What is the distance between points (16, -43) and (1, 51)?

Answer:1/4(1-3x)

Step-by-step explanation:

Answer:

[tex]\large\boxed{(5r+2)(3r-4)=15r^2-14r-8}[/tex]

Step-by-step explanation:

[tex](5r+2)(3r-4)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(5r)(3r)+(5r)(-4)+(2)(3r)+(2)(-4)\\\\=15r^2-20r+6r-8\qquad\text{combine like terms}\\\\=15r^2+(-20r+6r)-8\\\\=15r^2-14r-8[/tex]

Answer: Perimeter = 135 units      Area = 1200 Square units

Step-by-step explanation: I think you want the perimeter and area of XYZ so that's what I will answer for.

First, we are given that ABC and XYZ are proportional and that their longest sides are 24 units and 60 units respectively.

Using this, we can say XYZ = ABC * 5/2 (60/24 = 5/2)

Therefore, the other two sides of XYZ are 50 and 25.

We can get the perimeter using 60 + 50 + 25, that equals 135 units

Next, since the height of ABC was 8 units with 24 units being its base, it's likely safe to say the height = 1/3 base

We will apply with to triangle XYZ, height = 1/3 * 60 = 20

20 units * 60 units = 1200 square units

The perimeter and area of the ΔXYZ are 135 units and 600 sq. units. Where similar triangles are related by a scale factor.

The ratio of their respective sides of two similar triangles gives the scale factor. I.e.,

Consider ΔABC and ΔDEF are two similar triangles

Then its scale factor = DE/AB = EF/BC = DF/AC

The scale factor is also defined as follows:

(Scale factor)² = (Area of the triangle DEF)/(Area of the triangle ABC)

or

Scale factor = (perimeter of ΔDEF)/(perimeter of ΔABC)

Given that the sides of the triangle ABC are 10 units, 20 units, and 24 units. The longest side is 24 units.

The triangle XYZ has the longest side of length 60 units.

Since ΔABC ~ ΔXYZ

So, the ratio of their longest sides gives the scale factor. I.e.,

Scale factor = 60/24 = 2.5

The perimeter of the ΔXYZ is calculated by

Scale factor = (perimeter of the ΔXYZ)/(perimeter of the ΔABC)

⇒ 2.5 = (perimeter of the ΔXYZ)/(10 + 20 + 24)

⇒ perimeter of the ΔXYZ = 2.5 × 54

∴ the perimeter of the ΔXYZ = 135 units

The area of the ΔXYZ is calculated by

(Scale factor)² = (area of the ΔXYZ)/(area of the ΔABC)

So, the area of the ΔABC, whose height h = 8 units and base b = 24 units is

Area of the ΔABC = 1/2 × b × h

                              = 1/2 × 24 × 8

                              = 96 sq. units

Thus,

(Scale factor)² = (area of the ΔXYZ)/(area of the ΔABC)

⇒ (2.5)² =  (area of the ΔXYZ)/(96)

⇒  area of the ΔXYZ = (2.5)² × 96

∴  area of the ΔXYZ = 600 sq units

Thus, the perimeter and area of the ΔXYZ are 135 units and 600 sq. units.

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Answer:

18%

Step-by-step explanation:

We are given that the cost of a jacket increased from $95.00 to $112.10 and we are to find the percentage increase in the cost of the jacket.

We know that the formula of percentage increase if given by:

Percentage increase = (new value - initial value)/initial value × 100

So substituting the given values to get:

Percentage increase = [tex] \frac { 1 1 2 . 1 0 - 9 5 . 0 0 } { 9 5 . 0 0 } \times 1 0 0 [/tex] = 18%

Answer:

It is choice A.

Step-by-step explanation:

The general form is (x - h)^2 / a^2 + (x - k)^2/b^2 = 1 where (h, k) is the center, 2a = major axis and 2b = minor axis.

The ellipse in the question has a^2 > b^2 so the major axis is  parallel to the x axis.

The minor axis  which is parallel to the y-axis is of length 10 so b^2 = (1/2 * 10)^2

= 25 so we can eliminate C.

The center of the ellipse = the midpoint of a line joining the focii so it is:

( 3+ 7)/2,  6)

= (5,6).

As (h, k) is the center we have h = 5 and k = 6.

So it is choice A.

The equation of the eclipse will be [tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex]  i.e. option A.

The standard equation of the ellipse is [tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex].

Here,  

(h, k) is the center, and 2a and 2b are major and minor axis.

We have,

Length of minor axis = 10

i.e. 2b = 10

And,  b = 5

And,

Foci (c) located at (3,6) and (7,6),

i.e. Major axis is parallel to x-axis.   [Because y is constant]

And,

The foci (c) always lie on the major axis.

And,

c² = a² - b²

Now,

The center of an ellipse is the midpoint of both the major and minor axes, i.e.  the midpoint of a line joining the foci (c),

i.e. Center [tex]=( \frac{x_1 + x_2 }{2}, \frac{y_1 + y_2}{2}) =( \frac{3+7}{2}, \frac{6+6}{2}) =(5, 6)[/tex]

Now,

Foci (c) = 5 - 3 = 2

So,

c² = a² - b²

i.e.

2² = a² - 5²

4 =  a² - 25

⇒  a² = 29  

And, b² = 5² = 25

So,

h = 5 and k = 6

Now,

Putting the values in the standard form of equation of the ellipse,

i.e.

[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex]

i.e.

[tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex]

So, this is the equation of the eclipse i.e. option A.

Hence, we can say that the equation of the eclipse will be [tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex]  i.e. option A.

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Answer:

Step-by-step explanation:

(f · g)(x) = f(x) · g(x)

We have f(x) = 4x² and g(x) = x + 1. Substitute:

(f · g)(x) = (4x²)(x + 1)    use the distributive property

(f · g)(x) = (4x²)(x) + (4x²)(1)

(f · g)(x) = 4x³ + 4x²

Answer:

The coordinates of k' after k is rotated 90 degrees about the origin is (-1, -2)

From the question, we have the following parameters that can be used in our computation:

K = (-2, 1)

Transformation:

rotated 90 degrees about the origin

The rule of rotation by 90 degrees about the origin is represented as

(x,y)→(−y,x) .

Substitute the known values in the above equation, so, we have the following representation

K' = (-1, -2)

Hence, the image of K is (-1, -2)

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Answer: O^2= 71.36

               O=8.45  

Answer:

The complete question is attached.

To find the variance and deviation, we have to use their definition or formulas:

[tex]\sigma=\sqrt{\frac{\sum (x- \mu)^{2} }{N}}[/tex]

So, first we have to find the difference between each number and the mean:

76-81=-5

87-81=6

65-81=-16

88-81=7

67-81=-14

84-81=3

77-81=-4

82-81=1

91-81=10

85-81=4

90-81=9

Now, we have to elevate each difference to the squared power and then sum all:

[tex]25+36+256+49+196+9+16+1+100+16+81=785[/tex]

Then, we replace in the formula:

[tex]\sigma=\sqrt{\frac{785}{11}} \approx 8.45[/tex]

The variance is just the squared power of the standard deviation. So:

[tex]\sigma^{2}=(8.45)^{2}=71.40[/tex]

When a line is represented in the slope intercept formula as in the question you must remember that it is always set up like so...

y = mx + b

m is the slope and b is the y-intercept of the line

Since in the equation y = -3x + 1 the m is -3 then the slope is -3

Hope this helped!

~Just a girl in love with Shawn Mendes

Not enough information, please attach a photo next time.

Answer:

3 b^5 c^5

Step-by-step explanation:

3•b•b•b•b•b•c•c•c•c•c

There is 1 number 3  = 3

There are 5 letter b   = b^5

There are 5 letter c  = c^5

3 * b^5 * c^5

3 b^5 c^5

Answer:

In 3•b•b•b•b•b•c•c•c•c•c, there is one three, five b's, and five c's. By simplifying the expression, we get 3[tex]b^{5}c^{5}[/tex].

Answer:

The functions ordered from least to greatest y-intercept are

1) h(x) -----> y-intercept -1

2) g(x) ----> y-intercept 1

3) f(x) ----> y-intercept 2

Step-by-step explanation:

we know that

The y-intercept (or initial value) is the value of y when the value of x is equal to zero

Part 1) Find the y-intercept of g(x)

Remember that the initial value of the fuction is equal to the y-intercept

a=1 -----> is the initial value

therefore

The y-intercept of g(x) is 1

Part 2) Find the y-intercept of f(x)

Observing the table

For x=0

f(x)=2

therefore

The y-intercept of f(x) is 2

Part 3) Find the y-intercept of h(x)

Observing the graph

For x=0

h(x)=-1

therefore

The y-intercept of h(x) is -1

Answer:

1 3 2

Step-by-step explanation:

ANSWER

[tex]\frac{ {y}^{2} }{ 25} - \frac{ {x}^{2} }{ 64} = 1 [/tex]

EXPLANATION

The given hyperbola has a vertical transverse axis and its center is at the origin.

The standard equation of such a parabola is:

[tex] \frac{ {y}^{2} }{ {a}^{2} } - \frac{ {x}^{2} }{ {b}^{2} } = 1 [/tex]

Where 2a=10 is the length of the transverse axis and 2b=16 is the length of the conjugate axis.

This implies that

[tex]a = 5 \: \: and \: \: b = 8[/tex]

Hence the required equation of the hyperbola is:

[tex]\frac{ {y}^{2} }{ {5}^{2} } - \frac{ {x}^{2} }{ {8}^{2} } = 1 [/tex]

This simplifies to,

[tex]\frac{ {y}^{2} }{ 25} - \frac{ {x}^{2} }{ 64} = 1 [/tex]

Answer:

[tex]\frac{(y^2}{25}-\frac{x^2}{64}=1[/tex]

Step-by-step explanation:

We have been given an image of a hyperbola. We are asked to write an equation for our given hyperbola.

We can see that our given hyperbola is a vertical hyperbola as it opens upwards and downwards.

We know that equation of a vertical hyperbola is in form [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex], where, [tex](h,k)[/tex] represents center of hyperbola.

'a' is vertex of hyperbola and 'b' is co-vertex.

We can see that center of parabola is at origin (0,0).

We can see that vertex of parabola is at point [tex](0,5)\text{ and }(0,-5)[/tex], so value of a is 5.

We can see that co-vertex of parabola is at point [tex](8,0)\text{ and }(-8,0)[/tex], so value of b is 8.

[tex]\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{8^2}=1[/tex]

Therefore, our required equation would be [tex]\frac{(y^2}{25}-\frac{x^2}{64}=1[/tex].

Answer:

x = 5

Step-by-step explanation:

Since the triangle is right with hypotenuse of 13

Use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 12² = 13²

x² + 144 = 169 ( subtract 144 from both sides )

x² = 25 ( take the square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

As we know the given points

Center = (5, -4)

and

Point on circle = (-3,2)

The distance between point on circle and center will give us the radius of circle

So,

The formula for distance is:

[tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10[/tex]

The standard form of equation of circle is:

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where h and k are the coordinates of the center. So putting in the value:

[tex](x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100[/tex]

Answer:

gets smaller.

Step-by-step explanation:

Quick Answer

To give you a short quick answer, the supplement is going to have to decrease or get smaller.

Example

Suppose the acute angle is 10 (anything under 90 will do).

Then the supplement is going to be 180 - 10 = 170

Now suppose the acute angle increase to 50 degrees.

That means the supplement will go from 180 - 50 = 130

Conclusion

As the acute angle gets bigger, the supplement gets smaller. This is an important idea to get clear. Bigger and Smaller or More or Less can be ugly little words, so anytime you come across them, pay attention. It will make your life in science so much easier.

Answer:

5th term is 35a^4b^3

Step-by-step explanation:

We need to find the 5th term in binomial expansion (a+b)^7

The binomial theorem is:

[tex](x+y)^n = \sum_{n=0}^{k} {n\choose k}x^ky^{n-k}[/tex]

We are given

x=a,

y =b

n=7

and k= 4 since we have to find 5th term but k starts from zero

putting the values

[tex]={7\choose 4}a^4b^{7-4}\\={7\choose 4}a^4b^{3}\\=\frac{7!}{4!(7-4)!}a^4b^3\\=35a^4b^3[/tex]

So, 5th term is 35a^4b^3

Answer:

On Apex

Step-by-step explanation:

35a^4 b^3

Answer:

2z + 6

Step-by-step explanation:

Since nothing can be done with the brackets we can take those out. We would end up with

z + z + 6

As you can see we have two z's and we can add those together. This would give us our answer:

2z + 6

Answer:

Part 1) The inequality that describes the relationship between the number of cookies each one of them has is [tex]x^{2} -30x+224\geq 0[/tex]

Part 2) Jessica has at least 2 cookies more than Martha

Step-by-step explanation:

Part 1) Find the inequality that describes the relationship between the number of cookies each one of them has

Let

x----> the number of cookies when Jessica started

30-x ----> the number of cookies when Martha started

we know that

Each of them ate 6 cookies from their bag

so

The cookies left in each bag are

(x-6)  ----> Jessica

and (30-x-6)=(24-x) ---> Martha

The product is equal to (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

so

[tex](x-6)(24-x)\leq 80\\ \\24x-x^{2}-144+6x\leq 80\\ \\-x^{2} +30x-144-80\leq 0\\ \\-x^{2} +30x-224\leq 0[/tex]

Multiply by -1 both sides

[tex]x^{2} -30x+224\geq 0[/tex]

Part 2) Solve the quadratic equation

[tex]x^{2} -30x+224\geq 0[/tex]

Solve by graphing

The solution is x=16 cookies

so

(30-x)=30-16=14 cookies

therefore

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

The number of cookies left in each bag  is equal to

Jessica

16-6=10 cookies

Martha

14-6=8 cookies

Jessica has at least 2 cookies more than Martha

part 1- 30

part 2- 2

To simplify it at least those are the answers

Answer:

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

(x₁, y₁) - point

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

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The general fom of an equation of a line:

[tex]Ax+By+C[/tex]

We have the equation 3x - 2y = 4 in standard form.

Answer:

f

Step-by-step explanation:

4x+3

x>1  x=2

4*2+3= 11

y>or = to 11

Common difference of a sequence is difference between any two consecutive terms in the sequence.

So let's pick up any two consecutive terms,

0 and 5,

difference between 0 and 5 is 5-0 = 5

so common difference is 5

[tex]

f(x)=x+1 \\

g(x)=\dfrac{1}{x} \\

(f\cdot g)(x)=(x+1)\dfrac{1}{x} \\

(f\cdot g)(x)=\underline{\dfrac{x+1}{x}} \\ \\

0=\dfrac{x+1}{x} \\

0=\dfrac{x}{x}+\dfrac{1}{x} \\

0=1+\dfrac{1}{x} \\

-1=\dfrac{1}{x} \\

-x=1 \\

x=1

[/tex]

ANSWER

[tex]y \ne1[/tex]

EXPLANATION

The given functions are

[tex]f(x) = x + 1[/tex]

and

[tex]g(x) = \frac{1}{x} [/tex]

We want to find

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

We use function properties to obtain:

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

[tex](f \times g)(x) = (x + 1) \times \frac{1}{x} = \frac{x + 1}{x} [/tex]

There is a horizontal asymptote at:

[tex]y = 1[/tex]

Let

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

[tex]xy = x + 1[/tex]

[tex]xy - x = 1[/tex]

[tex]x(y - 1) = 1[/tex]

[tex]x = \frac{1}{y - 1} [/tex]

The range is

[tex]y \ne1[/tex]

Or

[tex]( - \infty ,1) \cup(1, \infty )[/tex]

Answer:

Rotation of 90 degrees clockwise and then Dilation (scale factor) of 0.5

Answer:

False.

Step-by-step explanation:

This is the absolute value of x  so if x < 0 then f(x) will be x not -x.

The function f(x) = 1/x can be represented as a piecewise function with different cases for x > 0, x < 0, and x = 0. It is not defined at x = 0, and it approaches positive or negative infinity as x approaches 0 from either side.

To represent the function f(x) = 1/x as a piecewise function, we need to consider the nature of the function around x = 0. The function is undefined at x = 0, and it approaches positive infinity as x approaches zero from the negative side and negative infinity from the positive side.

Piecewise Representation:

This can be written as a piecewise function:

Answer:

The approximate difference between m∠C and m∠A is 45° to the nearest degree

Step-by-step explanation:

* Lets talk about the right triangle

- It has one right angle and two acute angles

- The side opposite the the right angle is called hypotenuse

- The other sides are called the legs of the right angle

- In ΔABC

∵ AC is the hypotenuse

∴ ∠B is the right angle

∴ AB and BC are the legs of the right angle

∴ Angles A and C are the acute angles

∵ m∠B = 90°

- The sum of the measures of the interior angles of a Δ is 180°

∴ m∠A + m∠C = 180° - 90° = 90°

- We will use trigonometry to find the measures of angles A and C

- sin A is the ratio between the opposite side to angle ∠A and the

  hypotenuse

∵ BC is the opposite side of angle A

∴ sin A = BC/AC

∵ BC = 5 cm

∵ AC = 13 cm

∴ sin A = 5/13

- Lets find m∠∠A by using sin ^-1

∴ m∠A = [tex]sin^{-1}\frac{5}{13}=22.62[/tex]

- Lets use the rule of the sum of angles A and C to find the measure

 of the angle C

∵ m∠A + m∠C = 90°

∴ 22.62° + m∠C = 90 ⇒ subtract 22.62 from both sides

∴ m∠C = 67.38°

- Lets find the difference between m∠C and m∠A

∴ The approximate difference between m∠C and m∠A is:

  67.38° - 22.62° = 44.78° ≅ 45° to the nearest degree

Answer:

v = √( [tex]\frac{2E}{m}[/tex] )

Step-by-step explanation:

E=1/2mv²

v² = ( [tex]\frac{2E}{m}[/tex] )

v = √( [tex]\frac{2E}{m}[/tex] )

Answer:

[tex]v=\sqrt{\frac{2E}{m}}[/tex]

Step-by-step explanation:

[tex]E= \frac{1}{2} mv^2[/tex]

Solve the equation for v

To remove fraction , multiply both sides by 2

[tex]2 \cdot E= \frac{1}{2} mv^2 \cdot 2[/tex]

[tex]2E=mv^2[/tex]

Divide both sides by 'm' to isolate v^2

[tex] \frac{2E}{m}=v^2[/tex]

Now to remove square from V, we take square root on both sides

[tex]\sqrt{\frac{2E}{m}} =v[/tex]

[tex]v=\sqrt{\frac{2E}{m}}[/tex]

Answer:

y = [tex]\frac{36}{121}[/tex]

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 18 when x = 4

k = yx = 18 × 4 = 72, so

y = [tex]\frac{72}{x}[/tex] ← equation of variation

When x = 242, then

y = [tex]\frac{72}{242}[/tex] = [tex]\frac{36}{121}[/tex]