Use the difference of squares identity to write this polynomial expression in factored form : 9x^2-49

Answer:

2 2

1 -3

Step-by-step explanation:

2b=[4 4]

2 -6

b=[4/2 4/2]

2/2 -6/2

b=[2 2]

1 -3

Answer:

2,400,000,000,000

Step-by-step explanation:

2.4 x 10^12 means that the decimal point is moved 12 places to the right (hence the power of 12)

So by moving the decimal point 12 times you get this: 2,400,000,000,000

The reason why there are only 11 zeroes is because the 4 was a decimal place  to the right of 2, thus losing a zero.

Answer:

see explanation

Step-by-step explanation:

Calculate the slopes between pairs of the 3 points using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)

m = [tex]\frac{9-3}{-3-(-9)}[/tex] = [tex]\frac{6}{-3+9}[/tex] = [tex]\frac{6}{6}[/tex] = 1

Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)

m = [tex]\frac{9-1}{-3-5}[/tex] = [tex]\frac{8}{-8}[/tex] = - 1

If lines are perpendicular then the product of their slopes = - 1 , then

1 × - 1 = -1

Thus there is a right angle between the 2 lines

Then triangle is right- angled

Answer:

x = 24

Step-by-step explanation:

We know that lines s and t are parallel. Then by definition, the two labelled angles, which are same-side angles, are congruent and equal in measure.

Then, we set the expressions equal to each other:

7x - 48 = 5x

Subtract 5x from both sides:

7x - 5x - 48 = 0

2x - 48 = 0

Add 48 to both sides:

2x = 48

Divide by 2:

x = 48/2 = 24

Thus, x = 24.

~ an aesthetics lover

Step-by-step explanation:

x⁵+x-1

(2x-x+1) ( x³+x²-1 )

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Answer:

Answer:

[tex]y=\displaystyle \frac{1}{2}x+1[/tex]

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.

We're given the x-intercept, -2, and the y-intercept, 1. We can directly plug the y-intercept into the equation [tex]y=mx+b[/tex] :

[tex]y=mx+1[/tex]

Now, we must solve for the slope. The x-intercept -2 gives us the point (-2,0), since the x-intercept occurs when y=0. Plug this point into the equation and solve for m:

[tex]0=m(-2)+1\\0=-2m+1\\-1=-2m\\\\\displaystyle m=\frac{-1}{-2} \\\\\displaystyle m=\frac{1}{2}[/tex]

Therefore, the slope of the line is [tex]\displaystyle \frac{1}{2}[/tex]. Plug this back into [tex]y=mx+1[/tex]:

[tex]y=\displaystyle \frac{1}{2}x+1[/tex]

I hope this helps!

Answer:

C D E

Step-by-step explanation:

Edg

Out of the given options, options C, D and E are a difference of squares.

Difference of Squares, two terms that are squared and separated by a subtraction sign.

Given are, options,

D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²

E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴

C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²

Hence, out of the given options, options C, D and E are a difference of squares.

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Answer:

See below.

Step-by-step explanation:

Approximation:

The wall is 8 ft wide.

The frame is 22 1/4 inches wide. 22 1/4 inches is close to 2 ft since 2 ft = 24 inches.

8 ft - 2 ft = 6 ft

There will be approximately 6 ft of space tot he sides of the frame.

6 ft/2 = 3 ft

3 ft * 12 in./ft = 36 in.

There will be approximately 36 in. on each side of the frame.

Exact:

8 ft - 22 1/4 in. = 8 * 12 in. - 22 1/4 in. =

= 96 in. - 22 1/4 in.

= 95 4/4 in. - 22 1/4 in.

= 73 3/4 in.

The total amount of width of the wall not occupied by the frame is 73 3/4 in.

Half of that amount is on each side of the frame.

(73 3/4 in.)/2 = (73 3/4 in.) * 1/2 = (73 * 1/2 + 3/4 * 1/2) in. =

= 36 1/2 in. + 3/8 in.

= 36 4/8 in. + 3/8 in.

= 36 + 7/8 in.

= 36 7/8 in.

Answer:

let R represent red hair

let G represent green eyes

from Baye's theorem:

[tex]P( \frac{R}{G} ) = \frac{P(RnG)}{P(G)} [/tex]

P(RnG) = 5

[tex]P(G) = { \sum}(green \: hair) \\ = (3 + 5 + 5) \\ = 13[/tex]

Therefore:

[tex]P( \frac{R}{G} ) = \frac{5}{13} \\ = 0.385[/tex]

The conditional relative frequency = 0.385

The conditional relative frequency will be  0.385

It is a theorem showing how to compute the conditional probability of each of a set of possible causes for a given observed outcome using knowledge about the probability of each cause and the conditional probability of each cause's outcome.

let R represent red hair

let G represent green eyes

from Baye's theorem:

[tex]P=\dfrac{R}{G}=\dfrac{P(R\cap G)}{P(G)}[/tex]

P(RnG) = 5

P(G) = ∑(Green hairs)

P(G)= 13+5+5 = 13

Therefore:

[tex]P(\dfrac{R}{G})= \dfrac{5}{13}=0.385[/tex]

The conditional relative frequency = 0.385

Hence the conditional relative frequency will be  0.385

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Answer: Liz, she is 5 units away from Robbert.

Step-by-step explanation:

Ok, the data that we have is:

Robert is at (4,3 )

Lucy is at (6, 1)

Liz is at (1, 7)

We want to find the units between Robert and the person that is farther away from him.

The distance between Robert and Lucy can be calculated as:

First we calculate the difference in the point or in the position vector:

(4, 3) - (6, 1) = (4 - 6, 3 - 1) = (-2, 2)

To calculate the exact distance, we need to calculate the magnitude of this point, this is:

For a point (x, y), the magnitude is M = √(x^2 + y^2)

Then we have:

D = √( (-2)^2 + 2^2) = √8

Now, the distance between Robert and Liz can be calculated in the same way:

(4, 3) - (1, 7) = (4 - 1, 3 - 7) = (3, -4)

The magnitude is:

D = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5

Now, we know that 5 > √8

Then the person that is farthest away from Robert is Liz, and she is 5 units away.

Answer:

x=0, - 9

Step-by-step explanation:

x^2+9x=0

x(x+9)=0

x=0 or x=-9

Answer:

x =0  x= -9

Step-by-step explanation:

x^2 + 9x = 0

Factor out x

x(x+9) =0

Using the zero product property

x =0 x+9 =0

x =0  x= -9

Answer:

1. 2cm 3cm and 4cm

yes, because 2+3>4

2. 2cm 3 cm 6 cm

no, 2+3<6

3. 90 degrees 45 degrees 45 degrees

yes, 90+45+45 = 180

4. 90 degrees 60 degrees 60 degrees?

no, 90+60+60=210!=180

Answer:

Intersects; intersection point: (-2,3)

Step-by-step explanation:

Substitute -1.5x for y into y=0.5x+4:

-1.5x = 0.5x +4

-1.5x - 4 = 0.5x

-4 = 2x

x = -2

Plug in -2 for x into y=-1.5x

y = -1.5(-2)

y = 3

Organize the x and y values into an ordered pair:

(-2,3)

Answer:

y=0.5x+4 intersects y=-1.5x.

The intersection point is (-2,3)

Step-by-step explanation:

First, note that if two lines are not parallel, then they must intersect eventually in one way or another. Note that since these are two lines, they will only have one intersection points.

So we have the equation:

[tex]y=-1.5x[/tex]

Parallel lines have the same slope. Therefore, a line parallel to this line also has a slope of -1.5

The equation given to us is:

[tex]y=0.5x+4[/tex]

As we can see, this does not have a slope of -1.5. Therefore, the given equation is not parallel to y=-1.5x. However, this does mean that it will intersect y=-1.5x.

To find the x-value of their intersection, simply set the equations equal to each other and solve for x.

[tex]-1.5x=0.5x+4\\-2x=4\\x=-2[/tex]

Now, plug -4 into either of the equations:

[tex]y=-1.5(-2)=3\\y=0.5(-2)+4=-1+4=3[/tex]

Therefore, the point of intersection is (2,3).

Answer:

8

Step-by-step explanation:

total: 28 water attractions

pools: p

game areas: p + 2

water slides: 50% of 28 = 14

14 + p + p + 2 = 28

2p = 12

p = 6

game areas:

p + 2 = 6 + 2 = 8

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

Answer:

see below

Step-by-step explanation:

4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5

All exponent have to have the same number

42 x 10^5 − 1.2 x 10^5 − 2.5 x 10^5

Subtract the number

42 - 1.2 - 2.5 = 38.3

Add back the exponent

38.3 * 10 ^5

This is not in scientific notation

Move the decimal one place to the left and add one to the exponent

3.83 * 10^6

3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8

All exponent have to have the same number

3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

Add the numbers

3.3+2.6+.77 =6.67

Add back the exponent

6.67*10^9

This is in scientific notation

8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3

All exponent have to have the same number

8.0 x 10^4 − 3.4 x 10^4 − .12 x 10^4

Subtract

8.0 - 3.4 - .12 = 4.48

Add back the exponent

4.48* 10^4

This is in scientific notation

Answer:

That’s ez pz

Step-by-step explanation:

Answer:

The slope is -3 and the y intercept is -44

Step-by-step explanation:

6X+ 2Y= -88

The slope intercept form of a line is y= mx+b where m is the slope and b is the y intercept

Solve for y

6X-6x+ 2Y= -88-6x

2y = -6x-88

Divide by 2

y = -3x -44

The slope is -3 and the y intercept is -44

Answer:

The next step is add x to each side

Step-by-step explanation:

-x + 6 = 5 - 3x

Subtract 5 from each side

-x + 6-5 = 5-5 - 3x

-x+1 = -3x

Add x to each side

-x+1 = -3x+x

1 = -2x

Answer:

Step-by-step explanation:

all you need to do is solve for x right? so in that case when you subtract 5 from both sides you get -x+1=-3x

then you will add x on each side

you should now have 1=-2x

divide each side by -2 and then you will have

-1/2=x

======================================================

Explanation:

We get this point by doing two things.

If we started with x = -3, then x-2 = -3-2 = -5. Also, if we had y = -1 then y-7 = -1-7 = -8

So that's how we end up with Z(-3,-1) moving to Z ' (-5, -8)

You could also show your work like this

[tex](x,y) \to (x-2, y-7)\\\\(-3,-1) \to (-3-2, -1-7)\\\\(-3,-1) \to (-5, -8)\\\\[/tex]

Answer:

Hey there!

93 ÷ 5 can be written as 93/5.

5 goes into 93, 18 times, so we have [tex]18\frac{3}{5}[/tex]

Let me know if this helps :)

Answer:

number of child tickets sold on saturday is 21

number of adult tickets sold on saturday is 42

Step-by-step explanation:

Let's assume

number of child tickets sold on saturday is x

number of adult tickets sold on saturday is y

On saturday, twice as many adult tickets as child tickets were sold

so, we get

child admission is $6.30 and adult admission is $9.60

a total sales of $535.50

we get

now, we can plug y=2x

now, we can solve for x

now, we can find y

so,

number of child tickets sold on saturday is 21

number of adult tickets sold on saturday is 42.........Answer

Answer:

IU=161

Step-by-step explanation:

Angle Formed by Two Secants=  1/2 (difference of Intercepted Arcs)

42 = 1/2 (7m+5 - (3m-1))

Distribute the minus sign

42 = 1/2 (7m+5 - 3m+1))

Combine like terms

42 = 1/2 ( 4m+6)

Distribute the 1/2

42 = 2m+3

Subtract 3 from each side

42-3 = 2m+3-3

39 = 2m

Divide by 2

19.5 = m

The sum of the arcs = 360

IU+ 3m-1 + 7m+5 = 360

IU +10m+4 = 360

IU +10(19.5) +4 = 360

IU +195+4 = 360

IU = 360 - 199

IU=161

Answer:

y = -x +2

Step-by-step explanation:

y =x  has a slope of 1

Perpendicular lines have slopes that multiply to -1

m* 1 = -1

The slope of the perpendicular line is -1

We have a slope and a point

y = mx+b

y= -1x+b

Substitute the point into the equation

-3 = -1(5) +b

-3 =-5 +b

Add 5 to each side

-3+5 = b

2 =b

y = -x +2

Answer:

B(-5, 1)

Step-by-step explanation:

We can test each value in the equation and see if the equation works out.

[tex]y > |x| - 6[/tex]

Let’s try A - (-1, -5).

[tex]-5 > |-1|-6\\\\-5 > 1-6\\-5>-5[/tex]

-5 is NOT greater than -5, it is equal so A doesn’t work.

Let’s try B, (-5, 1).

[tex]1 > |-5| -6\\1 > 5-6\\1 > -1[/tex]

1 IS greater than -1, so B works.

Let’s try C for fun.

[tex]-1 > |5| -6\\-1 > 5-6\\-1 > -1[/tex]

-1 is NOT greater than -1, it is equal, so it doesn’t work.

Hope this helped!

Answer:

B(-5,1)

Let us simply just write this in all scenarios.

A(-1,-5)

-5>|-1|-6

-5>-5

(False)

B(-5,1)

1>|-5|-6

1>-1

(True)

C(5, -1)

-1>|5|-6

-1>-1

False

Answer:

10:5 OR 2:1

Step-by-step explanation:

Let x be the parts of 25% dextrose and

y be the parts of 10% dextrose are mixed so that

20% dextrose mixture is obtained.

amount of dextrose in the mixture will be 20% of (x+y).

We have to find the value of [tex]\frac{x}y \ OR\ x:y[/tex]

Now, we can apply the concept that sum of amount of dextrose in the two liquids will be equal to the amount of dextrose in the mixture.

[tex]\Rightarrow x \times 25\% + y \times 10\%=(x+y)\times 20\%\\\Rightarrow x \times\dfrac{25}{100} + y \times \dfrac{10}{100}=(x+y)\times \dfrac{20}{100}\\\Rightarrow x \times25 + y \times 10=(x+y)\times 20\\\Rightarrow 25x + 10y=20x+20y\\\Rightarrow 25x -20x =20y-10y\\\Rightarrow 5x=10y\\\Rightarrow \dfrac{x}{y} = \dfrac{10}{5}\\\Rightarrow \bold{x:y=10:5\ OR\ 2:1}[/tex]

So, the answer is 10:5 or 2:1.

Answer:

4.90% is approximately the new Dextrose concentration.

Explanation:

Volume by Volume percent is given by ;

Volume percentage of dextrose solution = 5%

In 100 mL of solution 5 ml of dextrose is present.

Now, volume sterile water added was equal to the 40% of volume of dextrose volume.

So, volume of the sterile water added =  

Total volume of the solution after addition of water = 100 mL + 1 mL = 102 mL

New concentration of dextrose will be;

4.90% is approximately the new Dextrose concentration.

Step-by-step explanation:

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation:

Answer:

obtuse

Step-by-step explanation:

because obtuse triangle would provide more support that acute or right as its bigger.