the Scientific notation 2 times 10^10-2 has what value

a system of linear equations with infinite solutions, is simply one that has the same equation twice, but but but, one of the equations is in disguise.

so, say we can just  hmmm multiply the coefficient of the "x" variable, which is the slope, by something that gives us 1, recall same/same = 1, hmmm say let's multiply it by hmmmm 7/7.

[tex]\bf y=\cfrac{2}{3}x-5\implies \stackrel{\textit{multiplying the slope by }\frac{7}{7}}{\cfrac{2}{3}\cdot \cfrac{7}{7}\implies \cfrac{14}{21}}\implies \stackrel{\textit{so we get this equation}}{y=\cfrac{14}{21}x-5}[/tex]

now, let's notice that 14/21 simplifies to 2/3, so is really the same slope and the same y-intercept.

so if we use those two equations in a system of equations and graph them, what happens is, the first one will graph a line, the second one will graph another line BUT right on top of the first one drawn, so the two lines will just be pancaked on top of each other, making every point in each line, "a solution", since they're meeting at every point, and since lines go to infinite, "infinitely many solutions".

Answer:

Sample Response/Explanation: To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.

Step-by-step explanation:

Answer:

12 ft long by 5½ ft wide  

Step-by-step explanation:

1. Set up an expression for the area.

   Let l = the length of the rectangle

and w = the width. Then

     2w = twice the width and

2w + 1 = 1 more than twice the width. Then

        l = 2w + 1

The formula for the area of a rectangle is  

                 A = length × width

                 A = lw

               66 = (2w +1)w

               66 = 2w² + w

2w² + w - 66 = 0

2. Solve the quadratic for w

2w² + w - 66 = 0

(a) Multiply the first and last terms

2 × (-66) = -132

(b) List all the factors of 132

 1  132

2   66

3    42

4    33

6    22

11     12

(c) Find a pair of factors whose product is -132 and whose sum is 1.

After some trial and error, you will choose -11 and +12,

-11 × 12 = -132 and -11 + 12 = 1.

(d) Rewrite w as -11w + 12w

2w² - 11w + 12w - 66 = 0

(e) Factor by grouping

w(2w - 11) + 6(2w - 11) = 0

(w + 6)(2w - 11) = 0

(f) Use the zero product theorem

w + 6 = 0     2w - 11 = 0

     w = -6          2w = 11

                           w = 5½

We reject the negative answer, so w = 5½ ft

3. Calculate l

l = 2w + 1 = 2 × 5½ + 1 = 11 + 1 = 12 ft

The rectangle is 12 ft long and 5½ ft wide.

The dimensions of the rectangle are length = 12 ft and wide = 5½ ft

The area of the triangle is the product f length and breath.

Calculation:-

  Let l = the length of the rectangle

        w = the width.

According to the question: length     l = 2w + 1

   The area of a rectangle is  

            ⇒   66 = (2w +1)w

             ⇒      66 = 2w² + w

             ⇒ 2w² + w - 66 = 0

wide=5.5 ft = 5½ ft

lenght =12 ft

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Answer:

The range is all real numbers.

The domain is all reals numbers that are greater than -4.

Step-by-step explanation:

[tex]y=\log_3(x+4)[/tex] only exists when [tex]x+4[/tex] is positive.

You can take the log of a negative or 0 number.

So [tex]x+4>0[/tex] implies [tex]x>-4[/tex].  (I just subtract 4 on both sides.)

So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.

Now the range.  The range is where the curve exist for the y-values.

The equivalent exponent form of [tex]y=\log_3(x+4)[/tex] is [tex]3^{y}=x+4[/tex]

We can solve this for x be subtract 4 on both sides:

[tex]x=3^y-4[/tex]

Now here y can be anything; there are no restrictions on the exponent.

Also if you look at the graph of [tex]y=\log_3(x+4)[/tex] you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).

Let's think about the inverse I found above a little more (I'm going to swap x and y).

[tex]y=3^x-4[/tex].

If we look at the domain and range of this we can just swap it to get the domain and range of [tex]y=\log_3(x+4)[/tex].

[tex]y=3^x-4[/tex] is an exponential function of 3^x that has been moved down 4 units.

The range since it has been moved down 4 units is [tex](-4,\infty)[/tex].

The domain of an exponential function is all real numbers.  There are no restrictions on what you can plug in for x.

So swapping these to find the domain and range of [tex]y=\log_3(x+4)[/tex]:

Domain:  [tex](-4,\infty)[/tex]

Range : [tex](-\infty,\infty)[/tex]

Answer: For Edg is x> -4

And for the second on it is all real numbers

Answer:

y =  -2x^2 -4x +1

Step-by-step explanation:

y-3 = -2 (x+1)^2

Foil (x+1)^2

(x+1)(x+1) = x^2 +x+x+1 = x^2 +2x+1

Substitute this back in

y-3 = -2(x^2 +2x+1)

Distribute

y-3 = -2x^2 -4x -2

Add 3 to each side

y-3+3 = -2x^2 -4x -2+3

y =  -2x^2 -4x +1

Answer:

Statements I and II

Step-by-step explanation:

In Statistics, parameter is any numerical value that characterizes a population while statistics are numerical values that characterizes a sample from a given population.

Statistics are most often used to estimate the population parameters

For example the sample mean is a statistic and the population mean is a paranmeter

The mean SAT score of all students from New York is the parameter.

The mean SAT score of 105 students from New York is called the statistic.

The correct choice is the third option.

6x + 2 + 40 = 90

Let x = the unknown

6x + 42 = 90

6x = 90 - 42

6x = 48

x = 48/6

x = 8

Answer:

x=8

Step-by-step explanation:

We know that 40 + (6x+2)  +90 = 180   since the three angles form a straight line

40 + (6x+2)  +90 = 180

Combine like terms

132 + 6x = 180

Subtract 132 from each side

132-132 +6x= 180-132

6x = 48

Divide each side by 6

6x/6 = 48/6

x = 8

Answer:

[tex]3i \sqrt{7}[/tex]

Step-by-step explanation:

The imaginary unit is [tex]i=\sqrt{-1}[/tex].

Now 63 itself is not a perfect square but 63 does contain a factor that is.

63=9×7 and 9 is a perfect square.

So [tex]\sqrt{-63}=i \sqrt{63}[/tex].

[tex]i \sqrt{63}=i \sqrt{9 \cdot 7}=i \sqrt{9} \sqrt{7}=i(3) \sqrt{7}=3i \sqrt{7}[/tex]

To find the square root of -63, you'll need to consider the concept of imaginary numbers because the square root of a negative number is not a real number. Here's how you can find the equivalent expression:
The square root of -63 can be expressed as √(-63). Since you cannot take the square root of a negative number in the real number system, you would use an imaginary unit, which we designate as "i". The imaginary unit "i" is defined as √(-1).
Now, you can factor -63 into -1 and 63, so the expression becomes:
√(-63) = √(-1 * 63)
This simplifies to:
√(-1) * √(63)
We already established that √(-1) is represented by the imaginary unit "i". So now the expression is:
i * √(63)
The √(63) doesn't simplify neatly into a whole number since 63 is not a perfect square. However, 63 can be factored into 9 and 7, where 9 is a perfect square. Let's do that:
√(63) = √(9 * 7)
√(63) = √(9) * √(7)
√(63) = 3 * √(7)
Therefore, the expression now looks like this:
i * 3 * √(7)
Since multiplication is commutative, you can reorder this:
3 * i * √(7)
Thus, the expression 3 * i * √(7) is equivalent to √(-63). This is because 3 * √(7) is the real number part and "i" indicates that it is an imaginary number due to the original square root of a negative number.

By substituting x = 5i in to the equation y = x+1/2-x, we find that y = 1/2.

To solve for y in the equation y= x+1/2-x given that x= 5i, we simply substitute x with 5i.

So, y = 5i + 1/2 - 5i

The term 5i in the numerator and the denominator cancels out so we are left with: y = 1/2

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Answer: 12 x X=78

Step-by-step explanation: An equation of this would be 12 x X =78.

Answer:

Don't know if this is correct but, I think the answer is 3/4.

Answer:

[tex]\dfrac{3}{4}[/tex]

Step-by-step explanation:

The given expression is

[tex]a^3b^{-2}c^{-1}d[/tex]

We need to find the value of this expression in reduced fraction if a=2 b=4 c=10 d=15.

Substitute a=2 b=4 c=10 d=15 in given expression.

[tex](2)^3(4)^{-2}(10)^{-1}(15)[/tex]

Using the property of exponent, we get

[tex](2)^3\times \left(\dfrac{1}{4^2}\right)\times \left(\dfrac{1}{10}\right)\times (15)[/tex]         [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]

[tex]8\times \left(\dfrac{1}{16}\right)\times \left(\dfrac{1}{10}\right)\times (15)[/tex]

Cancel out common factors.

[tex]1\times \left(\dfrac{1}{2}\right)\times \left(\dfrac{1}{2}\right)\times (3)[/tex]

[tex]\dfrac{3}{4}[/tex]

Hence, the required fraction is 3/4.

Answer:

1.19x=12

Step-by-step explanation:

The 12 represents his budget and 1.19 is the cost of each song, x is the amount of songs.

Answer: [tex]1.19x=12[/tex]

Step-by-step explanation:

Given : Doug can download new songs for $1.19 each.

Let the number of songs downloaded be x .

Then the total cost of x songs will be :-

[tex]1.19x[/tex]

To find the number of songs he can download for $12.00 , we need to put [tex]1.19x[/tex] equals to 12.

We get, the equation to show how many songs he can download for $12.00 will be

[tex]1.19x=12[/tex]

Answer:

it's B

Step-by-step explanation:

the set of numbers for which a function is defined is called a domain of a function

if a number is not in the domain of a function, then the function is undefined for that number

denominator must not be zero

if we plug -3 then the y

=(-3+1)/(9+-3-6)

=(-2)/9-9

=-2/0

which is undefined for x=-3

now

if we plug 2 we have

(2+1)/(4+2-6)

=3/0

the function is undefined for x=2

so

x≠3, x≠2

The domain of the given function is {x does not equal -3; x does not equal 2}.

The domain of a function is the set of all allowable input values. In this case, we need to find the values of x that make the denominator of the function equal to zero, because division by zero is undefined.

To find the domain, we set the denominator equal to zero and solve for x. The denominator is x^2 + x - 6, so we set it equal to zero and factor it: (x+3)(x-2) = 0. Now, we set each factor equal to zero and solve for x: x+3=0, x=-3; x-2=0, x=2.

The domain is the set of all values of x that make the function defined, so the answer is: (B) {x does not equal -3; x does not equal 2}.

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Answer:

B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}

Step-by-step explanation:

For a relation to be a function, every x value must have only one y value.  For a, c, and d, some of the x values have multiple different y values

Answer:

B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}

Step-by-step explanation:

For a function to be valid, each value within the domain of the function must give exactly one value in the range of the function.

That is to say, for a function to be valid, every value of x must give only 1 unique value for y.

So basically if you have one value of x which gives a value for y, and if the same value for x gives you another value of y which is different than the first time, then you do NOT have a function.

With this in mind, we can see that for option B, every unique value for x, gives an equally unique value for y. Hence this is a function.

Lets compare this with option A (for example)

For A, we can see that for (0,0), an input of x=0, gave y=0. But then notice that the next set of coordinates (0,2), an input of x=0 gave y=2!!!! (this contradicts the first set (0,0), hence this is not a function.

you'll see similar contradictions for

option C (2,-1) vs (2,1)

option D (2,2) vs (2,3)

Answer:

Explanation:

1) Make a change of variable:

2) The new equation with u is:

3) Factor the left side of the new equation:

4) Come back to the equation replacing the left side with its factored form and solve:

5) Come back to the original substitution:

If u = - 3 ⇒ xp = - 3 ⇒ x or p is negative and that is against the condition that x and p are both greater than zero, so this solution is discarded.

Then use the second solution:

Solve for p:

Answer:

9/64

Step-by-step explanation:

The probability that the marble on the first draw is blue is 3/8.

The probability that the marble on the second draw is blue is also 3/8.

So the probability that both are blue is:

3/8 × 3/8 = 9/64 ≈ 14%

The probability that both of the marbles drawn from the bag are blue is 9/64.

Probability is the chance that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that both of the marbles drawn are blue = fraction of blue marbles²

= 3/8 x 3/8 = 9/64

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Answer:

2.4 rad

Step-by-step explanation:

To convert degree measure to radian measure

radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]

Thus for 140°

radian = 140 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{7\pi }{9}[/tex] ≈ 2.4

Answer:

7π/9

Step-by-step explanation:

Degrees To Radians : × · π/180

Radians To Degrees : × · 180/π

Plug into Equation And Solve: 140π/180

Simplify: 7π/9

Answer:

answer is  b. 6x3 + 3x + 2

Step-by-step explanation:

Answer:

x = 1/3 and y = 3

Step-by-step explanation:

It is given the system of equations

3x + 2y = 7   ----(1)

-3x + 3y = 8    ----(2)

To find the solution

Add eq(1) and eq (2) we get,

3x + 2y = 7   ----(1)

-3x + 3y = 8    ----(2)

 0 + 5y = 15

y = 15/5 = 3

Substitute the value of y in eq(1)

3x + 2y = 7   ----(1)

3x + 2*3 = 7

3x + 6 = 7

3x = 7 - 6 = 1

x = 1/3

Therefore

x = 1/3 and y = 3

Answer:

Please let me know if your quadratic is [tex]y=-2(x+2)^2+2[/tex].

And if so your vertex is (-2,2) and your y-intercept is (0,-6)

Step-by-step explanation:

It says vertex so I'm thinking you meant [tex]y=-2(x+2)^2+2[/tex].  Please correct me if I'm wrong.

The vertex form of a quadratic is [tex]y=a(x-h)^2+k[/tex].  It is called that because it tells you the vertex (h,k).

So if you compare the two forms you should see -h=2 while k=2.

-h=2 implies h=-2.

So the vertex is (h,k)=(-2,2).

To find the y-intercept, set x=0 and find y.

[tex]y=-2(0+2)^2+2[/tex]

[tex]y=-2(2)^2+2[/tex]

[tex]y=-2(4)+2[/tex]

[tex]y=-8+2[/tex]

[tex]y=-6[/tex]

So the y-intercept is (0,-6).

Answer:

9

Step-by-step explanation:

Ok... So there are 12 donuts in a dozen. And if she bought 3 dozen, she will have 36 donuts. If she plans to share them with her 3 friends, there will be 4 people total sharing the donuts. Then all you have to do is divide the 36 donuts among the 4 friends. 36/4=9. So they will all get 9 donuts.

3(12)/4=x

36/4=x

9=x

x=9

Answer:

They are orthogonal.

Step-by-step explanation:

u = <3, 0> v = <0, -6>

u.v =|u| |v|cosθ

if u.v is 0 this means that cos θ is 0 so θ = 90°

[tex]\theta=cos^{-1}\frac{u.v}{|u|\ |v|}[/tex]

If u.v = 0 then they are orthogonal.

If u.v ≠ 0 then they are neither parallel nor orthogonal

If u.v ≠ 0 and u = kv where k is constant then they are parallel

u.v = 3×0+0×-6

⇒u.v = 0

They are orthogonal.

Answer:

y = - 5x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = - 5 and b = - 4, hence

y = - 5x - 4 ← equation of line

Answer:

(-5,2)

Step-by-step explanation:

It alogns with negative 5 on the X axis, and positive 2 on the Y axis, meaning its written as (-5,2)

Answer:

60

Step-by-step explanation:

We are given the triangles are congruent, that means the angles are the same measurement

<A = <X

<B = <Y

<C = <Z

We know A = 50  so X = 50

We know <Y = 70 so < B = 70

The three angles of a triangle add to 180

<A + <B + <C = 180

Substituting into the equation

50 + 70 + <C = 180

Combining like terms

120 + <C =180

Subtracting 120 from each side

120-120 +<C =180-120

<C = 60

Answer:

∠C = 60°

Step-by-step explanation:

Corresponding angles are congruent, thus

∠B = ∠Y = 70°

The sum of the 3 angles in ΔABC = 180°

∠C = 180° - (70 + 50)° = 180° - 120° = 60°

Answer:

A

Step-by-step explanation:

Using the substitution u = [tex]x^{\frac{1}{2} }[/tex]

noting that ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex], then

[tex]x^{\frac{1}{2} }[/tex] + 9[tex]x^{\frac{1}{4} }[/tex] + 20 = 0

Can be rewritten as

u + 9u² + 20 = 0, that is

9u² + u + 20 = 0 ← in standard form

Answer:

The area of the shaded region is [tex]8\ units^{2}[/tex]

Step-by-step explanation:

step 1

Find the curved area ACD (formed by segment AD, segment DC and the curved segment AC)

we know that

The curved area ACD is equal to the curved area ACB

The curved area ACD is equal to the area of the square minus the area of a quarter of circle

[tex]ACD=b^{2} -\frac{1}{4}\pi b^{2}[/tex]

we have that

[tex]b=4\ units[/tex]    

substitute

[tex]ACD=4^{2} -\frac{1}{4}(3)(4)^{2}[/tex]

[tex]ACD=16 -12=4\ units^{2}[/tex]

step 2

Find the area of the shaded region

The area of the shaded region is equal to the area of the square minus two times the curved area ACD

so

[tex]4^{2} -2(4)=16-8=8\ units^{2}[/tex]

Answer:

the answer is 20 meters

Answer:

20

Step-by-step explanation:

Answer:

1.5 = 1,500

Step-by-step explanation:

I actually converted 1.5 to milliliters.

That is how I got 1,500.

The bottle holds 1500 milliliters soda.

We know that, 1 liter = 1000 milliliters

So, to convert something from liter to milliliter, we have to multiply the given value by 1000.

Given, the bottle of soda holds 1.5 liters of soda.

So, we have to multiply 1000 with that to get the required value.

∴ 1.5 liters = (1.5 × 1000) milliliters

                 = 1500 milliliters

The required quantity of soda is 1500 milliliters.

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Erica raked 5% more, so she racked 1.05 times as much.

Divide the amount she racked by the 1.05:

357 / 1.05 = 340

Adam racked 340 liters.