The vertex form of Parabola is y= 1/4(x + 2)² -4 .
What is Vertex form of Equation?The general equation of a parabola is given by y = a(x – h)² + k or
x = a(y – k)² +h. Here (h, k) is vertex.
Given:
focus at (–2,–3) and a directrix at y = –5.
We know, the standard form is (x - h)² = 4p (y - k),
where the focus is (h, k + p) and the directrix is y = k - p
So, (h, k + p) = (-2, -3)
h = -2, k + p = -3
Directrix is y = k - p:
k - p = -5
k + p = -3
so, 2k = -8
k = -4
and, p = -3+ 4 = 1
Thus, the vertex is at (-2, -4) and p = 1, the equation is:
(x + 2)² = 4(y+ 4)
1/4(x + 2)² = y+4
y= 1/4(x + 2)² -4
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Eva needs to lease out a music studio to record her new album. The studio charges an
hourly fee of $50 and an initial studio-use fee of $100. Make a table of values and
then write an equation for P, in terms of t, representing the amount of money Eva
would have to pay to use the studio for t hours?
Answer:
Equation:
50t + 100 = P
Table:
T P
0 100
1 150
2 200
3 250
4 300
Step-by-step explanation:
$100 - starting value because it is the initial studio use fee
50t - since 50 dollars is the hourly fee, you have to multiply it by t (time)
Word problem 2: Paula wants to divide 480 tomatoes equally among 40 baskets. How man
will Paula put in each basked?
Answer:
12
Step-by-step explanation:
480 tomatoes/40 baskets = 12 per basket
Neha got 68% in a Nepali test. How many marks out of 25 is this? How many marks out of 25 did she get in English if her percentage of marks was 72?
Answer:
Nepali=17 English=18
Step-by-step explanation:
first in Nepali,
Marks= 68% of 25=68/100*25=17Likewise,in English,marks=72%of25=72/100*25=18pls help!!will give 18 points!!!PLS HELP
Answer:
a = 108°
b = 72°
c = 48°
d = 48°
Step-by-step explanation:
• ∠a and the 72° angle are on a straight line. Therefore they add up to 180°:
∠a + 72° = 180°
⇒ ∠a = 180 - 72°
⇒ ∠a = 108°
• ∠b and the 72° angle are corresponding angles (the angles make an F-shape). Therefore, they are equal:
∠b = 72°
• ∠d and the 48° angle are alternate angles (the angles make a z-shape). Therefore they are equal:
∠d = 48°
• ∠c and ∠d are vertically opposite angles. Therefore, they are equal:
∠c = ∠d
⇒ ∠c = 48°
Solve for x. 12x +7< -11 or 5x-8>40
The solution of the inequalities is x < - 3 / 2 or x > 48 / 5
How to solve inequalities?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Inequality expression always have the symbols <, >, ≤ and ≥.
Therefore, let's solve the inequalities.
12x + 7 < - 11 or 5x - 8 > 40
12x + 7 < - 11
subtract 7 from both sides of the inequalities.
12x + 7 - 7 < - 11 - 7
12x < - 18
divide both sides by 12
x < - 18 / 12
x < - 3 / 2
5x - 8 > 40
add 8 to both sides of the inequalities
5x - 8 + 8 > 40 + 8
5x > 48
divide both sides by 5
x > 48 / 5
x > 48 / 5
Therefore,
x < - 3 / 2 or x > 48 / 5
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can you solve the question that is showed below
5x5=9+3
The value of x is 1.1913
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
5[tex]x^5[/tex] = 9+3
5[tex]x^5[/tex] =12
[tex]x^5[/tex]=12/5
Take 5th root on both sides
[tex]x=\sqrt[^5]{12/5}[/tex]
x= 1.1913
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IXL Please Help Fast!
Suppose that the equations of line [tex]C[/tex] and [tex]D[/tex] are as follows;
[tex]C=a_{1}x+b{_1}y+c_{1}[/tex][tex]D=a_{2}x+b_{2}y+c_{2}[/tex]If these two lines are parallel to each other, the following equality must be satisfied.
[tex]\frac{a_{1}}{b_{1}} =\frac{a_{2}}{b_{2}}\neq \frac{c_{1}}{c_{2}}[/tex]In summary, the slope of the two lines must be equal to each other.
[tex]m_{C}=m_{D}[/tex]We know the equation of line [tex]C[/tex]. Then let us form the equation of line [tex]D[/tex].
[tex]C=x+7y-14[/tex][tex]D=x+7y+c_{1}[/tex]We must find the variable [tex]c_{1}[/tex] by placing the given point [tex](-3,-1).[/tex]
[tex]-3+7(-1)+c_{1}=0[/tex][tex]c_{1}=10[/tex]If we write it in slope-intercept form, the correct answer will be as follows;
[tex]y=-\frac{x}{7} -\frac{10}{7}[/tex]Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: 45, ordered pair: (0,94)
Answer:
[tex] \huge{ \bold{y = 45x + 94}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is represented by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = 45
In order to find c we substitute the point (0,94) into the equation y = mx + c
That's
[tex]94 = 45(0) + c \\ 94 = 0 + c \\ c = 94[/tex]
We now substitute m and c into the equation
We have the final answer as
[tex] \bold{y = 45x + 94}[/tex]
Hope this helps you
Enzo has fish in two aquariums. In one aquarium, the ratio of the number of guppies to the number of goldfish is 2:3. In the other, this ratio is 3:5. If Enzo has 20 guppies in total, the least number of goldfish that he could have is
A. 29
B. 30
c. 31
d. 32
A radio station has $400 to give away for a contest it gives away $50 prize each week. The equation y=400-50x represents the amount y the radio station has left to give away after x weeks. Find the x and y intercepts and interpret their meaning in the context of the situation
The y-intercept is (0, 400), which represents the amount of money the radio station originally had. The x-intercept is (8, 0), which represents the number of weeks it will take for the radio station to have $0 left.
How to find the x and y intercepts?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Similarly, the x-intercept can be defined as the point at which the graph of any function crosses the x-coordinate and the value of "y" is equal to zero (0).
For the y-intercept, x = 0 and we have the following:
y = 400 - 50x
y = 400 - 50(0)
y = 400.
For the x-intercept, y = 0 and we have the following:
y = 400 - 50x
0 = 400 - 50x
50x = 400
x = 400/50
x = 8.
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Suppose the doubling time of an investment of $10000 is 12 years. What is the annual
percentage growth rate?
A. 9.5%
B. 4.1%
C. 5.9%
The annual percentage growth rate is 5.9%
The doubling time of an investment of $10000 is 12 years
The compound interest caluclated annually can be given by
A=P(1 + r/n)^nt
where A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
20000 = 10000(1 + r)¹²
2⁻¹² = 1 + r
r = 1.059 - 1
r = 0.059
Rate of inetrest = 5.9%
Therefore, the annual percentage growth rate is 5.9%
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help 10 ponits thanks ∝
Answer:
First we convert the sentence to an equation so:
[tex] \frac{3}{4} x = 24[/tex]
Now to isolate x divide by the recuprical of 3 over 4 which is 4/3
[tex] \frac{3}{4} \times \frac{4}{3} = 24 \times \frac{4}{3} [/tex]
24x4= 96 and 3 remains.
[tex]x = \frac{96}{3} [/tex]
Now we can simplify by 3 and we will get the final answer which is
[tex]x = 32[/tex]
PLEASE HELPP!!!!! A number line going from negative 20 to positive 20. What is the absolute value of –20? Use the number line to answer the question. –20 0 20 40
Answer:
C) 20
Step-by-step explanation:
The absolute value of -20 is 20, because absolute value just keeps the same number, but makes positive.
Hope this helped!
A technician working for the Chase-National Food Additive Company would like to estimate the preserving ability of a new additive. This additive will be used for Auntie’s brand preserves. Based on past tests, it is believed that the time to spoilage for this additive has a standard deviation of 5 days. To be 99% confident of the true mean time to spoilage, what sample size will be needed to estimate the mean time to spoilage with an accuracy of one day?
The sample size will be needed to estimate the mean time to spoilage with an accuracy of one day is 166
What is the sample size?The formula for the margin of error is given as
[tex]E = Z*\frac{sd}{\sqrt{n} }[/tex]
The standard deviation is given as sd = 5 days
We have to find the critical value of Z at the confidence level of 99 %
This value is given as 2.576
E = 1 day because the accuracy has been said to be within one day.
We have to insert the values in the formula that we have here
[tex]1 = 2.576*\frac{5}{\sqrt{n} }[/tex]
√n = 12.88
square both sides to get rid of the square root sign
n = 12.88²
n = 165.89
n ~ 166
The sample size would be 166
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Solve the given initial value problem
y''-4y'-5y = 0, y(1) = 0, y'(1) = 2
The solution to the initial value problem in this problem is given as follows:
[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]
How to solve the initial value problem?The initial value problem is given as follows:
y''-4y'-5y = 0.
The first step is finding the roots of the characteristic equation, which is given as follows:
r² - 4r - 5.
The equation can be factored as follows:
r² - 4r - 5 = (r - 5)(r + 1).
Applying the inverse Factor Theorem, the roots are given as follows:
r - 5 = 0 -> r = 5.r + 1 = 0 -> r = -1.These roots are real, hence the format of the solution is given as follows:
[tex]y = Ae^{5x} + Be^{-x}[/tex]
Considering the initial condition at x = 1, we have that:
Ae^(5) + Be^(-1) = 0
Considering the initial condition of the derivative at x = 1, we have that:
5Ae^(5) - Be^(-1) = 2.
Adding the two equations, the condition A is obtained as follows:
6Ae^(5) = 2.
A = 2/(6e^5)
A = 0.0022.
Hence the condition B is:
B = -0.0022e^(5)/e^(-1)
B = -0.8853.
Hence the solution is:
[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]
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three means between 2 and 512
The three geometric mean between 2 and 512 are
When r = 4 , 8,32, 128When r = -4, -8, 32, -128The first term = 2
Consider the common ratio as r
Then the second term = 2r
The third term = [tex]2r^2[/tex]
The fourth term is = [tex]2r^3[/tex]
The fifth term is given that 512
The fifth term = [tex]2r^4[/tex]
Then the equation will be
[tex]2r^4[/tex] = 512
[tex]r^4[/tex] = 512 / 2
[tex]r^4[/tex] = 256
r = ±4
When r = 4
The three geometric mean between 2 and 512 are
2r = 2×4 = 8
[tex]2r^2[/tex] = 2×4×4 = 32
[tex]2r^3[/tex] = 2×4×4×4 = 128
When r = -4
The three geometric mean between 2 and 512 are
2r = 2×-4 = -8
[tex]2r^2[/tex] = 2×-4×-4 = 32
[tex]2r^3[/tex] = 2×-4×-4×-4 = -128
Hence, the three geometric mean between 2 and 512 are
When r = 4 , 8,32, 128When r = -4, -8, 32, -128The complete question is :
Find the three geometric means between 2 and 512.
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What number is equal to square root of 64?
Answer:
+8 or -8
Step-by-step explanation:
Both can be the qrt of 64 because -8 * -8 = + 64
A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as 3 c greater-than-or-equal-to 240. Which graph represents this inequality?
The number of chocolate bars, c, the sports club must sell in order to reach their goal is 80
The graph which represent the inequality 3c ≥ 240 is attached in the picture.What is the number of chocolate bars that must be sold to reach their goal?An inequality refers to a statement that has two quantities in which one is specifically less than (or greater than) another. Symbols of inequality includes:
Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤Let
The number of chocolate bars = cThe inequality that represent the situation is given by
3c ≥ 240
divide both sides by 3c ≥ 240/3
c ≥ 80
Therefore, all real whole numbers greater than or equal to 80 is the number of chocolate bars, c, the sports club must sell in order to reach their goal.
The shaded area to the right of the solid line c = 80 is the graph which represent the inequality.
Complete question:
A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as 3c > 240. Which graph represents this inequality?
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The Body for Life gym charges $15 a month membership fee and a $2 per day usage fee. What does the ordered pair (13, 41) mean?
The ordered pair (13, 41) simply means a daily usage fee of $41 would be charged to use the Body for Life gym for 13 days.
How to calculate the slope-intercept form of the equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x represents the number of days.y represents the daily usage fee.c represents the y-intercept.Based on the information provided, a linear equation which models the situation is given by:
y = 2x + 15
For the ordered pair (13, 41), we have:
y = 2x + 15
y = 2(13) + 15
y = 26 + 15
y = $41.
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The quadratic expression x^2+7x+N can be factored as (x+g)(x+h)(x+g), where N, g, and h are integers.
Prod wrote that N can be equal to -18.
Eleanor wrote that N can be equal to 13.
Assuming Pod wrote that N could be equal to -18, Pod is correct.
What are Quadratic Equations?
A quadratic equation is an equation with a variable to the second power as its highest power term.
The Standard Form of a Quadratic Equation:
ax² + bx + c = 0
where:
x represents an unknown (variable)a, b, and c represent known numbers, where a ≠ 0x² + 7x - 18 = (x + 9)(x - 2) . . . . . g = 9, h = -2
There are no integer factors of 13 that add to give 7. 13 is prime, so the sum of its integer factors is 1+13 = 14.
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Given a2 = 6 and a5 = –384 of a geometric sequence, what is the recursive equation for the nth term?m the text.
The recursive equation for the nth term is aₙ = -4aₙ₋₁
How to determine the recursive equation for the nth term?The definition of the functions is given as
a₂ = 2
a₅ = -384
Sequence type = Geometric sequence
The nth term of a geometric sequence is represented as
aₙ = arⁿ⁻¹
So, we have
a₂ = ar = 6
a₅ = ar⁴ = -384
Divide the equations
r³ = -384/6
Evaluate
r³ = -64
Take the cube roots
r = -4
The recursive equation for the nth term is represented as
aₙ = aₙ₋₁ * r
So, we have
aₙ = -4aₙ₋₁
Hence, the equation is aₙ = -4aₙ₋₁
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A geometric progression has 99 terms, the first term is 12 and the last term is 48. What is the 50-th term?
Answer:
21.5
Step-by-step explanation:
geometric progression formula: [tex]A_{n}[/tex]=A*[tex]r^{n-1}[/tex]
where An is nth term
A is first term
r is common ratio
given [tex]A_{99}[/tex] = 48
A=12
we find r
48=12 *[tex]r^{99-1}[/tex]
48/12=[tex]r^{98}[/tex]
[tex]\sqrt[98]{4}[/tex]=r
r=1.014
so to find 50th term
[tex]A_{50}[/tex]=12*[tex]1.012^{50-1}[/tex]
[tex]A_{50}[/tex]=21.53
I really need help step by step please
Answer:
190 cm²
Step-by-step explanation:
Area of prism:Area of one regular hexagon is given. Multiply 23 *2 and it will give the area of two regular hexagons.
There are 6 rectangles. Find the area of one rectangle and multiply it by 6.
Area of regular hexagon = 23 cm²
Area of rectangle = length * width
= 8 * 3
= 24 cm²
Area of the regular hexagon prism = 2* area of regular hexagon + 6*area of rectangle.
= 2*23 + 6*24
= 46 + 144
= 190 cm²
How much should be deposited in an account paying 4.5% interest, compounded semiannually, in order to have a balance of $ 5,000 after 19 years and 6 months?
*Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.*
Principal ≈ $ ____________
The suitable for blank is 2099.43 approximately.
Let the principle be P.
Time (t) = 19 years and 6 months = 19.5 years
Compound is semiannually.
Rate of Interest (r) = 4.5%
Amount will be (A) = $5000
So, suitable equation is given by,
[tex]A=P\left(1+\frac{r}{200}\right)^2t\\5000=P\left(1+\frac{4.5}{200}\right)^{2\times19.5}=P\left(1+\frac{9}{400}\right)^{39}\\\\P\approx2099.43[/tex]
Hence the suitable for the blank is 2099.43.
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Part 2: The xy-Plane
Use these two graphs to answer questions 4 and 5.
4. Do these graphs represent functions? Explain.
Answer:
Answer and explanation in image
Step-by-step explanation:
Please help with this question
Answer:
c.
Step-by-step explanation:
You want a linear combination of the given 3×3 matrices.
StrategyWe observe that the answer choices are different in most corresponding terms, so we only need to find the value of one term in order to choose the correct answer.
Linear combinationThe expression applied to the matrices is applied to corresponding terms of the matrices. That is, for ...
[tex]C = -2A +7B[/tex]
you will have ...
[tex]c_{11}=-2a_{11}+7b_{11}\\\\c_{11}=-2(4)+7(7)=-8+49\\\\c_{11}=41[/tex]
This matches choice c.
__
Additional comment
Many graphing calculators and all spreadsheets can do the necessary calculations to help you find the desired result matrix.
How much bigger is 5 x 10^4 than 4 x 10^4
Answer:its 10,00 more than it so one
Step-by-step explanation:
10^4=10,000
10,000x4=40,000
10000x5=50,000
Answer:
1 × 10^4
Step-by-step explanation:
5 × 10 ^ 4 = 5 × 10000
= 50,000
4 × 10 ^ 4 = 4 × 10000
= 40,000
Therefore; 50,000 - 40,000
= 10,000 or 1 × 10 ^ 4
Hence 5 × 10^4 is bigger than 4 ×10^4 by
1 × 10^4
Consider the following scenario.
the three-number bet
(a) Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)
dollars
(b) Interpret it. (Round your answer to one decimal place.)
Over time, you should expect to lose about
cents for every dollar you bet.
Refer to the picture if needed
Considering a discrete distribution modeling the situation, it is found that:
a) The expected value of each $1 bet in roulette is of: -$0.988.
b) The interpretation is given as follows: Over time, you should expect to lose about 999 cents for every dollar you bet.
What is the expected value of a discrete distribution?The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
The total number of outcomes for the three-number bet is of:
10 x 10 x 10 = 1000.
As three numbers are taken, and for each number, there are 10 possible outcomes.
Hence the probability of winning is of:
p = 1/1000.
As there is only one correct sequence.
The probability of losing is of:
p = 1 - 1/1000 = 999/1000.
Considering a payout of $11 for a $1 bet, the distribution of earnings is presented as follows:
P(X = 11) = 1/1000.P(X = -1) = 999/1000.Hence the expected value of a $1 bet is calculated as follows:
E(X) = 11/1000 - 999/1000 = -$0.988.
Which means that you are expected to lose approximately 99 cents for every dollar that you bet.
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The average rate of change from 3 seconds to 7 seconds for EACH?
PLEASE HELP HURRY
SLOPE
GOLF BALL
SECONDS METERS
0 0
3 14
7 32
9 24
12 2
BASEBALL
SECONDS METERS
0 0
3 6
7 15
9 13
12 0
Answer:
Golf ball = 4.5, Baseball = 2.25Step-by-step explanation:
The average rate of change between two points is the slope of the line between those points.
Golf ballThe points are:
(3, 14) and (7, 32)The slope is:
m = (32 - 14)/(7 - 3) = 18/4 = 4.5BaseballThe points are:
(3, 6) and (7, 15)The slope is:
m = (15 - 6)/(7 - 3) = 9/4 = 2.25Answer:
[tex]\textsf{Average rate of change of the golf ball}=\dfrac{9}{2}\; \sf m/s[/tex]
[tex]\textsf{Average rate of change of the baseball}=\dfrac{9}{4}\; \sf m/s[/tex]
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\boxed{\dfrac{f(b)-f(a)}{b-a}}[/tex]
To find the average rate of change from 3 to 7 seconds:
a = 3b = 7Therefore, use the formula:
[tex]\implies \dfrac{f(7)-f(3)}{7-3}[/tex]
Golf Ball
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&14\\\cline{1-2} 7&32\\\cline{1-2} 9&24\\\cline{1-2} 12&2\\\cline{1-2}\end{array}[/tex]
From inspection of the table:
f(3) = 14f(7) = 32Substitute these values into the formula to find the average rate of change of the golf ball from 3 seconds to 7 seconds:
[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{32-14}{7-3}=\dfrac{9}{2}\; \sf m/s[/tex]
Baseball
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&6\\\cline{1-2} 7&15\\\cline{1-2} 9&13\\\cline{1-2} 12&0\\\cline{1-2}\end{array}[/tex]
From inspection of the table:
f(3) = 6f(7) = 15Substitute these values into the formula to find the average rate of change of the baseball from 3 seconds to 7 seconds:
[tex]\implies \textsf{Average Rate of Change}=\dfrac{f(7)-f(3)}{7-3}=\dfrac{15-6}{7-3}=\dfrac{9}{4}\; \sf m/s[/tex]
I WILL GIVE YOU BRAINLIEST JUST HELP ME PLEASE!!!!!
Answer:
B. The graph of K has a greater y-intercept
D. The graph of J has a greater slope.
Step-by-step explanation:
Given a table for function J and an equation for function K, you want to know which has the greater slope, and which has the greater y-intercept.
Y-interceptThe y-intercept is the value of the function when x=0. We see from the table that y=2 corresponds to x=0 for function J.
We see from the equation for function K that the constant is 8. This is the value of y when x=0.
Function K has the greater y-intercept (8 vs. 2).
SlopeThe slope is the change in y-value when x increases by 1 unit. We see from the table that y=7 when x=1, so the change in y from x=0 to x=1 is 7-2 = 5. The slope of function J is 5.
The equation for function K has an x-coefficient of 3. This means a change in x of 1 unit will result in a change in y of 3 units. The slope of function K is 3.
Function J has the greater slope (5 vs. 3).
Additional comment
Both functions are graphed in the attachment. The y-intercepts have their points labeled. The graph with the steeper slope is the blue line, function J.