Use completing the square to solve for x in the equation (x 7) (x minus 9) = 25.

Answer:

3.67+(-0.43)+(-0.44)

3.67-0.43-0.44

3.24-0.44

2.8 Ans

4|a| + 8 - a, if a = -2

What we're doing here is plugging in the given value of a for every instance of a in the expression.

4|-2| + 8 - (-2)

---The absolute value of a number is its distance from 0. -2 is 2 units away from 0, so the absolute value of -2 is 2. And, remember two negatives make a positive!

4(2) + 8 + 2

8 + 8 + 2

16 + 2

18

Hope this helps!

Step-by-step explanation:

4x + 10 = -2 + 4

4x = -2 + 4 - 10

4x = -8

x = -2

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{4x + 10 = -2+ 4}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{4x + 10 = 2}[/tex]

[tex]\huge\textbf{Subtract 10 to both sides:}[/tex]

[tex]\mathsf{4x + 10 - 10 = 2 - 10}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{4x = 2 - 10}[/tex]

[tex]\mathsf{4x = -8}[/tex]

[tex]\huge\textbf{Divide 4 to both sides:}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{-8}{4}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x = \dfrac{-8}{4}}[/tex]

[tex]\mathsf{x = -2}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.

let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so

[tex]cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}[/tex]

The two positive numbers satisfying the given requirements are 15.56 and 15.56

For given question,

Let x and y be  two positive numbers satisfying the given requirements.

⇒ xy = 242             .............(1)

The sum of given two positive numbers is a minimum.

Let the sum of given two positive numbers is S.

⇒ x + y = S             ............(2)

From equation(1),

⇒ y = 242/x

Substitute above value of y in equation (2),

⇒ x + y = S  

⇒ S = x + (242 / x)    

Now, for above equation we find the derivative of x with respect to x.

⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]

⇒ 242/x² = 1

⇒ x² = 242

⇒ x = ±15.56

Since the numbers are positive, x = 15.56

For x = 15.56

⇒ y = 15.56

Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56

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X is the number of songs and Y the number of pics

our 2 equations will be - X+y=11 & 4x+2y=24

consider x=11-y

Lets replace x in 2:

=4(11-y) +2y=24

=44-4y+2y=24

=44-24= 4y-2y

=20= 2y

=Y=20/2

=Y=10

Lets replace y in 1

=X+10=11

=X=11-10

=X=1

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Given: [tex]2x^2 - 12x + 1 = 0[/tex]

Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]

Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]

Second answer:  [tex]2(x - 3)^2 - 17 = 0[/tex]

Explanation in detail:

The quadratic equation a[tex]x^{2} + bx + c = 0[/tex]'s vertex form is

where a[tex](x - h)^{2} + k[/tex] equals zero

A is the [tex]x^{2}[/tex] coefficient, and h is the vertex's x-coordinate on the equation's graph.

The vertex of the equation's graph, k, has the y-coordinate.

The completing square can be used to determine the vertex form.

[tex]2x^{2} - 12x + 1 = 0[/tex] is the equation.

Put[tex]2x^{2} -12x[/tex] in a bracket and subtract 2 from them as a common component to utilize the completing square.

∵ [tex]2(x^{2} - 6x) + 1 = 0[/tex]

To determine the product of the first and second terms in the binomial, divide the second term by two.

∵ [tex]6x / 2 = 3x[/tex]

∵[tex]3x = 3 * x[/tex]

∴ The binomial's first and second terms are x and 3, respectively.

The phrase in the bracket's middle is (-)

∴ Middle of the binomial's sign is (-)

∴ The binary value is [tex](x - 3)^2[/tex]

Square 3 is nine.

To keep the equation from altering, you must deduct the same number from the bracket after adding 9 there.

∴ [tex]2(x^2 - 6x + 9 - 9) + 1 = 0[/tex]

- Remove the brace and multiply -9 by 2.

∵ [tex]2 *-9 = -18[/tex]

∴ [tex]2(x^2- 6x + 9) + 1 - 18 = 0[/tex]

- Construct a square binomial from [tex](x^{2} - 6x + 9)[/tex]

∵ [tex]x^2 - 6x + 9 = (x - 3)^2[/tex]

∴ [tex]2(x - 3)^2 + 1 - 18 = 0[/tex]

Include related terms.

∴[tex]2(x - 3)^2 - 17 = 0[/tex]

∴ The equation's vertex form is[tex]2(x - 3)^2 - 17 = 0.[/tex]

Given that: [tex]2x^2 - 12x + 1 = 0[/tex]

Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]

Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]

Step 3:  [tex]2(x - 3)^2 - 17 = 0[/tex]

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Answer: Refer to the histogram diagram below

The frequency table is in another attachment, and may be optional.

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

Explanation:

The first task is to sort the values from smallest to largest. Luckily the data set is already sorted for us.

The smallest number is 22. This is the min. Since we're doing intervals of 10 percent, this means the first bin spans from 20% to 29%, assuming we're only involving whole number percentages. Then the next bin is from 30% to 39%, and so on, until reaching the last bin of 90% to 99%

The bin labels are shown along the bottom of the histogram.

-----------

The height of each bar represents how many students are in that specific bin. The first bar is 1 unit tall because there's only one student in the 20% to 29% range (that 22% mentioned earlier).

The next bar is 2 units tall because of the scores of 30% and 37%. They are in the range from 30% to 39%

The next bar is 4 units tall because of the scores 45,46,46,49.

This process is done with the other values to get the histogram you see below.

The frequency table is shown in a separate attachment, but your teacher may only want the histogram part. I would ask him/her for clarification.

The third column of the frequency table is optional to show where all the scores fit (and to help confirm the frequencies). This will help confirm the answer. Most histograms commonly only show the first two columns.

------------

While it's a good thing to know how to do this by hand, it's recommend to use software to generate the histograms when it comes to real world applications. Eg: making a presentation to the boss.

The program I used was LibreOffice which is free and effectively identical to excel. There are other options you could pick from.

Side note: There are no gaps between the bars when it comes to histograms. In contrast, a bar chart will have gaps.

Answer: 38 teachers.

Step-by-step explanation:

Let the share ratio be x.

So, quantity of teachers = 2x, quantity of male students = 17x,

quantity of female students = 18x.

17x+18x=665

35x=665

Divide the left and right sides of the equation by 35:

х=19.

2x=2*19

2x=38.

[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]

So, we need to find

[tex]\sum^{\infty}_{n=1} n(5/6)^n

[/tex]

Let this sum be S.

Then,

[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]

Answer:

11 units.

Step-by-step explanation:

the value of x is -3. Option B

WE have the expression to be;

4^x=(1/8)^x+5

With the knowledge of indices, we have that;

2 = 2 ^1

4 = 2^2

8 = 2^3

16 = 2^4

32 = 2^5

So from this given information,

we can express the expression as;

4^x = 2^2x

1/8^x = 2^-3x

Substitute into the formula

2^2x = 2^-3x - 15

Cancel out the like terms

2x = -3x - 15

collect like terms

2x + 3x = - 15

x = -15/ 5

x = -3

Thus, the value of x is -3. Option B

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The value of λ = 8s + 6

The zeroes of a function f(x) are the values of x at which f(x) = 0.

Given that a, s are the zeroes of 2 - 8x + λ ,such that a - s = 2.

Since we require λ,

So, let f(x) = 2 - 8x + λ.

At x = a, f(x) = 0.

So, substituting the value of x = a into f(x), we have

f(a) = 2 - 8a + λ

Since f(a) = 0, we have

2 - 8a + λ = 0   

2 + λ = 8a  (1)

Also, x = s, f(x) = 0.

So, substituting the value of x = s into f(x), we have

f(s) = 2 - 8s + λ

Since f(s) = 0,we have  

2 - 8s + λ = 0

2 + λ = 8s  (2)

Since a - s = 2

Making a subject of the formula, we have

⇒ a = s + 2

So, substituting the value of a into equation (1), we have

2 + λ = 8a  (1)

2 + λ = 8(s + 2)  (1)

2 + λ =  8s + 16

- 14 + λ = 8s   (3)

Adding equation (2) and (3), we have

-14 + λ = 8s   (3)

+

2 + λ = 8s     (2)

-12 + 2λ = 16s

2λ = 16s + 12

Dividing through by 2, we have

2λ/2 = (16s + 12)/2

λ = 4(4s + 3)/2

λ = 2(4s + 3)

λ = 8s + 6

So, the value of λ = 8s + 6

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Using the chord theorem, option C is the best solution since x = 5.

The four line segments that are created by two intersecting chords inside of a circle are explained by the chord theorem, sometimes referred to as the intersecting chords theorem, a statement in fundamental geometry. The products of the line segment lengths on each chord are equal, according to this assertion.

The value of x must be determined in order to answer the question.

We may determine the following using the chord property:

8*x = 4*10,

or, 8x = 40,

or, x = 40/8,

or x = 5.

Given that x = 5, option C is the best option according to the chord theorem.

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The description of this graph tells us that the equation 2x + 3y ≤ 15 was shaded to the bottom while x + y ≥ 3 was shaded to the top as shown in the diagram.

a. The first equation of the graph when it was drawn was shaded to the bottom, while the upper part of the shading has is that of the equation x + y ≥ 3.

b. (5,1) are the solutions for the equation 2x+3y<15. This is given that when x and y are substituted we would still have less than 15.

C The point in the graph would be 2,3. At this point, Michael would be able to buy 2 sandwiches and 3 hot lunches. This is still within his budget for 3 students.

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Answer:

Step-by-step explanation:

2,3 is the anwser

Answer:

11.692945103

Step-by-step explanation:

take out a calculator divide 1016 by 86.89

The time it will take for the car to skid for 150 feet is 8.23 seconds.

The function D(t) = 18t² − 130t gives the distance a car going a certain speed will skid in t seconds.

The time the it would take for the car to skid for 150 feet can be calculated as follows:

Therefore,

D(t) = 18t² - 130t

150 =  18t² - 130t

18t² - 130t - 150 = 0

divide by 3

9t² - 65t - 75 = 0

Hence,

t = 65 ± 5√277 / 18

t = 8.23425471586 or -1.01166666667

Hence,

t = 8.23 seconds.

Therefore, the time it will take for the car to skid for 150 feet is 8.23 seconds.

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Answer:

Step-by-step explanation:

assuming that the figure is a triangle with sides (5y + 9) and (3y + 15) and (7y + 3) we find the perimeter by adding everything

5y + 9 + 3y + 15 + 7y + 3 =

15y + 27

or

3(5y+9)

next time put all the data and figures, we are doing you a pleasure, at least put ALL the data.

Answer:I THINK IT IS 1,-3

Step-by-step explanation:

The weight of a 36-inch piece of PVC pipe is 0.20 pounds

The given parameters about the 36-inch piece of PVC pipe are

Height, h = 36 inches

Outside diameter, D = 0.82 inches

Inside diameter, d= 0.75 inches

The volume of the PVC pipe is then calculated as:

V = πh(D/2)^2 - πh(d/2)^2

Substitute the known parameters in the above equation

V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2

Evaluate the quotients

V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2

Evaluate the exponents

V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625

Evaluate the products

V = 19.002024 - 15.89625

Evaluate the difference

V = 3.105774 cubic inches

From the question, we have:

Weight =  0.063 pounds per cubic inch

So, the total weight is

Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch

Evaluate the product

Total weight = 0.195663762 pounds

Approximate

Total weight = 0.20 pounds

Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds

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The conjugate which is 3 - √7 is also a root of f(x).

The root of a polynomial function f(x) is the value of x for which f(x) = 0.

Now if a polynomial function has a root x = a + √b then the conjugate of x which is x' = a - √b is also a root of the function, f(x).

Given that the polynomial function, f(x), with rational coefficients has roots

3 + √7, then by the above, the conjugate which is 3 - √7 is also a root of f(x).

So, 3 - √7 is also a root of f(x).

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Answer:

dave needs 3/5

Step-by-step explanation:

Step-by-step explanation:

what is the question ?

what problem needs to be solved ?

is it to find the ratio between fruit and nuts ?

then remember, a ratio is a fraction.

so, the ratio fruit : nuts is

1/5 / 1/3 = 1×3 / 5×1 = 3/5 or 3 : 5

or is it about any fraction problems and we need to bring them to the same denominator to add our compare them ?

to compare the 1/5 cup of fruit with the 1/3 cup of nuts, the smallest common multiple of 5 and 3 is 15. so we need to bring all to .../15.

how to make 15 out of 5 ? by multiplying 5 by 3. and we need to do this on the top of the fraction as well to keep the original value of the fraction.

1/5 = 1/5 × 3/3 = 3/15.

and with the same line of thinking :

1/3 = 1/3 × 5/5 = 5/15.

so, when mixing 1/5 cup of fruit with 1/3 cup of nuts, we get 3/15 + 5/15 = 8/15 cup of trail mix.

here you can clearly see the ratio again : 3/15 : 5/15 = 3:5

the first solution to get only full cups of trail mix is

3 cups of fruit and 5 cups of nuts = 8 cups of trail mix.

anything less will always end up with parts of cups (since 3/5 can't be simplified anymore).

Based on the coordinates of the vertices of the parallelogram ORST, the coordinates of S can be found to be (a + b, d).

As this is a parallelogram, the horizontal distance between O and R would be the same as the horizontal distance between S and T.

The horizontal distance between O and R is represented by "b".

The horizontal distance between T and S would therefore be:

= a + b

The fact that R and S are on the same plane would mean that the y-value of S is the same as that of R which is d.

The coordinates of S is:

( a + b, d).

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Answer:

89.19

Step-by-step explanation:

           8 9  .  1     9

         79,56 . 00, 00

8    |  64

      |  1556

169 |  1521

      |      3500

1781 |      1781

              1719

17829|        6200

Answer:

the frequency is the number of times a particular value occurs in a given data.

The length of the line segment of octagon which is AB equal to 3.4 cm.

Given that the area of the regular octagon is 54 [tex]cm^{2}[/tex], apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.

We are required to find the length of the line segment AB.

A regular octagon has eight equal sides.

Area of regular octagon=Perimeter*apothem/2-----------1

We have to put the value of area and apothem in equation 1.

54=perimeter*4/2

Perimeter=(54*2)/4

=27 cm

Perimeter=27 cm.

Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,

Perimeter=8*side

27=8*AB

AB=27/8

=3.375 cm

After rounding off it will be equal to 3.4 cm.

Hence the length of line segment is equal to 3.4 cm.

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Answer:

A

Step-by-step explanation:

The value of the x from the given equation is a +i and -i and +5i and -5i.

According to the statement

we have given that the equation [tex]x^4 + 6x^2 +5 =0[/tex]

and we have to find the value of x by the u substitution.

So,

The given equation is

[tex]x^4 + 6x^2 +5 =0[/tex]

Put [tex]x^2 = u[/tex] 

By substitution method

Then the equation become

[tex]u^2 +6u +5 = 0[/tex]

And solve the equation then

[tex]u^2+ u +5u +5 = 0[/tex]

Then

u(u +1) + 5(u +1) = 0

(u+5) (u +1) = 0

Then

the value of u is -1 and -5 then

The value of x is

[tex]x = \sqrt{u}[/tex]

x = √-5 And √-1

Then the value of x is +i and -i and +5i and -5i.

So, The value of the x from the given equation is a +i and -i and +5i and -5i.

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Answer:

[tex] \frac{3}{2} [/tex]

Step-by-step explanation:

From the attached photo, we can deduce:

(2,2) as (x1,y1)

(-2,-4) as (x2,y2)

Slope Formula =

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

Now we can substitute these values into the formula to find the slope.

Slope of line =

[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]