Given f(x)=-2x-1f(x)=−2x−1, solve for x when f(x)=-7f(x)=−7

The equation for the Volume (V) of the cone given is,

We are to isolate 'h' in the equation above

SOLUTION

Multiply both sides by 3

Simplify

Divide both sides by πr²

Simplify

Hence, the answer is

Hello there. To solve this question, we'll have to remember some properties about the pythagorean theorem and right triangles.

Given a triangle with side lengths 10 m, 24 m and 26 m, we have to determine whether this is a right triangle or not.

First, let's assume these are the sides lengths of a right triangle, as follows:

Notice in this case we choose the largest side to be the hypotenuse. We know that the largest side of a triangle has to be less than the sum of the legs and any combination would do, but since we'll apply the Pythagorean theorem, we already know that the hypotenuse has to be the largest side of the triangle.

For a right triangle with legs a, b and hypotenuse c, the Pythagorean theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, that is

Hence we plug a = 10, b = 24 and c = 26.

We have to see if this equality will hold for the values;

On the right hand side, square the number

On the left hand side, square and add the numbers

Notice we got the same answer, then we say that these values satisfy the Pythagorean theorem.

Therefore, this is a right triangle.

Based on the probability values, it will take the student 2 hours to stay outside the home

The given parameters are:

Probabilities

P(1) = 0.4

P(2) = 0.3

P(3) = 0.3

Time

Time 1 = 2 hours

Time 2 = 3 hours

Time 3 = 1 hour

When the above are represented on a table, we have the following table of values

Time (x)                    |   2        3          1

Probability (P(x))       | 0.4      0.3     0.3

The expected value of the student is then calculated as

E(x) = ∑ x * P(x)

Substitute the known values in the above equation

E(x) = 2 * 0.4 + 3 * 0.3 + 1 * 0.3

Evaluate the products

E(x) = 0.8 + 0.9 + 0.3

Evaluate the sum

E(x) = 2

Hence, the expected value is 2

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The net force on the cart is 62N

and the vertical component =36.64 N

the horizontal component= 50N

What is revolution of vector?

The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component

30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.

40N tension isN 30° E which means

the vertical component= 40 sin60=36.64N

Horizontal component= 40 cos 60= 20N

sum of vertical = 36.64N +0= 36.64N

sum of horizontal= 30N+20N= 50N

60° was used for tension 40N because the angle of vector must always lie on the horizontal axis

therefore the net force F is obtained by using Pythagoras theorem

F= √(50^2+36.64^2)

= 62N to the nearest whole number.

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1) 1/6

3) -7/6

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Given:

The functions

Required:

Determine changes made in g(x) to get f(x).

Explanation:

The steps are:

So. fourth option is describing the f(x).

The graph

Answer:

Completed the answer.

Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

15/x = 3

Total number of slices = 15

Number of students = x

Each student's share = 3

(Total number of slices)/(Number of students) = Each student's share

Therefore, the mathematical statement representing the illustration is:

15/x = 3

At first ,we should know that :

The relation between x and y will be a function when each value of x appeared one time

We will check the options:

A. for the figure of option A, each value of x connected one time to a value of y

B . there are 2 arrows from 0 and 1

C. the values of x = -1 , connected four times to the value of y

So, the answer is option A

If 2+[tex]\sqrt{3}[/tex] is a polynomial root, then the another root of the polynomial will be 2 -[tex]\sqrt{3}[/tex]

The root of the polynomial =  2 +[tex]\sqrt{3}[/tex]

We know by using the quadratic equation we can find the solution of the polynomial

The quadratic equation of the polynomial

= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Then the root of the polynomial is [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Here one root is given that 2 + [tex]\sqrt{3}[/tex]

Then using the quadratic equation of the polynomial, the other root of  the polynomial will be the conjugate of the given root.

The other root of the polynomial = 2 - [tex]\sqrt{3}[/tex]

Hence, If 2 + [tex]\sqrt{3}[/tex] is a polynomial root, then the another root of the polynomial will be 2 - [tex]\sqrt{3}[/tex]

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Determine the amount paid by the Tony overall.

Number..................Difference1........... Difference 2.....Difference 3

6...........................................................................................

1................................ -5......................................................

0.............................. -1....................................4..............

10.............................. 10..................................11......................7

38.............................. 28................................18..................... 7

91.............................. 53................................25................... 7

176............................85..............................32

Answer:

Next number in sequence 176

Solution

For the solid line we can select two points:

(0,2) and (1,0)

We can calculate the slope and we have:

Then we can find the intercept and we got:

0= -2*1+ b

b =2

Then the equation is:

y= -2x +2

For the dashed line we can select (0,1) and (1,2) then the slope is:

The intercept is:

2= 1*1 +b

b=1

Then the equation is:

y= x +1

The probability that an odd number or a perfect square greater than one shows is 2/3.

Probability -  The area of mathematics known as probability deals with numerical representations of the like that an event will occur or that a statement is true.

total no. of outcomes - 1,2,3,4,5,6

odd number = 1,3,5

or a perfect square = 4

probability - dividing the favorable number of outcomes by the total number of possible outcomes.

probability =  favorable outcomes  / total no. of outcomes

= 4/6

= 2/3

The probability that an odd number or a perfect square greater than one shows is 2/3.

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Part 1

The y-intercept is when x=0, and [tex]f(0)=(0-7)(0+6)(0-5)=210[/tex]. So, the y-intercept is at (0, 210).

Part 2

The x-intercept(s) are when y=0, so:

[tex]f(x)=0\\\\(x-7)(x+6)(x-5)=0\\\\x-7=0, x+6=0, x-5=0\\\\x=-6, 5, 7[/tex]

So, the x-intercepts are: (-6, 0), (5, 0), (7, 0)

Using our roots from Part 2, we know that:

Part 3: [tex](-6, 5) \cup (7, \infty)[/tex]

Part 4: [tex](-\infty, -6) \cup (5, 7)[/tex]

Answer:

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Event that the number chosen is 2 = {2A, 2B, 2C}

Explanation:

The sample space is the set with all the possible outcomes, if she can select any number from 1, 2, or 3 and she can select any letter of A, B, or C, we get that the sample space is

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Then, the outcome for the event that the select number is 2 is

Event that the number chosen is 2 = {2A, 2B, 2C}

Therefore, the answers are:

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Event that the number chosen is 2 = {2A, 2B, 2C}

Answer:

y = 0.75x + 2

Step-by-step explanation:

Take two distinct points on the graph

Compute the slope m and y-intercept b

Equation of line in slope-intercept form is
y = mx + b

Take points (0, 2) and (4, 5)

Slope m = (5 - 2) /(4-0) = 3/4

y-intercept from the graph is 2

So y = 3/4 x + 2 =0.75x + 2

The total loss after 4 years is $47840.

From the information, we want to calculate the total loss after 4 years of 299000 is reduced by 4% per annum.

It should be noted that this simply means the calculation using the interest formula. In this case, the total loss will be gotten by knowing the interest.

In this case, the interest formula can be illustrated as:

Interest = PRT / 100

where P = Principal = 299000

R = Rate = 4%

T = Time = 4 years

Interest = (299000 × 4 × 4) / 100

Interest = 4784000 / 100

Interest = 47840

In this case, the calculation of the interest is the loss that the person gets.

Therefore, the loss is $47840.

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Explanation

Step 1

the distance between 2 points P1 and P2 is given by:

Step 2

let

P1=M(4,0)

P2=N(-2,-3)

replace

I hope this helps you

Parts C, D and E

Answer:

Explanation:

C) The maximum height is the highest point on the graph. On the x axis of the graph, each small square is 0.25 units. Thus, the x coordinate of the maximum height is is 1.25. The ball reached maximum height after 1.25 seconds

D) There were two different times when the ball was at 10m.

When y = 10 m, x = 0.5

when y = 10, x = 2

At 0.5 and 2 seconds, the ball was at 10m

E) A the time the when the ball hit the ground, the height is 0. Thus, the time when the ball hits the ground is 3 seconds

The augmented matrix is [tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex].

What is a matrix?

A rectangular array or table containing numbers, symbols, or phrases that are arranged in rows and columns is known as a matrix.

The given system of equations is:

9y - 5 +9z = 0

7x = -3y +7 + z

5x + 7y = 5

Rewrite the equations as:

0x + 9y + 9z =  5

7x +3y -1z = 7

5x + 7y + 0z= 5

Therefore, the augmented matrix for the system of equations is:

[tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex]

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We can show that one third + one fourth is not equal to 3/7 by following two ways.

We are given to prove that the one third and one forth combination of any object/value does not equals to the 3/7 of that same value/object.

let's Consider we have value as 1.

∴ one third of value will be [tex] \frac{1}{3} [/tex]

∴ one forth of value will be [tex] \frac{1}{4} [/tex]

∴ three of seven of value will be [tex] \frac{3}{7} [/tex]

Now we can do the mathematic calculation on one third and one forth of the value.

As given we have to calculate the addition of  one third and one forth of the value

∴ [tex] \frac{1}{3} + \frac{1}{4} [/tex]

= [tex] \frac{4}{12} + \frac{3}{12} [/tex] --(make base same )

= [tex] \frac{4\ + 3}{12}[/tex]

= [tex] \frac{7}{12}[/tex]

∴ By the calculation we clearly got that the addition of  one third and one forth of the value is equal to the seven of twelve of the value.

We can also prove it by analysis as follows ;

Consider a number say 120.

∴ 1/3 of 120 will be 40

∴ 1/4 of 120 will be 30

∴ 3/7 of 120 will be 51.42

Now Addition of 1/3 and 1/4 of 120 will be 40 + 30 = 70

Comparing it with 3/7 i.e 51.42 ≠ 70

Hence proved 1/3 + 1/4 ≠ 3/7 .

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If ∆ABC is congruent to ∆PQR, find the length of QR.

Given that If ∆ABC is congruent to ∆PQR:

The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent.

When all the sides of two triangles are congruent, the angles of those triangles must also be congruent.

From the triangle ABC, the side BC = 4,

Hence the PQR, the side QR = 4 since they are congruent

Recall that the "discriminat" of a quadratic equation of the form:

a x^2 + b x + c = 0

is given by the formula: b^2 - 4 a c

So for our equation:

x^2 - 5 x = -2, we start by adding 2 to both sides, in order to get the appropriate form equal to zero:

x^2 - 5 x + 2 = 0

Now we recognize:

a = 1

b = - 5

c = 2

and write the discriminant

b^2 - 4 a c = (-5)^2 - 4 (1) (2) = 25 - 8 = 17

Then, the discriminat of the equation is: 17.

Answer:

Triangle UVT and TSR are isosceles triangles (two equal sides).

Angle WUV = Angle WTV (base angles of isosceles triangle)

Angle RTS = Angle TRS (base angles of isosceles triangle)

Line VW is perpendicular to line UT.

Angle WTV = Angle RTS (vertically opposite angles)

Angle WTR = Angle VTS (vertically opposite angles)

The value of the variable 'x' in logarithmic expression is: 2

What is logarithm?

In mathematics, the term logarithmic expression can be explained as the exponent or the power which is raised on the base value of the logarithmic expression.

According to the question, the given logarithmic expression are as follows:

[tex]log_{1/2}x = -1[/tex]

Using standard logarithmic property, we get

x = (1/2)^-1

⇒x = 2

Hence, the logarithmic value of the variable 'x' is: 2

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Answer:

no

Step-by-step explanation:

because 3*2 isnot equal to13

First, 1 dozen is 12 units, so

Now, to solve the exercise you can use the rule of three. So, you have

*How many pounds of meat are recommended to feed 1 dozen people?

Therefore, 3 pounds of meat is recommended to feed a dozen people.

*How many pounds are recommended to feed 4 people?

Therefore, 1 pound of meat is recommended to feed 4 people.

*How many pounds are recommended to feed 1 person

Therefore, 1/4 pound of meat is recommended to feed 1 person.

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