Answers
Answer:
(i) (0, -32)
(ii) (-4, 0) and (8, 0)
(iii) x = 2
(iv) (2, -36)
(v) (2, -36) minimum
Step-by-step explanation:
Given quadratic equation:
[tex]y=x^2-4x-32[/tex]
Part (i)
The y-intercept is the point at which the curve crosses the y-axis.
To find the y-intercept, substitute x = 0 into the given equation:
[tex]\implies (0)^2-4(0)-32=-32[/tex]
Therefore, the y-intercept is at (0, -32)
Part (ii)
The zeros are the points at which the curve crosses the x-axis.
To find the zeros, substitute y = 0 into the given equation and factor:
[tex]\implies x^2-4x-32=0[/tex]
[tex]\implies x^2-8x+4x-32=0[/tex]
[tex]\implies x(x-8)+4(x-8)=0[/tex]
[tex]\implies (x+4)(x-8)=0[/tex]
Therefore:
[tex](x+4)=0 \implies x=-4[/tex]
[tex](x-8)=0 \implies x=8[/tex]
So the zeros are (-4, 0) and (8, 0)
Part (iii)
The axis of symmetry is a vertical straight line that divides the curve into two symmetrical parts. The axis of symmetry is the x-value of the mid-point of the zeros.
[tex]\sf \implies midpoint=\dfrac{8+(-4)}{2}=2[/tex]
Therefore, the axis of symmetry is: x = 2
Part (iv)
The vertex is the turning point of the parabola.
If the leading coefficient is positive, the parabola opens upwards and the vertex is the minimum point.
If the leading coefficient is negative, the parabola opens downwards and the vertex is the maximum point.
The axis of symmetry is the x-value of the vertex.
To find the y-value, substitute x = 2 into the equation:
[tex]\implies (2)^2-4(2)-32=-36[/tex]
Therefore, the vertex is (2, -36)
Part (v)
The optimal value is also known as the vertex.
Therefore, the optimal value is (2, -36).
As the leading coefficient of the given quadratic equation is positive, the parabola opens upwards and so the optimal value is a minimum.
Related Questions
What is the volume, in cubic meters of the prism below?
Answers
Answer:
1848 Cubic Meters
Step-by-step explanation:
The volume should be (7*24*22)/2
This is because this object is bascally half of a rectangular prism, so we need to divide the whole product by 2 at the end.
7*24*22 = 3696
3696/2 = 1848
Graph the set {x|x≤-5} on the number line.
Then, write the set using interval notation.
Answers
The interval notation that defines this set is: (-∞, -5]
And the graph can be seen below.
How to graph the inequality?Here we want to graph the inequality:
x ≤ -5
This refers to all the values of x equal or smaller than -5.
To graph this, we need to graph a closed circle at -5, and we need to draw an arrow that points to the left (values smaller than -5). The graph is the one that you can see below.
The interval notation that defines this set is: (-∞, -5]
The first end is open, and the second is closed (because of the symbol ≤).
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Savannah is 1.75 meters tall. At 11 a.m., she measures the length of a tree's shadow to
be 43.75 meters. She stands 39.2 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
Answers
The height of the tree is 1.95 meters.
At 11 AM, we have
Savannah = 1.75 m
Tree Shadow = 43.75 m
Savannah Shadow = 39.2 m
So, we make use of the equivalent ratio
Savannah :Tree::Savannah Shadow:Tree Shadow
Now, 1.75:Tree::39.2:43.75
In fraction Tree/1.75 = 43.75/39.2
Multiply both sides by 1.75
Tree =43.75/39.2 ×1.75
Tree=1.95
Therefore, the height of the tree is 1.95 meters.
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What are the zeros of the function f(x) = x4 – 4x² –5?
Answers
Answer:
[tex]x =i\\\\x =-i\\\\x=\sqrt 5\\\\x=-\sqrt 5[/tex]
Step-by-step explanation:
[tex]~~~~~~~~x^4-4x^2 -5 = 0\\\\\implies x^4-5x^2+x^2 -5 = 0\\ \\\implies x^2(x^2 -5)+(x^2-5) =0\\ \\\implies (x^2 +1)(x^2 -5) - 0\\\\\implies x^2+1 = 0~~~~~~~~~ \text{Or}~~~~~~~~~ x^2 -5 = 0\\\\\implies x^2 = -1~~~~~~~~~~~~ \text{Or}~~~~~~~~~x^2 = 5\\\\\implies x= \pm\sqrt{-1}~~~~~~~~~\text{Or}~~~~~~~~~x=\pm\sqrt 5\\\\\implies x = \pm i~~~~~~~~~~~~~~\text{Or}~~~~~~~~~x=\pm\sqrt 5\\[/tex]
What is 136x * 149y??
Answers
Answer:
20264xy is the answers for the question
Step-by-step explanation:
please mark me as brainlest
need help with this asap pls really need the answer
Answers
In the diagram, the area of the given shape is 102 cm²
Area of a KiteFrom the question question, we are to determine the area of the given shape
The given shape is a kite
The area of a kite is given by the formula,
[tex]A =\frac{pq}{2}[/tex]
Where A is the area
p and q are the diagonals
In the given diagram,
p = 6cm + 6 cm = 12 cm
q = 3 cm + 14 cm = 17 cm
Thus,
Area of the kite = [tex]\frac{12 \times 17}{2}[/tex]
Area of the kite = 6 × 17
Area of the kite = 102 cm²
Hence, the area of the given shape is 102 cm²
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In AXYZ, ZZ = 90°. Given that ZX = 58° and XZ = 4.9 m, find the length of XY
Answers
Answer:
Okay, I figured it out. XY=9.246691583 or 9.247 if you're rounding.
Step-by-step explanation:
In the right triangle of XYZ, Given that angle Z=90 degrees, angle X=58 degrees and XZ=4.9m.
Since it's a right triangle you can use SOHCAHTOA:
cosθ=adjacent/hypotenuse
cosθ=4.9/h
You can then manipulate the formula to this
h=4.9/cos(degree) = h=4.9/cos(58)
=9.246691583
hope this helps
A halloween bowl contains four snicker bars, five hershey bars, three milkway bars, and one twix bar. What is the probability that a snicker bar will be pulled out the bowl?
Answers
Answer:
1/3
Step-by-step explanation:
The total # of bars = 12. (4+5+3)
4 of those, are snickers
4/12 (Target / Total)
1/3 (simplified)
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
Enter the ordered pair that is the solution to the system of equations graphed below. Y=2x-5 y= 1/2x -2
Answers
Answer:
Step-by-step explanation:
2x - 5 = 1/2x - 2
3/2x - 5 = -2
3/2x = 3
3x = 6
x = 2
y = 4 - 5
y = -1
(2, -1)
What is the area of the parallelogram?
Answers
Answer:
Area = 120 in²Step-by-step explanation:
just follow the formula in the picture
Area = b × h
Area = 15 × 8
Area = 120 in²
Rebecca rolls a 6-sided number cube 1290 times. How many of the rolls are expected to show a factor of 6?
Answers
Answer:
215
Step-by-step explanation:
1/6 chance to roll a 6
1/6 * 1290
Please help me. I need to know the answer.
Answers
Step-by-step explanation:
Given =
AC = 6cm
BC = 9cm (hyp)
AB =
By pyth
A^2 = B^2 + C^2
9 = 6 + AB
AB = 9-6 = 3
AB =3
Hope this helps
A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was 36,800. Assuming this trend continues, which of the following is a linear function that properly models the relationship between the town's population, P, and the years that have passed since 2008, t.
Answers
The linear function that models the relationship is P = 28,200 + 1950t.
What is the linear function that models the relationship?A linear function is a function that has a single variable raised to the power of 1. An example is x + 2
The first step is to determine the rate of increase in the population:
Rate of increase = (population in 2012 - population in 2008) / number of years
(36.000 - 28,200) / 4 = 1950
P = 28,200 + 1950t
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While scuba diving, Rajeev dove to a depth of 12.6 feet below the surface of the water and then descended another 8.7 feet. What expression can be used to find Rajeev’s new position?
12.6 – 8.7
–12.6 – 8.7
–12.6 – (–8.7)
12.6 – (–8.7)
Answers
The answer is -12.6-8.7
Answer:
the answer is 16/20 feet oooooooooooo
What is the solution to this system of equations? -3x+2y=3 y+2z=0 x-y-z=-1
Answers
The solution is B, (x, y, z) = (-1, 0, 0).
Eliminate z from the last two equations:
(y + 2z) + 2 (x - y - z) = 0 + 2 (-1)
2x - y = -2
Eliminate y from this and the first equation:
(-3x + 2y) + 2 (2x - y) = 3 + 2 (-2)
x = -1
Solve for y :
2x - y = -2
2 (-1) - y = -2
y = 0
Solve for z :
x - y - z = -1
-1 - 0 - z = -1
z = 0
the range of a data set is 32.if the largest number in the set of 50 what isthe smallest number
Answers
The smallest number of the data set is 18.
What is the smallest number?Range is used to measure the spread of a dataset. Range is determined by subtracting the largest number from the smallest number.
Range = largest number - smallest number
Smallest number = largest number - range
50 - 32 = 18
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100 points! halp...
Which point could be removed in order to make the relation a function? ((-4.3). (-5. 6), (1, 0). (-4. 5). (9, 5), (0.-7))
(-5.6)
(1.0)
(-4, 5)
(9.51
Answers
Answer:
it is 3rd option C. -4, 5
Step-by-step explanation:
all the elements are associated with only one second element except -4
for -4 there are two second elements 3 and 5 from the ordered pairs (-4, 3) and (-4, 5)
so we can remove one of them to make R a function
since (-4, 3) is not in the options so the correct option is (-4, 5)
so c is the right one
Hope This Helped
As per defination of function
Every domain has an unique range
or
f(x)=yHere
f(-4)=3f(-4)=5One point need to be removed to get it function
Hence the point is (-4,5)
on December 1, a 350 gallon oil tank was full. on January 15, it was 1/4 full. how many gallons of fuel were used in that time period?
Answers
Answer:
262.5 gallons
Step-by-step explanation:
The amount used is the difference between the starting and ending amounts:
350 -(1/4) (350) = 262.5 gallons used
Drag the expressions into the boxes to correctly complete the table. Polynomial Not a polynomial
Answers
The answer to the given question is as below:-
Polynomials:-
x³-7x²+9x-5x⁴-20
x⁵-5x⁴+4x³+2x-1
3x²-5x⁴+2x-12
Non-polynomial:-
x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1
[tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]
[tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]
What are polynomials?A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.
So the table will be formed as:-
Polynomials:- Non-polynomial:-
x³-7x²+9x-5x⁴-20 x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1
x⁵-5x⁴+4x³+2x-1 [tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]
3x²-5x⁴+2x-12 [tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]
Therefore the polynomials and non-polynomials are shown in the table above.
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PLEASE HELP THIS IS DUE AND I NEED IT DONE
Answers
Answer:
The answers are in the picture. Remember that first is x and then y when you see those coordinated again. (10,11) X=10 and Y=11.
Step-by-step explanation:
A theater group made appearances in two cities. The hotel charge before tax in the second city as $1000 higher than in the first. The tax in the first city was 6.5%, and the tax in the second city was 7.5%. The total hotel tax paid for the two cities was $845. How much was the hotel charge in each city before tax? First city:
Answers
Drag the tiles to the table. Each tile can be used more than once. Determine the most likely action that an investor will take for each scenario. buy hold sell Scenario An investor is waiting until it is clearer whether a stock will do well after a purchase. An investor thinks that a particular stock is not performing and worries the price of the shares may drop in the future. An investor doesn't own a particular stock but is considering adding it to her portfolio depending on how well it does in the near future. An investor who tracks market trends notices that a bull market is starting. Reset Next Action
Answers
Considering the market options that an investor takes, Each scenario listed is attached to the right action that is shown on the tiles:
An investor is waiting until it is clearer whether a stock will do well after purchase. ____________________ HoldAn investor thinks that a particular stock is not performing and worries the price of the shares may drop in the future______ SellAn investor doesn't own a particular stock but is considering adding it to her portfolio depending on how well it does in the near future.______________ BuyAn investor who tracks market trends notices that a bull market is starting.________________ HoldMeaning of an InvestorAn investor can be defined as a name given to an individual that takes every opportunity opened to him to make a profit and by so doing doesn't use his money but puts it into a venture that will yield more.
In conclusion, the list above are the required actions for each scenario that is encountered by an investor
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Answer:
Step-by-step explanation:
hold
sell
buy
hold
43/14 as a decimal rounded to the nearest tenth.
Please explain in-depth step by step.
Answers
Explain:
To convert to a decimal, divide the numerator by the denominator
43 / 14 = 3.07142857
Now round to the nearest tenth, which is the first number to the right of the decimal (0).
Look to the number to the right of the tenth place, (7) if it’s 5 or bigger you round up the tenth place. 7 is bigger so round up the (0) to 1. Final answer is 3.1
X^2+4x+4=12 find the solutions to the equation
Answers
Step-by-step explanation:
X^2 +4X +4=12 subtract the 12 from both sides
X^2 +4x-8= 0
now factor if possible since this equation is not factorable you can use the quadratic formula
It takes a word processor 33 minutes to process and spell check 6 pages. Find out how long it takes her to process and spell check 28 pages.
Answers
Answer:
154 minutes to process and spell check 28 pages
Step-by-step explanation:
33 Minutes to process 6 pages
If we divide both of these numbers by 6 we will get the time taken to process 1 page
33 ÷ 6 = 5.5 minutes, and 6 ÷ 6 = 1 page
So 5 and a half minutes per page
To find out how long 28 pages will take, we multiply by 28
5.5 × 28 = 154 minutes, and 1 × 28 = 28 pages
Which gives us the time of 154 minutes to process and spell check 28 pages
Reducible interest at 6% pa is charged on a loan of $50 000. Annual repayments of
$5000 are made. Calculate how much is still owing after:
2) 2 years
3) 3 years
1) 1 year
[20pts] and Make Brainliest
Answers
1. The loan balance after 2 years is $45,262.
2. The loan balance after 3 years is $42,678.
3. The loan balance after 1 year is $47,700.
What is the loan balance?The loan balance is the amount remaining from the principal amount after the deduction of repayment and the addition of interest for the period.
The loan balance can be computed manually as below:
Data and Calculations:Loan amount = $50,000
Interest rate = 6%
Annual repayments = $5,000
1st year:
Loan amount = $50,000
Repayment = ($5,000)
Interest = $2,700 ($50,000 - $5,000) x 6%
Loan balance = $47,700 ($50,000 - $5,000 + $2,700)
2nd year:
Loan balance = $47,700
Repayment = ($5,000)
Interest = $2,562 ($47,700 - $5,000) x 6%
Loan balance = $45,262 ($47,700 - $5,000 + $2,562)
3rd year:
Loan balance = $45,262
Repayment = ($5,000)
Interest = $2,416 ($45,262 - $5,000) x 6%
Loan balance = $42,678 ($45,262 - $5,000 + $2,416)
Thus, the loan balance after 3 years is $42,678.
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Write the equation of the line that passes through (1, 5) and (−2, 14) in slope-intercept form.
Answers
The equation of line is y = -3x + 8
What is slope?Slope is the ratio of the change in the y coordinates to the change in the x coordinates.
Analysis:
slope (m) = y2 - y1 / x2 - x1
m = 14 -5 / -2-1 = 9/-3 = -3
when y = 5, x = 1
y = mx + c
5 = -3(1) + c
5 = -3 + c
c = 5+3 = 8
Y = -3x + 8
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what is the answer for
2(6p + 5) =
Answers
Answer:
2(6p+5) =
12p+10 =
12p = -10
p = -10/12
p = -5/6
N + M? N = 9.1 7.9 -2.4 0.2 -5.8 1.4 and M= 8.2 -0.6 -2.8 -1.8 -2.4 -6.1
Answers
Answer:
[tex]N + M = \begin{pmatrix}17.3&7.3\\ -5.2&-1.6\\ -8.2&-4.7\end{pmatrix}[/tex]
Step-by-step explanation:
[tex]\begin{pmatrix}9.1&7.9\\ -2.4&0.2\\ -5.8&1.4\end{pmatrix} +\begin{pmatrix}8.2&-0.6\\ -2.8&-1.8\\ -2.4&-6.1\end{pmatrix} =\begin{pmatrix}9.1+8.2&7.9-0.6\\ -2.4-2.8&0.2-1.8\\ -5.8-2.4&1.4-6.1\end{pmatrix}[/tex]
Then
[tex]\begin{pmatrix}9.1&7.9\\ -2.4&0.2\\ -5.8&1.4\end{pmatrix} +\begin{pmatrix}8.2&-0.6\\ -2.8&-1.8\\ -2.4&-6.1\end{pmatrix} =\begin{pmatrix}17.3&7.3\\ -5.2&-1.6\\ -8.2&-4.7\end{pmatrix}[/tex]
what percent is 38 of 80
Answers
Answer:
47.5
Step-by-step explanation:
38/80x100%=47.5
Answer:
47.5%
Step-by-step explanation:
Before we get started in the fraction to percentage conversion, let's go over some very quick fraction basics. Remember that a numerator is the number above the fraction line, and the denominator is the number below the fraction line. We'll use this later in the tutorial.
When we are using percentages, what we are really saying is that the percentage is a fraction of 100. "Percent" means per hundred, and so 50% is the same as saying 50/100 or 5/10 in fraction form.
So, since our denominator in 38/80 is 80, we could adjust the fraction to make the denominator 100. To do that, we divide 100 by the denominator:
100 ÷ 80 = 1.25
ow we can see that our fraction is 47.5/100, which means that 38/80 as a percentage is 47.5%.
We can also work this out in a simpler way by first converting the fraction 38/80 to a decimal. To do that, we simply divide the numerator by the denominator:
38/80 = 0.475
Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:
0.475 x 100 = 47.5%
And there you have it! Two different ways to convert 38/80 to a percentage. Both are pretty straightforward and easy to do, but I personally prefer the convert to decimal method as it takes less steps.
I've seen a lot of students get confused whenever a question comes up about converting a fraction to a percentage, but if you follow the steps laid out here it should be simple. That said, you may still need a calculator for more complicated fractions (and you can always use our calculator in the form below).
If you want to practice, grab yourself a pen, a pad, and a calculator and try to convert a few fractions to a percentage yourself.
Hopefully this tutorial has helped you to understand how to convert a fraction to a percentage. You can now go forth and convert fractions to percentages as much as your little heart desires!