Solve for m:

[tex]2=\frac{m}{2} -7[/tex]

Answer:

  FALSE

Step-by-step explanation:

The slope can be calculated using any two points on the line in any order and the result will be the same.

Answer:

We only need one simple theorem for this.

Theorem 7 - The Exterior Angle Theorem: An exterior angle of a triangle is equal to the sum of the two remote interior angles.

So in this case, the measurement of the exterior angle is (45x)°, and the interior angles are (25x)° and (57 + x)°.

=> Therefore, we have:

25x + (57 + x) = 45x

25x + x - 45x  = - 57

-19x                 = -57

x                      = -57/(-19) = 3

So x = 3

Outside angle = addition of the two inner angles.

45x = 25x + 57 + x

45x = 26x + 57

45x - 26x = 57

19x = 57

x = 57/19

x = 3

Did you follow the logic?

Answer:

(7,2)

Step-by-step explanation:

If you compare (4,1) to (x,y)

You should see that in place of x you have 4

and in place of y you have 1

so just plug them in

(4+3,1+1)

(7,2)

Answer:

x = - 10

Step-by-step explanation:

Answer:

x > 1/6

Step-by-step explanation:

Perform the indicated multiplication.  Then:

-16x + 8 < 2x + 5

Combining the x terms, we get:

8 < 18x + 5.

Simplifying further, we get:

3 < 18x, so that   3/18 < x, or x > 1/6

There are 25 total Seniors.

12 of the Seniors want to see more candid pictures.

The percent would be 12/25 = 0.48 x 100 = 48%

Answer:

Yes.

Step-by-step explanation:

Look at a Rhombus.

Answer:

Yes, rhombus have opposite sides that are parallel.

Step-by-step explanation:

A rhombus is a four-sided shape where all sides have equal length, let's say s.

Consider the picture given, here are some facts:

* All sides have equal length

* Opposite sides are parallel, and opposite angles are equal

* A rhombus is sometimes called a rhomb or a diamond.

Tags: Rhombus, opposite sides, parallel, rhomb, diamond

Answer:

  48

Step-by-step explanation:

The total number of ratio units is 3+2 = 5, and the 3 ratio units representing large bandages make up 3/5 of that total. Thus, large bandages will make up 3/5 of the total number of bandages:

  3/5×80 = 48 . . . . number of large bandages in the kit

Answer:

semi circle

Step-by-step explanation:

Answer:

Semicircle

Step-by-step explanation:

Answer:

Value of cos B is B)12/13

The value of cos B in triangle ΔABC cannot be definitively determined without additional information such as side lengths. However, assuming a right triangle configuration with an adjacent side of length 12 and a hypotenuse of length 13, the cos B could be calculated as 12/13.

In the triangle ΔABC, the value of cos B can be calculated if we know the measures of the sides of the triangle. Without the values of the sides, we can't give an exact value for cos B. However, from the given options, we would assume that the triangle is a right-triangle, and B is the angle formed by the adjacent side of length 12 and the hypotenuse of length 13. Thus, the value of cos B would be equal to the adjacent side (b) divided by the hypotenuse (c), which matches option B) 12/13.

Remember that in a right triangle:
The cosine of an angle (cos B) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. This formula, cos B = b/c is a direct application of the Pythagorean theorem.

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Answer:

1/3

Step-by-step explanation:

if you multiply 24 by 1/3, you recieve 8 which is the reduced dilation

Answer:

  (3, 5, 2)

Step-by-step explanation:

Many authors interpret the triangle inequality to mean the sum of the two short sides must exceed the length of the long side. For side measures 2, 3, 5, the sum of the two short sides is exactly equal to the long side, in violation of the triangle inequality. Hence (3, 5, 2) is not a triangle.

___

Comment on the triangle inequality

Other authors allow the "or equal to" case, meaning sides of lengths 2, 3, 5 will be considered to be a triangle because 2+3=5. This interpretation of the triangle inequality will result in no solution to your question.

A (3, 5, 2) "triangle" will look like a line segment of length 5. It will have an area of zero.

Answer:

The answer to your question would be

3, 5, 2.

Answer:

  all real numbers less than or equal to –3

Step-by-step explanation:

Look at the y-values that the graph shows. There are none greater than -3. Any value of -3 or less is possible.

Answer: D. all real numbers less than or equal to –3

Answer:

the function is odd

Step-by-step explanation:

A function f(x) is said to be even if f(-x) = f(x)

On the other hand, f(x) is said to be odd if f(-x)≠ f(x).

We plug in -x in place of x in the given function and simplify;

f(-x) = 3(-x-1)^4

f(-x) = 3[-1(x+1)]^4

f(-x) = 3 *(-1)^4 * (x+1)^4

f(-x) = 3(x+1)^4 ≠ f(x)

Therefore, the function given is odd

Answer:

The given function is odd

Step-by-step explanation:

we need to determine the function [tex]f(x)=3(x-1)^{4}[/tex] is odd or even

Since, A function f(x) is said to be even if [tex]f(-x) = f(x)[/tex]

and f(x) is said to be odd if [tex]f(-x)= - f(x)[/tex] and [tex]f(-x) \neq f(x)[/tex]

We Replace x with -x in the given function and solve;

[tex]f(x)=3(x-1)^{4}[/tex]

[tex]f(-x)=3(-x-1)^{4}[/tex]

take out the negative common,

[tex]f(-x)=3[-(x+1)]^{4}[/tex]

Since [tex](-1)^{4}=1[/tex]

[tex]f(-x)=3(x+1)^{4}[/tex]

[tex]f(-x) \neq f(x)[/tex]

Hence, the given function is odd

Answer:

  d.  43°

Step-by-step explanation:

KM is a bisector of ∠LKN, so ...

  ∠LKN = 2(∠4)

  7q +2 = 2(4q -5)

  12 = q . . . . . . . . . . . add 10-7q, simplify

Now, we can put 12 where q is in the expression for ∠4:

  ∠3 = ∠4 = 4·12 -5 = 43

Answer:

Step-by-step explanation:

Following your description I got

sin 29° = opp/hyp = 4.6/c

csin29 = 4.6

c = 4.6/sin29

= 9.48826.. or appr 9.5

Answer:

Option (D)

Step-by-step explanation:

Answer: Hence, there are 36 total number of invited guests.

Step-by-step explanation:

Let the total number of invited guests be 'x'

Part of those invited had already arrived = [tex]\dfrac{2}{3}x[/tex]

Number of people just arrived = 6

According to question, it brings the number at the party to [tex]\dfrac{5}{6}[/tex] of those invited.

So, it becomes,

[tex]\dfrac{2}{3}x+6=\dfrac{5}{6}x\\\\6=\dfrac{5}{6}x-\dfrac{2}{3}x\\\\6=\dfrac{5x-4x}{6}\\\\6=\dfrac{x}{6}\\\\x=6\times 6\\\\x=36[/tex]

Hence, there are 36 total number of invited guests.

Answer:

42 People

Step-by-step explanation:

P is the total amount of people. Before Cedric arrived, there were (2/3)P people at the party. After Cedric and six other people arrived, there are (2/3)P+7 people at the party. Since this is the same as (5/6)P, we solve (2/3)P+7=(5/6)P to find that P=42.

Answer:

Option D is the answer.

Step-by-step explanation:

The label on the car's antifreeze container claims to protect the car between -40°C and 140°C.

So inequality which models this situation will be -40°C < T < 140°C

Now we have to show this inequality in Fahrenheit temperature with the help of [tex]C=\frac{5}{9}(F-32)[/tex]

So the compound inequality in Fahrenheit temperature will be

[tex]-40<\frac{5}{9}(F-32)<140[/tex]

Answer: FLVS ALGEBRA 1

The answer would be  D  

Step-by-step explanation:

The label says that the cars antifreeze is -40°C and 140°C.

so the inequality which models this situation will be -40°C < T < 140°C

Now you got to show this inequality in Fahrenheit temperature.

So the compound inequality in Fahrenheit temperature will be Option D

Answer:

Yes, there will be enough root beer for everyone to have at least one cup

Step-by-step explanation:

step 1

Find the volume of the cylinder root beer keg

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=13/2=6.5\ in[/tex] -----> the radius is half the diameter

[tex]h=17\ in[/tex]

substitute

[tex]V=\pi (6.5)^{2} (17)[/tex]

[tex]V=718.25\pi\ in^{3}[/tex]

step 2

Find the volume of the cylinder cups

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] -----> the radius is half the diameter

[tex]h=4\frac{3}{4}\ in=4.75\ in[/tex]

substitute

[tex]V=\pi (1.5)^{2} (4.75)[/tex]

[tex]V=10.6875\pi\ in^{3}[/tex]

step 3

Multiply the volume of one cup by 50 (the total number of students) and then compare the result with the volume of the cylinder root beer keg

so

[tex]10.6875\pi*(50)=534.375\pi\ in^{3}[/tex]

[tex]534.375\pi\ in^{3}< 718.25\pi\ in^{3} [/tex]

therefore

There will be enough root beer for everyone to have at least one cup

Answer:

Yes. There is enough for everyone.

Step 1: Find the volume of the keg

Diameter : 13

Radius : 6.5

Height : 17

Formula for the area of a circle (base) is πr^2

Solve that using the above formula.

Base area = 132.73

Multiply that by the height.

Keg volume : 2,256.45 inches cubed

Step 2: Find the volume of the cups

Diameter : 3

Radius : 1.5

Height : 4 3/4

Formula for area of a circle (base) is πr^2

Solve that using the above formula.

Base area = 7.07

Multiply that by the height.

Cup volume : 33.58 inches cubed

Step 3: Multiply cup volume by 50

33.58 x 50 = 1,678.79

Step 4: Check how much root beer you have for everyone.

Root beer needed : 2,256.45

Root beer available : 1,678.79

Is there enough root beer?

Yes

Answer:

cl   +   1/(N+1)

Step-by-step explanation:

If we assume that the Nth harmonic number is cl. Then we are assuming that 1+1/2+1/3+1/4+...+1/N=cl

And we know that the (N+1)th harmonic number can be found by doing

1+1/2+1/3+1/4+...+1/N+1/(N+1)

=cl    +   1/(N+1)

The (N+1)th harmonic number is cl   +   1/(N+1) given that the Nth term is cl

Other way to see the answers:

Maybe you want to write it as a single fraction so you have

[cl(N+1)+1]/(N+1)=[cl*N+cl+1]/(N+1)

The expression value is [tex]hn+(\frac{1}{n+1} )[/tex].

Assume that [tex]n[/tex] is an integer variable whose value is some positive integer [tex]N[/tex].

Assume also that [tex]hn[/tex] is a variable whose value is the [tex]N_{th} [/tex] harmonic number.

An expression whose value is the [tex](N+1)th[/tex] harmonic number is [tex]hn+(\frac{1}{n+1} )[/tex].

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Answer:

The answer would be D.4.

Step-by-step explanation:

So first you would have to find the mean of the data by taking into account the amount of each type of numbers like this 1,2,2,3,3,3,4,4,4,4,5,5,5,6,6,7. Then add those all up which would give 64, since their is 16 numbers in total divide 64 by 16 which would give 4.

Answer:

C. –120a2b2c2

Step-by-step explanation:

We'll just the multiplications one at a time...

10ac × 6ab × (–2bc) = 60a²bc * (-2bc)  (multiplying 10ac × 6ab)

60a²bc * (-2bc)  = -120a²b²c²

We just have to multiply the numbers together (like 10 and 6),

then all similar letters together (like ac * ab = a²bc).  If a letter is already present (like a in this  example), then we add up its powers a * a = a², a² * a would be a³ and so on).  If the letter is not present (like 'b' in 'ac', we suppose it's there as b^0 which is equal to 1)... so we still add up its exponent (power)... so it makes b^0 * b = b

Answer:

[tex]\frac{1}{10c^{3}d^{4} }[/tex]

Step-by-step explanation:

THE GIVEN EXPRESSION IS

[tex]\sqrt[3]{\frac{1}{1000c^{9}d^{12} } }[/tex]

To simplify this expression, we just have to apply the cubic root to each part of the fraction, as follows

[tex]\frac{\sqrt[3]{1} }{\sqrt[3]{1000c^{9} d^{12} } }[/tex]

Then, we solve each root. Remember that to solve roots of powers, we just need to divide the exponent of the power by the index of the root, as follows

[tex]\frac{1}{10c^{\frac{9}{3} } d^{\frac{12}{3} } }[/tex]

Therefore, the equivalent expression is

[tex]\frac{1}{10c^{3}d^{4} }[/tex]

So, the right answer is the third choice.

Answer:

1 pi: 3pi

Step-by-step explanation:

Step 1: Formula of surface area and volume of sphere

Surface area of sphere = 4 x pi x r^2

Volume of sphere = 4 x pi x r^3

                                 3

Step 2: Apply values in the formula

r = radius

radius = diameter/2

r=18/2 = 9

S.A = 4 x pi x 9^2

S.A = 324pi

Volume = 4 x pi x 9^3

                3

Volume = 972pi

Step 3 : Show in ratio

Surface area : Volume

324pi : 972pi

= 1 pi: 3pi

Answer:

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

Step-by-step explanation:

The focus lies on the x axis and the directrix is a vertical line through x = 2.  The parabola, by nature, wraps around the focus, or "forms" its shape about the focus.  That means that this is a "sideways" parabola, a "y^2" type instead of an "x^2" type.  The standard form for this type is

[tex](x-h)=4p(y-k)^2[/tex]

where h and k are the coordinates of the vertex and p is the distance from the vertex to either the focus or the directrix (that distance is the same; we only need to find one).  That means that the vertex has to be equidistant from the focus and the directrix.  If the focus is at x = -2 y = 0 and the directrix is at x = 2, midway between them is the origin (0, 0).  So h = 0 and k = 0.  p is the number of units from the vertex to the focus (or directrix).  That means that p=2.  We fill in our equation now with the info we have:

[tex](x-0)=4(2)(y-0)^2[/tex]

Simplify that a bit:

[tex]x=8y^2[/tex]

Solving for y^2:

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

Answer: x = -1/8y^2

Step-by-step explanation

Focus: (-2,0)

Directrix: x=2

It meets the criteria.

Explanation:

DeMoivre's theorem tells you the 7th roots of unity are the 7 points evenly spaced around (on) the unit circle, including 1∠0°. They will be located at angles ...

  {0, 2π/7, 4π/7, 6π/7, 8π/7, 10π/7, 12π/7} . . . in radians

Given that the circle shown is graduated in increments of π/6, you will need to do some estimating as to the actual location of the root.

___

The attached graph shows lines at increments of π/7 radians, so your graph will match every other one.

[tex]3^{4}[/tex] + 2 × 5

To evaluate apply the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

Parentheses  

There are none for this steps so go on to the next step

Exponent:

[tex]3^{4}[/tex]

81

so...

81 + 2 × 5

Multiplication:

81 + 2 × 5

2 × 5

10

so...

81 + 10

No division in this equation so skip this step and go to the next one

Addition:

81 + 10

91

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

44

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do multiply from left to right.

2*5=10

Add the numbers from left to right to find the answer.

34+10=44

44 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

y = 3x - 2

Step-by-step explanation:

You can easily find the equation of a line through two points by using the point-slope form, [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is one of the points.

First, let's find the slope of the line through (0, -2) and (4, 10).

[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1} = \frac{10-(-2)}{4-0}=\frac{12}{4}=3[/tex]

Next, we plug this into point-slope form. Remember that we let (0, -2) be our first point, [tex](x_1,y_1)[/tex].

[tex]y-(-2)=3(x-0)[/tex]

Finally, we rearrange this equation to get the slope-intercept form [tex]y=mx+b[/tex], where b is the y-intercept.

[tex]y+2=3x \\ y=3x-2[/tex]

We can verify using the attached graph that both points lie on this line.

Formula and set up:

A = P(1 + r/n)^(nt)

You want A.

A = 1200(1 + (0.06)/2)^(0.06)(2)

Plug right side into calculator to find A.

Answer:

1. [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex] = [tex]\frac{2x^2+10x+6}{(x+3)(x+5)}\\[/tex]

2. [tex]\frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}[/tex] = [tex]\frac{1}{(x+2)(x-4)}[/tex]

3. [tex]\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}[/tex] = [tex]\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}[/tex]

4. [tex]\frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}[/tex] = [tex]\frac{1}{(x-2)(x-4)}[/tex]

Step-by-step explanation:

1. [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]

Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)

[tex]=\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}\\=\frac{x^2+5x+(x)(x+3)+2(x+3)}{(x+3)(x+5)} \\=\frac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)} \\=\frac{x^2+x^2+5x+3x+2x+6}{(x+3)(x+5)} \\=\frac{2x^2+10x+6}{(x+3)(x+5)}\\[/tex]

Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.

2. [tex]\frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}[/tex]

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)

Putting factors

[tex]=\frac{x+4}{(x+3)(x+2)}*\frac{x+3}{(x-4)(x+4)}\\\\=\frac{1}{(x+2)(x-4)}[/tex]

Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.

3. [tex]\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}[/tex]

Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)

Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)

Putting factors

[tex]\frac{2}{(x+3)(x-3)}-\frac{3x}{(x+3)(x-2)}[/tex]

Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)

[tex]\frac{2(x-2)-3x(x+3)(x-3)}{(x+3)(x-3)(x-2)}[/tex]

[tex]=\frac{2(x-2)-3x(x+3)}{(x+3)(x-3)(x-2)}\\=\frac{2x-4-3x^2-9x}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-9x+2x-4}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}[/tex]

Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.

4. [tex]\frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}[/tex]

Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

[tex]\frac{x+4}{(x-2)(x+3)}\div\frac{(x-4)(x+4)}{x+3}[/tex]

Converting ÷ sign into multiplication we will take reciprocal of the second term

[tex]=\frac{x+4}{(x-2)(x+3)}*\frac{x+3}{(x-4)(x+4)}\\=\frac{1}{(x-2)(x-4)}[/tex]

Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.

The given equations are the algebric equations for obtaining solution the equation can be simplified by algebric operations.

1).

[tex]\dfrac{x}{x+3} + \dfrac{x+2}{x+5}[/tex]

Taking LCM of denomenator (x+3) and (x+5).

[tex]=\dfrac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}[/tex]

Further simplification has been done by multtiplication in the numerator.

[tex]=\dfrac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)}=\dfrac{2x^2+10x+6}{(x+3)(x+5)}[/tex]

2).

[tex]\dfrac{x+4}{x^2+5x+6}\times \dfrac{x+3}{x^2-16}[/tex]

For further simplification of above equation factorization of [tex]x^2+5x+6[/tex] and [tex]x^2-16[/tex] has been performed.

[tex]= \dfrac{x+4}{(x+3)(x+2)}\times \dfrac{x+3}{(x-4)(x+4)}[/tex]

[tex]= \dfrac{1}{(x+2)(x-4)}[/tex]

3).

[tex]\dfrac{2}{x^2-9}-\dfrac{3x}{x^2-5x+6}[/tex]

For further simplification of above equation factorization of [tex]x^2-5x+6[/tex] and [tex]x^2-9[/tex] has been performed.

[tex]=\dfrac{2}{(x-3)(x+3)}-\dfrac{3x}{(x-3)(x-2)}[/tex]

Taking LCM of denomenator (x+3)(x-3) and (x-3)(x-2).

[tex]=\dfrac{(2\times(x-2))-(3x\times(x+3))}{(x-3)(x+3)(x-2)}=\dfrac{2x-4-3x^2-9x}{(x-3)(x+3)(x-2)}[/tex]

[tex]= -\dfrac{3x^2+7x+4}{(x-3)(x+3)(x-2)}[/tex]

4).

[tex]\dfrac{\dfrac{x+4}{x^2-5x+6}}{\dfrac{x^2-16}{x+3}}[/tex]

For further simplification of above equation factorization of [tex]x^2-5x+6[/tex] and [tex]x^2-16[/tex] has been performed.

[tex]=\dfrac{\dfrac{x+4}{(x-3)(x-2)}}{\dfrac{(x-4)(x+4)}{x+3}}=\dfrac{x+3}{(x-3)(x-2)(x-4)}[/tex]

For more information, refer the link given below

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