What are the solutions to x^2 + 4x - 12 = 0?

Answer:

The correct answer option is 'orthocenter'.

Step-by-step explanation:

The point of concurrency of the altitudes of a triangle is called the 'orthocenter'.

Orthocenter is the point in a triangle where all of the three altitudes of the triangle intersect each other.

Explaining further, a line which is perpendicular to the opposite side and passes from a vertex of a triangle is called the altitude of the triangle.

Therefore, the correct option is D. orthocenter.

Let's say BB' = a

2^2 + 1^2 = a^2

4 + 1 = a^2

a^2 = 5

a = √5

So the distance of BB' is √5

The distance of BB' is √5.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=(((x₂-x ₁)²+(y ₂-y ₁)²) to calculate the separation between any two locations.

Let's say BB' = a

2² + 1² = a²

4 + 1 = a²

a² = 5

a = √5

So the distance of BB' is √5

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Hello There!

Dividing a fraction is the same thing as multiplying by its reciprocal.

This means that [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{5}{12}[/tex] is the same as multiplying [tex]\frac{3}{4}[/tex] by [tex]\frac{12}{5}[/tex].

So basically when you divide you leave the first fraction alone but the second fraction in this case, 5/12 you would flip the number on top and the number on bottom to 12/5.

HAVE A GREAT DAY!

Answer:   [tex]\frac{12}{5}[/tex]

Step-by-step explanation:

When you divide fractions you can multiply the first fraction by the reciprocal of the second fraction.

To find the reciprocal of the fraction, you need to flip it. Then the original denominator will be the new numerator and the original numerator will be the new denominator.

Then, the reciprocal of the fraction [tex]\frac{5}{12}[/tex] is:

[tex]\frac{12}{5}[/tex]

Therefore:

[tex]\frac{3}{4}[/tex]÷[tex]\frac{5}{12}= \frac{3}{4}* \frac{12}{5}[/tex]

Answer:

depreciation is $3,333.33 per year

Step-by-step explanation:

Initially : date = 2006, worth = $34,500

Finally : date = 2009, worth = $24,500

if we let x = date and y = worth, we end up with two points (coordinates) on the x-y graph

i.e

Initial = Point 1 (2006, 34500)

Final = Point 2 (2009, 24500)

The rate of change is simply the slope, m of the line joining these two points

given by:

m = (34500 - 24500) / (2006-2009)

= 10000 / -3

= -3,333.33

hence the annual rate of depreciation is $3,333.33 per year

Final answer:

The boat's value depreciated by $10,000 over 3 years, resulting in an annual depreciation rate of $3,333.33.

Explanation:

The student's question involves calculating the annual rate of change of the value of a boat from the year it was bought (2006) to the year 2009. To find the rate of change, we need to determine how much the value of the boat depreciated over the given time period and then divide it by the number of years.

The boat depreciated from $34,500 in 2006 to $24,500 in 2009, which is a decrease of $34,500 - $24,500 = $10,000 over the course of 3 years. To find the annual depreciation rate, we divide the total depreciation amount by the number of years: $10,000 ÷ 3 years = $3,333.33 per year. Therefore, the annual rate of depreciation is $3,333.33 per year, rounded to the nearest hundredth if necessary.

Answer:

D

Step-by-step explanation:

Option A, does 6 and 2 added makes 8? Yes

does 6 and 2 subtracted makes 2? No

Option B, does 6 and 4 added makes 8? No

does 6 and 4 subtracted gives 2? Yes

Option C, does 4 and 4 added gives 8? Yes

does 4 and 4 subtracted gives 2? No

Option D

Does 5 and 3 added give 8? Yes

Does 5 and 3 subtracted give 2? Yes

So we can see, Option D is the correct answer because it satisfies both conditions.

Answer:

18

Step-by-step explanation:

Count I think. That's what I think the problem was asking.

Answer:

10. 65 = x

9. 8 = x

8. 63 = x [it gave you the answer]

7. 0 = x

6. -5 = x

Step-by-step explanation:

#6 uses the Associative Property of Multiplication. #7 uses the Zero Product Property of Multiplication. #8 gave you the answer because x = 1x. For #9, you have to multiply ⅛ by its multiplicative inverse [reciprocal (8)] to get 1. #10 uses the Commutative Property of Multiplication.

**Associative and Commutative are the same thing, EXCEPT Commutative does NOT use grouping symbols. Associative does.

Answer:

f(x) +g(x)  = -1.3 - 1.75x

Step-by-step explanation:

f(x) +g(x) is simply obtained by adding the two given functions, f(x) and g(x). We are given that;

F(x)= 3.7-2x and g(x)= 0.25x-5

f(x) +g(x)  = 3.7-2x + (0.25x-5)

f(x) +g(x)  = 3.7 -5 + 0.25x - 2x

f(x) +g(x)  = -1.3 - 1.75x

Answer:

f(x) +g(x)  = -1.3 - 1.75x

Step-by-step explanation:

Answer:

B. (5x - 7)(x+9)

Step-by-step explanation:

5x(x + 9) - 7(x + 9

Factor out the quantity (x+9)

(x+9) (5x-7)

Rearrange the order

(5x - 7)(x+9)

Final answer:

The expression 5x(x + 9) - 7(x + 9) is factored by finding the common term (x + 9) and factoring it out, resulting in the complete factored form (5x - 7)(x + 9), which is Option B.

Explanation:

The expression given is 5x(x + 9) - 7(x + 9). To factor this expression, we look for a common factor in both terms. Here, the common factor is (x + 9). We can use the distributive property, also known as factoring by grouping, to factor out the common factor. Applying this, we get:

(x + 9) is the common factor, so we pull it out in front: (x + 9)(5x - 7).

Thus, the expression in complete factored form is Option B: (5x - 7)(x + 9).

Answer:

15.85%

Step-by-step explanation:

Given:

Acres damaged (burned) = 6,500 acres

Acres in total forest = 41,000 acres

Hence the amount of damaged forest as a fraction of the total forest,

= [tex]\frac{6500}{41000}[/tex] = [tex]\frac{13}{82}[/tex]

expressed as percentage = [tex]\frac{13}{82}[/tex] x 100% = 15.85%

Answer:

An exterior angle is supplementary to the adjacent interior angle.

Step-by-step explanation:

An exterior angle of a triangle and its adjacent interior angle form a linear pair. This means they form a straight line, and a straight line has a measure of 180°. Since they combine for a total of 180°, this means they are supplementary.

Answer:

(x + 5)^2

Step-by-step explanation:

Learn to recognize perfect squares.  x^2+ 10x + 25 is a perfect square of a binomial:  x^2+ 10x + 25 = (x + 5)^2.

The polynomial expression of the equation [tex]x^2+ 10x + 25[/tex] is  [tex]&(x+5)^{2}[/tex].

A polynomial exists defined as an expression that exists composed of variables, constants, and exponents, that are connected utilizing mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).

Given expression [tex]x^2+ 10x + 25[/tex]

Rewrite in the form of [tex]$a^{2}+2 a b+b^{2}$[/tex] :

[tex]$25=5^{2}$[/tex]

[tex]$10 x=2 x \cdot 5$[/tex]

[tex]$$=x^{2}+2 x \cdot 5+5^{2}$$[/tex]

Apply Perfect Square Formula:

The perfect square formula exists described in the formation of two terms such as [tex](a + b)^{2}[/tex]. The expansion of the perfect square formula exists represented as[tex](a + b)^{2} = a^{2} + 2ab + b^{2}[/tex]

[tex]$\quad a^{2}+2 a b+b^{2}=(a+b)^{2}[/tex]

[tex]&x^{2}+2 x \cdot 5+5^{2}=(x+5)^{2} \\[/tex]

[tex]&=(x+5)^{2}[/tex]

The polynomial expression of the equation [tex]x^2+ 10x + 25[/tex] is  [tex]&(x+5)^{2}[/tex].

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Answer:

$370

Step-by-step explanation:

You already have 90 dollars so we can put that to the side for right now

If you're charged $35 at an hourly rate for 8 hours then you have to multiply the two together

30 x 8 = 240

5 x 8=40

240 + 40=280

Now is when your $90 dollars comes in. Now just add the two together and you'll end up with your final answer

280+90=370

Multiply the bracket by 4

4(3x+12)=-36

12x+48= -36

12x+48-48= -36-48

12x= -84

divide by 12 for 12x and -84

12x/12= -84/12

x= -7

Answer is x=-7

ANSWER

[tex]x = - 7[/tex]

EXPLANATION

The given equation is

[tex]4(3x + 12) = - 36[/tex]

Expand the parenthesis,

[tex]12x + 48 = - 36[/tex]

Group similar terms

[tex]12x = - 36 - 48[/tex]

[tex]12x = - 84[/tex]

Divide both sides by 12

[tex]x = \frac{ - 84}{12} [/tex]

[tex]x = - 7[/tex]

Step-by-step answer:

The answer is circled in red on the output of the calculator, attached.  This is how we need to look for when we use a graphing calculator, which says

"linear regression, y=5.10x+9.12"

However, we need to check the answer by looking at least one point on the curve.  Say we use the point (10,60) on the straight line, and compare with y(10) = 5.10*10+9.12 = 60.12, quite close to 60.  The other answer options all give numbers far away from 60 when x=10.

Answer:

The correct option is 2.

Step-by-step explanation:

The given data is

x               y

5              36

9              64

12            72

18            96

26           141

35           189

The general form of regression line is

[tex]y\approx ax+b[/tex]

From the given picture of graphing calculator, it is clear that the equation of regression line is

[tex]y\approx 5.098x+9.118[/tex]

Approx the value of a and b upto tenth.

[tex]y\approx 5.10x+9.12[/tex]

The equation of the line of best fit is y ≈ 5.10x+9.12. Therefore the correct option is 2.

Answer:

Option C is correct.

Step-by-step explanation:

The formula to find the slope given two points is:

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

We are given points (0,4) and (3,6)

where x₁ = 0 , y₁ = 4, x₂=3 and y₂=6

Putting values in the formula:

[tex]slope = \frac{6-4}{3-0} \\slope = \frac{2}{3}[/tex]

So, slope is 2/3

Since the slope of line to be found is parallel to line L. So both lines have the same slope.

Slope of line parallel to line L = 2/3

Option C is correct.

Answer:

B. x=0,2

Step-by-step explanation:

(x+4)      1

-------- = -----

6x          x

Using cross products

x * (x+4) = 1*6x

Distribute

x^2 +4x = 6x

Subtract 6x from each side

x^2 +4x-6x = 6x-6x

x^2 -2x = 0

Factor out an x

x (x-2) = 0

Using the zero product property

x=0  x-2 =0

x=0  x-2+2 =0+2

x =0   x=2

Answer:

Option C is correct.

Step-by-step explanation:

We need to solve the equation below and find value of x

[tex]\frac{x+4}{6x} =\frac{1}{x}[/tex]

Cross multiply

x(x+4)=6x

x^2+4x=6x

x^2+4x-6x=0

x^2-2x=0

Taking x common

x(x-2)=0

x=0 and x-2 =0

x=0 and x= 2

Verify solutions

putting x=0

x+4/6(0) = 1/0

the solution is undefined.

Putting x = -2

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

2+4/12 = 1/2

6/12=1/2

1/2=1/2

the solution is defined.

The solutions is x=2 as for x=0 the solution is undefined.

So, Option C is correct.

Answer:

2x

Step-by-step explanation:

(f*g)(x) = f(x)*g(x)=x*2

ANSWER

[tex](f \times g)(x) = 2x[/tex]

EXPLANATION

The given functions are

[tex]f(x) = x[/tex]

and

[tex]g(x) = 2[/tex]

We want to find

[tex](f \times g)(x) = f(x) \times g(x)[/tex]

This means we need to multiply the two functions to get:

[tex](f \times g)(x) = x \times 2[/tex]

This will simplify to

[tex](f \times g)(x) = 2x[/tex]

The correct answer is A

Answer:

should have multiplied before dividing the real answer is 15

Answer:

B. Her answer is incorrect. She should have multiplied before dividing.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First part of the second factor.

Start by noticing that you are not going to get 7s^2 with the factor you have. So the first thing to do is to write the second factor as

(s + 3)  (7s

Sign

The next problem is to figure out what the sign following the 7s is. The 12 holds the answer to that.

12 is positive. So what ever follows must also be positive. Otherwise you will get a negative for the 12.  So now you have

(s + 3)(7s +

What comes after the Plus Sign?

Last step. you need a number that when multiplied by 3 will give you 12. That has to be 4

(s + 3)(7s + 4) This is your answer.

Answer:

y < x + 7

Step-by-step explanation:

[tex]x^2=4\Longrightarrow x=4^{2^{-1}}=4^{\frac{1}{2}}=\sqrt{4}=\boxed{2}[/tex]

So the first one is correct which implies that the third one is also correct.

But these are not the only ones.

[tex]

2x=2\Longrightarrow x=\dfrac{2}{2}=\boxed{1}

[/tex]

The last one is also correct.

Hope this helps.

r3t40

The probability of a student chosen randomly from the class playing basketball or baseball is 0.84.

The probability that a student chosen randomly from the class plays basketball or baseball can be found using the principle of inclusion-exclusion. First, we add the number of students who play basketball (17) and baseball (10) together, which gives us a total of 27 students. However, we have double-counted the 6 students who play both sports, so we subtract that number from the total. Therefore, the number of students who play basketball or baseball is 27 - 6 = 21. The probability is then calculated by dividing the number of students who play basketball or baseball by the total number of students in the class: 21/25 = 0.84.

Answer:

Range = (-∞,0) U (0,∞)

Step-by-step explanation:

The given function is:

f(x) = (x-1)²/x³-2x²+x

We can reduce the denominator:

= (x-1)²/x(x²-2x+1)

we know that a²-2ab+b² = (a-b)²

= (x-1)²/x(x-1)²

= 1/x

The function 1/x is undefined for x = 0.

Hence, its domain lies in (-∞,0) U (0,∞).

Hence x can either be less than or greater than zero.

The function f(x) is greater than zero when x<0.

The function f(x) is less than zero when x>0.

There is no way the function can be zero because the numerator is constant.

Hence the domain of the function lies in the interval:

(-∞,0) U (0,∞)

Answer:

-20

Step-by-step explanation:

If Jeneesa started with, 0 points and she earned 50, then she would have 50. If she lost 80 points, she would go into the negatives. She would be at -30, and when she earned 10 more points, she would be at -20.

I don't know what your options look like, but look at the one(s) with -20 at the end and figure out what one best fits my explanation (and the numbers I use)!

The response explains how to represent Janeesa's ending score on a number line after earning and losing points in a game.

The number line that shows Janeesa’s ending score in the game is as follows:

Start at 0 points

Earn 50 points - Move to 50 points

Lose 80 points - Move back to -30 points

Earn 10 points - Move to -20 points

Her ending score on the number line would be -20 points.

Answer: [tex]158cm^2[/tex]

Step-by-step explanation:

You can use the following formula to calculate the surface area of the right rectangular prism:

[tex]SA = 2(wl +lh + hw)[/tex]

Where "w" is the width, "l" is the length, and "h" is the height.

Knowing that this rigth rectangular prism  has a length of 8 centimeters, a width of 3 centimeters and a height of 5 centimeters, you can substitute these values into the formula.

Then, the surface of the right rectangular prism is:

[tex]SA = 2[(3cm*8cm) + (8cm*5cm) + (5cm*3cm)]\\\\SA=158cm^2[/tex]

Answer:

Surface area of prism = 158 cm²

Step-by-step explanation:

Points to remember

Surface area of rectangular prism = 2(lb + lh + bh)

Where l - Length, b - Breadth and h - Height

To find the surface area of prism

Here l = 8 cm, b = 3 cm and h = 5 cm

Surface area = 2(lb + lh + bh)

 = 2[(8*3)  + (8 * 5) + (3 *5)]

 = 2[24 + 40 + 15]

 = 2 * 79

 =158 cm²

Surface area of prism = 158 cm²

Answer:

its y is less than -7

Step-by-step explanation:

Answer:

y > -7

Step-by-step explanation:

multiply both sides by -1, remember to reverse the inequality when multiplying (or dividing by -1 on both sides

Hence:

-y (-1) >  7(-1) -----> remember to reverse inequality

y > -7 (answer)

Answer:

all five are dangerous

checking his phone while crossing the street

driving impaired

driving unbuckled

hiking alone

not wearing safety goggles

All the situations described - Distracted walking, Drinking and driving, Not wearing a seatbelt, Hiking alone, and Not wearing safety goggles in a possibly hazardous environment - are dangerous.

All of the scenarios given can be considered as dangerous. Distracted walking, as portrayed by Dan who checks his cell phone while crossing the street, risks accidents because the person is not fully aware of his surroundings. Drinking and driving, like Enrique after a couple of beers, is extremely dangerous, often leading to severe accidents. Not wearing a seat belt while driving, regardless of the drive's duration, puts Emily in danger. Anita's situation where she is hiking alone can be dangerous due to the risk of injury, and going without help or immediate assistance. Lastly, Lorena's situation is hazardous because safety goggles are crucial for protecting the eyes during a science presentation, especially if it involves chemicals or physical contraptions.

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Answer:

5

Step-by-step explanation:

It's a right triangle so 7x + 11x = 90

Solve for x

7x + 11x = 90

18x = 90

  x = 5

Answer:

F

Step-by-step explanation:

√10 = 3.16

hence the point must be larger than 3.1 and smaller than 3.2

Only F satisfies this condition.