These are the vertex, focus, directrix, and focal width
Vertex: (0, 0), Focus: (0, 7), Directrix: y = -7, Focal width: 28
The vertex, focus, directrix, and focal width of the parabola described by the equation x^2 = 28y are:
Vertex: (0, 0)
Focus: (0, 7)
Directrix: y = -7
Focal width: 28
The vertex of a parabola is the midpoint of the directrix and the focus, which in this case is (0, 0). The focus is the point on the parabolic curve that is closest to the directrix, which in this case is (0, 7).
The directrix is the line along which the distance between the parabolic curve and its focus is minimized, which in this case is y = -7. The focal width is the distance between the focus and the directrix, which in this case is 28.
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A mattress store is having a sale. All mattresses are 30% off. Nate wants to know the sale price of a mattress that is regularly $1,000.
How much is the discount? Enter the amount in the table.
Answer:
$700
Step-by-step explanation:
1. We see the original price is $1,000.
2. Change 30% to a decimal
3. 30/100=0.30
4. Multiply the original cost of the item(mattress) by the percentage.
5. 0.3×1,000=300
6. $300 is the amount discounted.
7. For final price with discount: Take its original price($1,000) and subtract the discount from the original price
8. $1,000-$300=$700
Answer:
$300
Step-by-step explanation:
If 8% is 1400 what would be 100%
Taylor and Raimi each earn an hourly wage. Taylor earn $308 for working 14 hour. Raimi earn $288 for working 12 hour. Which tatement i true?
The statement that is true is that Taylor earned more than Raimi for the hours worked.
Taylor earned $308 for working 14 hours, which is equivalent to $22 per hour. Raimi earned $288 for working 12 hours, which is equivalent to $24 per hour. Therefore, Taylor earned a higher hourly wage than Raimi.
This statement can be further verified by computing the total wages earned by both Taylor and Raimi for the same amount of hours: if both Taylor and Raimi worked 14 hours, Taylor would have earned more than Raimi by $20. To demonstrate, Taylor would have earned $308 for 14 hours and Raimi would have earned $336 for 14 hours.
Therefore, Taylor would have earned the higher wage.
In conclusion, Taylor earned more than Raimi for the hours worked, verifying the statement that Taylor earned more than Raimi.
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The question is in the photo for you to answer.
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionSteps are in the attached photo, this question is testing on the concept of Similar Triangles.
Formula:
[tex]\frac{Shorter \ Length \ of \ line \ segment \ A}{Longer \ Length \ of \ line \ segment \ A} = \frac{Shorter \ Length \ of \ line \ segment \ B}{Longer \ Length \ of \ line \ segment \ B}[/tex]
The mass is 500
grams and the
volume is 40 cubic
centimeters
The mass is 125
grams and the
volume is v cubic
centimeters
The volume is 1.4
cubic centimeters
and the density is 80
grams per cubic
centimeter (et m
equal mass in
grams)
The mass is m
grams and the
volume is v cubic
centimeters.
Equation
The density of an object can be found by taking its mass
and dividing by its volume.
Write an equation to represent the relationship between
the three quantities (density, mass, and volume) in each
situation.
Let the density, D, be measured in grams/cubic
centimeters (or g/cm3).
The density is 12.5 grams per cubic centimeter and 80 grams per cubic centimeter.
What is the density?
Density is a measure of how much mass is contained in a given volume. It is defined as the ratio of mass to volume and is typically measured in units of grams per cubic centimeter (g/cm^3) or kilograms per liter (kg/L).
The mass is 500 grams and the volume is 40 cubic centimeters, therefore the density is:
density = mass / volume = 500 grams / 40 cubic centimeters = 12.5 grams per cubic centimeter
The mass is 125 grams and the volume is v cubic centimeters. To find the value of v, you can use the equation:
density = mass / volume = 125 grams / v cubic centimeters
so v = mass / density = 125 grams / 12.5 grams per cubic centimeter = 10 cubic centimeters
The volume is 1.4 cubic centimeters and the density is 80 grams per cubic centimeter. To find the mass you can use the equation:
mass = density x volume = 80 grams per cubic centimeter x 1.4 cubic centimeters = 112 grams
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PLS HELP ASAP!!! (40 POINTS)
Answer:
the answer is option A
Step-by-step explanation:
Distance between two points
/XY/ = √((X2-X1)²+(Y2-Y1)²)
Therefore
/XY/= √((7-(-5)²+(15-4)²)
Answer:
First a farl we should know,
Distance (d) = √(x2-x1)^2+ (y2-y1)^2
x(-5,4) = (x1, y1)
y(7,15) = (x2, y2)
Now,
Distance (d) = √(x2-x1) + (y2-y1)
Ans = √(7-5)^2 + (15-4)^2
Answred by : - ||Ziddiboy||
The house Trevor's family lives in has 6 66 people (including Trevor) and 3 33 bathrooms. In the past month, each person showered for an average of 480 480480 minutes and used an average 72 7272 liters of shower water (over the entire month). Water costs 0.20 0.200, point, 20 dollars per liter. How much money did Trevor's family spend, in total, on shower water in the past month? dollars
The total amount of money which Trevor's family spend, in total, on shower water in the past month is equal to $86.4.
How to calculate the required amount of money?Based on the information provided about the house Trevor's family lives in, we have the following important parameters;
The total number of persons in Trevor's family house is equal to 6The total volume of water which each person showered with during the month is equal to 72 liters of shower water (over the entire month). The cost of water is equal to $0.20 per liter.Next, we would calculate the total volume of water that is used to shower by six (6) persons as follows;
Total volume of water for 6 persons = 72 × 6
Total volume of water for 6 persons = 432 liters.
Furthermore, the total amount of money that was spent on shower water by Trevor's family in the previous month is given by;
Total amount of money = total volume of water used for shower × cost per liter of water
Total amount of money = 432 × 0.2
Total amount of money = $86.4.
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which of the following number lies between 5595 and 5610 a=5509 b=5590 c=5605
Answer:
The answer is c which is=5605
Answer:
C.
Step-by-step explanation:
Since there's no sequence of numbers, we assume that the number that lies between 5,595 and 5,610 is the mean of the 2 numbers.
However, if we calculate its mean, we can have 5,602.5 and it doesn't appear on any options. Thus, we will choose the nearest value from those options.
The Stock Market Alexander is a stockbroker. He earns 14% commission each week. Last week, he sold $7,100 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
The amount he earned last week in commission is $994.
The commission he earned in 2011 is $51,688
What is the commission?The commission earned is a fraction of the total sales of stocks.
Commission earned = amount of sales x percentage commission
14% x $7,100
= 14/100 x $7,100
= 0.14 x $7,100
= $994
Amount she earned in commission in a year = number of weeks in a year x commission earned per week
= $994 x 52 = $51,688
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What is the solution to the system of linear equations y =- 5x 3?.
The Solution to the system of linear equations given as "y = -5x+3" and "y= 1" is that x = 2/5 and y = 1 .
Linear equations are the equations that are made up of Variables and Constants which are joined by mathematical operators .
The system of linear equations is given to us is: "y = -5x+3" and "y= 1"
Substituting the values of y=1 in y = -5x+3 ,
we get ;
⇒ 1 = -5x + 3 ;
⇒ -5x = 1 - 3 ;
⇒ -5x = -2 ;
⇒ x = (-2)/(-5) ⇒ x = 2/5 .
Therefore , solution can be written as : x = 2/5 and y = 1 .
The given question is incomplete , the complete question is
What is the solution to the system of linear equations y = -5x+3 and y = 1 ?
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Can a graphing calculator be used as a scientific calculator?.
Yes , the graphing calculator can be used as a scientific calculator.
As given in the question,
Scientific calculator can not be used as a graphing calculator.
But graphing calculator can be used as a scientific calculator.
Calculators help us to make our calculation easy and save time.Scientific calculator help us to do the calculation of mathematics based on algebra and Engineering mathematics.Scientific calculator also help us to do statistics calculation.Graphing calculator have all the functions of scientific calculator with more addition of plotting coordinates of the given graph function.Therefore, yes the graphing calculator can be used in place of scientific calculator.
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Avery is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Avery will earn $40 every time one of her songs is played in a commercial and she will earn $140 every time one of her songs is played in a movie. Avery earned a total of $480 in royalties on 7 commercials and movies. Determine the number of commercials and the number of movies on which Avery's songs were played.
The number of commercials in which Avery's songs were played is 5.
The number of movies in which Avery's songs were played is 5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
The number of times the song played in commercials = x
The number of times the song played in a movie = y
Now,
Avery will earn $40 every time one of her songs is played in a commercial and earn $140 every time one of her songs is played in a movie.
We can make two equations.
x + y = 7 ____(1)
x = 7 - y _____(2)
40x + 140y = 480 _____(3)
Substituting (2) in (3) we get,
40(7 - y) + 140y = 480
280 - 40y + 140y = 480
100y = 480 - 280
100y = 200
y = 2
Now,
x = 7 - 2
x = 5
Thus,'
The number of commercials and the number of movies in which Avery's songs were played are 5 and 2.
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Please Help me with this question ASAP
The credit utilisation ratio to the nearest percentage is found as 17%.
Define the term credit utilisation ratio?The proportion of a borrower's total credit available that is presently being used is known as the credit utilisation ratio. When determining a borrower's credit score, credit reporting companies take into account the credit utilisation ratio.Steps:
You must collect all of the credit cards in order to determine your credit utilisation ratio. Add the credit limits after adding up all the remaining balance. Your credit usage ratio is expressed as a percentage by taking the entire amounts, dividing them but by total credit limit, and thereafter multiplying the result by 100.For the stated question:
Balance = $180 + $230 = $410.
credit limits = $1500 + $1000 = $2500.
Credit utilisation ratio = Balance / credit limits
Credit utilisation ratio = 410 / 2500 * 100 = 16.4%
Thus, the credit utilisation ratio to the nearest percentage is found as 17%.
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How many three digit numbers are divisible by 7?.
There are 128 three digit numbers divisible by 7
We know that the divisibility rule of 7 is:
If the difference between twice the unit digit of the given number and the remaining part of the given number is multiple of 7 or the difference is 0, then the number is divisible by 7.
the range of three digit numbers is 100 to 999
The first three-digit number divisible by 7 is 105 and the last three-digit number divisible by 7 is 994.
The numbers divisible by 7 must be: 105, 112, . . ., 994
We can observe that the above series represents the arithmetic progression with common difference d = 7, the first term a = 105 and the last term a_n = 994
We know that the formula for the n-th term of AP is:
a_n = a1 + (n - 1)d
994 = 105 + (n - 1)7
7n - 7 = 889
7n = 889 + 7
7n = 896
n = 128
Thus, there are 128 three digit numbers.
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Assertion : If both zeros of the quadratic polynomial x k2 2 x 2 − + are equal in magnitude but opposite in sign then
value of k is ½.
Reason : Sum of zeros of a quadratic polynomial ax bx c 2 + + is a
-b
The assertion that both zeros of the quadratic polynomial x² - 2kx +2 in magnitude but opposite in sign then value of k is 1/2 is false.
How to obtain the sum of the roots of the quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The sum of the roots of a quadratic function is given as follows:
S = -b/a.
The equation in this problem is given as follows:
x² - 2kx +2
Hence the parameters are:
a = 1, b = -2k.
If the roots are equal in magnitude but the opposite sign, the sum of the roots is of:
0.
Hence:
-b/a = 0.
b = 0.
Meaning that the value of k is obtained as follows:
-2k = 0.
k = 0.
And the statement is false.
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Is an example of distributive law *?.
Yes, 3 * ( 5 - 2 ) = ( 3 * 5 ) - ( 3 * 2 ) is an example of distributive law.
The distributive property is also known as the distributive law of multiplication over addition and subtraction. The name itself implies that the operation involves dividing or distributing something. The distributive law applies to addition and subtraction. The formula for the distributive property is expressed as:
Over addition : a( b + c ) = ab + ac
and subtraction : a( b - c) = ab - ac
Example: Solve the expression 7(20 + 3)
Multiplication of 7(20) and 7(3) is done before addition. This leads to 7(20) + 7(3) = 140 + 21 = 161.We have, an expression 3×(5 - 2) =(3 × 5 ) - (3× 2 ).
Consider the left hand side, 3×(5 - 2)
=> 3× 5 - 3× 2 = 15 - 6 = 9
Now, the right hand side, (3 × 5 ) - (3× 2 ) => 15 - 6 = 9 = LHS
Hence, it is an example of distributive law.
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Complete question:
Is 3 * ( 5 - 2 ) = ( 3 * 5 ) - ( 3 * 2 ) an example of distributive law *?.
What is the inverse of the logarithmic function f/x log9 X?.
The inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex] is [tex]e^{x}[/tex].
In the given question, we have to find the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex].
The given function is f(x) = [tex]\log_{e}x[/tex].
The features of logarithms will simply follow from our understanding of exponents if the logarithm is viewed as the inverse of the exponential function.
Now let, y = [tex]\log_{e}x[/tex]
Now x = log y
Then, y = [tex]e^{x}[/tex]
So, f(x) = [tex]e^{x}[/tex]
As a result, [tex]e^{x}[/tex] is the logarithmic function's inverse, where f(x) = [tex]\log_{e}x[/tex].
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The complete question is:
What is the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex]?
z+5=55(5^z)
How to solve this.
The given equation's answer is [tex]$z+5=55\left(5^z\right):$[/tex] [tex]$z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex], [tex]$z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex]
What is the solution of the given equation ?[tex]$z+5=55\left(5^z\right):$[/tex] [tex]$z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex], [tex]$z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex]
[tex](Decimal: $z=-1.75934 \ldots, z=-4.98187 \ldots$ )[/tex]
[tex]$$z+5=55\left(5^z\right)$$[/tex]
Prepare [tex]$z+5=55\left(5^z\right)$[/tex] Lambert form: [tex]$(z+5) e^{-\ln (5) z}=55$[/tex]
the equation once more using [tex]$(-z-5) \ln (5)=u$[/tex] and [tex]z=-\frac{u+5 \ln (5)}{\ln (5)}$[/tex]
[tex]$$\left(\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)+5\right) e^{-\ln (5)\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)}=55$$[/tex]
[tex]$$e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$$[/tex]
Rewrite [tex]$e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$[/tex]in Lambert form: [tex]$e^u u=-\frac{11 \ln (5)}{625}$[/tex]
Solve [tex]$e^u u=-\frac{11 \ln (5)}{625}: \quad u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)$$$u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{w}_0\left(-\frac{11 \ln (5)}{625}\right)$$[/tex]
Substitute back [tex]$u=(-z-5) \ln (5)$[/tex] , solve for z
[tex]$$\begin{aligned}& \text { Solve }(-z-5) \ln (5)=W_{-1}\left(-\frac{11 \ln (5)}{625}\right): \quad z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& \text { Solve }(-z-5) \ln (5)=W_0\left(-\frac{11 \ln (5)}{625}\right): z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}, z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}\end{aligned}$$[/tex]
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PLSSS HELP IF YOU TURLY KNOW THISSSS
The next operation that should be done when evaluating this expression is -12
Which are the 6 steps of order of operation?The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are the sequence in which the operations are performed (from left to right).
The next operation that should be done when evaluating this expression is
9-12+6/-3+3(-3)
Addition or Subtraction (from left to right)
9-12=-5
Multiplication or Division (from left to right)
6 /-3 = -2
-5 + -2+3(-3) = -12
The next operation that should be done when evaluating this expression is -12
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The lengths of salamanders have a normal distribution with mean 15cm, and standard deviation 2cm.
In a collection of 200 salamanders, about how many have length greater than 16.5cm?
Answer:
2cm
Step-by-step explanation:
103. 68 in. 2
2cmo salamanders
x² × 7x²- x² × 5x - x² × 5 + 9 × 7x² - 9×5x - 9×5
You have to distribute it. To do this, multiply x^2 to (7x^2-5x-5) and do the same to 9 times (7x^2-5x-5). Add like variables. The attached image is your answer.
I hope this was able to help you :D
What is a 1/10 gradient?.
The 1/10 gradient means 6 degrees is the angle of 1 in 10 slopes.
The gradient is the inclination of a line. The gradient is often referred to as the slope (m) of the line. The gradient or slope of a line inclined at an angle θ is equal to the tangent of the angle θ.
In geometry, 1 in 10 means for every ten units of horizontal distance crosses there is 1 unit of vertical drop or rise. The angle of tan is used to measure this value of the slope. Let x be the angle to be used for tan.
[tex]tanx=\frac{horixontal distance}{vertical distance}[/tex]
[tex]tanx= \frac{1}{10}=0.1[/tex]
[tex]x=tan^{-1}(0.1)\\x=5.71'[/tex]
By rounding to the nearest digit, the degree value will be 6.
Hence, 6 degrees is the angle of 1 in 10 slopes.
Hence, the 1/10 gradient means 6 degrees is the angle of 1 in 10 slopes.
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Raul crosses Main Street when he walks home from school. The graph of the function d(t)=4|t-0.75) shows Raul's distance, in miles, from Main Street after thours. The domain of the function is 0 <= x <= 1.5 The graph shows his entire trip
Raul's distance from Main street decreases in the interval,
0 ≤ t ≤ 0.75. And Raul walks 6 miles to get to school.
What is the distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}.
Given:
Raul crosses Main Street when he walks home from school.
The graph of the function d(t)=4I(t-0.75)I shows Raul's distance, in miles, from Main Street after t hours.
The domain of the function is 0 ≤ x ≤ 1.5.
The graph shows his entire trip.
From the graph;
Raul's distance from Main street decreases in the interval,
0 ≤ t ≤ 0.75.
And to get to school,
Raul walks,
distance = (distance when t = 1.5) - (distance when t = 0)
Distance = (4 x 0.75) - (4 x -0.75)
Distance = 3 -(-3)
Raul walks = 6 miles.
Therefore, Raul walks 6 miles to get to school.
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The complete question is given on the attached image,
Write each calculation as a single power. 8 to the power of 5 Multiply by 8 to the power of 4 REMEMBER TO WRITE THE ANSWER AS A SINGLE POWER PLS HELP
Answer:
[tex]8^{9}[/tex]
Step-by-step explanation:
[tex]8^{5}[/tex] x [tex]8^{4}[/tex]
In expanded form this would be
8·8·8·8·8·8·8·8·8
The product of power principle tells us that when we are multiplying powers with the same bases, we add the exponents.
The perimeter of a train ticket is 60 centimeters. It is 17 centimeters long. How tall is it?
If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter
What is perimeter of a rectangle?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;
P = l+l+w+w
P= 2(l+w)
60 = 2( 17+w)
60 = 2( 17+w)
17+w= 60/2
17+ w = 30
w = 30-17
w = 13cm
Therefore the height of the train ticket is 13cm
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please help me i dont know this
When the coin is tossed and then dice is rolled, the possible outcomes are 12.
Define the term sample space/possible outcome?All potential results make up as sample space of such a random experiment.A subset of such sample space is an event connected to a random experiment.Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.The total likelihood of all outcomes in an event A is the probability of that event.For the stated question.
Sample space for tossing coin. { H, T}.
Sample space for rolling dice. { 1, 2, 3, 4, 5, 6 }
Then,
Total sample = { H1, H2, H3,H4, H5, H6, T1, T2, T3, T4, T5, T6}
Thus, the total possible outcomes for tossing coin and rolling dice is 12.
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Simplify this expression:
13x+2y-10x-7y
Answer:
3x-5y
Step-by-step explanation:
⇒13x+2y-10x-7y
arrange the like terms together
⇒13x-10x-7y+2y
⇒3x-5y ...answer
hope that helps...
Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted. Starting on one of the plotted points, how can you plot more equivalent ratio points? Move up one and right one and one-half. Move up one and one-half and right three. Move up two and right three. Move up one and right two
To plot more equivalent ratios on the coordinate plane, move up one and right one and half.
What are equivalent ratios?Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not.
Given that, Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted.
As we see, the x-coordinates are 1, 2, 5 and y-coordinates are 0.5, 1, 2.5
We see that, x-coordinates are increasing by 1, and y-coordinates are increasing by a half,
Therefore, to plot more equivalent coordinates, we will move up 1 on y-axis and a half right on x-axis,
Hence, to plot more equivalent ratios on the coordinate plane, move up one and right one and half.
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(Theoretical Probability LC)
When rolling a fair, eight-sided number cube, determine P(number greater than 6).
A: 0.25
B: 0.50
C: 0.66
D: 0.75
Answer:0.25
Step-by-step explanation:
i passed the test
factorise
3x^2+22x+7
Answer:
(3x + 1)(x + 7)
Step-by-step explanation:
3x² + 22x + 7 =
3x² must factor into 3x and x.
= (3x + )(x + )
7 factors into 7 and 1. We can place 7 and 1, or 1 and 7.
= (3x + 7)(x + 1)
or
= (3x + 1)(x + 7)
Now we multiply both possibilities out to see which one produces the middle term 22x that we need.
= (3x + 7)(x + 1) = 3x² + 10x + 7 No what we need
or
= (3x + 1)(x + 7) = 3x² + 2x + 7 Exactly what we need
Answer: (3x + 1)(x + 7)
