Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?
O 1-6 - 751, - 6 + V51)
O 1-6 - 121, -6 + V21)
O 16 - 151,6 + V51)
O (6 - 121,6 + V21)

You already did. That is a true statement.

32 > 29 [and vice versa]

I am joyous to assist you anytime.

The inequality 29 < 32 is true.

After calculating 36 - 7 which equals 29, we compare this result to 32. The inequality 29 < 32 holds true, so the original inequality 36 - 7 < 32 is correct.

The student has asked to solve the inequality 36 - 7 < 32. To solve this inequality, we need to perform the subtraction on the left side of the inequality first.

When we calculate 36 - 7, we get 29. Now we can compare this result to 32 to determine if the inequality holds true.

Since we are dealing with an inequality, we know that if a value a is less than a value b, then a is indeed smaller in quantity or value compared to b. Here, 29 is indeed less than 32. Therefore, the inequality 29 < 32 is true.

Answer:

A

Step-by-step explanation:

Calculate the midpoint using the midpoint formula

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

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

midpoint = [ 0.5(- 1 + 5), 0.5(5 + 5) ]

              = [ 0.5(4), 0.5(10) ] = (2, 5 ) → A

Answer:

The answer would be A 2,5

Step-by-step explanation:

Answer:

9 : 16

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

area ratio = a² : b² and

volume ratio = a³ : b³

Here the volume ratio = 27 : 64, hence

linear ratio = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{64}[/tex] = 3 : 4

Hence area ratio = 3² : 4² = 9 : 16

Answer:

[tex]x < 10[/tex]

Step-by-step explanation:

[tex]2x - 8 < 12 \\ 2x - 8 + 8 < 12 + 8 \\( 2x < 20) \div 2 = x < 10[/tex]

x<10 is the solution to the inequality 2x - 8 < 12

To solve the inequality 2x - 8 < 12, you can follow these steps:

Add 8 to both sides of the inequality:

2x - 8 + 8 < 12 + 8

This simplifies to:

2x < 20

Divide both sides of the inequality by 2:

(2x)/2 < 20/2

This simplifies to:

x < 10

Therefore, the solution to the inequality 2x - 8 < 12 is x < 10.

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Answer:

98.518 repeating prercent

Step-by-step explanation:

2 out of 135 can also be written as 2/135

2 divided by 135 is 0.014814814814

that number is the percentage of failures

100% in decimal form is 1.00

1.00 subtracted by the percentage of failures is the percentage of successes

which is .98518518518, 518 repeating move the decimal over 2 and you got the percentage 98.518 repeating

[tex]-8(5x+5)+9x(10x+9)=20\\-40x-40+90x^2+81x-20=0\\90x^2+41x-60=0\\\\\Delta=41^2-4\cdot90\cdot(-60)=1681+21600=23281\\\\x=\dfrac{-41\pm \sqrt{23281}}{2\cdot90}=\dfrac{-41\pm \sqrt{23281}}{180}[/tex]

Answer:

It is 132 just took it

Step-by-step explanation:

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle. The measure of ∠AOE is 132°. The correct option is B.

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.

In circle O, AD and BE are diameters. Also, the measure of ∠EOD and ∠AOB will be equal because the two angles are vertically opposite angles. Therefore,

∠EOD = ∠AOB = 3x

As it is given that the measure of ∠AOC is 90°. Therefore, we can write,

∠AOC = ∠AOB + ∠BOC

90 = 3x + 0.5x + 34

56 = 3.5x

x = 16

Now, the measure of ∠EOD will be,

∠EOD = 3x

∠EOD = 3(16°)

∠EOD = 48°

Further, we can write,

∠AOD = ∠AOE + ∠EOD

180° = ∠AOE + 48°

∠AOE = 132°

The complete question is mentioned in the below image.

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Answer:

x= -3.75

Step-by-step explanation:

Answer:

x = -15/4

Step-by-step explanation:

7(x+6)=3(x+9)

Distribute

7x+42 = 3x+27

Subtract 3x from each side

7x-3x+42 = 3x-3x+27

4x +42 = 27

Subtract 42 from each side

4x+42-42 = 27-42

4x =-15

Divide each side by 4

4x/4 =-15/4

x = -15/4

Answer:

Triangle APB is an isosceles triangle ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the how to solve the problem

- ABCD is a square

∴ AB = BC = CD = AD

∴ m∠A = m∠∠B = m∠C = m∠D = 90°

- DPC is equilateral triangle

∴ DP = PC = DC

∴ m∠DPC = m∠PCD = m∠CDP = 60°

- In the Δs APD , BPC

∵ AD = BC ⇒ sides of the square

∵ PD = PC ⇒ sides of equilateral triangle

∵ m∠ADB = m∠BCP = 30° (90° - 60° = 30) ⇒ including angles

∴ Δs APD , BPC are congregant ⇒ SAS

- From congruent

∴ AP = BP

∴ Triangle APB is an isosceles triangle

Answer:

Step-by-step explanation:

AC is a midsegment of the trapezoid DFBE.

The formula of a midsegment of trapezoid is:

[tex]m=\dfrac{a+b}{2}[/tex]

a, b - bases of a triangle

We have

a = x, b = 4.4, m = 5.5

Substitute:

[tex]5.5=\dfrac{x+4.4}{2}[/tex]          multiply both sides by 2

[tex]11=x+4.4[/tex]       subtract 4.4 from both sides

[tex]6.6=x\to x=6.6[/tex]

Answer:

7/11

Step-by-step explanation:

Two events are disjoint events if they cannot occur at the same time. It is given that A and B are disjointed events, so A and B cannot occur at the same time i.e. the intersection of two disjoint events will be 0.

For two disjoint events A and B:

P(A or B) = P(A) + P(B)

P(A) is given to be 4/11 and P(B) is given to be 3/11. Using these values in the equation, we get:

P(A or B) = [tex]\frac{4}{11}+\frac{3}{11} = \frac{3+4}{11}=\frac{7}{11}[/tex]

[tex]\huge{\boxed{\text{9,000 meters}}}[/tex]

There are 1,000 meters in each kilometer, so multiply to find the daily number of meters.  [tex]3*1000=3000[/tex]

Multiply this by 3 to find the number of meters Rowena walks in three days.  [tex]3000*3=\boxed{9000}[/tex]

Answer:

8.8.8.

Step-by-step explanation:

8.8.8  = 8^3  = 512    Perfect cube.

8+8+8 =24

9.9.9.9 = 6561

9+9+9+9+9 = 45.

None of the others are perfect cubes.

Answer:A 8.8.8

Step-by-step explanation:i did the quiz

Answer:

[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex] given you are asked to simplify

[tex]\frac{-3+5i}{-3-4i}[/tex]

Step-by-step explanation:

You have to multiply the numerator and denominator by the denominator's conjugate.

The conjugate of a+bi is a-bi.

When you multiply conjugates, you just have to multiply first and last.

(a+bi)(a-bi)

a^2-abi+abi-b^2i^2

a^2+0         -b^2(-1)

a^2+-b^2(-1)

a^2+b^2

See no need to use the whole foil method; the middle terms cancel.

So we are multiplying top and bottom of your fraction by (-3+4i):

[tex]\frac{-3+5i}{-3-4i} \cdot \frac{-3+4i}{-3+4i}=\frac{(-3+5i)(-3-4i)}{(-3-4i)(-3+4i)}[/tex]

So you will have to use the complete foil method for the numerator. Let's do that:

(-3+5i)(-3+4i)

First: (-3)(-3)=9

Outer::  (-3)(4i)=-12i

Inner: (5i)(-3)=-15i

Last: (5i)(4i)=20i^2=20(-1)=-20

--------------------------------------------Combine like terms:

9-20-12i-15i

Simplify:

-11-27i

Now the bottom (-3-4i)(-3+4i):

F(OI)L (we are skipping OI)

First:-3(-3)=9

Last: -4i(4i)=-16i^2=-16(-1)=16

---------------------------------------------Combine like terms:

9+16=25

So our answer is [tex]\frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:

[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex]

Answer:

Answer in factored form (3x+10)(2x+6)

Answer in standard form 6x^2+38x+60 ( I bet you they want this answer)

Step-by-step explanation:

The assumption is this is a rectangle.

If you have the dimensions of a rectangle are L and W, then the area is equal to L times W.

So here we just need to multiply (3x+10) and (2x+6).

The answer in factored form is (3x+10)(2x+6).

I bet you they want the answer in standard form.

So let's use foil.

First: 3x(2x)=6x^2

Outer: 3x(6)=18x

Inner: 10(2x)=20x

Last: 10(6)=60

----------------Add up!

6x^2+38x+60

The area of the window is 3x² + 19x + 30

The dimension of the window are  3x + 10 and 2x + 6.

The area of the window can be calculated as follows;

area = lw

Therefore,

area = (3x + 10)(2x + 6)

area = 6x² + 18x + 20x + 60

area = 6x² + 38x + 60

area  = 3x² + 19x + 30

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Answer:

T10= -21

Step-by-step explanation:

If Sn=n^2+3 then t10=?

Sn= n²+5

put n=1, 2

S1= T1 =  (1)²+5

=1+5 =6

S2= n²+5

S2=(2)²+5

S2=4+5

S2=9

T2 = S2 - S1

T2 = 9-6

T2=3

T10 = a+(n-1)d

where a = 6, d = -3, n=10

T10= 6+(10-1)*-3

T10=6+(9)*-3

T10=6+(-27)

T10=6-27

T10= -21

Therefore T10= -21 ....

Answer:

12 pounds

Step-by-step explanation:

After trimming:

50 − 0.40 (50) = 0.60 (50) = 30

After cooking:

30 − 0.60 (30) = 0.40 (30) = 12

Answer:

[tex]\large\boxed{y-5=-4(x-3)}\\\boxed{y-8=\dfrac{1}{2}(x+1)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

[tex]m=-4,\ (3,\ 5)\\\\y-5=-4(x-3)[/tex]

[tex]m=\dfrac{1}{2},\ (-1,\ 8)\\\\y-8=\dfrac{1}{2}(x-(-1))\\\\y-8=\dfrac{1}{2}(x+1)[/tex]

Answer:

It's 53.

Step-by-step explanation:

Let the number be xy so the digits are x and y, so:

x + y = 8...........(1)

Reversing the 2 digits we have the number 10y + x and this equals

10x + y - 18 so we have the equation:-

10x + y - 18 = 10y + x

9x - 9y = 18

x - y = 2...........(2)   Adding equations (1) and (2) we have:

2x = 10

x = 5

and y = 8 - 5 = 3.

So the original number is  53.

We can check this  as follows

Original number is 53 so the reverse is 35 .

53 - 35 = 18  which checks out.

Answer:

13

Step-by-step explanation:

(f∘g)(4) is another way of writing f(g(4)).

First, find g(4).

g(x) = 2x − 3

g(4) = 2(4) − 3

g(4) = 5

Now substitute into f(x).

f(x) = 4x − 7

f(g(4)) = 4g(4) − 7

f(g(4)) = 4(5) − 7

f(g(4)) = 13

[tex](f\circ g)(x)=4(2x-3)-7=8x-12-7=8x-19\\\\(f\circ g)(4)=8\cdot4-19=13[/tex]

Answer:

-5/4

Step-by-step explanation:

The average rate of change of f from x=0 to x=4 is_____.

This means we are being asked to evaluate [tex]\frac{f(4)-f(0)}{4-0}[/tex].

To do this we will need to find f(0) and f(4).

f(0) means what y-coordinate corresponds to x=0 on the curve.  Find x=0, the curve is above there, go straight up and see  y=5 there.  This means f(0)=5.

f(4) means what y-coordinate corresponds to x=4 on the curve. Find x=4, then curve is above there, go straight up and see y=0 there.  This means f(4)=0.

So we have:

[tex]\frac{f(4)-f(0)}{4-0}=\frac{0-5}{4-0}=\frac{-5}{4}[/tex].

166

27 + 42 + 21 + 76 = 166

Answer: A. y=(1/2)^x+6

Step-by-step explanation: If this is the graph you’re talking about-

When “a” is less than one, the graph increases exponentially to the left. The smaller the value of a, the steeper the slope of the line.

There is a vertical shift up 6 as well

All except combine like terms. Since you only have 1 variable.

Hope this helps.

r3t40

Answer:

log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.

Step-by-step explanation:

By the logarithm product rule, for two nonzero numbers [tex]a[/tex] and [tex]b[/tex],

[tex]\log{(a \cdot b)} = \log{(a)} + \log{(b)}[/tex].

Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.

For example, [tex]3(x + 4)[/tex] is the number in the logarithm [tex]\log{[3(x + 4)]}[/tex]. Since [tex]3(x + 4)[/tex] is a product of the two numbers [tex]3[/tex] and [tex](x + 4)[/tex], the logarithm [tex]\log{[3(x + 4)]}[/tex] can be split into two. By the logarithm product rule,

[tex]\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}[/tex].

However, [tex]\log{(x + 4)}[/tex] cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.

Answer:

c

Step-by-step explanation:

Answer:

2/12

Step-by-step explanation:

Rolling a 5 on one die the probability is 1 out of 6 or 1/6 so when you add the second die the probability increases as well as the number of outcomes so you have 1/6+1/6 or 2/12. hope this helps

Answer:

1/36

Step-by-step explanation:

A cube has six sides.  On number cubes (also called dice), the sides are numbered 1 through 6.  So the probability of rolling a 5 on either cube is 1/6.  The probability of rolling a 5 on both cubes is:

P(A and B) = P(A) × P(B)

P(A and B) = 1/6 × 1/6

P(A and B) = 1/36

as you may already know, the inverse of a function has the same exact x,y pairs but backwards, namely f(x)'s domain is f⁻¹(x)'s range.

[tex]\bf \stackrel{f(x)}{\begin{array}{|cc|ll} \cline{1-2} \stackrel{domain}{x}&\stackrel{range}{y}\\ \cline{1-2} 3&4\\ 4&3\\ -2&6\\ \cline{1-2} \end{array}}~\hspace{10em} \stackrel{inverse~of~f(x)}{\begin{array}{|cc|ll} \cline{1-2} \stackrel{domain}{x}&\stackrel{range}{y}\\ \cline{1-2} 4&3\\ 3&4\\ 6&-2\\ \cline{1-2} \end{array}}[/tex]

Answer:

By 2.

Step-by-step explanation:

You need to eliminated the x-terms, so the first step is to focus only in those terms.

So yo have 4x and -2x, since you are thinking in eliminate then you have this equation>

[tex]4-2*K=0[/tex]

Note that we dont put the x variable, since we are studying its coefficients in the equations system.

Solving for K, Gives us that K=2

So.

Multiplying the second equation by 2 results in

[tex]-4x+6y=8[/tex]

When you put them together, it gives you the following

[tex]4x-9y -4x+6y- 7+8[/tex]

and the final equation is

[tex]-3y=15\\[/tex]

giving you the answer for y, that is [tex]y=-5[/tex]

Answer: 2 and 3.

Step-by-step explanation:

Answer:

Plane B was farthest away from the airport

Step-by-step explanation:

This question requires you to visualize the run way as the horizontal distance to be covered, the height from the ground as the height gained by the plane after take of and the distance from the airport as the displacement due to the angle of take off.

In plane A

The take-off angle is 44° and the height gained is 22 ft.

Apply the relationship for sine of an angle;

Sine Ф°= opposite side length÷hypotenuse side length

The opposite side length is the height gained by plane which is 22 ft

The angle is 44° and the distance the plane will be away from the airport after take-off will be represented by the value of hypotenuse

Applying the formula

sin Ф=O/H where O=length of the side opposite to angle 44° and H is the hypotenuse

[tex]Sin44=\frac{O}{H} \\\\\\Sin44=\frac{22}{H} \\\\\\H=\frac{22}{sin44deg} \\\\\\H=31.67[/tex]

31.67 miles

In plane B

Angle of take-off =40°, height of plane=22miles finding the hypotenuse

[tex]sin40deg=\frac{O}{H} \\\\\\sin40deg=\frac{22}{H} \\\\\\H=\frac{22}{sin40deg} \\\\\\H=34.23miles[/tex]

34.23miles

Solution

After take-off and reaching a height of 22 ft from the ground, plane A will be 31.67 miles from the airport

After take-off and reaching a height of 22 ft from the ground, plane B will be 34.23 miles away from the airport.

Answer:

9.33 (flvs)

Step-by-step explanation:

i took the test

Answer:

C.  6√2.

Step-by-step explanation:

Since this is a right angled isosceles triangle bot legs are 6 units long

So h^2 = 6^2 + 6^2 = 72

h = √72 = 6√2.

Answer:

The correct option is C) 6√2.

Step-by-step explanation:

Consider the provided triangle.

The provided triangle is a right angle triangle, in which two angles are 45° and one is 90°.  

As both angles are equal there opposite side must be equal.

Thus, the leg of another side must be 6.

Now find the hypotenuse by using Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute a = 6 and b = 6 in [tex]a^2+b^2=c^2[/tex].

[tex](6)^2+(6)^2=(c)^2[/tex]

[tex]36 + 36=(c)^2[/tex]

[tex]72=(c)^2[/tex]

[tex]6\sqrt{2}=c[/tex]

Hence, the length of the hypotenuse in the right triangle is 6√2.

Therefore, the correct option is C) 6√2.