The area of a rectangle is given by the expression x^2 + 6x – 16. What are the dimensions of the rectangle?


(x+4) by (x+4)
(x+4) by (x-4)
(x+8) by (x-2)
(x-8) by (x+2)

Answers:

Note: The answer to problem 7 is a single value. The comma is there to make the number more readable.

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Explanation for problem 7)

There are 26 red cards (13 diamonds + 13 hearts).

We have 26 ways to pick the first red card, and then 25 ways to pick the second red card. If order mattered, then we'd have 26*25 = 650 ways to do this. However, order doesn't matter. All that matters is the hand itself rather than the individual cards. By "hand" I mean the collection of cards, and not the literal physical hand holding them.

Since the count 650 is a double count, this means 650/2 = 325 is the correct count where order doesn't matter. The black cards will follow identical logic to get the same value. There are 325 ways to pick the two black cards. This is because there are an equal number of red and black cards, and we're selecting an equal number of both colors.

So we have 325*325 =  105,625 different hands possible.

To help show some context, there are 52C4 = 270,725 different ways to pick four cards without any restrictions. I'm using the nCr combination formula.

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Explanation for problem 8)

The face cards are Jack, Queen, King. There are 3 face cards per suit and 4 suits total, so 3*4 = 12 face cards in all.

We have 12*11*10 = 1320 permutations and 1320/(3!) = 1320/6 = 220 combinations. We side with combinations because like before, order doesn't matter. There are 220 different ways to pick the three face cards. Then we have 52-12 = 40 ways to pick the fourth non-face card.

Overall, we have 220*40 = 8800 different ways to pick exactly three face cards.

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Explanation for problem 9)

There are 13 diamond cards, so n = 13. We're filling r = 4 slots.

Use the nCr combination formula to find that 13C4 = 715

See the attached image below for more detailed steps.

We have 715 ways to pick all diamonds.

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Explanation for problem 10)

We'll build from problem 9. We found there are 715 ways to pick four diamonds. This is the same number of ways to pick four hearts, or four clubs, or four spades. The actual suit doesn't matter. So we have 4*715 = 2860 different ways to pick 4 cards of the same suit

In poker, having all cards of the same suit is known as a flush. Though with poker, it involves 5 cards instead of 4.

Answer:

missing angle=36 degree

Answer:

3x² + 8 = 20

x = 2

Step-by-step explanation:

3 times x squared increased by 8 is 20

3x² + 8 = 20

3x² = 12

x² = 4

x = 2

Answer:

C. 8/25 - 19/25i

Step-by-step explanation:

Given that:

[tex]\dfrac{4-i}{3+4i}[/tex]

[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)}[/tex]

[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)} \\ \\ =\dfrac{12 -16i -3i+4i^2}{9 - 12i +12i -16i^2} \\ \\ = \dfrac{12-19i+4i^2}{9-16i^2} \\ \\ = \dfrac{8-19i}{25}[/tex]

[tex]=\dfrac{8}{25}- \dfrac{19i}{25}[/tex]

Answer:

Step-by-step explanation:

take 64 degree as reference angle

using cos rule

cos 64=adjacent/hypotemuse

0.43=QR/10

10*0.43=QR

4.3=QR

Answer:

Step-by-step explanation:

Right side =

sin A / cos A + sinB/ cosB         (sinAcosB + sinB cos A ) *   cosA cosB

-------------------------------------    =          cosA cosB                (sinAcosB - snBcosA )        sinA/cosA -  sinB/cos B

= Left side.

The trigonometry identity [tex]\frac{sin(A+B)}{sin(A-B)}[/tex] is equals to [tex]\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex].

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

According to the given question.

We have a trigonometric identity.

[tex]\frac{sin(A+B)}{sin(A-B)} =\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex]

To prove the above  trigonometric identity we will show L.H.S = R.H.S

[tex]L.H.S=\frac{sin(A+B)}{sin(A-B)}[/tex]

⇒ [tex]L.H.S = \frac{cosBsinA-sinBcosA}{sinAcosB-cosAsinB}[/tex]

⇒ [tex]L.H.S = \frac{\frac{sinAcosB}{cosAcosB} + \frac{sinBsinA}{cosBcosA} }{\frac{sinAcosB}{cosAcosB}-\frac{cosAsinB}{cosAcosB} }[/tex]     (dividing the numerator and denominator by [tex]cosAcosB[/tex] )

⇒ [tex]L.H.S = \frac{\frac{sinA}{cosA} +\frac{sinB}{cosB} }{\frac{sinA}{cosA}-\frac{sinB}{cosB} }[/tex]

⇒ [tex]L.H.S = \frac{tanA+tanB}{tanA- tanB}= R.H.S[/tex]

Hence, L.H.S = R.H.S

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Answer:

Solution given:

5,6,7,8,9,

When repeated:

it has

5 ways for each

different five digit members can be formed from the digits:5*5*5*5*5=3125

When not repeated:

it has

5 ways for 1st

4 ways for 2nd

3 ways for 3rd

2 ways for 4th

1 ways for 5th

different five digit members can be formed from the digits:5*4*3*2*1=120

Answer:

Yes 5+2y=13 is a linear relationship

Answer:

Fossil > Arrow Head > Pottery > Shell > Fishbone > Fish Hook

Step-by-step explanation:

Arrowhead = ___20___ feet

Fishbone = __-10___ feet

Fish Hook = ___-40__ feet

Fossil = __30___ feet

Pottery = ___10___ feet

Shell = ____0___ feet

If something is above sea level, it would have a positive elevation, and if below sea level, a negative elevation.  And at sea level, you have 0 elevation.

After this, just put them in order of decreasing elevation.  So, the highest elevation is  30ft with the fossil, then 20 with the arrow head, pottery at 10, shell at 0, fishbone at -10, fish hook at -40.

Answer:

What is the anwser i ned help

Step-by-step explanation:

2^( - 1 ) × 4^( -1 ) =

2^( -1 ) × 2^( 2 × ( - 1) ) =

2^( - 1 ) × 2^( - 2 ) =

2^( - 1 - 2 ) =

2^( - 3 ) =

1/ 2^( 3 ) =

1/8

Answer:

0.0416

Step-by-step explanation:

Given :

Number of balls :

Pink = 8 ; black = 9

Total number of balls = 8+9 = 17

Choosing with replacement :

Probability = required outcome / Total possible outcomes

Required outcome = number of black balls

Total possible outcomes = total number of balls

P(black) = 9/17

Number of picks = 5

Hence, Probability that all 5 picks are black :

P(all black) = 9/17 * 9/17 * 9/17 * 9/17 * 9/17 = 0.0415879

= 0.0416

Answer: 61/100 would be the answer

Answer:

Step-by-step explanation:

Use two points on the graph to get an equation:

The slope: m = (60 - 8)/6 = 8.667

The y- intercept is 8

The equation of the line of best fit:

The answer to your question is y = 8.667x + 8. Hope this helps; have a great day!

Answer:

4/10 8/20 16/40

Step-by-step explanation:

Answer:true

Step-by-step explanation:

just took the test < 3

The statement : "for a sample size of n = 26 and a population parameter of  p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.

Normal curve is used to represent the class shapes in the statistical probability. Mathematically, we can describe the normal curve as -

[tex]$f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}[/tex]

where -

f(x) = probability density function

σ = standard deviation

μ = mean

Given is that for a sample size of n = 26 and a population parameter of

p = 0.6, a normal curve can be used to approximate the sampling

distribution.

It is asked to identify whether the given statement regarding the normal curve is true or false. The given statement is - "for a sample size of n = 26 and a population parameter of  p = 0.6, a normal curve can be used to approximate the sampling distribution". The given statement is true.

Therefore, the statement : "for a sample size of n = 26 and a population parameter of  p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.

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Answer:

Kyle typed 574 words in 14 minutes. How many...........?????????

il.l just divide 574 divided by 14= 41

Step-by-step explanation:

:)

Answer:

41 like I said in the comments.

Step-by-step explanation:

Answer:

100 cm2

Step-by-step explanation:

If the area is 64 cm2 that means that the side is 8 cm (square root of 64 is 8)

8 increased by 2 = 10

area 10x10 = 100 cm2

Answer:

the answer is 100cm²

since originally is 64 cm²

so square root of 64 is 8 cm.

after you get 8cm you get,

8+2 = 10cm (a side of square)

and then to find a new area you get,

10 × 10 = 100 cm²

Answer:

13 =x

Step-by-step explanation:

The width is x

The length is 2 times the width or 2x

A = length * width

A = 2x* x

338 = 2x^2

Divide by 2

338/3 = 2x^2/2

169 = x^2

Taking the square root of each side

sqrt(169) = sqrt(x^2)

13 =x

Answer:

dvffdd

Step-by-step explanation:

Answer: 166.666 mcgs

Step-by-step explanation:

If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting is 166.667 mcg.

A ratio shows us the number of times a number contains another number.

Given that 300 ml of an IV fluid contains 50 mcg of Drug A. Therefore, the ratio of IV fluid to drugs A can be written as,

IV fluid / Drug A = 300ml / 50 mcg

IV fluid / Drug A = 6 ml/ mcg

Now, If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting,

IV fluid / Drug A = 6 ml/ mcg

1000 ml / Drug A = 6 ml/ mcg

Drug A = 1000 ml / 6 ml/ mcg

Drug A = 166.667 mcg

Hence,  If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting is 166.667 mcg.

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Answer:

The vertex of the parabola is [tex]V(x,y) = (0, 3)[/tex].

Step-by-step explanation:

In this case, the vertex of the parabola is the absolute maximum of the graph, that is, the point [tex]V(x,y) = (0, 3)[/tex].  Mathematically speaking, the vertex of the parabola is represents the only point of the range ([tex]y[/tex]) which is related to an only value of the domain ([tex]x[/tex]).

Answer:

She Bought 40 Gallons of Milk

Step-by-step explanation:

Answer:

37.7

Step-by-step explanation:

Circumference = [tex]2\pi r[/tex]

Circumference = [tex](2)(\pi )(6)[/tex]

Circumference = 37.69911184 / 37.7

Therefore, circumference of the circle with the radius 6 cm is 37.7.

Answer:

37.7

Step-by-step explanation:

formula for circumference of a circle=2πr

2×π×6=37.7cm

Answer: perpendicular lines

Step-by-step explanation:

look up "Two straight lines that intersect at a right angle"

Answer:

Perpendicular! hope this helps :)

Answer:

how much are they selling them for

This question is incomplete, the complete question is;

A gymnasium floor is being covered by square shock-absorbing tiles.

The old gym floor required 864 square tiles. The new tiles are 2 inches larger in length and width than the old tiles. The new flooring will require only 600 tiles. What is the length of a side of one of the new shock-absorbing tiles  

Answer:

Length of the side of one of the new shock-absorbing tiles is 12 inches

Step-by-step explanation:

Given the data in the question;

Since both the area for old tiles and new tiles are the same;

so Area of old tiles = Area of new tiles,

given that; The old gym floor required 864 square tiles and new flooring will require only 600 tiles as new tiles are 2 inches larger in length and width than the old tiles.

Now let the length of the sides of the square tiles be x

Area of a square = length × length = x × x = x²

So, Area of Old tiles = 864 × x² = 864x²

Area of New tiles = 600( x + 2 )²

= 600( x² + 4x + 4 )

= 600x² + 2400x + 2400

Now, Area of old tiles = Area of new tiles

864x² - 600x² - 2400x - 2400 = 0

264x² - 2400x - 2400 = 0

we find x

Using; x = [-b ±√( b² - 4ac )] / 2a

x = [-( -2400) ±√( (-2400)² - (4 × 264 × -2400 )] / 2( 264 )

x = [ 2400 ±√( 5760000 + 2534400) ] / 528

x = [ 2400 ±√8294400 ] / 528

x = [ 2400 ±2880 ] / 528

x = [ 2400 - 2880 ] / 528  or  [ 2400 + 2880 ] / 528

x = [ -480 / 528 ] or  [ 5280 / 528 ]

x = [ -0.909 ] or  [ 10 ]

the length of the sides of the square tiles cannot be Negative

Hence, x = 10

Therefore, the length of a side of one of the new shock-absorbing tiles will be;

⇒ x + 2 = 10 + 2 = 12 inches

Length of the side of one of the new shock-absorbing tiles is 12 inches

Answer:

20 mph

Step-by-step explanation:

Varies inversely

ts = k

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It takes Danielle 24 minutes to get to work when he drives at an average speed of 30 mph

24(30) = 720

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What is Danielle's average speed if he gets to work in 36 minutes.

36s = 720

s = 720/36

s = 20

20 mph

Answer:

A rectangle has its Opposite sides Equal.

Draw one so you'd grab it better.

AB=CD

BC= AD

Since CD=AB and We're given AB=x+7...

CD = x + 7

OPTION B IS LEGIT!!