Find the distance between the two points. (-2,-4), (4,1)


61
11
Square Root 61
Square root 22

Answer:

-3x

Step-by-step explanation:

    x                            x

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

x^2 -4x + 4            x^2-3x+2

          x                            x

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

   (x -2)^2            (x - 2)(x - 1)

       x (x-1)  - x(x +2)                       

= ----------------------------

         (x -2)^2 (x - 1)

     x^2 -x -x^2 - 2x                    

= --------------------------

     (x -2)^2 (x - 1)

          -3x                    

= -----------------------

     (x -2)^2 (x - 1)

Therefore; the missing term is -3x

Final answer:

Algebra and algorithm are mathematical terms originating from al-Khwarizmi, a prominent Arab mathematician.

Explanation:

Algebra and algorithm are two mathematical terms that originated from the Arabic mathematician al-Khwarizmi. Al-Khwarizmi's work in the ninth-century book 'ilm al-jabr wa'l-muqabala laid the foundation for these terms and significantly influenced the field of mathematics.

Answer:

Step-by-step explanation:

Answer:

cos(18°)=sin(72°)

Step-by-step explanation:

we know that

In a right triangle

cos(A)=sin(B)

If A and B are complementary angles

so

A+B=90°

In this problem

A=18°

B=90-18=72°

therefore

cos(18°)=sin(72°)

if the tax rate is 8.5% stan payed $7.22

Answer:

Stan paid $7.23 in tax

Step-by-step explanation:

8.5/100=t/85

85•8.5=100t

722.5=100t

722.5/100=t

7.225=t

Answer:   [tex]\bold{c)\quad f^{-1}(x)=\dfrac{ln(x)}{2}}[/tex]

Step-by-step explanation:

Inverse is when you swap the x's and y's and solve for y. Note: f(x) is y

[tex]y=e^{2x}\\\\\text{Swap the x's and y's:}\\x=e^{2y}\\\\\text{Apply ln to both sides:}\\ln\ x=ln\ e^{2y}\\\\\text{ln e cancels out}\\ln\ x=2y\\\\\text{Divide both sides by 2:}\\\dfrac{ln\ x}{2}=y[/tex]

Answer:

  |x-4| +|y-5|=0

Step-by-step explanation:

There are many equations that will graph as the point (x, y) = (4, 5). One of them is ...

|x-4| +|y-5| = 0

Let's do this in steps, show your work!

#1. We need to move all terms to one side.

x^2 - 7x = 0

#2. Then factor out the common term x.

x(x - 7) = 0.

#3. Simplify to get..

x = 0, 7.

If you need help with any other question let me know.

Answer:

B) 2x + 18 = 100

Step-by-step explanation:

Given: Perimeter = 100 feet and width = 9 ft

We know that the perimeter of a rectangle = 2(length + width)

Let "x" be the length of the rectangle.

Plugging in the given values in the above formula, we get

100 = 2(x + 9)

On the right hand side, we can use the distributive property a(b + c) = ab + ac

and expand.

100 = 2x + 2*9

100 = 2x + 18

This is same as 2x + 18 = 100

Therefore, the answer is B) 2x + 18 = 100

Fencing a garden would be Perimeter because your trying to find how much fencing you would need so you can surround the garden.

The area of the garden is how much space there is. Ex. 5ft×9.5ft=47.5ft² . The 5ft would be the length of the garden, and the 9.5ft would be the width. But to find area, you would need to do L×W, or 5ft×9.5ft in this case for area.

But to find Perimeter, you need to do L+L+W+W. If we use the numbers from before for the area example, you would be doing 5ft+5ft+9.5ft+9.5ft, you would be getting 29ft.

If you want the definitions to better understand this, here they are:

Perimeter: the total distance around the edge of the figure.

Area: the number of unit squares that can be contained within it.(hence the reason "²" was at the end of the total in the example for area I provided.)

Answer:

Option B. 3 bags

Step-by-step explanation:

step 1

Find the area of the flower bed

The area of the flower bed is the area of a triangle

A=(1/2)bh=(1/2)(20)(6)=60 m^2

step 2

Divide the area by 20 square meters to find the number of bags of topsoil

(60)/(20)=3 bags

Answer:

B. 3 Bags

Step-by-step explanation:

Because the formula is rise over run, it would be 3/12, and simplified is 1/4.

Answer:

D. 21

Step-by-step explanation:

28-21=7

28-7=21

92%. 23 divided by 25 is .92 pretty much meaning he got a 92 on that math test (A-)

Devon answered 92% of the problems that were applied on test correctly.

Percentage is a way of expressing a proportion or a fraction as a portion of 100. It is commonly used to compare quantities, indicate relative amounts, or express the part-to-whole relationship.

The term "percent" originates from the Latin phrase "per centum," meaning "by the hundred." It is represented by the symbol "%".

We know that;

Percent = Correct answers/Total answers * 100/1

= 23/25 * 100/1

92%

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Answer:

The answer is D

Step-by-step explanation:

4.8 times 0.5 equals 2.4+ 1.2 = 3.6 which is the total number of miles he ran/walked

Hope it helped!

Answer:

For two points (x,a) and (x,b), the distance would be |a-b| or |b-a| both would be the same.

Step-by-step explanation:

What is the rule without an absolute value?  basically we are looking for the difference (which is the answer to a subtraction problem) between the two.

Say the two points are (x,a) and (x,b)  So they have the same x value but different y values.  Now, when you want to take the difference you usually want to subtract the smaller number from the larger, but hat happens if you don't?  So instead subtract the larger number from the smaller number?  I'm gonna show a few examples.

7-5 = 2

5 - 7 = -2

7 - 3 = 4

3 - 7 = -4

As you can see, no matter which order you subtract you will always get the same number, just either positive of negative.  We are going to use that.  Basically, we can have the two in either order, as long as we have them inside of an absolute value, we will always get the same answer.

so, for our two y values, a and b, it doesn't matter which is larger |a-b| = |b-a| and this is the distance.  

The distance between two points that have the same x-coordinate on a coordinate plane can be calculated by taking the absolute difference of their y-coordinates. This calculation will always yield a positive value, reflecting the fact that distance is a scalar quantity.

The distance between two points with the same x-coordinate on a coordinate plane (i.e., two points on a vertical line) can be determined using absolute value. If these points have y-coordinates of y1 and y2, the distance between them (d) is the absolute difference of their y-coordinates. Mathematically, this is expressed as:

d = |y2 - y1|

Here, the symbol '|' surrounding the difference represents the absolute value, which makes any negative result positive. For example, if we have points A(3, 4) and B(3, 1), using our rule, the distance between these points would be |1 - 4| = |-3| = 3 units.

This absolute value method ensures that the distance is always a positive number, regardless of whether y2 is bigger than y1 or not. This essentially reflects the basic principle of distance being a scalar (having only magnitude but not direction).

Answer:

l = 9 cm

b = 7 cm

h = 3 cm

Step-by-step explanation:

Formula:-

Volume of cuboid = lbh

l - Length of cuboid

b - breadth of cuboid

h - Height of cuboid

To find the dimensions of prism

Here prism is like a cuboid.

Volume of prism = 189 cm^3

Height h = 3 cm

Volume = lbg

189 = l * b* 3

l * b = 189/3 = 63 = 9 * 7

Therefore l and b may be 9 and 7

Answer:

Alan: 200 m/min

Brian: 150 m/min

Step-by-step explanation:    

Given : Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes.

To find : What are their rates, in meters per minute?

Solution :

Let n represent the number of laps that Alan completes in 9 minutes.

Then n-1 is the number of laps Brian completes.

45 seconds = 3/4 minutes.

The difference in their lap times in minutes per lap is

[tex]\frac{9}{(n -1)}-\frac{9}{n} =\frac{3}{4}[/tex]

Solving the equation we get,

[tex]\frac{9n-9n+9}{n(n -1)} =\frac{3}{4}[/tex]

[tex]9\times 4=3\times n(n -1)[/tex]

[tex]36=3\times n(n -1)[/tex]

[tex]n^2-n-12=0[/tex]

[tex]n^2-4n+3n-12=0[/tex]

[tex]n(n-4)+3(n-4)=0[/tex]

[tex](n-4)(n+3)=0[/tex]

[tex]n=4,-3[/tex]

Neglecting n=-3

So, n=4

Then Alan's speed in m/min is

[tex]S=\frac{D}{T}[/tex]

[tex]S_a=\frac{4\times 450}{9}[/tex]

[tex]S_a=200 m/min[/tex]

Brian completes 3 laps in that 9-minute time, so his rate is

[tex]S_b=\frac{3\times 450}{9}[/tex]

[tex]S_b=150 m/min[/tex]

Therefore, Alan: 200 m/min

Brian: 150 m/min

Answer:

The correct answer is (FALSE)

Step-by-step explanation:

(APEX)

The statement is false. Credit Unions are subject to federal regulations and are overseen by the National Credit Union Administration (NCUA) in the United States.

The statement, 'Credit unions are not subject to federal regulations,' is False. Credit unions, like other financial institutions, must adhere to several federal regulations. The National Credit Union Administration (NCUA) is the federal agency that charters and supervises federal credit unions in the United States. Among other duties, it's their role to administer the National Credit Union Share Insurance Fund (NCUSIF), which provides deposit insurance for credit union members, much like the FDIC does for bank customers.

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♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷To find the area you need to multiply length and width.

45*25 = 1125 square inches for the area

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ To find the area of the floor, you need to multiply the length and the width.

Width:25 inches

Length:45 inches

Multiply: 45*25=1125

Final answer:

1125 square inches

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

The given system of equations has equivalent equations, hence it has infinitely many solutions. The best answer to the question is option A.

The system of equations presented in the question is:

4x + 5y = 7

8x + 10y = 14

These two equations are equivalent, meaning they are different forms of the same equation. This is because the second equation is just the first one multiplied by 2. When two or more equations are equivalent in a system, it means that they intersect at infinitely many points, hence they have infinitely many solutions. Therefore, the best description for the solution to this system of equations is option A: The system has infinitely many solutions.

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As per the values, C. the system of equations has no solution.

To determine the solution to the system of equations, we can solve the equations using the method of elimination.

First, we can multiply the first equation by 2 to make the coefficients of x in both equations the same. This gives us the equations 8x + 10y = 14 and 8x + 10y = 7.

Subtracting these equations, we get 0 = 7 - 14, or 0 = -7.

Since this is not a true statement, the system of equations has no solution.

Therefore, the correct answer is C. The system of equations has no solution.

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Answer:

80

Step-by-step explanation:

times it all

Answer:

68 in^2

Step-by-step explanation:

Bottom and Top

base of parallelogram  = 4*4 = 16

Since there are two of them, the area = 2 * 16 = 32

left and right faces

I think you have to assume this is a  rectangle. We do not know the height for a parallelogram.

Area = l*w

Area = 4 * 2.5

Area = 10 in^2

But there are two of them.

Area = 2* 10 = 20 in^2

Front and back faces

The area is the area of a parallelogram

Area = b * h

Area = 2 * 4

Area = 8 in^2

But there are 2 of them

The area for 2 is 8*2 = 16 in^2

Total Area

Total Area = 16 + 20 + 32

Total Area = 68 in^2  

Answer:

A = 77.32

Step-by-step explanation:

Since this is a right triangle we can use trigonometric functions

sin  = opposite side/ hypotenuse

sin A =  80/82

sin A =40/41

Take the inverse sin of each side

sin^-1 (sin A ) =sin ^-1 (40/41)

A =77.31961651

Rounding to the nearest hundredth

A = 77.32

Answer:

77.32°

Step-by-step explanation:

Using cosine law:

80² = 18² + 82² - 2(18)(82)cos

cosA = 9/41

A = 77.31961651°

Answer:

The function is odd.

Step-by-step explanation:

A function is even if the graph of the function is symmetric with respect to the y-axis. A function is odd if the graph of the function is symmetric with respect to the origin. To find if the function is even or odd, we're going to graph the function using DESMOS.

As you can see in the attached picture, the function is symmetric with respect to the origin. Therefore, the function is odd.

Answer:

D) MNO

Step-by-step explanation:

A) and B) are over the y axis

C) is over both axes

D) is correct: it is a reflection over the x axis.

Answer:

The answer is D

Step-by-step explanation:

Answer: FIRST OPTION

Step-by-step explanation:

According the quotient of powers property, when you have the division of two powers with the same base, then you must subtract the exponents.

Therefore, keeping the property above on mind, you have that the quotient is the shown below:

[tex]\frac{(-7)^2}{(-7)^{-1}}=(-7)^{(2-(-1))}=(-7)^{(2+1)}=(-7)^3=-343[/tex]

Answer:

She needs 0,75 ft of wire

Step-by-step explanation:

Hello

She needs (0.30 ft)*(2.5) = 0,75

Best regards