Use the discriminant to determine the number of real solutions to the equation. 8n^2−7n=−7

Answer:

Step-by-step explanation:

Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.

Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)

On expansion

(3 - i)(3 + i)

=  9+3i-3i-i²

= 9-(-1)

= 9+1

(3 - i)(3 + i) = 10

For the expression (2 + i)(1 - i), we have;

(2 + i)(1 - i)

= 2-2i+i-i²

= 2-i+1

= 3-i

Multiplying 3-i with the last expression (1 + 2i)

(2 + i)(1 - i)(1 + 2i)

= (3-i)(1+2i)

= 3+6i-i-2i²

= 3+5i-2(-1)

= 3+5i+2

= 5+5i

Finally,  [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]

= 10(5+5i)

= 50+50i

Hence,  (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i

Answer:

that would be false

Step-by-step explanation:

all whole numbers are integers, but not all integers are whole numbers

Complete question :

Zen is participating in an all-day hike to the Grandfather Mountain Summit on the Blue Ridge Parkway.

Starting at elevation zero, Zen climbs to an elevation of 4,646.4 feet to reach the Cragway Trail. From there, he hikes up another 1,817.6 feet to the Calloway Peak Summit, the highest point on Grandfather Mountain. Based on these numbers, the Calloway Peak Summit is at a height of _____ feet.

On his return trip, Zen descends from the Calloway Peak Summit to an elevation of 2,402.5 feet, arriving at the Flat Rock Junction. So, the elevation at Flat Rock is ______ feet.

Answer:

6,464 Feets; 4,061.5 Feets

Step-by-step explanation:

Given the following:

Starting elevation = 0

Elevation of the Cragway Trail = 4,646.4 feets

Elevation of Cragway Trail to Calloway peak summit = 1,817.6

From Calloway peak summit, Zen descends to an elevation of 2,402.5 Feets (flat Rock junction)

The Calloway Peak Summit is at a height of _____ feet.

Height of Calloway Peak Summit:

(Starting elevation to Cragway trail) + (Cragway trail elevation to Calloway peak Summit)

4,646.4 Feets + 1,817.6 Feets = 6,464 Feets

B) Elevation at Flat Rock Junction:

Height of Calloway peak summit - 2,402.5

(6464 - 2402.5) Feets = 4,061.5 Feets

Answer:

653.12 ft²

Step-by-step explanation:

2πrh + 2πr²

2(3.14)(8)(5) + 2(3.14)(8)²

251.2 + ²401.92 = 653.12

Step-by-step explanation:

Here,

radius of a cylinder (r)= 8 ft.

height (h)= 5 ft.

now,

area of a cylinder (a)= 2.pi.r(r+h)

now, putting the values we get,

a = 2×3.14×8(8+5)

after simplification we get,

Area of cylinder is 653.12 sq.ft.

Hope it helps....

Answer:

1 hour

Step-by-step explanation:

No. of pages print in 1.5 hours = 900

dividing LHS and RHS by 1.5 so that we get 1 hour in LHS

no. of page print in 1.5/1.5 (1) hours = 900/1.5 = 600.

Thus, it takes 1 hour to print 600 pages.

Given that we have to find  how

long will it take her to print a book of 600 pages.

Answer is 1 hour.

Answer:

parallel lines

Step-by-step explanation:

Lines IJ and KL are parallel. Since in a dilation there is no rotation, a line becomes either the same line or a parallel line.

Answer:

The correct ans is...

3 x square + 5 x - 5

Step-by-step explanation:

U can only subtract or add if u hv the same variable..

here -2x and 7x have the same variable...

so -2x + 7x = 5x

Therefore the ans is....

3 x square + 5 x - 5

Hope this helps....

Have a GOOD DAY !!!!

Pls mark my ans as brainliest

If u mark my ans as brainliest u will get 3 extra points

Sry to say....

U really need to read ur Math TBK

Answer:

3x²+5x-5

Step-by-step explanation:

collect like terms.

3x²+(-2x+7x)-5

3x²+ 5x-5

Sandy got 350 out of 2400.

Her portion is 350/2400 which can be reduced to:

35/240 = 7/48

The portion is 7/48

Answer:

x = 4.5

y = 3.25

Step-by-step explanation:

Use elimination

5x + 2y = 29

x + 4y = 13 (-5)

4y(-5) = 13(-5)

2y = 29

-20y = -65

y = 3.25

Sub it back into the equation

5x + 6.50 = 29

5x = 22.5

x = 4.5

Answer:

+5

Step-by-step explanation:

So you can see the 5 pattern, so you add 9+5= 14 which goes in the middle square and 14+5=18 in the left square

Now between 18 and 11 it is 7 so you subtract 7 which equals 4 then - 5= -1 then -5= -6

Answer:

4  5  9

11  6  1

3  7  8

Step-by-step explanation:

In a magic square, all rows, columns, and diagonals have the same sum.

Let's call the cells a - i this way:

a  b  c

d  e  f

g  h  i

Now lets's fill in what we have:

a  b  9

11  6  1

g  h  i

2nd row: 11 + 6 + 1 = 18

3rd column: 9 + 1 + i = 18; i = 8

a  b  9

11  6  1

g  h  8

Main diagonal: a + 6 + 8 = 18; a = 4

4  b  9

11  6  1

g  h  8

1st row: 4 + b + 9 = 18; b = 5

4  5  9

11  6  1

g  h  8

1st column: 4 + 11 + g = 18; g = 3

4  5  9

11  6  1

3  h  8

2nd column: 5 + 6 + h = 18; h = 7

4  5  9

11  6  1

3  7  8

Answer:

64 students drink coke only

34 students drink pepsi only

Step-by-step explanation:

Here, we want to know the number of students that drink coke only and number of students that drink pepsi only.

Let the number of students that drink both be x

Mathematically,

n(μ) = 119 where μ represents the universal set

n(P) = 39

n(C) = 69

n(C n P) = x

n(C n P)’ = 16

n(P) only = 39 - x

n( C) only = 69 - x

Mathematically;

119 = (69-x) + (39-x) + x + 16

119 = 69 + 39 + 16 -2x + x

119 = 124 - x

x = 124 - 119

x = 5

So the number of students drinking pepsi only = 39 -5 = 34

The number of students drinking coke only = 69-5 = 64

Step-by-step explanation:

A is directly proportional to B is written as

where k is the constant of proportionality

First we must find the relationship between the two variables

when

A = 5/3

B = 5/6

Substitute the values into the formula to find k

[tex] \frac{5}{3} = k \frac{5}{6} [/tex]

Multiply through by the LCM which is 6

That's

[tex]5 \times 2 = 5k[/tex]

5k = 10

Divide both sides by 5

k = 2

So the formula for the variation is

when B = 1/3

[tex]A = 2 \times \frac{1}{3} [/tex]

When A = 15/2

[tex] \frac{15}{2} = 2B[/tex]

Multiply through by 2

[tex]4B = 15[/tex]

Divide both sides by 4

Hope this helps you

Answer:

Step-by-step explanation:

Principal ( P ) = $ 300

Rate ( R ) = 3%

Time ( T ) = 2 years

Now, let's find the simple Interest:

I = [tex] \mathsf {\frac{PTR}{100} }[/tex]

[tex] \mathsf{ = \frac{300 \times 2 \times 3}{100} }[/tex]

[tex] \mathsf{ = \frac{1800}{100} }[/tex]

[tex] \mathsf{ = 18}[/tex]

Extra information:

Simple Interest

In our daily life when we borrow a sum of money either from a moneylender or from any financial company, we have to pay the money back by adding with extra sum of money. This borrowed money is called principal. The extra money to be paid for the borrowing money is called interest , which is paid after certain duration in certain rate. At last, the borrowed money should be paid back along with interest which is called amount.

Interest is based on three factors : Principal ( P ) , Rate of interest ( R ) and Time ( T ). While computing the interest, the rate must be in percent and time in years.

[tex] \mathsf{ \: simple \: interest \: = \frac{PTR}{100} }[/tex]

On simplifying

[tex] \mathsf{p = \frac{I \times 100}{T \times R} }[/tex]

[tex] \mathsf{t = \frac{I \times 100}{P \times R} }[/tex]

[tex] \mathsf{r = \frac{I \times 100}{P \times T}} [/tex]

And from the definition,

Amount ( A ) = Principal ( P ) + Interest ( I )

Principal ( P ) = Amount ( A ) - Interest ( I )

Interest ( I ) = Amount ( A ) - Principal ( P )

Hope I helped!

Best regards!

Answer:$18

Step-by-step explanation:3% of $300 is $9.$9 is the interest of 1 year so the interest of 2 years is 2 multiplied by 9 which is $18.

Answer:

256

Step-by-step explanation:

First, handle the exponent:

2²=4 (2*2=4)     and     4³=64 (4*4=16*4=64)

Now multiply those two outcomes:

4*64=256

This equation is also known as 4⁴

Answer:

1.5

Step-by-step explanation:

1.54324

The 5 is in the tenths place

We look at the next digit to determine if we need to round up or we leave it alone

The next digit is a 4.  It is under 5 so we leave the 5 alone

1.5

The tenths place is one place to the right of the decimal point.

This means the digit in the rounding place is 5

Since the digit to the right of the rounding

place, 4, is less than 5, round down.

This means that the digit in the rounding place, 5, stays the same and

we change all digits to the right of the rounding place to 0.

So our answer is 1.50000 or 1.5.

Answer:

a) 3 x 20 = 60

b) -2x20 = -40

question c and d are unclear as we do not know how many questions were wrong and how many were not answered.

Sorry but I hope that helped

Answer:

a)  60 points

b)  0 point

c)  22 points

d)  -11 points

Step-by-step explanation:

a)  20 * 3 = 60 points (all answered correct)

b)   0 point (Minimum score if you don't answer any of the questions)

c)  10 * 3 = 30 points

    (14 - 10)  * -2 = -8 points

    right minus wrong =  30 - 8 = 22 points  

d)  5 * 3 = 15 points

    (18 - 5) * -2 = -26 points

    right minus wrong = 15 - 26 = -11 points

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

[tex]pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

[tex]or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] 8[/tex]

Now,

again finding the distance between PR,

[tex] pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} } [/tex]

or,

[tex] \sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] = \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } [/tex]

now, finding the distance of QR,

[tex]qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} } [/tex]

or, by simplification we get,

[tex] \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

now, equating PR and QR,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

we cancelled the root ,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29[/tex]

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8} [/tex]

cancel the roots,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = 8[/tex]

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

Hope it helps...

Answer:

1,8.9

Step-by-step explanation:

Answer:

[tex] \boxed{13}[/tex]

Step-by-step explanation:

Arranging the data in ascending order:

8 , 8 , 10 , 11 , 13 , 13 ,13 , 14 , 14 , 15 , 16 , 17 , 18 , 18 ,

In the case of discrete data, mode can be found just by inspection, i.e just by taking an item with highest frequency.

Here, 13 has the highest frequency

So, Mode = 13

Extra information

Mode

The mode of a set of data is the value with the highest frequency. A distribution that has two modes is called bimodal. The mode of a set of data is denoted by Mo.

Hope I helped!

Best regards!

(0,8)+(7,-52) eso es la problema

Answer:

D

Step-by-step explanation:

So we want to find θ. We are already given the hypotenuse and the side length opposite to θ. Therefore, we can use the trig function sine to find θ.

Recall that:

[tex]\sin(\theta)=opp/hyp[/tex]

Plug in 10.2 for the opposite side and 15 for the hypotenuse:

[tex]\sin(\theta)=10.2/15[/tex]

Solve for θ. Use a calculator:

[tex]\theta=\sin^{-1}(10.2/15)\\\theta\approx42.8436\textdegree[/tex]

The answer is D.

[tex]\frac 1c=\frac1{c_1}+\frac1{c_2} [/tex]

$\frac1c=\frac{c_1+c_2}{c_1c_2}$

$\implies c=\frac{c_1c_2}{c_1+c_2}$

Answer:

112°

Step-by-step explanation:

Angle A is an inscribed angle that intercepts arc BCD.

Therefore:

m<A = ½ of arc BCD (Inscribed Angle Theorem)

Arc BCD = BC + CD = 146 + CD

An equation can be written to enable us find the measure of arc CD. See below:

Let x = measure of arc CD

Thus,

129° = ½(146 + x)

Solve for x

129*2 = 146 + x

258 = 146 + x

Subtract 146 from both sides of the equation.

258 - 146 = x

112 = x

x = measure of arc CD = 112°

Answer:

1/12

Step-by-step explanation:

3/4 + z = 5/6

Subtract 3/4 from each side

3/4 -3/4+ z = 5/6-3/4

z = 5/6 -3/4

Get a common denominator of 12

z = 5/6 *2/2 -3/4 *3/3

z = 10/12 - 9/12

z = 1/12

Answer:

Step-by-step explanation:

39/5 as a mixed number;

39/5 as a mixed number;39 ÷ 5 = 6 remaining 9

Therefore:

6 9/5

hope it helps.I was reading the same chapter

Answer:

Part A:

Two types of translation are;

1) Horizontal translation left T(0, 8),

2) Vertical translation T(16, 0)

Part B:

For the horizontal translation transformation, k = 8

For the vertical translation transformation, k = 16

Part C:

For the horizontal translation transformation, the equation is f(x + 8) = g(x)

For the vertical translation transformation, the equation is f(x) + 16 = g(x)

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Part A

We can shift f(x) up to g(x)

or we can shift f(x) to the left into g(x)

Part B

y = f(x) + k  k > 0 moves it up

f(x) goes from -1 to 17 for a distance of 18 units

We are moving up 18 units

k = 18

y = f(x + k) k> 0 moves it left

We are moving to the left from 0 to -6 units for a distance of 6 units

k = 6

Part C

Up:

g(x) = f(x) +18

Left:

g(x) = f(x+6)

Anjdjdnjadnosepsjkdsksksks

bzjd

Answer:

a)45min

b)900min

Step-by-step explanation:

We were told that it takes Matt 3 minutes to read one page in a book.

It implies that 3minutes = 1page of the book

Then he continues to read at the same pace, he can read 15 similar pages in minutes.

a)Then, he can read 15 similar pages in

15x3 minutes.which is 45minutes.

b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins

Answer: has anyone seen my dad?