What are the coordinates of the vertex?What is the equation of the axis of symmetry?What is/are the x-intercept(s)?What is the y-intercept?
Answers
We will find the vertex of the parabola as follows:
*Given a quadratic function of the form:
[tex]y=ax^2+bx+c[/tex]We will have that the vertex is given by:
[tex](-\frac{b}{2a},\frac{b^2-4ac}{4a})[/tex]So, for the function given we will have the following vertex:
[tex](-\frac{(-8)}{2(-1)},\frac{(-8)^2-4(-1)(0)}{4(-1)})\to(-4,16)[/tex]So, the vertex for the function is given by the ordered pair (-4, 16).
We will have that the equation of the axis of symmetry is given by:
[tex]x=-4[/tex]So, the axis of symmetry is x = -4.
We will determine the x-intercepts as follows:
[tex]-x^2-8x=0\Rightarrow x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(-1)(0)}}{2(-1)}[/tex][tex]\Rightarrow\begin{cases}x=-8 \\ \\ x=0\end{cases}[/tex]So, we will have that the x-intercepts are located at x = -8 & x = 0.
From the previous point we can see that the point (0, 0) belongs to the parabola, thus the y-intercept is y = 0.
Related Questions
10. Two classes work together on a project. One class has 18 students,8 of whom are girls. The other class has 10 girls and 7 boys.What is the ratio of boys to the total number of students working on theproject? Express your answer as a fraction.lo0OOOOOOCOOOOO
Answers
Solution
For this case we have the following info:
Class 1: Total 18 students, 8 girls and 10 boys
Class 2: Total 17 students, 10 girls and 7 boys
The total of students are: 18+17 = 35
Total of boys: 10 + 7 = 17
Then the ratio of boys to the total number of students is given by:
r = 17/35
the measure of two angle are (8x+24) and (12x-16) what is the value of x if theses angle ar congruent
Answers
Answer: 10
Step-by-step explanation: Congruent means they are the same, so you set up the problem as 8x+24=12x-16. Then you just solve for x. Subtract 8x from both sides to get 24=4x-16. Then add 16 to both sides. 40=4x. Then divide by 4 into both sides to get x=10.
You have 400000 saved for retirement. your account earns 7% interest. how much will you be able to pull out each month if you want withdraws for 25 years
Answers
Answer:
$1,426.7
Step-by-step explanation:
Let's say the unit currency is dollars
$400,000
7% of $400,000
= $28,000
400,000 + 28,000
= $428,000
For 25 years,
= 25 × 12
= 300
$428,000/300
= $1,426.7
~ $1,427
The area a of a circle is pi times the radius R squared as an equation
Answers
Answer:
pi r squared
Step-by-step explanation:
A=pir2
pi is 3.14
hope it helps
Please help fast f(x) = 4x2 - 2x + 4 Find f(-9)
Answers
Answer:
346
Step-by-step explanation:
substitute the -9 for the x and solve. you will get 346 that will be the function of -9 for this equation
Which exponential function models this situation ?
Answers
Exponential function models is v(x) = 9,000(0.9)ˣ
Lets take two year data (0,9000) and (1,8100)
using the general form of exponential function y = abˣ and substitute value of x and y as (0,9000)
9000 = ab⁰
9000 = a.1
9000 = a
Again using general form of exponential function and taking x and y as (1 , 8100)
8100 = ab¹
substitute a = 9000 in above equation
8100 = 9000×b
b = 8100/9000
b=0.9
putting value of a and b in general form of exponential function
v(x) = 9000(0.9)ˣ is required exponential function model
correct answer is option B
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The height of a triangle is 3 feet less than the base. The area of the triangle is 230 square feet. Find the length of the baseand the height of the triangle,
Answers
Let b be the base of the traingle
Let h be the height of the triangle
The height of a triangle is 3 feet less than the base:
[tex]h=b-3[/tex]The area of the triangle is 230 square feet.
The area of a triangle is:
[tex]A=\frac{1}{2}(b\cdot h)[/tex]For the given triangle:
[tex]\begin{gathered} A=\frac{1}{2}(b\cdot(b-3)) \\ \\ 230=\frac{1}{2}(b\cdot(b-3)) \end{gathered}[/tex]Solve b in the equation above:
[tex]\begin{gathered} 230=\frac{b^2-3b}{2} \\ \\ 2\cdot230=b^2-3b \\ \\ 460=b^2-3b \\ \\ b^2-3b-460=0 \end{gathered}[/tex]Use the quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} b=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(1)(-460)}}{2(1)} \\ \\ b=\frac{3\pm\sqrt[]{9+1840}}{2} \\ \\ b=\frac{3\pm\sqrt[]{1849}}{2} \\ \\ b=\frac{3\pm43}{2} \\ \\ b_1=\frac{3+43}{2}=\frac{46}{2}=23 \\ \\ b_2=\frac{3-43}{2}=-\frac{40}{2}=-20 \end{gathered}[/tex]As the length of the base cannot be a negative quantity you use the solution 1.
The base of the triangle is 23ft
Use the value of b to find the heigth:
[tex]\begin{gathered} h=b-3 \\ h=23-3 \\ h=20 \end{gathered}[/tex]Then, the given triangle has the next dimensions:base: 23ftheight: 20ftWhich statement is true about the function f(x) = 4x^5?
A) The function is even because f(–x) = f(x).
B) The function is odd because f(–x) = f(x).
C) The function is odd because f(–x) = –f(x).
D) The function is even because f(–x) = –f(x).
Answers
The function is odd because f(–x) = –f(x).
What is a function?
A function is a special form of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation rather than a function is depicted in the above graph because one is mapped to two different values. However, if one were instead mapped to a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly.
Odd function means f(-x) = -f(x)
and Even function means f(-x) = f(x)
Here the given function f(x) = 4[tex]x^{5}[/tex]
Put, x = -x
We have f(-x) = 4 ([tex](-x^){5}[/tex])
5 is an odd number so we will get a negative value. So f(-x) = -f(x)
Hence, The function is odd because f(–x) = –f(x).
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Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answers
Step by step
We know slope intercept form is
y =mx + b
m = slope
b = y intercept
We find slope on the graph by creating a slope triangle as shown on the attachment.
We find rise 3 and run 6, slope is rise over run so 3/6 simplified to 1/2
We find the y intercept is at 3 on the y axis
So y = 1/2x + 3 is your answer
find the area of a sector with a central angle of 1/2 pi and a radius of 11.3
Answers
First, let's find the length of an arc:
[tex]L=\text{r}\cdot\theta=11.3\cdot\frac{\pi}{2}=\frac{113\pi}{20}[/tex]Therefore, the area is:
[tex]A=\frac{rL}{2}\approx100.3[/tex]PLEAS HELP ME TYYYYYYY
Answers
Answer:I would say if there are 15 leaches then there will be 20 toads
Step-by-step explanation: I multiplied the 4 times 5
DIRECTIONS: Use this diagram to answer Parts A and B. 60° 55° Part A Find the value of x in the diagram.
Answers
By using the properties of triangles and straight lines we get the values of x as 65° and the value of y as 115°
A) In the given triangles we know that the sum of all the angles is 180 .
Hence :
60 + 55 + c = 180
or, c = 180° - 115°
or, c = 65°
Now the angle marked x is vertical angle to the angle c , hence the value of x is also 65°.
B) Now we know that the value of x is 65°
Again x + y = 180°
Therefore : 65° + y = 180° or, y = 180° - 65° or, y = 115°
Three vertices, three sides, and three angles make up a closed triangle. PQR serves as the symbol for a triangle with the vertices P, Q, and R.
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What is the slope of the line shown?
A. slope = 3
B.slope = 12
C. slope = 2
D. slope = -3
Answers
The slope of the line shown is 0.5 .
How to find the slope of a given line?
For a line passing through the points (x₁, y₁) and (x₂, y₂), the slope for the same can be defined with the mathematical value of m i.e.,
m = (y₂ - y₁)/(x₂ - x₁)
Given, the line in picture passes through the points (0, -3) and (6, 0).
Following the formula established in the literature above, the given line has slope as m, which is:
m = (y₂ - y₁)/(x₂ - x₁) = (0 - (-3))/(6 - 0) = 3/6 = 0.5
Thus, the slope of the given line in question is 0.5 .
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PLEASE I NEED HELP ASAP!!
What are the three forms of quadratic functions?
For each of the three forms, list all features we can use to characterize the equation.
Answers
The three types of quadratic functions are as follows: We can quickly find the y-intercept using the standard form. We can quickly locate the vertex in vertex form, and we can quickly determine the roots/zeros in factored form.
What are the 3 forms of a quadratic function and their features?The three forms of quadratics are the standard form, the vertex form, and factored form. Each of them reveals a specific part of the quadratic.
A quadratic has the following standard form:
A quadratic in standard form can immediately convey only two details: (1) the leading coefficient a and (2) the y-intercept. The leading coefficient a determines whether the parabola curves upwards or downwards. The y-intercept will be given by the constant c.
Vertex Form: The vertex form of a quadratic is:
There are also two details that can be conveyed by a quadratic in vertex form: (1) the vertex, and (2) the leading coefficient. The leading coefficient is given by a. This tells us the orientation of the parabola. The vertex is given by (h, k). Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.
Factored Form: The factored form of a quadratic is:
Where p and q are the zeros/roots/solutions of the quadratic. Factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros. The zeros tell us when the parabola crosses the x-axis, which can assist in graphing.
Therefore,
Each form of a quadratic equation has its own benefits.
The standard form allows us to find the y-intercept.
The vertex form allows us to quickly locate the vertex.
The factored form allows us to quickly determine the roots/zeros.
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Solve for g: g + 8 > 10
Answers
Given the inequality:
[tex]g+8>10[/tex]Solve for g, subtract 8 from both sides
[tex]\begin{gathered} g+8-8>10-8 \\ \\ g>2 \end{gathered}[/tex]so, the answer will be:
[tex]g=(2,\infty)[/tex]DCF = FB and AE = EBCB = 38 and AB = 22DE = [?]EBFLLEnter
Answers
Given
Also, CF = FB and AE = EB, CB = 38 and AB = 22.
To find the length of DE.
Explanation:
It is given that,
Also, CF = FB and AE = EB, CB = 38 and AB = 22.
That implies,
By using midpoint theorem of triangle, we have,
[tex]DE=\frac{1}{2}BC[/tex]Therefore,
[tex]\begin{gathered} DE=\frac{1}{2}\times38 \\ =19 \end{gathered}[/tex]Can I get some help on this please?Options 1: reflection accross the y-axis, 90 degree counterclockwise rotation about the point a, 90 degree clockwise rotation about the point a, 90 degree counterclockwise rotation about point bOptions 2: clockwise rotation about point b and a translation 20 units down, reflection across the y-axis and 20 units down, reflection across the x-axis and 15 units down, reflection across the y-axis and 25 units down
Answers
Answer:
The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.
Explanation:
The sequence of transformations are described in the following figure:
Therefore, the first transformation is a rotation of 90 degrees counterclockwise about point A. After that transformation, we get the figure A'B'C'D'
Then, we reflect the figure across the y axis, so we get A''B''C''D''
Finally, we translate the figure 20 units down to get GHIJ
So, the answers are:
The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.
Ethanol fuel mixtures have "E" numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10% ethanol and 90% gasoline. How much E7 should be mixed with 4000 gal of E10 to make an E9 mixture?
Answers
We have to blend two mixtures of ethanol (E7 and E10) to make an E9 mixture.
We know that the amount of E10 mixture is 4000 gal.
Let x be the amount of E7 mixture.
As we have x gallons of E7 and 4000 gallons of E10, the volume of the E9 mixture will be (x+4000).
The volume of ethanol in the E7 mixture will be 0.07*x gallons.
The volume of ethanol in the E10 mixture is 0.1*4000 = 400 gallons.
The volume of ethanol in the E9 mixture will be 0.09*(x+4000) gallons.
As the sum of the ethanol volume in the E7 and E10 mixtures has to be equal to the ethanol in the E9 mixture, we can write:
[tex]0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000)[/tex]We can use this equation to solve for x:
[tex]\begin{gathered} 0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000) \\ 0.07x+400=0.09x+0.09\cdot4000 \\ 0.07x+400=0.09x+360 \\ 0.07x-0.09x=360-400 \\ -0.02x=-40 \\ x=\frac{40}{0.02} \\ x=2000 \end{gathered}[/tex]Then, the volume of the E7 mixture has to be 2000 gallons.
Answer: 2000 gallons of E7 mixture.
Which of the following statistics could you find given the information above (see
question #1)? Select all that apply.
mode
range
standard deviation
interquartile range
Answers
The statistics you could find given the information above (see attachment) include the following:
range.standard deviation.interquartile range.What is a box and whisker plot?A boxplot is also referred to as box and whisker plot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
In Mathematics, the five-number summary of any box and whisker plot include the following:
MinimumFirst quartileMedianThird quartileMaximumFor the range, we have:
Range for women = 150 - 0 = $150
Range for men = 35 - 0 = $35
For the standard deviation, we have:
Standard deviation for women = range/4
Standard deviation for women = 150/4 = 37.5
Standard deviation for men = range/4
Standard deviation for men = 35/4 = 8.75.
For the interquartile range, we have:
Interquartile range = third quartile - first quartile.
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Write an equation of the line passing through point P(0, −1) that is parallel to the line y = −2x+3.
Answers
Answer:
y = -2x - 1
Step-by-step explanation:
Equation of line: y =mx + bHere, m is the slope and 'b' is the y-intercept
y = -2x + 3
m = -2
Parallel lines have same slope.
Substitute m = -2 in the equation,
y = -2x + b
The line is passing through (0 ,-1). So, substitute this point in the equation and find the value of b.
-1 = -2*0 + b
-1 = b
Equation of line:
[tex]\sf \boxed{y = -2x - 1}[/tex]
Determine if each expression is equal to (2) (-3) (-4)(6) (-4)(-3) (8)(12) (2)(-4) (-6)
Answers
The product of the numbers (2) (-3) (-4) is:
[tex]2\times-3\times-4=24[/tex]By verifying the options one after the other, to check which is also equal to 24, we have:
[tex](6)(-4)=-24[/tex][tex](-3)(8)=-24[/tex][tex](12)(2)=24[/tex][tex](-4)(-6)=24[/tex]Hence, the correct options are C and D
4. Felix and Oscar applied for the same credit card from the same bank.
The bank checked both of their FICO scores. Felix had an excellent
credit rating, and Oscar had a poor credit rating.
a. Felix was given a card with an APR of 12%. What was his
monthly percentage rate?
b. Oscar was given a card with an APR of 15%. What was his
monthly payment?
c. If each of them had an average daily balance of $800 and had to
pay a finance charge, how much more would Oscar pay than Felix?
Answers
A) The monthly percentage rate of Felix is; 1%
B) The monthly percentage rate of Oscar is; 1.25%
C) The amount that Oscar will pay more than Felix is; $2
What is the monthly Percentage Rate?A monthly interest rate is simply how much percentage interest you would be charged in one month while annual percentage interest rate is defined as the percentage interest rate you will be charged annually.
A) We are told that Felix was given a card with APR of 12%.
Thus;
Monthly percentage rate = 12%/12 = 1%
B) We are told that Oscar was given a card with an APR of 15%. Thus;
Monthly percentage rate = 15%/12 = 1.25%
C) We are told that each of them had an average daily balance of $800 for a specific month.
Thus;
Amount paid by Felix = 800 * 1%
Amount paid by Felix = $8
Amount paid by Oscar = 800 * 1.25%
Amount paid by Oscar = $10
Difference in Payments = $10 - $8 = $2
Thus, Oscar pays $0.96 more than Felix.
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Porch areas of successful sales are given below decide what study uses population in Parameter
Answers
Remember that a population parameter is a number that describes something about an entire group or population.
The only study that states a conclusion about an entire group or population is the one in the first option.
Answer: Option 1
.
Tyler owns a food truck that sells chicken wings and hamburger sliders. Each order of
chicken wings sells for $7.25-while each order of hamburger sliders sells for $3. On
Friday, Tyler made a total of $595 in revenue from all sliders and wings-sales. There
were twice as many chicken wing orders sold than there were sliders sold.
Answers
The number of chicken wing orders is 90 and the number of sliders is 45.
According to the question,
We have the following information:
Each order of chicken wings sells for $7.25-while each order of hamburger sliders sells for $3. On Friday, Tyler made a total of $595 in revenue from all sliders and wings-sales. There were twice as many chicken wing orders sold than there were sliders sold.
Now, let's take the number of sliders to be x and the number of chicken wing orders to be y.
y = 2x
Now, we have the following expression:
7.25x+3(2x) = 595
7.25x+6x = 595
13.25x = 595
x = 45 (This value is rounded off to a whole number)
Now, the number of wing sales:
y = 2*45
y = 90
Hence, the number of chicken wing orders is 90 and the number of sliders is 45.
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Solve: -4x + 3 > 27
Please explain and show your work step-by-step.
Answers
The value of x is less than -6.
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, -4x + 3 > 27
-4x + 3 > 27
-4x + 3 - 3 > 27 - 3 → (subtracting 3 from both sides)
-4x > 24
-4x/4 > 24/4 → (dividing by 4 both the side)
-x > 6x
x < -6
Hence, x < -6
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The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13, the altitude is x+7, and the base is 2x. 13 x + 7 2x 13 What is the length of the base? Your answer
Answers
we have that
the altitude divide the isosceles triangle into two congruent right triangles
so
Applying the Pythagorean Theorem
(x+7)^2=13^2+x^2
solve for x
x^2+14x+49=169+x^2
simplify
14x+49=169
14x=169-49
14x=120
x=120/14
simplify
x=60/7
Find the length of the base
2x=2(60/7)=120/7
answer is 120/7 unitsSydney measured a line to be 4.9 inches long. If the actual length of the line is 5.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answers
The percent error of the measurement will be 5.8%.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Sydney measured a line to be 4.9 inches long.
And, The actual length of the line is 5.2 inches.
Now,
The percent error is calculated as;
The difference between the measures = 5.2 - 4.9
= 0.3 inches
So, The percent error = 0.3/5.2 x 100
= 5.76%
Thus, The percent error of the measurement to the nearest tenth of a percent will be 5.8%.
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Just help with the problem and do it quickly please
Answers
SOLUTION
In 2020 black engineers under 30 is 70% of 500, which is
[tex]\frac{70}{100}\times500=350[/tex]In 2021 500 members joined making a total of 1000 members.
The black engineers together are now 50% of 1000, which is 500
So the numbers of black engineers that joined in 2021 becomes
[tex]500-350=150[/tex]Hence the answer is 150
What would be the property of all ( 7=2x-5) (12=2x) and (6=x), which property would they be, Addition property of equality, Subtraction Property of Equality, Multiplication property of equality, Division Property of Equality, or Substitution Property
Answers
Answer
Step-by-step Explanation
7 = 2x - 5
12 = 2x
6 = x
The movement from the first step to the second step involves adding 5 to both sides.
7 = 2x - 5
7 + 5 = 2x - 5 + 5
12 = 2x
Adding 5 to both sides, is what the addition property of equality means.
Then, the movement from the second step to the third step involves dividing both sides by 2.
it takes james 15 minutes to cut a log into 4 pieces. find how long it will take him to cut a log into 15 pieces.
Answers
It will take 56.25 minutes to cut the log into 15 pieces.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, James takes 15 minutes to cut the log into 4 pieces, which can be represented by:
4 pieces = 15 minutes
1 piece = 15/4 minutes
15 pieces = (15/4)×15 minutes
15 pieces = 56.25
Hence, it will take 56.25 minutes to cut the log into 15 pieces.
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