Considering a parabolic equation with a vertex of (-7,-2) and directrix of x = -1. This is a horizontal parabola
What is directrix of a parabola?The directrix of a parabola is a straight line perpendicular to the axis of symmetry of the parabola.
The directrix does not touch the parabola
How to determine if a parabola is vertical or horizontal using the directrixA parabolic equation is also called quadratic equation.
Since the directrix is perpendicular to the axis of symmetry of the parabola it means that if:
when the directrix is given at x, the directrix runs in the vertical direction and the parabola is a horizontal parabolawhen the directrix is given at y, the directrix runs in the horizontal direction and the parabola is a vertical parabolaThe axis of symmetry says if the parabola is vertical or horizontal, when the axis of symmetry is parallel:
the y direction the parabola is a vertical parabolathe x direction the parabola is a horizontal parabolaIn the given problem, the directrix is given at x, the axis of symmetry is along the x direction and hence a horizontal parabola
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y=tan(x/8) Find the period, x intercepts, and vertical asymptotes
Given:
[tex]y=\tan(\frac{x}{8})[/tex]Find-: Period, x-intercepts, and vertical asymptotes.
Sol:
Graph of function is:
The period of the function is:
[tex]\text{ Period}=8\pi[/tex]The x-intercept of function is:
For the x-intercept value of "y" is zero so,
[tex]\begin{gathered} y=\tan(\frac{x}{8}) \\ \\ \tan(\frac{x}{8})=0 \\ \\ \frac{x}{8}=\tan^{-1}(0) \\ \\ x=8\tan^{-1}(0) \\ \\ x=-8\pi,0,8\pi,16\pi...... \end{gathered}[/tex]Vertical asymptotes are:
For the function can't find vertical asymptotes.
f(x) = 4x3 + 5x2 – 3x - 6g(x) = 4x - 5Find (f - 3)(x).O A. (f - g)(x) = 4x3 + 5x2 – 7x – 1O B. (f - g)(x) = 4x3 + 5.02 +0 - 1O c. (f - g)(x) = 4x3 + 5x2 – 7x – 11O D. (f - g)(x) = 4x3 + 5x2 + x - 11SUBMIT
what number is 90% of 20
Let's begin by listing out the given information:
[tex]\begin{gathered} 90\text{\%}\cdot20\Rightarrow\frac{90}{100}\cdot20 \\ \Rightarrow0.9\cdot20=18 \\ \Rightarrow18 \end{gathered}[/tex]Therefore, 90% of 20 is equal to 18
Introduction to the probability of an eventA spinner with 8 equally sized slices has 8 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellowslice?write your answer as a fraction in simplest form.
Step 1:
[tex]Probability\text{ of any event = }\frac{Number\text{ of required outcomes}}{\text{Number of possible outcomes}}[/tex]Step 2:
There are 8 slices, hence the possible outcomes = 8
All the slices are color yellow. hence the required outcomes = 8
Step 3:
[tex]\text{The probability that the dial stops on yellow slice = }\frac{8}{8}\text{ = 1}[/tex]The probability that the dial stops on yellow slice = 1
Final answer
pair of shoes $80 find the total paid if taxes 6%
The first step is to find the value of the tax, you do it by multiplying the price of the shoes by the tax (in decimal form), this way:
[tex]t=80\cdot0.06=4.8[/tex]Now, add this value to the price of the shoes:
[tex]80.00+4.8=84.80[/tex]The total paid is $84.80.
Ahmad spends $16 each time he travels the toll roads. He started the month with $224 in his toll road account. The amount, A (in dollars), that he has left in the account after t trips on the toll roads is given by the following function.
A (t) = 224 - 16t
Answer the following questions.
a. How much money does Ahmad have left in the account after 11 trips on the toll roads?
b. How many trips on the toll roads can he take until his account is empty?
Part a
[tex]A(11)=224-16(11)=\boxed{\$48}[/tex]
Part b
[tex]A(t)=0\\\\224-16t=0\\\\t=\frac{224}{16}\\\\t=\boxed{14 \text{ trips}}[/tex]
a) The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48
b) The number of trips on the toll roads can he take until his account is empty is 14 trips
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A ( t ) = 224 - 16t , where t is the number of trips
a)
The amount of money does Ahmad have left in the account after 11 trips on the toll roads be P
Substituting the value of t = 11 in the equation , we get
A ( 11 ) = 224 - 16 ( 11 )
A ( 11 ) = 224 - 176
A ( 11 ) = $ 48
So , The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48
b)
The number of trips on the toll roads can he take until his account is empty be n
when A ( t ) = 0
224 - 16t = 0
Adding 16t on both sides of the equation , we get
224 = 16t
Divide by 16 on both sides , we get
t = 14 trips
Hence , the equations are solved
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⚠⚠⚠⚠⚠⚠⚠⚠⚠ Pleases Help ME!!!!!!!
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.20). What is the slope of the graph? What is the unit rate? Complete the explanation.
The slope is _____. The unit rate is $_____/min. If the graph of a proportional relationship passes through the point (_____, r), then r equals the slope and unit rate.
The complete statement is:
The slope is 3.20. The unit rate is $3.20/min. If the graph of a proportional relationship passes through the point (1, r), then r equals the slope and unit rate.How to complete the statement?The slope
From the question, we have the following parameters
Point = (1, 3.20)
The point is a proportional relationship
So, the slope of the proportional relationship is
Slope = y/x
Where
(x, y) = (1, 3.20)
Substitute the known values in the above equation
So, we have the following equation
Slope = 3.20/1
Evaluate
Slope = 3.20
The unit rate
Here, we have
Point = (1, 3.20)
Also, we have
The point is a proportional relationship
The unit rate is
Rate = y/x
Where
(x, y) = (1, 3.20)
Substitute the known values in the above equation
So, we have the following equation
Rate = 3.20/1
Evaluate
Rate = 3.20
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If you had half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have altogether?
If we have half a dollar, three quarters, eight dimes, six nickels, and nine pennies , then we altogether have $2.44 .
In the question ,
it is given that
we have half a dollar ,
which means half a dollar = $0.50
we have , three quarters means
we have 75 cents
and 75 cents = $0.75
we have 8 dimes ,
we know that 1 dime [tex]=[/tex] 10 cents
so , 8 dimes = 80 cents
and 80 cents = $0.80
we have six nickels,
we know that 20 nickels = $1
so , 1 nickel = $1/20
and 6 nickel = $ 6/20 = $0.30
we have nine pennies ,
we know that 100 pennies = $1
So ,1 Pennie = $1/100
and 9 pennies = $ 9/100 = $0.09
Combining all together we get
total money = half a dollar + three quarters + 8 dimes + six nickels + nine pennies .
Substituting the values , we get
total money = $0.50 + $0.75 + $0.80 + $0.30 + $0.09
= $2.44
Therefore , if we have half a dollar, three quarters, eight dimes, six nickels, and nine pennies , then we altogether have $2.44 .
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During second period, Anita completed a grammar worksheet. Of the 18 questions, Anita got 50% right. How many questions did Anita get right?
Answer:
Anita answered nine questions correctly.
Step-by-step explanation:
50% is 1/2 and 1/2 of 18 is 9.
Sorry for bad English, love from Vanuatu!
maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day. Create a table of values to represent the relationship between the number of days and the number of puzzles she has completed determine if it is proportional and show your reasoning Brainliest will possibly be a prize :)
The table of values to represent the relationship between the number of days and the number of puzzles she has completed will be:
Days Puzzle completed
1. 4
2. 8
3. 12
4. 16
5. 20
How to illustrate the information?From the information, Maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day.
Therefore, the first day, she will do 4 puzzles. The second day will be:
= 2 × 4 = 8 puzzles
Third day = 3 × 4 = 12 puzzles.
In this case, the method that was used is simply to multiply the number of days by 4 since he does 4 puzzles everyday.
It should be noted that this illustrates a proportional relationship
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does the mean of a data set have to be one of the data values?
No, the mean of a data set doesn't have to be one of the data values of the data set.
What is mean of a data set?The mean equals the total of all the values in the data set divided by the number of values in the data set. It is the most commonly used value. However, you will note that the mean is not always one of the actual values in your data set. An important aspect of the mean is that it incorporates every value in your data set as part of the computation. Furthermore, the mean is the only measure of central tendency in which the sum of the deviations from the mean is always zero.To know more about mean visit:
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Find the area using A = 1 * W. Mr. Janacek's class is doing an art projec with different-colored squares. How many 1-inch squares can be cut from an 18-inch by 24-inch piece of construction paper?
We have the following:
The area is
[tex]A=L\cdot W[/tex]L (long) is 24 inch and W (wide) is 18 inch, replacing:
[tex]\begin{gathered} A=24\cdot18 \\ A=432 \end{gathered}[/tex]The area is 432 squares inch, therefore:
[tex]\frac{432}{1}=432[/tex]Therefore a total of 432 1-inch squares can be cut
please help I've been trying to solve this for over an hour
24x +8y ≥ 20
3x - 6y > 24
First, express both equations in slope-intercept form
y= mx+b
Where:
m= slope ( rise (y) / run (x))
b= y-intercept (where the line crosses the y axis)
Solve for y:
24x +8y ≥ 20
8y ≥ -24x +20
y ≥ (-24x +20 ) / 8
y ≥ -3x + 2.5
3x - 6y > 24
-6y > 24- 3x
y < (24 -3x) / -6
y < 1/2x -4
System:
y ≥ -3x + 2.5
y < 1/2x -4
Solution = the area where the 2 solutions overlap (blue+ red)
please help me (question “e”)
Answer:
42 - 6 ÷ (6 - 3) = 40
Step-by-step explanation:
BODMAS
The BODMAS rule is an acronym representing the order of operations in math:
BracketsOrders (Powers and Square Roots, etc.)Division and Multiplication (from left to right)Addition and Subtraction (from left to right)Given calculation:
42 - 6 ÷ 6 - 3 = 40
Following the order of operations, where division comes before subtraction, the current calculation is:
⇒ 42 - 6 ÷ 6 - 3
⇒ 42 - 1 - 3
⇒ 41 - 3
⇒ 38
Therefore, brackets should be added around (6 - 3) to make the calculation correct:
⇒ 42 - 6 ÷ (6 - 3)
⇒ 42 - 6 ÷ 3
⇒ 42 - 2
⇒ 40
Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score
Problem
Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score
Solution
Let x the score for Steve and y the score for Denia.
We know that the score of Denia is the opposite of Steve
So then the scores needs to be:
Steve =-5
Denia =5
And with this we satisfy all the requirements
Identify the variables, coefficients, and constants of the following equations.
3x = 12
y = 1/2x - 6
Answer:
Variables are the letters that represent a number. So, it would be the ones bolded here: 3x=12 and y=1/2x-6
The coefficients are next to the variables-the ones being multiplied with the variable. They are bolded here: 3x= 12 and y= 1/2x-6
The constants are the numbers that aren't coefficients or variables. So they are bolded here: 3x=12 and y=1/2x-6
Which is a better value for money, $5.99 for a package of 8 cold remedy
capsules or $2.85 for 2 capsules?
Answer:
the 8 pack
Step-by-step explanation:
So to start we should find how much an individual capsule in each is
Well start off by 5.99/8 which will give us 0.74875 per capsule and well round in to 0.75 each to put it in terms of money.
Now we will do 2.85/2 which then gives you 1.425 and well say that's about 1.43 per capsule
Suppose that the function f is defined, for all real numbers, as follows.1--x' +4 if x13f(x) = 24if x=1Find f(-4).f(1), and f(3).1(-4) = 0음f(1) = 0X Х?f(3) =
Answer:
[tex]\begin{gathered} f(-4)=-\frac{4}{3} \\ f(1)=4 \\ f(3)=1 \end{gathered}[/tex]Step-by-step explanation:
These types of functions are called Piecewise-defined functions since it use a different formula for different parts of its domain because it has a point of discontinuity.
We have the following function:
[tex]f(x)=\begin{cases}-\frac{1}{3}x^2+4\rightarrow ifx\ne1^{} \\ \text{ 4 if x=1}\end{cases}[/tex]So, to find f(-4), we need to substitute x=-4 into the function for x≠1.
[tex]\begin{gathered} f(-4)=\frac{-1}{3}(-4)^2+4 \\ f(-4)=-\frac{1}{3}(16)+4 \\ f(-4)=-\frac{16}{3}+4 \\ f(-4)=-\frac{4}{3} \end{gathered}[/tex]Now, for f(1) we know that the outcome is 4.
[tex]f(1)=4[/tex]Then, for f(3), substitute x=3 into the function for x≠1.
[tex]\begin{gathered} f(3)=-\frac{1}{3}(3)^2+4 \\ f(3)=-\frac{1}{3}(9)+4 \\ f(3)=1 \end{gathered}[/tex]Write a quadratic function in standard form whose graph has the given characteristics.
The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
The standard form of a quadratic equation in vertex form is given as,
y = a(x-h)² + 8
Where (h,k) is the coordinate of the vertex and a is constant.
Given the vertex (h,k) = (-1,8)
Substitute, vertex, and (0,2)
2 = a(0 + 1)² + 8
a = -6
Therefore, the equation converts as,
y = -6(x+1)²+8
Hence "The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8".
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Simplify: - 1x - 11 - 16x - 22 =
The given expression is
[tex]-x-11-16x-22[/tex]To simplify it add the like terms
[tex]\begin{gathered} (-x-16x)+(-11-22)= \\ \\ -17x+(-33)= \\ \\ -17x-33 \end{gathered}[/tex]Then the simplest form is
-17x - 33
can you pleasee help meeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
if x is the number of years since 2000 and y is the percent of people using travel services the following equations represent the percent of people using travel agents and the percent of people using the internet to plan travel. y=-2x+30 y=6x+41 Find the year travel agents and the Internet were used equally
We need to solve a system of two variables with two equations, using elimination method.
y=-2x+30 (1)
y=6x+41 (2)
We are going to multiply first equation by 3, doing so the equation (1) can be written as:
3y = -6x + 90 (1)
Then, we are going to add the last equation to the second equation
3y = -6x + 90 (1)
+ y= 6x + 41 (2)
-----------------------------
4y = 131
y = 131 / 4 Isolating y
y= 131/ 4
Then, we replace y= 131/4 in the first equation and solve for x
[tex]\begin{gathered} \frac{131}{4}=-2x+30 \\ \frac{131}{4}-30=-2x\text{ Transposing 30 to the other side of the equation} \\ \frac{131}{4}-\frac{120}{4}=-2x\text{ Converting 30 to an improper fraction} \\ \frac{11}{4}=-2x\text{ Operating homogeneous fractions} \\ \frac{\frac{11}{4}}{-2}=-\frac{2}{-2}x\text{ Dividing by -2 on both sides of the equation} \\ -\frac{11}{8}=x \end{gathered}[/tex]Since -11/8 is equal to -1.4 and x represents the number of years since 2000, then the year travel agents and the Internet were used equally was 1998.
Marshall's Theater Company claims that of its 2,937 costumes in inventory, 972 are just old used clothes, while the rest are collector's items. What percent of total inventory is collector's items?
In order to calculate the percent of items that are collector's items, let's first find the amount of collector's items by subtracting the total number of items by the number of old used clothes:
[tex]2937-972=1965[/tex]Now, to find the percent from the total, let's divide this amount we calculated by the total number of items:
[tex]\frac{1965}{2937}=0.669=66.9\text{\%}[/tex]Therefore the percent of items that are collector's items is 66.9%.
a new ipad costs $101.99 in the store. what would your total cost be if the sales tax is 7.5% round your answer to the nearest cent, if necessary
ANSWER:
$109.64
STEP-BY-STEP EXPLANATION:
The price after applying the tax would be the sum between the original value and the value equivalent to the established percentage, just like this:
[tex]\begin{gathered} p=101.99+101.99\cdot\frac{7.5}{100} \\ p=101.99+7.65 \\ p=109.64\cong\text{ \$109.6}4 \end{gathered}[/tex]What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?
The area of the triangle bounded by the x-axis, the y-axis, and the line y = −4x + 4 is 2 square units
How to find the area of the trianglegiven data
y = −4x + 4
Area of a triangle is equal to 1/2 * base * height
Assuming the y direction to be the height and the base is x direction
Point on the y direction is the y intercept since the line bounds the area
y intercept = −4( 0 ) + 4
y intercept = 0 + 4
y intercept = 4
Point on the x direction is the x intercept since the line bounds the area
y = −4x + 4
4x = 4 - y
4x = 4 - 0
x = 1
Area of a triangle = 1/2 * 1 * 4
= 2 square units
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If x
2 = 25 , where x ε z then x =
After thoroughly calculation, we have come to find that, If equation x² = 25, where x ε z then x = √25 = 5, thus x is 5.
What is equation?Equation, also known as a statement of equality between two expressions with variable- and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics.
From straightforward algebraic equations that only require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them.
Simultaneously occurring equations, or system of equations Algebra requires the simultaneous solution of two or more equations (i.e., the solution must satisfy all the equations in the system). The quantity of equations must match the quantity of unknowns for a system to have a distinct solution.
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Leonard Desmond founded his traveling circus many years ago, and since that time he has featured 32 high-wire unicyclists and 24 ball-balancing seals. What is the ratio of high-wire unicyclists to ball-balancing seals?
Answer:
The ratio of the high-wire unicyclists to ball-balancing seals is;
[tex]4\colon3[/tex]Explanation:
Given that;
He has featured 32 high-wire unicyclists and 24 ball-balancing seals.
The ratio of the high-wire unicyclists to ball-balancing seals can be written as;
[tex]32\colon24[/tex]Reducing toits lowest form, we have;
divide both sides by 8;
[tex]\begin{gathered} \frac{32}{8}\colon\frac{24}{8} \\ 4\colon3 \end{gathered}[/tex]Therefore, the ratio of the high-wire unicyclists to ball-balancing seals is;
[tex]4\colon3[/tex]4n+1=25Please help with an explanation as well
Question:
Solve
4n + 1 = 25
Solution:
Consider the following formula:
[tex]4n+1\text{ = 25}[/tex]this is equivalent to:
[tex]4n\text{ = 25 -1}[/tex]this is equivalent to:
[tex]4n\text{ = 24}[/tex]solving for n, we get
[tex]n\text{ = }\frac{24}{4}=\text{ 6}[/tex]Then, we can conclude that the correct answer is:
[tex]n\text{ = 6}[/tex]4. What is the mean of the following data? (Show your work){5, 6, 8, 4, 5, 7, 4, 3, 2, 6)
The mean of the data values is their average.
To obtain the average, find the sum of the data values and then divide the sum by total number of data.
In the given, we have 10 data values. Thus, the mean is as follows.
[tex]\begin{gathered} \overline{x}=\frac{5+6+8+4+5+7+4+3+2+6}{10} \\ =\frac{50}{10} \\ =5 \end{gathered}[/tex]Therefore, the mean is 5.
Select the correct answer.
What is the sum of this expression?
Answer:
l think its B
Step-by-step explanation: