetic operations from the given link
brainly.com/question/30283549
#SPJ1
For problems 6 and 7 set up a proportion and solve.
pleaseeeee helpppp i’ll give brainlist
Using proportions we can find,
6. The weight of the adult bear = 750 pounds.
7. The measure of each angles are: 10°, 75° and 95°
Define proportions?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
Here in the question,
The weight is in the ratio = 3:1000
The average birth weight = 12 ounces = 3/4 pounds.
Now the weigh of adult bear = 1000 × 3/4 = 750 pounds.
In the second part the angles are in the ratio, 2:15:19.
So, 2x+ 15x + 19x = 180
x = 180/36
x = 5
Hence, the measure of each angles are: 10°, 75° and 95°
To know more about proportions, visit:
https://brainly.com/question/30675547
#SPJ1
HELPPPPP MEEEEEE!!! PLEASEEEEE
1.
Factor:
2x^2 + 9x + 18
What multiples to get 18 and adds to get 9?
a. (X+9) (x+2)
b. (X+6) (x+3)
c. (X-6) (x-3)
d. (X-9) (x-2)
2.
Factor:
X^2 - 20x + 36
What multiples to get 36 and adds to get -20?
a. (x-6) (x-6)
b. (x+3) (x+12)
c. (x-9) (x-4)
d. (x-18) (x-2)
3.
factor:
2x^2 - 5x -3
STEPS.
STEP 1* - Slide and Multiply the First Number to the Last
STEP 2 - Factor - What Multiplies to get the Last Number and Adds to get the
Middle Number?
STEP 3 - Divide and Reduce - The number we divide by is the same number we slid.
STEP 4 - Bottoms Up - If a fraction remains, move bottom number in front of the
variable.
*Unless there is a GCF. If there is, pull that out first.
a. (x-3)(x+1)
b. (2x+1)(x-3)
c. (2x-1)(x+3)
d. (x-3)(2x-3)
4.
what is the greatest common factor?
8x^2 + 18x + 4
a. 2
b. 4
c. 2x
d. 4x
5.
factor:
8x^2 + 18x + 4
STEPS.
STEP 1* - Slide and Multiply the First Number to the Last
STEP 2 - Factor - What Multiplies to get the Last Number and Adds to get the
Middle Number?
STEP 3 - Divide and Reduce - The number we divide by is the same number we slid.
STEP 4 - Bottoms Up - If a fraction remains, move bottom number in front of the
variable.
*Unless there is a GCF. If there is, pull that out first.
a. (x-2)(4x+1)
b. 2(x-2)(4x-1)
c. 2(x+2) (4x+1)
d. (x+2)(x+4)
The answer to the all questions was solved by the methods of factoring:
b. (x+6)(2x+3)c. (x-2)(x-18)a. (2x-3)(x+1)2b. 2(x-2)(4x+1)What is factoring?Factoring is the process of breaking down a mathematical expression or equation into simpler components, such as factors that when multiplied together give the original expression.
In the given questions,
1.Factoring 2x² + 9x + 18:
First, we need to find two numbers that multiply to 2×18=36 and add up to 9.The numbers are 6 and 6, since 6×6=36 and 6+6=12, but we need to adjust them to fit the middle term, which is positive.Therefore, we use 6 and 3: 6×3=18 and 6+3=9.We can write the expression as: 2x²+ 6x + 3x + 18.Now we can factor by grouping: (2x+6)(x+3).The answer is (a) (2x+6)(x+3).2.Factoring x² - 20x + 36:
First, we need to find two numbers that multiply to 36 and add up to -20.The numbers are -2 and -18, since -2×(-18)=36 and -2+(-18)=-20.We can write the expression as: x² - 2x - 18x + 36.Now we can factor by grouping: (x-2)(x-18).The answer is (d) (x-2)(x-18).3.Factoring 2x² - 5x - 3:
We can start by multiplying the first and last coefficients: 2×(-3)=-6.We need to find two numbers that multiply to -6 and add up to -5.The numbers are -6 and 1, since -6×1=-6 and -6+1=-5.We can write the expression as: 2x² - 6x + x - 3.Now we can factor by grouping: (2x-3)(x+1).The answer is (a) (2x-3)(x+1).4.Finding the greatest common factor of 8x² + 18x + 4:
We can start by factoring out any common factors of the coefficients, which is 2.Then we need to find the greatest common factor of the terms with x.The terms are 8x^2 and 18x, and the greatest common factor is 2x.The constant term, 4, is a factor of 2, so we can factor out another 2.The greatest common factor is 2(2x² + 9x + 2).The answer is (d) 4x.5.Factoring 8x² + 18x + 4:
First, we need to factor out any common factors, which is 2.Then, we can follow the steps:STEP 1* - Slide and Multiply the First Number to the Last: (2x+1)(4x+2).STEP 2 - Factor - What Multiplies to get the Last Number and Adds to get the Middle Number? The last number is 2, and the only factors are 1 and 2, which add up to 3, not 9. Therefore, the expression is prime and cannot be factored further.The answer is none of the given options.To know more about factoring expression, visit:
https://brainly.com/question/11994048
#SPJ1
Divide (-18) by (3). Then multiply the quotient by (-4).
Answer:
1.5
Step-by-step explanation:
-18/3 = -6
-6/-4 = 3/2 or 1.5
Answer: 24
Step-by-step explanation:
1.2541 rounded to nearest tenth
Answer:
1.3
Step-by-step explanation:
look at the hundredths place to decide how to round (1.2541).
when a digit is greater than or equal to 5, we round up
in this number, the hundredths place is 5, meaning we round up to get 1.3
i hope this helps :D
Find the area of a square that has a side length of 2x + 4. Write your answer in standard
form without any spaces and use ^ to indicate an exponent, if necessary.
As given:
The side of the Square= (2x+
As we know:
The area of a square = Side × side
Putting the values of side in above formula we get:
Area = (2x+4) ×(2x+4)
on solving we get:
Area= 2x×2x + 2x×4 +4×2x + 4×4
Area= 4x^2 + 8x + 8x + 16
Area= 4x^2 + 16x + 16
Hence,The Area of the Square is (4x^2+ 16x +16)
If ƒ is an entire function such that lim_|z|-->00 |ƒ (z)| = ∞ then?.
ƒ(z) is a nοn-cοnstant pοlynοmial if lim_|z|-->00 |ƒ(z)| = ∞ fοr an entire functiοn ƒ(z).
Hοw tο calculate entire functiοn such that lim_|z|-->00 |ƒ (z)| = ∞?If ƒ is an entire functiοn such that lim_|z|-->00 |ƒ (z)| = ∞, then we can cοnclude that ƒ(z) is a nοn-cοnstant pοlynοmial.
Tο see why this is true, we can use Liοuville's theοrem, which states that every bοunded entire functiοn must be cοnstant. Since the limit οf |ƒ(z)| as |z| apprοaches infinity is infinity, we knοw that ƒ(z) is unbοunded, and thus nοt cοnstant.
Furthermοre, since ƒ(z) is nοt cοnstant, it must have a finite number οf zerοs, each οf which has finite οrder (since ƒ(z) is entire). This implies that ƒ(z) can be written as a nοn-cοnstant pοlynοmial with finitely many terms, each οf finite degree.
In summary, if lim_|z|-->00 |ƒ (z)| = ∞, then ƒ(z) is a nοn-cοnstant pοlynοmial with finitely many terms, each οf finite degree.
To learn more about pοlynοmial , visit:
https://brainly.com/question/15493909
#SPJ9
please help ! QUICK no trolling
Answer:10.9
Step-by-step explanation:
using soh cah toa:
[tex]Sin40=\frac{b}{17}[/tex]
[tex]B=sin40 .17[/tex]
B=10.9
si tengo 3657 manzanas y me quitan 84648 pero juan me regala otras 8469 cuantas me quedan para comer?
Answer:
0 (-72522)
Step-by-step explanation:
ahora tienes negativo manzanas
One of outstanding journal recently published an article indicating differences in perception of gender equality on the job between men and women. The article claimed that women perceived the gender equality problem to be much more compared to men. One question asked of both men and women was: "Do you think gender equality is a major problem in the workplace?" 60% of the women responded "Yes", compared to men about 25%. Assuming W designates women's responses and M designates men's, what hypothesis should journal test in order to show that its claim is TRUE?
The journal could use a one-tailed hypothesis test with a significance level (α) of 0.05 to determine whether there is a significant difference between the proportion of women and men.
What is p value?In statistics, the p-value is a measure of the evidence against the null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming that the null hypothesis is true. In other words, the p-value is the probability of obtaining the observed results, or more extreme results, if the null hypothesis were true.
Given by the question.
To test the claim that women perceive the gender equality problem to be much more compared to men, the journal could test the following hypothesis:
Hypothesis: The proportion of women who perceive gender equality to be a major problem in the workplace (W) is significantly greater than the proportion of men who perceive gender equality to be a major problem in the workplace (M).
H0: W = M (there is no significant difference in perception of gender equality between men and women)
Ha: W > M (women perceive gender equality to be a major problem more than men do)
who perceive gender equality to be a major problem in the workplace. They could calculate the p-value and compare it to α. If the p-value is less than α, they would reject the null hypothesis and conclude that the proportion of women who perceive gender equality to be a major problem in the workplace is significantly greater than the proportion of men who perceive it to be a major problem.
To learn more about probability:
https://brainly.com/question/30034780
#SPJ1
I need some help please
Answer:
question where is the question?
A sphere has a surface area of 60 square feet. Which choice is the best approximation of its radius? Use 3.14 to approximate pi.\
Answer:
Step-by-step explanation:
The surface area of a sphere is given by the formula:
S = 4πr^2
where S is the surface area and r is the radius of the sphere.
We are given that the surface area of the sphere is 60 square feet. Using the formula above, we can solve for the radius:
60 = 4πr^2
Dividing both sides by 4π, we get:
15/π = r^2
Taking the square root of both sides, we get:
r = sqrt(15/π)
Using 3.14 as an approximation for π, we can evaluate this expression:
r ≈ sqrt(15/3.14)
r ≈ 2.20
Therefore, the best approximation for the radius of the sphere is 2.20 feet.
Answer:
Radius is 2.18
Step-by-step explanation:
;)
ASTORY OF RATIOS
Lesson 8 Problem Set 6.5
Plot the points for each shape, determine the area of the polygon, and then write an expression that could be used to
determine the area of the figure. Explain how each part of the expression corresponds to the situation..
1 A(1,3), B(2.8), C8, 8), D(10,3), and E(5,-2)
y
#D what is the area of this shape
Thus, the area of the pentagon formed by the given coordinates is:
A = 28.5 sq. units.
Explain about the pentagon?A pentagon is just a five-sided polygon in geometry having five straight sides and five inner angles totaling 540 degrees. A pentagon is a five-sided, flat (two-dimensional), plane geometric form.
The coordinates of polygon are:
A(1,3), B(2,8), C(8, 8), D(10,3), and E(5,-2).
Plot the points on the graph as shown.
The area of a pentagon calculation is used to determine the area of a pentagon with apothem, a, but one side length, s:
A = 1/2 * a * (5s)
a = apothem, of perpendicular distance from the centre.
s = length of side.
From graph:
s = 6 units.
a is calculated using the tan function.
each interior angle of pentagon = 54 degrees.
So,
tan (54/2) = a/ (s/2)
tan (36) = a/3
a = 3*tan (36)
a = 1.90 units
A = 1/2 * 1.90 * (5*6)
A = 28.5 sq. units.
Thus, the area of the pentagon formed by the given coordinates is:
A = 28.5 sq. units.
Know more about the pentagon
https://brainly.com/question/11759904
#SPJ1
Complete the square to write an equation in general form of 4x2 – 9y2 + 24x + 18y – 9 = 0 in the standard form shown below, and then identify the key features of the graph.
h = center: (, )
k =
a = slope of asymptote:
b =
The equation is now in the standard shape of a hyperbola, as per the provided assertion. [(x - h)² / a²] - [(y - k)² / b²] = 1
What, in plain words, is a hyperbola?A curve formed by the junction of a double right-angled cone and a plane that slices one half of the cone. a plane curve produced by a point so mobile that the difference between its distance from two fixed locations is a constant.
To complete the square for the given equation, we will group the x and y terms and complete the square separately for each.
4x² + 24x - 9y² + 18y - 9 = 0
4(x² + 6x) - 9(y² - 2y) = 9
4(x² + 6x + 9 - 9) - 9(y² - 2y + 1 - 1) = 9
4(x + 3)² - 9(y - 1)² = 36
Dividing by 36, we get:
(x + 3)² / 9 - (y - 1)² / 4 = 1
So, the equation is now in the standard form of a hyperbola:
[(x - h)² / a²] - [(y - k)² / b²] = 1
where h and k are the coordinates of the center, a is the distance from the center to the vertices along the x-axis, b is the distance from the center to the vertices along the y-axis, and the slope of the asymptotes is b/a.
Comparing with the standard form, we can see that:
h = -3, k = 1, a = 3, b = 2, and the slope of the asymptotes is b/a = 2/3.
The center is (-3, 1). The hyperbola opens horizontally, and its vertices are located at (-3 + a, 1) and (-3 - a, 1). So, the vertices are (-6, 1) and (0, 1).
The asymptotes are two straight lines passing through the center with a slope of ±(b/a) = ±2/3. So, the equations of the asymptotes are y - 1 = (2/3)(x + 3) and y - 1 = -(2/3)(x + 3), which simplify to y = (2/3)x + 5/3 and y = -(2/3)x + 1/3.
The distance between the center and the foci is c = sqrt(a² + b²) = √(13). The foci are located at (-3 + c, 1) and (-3 - c, 1). So, the foci are approximately (-0.16, 1) and (-5.84, 1).
The graph of the hyperbola looks like two mirrored U-shaped curves, with the vertices being the endpoints of the transverse axis.
The asymptotes intersect at the center and divide the hyperbola into four parts, called branches. The foci are located on the transverse axis, inside the branches.
To know more about Hyperbola visit:
brainly.com/question/28989785
#SPJ1
The perimeter of the base of a square pyramid is 48 inches. The height of the pyramid is 8 inches. What is the surface area of the pyramid? Responses
Answer:
To find the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces, and then add them together.
First, let's find the length of one side of the base of the pyramid:
Perimeter of the square base = 4 x side length
48 inches = 4 x side length
Side length = 12 inches
Now we can find the area of the base:
Area of the base = side length squared
Area of the base = 12 inches x 12 inches
Area of the base = 144 square inches
Next, we need to find the area of each triangular face. To do this, we need to find the length of the slant height of the pyramid. We can use the Pythagorean theorem to do this:
Slant height squared = height squared + (1/2 base length) squared
Slant height squared = 8 inches squared + (6 inches) squared
Slant height squared = 64 inches squared + 36 inches squared
Slant height = square root of (64 + 36) inches
Slant height = 10 inches
Now we can find the area of each triangular face:
Area of a triangular face = (1/2 base length) x slant height
Area of a triangular face = (1/2 x 12 inches) x 10 inches
Area of a triangular face = 60 square inches
Finally, we can add the area of the base and the area of the four triangular faces together to find the total surface area of the pyramid:
Total surface area = Area of the base + (4 x Area of a triangular face)
Total surface area = 144 square inches + (4 x 60 square inches)
Total surface area = 384 square inches
Therefore, the surface area of the pyramid is 384 square inches.
Mason’s pumpkin had a weight of 3 kg 250 g in August and 4 kg 125 g in October. What was the difference in weight from August to October?
23 x _ = 23 x 4
(help me)
Answer:
4
Step-by-step explanation:
To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4. Therefore the missing value will be 4.
Hope this helped :)
Answer: the answer is 4
Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4
What is the standard equation of a circle whose center is (-3, 5) and radius is 2?
Answer:
Step-by-step explanation:
The standard equation of a circle with center (a, b) and radius r is:
(x - a)^2 + (y - b)^2 = r^2
Using the given values, we have:
(x - (-3))^2 + (y - 5)^2 = 2^2
Simplifying:
(x + 3)^2 + (y - 5)^2 = 4
Therefore, the standard equation of the circle is (x + 3)^2 + (y - 5)^2 = 4.
Answer:
[tex] (x + 3)^2 + (y - 5)^2 = 4 [/tex]
Step-by-step explanation:
[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]
[tex] (x - (-3))^2 + (y - 5)^2 = 2^2 [/tex]
[tex] (x + 3)^2 + (y - 5)^2 = 4 [/tex]
Pleaseeeeeee HELP!!!!!!
A piece of farm machinery clears 2/15 acre of land in 1/5 of an hour
Answer: D. 2/3
Step-by-step explanation:
If it is 1/5 of an hour, we times it by 5, to get full hour, right?
So, we also do ×5 for the acre of land, so we can get the amount of acres in a full 1 hour.
5 is the same as 5/1 as a fraction
1/5 × 5 = 5/5 ......1 hour
2/15 × 5/1 = 10/15
So we get, 10/15 acre of land cleared in 1 hour
We simplify 10/15,
Which becomes,
2/3.
In conclusion, this is the working out =
2/15 × 5 = 10/15 = 2/3
Mark my answer as the brainliest!Mrs. Andretti is having new drapes made for her living
room. The cost of the fabric is $15 per yard. The fee to
make and hang the drapes is $250. She uses the expression
15x + 250 to calculate the total cost of the drapes. Mrs.
Andretti states that x represents the total cost of the fabric.
Is she correct?
• Yes, x represents the total cost of the fabric.
O No, x represents the total cost of the drapes.
• No, x represents the total yards of fabric used.
O No, x represents the total amount of fabric she
already has.
Fabric cost ($15 per yard) and curtain making and hanging ($250). x represents the total cost of the fabric and Mrs. Andretti can use the formula 15x to calculate the fabric cost and add the $250 fixed charge to get the total cost of the curtain.
Why do we determine costs?Cost computation helps in deciding on pricing, manufacturing output, and sales. It also helps in figuring out the costs of the products and services the company sells.
X does not represent the cost of fabric. X represents the number of yards of fabric used.
15x + 250
Could be read as ($15 × # of yards) + $250
She must therefore pay $15 per yard of cloth in addition to the $250 base cost of having them produced and hung.
She may indicate the price of fabric with an additional variable.
Example: Y
Y= 15x
Cost of fabric is equal to $15 per yard × # of yards.
To know more about cost visit:
brainly.com/question/25109150
#SPJ1
The following ordered pairs are found on the graph of the same line.
(-3,9), (-1,4), (1, -1)
Which one of the following points would NOT be found on the line?
A.(-7,19)
B.(7,-16)
C.(-8,20.5)
D.(8,-18.5)
the point that would not be found on the line is option A, (-7,19).
How to calculate the line?
We can use the equation of the line that passes through these three points to determine which of the given points would not be on the line.
First, we can find the slope of the line using the first two points:
slope = (y₂ - y₁)/(x₂- x₁) = (4 - 9)/(-1 - (-3)) = 5/2
Now, we can use the point-slope form of the equation of a line with the slope we just found and the first point (-3,9):
y - y₁= m(x - x₁)
y - 9 = (5/2)(x + 3)
Simplifying this equation gives us:
y = (5/2)x + (27/2)
We can check that the third point (1,-1) also lies on this line by plugging in the values of x and y into the equation above.
Now, we can check which of the given points would not be on this line by plugging in the values of x and y into the equation above.
A. (-7,19): y = (5/2)(-7) + (27/2) = 5.5, which does not equal 19, so this point is not on the line.
B. (7,-16): y = (5/2)(7) + (27/2) = 22.5, which does not equal -16, so this point is not on the line.
C. (-8,20.5): y = (5/2)(-8) + (27/2) = 4.5, which does not equal 20.5, so this point is not on the line.
D. (8,-18.5): y = (5/2)(8) + (27/2) = 25.5, which does not equal -18.5, so this point is not on the line.
Therefore, the point that would not be found on the line is option A, (-7,19).
To know more about line visit :-
https://brainly.com/question/24644930
#SPJ1