A parabola has the focus at (4,6) and the directrix of Y equals -6
Answer:
y = (x-4)²
Step-by-step explanation:
vertex (h , k)
h = 4 .... axis of symmetry
k = (6 + -6) / 2 = 0 .... midpoint of focus and directrix
equation of parabola: y = (x-4)² y = (x-h)² + k
If f(x) = x + 1, and g(x) = 2x
Answer:
B. (f-g)(x)=4^x-1-2x+11
(f-g)(x) = (4^x-1+6) - (2x-5)
apply like terms while retaining order of operations
6 - (-5) = 11
4^x - 1 - 2x + 11
Step-by-step explanation:
Answer:
f(g(x)) = 2x + 1
Step-by-step explanation:
Substitute x = g(x) into f(x) , that is
f(g(x))
= f(2x)
= 2x + 1
Ms. Haven recorded the number of homework assignments her students completed
and their test grades. Her findings are shown in the table. Which ordered pair is an
outlier in this data set?
Answer:
(6, 97) is the outlier.
Step-by-step explanation:
When we have a data set:
x: x₁, x₂, x₃, ..., xₙ
y: y₁, y₂, y₃, ..., yₙ
Each one of the pairs (x₁, y₁), (x₂, y₂), etc, is an ordered pair that belongs to the data set.
Usually, these values are distributed in some way that, we assume, is normalized. So if one of these ordered pairs is really different from the others, then that pair is called an "outlier".
In the data set, we have:
Number of homework completed vs Score assigned.
You can see that, as the number of homework completed increases, also does the score
For example, for the smaller number of homework completed, (5) the score is 67, the minimum score.
And as the number of homework completed reaches to 10, the score increases to 90 or 98.
But there is an outlier there, you can see that a student that only completed 6 times the homework, has a score of 97 (one of the largest scores) (this score is more than all the scores for the students with 6, 7, 8 and 9 completed homeworks) so we can conclude that this one is the outlier.
(6, 97) is the outlier.
Solve for brainliest!
Igor’s summer job at the frozen yogurt shop paid him the following amounts in his first three days on the job (he got paid the same hourly rate every day).
Answer:
$9.50
Step-by-step explanation:
Answer: the unit rate is $9.50
and graph x to (0,0) and y to (1,9.5)
Step-by-step explanation:
make sure answer is in degrees.
sin^-1(sin 17°)
Answer:
uhm 0 degrees
Step-by-step explanation:
The value of the inverse trigonometric expression sin⁻¹(sin 17°) will be 17°.
What is inverse trigonometry?Simply put, inverse trigonometric operations are the opposites of the fundamental trigonometric parameters sine, cosine, secant, cosecant, tangent, and cotangent.
The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The inverse trigonometric expression is given below.
⇒ sin⁻¹(sin 17°)
We know that the value of sin⁻¹(sin θ) is θ.
Then the value of the inverse trigonometric expression will be
⇒ sin⁻¹(sin 17°)
⇒ 17°
Thus, the value of the inverse trigonometric expression sin⁻¹(sin 17°) will be 17°.
More about the inverse trigonometry link is given below.
https://brainly.com/question/20595059
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quick please
7.find the area of the shaded region of the rectangle:
Answer:
6x+2
-2x+1
=
4x+1
just find the area of each and subtract the non-shaded one from the shades area.
Kirk made the graph to show his prediction of a population of bacteria over time. Which function best models the data in the graph?
mc001-1. jpg
mc001-3. jpg
mc001-2. jpg
mc001-4. jpg
Jana predicts that the population, y, will grow according to y = 12 log(x + 1) + 10, where x is the time in minutes. How much greater does Kirk’s model predict the population will be after 60 minutes than Jana’s model?
✔ greater by about 50 bacteria
Answer:
greater by about 50 bacteria
hope this helps,
T
Step-by-step explanation:
Populations can be modeled by exponential functions and logarithm functions.
Kirk's function is: [tex]\mathbf{f(x) = (10)2^{\frac{x}{20}}}[/tex]Kirk’s model predict the population will be greater than about 50 bacteria after 60 minutes than Jana’s modelKirk's graph is an exponential function, and it is represented as:
[tex]\mathbf{y = ab^x}[/tex]
From the graph (see attachment);
x = 0, when y =10.
So, we have:
[tex]\mathbf{10 = ab^0}[/tex]
[tex]\mathbf{10 = a\times 1}[/tex]
[tex]\mathbf{10 = a}[/tex]
Rewrite as:
[tex]\mathbf{a = 10 }[/tex]
Substitute [tex]\mathbf{a = 10 }[/tex] in [tex]\mathbf{y = ab^x}[/tex]
So, we have:
[tex]\mathbf{y = 10(b)^x}[/tex]
x = 20, when y =20.
[tex]\mathbf{20 = 10(b)^{20}}[/tex]
Divide both sides by 10
[tex]\mathbf{2 = b^{20}}[/tex]
Take 20th root of both sides
[tex]\mathbf{b = 2^{\frac{1}{20}}}[/tex]
Substitute [tex]\mathbf{b = 2^{\frac{1}{20}}}[/tex] in [tex]\mathbf{y = 10(b)^x}[/tex]
[tex]\mathbf{y = 10(2^{\frac{1}{20}})^x}[/tex]
[tex]\mathbf{y = (10)2^{\frac{x}{20}}}[/tex]
Represent as function
[tex]\mathbf{f(x) = (10)2^{\frac{x}{20}}}[/tex]
So, Kirk's function is: [tex]\mathbf{f(x) = (10)2^{\frac{x}{20}}}[/tex]
When x = 60, we have:
[tex]\mathbf{f(60) = (10)2^{\frac{60}{20}}}[/tex]
[tex]\mathbf{f(60) = (10)2^3}[/tex]
[tex]\mathbf{f(60) = (10)8}[/tex]
[tex]\mathbf{f(60) = 80}[/tex] ---- Kirk's model
For Jana's model, we have:
[tex]\mathbf{y = 12log(x + 1) + 10}[/tex]
Substitute 60 for x
[tex]\mathbf{y = 12log(60 + 1) + 10}[/tex]
[tex]\mathbf{y = 12log(61) + 10}[/tex]
Using a calculator, we have:
[tex]\mathbf{y \approx 31}[/tex] --- Jana's model
Calculate the difference between both models
[tex]\mathbf{d = 80 - 31}[/tex]
[tex]\mathbf{d = 49}[/tex]
Approximate
[tex]\mathbf{d \approx 50}[/tex]
Hence, Kirk’s model predict the population will be greater than about 50 bacteria after 60 minutes than Jana’s model
Read more about population models at:
https://brainly.com/question/8993571
Which is the answer ? Please help
Answer:
C
Step-by-step explanation:
1/2 is equal to 2/4 so 1/2 is greater than 1/4
Answer:
C
Step-by-step explanation:
A)
[tex]\frac{1}{2} = \frac{4}{8}[/tex]
[tex]\frac{4}{8} < \frac{1}{8}\ is\ wrong!\ Therefore\ A\ is\ wrong[/tex]
B)
[tex]\frac{2}{1} = \frac{4}{2}[/tex]
[tex]\frac{1}{2} = \frac{4}{2}\ is\ wrong!\ Therefore\ B\ is\ wrong[/tex]
C)
[tex]\frac{1}{2} = \frac{2}{4}[/tex]
[tex]\frac{2}{4} > \frac{1}{4}\ is\ correct!\ Therefore\ C\ is\ correct[/tex]
D)
[tex]\frac{1}{2} = \frac{2}{6}[/tex]
[tex]\frac{2}{6} < \frac{1}{6}\ is\ wrong!\ Therefore\ D\ is\ wrong[/tex]
Margaret is saving money for her summer vacation. She calculates that her starting amount is 0.4% of the total amount she wants to save. What is 0.4% written as a decimal?
Will give brainliest for help with Geometry
Answer for first question:
tangent of P= 4/3
cosine of P= 3/5
sine of P= 4/5
Explanation:
tangent = opposite/ adjacent
cosine = adjacent/ hypotenuse
sine = opposite/ hypotenuse
2nd question: x=12
Explanation: When you have a 45-45-90 degree angle the hypotenuse will always be twice the base of the triangle and the longer leg will always be √2 times the base. Here you have the measurement of one of the longer sides- 6√2. Because we have this measurement, we know the base is going to be 6 and the hypotenuse, x, will be 12.
3rd question: cos y
Explanation: Let's give the triangle some measurements to make this easier.
The hypotenuse= 5.
The adjacent side of x= 3.
The opposite side of x= 4.
sine= opposite/ hypotenuse = sin x = 4/5
cosine= adjacent/ hypotenuse = cos x = 3/5
As you see, 3/5 and 4/5 are not equal, but when you try cos y and sin x. You will find that they are equal.
These cones are similar. Find the volume of the smaller cone. Round to the nearest tenth. 2 cm 5 cm Volume=[?]cm^ 3 Volume me = 131 cm ^ 3
Answer:
8.4 cm^3 to the nearest tenth.
Step-by-step explanation:
The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.
So:
5^3 / 2^3 = 131 / v
v = 2^3 * 131 / 5^3
= 8 * 131 / 125
= 8.384.
The volume of smaller cone is 8.4 cm³
What is Volume of Cone?The volume of a cone formula is given as one-third the product of the area of the circular base and the height of the cone. According to the geometric and mathematical concepts, a cone can be termed as a pyramid with a circular cross-section. By measuring the height and radius of a cone, you can easily find out the volume of a cone. If the radius of the base of the cone is "r" and the height of the cone is "h", the volume of cone is given as V = (1/3)πr²h.
By applying Pythagoras theorem on the cone, we can find the relation between volume and slant height of the cone.
We know, h² + r² = L²
⇒ h = √(L² - r²)
where,
h is the height of the cone,
r is the radius of the base, and,
L is the slant height of the cone.
The volume of the cone in terms of slant height can be given as V = (1/3)πr²h = (1/3)πr²√(L² - r²).
Given:
The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.
Then,
5³ / 2³ = 131 / v
v = 2³ * 131 / 5³
v = 8 * 131 / 125
v = 8.384 cm³
Learn more about volume here:
https://brainly.com/question/1984638
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Janessa is playing a board game with two friends. Using a single die, one friend rolled a four, and the other friend rolled a three. Janessa needs to roll a number higher than both friends to win the game, and she wants to calculate her probability of winning.
What is the sample space for Janessa’s calculation?
[5, 6]
[1, 2, 5, 6]
[1, 2, 3, 4, 5, 6]
[3, 4]
Answer:
C) [1, 2, 3, 4, 5, 6]
Step-by-step explanation:
Sample space is all possible outcomes of the event so she could roll any number on the die.
Answer:
5,6 she needs a higher number not anything lower then 5 or 6.
Step-by-step explanation:
im struggling and need help fast please show work and tell me how to do it. no links
-22.8 = 6n check your solution
Answer:
-3.8=n
Step-by-step explanation:
My goal is to get n all by itself, but its multiplied by 6. If I do the inverse operation (which is division) on both sides I will get -22.8/6=n. Now I can just simply combine the like terms and finalize my answer. 6 * 3=18 but -22.8 is a decimal number so my answer will range from around 3.5-3.9. if I divide -22.8/6 I get -3.8. My final answer is n=-3.8
the coordinates of point D are (-10, -3) and the coordinates for point G are (-2, -3). Where is point D in relation to point G?
Answer: Choice C
Point D is 8 units to the left of point G
=================================================
Explanation:
Refer to the diagram below. I've graphed both points on the same xy grid. We can draw a horizontal line through points D and G to form a number line of sorts. Count the number of spaces along this number line to go from G to D. You should count 8 spaces to the left.
Effectively, this is the same as drawing a number line and plotting -10 and -2 on this number line. We only worry about the x coordinates of the two points since the y coordinates are the same (both are y = -3). Note how -10 is eight units to the left of -2 on the number line.
help me i need help will mark brainliest
Answer:
C
Step-by-step explanation:
i am smart
Answer: -3? i think..
Step-by-step explanation:
Could someone please answer this, and give an explanation. So I can fully understand it.
what's the answer ?
[tex] \sqrt{36 \times 9} [/tex]
Answer:
36/2=18
18/2=9
9/3=3
3/3=1
List out the factors used: 2, 2, 3 & 3.
Pick one out of pairs of factors available: 2 & 3.
Multiply them: 2×3 = 6
6 is the square root of 36.
Step-by-step explanation:
hope it helps
please mark brainliest
Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $19.50. The oil change for the other car required 7 quarts of oil and cost $22.00. How much is the labor fee and how much is each quart of oil?
Answer:
quart of oil = $1.25
labour = $13.25
Step-by-step explanation:
let x = cost of each quart of oil
y = flat fee for labour
two equations can be formed from the question
5x + y = 19.50 equation 1
7x + y = 22 equation 2
subtract equation 1 from 2
2x = 2.5
divide both sides by 2
x = 1.25
substitute for x in equation 1
5(1.25) + y = 19.50
y = 19.50 - 6.25
y = $13.25
which of the following is equivalent
Answer: 20√2
Step-by-step explanation:
At a carnival, Hayley gets to spin a prize wheel. It has a radius of 8 inches. What is the prize wheel's area?
Answer:
201.06in^2
Step-by-step explanation:
Use area formula which is pi(r)^2
Answer:
200.96 in.
Step-by-step explanation:
**THE PRIZE WHEEL IS THE SHAPE OF A CIRCLE.**
The formula for area of a circle is: πr² (3.14 × radius × radius).
**3.14 IS COMMONLY USED FOR PI**
According to the word problem, the prize wheel has a radius of 8.
πr² (3.14 × radius × radius)
π8² (3.14 × 8 × 8) = 200.96
Therefore, the area of the prize wheel is 200.96 in.
Help me plz and thank you
[tex]1) \: 21 + 35.[/tex]
[tex]2) \: 5.[/tex]
Answer:
21 + 355Step-by-step explanation:
1.
To expand the expression 7(3+5), multiply 7 into the numbers in the blanket. That means 7×3 + 7×5 = 21 + 35.
2.
It's the result of the expression on the right. It's 5 because 5(3-2) = 5×3 + 5×2 = 15 - 10.
How would you prove that QRST is a rectangle?
The solution of the quadratic equation 3x^2=4x is written by a student as the following: According to you, is this students solution correct or not? Explain your answer with reasons?
Solution:
Step 1:3x2 = 4x
Step 2: 3xx = 4x
Step 3:3x = 4
Step 4: x = 4/3
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Arun sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 128 visitors purchased no costume. 3 visitors purchased exactly one costume. 5 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase exactly one costume as a fraction in simplest form.
Answer:
3/136
Step-by-step explanation:
128 + 3 + 5 = 136
= 3/136 (simplest form)
What are the x and y coordinartes of the point at 4pi/3
This week only, the local coffee shop is reducing the price of a cup of coffee from $3.00 to $2.28. By what percentage is the price reduced?
Answer:
31.6% decrease
Step-by-step explanation:
percent of change = difference between original and new values divided by the original value
n = % change
n = 0.72/2.28
n = .3157
n = 31.6%
If bookshelf A is 6 feet long and bookshelf B is 8 feet long, what is the length of bookshelf C?
A.14
B.12
C.16
D.10
Help me please
Answer:
3.5 feet = 3 feet 6 inches
3 * 12 = 36
36 + 6 = 42 inches long
42 / 5/8 → 42 * 8/5 = 42*8/5
336 / 5 = 67.2
We can't put up part of a book, so we can fit 67 books.
Step-by-step explanation:
Solve x3 = 270. A) x = 3 10 B) x = 10 3 C) x = 30 9 D) x = 9 30
Answer:
A.) 3[tex]\sqrt[3]{10}[/tex]
Step-by-step explanation:
x3 = 270
↓
[Take the root from from both sides and solve]
↓
x = 3[tex]\sqrt[3]{10}[/tex]
[Assuming you couldn't paste the square root symbol and subscript numbers, the answer should be A]
↓
A.) 3[tex]\sqrt[3]{10}[/tex]
[ANSWER CHOICES]
A.) x = 3 10
B.) x = 10 3
C.) x = 30 9
D.) x = 9 30
2. Enrico earns a 3% commission on everything he sells at a store. On one day, he sold items priced at $86, $245, and $295. How much commission did he earn that day?
Answer
A. $18.78
B. $88.50
C. 5187.80
D. $626
Answer:18.75
Step-by-step explanation:
what is the solution to the equation x^2-2x=-2
Step-by-step explanation:
[tex] {x}^{2} - 2x = - 2 \\ {x}^{2} - 2x + 2 = 0 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{ - ( - 2)± \sqrt{ {( - 2)}^{2} - (4 \times 1 \times 2)} }{2 \times 1} \\ x = \frac{2± \sqrt{ - 4} }{2} \\ x = \frac{2±2i}{2} \\ x = \frac{2 + 2i}{2} \: or \: \frac{2 - 2i}{2} \\ x = 1 + i \: \: or \: \: 1 - i \\ x = 1±i[/tex]