i needs help with it please ​

I Needs Help With It Please

Answers

Answer 1

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

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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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

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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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]

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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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

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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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]

43/14 as a decimal rounded to the nearest tenth.
Please explain in-depth step by step.

Answers

Answer: 3.1

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

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

If I saw a dinosaur on the left of me and a giraffe in the right of me which one would u go for

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 136x * 149y??

Answers

Answer:

20264xy is the answers for the question

Step-by-step explanation:

please mark me as brainlest

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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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

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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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

what is the answer for
2(6p + 5) =

Answers

Answer:

2(6p+5) =

12p+10 =

12p = -10

p = -10/12

p = -5/6

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)

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.________________ Hold

Meaning of an Investor

An 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

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

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

What is the area of the parallelogram?

Answers

Answer:

Area = 120 in²

Step-by-step explanation:

just follow the formula in the picture

Area = b × h

Area = 15 × 8

Area = 120 in²

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)=y

Here

f(-4)=3f(-4)=5

One point need to be removed to get it function

Hence the point is (-4,5)

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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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:

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 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!

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 Kite

From 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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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

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