In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, if a=2 root3 , c=2b

Using complex numbers, you can have negative squares, since [tex] i^2=-1 [/tex]

So, you can find the solutions to

[tex] x^2+20=0 \iff x^2 = -20 \iff x=\pm\sqrt{-20}=\pm i \sqrt{20}=\pm 4i\sqrt{5} [/tex]

So, using the factorization [tex] (x-x_1)(x-x_2) [/tex] where [tex] x_{1,2} [/tex] are the roots of the quadratic equation, you have

[tex] x^2+20 = (x-4i\sqrt{5})(x+4i\sqrt{5})[/tex]

This expression can't be further factorized, because all terms have degree 1.

To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.

To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.

Using the quadratic formula, we start by finding the values of x that satisfy the equation x^2 + 20 = 0.

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 1, b = 0, and c = 20. Substituting these values into the quadratic formula, we get: x = ± √-20.

Since we are factoring over the complex numbers, we can express the solution as: x = ± √20i.

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(2, 0) would be the new x - intercept.

The equation of a parabola can be written in vertex form as:

y = a(x - h)² + k

Here, h represents the x-coordinate of the vertex. The x-intercepts of the parabola are the points where the parabola crosses the x-axis (i.e., where y = 0).

Given that one x-intercept is at (-4, 0), we know that x-intercepts are symmetrically located around the vertex. If the vertex's x-coordinate h is increased by 6, the entire parabola shifts horizontally to the right by 6 units.

Since the x-intercept is affected by the shift in the vertex:

Before the shift: one of the x-intercepts is at -4.

After the shift by h, the new x-intercept will be located 6 units to the right of the original intercept.

Therefore, the new x-intercept will be at:

-4 + 6 = 2

(3x^2 + 2x + 7X^3) + (10x^2 + 6x + 9)

Combine all the like terms.

There is only one term with X^3 so that stays the same.

Add 3X^2 and 10x^2 to get 13x^2.

Add 2x and 6x to get 8x.

There is only one term with a variable, so that also stays the same.

Now place them in order from highest exponent to lowest:

7x^3 + 13x^2 + 8x + 9

The answer is A.

Solution :

Given that in the right triangle , ∠A=30° and AB = 12√3 .

As the figure is missing and its not clearly mentioned that AB is the base or hypotenuse of the right triangle. So two cases arises-

Case 1: AB is the base for ∠A of  the right triangle (as shown in figure 1).

As we know from the trigonometric ratio that, [tex]cos(\theta) = \frac{base}{hypotenuse}[/tex]

Here , AB is the base and AC is the hypotenuse , and ∠A=30°

[tex]\Rightarrow cos(30)=\frac{AB}{AC} \\\\\Rightarrow AC=\frac{AB}{cos(30)}[/tex]

The value of [tex]cos(30)=\frac{\sqrt{3} }{2}[/tex]

[tex]\Rightarrow AC=12\sqrt{3}\times\frac{2 }{\sqrt{3} }\\\\\Rightarrow AC=24[/tex]

Hence, AC is 24 unit long.

Case 2: AB is the hypotenuse for ∠A of  the right triangle (as shown in figure 2).

As we know from the trigonometric ratio that, [tex]cos(\theta) = \frac{base}{hypotenuse}[/tex]

Here , AB is the hypotenuse and AC is the base, and ∠A=30°

[tex]\Rightarrow cos(30)=\frac{AC}{AB} \\\\\Rightarrow AC=AB\timescos(30)[/tex]

The value of [tex]cos(30)=\frac{\sqrt{3} }{2}[/tex]

[tex]\Rightarrow AC=12\sqrt{3}\times\frac{\sqrt{3}}{2}\\\\\Rightarrow AC=18[/tex]

Hence, AC is 18 unit long.

The digit in the hundred millions place is 9.

Final answer:

The digit in the hundred-millions place of the number 875,932,461,160 is 7.

Explanation:

The digit in the hundred-millions place of the number 875,932,461,160 is 7. Let's break down the places of the number:

So in the number 875,932,461,160, 7 is the digit in the hundred-millions place.

∠C and ​ ∠D ​ are vertical angles

so <C = <D because vertical angles are equal

Substitute

−3x + 58  = x−2

Solve for x

Subtract x from both sides

-4x + 58 = - 2

Subtract 58 from both sides

-4x = - 60

Divide both sides by -4

x = 15

<D = x−2  = 15 - 2 = 13

Answer

<D = 13°

Answer:

The measure of angle D is 13°

Step-by-step explanation:

-3x+58=x-2

+3x to each side

58=4x-2

Add 2 to each side

60=4x

Divide each side by 4

X=15

Now substitute that in:

-3(15)+58=13

(15)-2=13

The measure of angle D is 13°

Answer : A

Example: 5 × 8 = 40

A.  8 × 5 = 40

the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here applies commutative property of multiplication.

B.  10 × 4 = 40

the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here it does not applies commutative property of multiplication.

C.  20 × 2 = 40

the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here it does not  applies commutative property of multiplication.

The answer is 32 Why?

Because since it's getting added by times 2 for every number the number after 16 would be 32 when doing 16 x 2 and since the last number being -16 was negative the number after it would be positive, also if you want it more straight forward the 32 cannot be negative because when you times a negative with a positive you get a positive. Hope this helps!  

If you distribute the multiplication, your function is written as

[tex] y=f(x)=3x-6 [/tex]

Like every function in the form [tex] y = mx+q [/tex], this function represents a line. A line has no vertex and no axis of symmetry (actually, it is symmetric with respect to every perpendicular line).

The number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number.

Total letters = 26

Total numbers = 10

As the repetitions are allowed.

Number of ways = 26×26×26×10×10×(26+10)

N=63,273,600 Ways

P(abc123 or 123abc) = P(abc123)+P(123abc) - P(abc123 and 123abc)

The intersection of abc123 and 123abc is zero because both license plates are not possible at a time

P(ABC123 or 123ABC)=P(ABC123)+P(123ABC)

[tex]\rm P=\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}\dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8} + \dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8}\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}[/tex]

P= 2/5616000

or

P = 1/2,808,000

Thus, the number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

Learn more about the probability here:

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we are given

[tex]f(x)=2x^4-x^3+x-2[/tex]

we can check each options

option-A:

-1,1

we can plug x=-1 and x=1 and check whethet f(x)=0

At x=-1:

[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]

[tex]f(-1)=0[/tex]

At x=1:

[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]

[tex]f(1)=0[/tex]

so, this is TRUE

option-B:

0,1

we can plug x=0 and x=1 and check whethet f(x)=0

At x=0:

[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]

[tex]f(0)=-2[/tex]

At x=1:

[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]

[tex]f(1)=0[/tex]

so, this is FALSE

option-C:

-2,-1

we can plug x=-2 and x=-1 and check whethet f(x)=0

At x=-2:

[tex]f(-2)=2(-2)^4-(-2)^3+(-2)-2[/tex]

[tex]f(-2)=36[/tex]

At x=-1:

[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]

[tex]f(-1)=0[/tex]

so, this is FALSE

option-D:

-1,0

we can plug x=-1 and x=0 and check whethet f(x)=0

At x=-1:

[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]

[tex]f(-1)=0[/tex]

At x=0:

[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]

[tex]f(0)=-2[/tex]

so, this is FALSE

The original price of the computer was $411. This was found by adding the reduction amount to the final price, i.e., $355 + $56.

This question is concerned with a simple arithmetic operation. It's provided that the price of the computer was reduced by $56 to $355. The original price should thus be the markdown plus the final price.

Performing this calculation:
Add the amount of reduction ($56) to the current price ($355).

The solution is:
$355 (final price) + $56 (reduction) = $411 (original price)

Therefore, the original price of the computer was $411

So, option D is ($411) correct .

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Algebraically, you have to factor the square root of 7 to see why you're wrong:

[tex] 3\sqrt{7}-\sqrt{7} = \sqrt{7}(3-1) = 2\sqrt{7} [/tex]

Conceptually, think that any object - say an apple - represents the square root of seven.

So, you have three apples, and you take away one apple. You have two apples remaining, i.e. [tex] 2\sqrt{7} [/tex]

[tex]3\sqrt{7} - \sqrt{7}[/tex]

Let x represent [tex]\sqrt{7}[/tex], then you can rewrite the expression as 3x - x.

3x - x = 2x.  Now replace "x" with  [tex]\sqrt{7}[/tex] and you get 2[tex]\sqrt{7}[/tex].

The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.

Answer:

4606.48 $

Step-by-step explanation:

Amount invested P = 3500 $

Rate of interest r = 6.12%

Compounding monthly

Monthly rate of interest = 6.12/12 =0.51%

Time = 4.5 years = 4.5 (12) = 54 months

Hence final amount would be

P(1+0.01r)^t

Here r = 0.51 and t = no of months = 54

Hence final amount

= 3500(1.0051)^54

= 3500(1.31613)

=4606.48 $

Thus 3500 if invested now will become 4606.48 in 4.5 years at the rate of interest of 6.12% compounding monthly.

That triangle has a horizontal base with y=2.  The length of that base is RS=1-(-4)=1+4=5.  The height of the triangle is the vertical distance  from line y=2 to T(-5,-4).  That height is  2-(-4)=2+4=6.  The area of the triangle is  base * height/2 = 5*6/2= 15

The answer is 15 units ^2

Answer:

The answer is 15 units².

Step-by-step explanation:

I am a hundred percent sure. I did the math and got it right on my test.

1.  2a=9b  first we will divide the both sides with parameter b and get

2(a/b)=9 now we will divide both sides with number 2 and get

a/b=9/2 => a : b = 9 : 2

2. 6a-3b=5b first we will add to both sides number (+3) and get

6a=5b+3b => 6a=8b then divide the both sides with parameter b and get

6(a/b)=8 now we will divide the both sides with number 6 and get

a/b=8/6 if we simplify the fraction we get  

a/b=4/3 => a : b = 4 : 3

3.  a+b=3b we will add to the both sides parameter (-b) and get

a=3b-b => a=2b then divide the both sides with parameter b and get

a/b=2 => a/b=2/1 => a : b = 2 : 1

4.  a/5=b/7 first we will divide the both sides with paremeter b and get

a/(5b)=1/7 now we will multiply the both sides with number 5 and get

a/b=5/7 => a : b = 5 : 7

Good luck!!!

The ratio a:b in the four problems given are 9:2, 4:3, 2:1, and 5:7 respectively. This is achieved by isolating 'a' in each equation and simplifying the resulting expression.

Let's find the ratio between a:b for each of the problems you've provided:

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Isolate the x. Note the equal sign. What you do to one side, you do to the other. First, add 1/3y to both sides

8x - 1/3y (+1/3y) = 15 (+1/3y)

8x = 15 + 1/3y

Divide 8 from both sides

(8x)/8 = (15 + 1/3y)/8

x = 15/8 + 1/24y

x = 1/24y + 1.875

x = 1/24y + 1.875 is your answer

hope this helps

B. is the graph that fills the requirements

Graph2 with slope of 25 is the graph that shows the relationship on the table.

To find the equation of the line passing through points A(3, 75) and B(12, 300) follow these steps:

1. Calculate the slope m:

m = (y₂ - y₁)/x₂ - x₁)

m = (300 - 75)/(12 - 3)

m = 225/9

m = 25.

Graph2 with same slope as the calculated slope is the graph that shows the relationship on the table.

2. Use the point-slope form with one of the points (e.g., A(3, 75)

y - y₁ = m(x - x₁)

y - 75 = 25(x - 3)

3. Simplify the equation:

y - 75 = 25x - 75.

4. Isolate y

y = 25x.

So, the equation of the line passing through points A(3, 75) and B(12, 300) is y = 25x

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The tax on a $9.95 purchase with a 6.8% tax rate, rounded to the nearest hundredth, is approximately $0.68.

To calculate the tax on a purchase, you can multiply the purchase amount by the tax rate. In this case, $9.95 is being multiplied by 6.8% (or by 0.068 as a decimal). So, the calculation would look like this: $9.95 * 0.068 = $0.6766. However, the question asks to round to the nearest hundredth. So, the final tax would be approximately $0.68.

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2x+50=7x

50 = 5x

x = 10

2(10) + 50

20 + 50

= 70 degrees

Given that Bart and Melinda are grand children and Bart lives

6 blocks from his grand parents.

Also given that Melinda lives 8 blocks farther from her grandparents as Bart does .

This means Melinda lives 6+8 = 14 blocks from her grand father house

This question involves addition because farther as Bart does means , Melinda lives 8 +6 hence we get 14

Answer is: Melinda lives 14 blocks from her grandfathers

I think your answer is B.

Answer:

Quadratic, because the height increases and then decreases.

Step-by-step explanation:

In an exponential function, the graph will either increase or decrease over the entire domain.  It does not change direction.

We can see from the table that the heights increase and then decrease; this means it cannot be an exponential function.

A quadratic function has a graph that is u-shaped.  It will start out either increasing or decreasing, and then after the maximum or minimum is reached, it changes direction.

We can see from the table that this is what the heights do; this means it is a quadratic function.

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

[tex]P(\text{ getting a commemorative stamp})=0.16[/tex]

and

[tex]P(\text{getting a special delivery stamp})=0.18[/tex]

So, we need to find,

[tex]P(\text{getting either a commemorative or a special delivery stamp})\\=P(\text{getting a commemorative stamp})+P({\text{ getting a special delivery stamp})[/tex]

(∵they are independent events .)

[tex]P(\text{getting either a commemorative or a special delivery stamp})\\=0.16+0.18\\=0.34[/tex]

So, option 'D' is correct.

Each friend received 10 ounces of pears after Dillion divided the 3 1/3 pound bag among them.

First, we need to convert the weight of the pears from pounds and thirds to decimal form.

To do this, we divide the 3 1/3 pounds by 16 (since there are 16 ounces in a pound):

3 1/3 pounds = 3 * (1 + 1/3) pounds = 3.333 pounds

Now we know that each friend received 3.333 pounds / 5 friends = .6666 pounds of pears. To convert this decimal into something more understandable, multiply it by 16 since there are 16 ounces in a pound:

.6666 pounds * 16 = 10 ounces

So, each friend received 10 ounces of pears.

Each friend received 10 ounces of pears after Dillion divided the 3 1/3 pound bag among them.

First, we need to convert the weight of the pears from pounds and thirds to decimal form.

To do this, we divide the 3 1/3 pounds by 16 (since there are 16 ounces in a pound):

3 1/3 pounds = 3 * (1 + 1/3) pounds = 3.333 pounds

Now we know that each friend received 3.333 pounds / 5 friends = .6666 pounds of pears. To convert this decimal into something more understandable, multiply it by 16 since there are 16 ounces in a pound:

.6666 pounds * 16 = 10 ounces

So, each friend received 10 ounces of pears.

its (a.) thats  it try it

D

a direct linear variation equation has the form f(x) = kx

f(x) = x - 12 is not in this form thus does not show a direct linear variation