a diagnol of a cube measures 15 cm and the length of an edge is 75 square root.What is the length of the diagnol of a face of the cube? Round to the nearest tenth
A. 7.1
B. 12.2
C. 13
D. 15

Answer:

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

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

y-1+(-1/2)^2=x^2-x+(-1/2)^2

This allows me to write the right hand side as a square.

y-1+1/4=(x-1/2)^2

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

[tex]\pm \sqrt{y-3/4}=x-1/2[/tex]

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

[tex]\sqrt{y-3/4}=x-1/2[/tex]

Add 1/2 on both sides:

[tex]1/2+\sqrt{y-3/4}=x[/tex]

The last step is to switch x and y:

[tex]1/2+\sqrt{x-3/4}=y[/tex]

[tex]y=1/2+\sqrt{x-3/4}[/tex]

[tex]f^{-1}(x)=1/2+\sqrt{x-3/4}[/tex]

Answer:

Var(U)=50

Step-by-step explanation:

Given

Var(X) = 2

We have to find

Var(U) when U = 5x+2

So,

When a variable is multiplied with an integer, the variance of that variable is multiplied with the square of that number i.e. Var(aX) = a^2 Var(X) This the property of variance.

As here x is multiplied with 5,

Var(5x) = 5^2 var(X) = 25*2 = 50

If the same integer is added to all the data values, there is no change in variance that is why the +2 will not affect the variance of U ..

For this case we must reduce the following fraction:

[tex]\frac {130xy} {50x}[/tex]

Canceling similar terms in the numerator and denominator:

[tex]\frac {130y} {50}[/tex]

Dividing by 10 the numerator and denominator we have:

[tex]\frac {13y} {5}[/tex]

Finally, the expression is reduced to:

[tex]\frac {13y} {5}[/tex]

Answer:

[tex]\frac {13y} {5}[/tex]

The completed table:

x y

2 2

4 6

6 10

7 12

For each value of x, we substitute it into the function rule y = 2x - 2 and evaluate to find the corresponding value of y.

Calculations:

When x = 2: y = 2(2) - 2 = 4 - 2 = 2

When x = 4: y = 2(4) - 2 = 8 - 2 = 6

When x = 6: y = 2(6) - 2 = 12 - 2 = 10

When x = 7: y = 2(7) - 2 = 14 - 2 = 12

Answer:

See below.

Step-by-step explanation:

[tex] f(x) = x^2 - 16 [/tex]

Replace f(x) with y.

[tex] y = x^2 - 16 [/tex]

Switch x and y.

[tex] x = y^2 - 16 [/tex]

Solve for y.

[tex] y^2 = x + 16 [/tex]

[tex] y = \pm\sqrt{x + 16} [/tex]

Replace y with f^(-1)(x).

[tex] f^{-1}(x) = \pm\sqrt{x + 16} [/tex]

The relation above is not a function, so the given function f(x) does not have an inverse unless the domain is restricted.

Answer:

F-1(x) =  √(x + 16).

Step-by-step explanation:

Let y = x^2 - 16

First make x the subject:

x^2  = y + 16

x = √(y + 16)

Now  replace x by the inverse  f-1(x) and replace y by x:

f-1(x) =  √(x + 16).

Note we only take the positive square root otherwise we would not have a function.

Answer:

The correct option is D.

Step-by-step explanation:

Let the number of cars Zane washed on Saturday be x.

It is given that he gets paid $8 for every car he washes and made a total of $64 on Saturday.

We need to write an equation to show how many cars Zane washed on Saturday.

If he get $8 for one car, then the total amount he get for x cars is

Total amount = 8x

He made a total of $64 on Saturday, so

[tex]8x=64[/tex]

The required equation is 8x=64.Therefore the correct option is D.

Answer:

x = 2, y = -6, and z = 9

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

•  3  -4   1      |  39

•  -3   1  -2     |  -30

•  2  -2  3      |  43

Step 2: Add row 1 it into row 2:

•  3 -4   1 |  39

•  0  -3  -1 |   9

•  2 -2  3 |  43

Step 3: Multiply row 1 with -2/3 and add it in row 3 and then multiply row 3 with 3:

•  3 -4   1   |  39

•  0  -3  -1   |   9

•  0  2    7  |  51

Step 4: Multiply row 2 with 2/3 and add it in row 3 and then multiply row 3 with 3:

•  3 -4     1       |  39

•  0 -3    -1       |   9

•  0 0   19/3     |  57

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• 3x - 4y + z = 39  

• -3y - z = 9

• (19/3)z = 57 (This implies that z = 9.)

Step 6: Since we have calculated z = 9, put this value in equation 2:

• -3y - 9 = 9

• -3y = 18

• y = -6.

Step 8: Put z = 9 and y = -6 in equation 1:

• 3x - 4(-6) + 9 = 39

• 3x + 24 + 9 = 39

• 3x = 6.

• x = 2.

So final answer is x = 2, y = -6, and z = 9!!!

After simplifying each proportion or using cross-multiplication, it is clear that option B.) 18/48 = 20/50 is the false proportion.

For A.) 24/30 = 20/25, we can simplify by dividing both sides by 5. Simplified, it becomes 4/5 = 4/5, which is true.

For B.) 18/48 = 20/50, simplifying both sides by 2 gives us 9/24 = 10/25, which is not equivalent since 9x25 is not equal to 24x10. Therefore, this proportion is false.

For C.) 25/45 = 75/135, simplifying by dividing both numbers by 15 gives us 5/9 = 5/9, which is true.

For D.) 10/25 = 40/100, simplifying by dividing both sides by 10 gives us 1/2.5 = 4/10. If we further simplify 4/10 by dividing both the numerator and denominator by 2, we get 1/2.5 = 2/5, which is true after rounding the decimal in the first ratio to 2.5.

Comparing these results, option B is the false proportion.

38<4x+3+7-3x

38<x+10

28<x

Ans: x>28

For this case we must solve the following inequality:

[tex]38 <4x + 3 + 7-3x[/tex]

We add similar terms to the right side of inequality:

[tex]38 <4x-3x + 3 + 7\\38 <x + 10[/tex]

We subtract 10 from both sides of the inequality:

[tex]38-10 <x\\28 <x[/tex]

Thus, the solution will be given by all values of "x" greater strict to 28.

Answer:

[tex]x> 28[/tex]

Answer:

[tex]\large\boxed{\$10,999}[/tex]

Step-by-step explanation:

In this question, we're trying to find the value of Tom's car after 3 years.

From the question, we know that:

With the information above, we can solve the question.

We can do the simplest way by multiplying 250 by 36, since there's 36 months in 3 years, and then we would subtract that from our starting value.

Solve:

[tex]250*36=9000\\\\\text{We would then subtract 9000 from 19,999}\\\\19,999=10,999\\\\\text{Cars value after 3 years is}\, \bf\$10,999[/tex]

When you're done solving, you should get 10,999.

This means that Tom's car worth in 3 years is $10,999.

Answer:

10,999

Step-by-step explanation:

250 x 36 = 9,000

9,000 is how much the car went down in value it went down 3,000 a year for three years

19,999 - 9,000 = 10,999

10,999 is how much the car is worth after 3 years

Answer: y=-6/7x

Step-by-step explanation: A perpendicular slope is opposite reciprocal. The opposite reciprocal of 7/6 is -6/7. The equation of the perpendicular line is y=-6/7x.

Answer:

y+1 = 2/5(x+3)

Step-by-step explanation:

We have a point and a slope so we can use point slope form

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y--1 = 2/5 (x--3)

y+1 = 2/5(x+3)

Answer:

-1 and 3

Step-by-step explanation:

The x intercepts are where the graph crosses the x axis.

Looking at the graph it crosses at two points

x = -1 and x=3

Answer:

12 students from math club

Step-by-step explanation:

Number of vans = 2

Number of students in each van = 6

Number of students who went from math club to the soap box = ?

You can apply the following expression:

Total  number of students=Number of students per van * Number of vans

Total  number of students= 6 *2

= 12 students from math club....

Answer:

Step-by-step explanation:

Answer:

y+4=-(2/5)(x-5) ----> equation of the line into point slope form

y=-(2/5)x-2 ----> equation of the line into slope intercept form

2x+5y=-10 ----> equation of the line in standard form

Step-by-step explanation:

step 1

Find the slope of the given line

we have

5x-2y=-6

isolate the variable y

2y=5x+6

y=2.5x+3

The slope m of the given line is m=2.5

step 2

Find the slope of the line perpendicular to the given line

We know that

If two lines are perpendicular, then their slopes are inverse reciprocal each other

so

m1=5/2

the inverse reciprocal is

m2=-2/5

step 3

Find the equation of the line into point slope form

y-y1=m(x-x1)

we have

m=-2/5

point (5,-4)

substitute

y+4=-(2/5)(x-5) ----> equation of the line into point slope form

y=-(2/5)x+2-4

y=-(2/5)x-2 ----> equation of the line into slope intercept form

Multiply by 5 both sides

5y=-2x-10

2x+5y=-10 ----> equation of the line in standard form

The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) are as follows:

[tex]y+4=-\frac{2}{5}(x-5)[/tex]  

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

2x + 5y = - 10

Perpendicular lines follows the mathematical principle below.

where

m₁ and m₂ are slopes.

Therefore, using slope intercept form,

y = mx + b

where

m = slope

b = y-intercept

Therefore,

5x - 2y = -6

-2y = -5x - 6

y =  5 / 2 x + 3

The slope is 5 / 2 x

Applying perpendicular rule,

5 / 2m₂ = - 1

m₂ = - 2 / 5

Passing through (5, -4)

-4 = -2/5 (5) + b

-4 + 2 = b

b = - 2

Therefore, the equation is [tex]y=-\frac{2}{5}x-2[/tex]. It can be simplified as follows

5y = -2x - 10

Therefore,

2x + 5y = - 10

using y - y₁ = m (x - x₁)  it will be as follows:

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

learn more on perpendicular line here: https://brainly.com/question/13254903

Answer:

the IQR is 41 because 62-21=41

Answer:

83

Step-by-step explanation:

12, 21, 43, 62, 71

Median: 43

Lower quartile: 16.5

Upper quartile: 66.5

Interquartile range: 66.5 - 16.5 = 83

Answer:

28

Step-by-step explanation:

8C2 = 28

Answer:

C

Step-by-step explanation:

When we set the numerator equal to 0 and solve for x, that value is the horizontal asymptote (a line the graph come towards, but never crosses).

Looking at the graph, the horizontal asymptote is x = 2, so which one of the 4 functions has a horizontal asymptote of 2? Let's check.

A) 2x - 1 = 0

x = 1/2

B) same, x = 1/2

C) 2x -4 = 0

x = 2

D) same as A,B, x = 1/2

As we can see, option C has the right horizontal asymptote and A,B,D are eliminated. So answer is C.

Answer:

Step-by-step explanation:

We know: measures of angles in a triangle add up to 180°.

Therefore we have the equation:

[tex]\gamma+\gamma+72^o=180^o[/tex]      subtract 72° from both sides

[tex]2\gamma=108^o[/tex]       divide both sides by 2

[tex]\gamma=54^o[/tex]

Answer:

I. 45.

Step-by-step explanation:

3 green peppers      g green peppers

--------------------     =  --------------------------

4 red peppers           60 red peppers

Using cross products

3 * 60 = 4 * g

180 = 4g

Divide each side by 4

180/4 =4g/4

45 = g

There are 45 green peppers

Answer:

four thousand one hundred

Step-by-step explanation:

expand the form

Answer:

Option B

Step-by-step explanation:

As per the contract

"The Buyer shall make each monthly payment by the first day of the month it is due."

this makes option a :"Pay the monthly payment on time." responsibility of the buyer.

"A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00."

this makes option c :"Pay an additional $75.00 with a payment made after the 15th day of the month it was due." responsibility of the buyer.

"Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”

this makes option d :"Notify the bank of his or her intent to split a late payment into three partial payments." responsibility of the buyer.

So,buyer needs to only notify the bank about the monthly payments in case of delinquency and not about if payment is going to be late or not.  

Hence Option B is correct  

Notify the bank if a payment is going to be late!

The option that is not a responsibility of the buyer is notify the bank if a payment is going to be late.

A contract is an agreement that is enforceable legally between two or more parties to give something or render a services.

To learn more about contracts, please check: brainly.com/question/12991600

Answer:

t = 3.5c

Step-by-step explanation:

The correct table is attached in the image below. Since the papers are being folded at a constant rate, there is a linear relationship between c, the number of crane and t, the total time in minutes.

We can find the equation of this linear relation using any two pair of points from the table. Using the first two points: (5, 17.5) and (8, 28)

First we need to find the slope of the line which gives the relation between the two variables.

[tex]Slope=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}[/tex]

y coordinates represents the dependent variable which is the time in this case and x coordinates represents the independent variable which is number of cranes in this case. Using the values from the two points we considered:

[tex]Slope=\frac{28-17.5}{8-5}=3.5[/tex]

Thus, the equation of the line will be of the form:

t = mc + b

m is the slope here. Using its values, we get:

t = 3.5c + b

b is known as y-intercept. We need the value of b to complete the equation. Substituting the value of t and c from any pair we can find the value of b.

Using the point (5, 17.5), we get:

17.5 = 3.5(5) + b

b = 0

This means, the equation of the line would be:

t = 3.5c

Answer:

t=3.5c

Step-by-step explanation:

Answer:

[tex]y = \frac{1}{3} x + 20[/tex]

Step-by-step explanation:

We know that the toll road is 3 times faster than the side streets.

If 'x' represents the number of minutes she usually spend taking the side streets. The [tex]\frac{1}{3} x[/tex]  represents the time she takes taking the toll road.

Also we need to create an equation to represent her total travel time, including wait time. Therefore, the equation is:

[tex]y = \frac{1}{3} x + 20[/tex]

Therefore, the equation is:  [tex]y = \frac{1}{3} x + 20[/tex]

Answer:

The answer is 9

Step-by-step explanation:

When you divide 54 by 6 you get 9 because 10 times 6 equals 60 so if you minus 6 you get 54 which equals 6 times 9. :)

Answer:

9 or 9/1

Step-by-step explanation:

To convert improper fractions to whole numbers, you have to divide the numerator by the denominator.

So, 54 divided by 6 is 9

So 54/6 as a whole number 9

If you want to keep as a fraction it would be 9/1

Answer:

4

Step-by-step explanation:

16/4 = 4

if 75% of equipment is iron then do the math.

So it would be 4(2) + 4 = 75% of 16

So if 75% of 16 is 12 you need that extra 4 to get you to 16

The number of woods are [tex]\fbox{\begin \\\math{4}\\\end{minispace}}[/tex].

Further explanation:

Consider the number of woods as [tex]x[/tex] and number of irons as [tex]y[/tex].

Since the number of irons is four more than two times the number of woods, the number of irons is calculated as follows:

[tex]y=2x+4[/tex]                                                      ......(1)

The number of equipment consists of the woods and irons, therefore, the number of equipment [tex]n[/tex] is written as the sum of number of woods [tex]x[/tex] and number of irons [tex]y[/tex] as follows:

[tex]n=x+y[/tex]                                                                  ......(2)

From equation (1), substitute [tex]2x+4[/tex] for [tex]y[/tex] in above equation.

[tex]n=x+2x+4\\n=3x+4[/tex]

Since the total equipment contains [tex]75\%[/tex] of irons, it can be written as follows:

[tex]y=0.75n[/tex]

From equation(1) and (2) substitute [tex]2x+4[/tex] for [tex]y[/tex] and [tex]3x+4[/tex] for [tex]n[/tex] in above equation.

[tex]2x+4=0.75(3x+4)\\\Leftrightarrow2x+4=2.25x+\\\Leftrightarrow4-3=2.25x-2x\\\Leftrightarrow1=0.25x\\\Leftrightarrow x=1/0.25\\\Leftrightarrow x=4[/tex]

Substitute 4 for [tex]x[/tex] in equation (1) to obtain the number of irons.

[tex]y=2(4)+4\\y=8+4\\y=12[/tex]

Thus, the number of woods are 4 and number of irons are 12.

Learn more:  

1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)  

https://brainly.com/question/1332667  

2. which is the graph of f(x) = (x – 1)(x + 4)?  

https://brainly.com/question/2334270  

Answer details:  

Grade: Middle school.  

Subjects: Mathematics.  

Chapter: Linear equation.  

Keywords: Linear equation, Function, Golf club, woods, y=2x+4, Variable, Middle term split method, Binomial, straight lines, Quadratic, Polynomial, Zeros, Zeros of a function, Expression, Equation, x, -x.

Answer:

Look at the picture.

Step-by-step explanation:

A height  of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the side opposite the vertex).

Answer:

[tex]\large\boxed{d.\ (-4,\ 0)}[/tex]

Step-by-step explanation:

The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):

[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points F(-5, -3) and G(-3, 3).

Substitute:

[tex]M_{FG}(x,\ y)\\\\x=\dfrac{-5+(-3)}{2}=\dfrac{-8}{2}=-4\\\\y=\dfrac{-3+3}{2}=\dfrac{0}{2}=0[/tex]

Answer:

9

Step-by-step explanation:

Each animal have 2 eyes so basically 18/2 = 9

That's the answer, hope this helps.

:)

Answer:

20 animals.

Step-by-step explanation:

Sparkles the unicorn is eating an apple, when a chango removes the apple from its mouth and bites it. We already have 2 animals in the forest: the unicorn and the monkey.

Then,  the unicorn realizes that 18 pairs of eyes are watching the monkey. That gives us another 18 animals (considering everyone has 2 eyes).

so, in total we have 20 animals:  (18 + unicorn + monkey) = 20 animals.

Answer:

The correct answer is last option 362.9 ft

Step-by-step explanation:

Points to remember

Sin θ = Opposite side/Hypotenuse

To find the value of x

It is given that length of slope = 1500 ft

From the figure we can get,

Sin 14 =  Opposite side/Hypotenuse

 =  x/1500

x = 1500 * sin(14)

 = 1500 * 0.2419

 = 362.88 ft ≈ 362.9 ft

The correct answer is last option 362.9 ft