One side of a triangle is 3 times the second side. The third side is 13 feet longer than the second side. The perimeter of a triangle is 68 feet. Find the length of each side.

Answer:

-2

Step-by-step explanation:

So we want to find the value of:

[tex](-6)+(4)[/tex]

Simply add:

[tex](-6)+4=-2[/tex]

Thus, drop the word SUM on -2.

Further notes:

To use the number line to solve, first start by placing your point on -6.

Since we are adding 4 to -6, we move to the right. Thus, move from -6 four spaces to the right.

If you do so correctly, you will end up at -2, the same answer we acquired previously.

Answer:

[tex]\Huge \boxed{-2}[/tex]

Step-by-step explanation:

The sum is the result from adding two or more numbers to each other.

[tex]-6 + 4 = - 2[/tex]

-6 is the starting point on the number line.

4 is added to -6, so an arrow from -6 goes 4 units to the right of the number line.

The arrow stops at -2.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Large eggs : ≥2 ounces

Mean of 48 large eggs = 2.1 ounces

Mean absolute deviation = 0.08 ounces

0.08 ounces here is the mean absolute deviation of the 48 large eggs weighed, meaning that:

The average of the sum of the absolute differences in each individual egg and the mean value of all eggs weighed is 0.08.

This means that the average difference, variability or deviation in the weight of large eggs weighed is 0.08 ounces around the mean value of all eggs weighed.

Mean Absolute Deviation (MAD) :

Σ|xi - mean| / n

xi = each individual value

n = number of values

Answer:

$2800[tex]x[/tex]

Step-by-step explanation:

Tuition fee per student = $2800/student

if there are [tex]x[/tex] amount of students, then the total costs of tuition that will be generated will be

([tex]x[/tex] students) x ($2800/student) = $2800[tex]x[/tex]

If for example, there are 200 students in this school, then in this case, [tex]x[/tex] = 200 students.

Total cost = (200 students) x ($2800/student) = $560000.

In simple terms, the cost of [tex]x[/tex] students paying tuition of $2800, is [tex]x[/tex] multiplied by the $2800 tuition for each student which is $2800[tex]x[/tex]

Answer:

16

Step-by-step explanation:

Given the equation, [tex] 200 + 10x = 120 + 15x [/tex], let's solve for x as follows,

Subtract 200 from both sides

[tex] 200 + 10x - 200 = 120 + 15x - 200 [/tex]

[tex] 10x = - 80 + 15x [/tex]

Subtract 15x from both sides

[tex] 10x - 15x = - 80 + 15x - 15x [/tex]

[tex] -5x = - 80 [/tex]

Divide both sides by -5

[tex] \frac{-5x}{-5} = \frac{-80}{5} [/tex]

[tex] x = 16 [/tex]

The discriminant is:

[tex]D=4^2-4(1)(2)=8[/tex]

So [tex]D>0[/tex] which means there are two distinct real solutions.

Hope this helps.

Answer:

2 real solutions

Step-by-step explanation:

x^2 +4x+2 =0

This is in the form ax^2 + bx +c

The discriminant is

b^2 -4ac

4^2 - 4*1*2

16 - 8

8

Since this is greater than 0, we have 2 real solutions

Answer:

9x

Step-by-step explanation:

X=1/7y-9

X+9=1/7

7x + 63 = y

Y=7x+63

Y-7x=63

Y=63/7x

Y=9x

Answer:

7, -2

Step-by-step explanation:

we call the first number "X" and the second one "Y"

X is 9 more than Y! which means we need to add 9 to Y so it'll be equal to X. so: Y+9=X

also 2×(X+Y)=10

you can also write this down as: 2X+2Y=10

now we have:

X=Y+9

2X+2Y=10

you can now put what equals to X in the second Equation:

2(Y+9)+2Y=10 => 2Y+18+2Y=10 => 4Y=10-18 =>Y= -2

the only thing left to do is to put Y= -2 in the first equation:

X= -2+9 => X=7

An algebraic equation is an equation with unknown variables which can be represented using any number of the alphabet.

The two numbers are  7 and -2

Let's represent the unknown numbers which are the unknown variables with the letters

Let the first number = m

The second number = n

A number is 9 more than another number. This statement is represented by the algebraic equation:

m = 9 + n .......... Equation 1

Twice the sum of the two numbers is 10. This statement is represented by the algebraic equation:

2 (m + n) = 10

2m + 2n = 10...................Equation 2

We substitute 9 + n for "m" in Equation 2

2(9 + n) + 2n = 10

18 + 2n + 2n = 10

Subtract 18 from both sides

18 - 18  + 2n + 2n = 10 - 18

4n = -8

Divide both sides by 4

4n/4 = -8/4

n = -2

We solve for m using Equation 1

m = 9 + n

m = 9 + (-2)

m = 9 - 2

m = 7

Therefore, the two numbers are  7 and -2

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Answer:

p=-3

Step-by-step explanation:

Answer:

-4/2=2p

Step-by-step explanation:

5p - 8/2 = 7p +4/2

-5p           -5p

        -8/2 = 2p + 4/2

        -4/2            -4/2

Step-by-step explanation:

The domain and target set of functions f and g given is expressed as;

f(x) = 2x+3 an g(x) = 5x+7 on R. To calculate the given functions, the following steps must be followed.

a) f◦g

f◦g = f(g(x)]) = f(5x+7)

To solve for the function f(5x+7), the variable x in f(x) will be replaced with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Therefore the function f◦g is equivalent to 10x+17

b) For the composite function g◦f  

g◦f = g(f(x)])

g(f(x)) = g(2x+3))

To drive the functon g(2x+3), the variable x in g(x) will be replaced with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

This shoes that the composite function g◦f = 10x+22

c) To get the inverse of the composite function f◦g i.e (f◦g)⁻¹

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = (x-17)/10

Hence (f◦g)⁻¹ = (x-17)/10

d) For the function f⁻¹◦g⁻¹

First we need to calculate for the inverse of function f(x) and g(x) as shown:

For f⁻¹(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = (x-3)/2

f⁻¹(x) = (x-3)/2

Similarly for the function g⁻¹(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = (x-7)/5

g⁻¹(x) = (x-7)/5

Now to get f⁻¹◦g⁻¹

f⁻¹◦g⁻¹= f⁻¹(g⁻¹(x))

f⁻¹(g⁻¹(x)) = f⁻¹((x-7)/5)

Since f⁻¹(x) = (x-3)/2

f⁻¹((x-7)/5) = [(x-7)/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f⁻¹◦g⁻¹= (x-22)/10

e) For the composite function g⁻¹◦f⁻¹

g⁻¹◦f⁻¹= g⁻¹[f⁻¹x)]

g⁻¹[f⁻¹(x)] = g⁻¹((x-3)/2)

Since g⁻¹(x) = (x-7)/5

g⁻¹(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5  

= [(x-17)/2]/5

= (x-17)/10

Therefore the composite function g⁻¹◦f⁻¹= (x-17)/10

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

the third option

Answer:

[tex]n = \frac{11}{2} = 5.500[/tex]

Answer:

35:53

3:8

Step-by-step explanation:

Answer:

For x = 0, P(x = 0) = 0.35

For x = 1, P(x = 1) = 0.54

For x = 2, P(x = 2) = 0.11

For x = 3, P(x = 3) = 0

Step-by-step explanation:

We are given that the Sky Ranch is a supplier of aircraft parts. Included in stock are 6 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected, one at a time, without replacement.

Let X = the number that are not correctly calibrated.

Number of altimeters that are correctly calibrated = 6

Number of altimeters that are not correctly calibrated = 2

Total number of altimeters = 6 + 2 = 8

(a) For x = 0: means there are 0 altimeters that are not correctly calibrated.

This means that all three selected altimeters are correctly calibrated.

Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]

The number of ways of selecting 3 altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_3[/tex]

So, the required probability = [tex]\frac{^{6}C_3}{^{8}C_3}[/tex]  

                                              = [tex]\frac{20}{56}[/tex]  = 0.35

(b) For x = 1: means there is 1 altimeter that is not correctly calibrated.

This means that from three selected altimeters; 1 is not correctly calibrated and 2 are correctly calibrated.

Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]

The number of ways of selecting 2 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_2[/tex]

The number of ways of selecting 1 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_1[/tex]

So, the required probability = [tex]\frac{^{6}C_2 \times ^{2}C_1 }{^{8}C_3}[/tex]  

                                                = [tex]\frac{30}{56}[/tex]  = 0.54

(c) For x = 2: means there is 2 altimeter that is not correctly calibrated.

This means that from three selected altimeters; 2 are not correctly calibrated and 1 is correctly calibrated.

Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]

The number of ways of selecting 1 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_1[/tex]

The number of ways of selecting 2 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_2[/tex]

So, the required probability = [tex]\frac{^{6}C_1 \times ^{2}C_2 }{^{8}C_3}[/tex]  

                                                = [tex]\frac{6}{56}[/tex]  = 0.11

(d) For x = 3: means there is 3 altimeter that is not correctly calibrated.

This case is not possible, so this probability is 0.

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

{z = 3 y + (-x - 15)

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

-30 - x + 7 y = 1

Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

-30 - x + 7 y = 1

Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

y = 4

Hint: | Perform a back substitution.

Substitute y = 4 into the first and second equations:

{z = -x - 3

x = -3

y = 4

Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

{z = 0

x = -3

y = 4

Hint: | Sort results.

Collect results in alphabetical order:

Answer:  {x = -3 , y = 4 , z = 0

Answer:

y = -7.

Step-by-step explanation:

It is horizontal so it will pass through the y axis where y = -7. It is parallel to the x axis so will never pass through it.

Answer:

C. . how old they are

Step-by-step explanation:

Geologist are people that deal with the internal structure of the earth.

They study Rocks, and it's deposit accumulated millions of years back.

They can also give account of what happened in the past and the types of organisms that existed in the past.

Fossils are traces of event, remains of dead animals and decomposed object.

So geologist can give account of how many years a particular fossil has lived in that particular environment.

Answer:

x = 12

Step-by-step explanation:

they are virtical menaing they are the same value

6x + 7 = 8x - 17

6x + 24 = 8x

24 = 2x

12 = x

Answer:

x = 12

Step-by-step explanation:

Opposite angles are equal, so 6x + 7 = 8x - 17.

6x + 7 = 8x - 17

7 = 2x - 17 (take away 6x from both sides)

2x = 24 (Add 17 to Both Sides)

x = 12 (answer)

Answer:

x²-7x+2

Step-by-step explanation:

x²+2-7x in standard form is

x²-7x+2

====================================================

Explanation:

Set A = {4,5,6,7,8,9} since these values are larger than 3 and smaller than 10. We only consider whole numbers in this range.

Set B = {1,2,3,4,5,6,7} represents positive whole numbers less than 8

To find the set [tex]A \cap B[/tex] we need to see which values are in both A and B at the same time. Those values are {4,5,6,7}

So [tex]A \cap B = \{4,5,6,7\}[/tex]

--------

side note: the notation [tex]A \cap B[/tex] means "A intersect B", so we're looking at where the two sets intersect or overlap (ie what they have in common).

Answer:

Step-by-step explanation:

y=-1/5x+4

----------

The slope of the perpendicular line is always the opposite reciprocal of the original line

For example: the opposite reciprocal of 5 is -1/5

Answer:

Step-by-step explanation:

Given:

u = 1, 0, -4

In unit vector notation,

u = i + 0j - 4k

Now, to get all unit vectors that are orthogonal to vector u, remember that two vectors are orthogonal if their dot product is zero.

If v = v₁ i + v₂ j + v₃ k is one of those vectors that are orthogonal to u, then

u. v = 0                    [substitute for the values of u and v]

=> (i + 0j - 4k) . (v₁ i + v₂ j + v₃ k)  = 0               [simplify]

=> v₁ + 0 - 4v₃ = 0

=> v₁ = 4v₃

Plug in the value of v₁ = 4v₃ into vector v as follows

v = 4v₃ i + v₂ j + v₃ k              -------------(i)

Equation (i) is the generalized form of all vectors that will be orthogonal to vector u

Now,

Get the generalized unit vector by dividing the equation (i) by the magnitude of the generalized vector form. i.e

[tex]\frac{v}{|v|}[/tex]

Where;

|v| = [tex]\sqrt{(4v_3)^2 + (v_2)^2 + (v_3)^2}[/tex]

|v| = [tex]\sqrt{17(v_3)^2 + (v_2)^2}[/tex]

[tex]\frac{v}{|v|}[/tex] = [tex]\frac{4v_3i + v_2j + v_3k}{\sqrt{17(v_3)^2 + (v_2)^2}}[/tex]

This is the general form of all unit vectors that are orthogonal to vector u

where v₂ and v₃ are non-zero arbitrary real numbers.

[tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]

A vector is a quantity that has both magnitude and direction.

Two vectors are said to be orthogonal if they are perpendicular to each other.

Unit vectors orthogonal to [tex]u=\left ( a,b,c \right )[/tex] are given by [tex]\left ( \frac{a}{\sqrt{a^2+b^2+c^2}},\frac{b}{\sqrt{a^2+b^2+c^2}},\frac{c}{\sqrt{a^2+b^2+c^2}} \right )[/tex]

So, vectors orthogonal to [tex]u=\left ( 1,0,-4\right )[/tex] are [tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )[/tex]

[tex]\left ( \frac{1}{\sqrt{1^2+0^2+(-4)^2}},\frac{0}{\sqrt{1^2+0^2+(-4)^2}},\frac{-4}{\sqrt{1^2+0^2+(-4)^2}} \right )=\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]

So, unit vector orthogonal to [tex]u[/tex] is [tex]\left ( \frac{1}{\sqrt{17}},0, \frac{-4}{\sqrt{17}}\right )[/tex]

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Answer:

A simple random technique used to choose let's say 100 students can be adopted

Step-by-step explanation:

Because it give each student equal opportunity of being selected to avoid bias

Answer:

Sebastian didn't interpret the numbers correctly (See explanation)

Step-by-step explanation:

If you go up an elevator, you are gaining floors, so the number is positive.

If you go down an elevator, you are losing floors, so the number is positive.

Looking at the statement, he went 7 floors up to his room, then 9 floors down to the parking garage this can be represented as [tex]7 - 9[/tex], since the 7 is positive and the 9 is negative.

Sebastian described the movement as [tex]9 + -7[/tex], which is wrong - 9 should be -9 and -7 should be 7.

Hope this helped!

Answer:

Step-by-step explanation:

Let the lobby level be the reference point for Seb's movement.

The following describes his motion:  +7 - 9.  This puts him 2 floors below the lobby level.

Seb's "9 + (-7)" is incorrect because it indicates an upward trip, whereas the actual direction was downward.  Similarly, "-7" indicates a downward trip, whereas the action direction was upward.

Answer:

a^7

Step-by-step explanation:

[tex]\frac{a^{10}}{a^3}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\frac{a^{10}}{a^3}=a^{10-3}\\\\=a^7[/tex]

Answer:

7r + 4t = 14

<=> 7r = 14 - 4t

<=> r = (14 - 4t) / 7

Answer: r = f(t)

[tex]r = 2 - \frac{4}{7} t[/tex]

The relationship 7r+4t=14 in terms of t or as a subject r is r = (14 - 4t)/7.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

 7r+4t=14

Write the relationship as a function r=f(t).

Make subject as r

7r = 14 - 4t

r = (14 - 4t)/7 = f(t)

Thus, the relationship 7r+4t=14 in terms of t or as a subject r is r = (14 - 4t)/7.

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Answer:

6

Step-by-step explanation:

f(x)= x

g(x) = x + 6,

g(f(o))

Let x = 0

f(0) = 0

g(f(0) = g(0) = 0+6 = 6

Answer:

2.22

Step-by-step explanation:

To get 2 2/9 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction. Here are the detailed math steps we use to convert 2 2/9 mixed number to decimal form:

Step 1: Multiply the whole number by the denominator:

2 × 9 = 18

Step 2: Add the product you got in Step 1 to the numerator:

18 + 2 = 20

Step 3: Divide the sum from Step 2 by the denominator:

20 ÷ 9 = 2.222222

That's it! The answer to 2 2/9 in decimal form is displayed below:

2 2/9 ≈ 2.22

Answer:

27 minutes

Step-by-step explanation:

Given that :

Total number of planes = 100

10 planes were delayed by an hour each= 60 minutes;

Total delay time for the 10 planes = (60 * 10) = 600 minutes

Of the 90 remaining :

Half (45) left on time = no delay

(Delay2) : Half (45) experieced a average delay of 20 minutes.

Total delay time for the 45 planes = (45 * 20) = 900

Hence,

Overall delay time = (600 + 900) = 1500 minutes

Number of planes delayed = (10 +45) = 55 planes

Average flight delay :

(Overall delay time / number of planes delayed)

(1500 / 55) = 27.27

= 27 minutes ( to the nearest minute)

Answer:

27

Step-by-step explanation: