-5=6m-1 solve for m

Answer:

There are 720 ways to award the medals

Step-by-step explanation:

* Lets explain the difference between permutations and combinations

- Both permutations and combinations are collections of objects

- Permutations are for lists (order matters)  

- Combinations are for groups (order doesn't matter)  

- A permutation is an ordered combination.  

- Permutation is nPr, where n is the total number and r is the number  

 of choices

# Example: chose the first three students from the group of 10

  students, n = 10 and r = 3,then 10P3 is 720

- Combinations is nCr, where n is the total number and r is the number  

  of the choices

# Example: chose a group of three students from the group of 10

  students n = 10 and r = 3,then 10C3 is 120

* Lets solve the problem

- There are six runner

- There are 6 medals awarded for first place through sixth place

- Each medal is different

- The order is important because they arranged from 1st position to

  the 6th position

∴ We will use the permutation

∵ There are 6 medals for 6 runners

∵ 6P6 = 6 × 5 × 4 × 3 × 2 × 1 = 720

∴ There are 720 ways to award the medals

Answer:

5/6

Step-by-step explanation:

Dividing fractions:

Step 1: Rewrite the first fraction as it is.

Step 2: Replace the division sign with a multiplication sign.

Step 3: Flip the second fraction.

Step 4: Multiply the fractions and reduce the product if necessary.

Let's use the rule of dividing fractions on your problem.

Step 1: Rewrite the first fraction as it is.

[tex] \dfrac{5}{8} [/tex]

Step 2: Replace the division sign with a multiplication sign.

[tex] \dfrac{5}{8} \times [/tex]

Step 3: Flip the second fraction.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} [/tex]

Step 4: Multiply the fractions and reduce the product if necessary.

To multiply fractions, multiply the numerators together, and multiply the denominators together.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} = \dfrac{5 \times 4}{8 \times 3} = \dfrac{20}{24} [/tex]

We notice that the greatest common factor of 20 and 24 is 4, so we divide both the numerator and denominator by 4 to reduce the fraction.

[tex] = \dfrac{4 \times 5}{4 \times 6} = \dfrac{5}{6} [/tex]

Answer: The answer is b, 2x=14

Step-by-step explanation:

You add the equations...

2x-14=0

Move -14 over...

2x=14

Answer:  The correct option is

(B) 2x = 14.

Step-by-step explanation:  We are given to solve the following system of equations by the method of Elimination :

[tex]x+y-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Also, to select the resulting equation when we eliminate y.

Adding equations (i) and (ii), we get

[tex](x+y-6)+(x-y-8)=0+0\\\\\Rightarrow 2x-14=0\\\\\Rightarrow 2x=14~~~~~~~~~~[\textup{this is the resulting equation}]\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]

From equation (i), we get

[tex]7+y-8=0\\\\\Rightarrow y-1=0\\\\\Rightarrow y=1.[/tex]

Thus, the required solution is (x, y) = (-1, 7) and the resulting equation while eliminating y is 2x = 14.

Option (B) is CORRECT.

Answer:

The answer is 6

Step-by-step explanation:

The given function F(x) = x^2-8x+7 has a minimum point of (4, -9). This is found by using the formula for the vertex of a quadratic function.

This question seems to be incomplete as only one function, F(x) = x^2-8x+7, is provided. However, I can still help you find the minimum of this function. A quadratic function, such as this one, has a minimum or maximum at its vertex. The x-coordinate of the vertex (h) can be found using the formula h = -b/2a.

In this function, a = 1 and b = -8, so h = 8/2 = 4. So the minimum point of the function is at x = 4. To find the corresponding y value, we substitute x = 4 in our function. F(4) = 4^2-8*4+7 = -9. So the minimum point of F(x) = x^2-8x+7 is (4, -9).

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Answer:

3.55 as a percentage is around an 80%

Step-by-step explanation:

1. Divide the number by 20.

2. Subtract 1 from that number.

Answer:

Somewhere around 80%

Step-by-step explanation:

Answer:

the values of x, y and z are: x=8, y = -5 and z = -7

Step-by-step explanation:

2x+6y+4z=−42       eq(1)

4x+3y+8z=−39       eq(2)

4x+3y+2z=3          eq(3)

We would solve the above equations using elimination method.

Subtracting eq(3) from eq(2)

4x+3y+8z=−39      

4x+3y+2z=3

-   -     -       -

_____________

0+0+6z = -42

z = -42/6

z = -7

Multiplying eq(1) with 2 and subtracting with eq(2)

4x + 12y +8z = -84

4x +3y +8z = -39

-    -      -        +

_______________

0+9y+0=-45

9y = -45

y = -45/9

y = -5

Putting value of y and z in eq(1)

2x + 6y +4z = -42

2x + 6(-5) +4(-7) = -42

2x -30 -28 = -42

2x -58 = -42

2x = -42 +58

2x = 16

x = 16/2

x= 8

So, the values of x, y and z are: x=8, y = -5 and z = -7

ANSWER

Point if discontinuity:

[tex]{x}= \pm3[/tex]

Zero of the function is

[tex]x = 0[/tex]

EXPLANATION

The given rational function is:

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

This function is not continous when

[tex] {x}^{2} - 9 = 0[/tex]

[tex] {x}= \pm \sqrt{9} [/tex]

[tex]{x}= \pm3[/tex]

The function is zero when,

[tex]3x = 0[/tex]

[tex]x = 0[/tex]

Answer:

D

Step-by-step explanation:

Answer:

5 (Answer B)

Step-by-step explanation:

As we move from A to B, x increases by 3 and y decreases by 4.  Apply the Pythagorean Theorem:

(length of AB) = √(3² + [-4]²) = 5 (Answer B)

Answer:

Proved,

P(A∪B)=0.72

Step-by-step explanation:

Sue travels by bus or walks when she visits the shops.

Probability( catch the bus to the shop ), P(A) = 0.4

Probability( catch the bus from the shop ), P(B) = 0.7

Both A and B are independent events.

Therefore,

P(A∩B) = 0.4×0.7

           = 0.28

Probability Sue walks one way = 1 - P(A∩B)

                                                   = 1 - 0.28

                                                   = 0.72

Hence, the probability that Sue walks at one way is 0.72

The probability that Sue walks one way is 0.18, derived by subtracting the probability that Sue takes a bus one way (0.82) from 1.

The question refers to the probability involving Sue's mode of transport to and from the shops. To show the probability that Sue walks one way, we need to first determine the probability that she takes a bus either to or from the shops, since taking a bus one way implies she walked the other way.

The probability that Sue takes a bus to the shops OR from the shops, but not both, can be calculated using the formula: P(A U B) = P(A) + P(B) - P(A ∩ B). In this case, A represents the probability Sue takes a bus to the shop (0.4) and B represents the probability she takes a bus from the shop (0.7). P(A ∩ B) is the probability she takes a bus both ways, which is 0.4 * 0.7 = 0.28.

Therefore, the probability she takes the bus one way is P(A U B) = 0.4 + 0.7 - 0.28 = 0.82.

Since Sue either takes a bus or walks, the sum of these two probabilities should be 1. Therefore, the probability Sue walks one way is 1 - the probability she takes the bus one way = 1 - 0.82 = 0.18, not 0.72 as suggested in the question.

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Answer:

Shanna's family

Step-by-step explanation:

d/t = r (distance/time = rate)

Harlin: 363/6 = 60.5 mph

Kevin: 435/7 = 62.14 mph

Shanna: 500/8 = 62.5 mph

Hector: 215/5 = 43 mph

Answer: 11/156

Step-by-step explanation: There are 13 marbles at the beginning, and 12 at the end.

13 x 12 = 156

Since there are 2 marbles being picked from the 13, subtract 2 from 13.

13-2 = 11

The probability of choosing different colors is 11/156.

Answer: Option C

all real numbers

Step-by-step explanation:

We have the following equation

[tex]-2(x + 3) =-2x - 6[/tex]

We must solve for the variable x

[tex]-2(x + 3) =-2x - 6[/tex]

Apply the distributive property of the left side of equality

[tex]-2*x -2*3 =-2x - 6[/tex]

[tex]-2x -6 =-2x - 6[/tex]

Add 6 on both sides of equality

[tex]-2x -6 +6=-2x - 6+6[/tex]

[tex]-2x=-2x[/tex]

Divide between -2x on both sides of the equation

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

[tex]1=1[/tex]

The variable x is eliminated. This means that equality does not depend on the value of x. In other words, equality is satisfied for any value of x. Therefore the equation has infinite solutions

The answer is  all real numbers

Answer:

all real numbers

Step-by-step explanation:

trust me it will pay off

Answer:

Number One

Step-by-step explanation:

This is because a natural number is a positive integer so it can't be 2,3,or 4 so the only other option is 1!!

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have

A(0, 0), C(a, b)

[tex]AC=\sqrt{(a-0)^2+(b-0)^2=\sqrt{a^2+b^2}[/tex]

B(a, 0), D(0, b)

[tex]BD=\sqrt{(0-a)^2+(b-0)^2}=\sqrt{(-a)^2+b^2}=\sqrt{a^2+b^2}[/tex]

Therefore AC = BD.

Answer:

1q = 2p

Step-by-step explanation:

One quart of liquid is the equivalent of 2 pints... one of the rare easy measures in the American measure system.

So, the equation needs to have 1 quart on one side, and 2 pints on the other side.  It's an equation because both values are equal, just expressed in different units.

1 quart = 2 pints, then rewritten to match the variables given in the question:

1q = 2p

Answer:

The volume of the cylinder is 150.72 cm³ ⇒ last answer

The volume of the cone is 314 cm³ ⇒ 1st answer

The volume of the pyramid is 160 cm³ ⇒ 2nd answer

The volume of the pyramid is 48 cm³ ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the volumes of some shapes

- The volume of the cylinder of radius r and height h is:

 V = π r² h

- The volume of the cone of radius r and height h is:

 V = 1/3 π r² h

- The volume of the pyramid is:

 V = 1/3 × its base area × its height

* Lets solve the problem

# A cylinder with radius 4 cm and height 3 cm

∵ V = π r² h

∵ π = 3.14

∵ r = 4 cm , h = 3 cm

∴ v = 3.14 (4)² (3) = 150.72 cm³

* The volume of the cylinder is 150.72 cm³

# A cone with radius 5 cm and height 12 cm

∵ V = 1/3 π r² h

∵ π = 3.14

∵ r = 5 cm , h = 12 cm

∴ V = 1/3 (3.14) (5)² (12) = 314 cm³

* The volume of the cone is 314 cm³

# A pyramid with base area 16 cm² and height 30 cm

∵  V = 1/3 × its base area × its height

∵ The area of the base is 16 cm²

∵ The height = 30 cm

∴ V = 1/3 (16) (30) = 160 cm³

* The volume of the pyramid is 160 cm³

# A pyramid with square base of length 3 cm and height 16 cm

∵  V = 1/3 × its base area × its height

∵ The area of the square = s²

∵ The area of the base = 3² = 9 cm²

∵ The height = 16 cm

∴ V = 1/3 (9) (16) = 48 cm³

* The volume of the pyramid is 48 cm³

a right cylinder with radius 4 cm

and height 3 cm = 150.72 cu cm

a pyramid with base area

16 sq cm and height 30 cm = 160 cu cm

a pyramid with a square base of

length 3 cm and height 16 cm  = 48 cu cm

a cone with radius 5 cm and

height 12 cm = 314 cu cm

Answer:

m<5 = 45 deg

Step-by-step explanation:

Since lines g and h are parallel, you have a transversal cutting parallel lines. Then, corresponding angles are congruent.

Angles 1 and 5 are corresponding angles, so they are congruent, and their measures are equal.

m<5 = m<1 = 45 deg.

Angles 5 and 8 are vertical angles, so they are congruent, and their measures are equal.

m<8 = m<5 = 45 deg

Answer: m<5 = 45 deg

Substitution.

Here is an example.

Let x be equal to 3 and y equal to 3.

[tex]x=3, y=3[/tex]

From this we can conclude that the values of both x and y are equal to three therefore x and y have the same value and are equal.

[tex]x\wedge y=3\Longrightarrow x=y[/tex]

Here in your case we have:

[tex]

AB=1, BC=1 \\

AB\wedge BC=1\Longrightarrow AB=BC[/tex]

Hope this helps.

r3t40

[tex]m^{24}n^{18}[/tex]

We can distribute the terms using the distributive property first. [tex](m^4)^6 * (n^3)^6[/tex]

Then, use the power of a power property to multiply the powers. [tex]m^{4*6} * n^{3*6} = m^{24}n^{18}[/tex]

We know that because it forms a right angle, BOF is 90 degrees. We also know that FAO and AOB combine to make 90 degrees.

We already know the value of FOA, so subtract that from 90.

90-35=55.

The measure of AOB is C. 55.

Hope this helps!

Answer:

Here's what I get.

Step-by-step explanation:

[tex]x = 7\frac{1}{2} \div \frac{3}{4}[/tex]

1. Convert the mixed number to an improper fraction

[tex]x = \dfrac{15}{2} \div \dfrac{3}{4}[/tex]

2. Invert the proper fraction and change division to multiplication

[tex]x = \dfrac{15}{2} \times \dfrac{4}{3}[/tex]

3. Multiply numerators and denominators

[tex]x = \dfrac{60}{6}[/tex]

4. Divide the numerator and the denominator

[tex]x = 10[/tex]

The quotient is what you get after you invert the denominator in Step 2 and then multiply the two fractions in Step 3.

Here I'm assuming 7 1/2 / 3/4 is  [tex]7\frac{1}{2} / \frac{3}{4}[/tex]

So let's solve, this first convert the mixed fraction into an improper fraction that is its ideal form to solve an equation

[tex]7\frac{1}{2} = \frac{15}{2}[/tex]

therefore,

= [tex]\frac{15}{2} /\frac{3}{4}[/tex]

= [tex]\frac{15}{2} * \frac{4}{3}[/tex]

= 5 * 2

= 10

A mixed fraction is a combination of a whole number and proper fraction.

Improper fractions and proper fractions are the types of fraction numbers (A fraction number which is written in the form of a/b i.e., " [tex]\frac{a}{b}[/tex] " in which a is called as numerator and b is denominator). A fraction is called improper fraction when its numerator is greater than its denominator and for proper fraction, it's vice versa.

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Answer:

BD=AD-AB=6-4=2

Step-by-step explanation:

You have a line segment AD that measures 6 units

AB is part of it and it is 4 units

There is only one part left of AD and it is BD so you just find what's left of 6 if 4 is already spoken for.

For this case we have that the radius of the large circle is given by AD = 6, while the radius of the small circle is given by AB = 4. We want to know the length BD, that is, the difference of the radius of the big circle and the small one.

[tex]BD = AD-AB = 6-4 = 2[/tex]

So, [tex]BD = 2[/tex]

Answer:

[tex]BD = 2[/tex]

Using the properties of exponents the expression rewritten as

3 • b^5 • c^5

You can group the repeated factors (b and c) and use exponents to represent their multiplication.

The expression 3•b•b•b•b•b•c•c•c•c•c can be written as:

(3)•(b•b•b•b•b)•(c•c•c•c•c)

This can be further simplified by raising b and c to their respective exponents:

(3)•(b^5)•(c^5)

Therefore, the rewritten expression is 3•b^5•c^5.

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Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 2x + 3 + x² - 8 ← collect like terms

               = x² + 2x - 5 ← in standard form → C

The answer can be stated as "The solution to a system of two linear equations in two variables corresponds to the intersection of straight lines represented by them."

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

A system of linear equation in two variables can be written as,

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂= 0

In order to find their solution these equations are solved either by substitution or elimination.

A linear equation in two variable represents a straight line.

Thus, the solution to these equations are the coordinates of the intersection point of these two lines.

Hence, the solution to a system of linear equation in two variables indicate the coordinate of their intersection.

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5 sqrt 3i is the correct answer

Answer: b) √108

c√18.√6

e)√3.√36

Step-by-step explanation:

We know that, for example, √4 = √2² = 2

As the index of the number inside the root maches the index of the root, we can remove it from the root.

And the inverse process is also correct, so 2 can be written as

√2² = √4, this way:

6√3 = √3.√6² = √3.√36 = √108

a) √54 ≠ √108

b) √108 = √108 ok

c) √18.√6 = √108 ok

d) √3.√6 = √18 ≠ √108

e) √3.√36 = √108 ok

f) 108 ≠ √108

The question is asking about how long it will take 3 people to trim a hedge if we know that 4 people can do it in an hour. This is an example of an inverse proportion problem. It would take the three people 45 minutes to trim the hedge.

The question asked is about the concept of rate and inverse proportion in mathematics. The problem states that four people can trim a hedge in one hour. If three people were to do the task, they would collectively be less productive per hour, consequently, it would take them longer to trim the hedge. We can calculate the new time by setting up a proportion of 4 people / 1 hour = 3 people / x hours

Cross-multiplying gives: 4x = 3 which simplifies to x = 3/4 hours. Since there are 60 minutes in an hour, multiply the fraction by 60 to convert to minutes. Thus, it would take the three people 45 minutes to trim the hedge.

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Answer:

Third option

Step-by-step explanation:

By observing the diagram we can see that the diameter of circular base is 6 inches. The diameter will be sued to find the radius.

r = 6/2 = 3 inches

We can also see from the diagram that lateral height denoted by l is 5 in.

We know that the formula for surface area of a cone is given by:

[tex]SA = \pi rl+\pi r^2\\Putting\ the\ values\ of\ r\ and \l\\SA = \pi (3)(5)+\pi (3)^2[/tex]

Comparing it with the options we get that the third option is correct ..

Answer:

The correct answer is third option

 π(3)(5) + π3²

Step-by-step explanation:

Points to remember

Surface area of cone = πrl + πr²

Where r is the radius of the cone and l is the slant height of cone

To find the correct answer

Here r = 6/2 = 3 in

l = 5 in

Surface area =  πrl + πr²

 =  π(3)(5) + π3²

The correct answer is third option

 π(3)(5) + π3²

Answer: option b.

Step-by-step explanation:

You need to remember that:

[tex]b^\frac{m}{n}=\sqrt[n]{b^m}\\\\\sqrt[n]{a^n}=a[/tex]

Then, you can rewrite [tex](-32)^\frac{3}{5}[/tex] as:

[tex]=\sqrt[5]{(-32)^3}[/tex]

Now you need to descompose 32 into its prime factors:

[tex]32=2*2*2*2*2=2^5[/tex]

Rewriting:

 [tex]=\sqrt[5]{(-2^5)^3}[/tex]

The power of a power property states that:

[tex](a^b)^c=a^{(bc)}[/tex]

Then:

[tex]=\sqrt[5]{(-2)^{15}}=(-2)^3=-8[/tex]