Answers
The standard equation of parabola with vertex (h,k) is :
(x - h)² = 4a(y - k)
The given eqation is : (x + 2)² = 4(y - 1)
On comparing the given equation with the standard equation we get
h = -2, a = 1 and k = 1
Vertex is ( h,k)
So, the vertex of the given equation of parabola is (-2, 1)
Answer : B (-2, 1)
Related Questions
Unit 4 What is the rate of return when 20 shares of Stock A, purchased for $20/share, are sold for $490? The commission on the sale is $6. Rate of Return = [?] % Give your answer as a percent rounded to the nearest tenth.
Answers
Answer:
21%
Step-by-step explanation:
You want the rate of return on 20 shares of stock bought for $20 per share and sold for $490 with a commission on the sale of $6.
Rate of returnThe rate of return is the percentage change between the sale proceeds and the cost of the stock.
rate of return = (proceeds/cost -1) × 100%
= ((490 -6)/(20·20) -1) × 100% = 21%
The rate of return is 21%.
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Two more than the cube root of a number
Answers
We have
[tex]undefined[/tex]PLEASE HELP ME.Match the shape with its area formula Column A Column B 1: Triangle a. A= LW2: Parallegram. b: A=(TTr^2)/23: Semi- circle. c:(bh)/2 or 1/2(bh)4:Trapizoid. D. A= (b1+b2)(h)2
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1. Triangle: the area of the triangle is C. (bh)/2
2:Parallegram: the area is a. LW
3. Semi-circle: the area is b. (pi r^2)/2
4. Trapezoid: the area will be D. (b1+b2)(h)2
2 (3s' + 9s + 3) - (6s + 1) Submitadd and subtract polynomialswe're doing subtract for this one
Answers
SOLUTION
[tex]undefined[/tex]Andy, Bobby, and Cathy each went for a walk yesterday afternoon. Andy walked 1 3/4 mi at a constant speed of 1 1/4 mi/h. Bobby walked 2 3/4 mi at a constant speed of 2 1/2 mi/h. Cathy walked for 1 h and 22 min at a constant speed of 1 1/4 mi/h. List the three people in order of the times they spent walking from least time to greatest time.
Answers
Answer:
In order of the times they spent walking from the least to the greatest time, we have:
Cathy
Andy
Bobby
Explanation:
Given the following:
Andy walked 1 3/4 min at a constant speed of 1 1/4 mi/h
Bobby walked 2 3/4 mi at a constant speed of 2 1/2 mi/h
Cathy walked for 1 h and 22 min at a constant speed of 1 1/4 mi/h
We are required to list the three people in order of the times they spent walking from least to the greatest time,
This is the same thing as listing the following numbers:
1 3/4, 2 3/4, and 1h 22min from least to greatest.
Andy: 1 3/4 = 7/4 = 1.75 = 2 hours, 15 minutes
Bobby: 2 3/4 = 11/4 = 2.75 = 3 hours, 15 minutes
Therefore, from the least to the greatest time, we have:
Cathy
Andy
Bobby
[tex] \frac{1}{5} [/tex]convert into a prercentage
Answers
Answer:
20%
Explanation:
To convert a fraction into a percentage, multiply the fraction by 100.
Thus, the fraction 1/5 as a percentage is:
[tex]\begin{gathered} =\frac{1}{5}\times100 \\ =\frac{100}{5} \\ =20\% \end{gathered}[/tex]The percentage equivalent of 1/5 is 20%.
9. Leyla has 18 50-cent and 20-cent coins altogether. She has a total of $6.90. How many 20-cent coins does she have?
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According to the information given in the exercise:
- Leyla has 18 coins of 50 cents and 20 cents.
. She has a total of $6.90.
Let be "f" the number 50-cent coins and "t" the number 20-cent coins.
Since 1 dollar is equal to 100 cents, you know that:
[tex]6.90dollars=690cents[/tex]Then, knowing the above, you can set up the following System of Equations:
[tex]\begin{cases}f+t=18 \\ \\ 50f+20t=690\end{cases}[/tex]To find the value of "t", you can apply the Substitution Method:
1. Take the first equation and solve for "f":
[tex]f=18-t[/tex]2. Substitute this equation into the second equation and solve for "t":
[tex]\begin{gathered} 50f+20t=690 \\ \\ 50(18-t)+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 50(18-t)+20t=690 \\ \\ 900-50t+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 900-30t=690 \\ \\ -30t=690-900 \\ \\ -30t=-210 \end{gathered}[/tex][tex]\begin{gathered} t=\frac{-210}{-30} \\ \\ t=7 \end{gathered}[/tex]Therefore, the answer is: She has 7 coins of 20 cents.
graph the function f(x)=3-(x)
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The given function is
[tex]f(x)=3-x[/tex]To graph this linear function we have to complete a table of values. We replace each x-value in the function to get each y-values to form coordinated pairs.
x f(x)
-2 5
-1 4
0 3
1 2
Let's do the calculations for each f(x) value.
[tex]\begin{gathered} f(-2)=3-(-2)=3+2=5 \\ f(-1)=3-(-1)=3+1=4 \\ f(0)=3-0=3 \\ f(1)=3-1=2 \end{gathered}[/tex]At last, we have to graph each point and draw a straight line. The graph below shows the graph for the function.
An uber charges a flat fee of $1.50, plus an additional $0.75 per mile. If Max only
has up to $12 to spend?
Answers
Answer:
14 miles
Step-by-step explanation:
If you have $12 to spend and there's a flat fee $1.50
You subtract your $1.50 from $12
12-1.50=10.50
Then you divide 10.50 by .75
10.50÷.75=14
So you get 14 miles with $12
2. Find the radian measure of an angle of 320°. (Leave in terms of rr.) A. 9 16 0 B. 16 9t 0 90 ID 10
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SOLUTION
Find the radian measure of an angle of 320°. (Leave in terms of rr.)
We have that 360° × π/180 = 6.283rad
Do you
320° x π / 180 =
expand and simplify(p+4)(P+3)P-1)
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In linear equation, p³ - 6p² + 5p - 12 is simplify od equation .
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).(p+4)(P+3)(P-1)
= p² + 3p + 4p + 12
= ( p - 1 ) ( p² + 3p + 4p + 12 )
= p³ + 7p² + 12p - p² - 7p - 12
= p³ - 6p² + 5p - 12
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Which of these frequency counts would be represented by the largest number of dots in a dot plot?
A. 25
B.23
C.24
D.22
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The frequency count that a dot plot's greatest number of dots would depict is 25 (option A).
Given that,
The Option a is 25, b is 23, c is 24 and d is 22.
What is a dot plot?A dot plot is a graph that shows the frequency of a set of data and is comparable to a histogram. The frequency of the data is represented by the dots in the dot plot. The number of dots increases as the frequency of a data increases.
According to the information in this question, 25 would have the most dots, whilst 22 would have the fewest. A dot plot is a useful tool for displaying frequencies. Additionally, it works well with small data sets.
Therefore, The frequency count that a Gain on equipment sale equals selling price minus book value of equipment dot plot's greatest number of dots would depict is 25 (option A).
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The left and the right page of numbers of an open book are two consecutive integers whose sum is 381 . Whats are the page numbers
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In order to determine the number of page numbers, let x the number of one page and x + 1 the number of the other page.
The sum of both numbers is 381, then:
x + (x + 1) = 381
Solve the previous equation for x, as follow:
x + x + 1 = 381 simplify like terms
2x + 1 = 381 subtract 1 both sides
2x = 381 - 1
2x = 380 divide by 2 both sides
x = 380/2
x = 190
Then, the numbers are 190 + 191
to rent a booth at a County Fair cost $42 per day plus a one-time equipment fee of $85 find the number of days mr. Jones rented a booth if he paid a total of $337
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Solve the following equation for x. Please show all your solution steps. 2x - 5 + 3x = x - 41
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a 180 ounce bag weighs more than an 11 lb bag true or false
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Let's make a conversion:
[tex]180oz\times\frac{1lb}{16oz}=11.25lb[/tex]Since:
[tex]11.25lb>11lb[/tex]It's true
Consider the following quadratic equation - x ^ 2 + 3x - 7 = 0 Step 1 of 2 Find the values of a , b, and that should be used in the quadratic formula to determine the solution of the quadratic equation
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Recall that the quadratic formula states that the solution to the quadratic equation:
[tex]ax^2+bx+c=0[/tex]are:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]Notice that a is the coefficient of the quadratic part, b is the coefficient of the linear part and c is a constant.
We can rewrite the given equation as follows:
[tex](-1)x^2+3x+(-7)=0.[/tex]Therefore, the values a, b, and c that should be used in the quadratic formula to compute the solutions to the quadratic equation:
[tex]-x^2+3x-7=0[/tex]are:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} a=-1, \\ b=3, \\ c=-7. \end{gathered}[/tex]what is 9/7 ÷ 2/3 ?
Answers
we have the expression
[tex]\frac{9}{7}\div\frac{2}{3}=\frac{9*3}{2*7}=\frac{27}{14}[/tex]The answer is 27/14Traci needs to change $300 US Dollars into Euros. the exchange rate is 1 euro for 1.25 dollars. how many euros does Traci get for her dollars?
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Let's begin by identifying key information given to us:
Amount = $300
Amount (after changing) = ?
Exchange rate: €1 = $1.25
We will calculate how much Euros Traci gets for her dollar using simple proportion:
[tex]\begin{gathered} x=\text{\$}300 \\ \euro1=\text{\$}1.25 \\ \text{Cross multiply, we have:} \\ 1.25(x)=300\cdot1 \\ x=\frac{300}{1.25}=240 \\ x=\euro240 \end{gathered}[/tex]Therefore, Traci gets €240 for her dollars
9. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel.
Answers
Answer:
If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding, consecutive interior) angles are congruent, then the lines are parallel
Explanation:
When two lines are cut by a transversal so that alternate interiors, alternate exterior or corresponding, are congruent, then the line must be parallel
If;
[tex]\begin{gathered} \measuredangle a=\measuredangle b\text{ (alternate interior)} \\ \measuredangle x=\measuredangle y\text{ (alternate exterior)} \\ \measuredangle x=\measuredangle b\text{ (corresponding angles)} \end{gathered}[/tex]then the lines are parallel.
Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5
Answers
As given by the question
There are given that the graph of the line.
Now,
To find the slope and y-intercept of the line, first select two intersect point from the graph.
Then,
The points are:
[tex](0,\text{ 5) and (5, 0)}[/tex]Then,
First find the slope,
So,
From the formula of slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]Then,
Put all the value into the given formula.
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]Now,
From the standard form of the line,
[tex]y=mx+b[/tex]Then,
Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept
So,
[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]Hence, the value of the y-intercept is 5.
Now,
The line equation is shown below:
[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.
5. The shadow of a tree extends 25 feet from the top of the tree to the ground. Sarah measures thatthe distance from the base of the tree to the tip of its shadow is 15 feet. How tall is the tree?A. 20 feetB. 25 feetC. 29.2 feetD. 40 feetO
Answers
Given :
The shadow of the tree = 25 feet from the top of the tree to the ground
the distance from the base of the tree to tip of its shadow is 15 feet
Let the height of the tree = x
So, 25 , 15 and x are forming a right angle triangle
25 is the hypotenuse of the triangle ,
x and 15 are the legs of the triangle
WE will find x using Pythagorean theorem
So,
[tex]\begin{gathered} x^2+15^2=25^2 \\ x^2=25^2-15^2=625-225=400 \\ x=\sqrt[]{400}=20 \end{gathered}[/tex]So, the height of the tree = 20 feet
The answer is option A. 20 feet
Trey made $2000 in taxable income last year. suppose the income tax rate is 10% for the first $9500 plus 14% for the amount over $9500. How much must trey pay in income tax for last year?
Answers
SInce he made $2000 , and this is less than the limit for the first bracket, Trey will need to pay just 10% on his gain:
10% of $2000 = 0.1 * 2000 = $200.
His tax is $200.
Sam paid $4.50 to have two shirts cleaned. If the dry cleaning service charges the same amount for any shirt, which equation can be used to represent the total cost, c, of having n shirts cleaned? A c = 4.5n B. c = 2.25n C. c = 4.5 +n D. c = 2.25 + n
Answers
Sam paid $4.50 to have two shirts cleaned.
If the dry cleaning service charges the same amount for any shirt then it means that for each shirt the rate is
[tex]\frac{\$4.50}{2}=\$2.25[/tex]If there are n shirts then the total cost (c) of the shirts can be represented by the following equation.
[tex]c=2.25n[/tex]If you substitute n = 2 shirts into the above equation then the total cost will be $4.50 which satisfies the given information.
Therefore, the correct answer is option B
Find the Value of X, round your answer to the nearest 10th
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The value of x is 13.31 units.
What is trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given a right angle with perpendicular = 8 units and base = x units and one acute angle = 59°
tangent of an angle = perpendicular/base
Therefore,
tan59° = x/8
x = tan59°*8
x = 13.31
Hence, the value of x is 13.31 units.
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The following histogram represents the points earned by students on a vocabulary pre-test.
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Explanation
By observation, the number of student scores represented on the histogram can be gotten by adding up the frequency. This can be seen below.
[tex]3+2+7+8+4=24[/tex]Answer: 24(option 1)
I need help with my practice questions. I don’t know where i’m supposed to plot the points on the graph and I need an explanation please.
Answers
Step by step
When rotating a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means, you change the sign on your x value first and then switch positions of x and y.
X = (2, -1) ➡️ X’ = (-1, -2)
Y = (-4, -3) ➡️ Y’ = (-3, 4)
Z = (3, 2) ➡️ Z’ = (2, -3)
Now to graph, start with your pre image points. (x, y)
From (0, 0) center /origin, move your cursor (left negative or right positive) for x, (down negative or up positive) for y.
Then plot your image points to see how the figure has transformed.
I graphed them for you in the attachment
If the population of a small town satisfies the exponential model A = Aoe^0.015t, where is measured in years, how long will it take for the town's population to increasefrom 5,450 to 10,355? Round your answer to two decimal placesAnswer
Answers
ANSWER :
The answer is 42.79 years
EXPLANATION :
From the problem, we have the function :
[tex]A=A_oe^{0.015t}[/tex]Solve for the value of t when A = 10,355 and Ao = 5,450
That will be :
[tex]\begin{gathered} 10355=5450e^{0.015t} \\ \frac{10355}{5450}=e^{0.015t} \\ 1.9=e^{0.015t} \\ \text{ Take the ln of both sides :} \\ \ln(1.9)=\ln(e^{0.015t}) \\ \ln(1.9)=0.015t \\ t=\frac{\ln(1.9)}{0.15} \\ t=42.79 \end{gathered}[/tex]Diane opened a savings account 3 years ago the account earns 9% interest compounded monthly if the current balance is 100.00 how much did she despoit initially
Answers
Answer:
The amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]Explanation:
We want to find the amount of Principal she deposited initially.
Recall that the formula for calculating the Principal of a compound interest is;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Where;
P = Principal / initial amount
A = Future/ final amount
r = Interest rate (decimal)
n = number of times the interest is compounded per year.
t = Time in years
From the question, we were given the following;
A = $100.00
r = 9% = 0.09
n = monthly (12 months in a year) = 12 times
t = 3 years
Substituting the given values into the formula, we have;
[tex]\begin{gathered} P=\frac{100.00}{(1+\frac{0.09}{12})^{12(3)}} \\ P=\frac{100.00}{(1+0.0075)^{36}} \\ P=\frac{100.00}{(1.0075)^{36}} \\ P=76.41 \\ P=\text{ \$76.41} \end{gathered}[/tex]Therefore, the amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]-4x-5-2x+3 simplify
Answers
Starting with the expression:
[tex]-4x-5-2x+3[/tex]Use the commutative property to bring like terms together:
[tex]-4x-5-2x+3=-4x-2x-5+3[/tex]Add like terms:
[tex]-4x-2x-5+3=-6x-2[/tex]Therefore:
[tex]-4x-5-2x+3=-6x-2[/tex]