calculate the slope of the line that contains the points (2,-3) and (6,-3)

Answer:

(-1,6)

Step-by-step explanation:

P= 1A + 2B

AP + PB

= 1(-3,6) + 2(0,6)

3

= (-3,6) + (0,12)

3

= (-3 + 18)

3

= (-1,6)

Answer:

5 : 4

Step-by-step explanation:

To simplify the ratio , find the greatest common factor of 60 and 48, then divide both parts of the ratio by it

the greatest common factor of 60 and 48 is 12, hence

60 ÷ 12 : 48 : 12 = 5 : 4 ← in simplest form

30:24 = 10:8 = 5:4

Step-by-step explanation:

First divide them by 2

then divide the answer (30:24) with 3

then divide the answer with 2

And the answer comes as 5:4

c = 2x + 3. The third side of the triangle is 2x + 3.

The key to solve this problem is using the perimeter of a triangle equation which is P = a + b + c, where a, b, and c are the sides of the triangle.

We know that the perimeter P = 3x² + 7x, let's suppose a = 6x - 7, b = 3x² - x + 4, and c is the unknow.

Clearing c from the equation:

c = P - (a + b)

c = 3x² + 7x - (6x - 7 + 3x² - x + 4)

c = 3x² + 7x - 6x + 7 - 3x² +x - 4

Grouping the equal terms:

c = 3x² - 3x² + 7x + x - 6x + 7 - 4

c = 0 + 8x - 6x + 3

c = 2x + 3

Check the picture below.

Answer:

the answer is 77

Step-by-step explanation:

46.20 divided by 60 cents = 77

The answer is:

The first option,

[tex]y=-\frac{1}{2}x-3;x<-2[/tex]

To answer the question, we need to look for an inequality that fits with the following description:

- Negative slope, since the segment "a" is decreasing.

- x- axis interception at x equal to -6

- One of its point is located at (-2,-2)

- The segment exists from -∞ to -2.

So, checking we have:

Firs option

[tex]y=-\frac{1}{2}x-3[/tex]

With,

[tex]x<-2[/tex]

- Finding the y-axis component when x is equal to -2, we have:

[tex]y=-\frac{1}{2}*(-2)-3\\y=1-3=-2[/tex]

We have that one of the points of the segments is located at (-2,-2)

- Finding the "x" intercept, we have:

[tex]0=-\frac{1}{2}x-3\\\\\frac{1}{2}x=-3\\\\x=2*-3=-6[/tex]

Also, (from the inequality and the graph) we know that, the given segment exists from the negative infinite numbers to -2.

Hence, we can know that the first option meets all the requirements:

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

[tex]x-axis_{interception}=-6[/tex]

[tex]Point(-2,-2)[/tex]

and from the inequality, we know that the segment exists from -∞ to -2.

Have a nice day!

Answer:

The answer would be eight.

Step-by-step explanation:

The range is the difference between the largest and smallest number you need to make sure you have them in order or it won’t work.

Answer:

the answer is eight

Step-by-step explanation:

Answer:

2970

Step-by-step explanation:

2700+ 270

270 because that is 10% of 2700

2700 because that is 75 x 36

Answer:

9?

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

a linear function is

y = ax + b

so, for the first pair of x, y

8.5 = 2a + b

b = 8.5 - 2a

the second pair

15.25 = 5a + b

let's use the substitution information from the first pair :

15.25 = 5a + 8.5 - 2a

6.75 = 3a

a = 2.25

b = 8.5 - 2×2.25 = 8.5 - 4.5 = 4

so, we get as linear function

y = 2.25x + 4

that means the y-intercept (x = 0) is at y = 4

y = 2.25×0 + 4 = 4

The y-intercept of this function will be at (0, 4).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

In the table below, x represents miles traveled and y represents the cost to travel by train.

Miles (x)    Cost (y)

   2            8.50

   5           15.25

   8          22.00

  12          31.00

Then the linear equation will be

y - 8.50 = [(31.00 - 8.50) / (12 - 2)] (x - 2)

y - 8.50 = 2.25(x - 2)

y - 8.50 = 2.25x - 4.5

          y = 2.25 + 4

The graph of the equation is given below.

Then the y-intercept of this function will be at (0, 4).

More about the linear system link is given below.

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Step-by-step explanation:

[tex]8^{2x-4}=8^{5x+1}\iff2x-4=5x+1\qquad\text{add 4 to both sides}\\\\2x=5x+5\qquad\text{subtract 5x from both sides}\\\\-3x=5\qquad\text{divide both sides by (-3)}\\\\\boxed{x=-\dfrac{5}{3}}\\\\================================[/tex]

[tex]2^{x+6}=16^{3x+4}\\\\2^{x+6}=(2^4)^{3x+4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{x+6}=2^{4(3x+4)}\iff x+6=4(3x+4)\qquad\text{use the distributive property}\\\\x+6=(4)(3x)+(4)(4)\\\\x+6=12x+16\qquad\text{subtract 6 from both sides}\\\\x=12x+10\qquad\text{subtract 12x from both sides}\\\\-11x=10\qquad\text{divide both sides by (-11)}\\\\\boxed{x=-\dfrac{10}{11}}\\\\================================[/tex]

[tex]\left(\dfrac{1}{2}\right)^x=2^{x+3}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^{-1})^x=2^{x+3}\\\\2^{-x}=2^{x+3}\iff -x=x+3\qquad\text{subtract x from both sides}\\\\-2x=3\qquad\text{divide both sides by (-2)}\\\\\boxed{x=-\dfrac{3}{2}}\\\\================================[/tex]

[tex]36^{2x}=216^{3x-1}\\\\(6^2)^{2x}=(6^3)^{3x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\6^{(2)(2x)}=2^{3(3x-1)}\iff(2)(2x)=3(3x-1)\qquad\text{use the distributive property}\\\\4x=(3)(3x)+(3)(-1)\\\\4x=9x-3\qquad\text{subtract 9x from both sides}\\\\-5x=-3\qquad\text{divide both sides by (-5)}\\\\\boxed{x=\dfrac{3}{5}}\\\\================================[/tex]

[tex]p\%=\dfrac{p}{100}\\\\100\%-12.6\%=87.4\%=\dfrac{87.4}{100}=0.874\\\\8\ years\to(0.874)^4\approx0.584\to58.4\%\\\\\text{After 8 years, the car will be worth 58.4}\%\ \text{of the initial price.}[/tex]

Answer:

Yes, the following equation is a quadratic function in vertex form

Step-by-step explanation:

we know that

The quadratic function of the vertical parabola into vertex form is equal to

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

where

(h,k) is the vertex of the parabola

If the coefficient a is > 0 ----> the parabola open upward (vertex is a minimum)

If the coefficient a is < 0 ----> the parabola open downward (vertex is a maximum)

in this problem we have

[tex]y=4(x-2)^{2} +6[/tex]

The squared term contain the x-coordinate of the vertex

[tex]h=2[/tex]

The constant term is the y-coordinate of the vertex

[tex]k=6[/tex]

The vertex is the point (2,6)

The coefficient is equal to

[tex]a=4[/tex] ----> open upward (vertex is a minimum)

Answer:

f(-3) = -5/2

f(-1) = 3/2

f(3) = 3/4

Step-by-step explanation:

To find the values, we just have to replace by the values given (-3, -1, 3).  Since there are different definitions of the function depending on the range of x, we just have to pick the right one before replacing x by its value.

x = -3

When x ≤ -1, the function is 7/2 + 2x

So, x = -3 is certainly  ≤ -1, so....

f(-3) = 7/2 + 2 (-3) = 7/2 - 6 = 7/2 - 12/2 = -5/2

x = -1

When x ≤ -1, the function is 7/2 + 2x

So, we do the same calculation:

f(-1) = 7/2 + 2 (-1) = 7/2 - 2 = 7/2 - 4/2 = 3/2

x = 3

When x ≥ 3, the function is defined as: (1/4)x or x/4.  So,

f(3) = 3/4

The output values of f(-3), f(-1), and f(3) in the piece-wise function are -5/2,  3/2, and 3/4 respectively.  

To determine the output value of f(-3), f(-1), and f(3) in the piece-wise function, we simply plug in the values of x in the piece that is within the domain.

To solve for f(-3), plug x = -3 into the piece with the domain of x ≤ -1:

f( x ) = 7/2 + 2x

Pug in x = -3:

f( -3 ) = 7/2 + 2(-3)

f( -3 ) = -5/2

To solve for f(-1), plug x = -1 into the piece with the domain of x ≤ -1:

f( x ) = 7/2 + 2x

Pug in x = -1:

f( -3 ) = 7/2 + 2(-1)

f( -3 ) = 7/2 - 2

f( -3 ) = 3/2

To solve for f(3), plug x = 3 into the piece with the domain of x ≥ 3:

f( x ) = (1/4)x

Pug in x = 3:

f( 3 ) = (1/4) × 3

f( 3 ) = 3/4

Therefore, the values for f(-3), f(-1), and f(3) are -5/2,  3/2, and 3/4 respectively.  

Is it equal to the measure if angle C

In an isosceles triangle, the measure of the vertex angle (Angle B in this case) is equal to the measure of the other base angle. This is because in an isosceles triangle, the angles opposite the equal sides are also equal.

In an isosceles triangle ABC, Angle B, the angle between the two sides of equal length, is known as the vertex angle. The two base angles of an isosceles triangle are always equal. Therefore the measure of Angle B will be equal to the measure of Angle C. This property comes from the fundamental characteristics of an isosceles triangle, where two sides are of equal length and the angles opposite these equal sides are also equal.

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ANSWER

[tex]P(4)'= \frac{1}{3} [/tex]

EXPLANATION

The sample space of rolling a 6-sided die is

{1,2,3,4,5,6}

The even numbers apart from 4, are

{2,6}

The probability of rolling an even number that is not 4 is

[tex]P(4)'= \frac{2}{6} = \frac{1}{3} [/tex]

Answer:

True

Step-by-step explanation:

The numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.

A triangle with sides of lengths 20, 21, and 29 is a right triangle.

Three numbers can be the sides of a triangle if the sum of two of them is greater than the third. So, since

20+21 > 29,

20+29 > 21, and

21+29 > 20

Are trivially true, they can be the sides of a triangle.

The given numbers are a Pythagorean triplet and can be the dimensions of a right triangle.

20,21 and 29 is a Pythagorean triplet, since

[tex]20^2+21^2=29^2[/tex]

So you also know that they form a right triangle.

Hence, the numbers 20, 21, and 29  are a Pythagorean triplet and can be the dimensions of a right triangle.

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I'm pretty sure that question 1 is 254.5 m but i'm not entirely sure about my answer to question 2. sorry i couldn't be more help to you :( good luck!

Answer:

B [tex]log_{2} 42[/tex]

Step-by-step explanation:

Due to the product rule of logarithms, we can combine them as such. Then it will simplify to our answer.

[tex]log_{2} 6+log_{2} 7=log_{2} (6*7)\\\\log_{2} 42[/tex]

The single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex]  is [tex]log_{2} 42[/tex]. The correct answer is option B.

To express [tex]log_2^{6} + log_2^{7}[/tex] as a single logarithm, we can use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

Simplifying the expression within the logarithm, we get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex]. The correct answer is option B.

Logarithms are used to simplify complex mathematical calculations involving large numbers. They allow us to break down a number into its constituent parts and perform operations on those parts more easily. In this problem, we are asked to express the sum of two logarithms as a single logarithm. To do this, we use the logarithmic identity log a + log b = log ab.

Applying this identity to the given expression, we get:

[tex]log_2^{6} + log_2^{7}[/tex] = [tex]log_{2} (6 * 7)[/tex]

We simplify the expression on the right-hand side of the equation to get:

[tex]log_{2} (6 * 7)[/tex] = [tex]log_{2} 42[/tex]

Therefore, the single logarithm equivalent to [tex]log_2^{6} + log_2^{7}[/tex] is [tex]log_{2} 42[/tex].

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Answer:

Step-by-step explanation:

[tex]METHOD\ \#1\\\\\text{Put b = 3 to each equation and check equality:}\\\\A.\ 3-24b=75\\L_s=3-24(3)=3-72=-69\\R_s=75\\L_s\neq R_s\\\\B.\ 65+9b=38\\L_s=65+9(3)=65+27=92\\R_s=38\\L_s\neq R_s\\\\C.\ -2b+30=24\\L_s=-2(3)+30=-6+30=24\\R_s=24\\L_s=R_s\\\\D.\ 102b-21=-55\\L_s=102(3)-21=306-21=285\\R_s=-55\\L_s\neq R_s[/tex]

[tex]METHOD\ \#2:\\\\\text{Solve each equation:}\\\\A.\\3-24b=75\qquad\text{subtract 3 from both sides}\\-24b=72\qquad\text{divide both sides by (-24)}\\b=-3\neq3\\\\B.\\65+9b=38\qquad\text{subtract 65 from both sides}\\9b=-27\qquad\text{divide both sides by 9}\\b=-3\neq3\\\\C.\\-2b+30=24\qquad\text{subtract 30 from both sides}\\-2b=-6\qquad\text{divide both sides by (-2)}\\b=3\\\\D.\\102b-21=-55\qquad\text{add 21 to both sides}\\102b=-34\qquad\text{divide both sides by 102}\\b=-\frac{1}{3}[/tex]

Answer:

x = (8.75 - 2 5/6) / 7.1 + (4 1/2 + 2 2/3) / 4 3/10

x = 2.5

Answer:

2  1/2

Step-by-step explanation:

Order of operations rules require that we do any work within parentheses first.  Thus, calculate (8.75 - 2  5/6); it is (5  11/12).  Next, calculate (4  1/2 + 2  2/3); it is ( 7  1/6).  So what we have now looks like:

(5  11/12) / 7.1  + (7  1/6) / (43/10)    (Note that 4  3/10 = 43/10)

Performing the two indicated divisions, we get:

5/6 + 1  2/3.

Since the LCD here is 6, we add:    5/6 + 1  4/6, which comes out to

                                                          1  9/6, or 1 + 1  1/2, or    2  1/2 (answer)

Answer:

36g + 81

Step-by-step explanation:

9 is your multiplier.  Multiply each of the two terms inside the parentheses by this 9, one at a time:  

36g + 81

Answer:

9 (4g + 9) = 9*(4g) + 9* (9) = 36g + 81

Step-by-step explanation:

Answer:

(2,-1)

Step-by-step explanation:

The solution of the system of equations 2x + 3y = 1 and 5x + 2y = 8 is x = 2 and y = -1.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.

And simultaneous equation is the system of equation.

Given:

System of equations,

2x + 3y = 1,  {equation 1}

And 5x + 2y = 8.    {equation 2}

To find the solution:

Multiply 5 to the equation 1 and multiply 2 to the equation 2.

And then subtract the equation 2 to the equation 1.

We get,

11y = -11

y = -1

And 2x = 4

x = 2

Therefore, the solution is x = 2 and y = -1.

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Answer:

The answer is 48pi

Step-by-step explanation:

what you have to do is you have to do 8*6=48 and there you go your answer

Answer:

48pi

Step-by-step explanation:

I think 5x represents 90 degrees.

5x = 90

x = 90/5

x = 18

ANSWER

[tex]x = 18 \degree[/tex]

EXPLANATION

A semicircle subtends an angle of 90° at the circumference.

From the diagram, the semicircle subtends an angle of (5x)° at the circumference.

We equate this angle to 90° and solve for x.

This implies that,

[tex]5x = 90 \degree[/tex]

Divide both sides by 5.

[tex]x = \frac{90}{5} [/tex]

[tex]x = 18 \degree[/tex]

Answer:

7:2:8.

Step-by-step explanation:

The income form the raffle = £350

Income from the quiz = 14*4 = £56 + £44 = £100

Income from membership fees = 20*20 = £400.

The ratio of raffle : quiz : fees

= 350:100:400

Dividing each number by 50:

= 7:2:8   in simplest form.

Answer:

A ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

Step-by-step explanation:

Given : The table shows a darts club's income in 2017 from a raffle, a quiz and membership fees.

To find : Express as a ratio the income from the raffle to the income from the quiz to the income from membership fees ?

Solution :

The raffle amount is £350.

Quiz, entry fees is 14 at £4 each and refreshment is £44.

The quiz amount is £[tex]14\times 4[/tex]+£44=£56+£44=£100

Membership fees=20 at £20 each.

The membership amount is £[tex]20\times 20[/tex]=£400

Now, the ratio of income from the raffle to the income from the quiz to the income from membership fees is

The ratio of raffle : quiz : membership

[tex]R= 350:100:400\\\\R= 35:10:40\\\\R=7:2:8[/tex]

Therefore, a ratio the income from the raffle to the income from the quiz to the income from membership fees is 7:2:8.

Looking at the shape, you should be able to tell immediately that this will be an absolute value function. Noticing that it is both 1 over and 1 up, you will get the equation y = - | x + 1 | + 1

Answer:

y=-|x+1|+1

Step-by-step explanation:

Down

The formula for a quadratic equation is y = ax^2 + bx + c. In this case, a = -4, b = 8, and c = 12. The direction of the parabola can be determined by a. If a is positive, the parabola opens upwards, and if a is negative, the parabola will open downwards.

Answer:

The correct answer option is (5, -6).

Step-by-step explanation:

We know that the following are the coordinates of a point:

[tex] ( - 5 , - 6 ) [/tex]

If this point is reflected through y axis, we are to find the coordinates of its image?

If a point is reflected through y-axis, the sign of the x coordinate is changed so we get:

[tex] ( - 5 , -6 ) [/tex] [tex] \implies [/tex] (5, -6)

Answer:

If "m" stands for meters, then thats not possible.

Step-by-step explanation:

if m is meters then i would say 0.075 meters i’m pretty sure