In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find AC, if CD = 6 sqrt 3

Answer: The price per pound is $18

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}.

Step-by-step explanation:

The vertex of a parabola is given by

[tex](\frac{-b}{2a}, \frac{4ac-b^2}{4a})[/tex].

As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).

As a is negative, it opens downward, so the range is  {y|y ≤ 16}.

Meanwhile, all parabolic functions have a domain of [tex]\mathbb{R}[/tex].

Answer:

Option A is correct.

[tex]x = -6 \pm \sqrt{30}[/tex]

Explanation:

Given the expression: [tex]x^2+12x+6 = 0[/tex]

[tex]x^2+12x+6=0[/tex]  

Subtract 6 from both sides, we get

[tex]x^2+12x=-6[/tex]  

halve linear coefficient,then  square it, and add it to both sides

[tex]x^2+12x+36=30[/tex]

Now, the left side is a perfect square

[tex](x+6)^2=30[/tex]  

Now, take square root to both sides.

[tex]x+6=\sqrt{30}[/tex] 

Subtract 6 from both sides, we get;

[tex]x = -6 \pm \sqrt{30}[/tex]

So, the solutions are : [tex]x = -6 \pm \sqrt{30}[/tex]

Answer:

The correct answer is A

[tex]x=-6\pm \sqrt{30}[/tex]

Step-by-step explanation:

The given expression is

[tex]x^2+12x+6=0[/tex]

Add [tex]-6[/tex] to both sides

[tex]x^2+12x=-6[/tex]

Add [tex](\frac{12}{2} )^2=(6)^2[/tex] to both sides.

[tex]x^2+12x+(6)^2=-6+(6)^2[/tex]

We got a perfect square on the left hand side

[tex](x+6)^2=-6+36[/tex]

Simplify the left hand side to get,

[tex](x+6)^2=30[/tex]

Take square root of both sides

[tex](x+6)=\pm \sqrt{30}[/tex]

Solve for [tex]x[/tex].

[tex]x=-6\pm \sqrt{30}[/tex]

Answer: [tex]\bold{(12x - 7 - i\sqrt{47})(12x - 7 + i\sqrt{47})=0}[/tex]

Step-by-step explanation:

[tex]\dfrac{21x^2-7x - 16}{3x^2-4}=5[/tex]

cross multiply:  21x² - 7x - 16 = 15x² - 20

set equal to 0:  6x² - 7x + 4 = 0

Use quadratic formula to find the roots:

a=6, b=-7, c=4

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

   [tex]=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(6)(4)}}{2(6)}[/tex]

   [tex]=\dfrac{7 \pm \sqrt{49-96}}{12}[/tex]

   [tex]=\dfrac{7 \pm \sqrt{-47}}{12}[/tex]

   [tex]=\dfrac{7 \pm i\sqrt{47}}{12}[/tex]

[tex]x_1 =\dfrac{7 + i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 - i\sqrt{47})= 0[/tex]

[tex]x_2 =\dfrac{7 - i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 + i\sqrt{47})= 0[/tex]

The complete statement is a division of long form ends with zeroes as remainders

We have the following statement -

A division of _____ ends?

The complete statement is -

A division of long division form ends with zeroes as remainders

Therefore, the complete statement is a division of long form ends with zeroes as remainders.

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y = 2x + 2

for x = 0 → y = 2(0) + 2 = 0 + 2 = 2 → (0, 2)

for x = -1 → y = 2(-1) + 2 = -2 + 2 = 0 → (-1, 0)

y = x - 1

for x = 0 → y = 0 - 1 = -1 → (0, -1)

for x = 1 → y = 1 - 1 = 0 → (1, 0)

Look at the picture.

Answer:

Step-by-step explanation:

Please find attachment for step by step explanation.

[tex](f-g)(x)=f(x)-g(x)\\\\\text{We have}\ f(x)=2x^2-5\ \text{and}\ g(x)=3x+3.\ \text{Substitute:}\\\\(f-g)(x)=(2x^2-5)-(3x+3)=2x^2-5-3x-3=2x^2-3x-8\\\\Answer:\ \boxed{(f-g)(x)=2x^2-3x-8}[/tex]

Answer:

B.) transitive property of equality

Step-by-step explanation:

x = –3 and –3 = z, then x = z.

Symmetric property of equality: if a = b then b = a

Transitive property of equality:  if a = b and b = c, then a = c

Closure property of multiplication:  the set is closed under multiplication

Closure property of addition:  the set is closed under addition

Answer:

Step-by-step explanation:

3x + 5 = 19 - 4x     subtract 5 from both sides

3x = 14 - 4x      add 4x to both sides

7x = 14    divide both sides by 7

x = 2

Answer:

x=2

Step-by-step explanation:

3x + 5 = 19 - 4x

Add 4x to each side

3x + 5 +4x= 19 - 4x+4x

7x+5 = 19

Subtract 5 from each side

7x+5-5 =19-5

7x =14

Divide each side by 7

7x/7 = 14/7

x = 2

To find the area that is shaded red, you find the area of the rectangle and subtract it by the area of the triangle.

Area of a rectangle:

A = l × w             [ l = 11 in ; w = 6in ]    Plug these numbers into the equation

A = 11 · 6

A = 66 in²

Area of a triangle:

[tex]A=\frac{1}{2}bh[/tex]     [ b = 4 in ; h = 6 in ] Plug these #s into the equation

[tex]A = \frac{1}{2}(4)(6)[/tex]

[tex]A=\frac{24}{2}[/tex]

A = 12 in²

Area of rectangle - Area of triangle = Area of the shaded region

66 in² - 12 in ² = 54 in²

Your answer is B

The required red shaded region has the area of 54 in²

A figure bounded by 4 sides in which the opposite sides are equal and all the internal angles are 90 ° is called a rectangle.

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

Area  = (1/2)(base)(height)

Area of the rectangle = (11 x 6) in² = 66 in²

Area of the right angled triangle = (1/2)(6 x 4)  in² = 12 in²

∴ Area of the red shaded region = (66 - 12)  in² = 54 in²

Option B is correct.

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[ Answer ]

Y = -9

[ Explanation ]

Subtract 15 from both sides:

2/3y + 15 - 15 = 9 - 15

Simplify:

2/3y = -6

Multiply each side by 3:

3 * 2/3y = 3 (-6)

Simplify:

2y = -18

Divide both sides by 2:

2y / 2 = -18/2

y = -9

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Using the simplification, it is proven that the y = -9 from the equation 2/3y + 15 = 9.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given that 2/3y + 15 = 9

Subtract 15 from both sides;

2/3y + 15 - 15 = 9 - 15

Now Simplify,

2/3y = -6

Multiply each side by 3,

3  (2/3y) = 3 (-6)

2y = -18

y = -9

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Answer:

True

Step-by-step explanation:

Each week the amount of radio active material is 100*(1/4)^x which is correct.

So at the end of 4 weeks she will have

amount = 100*(1/4)^x

amount = 100*(1/4)^4

amount = 100 * (1/256)

amount = 0.390625 grams after 4 weeks.

Answer:

Step-by-step explanation:

There is the answer.

Answer:

72 / 50 = 36/25

x^16 / x^36  

= x^-20

Answer:

[tex]\frac{36}{25x^{20} }[/tex]

Step-by-step explanation:

In order to simplify this function, we have to divide by the maximum common divisor:

[tex]\frac{72x^{16} }{50x^{36} }\\ 72/2=36\\50/2=25\\\frac{36}{25} \\(x^{16} )(x^{-36})=x^{-20}=\frac{1}{x^{20} } \\\frac{36}{25x^{20} }[/tex]

By doing this you can simplify the function into the simplified form.

Answer:

Each pound of chocolate costs $7.30

Step-by-step explanation:

if 5 pounds of chocolate costs $36.50 then you could simply divide the $36.50 by 5 to calculate the cost of 1 pound of chocolate.

So, 36.50 ÷ 5 = 7.30

Each pound of chocolate costs $7.30

To find the cost of each pound of chocolate, you divide the total cost by the total number of pounds. Given a total cost of $36.50 for 5 pounds of chocolate, the resulting calculation is $36.50 ÷ 5 = $7.30. Thus, each pound costs $7.30.

If you have 5 pounds of chocolate that cost $36.50 in total, and you need to find the cost of each pound of chocolate, you can determine this by dividing the total cost by the number of pounds. This is similar to how in our reference material, to compute the cost of each piece of fruit, you divided the total expense by the quantity of fruit.

In this case, you need to divide the total cost, which is $36.50, by the quantity, which is 5 pounds. So the calculation is $36.50 ÷ 5 = $7.30. Therefore, each pound of chocolate costs $7.30.

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Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer:

y=5x+17

Step-by-step explanation:

perpendicular slope is 5

y-7=5(x+2) convert this equation into slope intercept and that's your answer

Answer:

Let 5 consecutive no's be x,x+1,x+2,x+3,x+4

90 = x+ x+1+x+2+ x+3+x+4

90 = 5x+10

18 = x+2

x= 16

so smallest is 16

greatest = 16+4 = 20

sum = 16 +20 = 36

For each part A through D below, the idea is to find the common factor between the terms, which you'll then use the distributive property to pull out.

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

Part A

3x + 18 = 3(x+6)

Note how we pulled out a 3. If we distribute it back in, we end up with 3x+18 again. The other problems are done in a similar fashion

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

Part B

2x - 14 = 2(x - 7)

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

Part C

6x + 4 = 2(3x + 2)

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

Part D

9x - 15 = 3(3x - 5)

Answer: the answer is 23

Step-by-step explanation: since you are trying to find the number of boxes, b, the first thing you do is isolate it by dividing 4b by 4 this eliminates the 4, and because you did it on one side you have to do it on the other so you work would look like this 4b/4=92/4 you equation would look like this when done b=23

To find the number of boxes Mr. Reed bought, we solve the equation 4b = 92. This involves dividing 92 by 4 which results in 23 boxes of markers.

The subject of this question is Mathematics, particularly algebra. We need to solve the equation 4b = 92, where 'b' represents the number of boxes Mr.Reed bought.

Step 1: Write down the equation: 4b = 92.

Step 2: We solve for 'b' by dividing each side of the equation by 4. This gives us: b = 92/4.

Step 3: Doing the division, we find that 'b' is 23. Therefore, Mr. Reed purchased 23 boxes of markers with $92.

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Answer:

SEgment AC is congruent to segment AB

Step-by-step explanation:

given is a triangle ABC with a segment joining A to D on side BC.

To prove that ABD is congruent to ACD

Let us compare these two triangles.

AD = AD (reflexive) Thus one side is equal.

IF AB = AC, then by isosceles triangles property we have angle B = angle C

Thus we get two sides equal.  But this is a necessary condition not sufficient.

Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB

Thus if either AD is angle bisector, or D is mid point besides AC = AB we get

the two triangles are congruent.

Answer:

The answer is B and E

Step-by-step explanation:

Julia runs 5 time and lifts 5 times in B. She also runs 10 times and lifts 10 times in E.

The average acceleration of the car is 4 m/s²

The given parameters:

initial velocity of the car, u = 2 m/s

final velocity of the car, v = 16 m/s

time of motion of the car, t = 3.5 s

To find:

The average acceleration of the car is calculated as the change in velocity per change in time.

The formula for average acceleration is given below;

[tex]a = \frac{\Delta v}{\Delta t} = \frac{v- u}{t} = \frac{16 - 2}{3.5} = 4 \ m/s^2[/tex]

Thus, the average acceleration of the car is 4 m/s²

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So to factor this expression, I'm going to be factoring by grouping. Firstly, what two terms have a sum of 4x and a product of -32x²? That's going to be 8x and -4x. Replace 4x with 8x - 4x:

[tex]x^2+8x-4x-32[/tex]

Now, factor x² + 8x and -4x - 32 separately. Make sure that they have the same quantity on the inside of the parentheses:

[tex]x(x+8)-4(x+8)[/tex]

Now you can rewrite the expression as:

[tex](x-4)(x+8)[/tex]

In short, the two binomial factors are (x - 4) and (x + 8).

Answer:

x-4 and x+8

Step-by-step explanation:

Factoring a quadratic equation of the form x^2+bx+c:

Divide b into two numbers p and q, so that p+q = b and p*q = c

8 + (-4) = 4 = b

8 * (-4) = -32 = c

x^2+8x-4x-32

Factor by grouping

(x^2+8x)+ (-4x-32) =

x*(x+8) + -4* (x+8) = (x-4)(x+8)

Answer:

A. The equation has no solution

Expand to get 35x^3+49x^2-20x-28

Answer:

3x(3x + 2)

Step-by-step explanation: