What is the solution of the following quadratic inequality? x2 – 4x – 21 ≤ 0

10. 4w^2 + 7w^2 + 7z^2

Combine each term with the same variable.

11w^2 + 7z^2

This is in simplest form.

11. 3x + 4(5x + 2)

Multiply each term inside the parentheses by 4.

3x + 20x + 8

Combine all the terms with the same variable.

23x + 8

This is in simplest form.

Answer:

Step-by-step explanation:

Hello,

We know that

[tex]|x|=\begin{cases}x & \text{if } x\geq 0 \\ -x & \text{if } x<0 \end{cases}[/tex]

So we need to take into account two cases

Case 1 - [tex]x-3\geq 0<=> x\geq 3[/tex]

Then, |x-3|=x-3

||x-3|-2|=|x-3-2|=|x-5|

Either x-5 is positive and then |x-5|=x-5 and

[tex]|x-5|\leq 1<=>x-5\leq 1<=>x\leq 6[/tex]

Or x-5 is negative and then, |x-5|=-x+5

[tex]|x-5|\leq 1<=>-x+5\leq 1<=>4\leq x[/tex]

So the solution is [4;6]

Case 2 - [tex]x-3< 0<=> x< 3[/tex]

Then, |x-3|=-x+3

||x-3|-2|=|-x+3-2|=|-x+1|

Either -x+1 is positive and then |-x+1|=-x+1 and

[tex]|-x+1|\leq 1<=>-x+1\leq 1<=>0\leq x[/tex]

Or -x+1 is negative and then, |-x+1|=x-1

[tex]|-x+1|\leq 1<=>x-1\leq 1<=>x\leq 2[/tex]

So the solution is [0;2]

Conclusion

The solution is [0;2]∪[4;6]

Thanks

Answer:

x = 9/7 - (3 y)/7

Step-by-step explanation:

Solve for x:

3 y + 7 x = 9

Hint: | Isolate terms with x to the left-side.

Subtract 3 y from both sides:

7 x = 9 - 3 y

Hint: | Solve for x.

Divide both sides by 7:

Answer: x = 9/7 - (3 y)/7

Answer:

x = ( 9 - 3y ) / 7

Step-by-step explanation:

To solve this equation for x, we will simply isolate the x.

7x + 3y = 9

7x = 9 - 3y

x = ( 9 - 3y ) / 7

Cheers.

The final customers of a companies' products and services are the households. They generate demand in the market dependent on their preferences, and further discussion can be defined as follows:

Therefore, the final answer is "Choice D"

Learn more:

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Answer:

D.Households act as consumers for goods made by businesses.

Step-by-step explanation:

Step-by-step explanation:

Y=90° as its a right angled triangle

Answer: C

Step-by-step explanation:

To find the slope of the line, we need to use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. Let's take any 2 points in the graph. (-2,-1) and (1,5)

[tex]m=\frac{5-(-1)}{1-(-2)}=\frac{6}{3}=2[/tex]

Now, we know that the slope is 2.

Answer:

2

Step-by-step explanation:

To get the slope, identify two points where the line cuts both the x and the y axes.

Then apply the formula for finding the slope;

Slope = (changer in y-coordinates) ÷ (change in x-coordinates)

And the answer is 2

Answer: The variance of their weights = 9,752,155,009 kg.

Step-by-step explanation:

So if standard deviation of 10 subjects = 98753 kg

Then, variance = [tex](9 8753 )^2\ kg=9,752,155,009\ kg[/tex]

Hence, the variance of their weights = 9,752,155,009 kg.

Answer:

Step-by-step explanation:

If EC is a bisector of AC and CD, then AC is equal to CD.

Given AC = 3x+6 and CD = 2x + 14, since AC = CD then;

3x+6 = 2x+14

subtract 6 from both sides

3x+6-6 = 2x+14-6

3x = 2x+8

subtract 2x from both sides

3x-2x = 2x+8-2x

x = 8

Hence the value of x is 8

Answer:

Step-by-step explanation:

Step-by-step explanation:

∫ t⁷ e^(-t⁴) dt

If x = -t⁴, then dx = -4t³ dt, and ¼ x dx = t⁷ dt.

∫ ¼ x eˣ dx

If u = ¼ x, then du = ¼ dx.

If dv = eˣ dx, then v = eˣ.

∫ u dv = uv − ∫ v du

= ¼ x eˣ − ∫ ¼ eˣ dx

= ¼ x eˣ − ¼ eˣ + C

= ¼ eˣ (x − 1) + C

Substitute back:

= ¼ e^(-t⁴) (-t⁴ − 1) + C

The procedure would be as demonstrated in the attachment(s). As you can see your solution will be,

[tex]\frac{1}{4}\left(-e^{-t^4}t^4-e^{-t^4}\right)+C[/tex]

Answer:

4i

Step-by-step explanation:

I hope its not too complicated

[tex]\sqrt{-16} \\\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}\\\\\sqrt{-16}=\sqrt{-1}\sqrt{16}\\\\\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i\\\\=\sqrt{16}i\\\\\sqrt{16}=4\\\\=4i[/tex]

Answer:

[tex]\boxed{k = -6}[/tex]

Step-by-step explanation:

[tex]13 +\frac{k}{3} =11[/tex]

→ Multiply everything by 3

[tex]39 + k = 33[/tex]

→ Minus 39 from both sides to isolate k

[tex]k = -6[/tex]

Answer: [tex]2 + \sqrt{3}[/tex]

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

Work Shown:

[tex]\frac{6 + \sqrt{27}}{3}\\\\\frac{6 + \sqrt{9*3}}{3}\\\\\frac{6 + \sqrt{9}*\sqrt{3}}{3}\\\\\frac{6 + 3\sqrt{3}}{3}\\\\\frac{3(2 + \sqrt{3})}{3}\\\\2 + \sqrt{3}\\\\[/tex]

The idea with simplifying the square root (steps 2 through 4) has us factoring 27 so that one factor is a perfect square. We want the largest perfect square factor possible.

That way when we use the rule sqrt(x*y) = sqrt(x)*sqrt(y), we pull out that perfect square to then use the rule sqrt(x^2) = x where x is nonnegative.

After simplifying the square root, we factor out the GCF and then cancel out the 3's.

The inverse of g(x) is x² + 7

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The inverse function is defined as a function obtained by reversing the given function.

To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.

We have to find the inverse of the function below :

g(x) = √(x-7)

So after switching x and y,

g(x) = y = √(x - 7)

becomes

x = √(y - 7)

Now, we solve for y regularly.

g(x) = y = √(x - 7)

Solve for y :

⇒ y² = x - 7

⇒ x² = y - 7

⇒ y = x² + 7

Therefore the inverse of g(x) is x² + 7

Learn more about inverse function here:

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#SPJ2

Answer:

I believe the Slope is (m) =

ΔY

ΔX

= 1/1 = 1. The answer is 1/1 instead of 1.

Step-by-step explanation:

Answer:

vertical angles theorem

Step-by-step explanation:

Just took the test

Answer:

A. corresponding angles theorem

Step-by-step explanation:

Answer:

Step-by-step explanation:

Coordinate geometry is always used in a certain cartesian system such as the X-Y cartesian system to represents the location of a point.

For example a point  

P  ( x , y )  , occupies an identical position in the cartesian system and the coordinate 'x' and 'y' represents the distances of the point from the X and Y-axis respectively with respect to the origin.  If a point  

P ( x , y )  between two other points  

A ( x 1 , y 1 )  

and  

B ( x 2 , y 2 ) , divides in just two halfs then point P is known as the Midpoint of the points A and B.

And

P ( x = x 1 + x 2 2 ,     y = y 1 + y 2 2 )

Answer:

Step-by-step explanation:

Add x to both sides.

70 +x = 8

Subtract 70 from both sides.

x = 8 - 70

x = - 62

None of the answers fit.

Answer:

Your first instinct might be to go ahead and add the x terms together, BUT this would be a bad thing to do! You cannot combine the x2 and 2x, because the first term has an exponent (2) and the second one does not have an exponent; therefore, you cannot add them together!

Step-by-step explanation:

Answer:

Not sure if you mean multiplying or adding by "combine". But generally the rule of thumb with exponents is when you are adding and they are not like terms, you cannot combine the two terms together. So in other words, they would be left as x²+x. However, when you are multiplying you can add the exponents together. So, it will be like this: x²·x = x³

Answer:

3640 and hi its meeeee i finally found you

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

∠ABE=∠BEF=4x (AC║EF)

∠DBE=5x

∠DBF=180=∠DBE+EBF=5x+65

5x=180-65

x=23

Answer:

100%-75.3%

Step-by-step explanation:

The total probability of all outcomes is 100%.

If the probability of a particular result is 75.3% then all other possibilities (not the particular event) must equal 100% - 75.3%.

Answer:

( − 7 , − 2 ) , ( − 3 , 0 ) , ( 1, 2 ) , ( 5 , 4 ) , ( 7 , 5 )

From: iOE Your friend

:D :) *Be awesome.Be You*

Answer:

Multiplication

Step-by-step explanation:

Follow GEMDAS or PEMDAS. I would recommend GEMDAS. GEMDAS stands for Grouping symbols, exponents, multiply, divide, addition, subtraction. GO form the order G to S

Answer:

The distance between the point is 1806 unit

Step-by-step explanation:

Given that,

The distance between the point in Maine and the point in Tennessee.

Suppose, The points are (-801,670) and (990,900)

We need to calculate the distance between the point

Using formula of distance

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

Put the value into the formula

[tex]d=\sqrt{(990-(-801))^2+(900-670)^2}[/tex]

[tex]d=1806\ unit[/tex]

Hence, The distance between the point is 1806 unit.

Answer:

.27

Step-by-step explanation:

4.5*6/100

=.27

Answer:

$27.00

I stayed up all night studying for this test and I got the question right haha

Answer:

46.818 kg

Step-by-step explanation:

First, find the surface area of your yard. This is found by multiplying the length and width.

The equation for this is (l*w)=sa

So,

l=20ft

w=17ft

(20*17)= 340 square feet.

So, if each square foot gets 1350 new flakes per minute, you are going to find how much the entire yard gets in a minute by multiplying the surface area by 1350.

So,

(340*1350)= 459000  flakes for the entire yard in one minute.

Since there is 60 minutes in an hour, multiply 459,000 by 60.

459,000*60= 27,540,000  new flakes in the yard per hour.

Now, to find the weight in milligrams:

27,540,000*1.7= 46,818,000  mgs

Finally, because a kilogram is equal to one million milligrams (mg),

46,818,000/1,000,000= 46.818 kg

Answer:

A. [tex] 8n + 200 [/tex], $400.

Step-by-step explanation:

Monthly rent per acre for pasture land = $8

Additional monthly fee = $200

Let n represent the number of acres.

Therefore, expression for the total monthly cost would be:

[tex] 8n + 200 [/tex].

If the farmer wants to rent 25 acres of pasture land, the expression, [tex] 8n + 200 [/tex], can be used in calculating the total cost by simply plugging in the value of n, which would be 25 in this case.

Total monthly cost for 25 acres = [tex] 8(25) + 200 [/tex].

[tex] = 200 + 200 [/tex]

[tex] 400 [/tex].

Total monthly cost = $400