Rewrite in vertex form by completing the square:
x^2+4x+3x

The 3 geometric means between 5 and 3125 is 5, 25, 125, 625, 3125 using Geometric progression.

The geometric mean is a mean or average used in mathematics that uses the product of the values of a collection of numbers to show the central tendency of that set of numbers. The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. An average that multiplies all values and determines the number's root is known as the geometric mean. You locate the nth root of their product for a collection of n integers. This descriptive statistic can be used to sum up your data.

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Answer:

Step-by-step explanation:

3x + 4y when x = 6 and y = -3

Put in values of x and y:

3(6) + 4(-3) = 18 + (-12) = 6

30 L of 26% and 15L of 20% of each mixture should be added to make 45 l of a solution that is 24% alcohol.

The quantity of a substance, like salt, that is present in a specific volume of tissue or liquid, like blood, according to science. When there is less water present, the substance becomes more concentrated. You can determine how much solute has been dissolved in the solvent by looking at the concentration of the solution.

Here,

26x + 20(45-x) = 45(24) 

26x -20x = 45(24) -(20(45) 

6x = 4(45) = 180 x = 180/6 = 30 L of 26%

45-x = 45-30 = 15L of 20%

To make 45 l of a 24% alcohol solution, combine 30 l of 26% and 15 l of each mixture.

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Answer:

slope: (6+10)/(15-0)

M: 16/15

B = -10

y = 16/15x -10

Answer:

Step-by-step explanation:

Least to greatest :

-3/5,-2/3,0,0.7

The given relation is not function, because 15 is repeating twice. In domain 15 is with 8 and 2.

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In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree.

The use of computing algorithms, tools, and programmes to phylogenetic analysis is known as computational phylogenetics. The purpose is to create a phylogenetic tree that represents a hypothesis about a set of genes, species, or other taxa's evolutionary ancestry.

There was not enough computational power to construct every possible tree in all of the world. So the probable solution for this problem will be:

Use math to avoid constructing improbable trees

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The equation of a line that passes through the point (0,-1) and has a gradient of -3 is y = -3x - 1

From the question, we have the following points that can be used in our computation:

(x, y) = (0, 1)

Also, we have the slope to be

gradient = -3

Rewrite as

m = -3

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

(x, y) = (0, -1)

m = -3

Substitute the known values in the above equation, so, we have the following representation

y = -3 * (x - 0) - 1

Evaluate

y = -3 * x - 1

So, we have

y = -3x - 1

Hence, the line equation is y = -3x - 1

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Answer:

True

Step-by-step explanation:

True.

1 and 2/5 can be rewritten as 1 and 4/10, and thus is equal to 1.4.

The answer will be:

The equation has one real root. And the root is -1/2.

The equation y= 2[tex](x+1)^2[/tex] has one real root and that is x=-1.

What is real roots of the equation?

    We are aware that when we resolve a linear or quadratic equation, we always arrive at the value variable of the equation, or, to put it another way, we always locate the equation's solution. This "solution" is what we refer to as the real roots. For instance, when the equation [tex]X^2[/tex]-7x+12=0 is solved, the actual roots are 3 and 4.

Here given,

=> y = 2[tex](x+1)^2[/tex]

Take y=0 then,

=> 2[tex](x+1)^2[/tex]=0

=> [tex](x+1)^2[/tex]=0

=>(x+1)=0

=> x=-1

Hence the given equation has one real root and that is x=-1.

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The cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

Given:

If it' 50 c outside and the temperature will drop 70 c in next 3 hour.

Temperature (cold) = present temperature - temperature in next 3 hour.

= 50 - 70

= -20 c.

Therefore the cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

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Answer:

Take a look at the attachment...

Hope this helps! :)

Answer: Simplify your answer and write it as a proper fraction, improper fraction, or whole number

Step-by-step explanation:

Answer:

Total surface area of the cone = 208.81 sq cm

explanation

Diameter of the cone (d) = 7 cm

Slant height (L) = 15.5 cm

1) The radius of the cone= Half of the diameter

= 7/2 cm = 3.5 cm

⇒ r = 3.5 cm

Now, Total surface area of the cone =

taking π = 3.14

We get

and πrl = 3.14 x 3.5 + 15.5 = 170.345

So, Total surface area of the cone = 38.465 + 170.345 = 208.81 sq cm

Answer:

x = - 1/2

Step-by-step explanation:

3x - 6 = -7.5

3x = -7.5 + 6

3x = - 1.5

3/3 x = -1.5 / 3

x =  - 0.5

x = - 1/2

Answer:

x = -1/2

Step-by-step explanation:

Given equation,

→ 3(x - 2) = -7 1/2

Now the value of x will be,

→ 3(x - 2) = -7 1/2

→ 3x - 6 = -15/2

→ 3x = -7.5 + 6

→ x = -1.5/3

→ [ x = -1/2 ]

Hence, value of x is -1/2.

The measured distance of 1.15 meters from Levi's eyes to to the ground indicates that the height of the goalpost located 12.05 meters from the mirror when Levi is 2 meters from the mirror, found using similar triangles is approximately 6.93 meters.

Two triangles are similar if two angles in one triangle are congruent to two angles in the other triangle.

According the laws of reflection, the angle made by the incident ray with the normal is the same as the angle made by the reflected ray and the normal

Both the angle made by Levi and the angle made by the goalpost with the ground are perpendicular or 90°.

Therefore, the triangle formed by the line of site to the mirror and the reflected ray to the top of the goal post are similar triangles by Angle-Angle similarity postulate.

The ratio of corresponding sides is the same in similar triangles, therefore;

[tex]\dfrac{Levi's \, distance \, from \, the \, mirror}{Goalpost \, distance \, from \ the \ mirror }=\dfrac{Levi's \,height}{Height\, of \, the \, goalpost, H}[/tex]

[tex]\dfrac{2}{12.05} =\dfrac{1.15}{H}[/tex]

[tex]H =\dfrac{1.15\times 12.05}{2} \approx 6.93[/tex]

The height of the goalpost is approximately 6.93 meters

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The elevation is represented by y = -t + 9, and after 5 minutes would be 4 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the height of the elevator above the ground after t seconds.

As you begin, you are nine feet above ground level. Your elevation changes at the rate of negative one foot per second. Hence:

y = -t + 9

In 5 minutes:

y = -(5) + 9 = 4

The elevation in 5 minutes would be 4 feet.

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A system of equations to describe this situation is:

c(n) = 25n + 30

c(n) = 15n + 50

The total cost is equal to $80.

The solution to this system of equations is 2.

In order to write a system of equations to describe this situation, we would assign variables to the number of portrait sheets and cost of a photography session respectively, and then translate the word problem into algebraic equation as follows:

The cost for Murray Photography is given by:

c(n) = 25n + 30

The cost for Lasting Memories Company is given by:

c(n) = 15n + 50

Next, we would solve the system of equations as follows:

25n + 30 = 15n + 50

25n - 15n = 50 - 30

10n = 20

n = 20/10

n = 2.

Now, we can calculate the total cost:

c(n) = 25n + 30

c(2) = 25(2) + 30

c(2) = $80.

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Answer:

A: 7

Since the slope is 3 and passes down (1, 10), the answer will be 7

The cost of the ticket for everyone, given the amount raised by the PTA, can be found to be  $63.88

The cost of the tickets to each individual person, or to everyone, can be found by the formula:
= Amount raised by PTA / Number of students and teachers going on the trip

Amount raised by PTA = $7, 985

The number of students and teachers going on the trip:

= 112 + 13

= 125 people

The cost of the tickets are:

= 7, 985 / 125

= $63.88

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If the volume of a sphere is decreasing at a constant rate of 55 cubic feet per minute. The volume of a sphere  is  0.036.

Using this formula to find the  volume of a sphere

V = 4/3 π r³

Taking the derivative with respect to time:

dV/dt = 4π r² dr/dt

Let plug in the formula

55 = 4π (11)² dr/dt

dr/dt = 55/ (484π)

dr/dt = 55/1,520.5308

dr/dt = 0.036

Therefore the  volume of a sphere is 0.036.

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Answer:

$90

Step-by-step explanation:

The amount Oliver borrowed = 1,500

The interest rate applied to the loan = 12%

Required: To calculate the simple interest using the formula, I = P•R•T

Where;

I = The simple interest

P = The principal borrowed = $1,500

T = The time or loan duration = 6 months = 1/2 year

R = The rate at which the loan is applied = 12% = 0.12

Therefore;

I = $1,500 × 0.12/year × 6/12 year = $90

The correct option for the interest paid on the loan is therefore;

$90

The slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.

First, let us understand the slope of a line:

A slope of a line is defined in mathematics as the change in the y coordinate with regard to the change in the x coordinate.

We are given the points:

(0, 1) and (1, -2)

We will calculate the slope of the line using the following formula:

m = (y_2 - y_1) / (x_2 - x_1)

Let x_1 = 0, x_2 = 1, y_1 = 1 and y_2 = -2.

Substitute the given values in the above formula, we will get:

m = (-2 - 1) / (1 - 0) = -3 / 1 = -3

So, the slope of the line is -3.

Thus, the slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.

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The answer to the question is: x = 8                      

Answer:

x = 8

Step-by-step explanation:

4x + 2 - 3 - 3x = 7

x -1 = 7

x = 7 + 1

x = 8

The equation to solve for W is W = (P-2L)/2.

According to the question,

We have the following information:

P = 2L + 2W

Now, we have to solve this equation for W.

Subtracting 2L from both sides of the equation will give us the following expression:

P-2L = 2W

Now, we will divide both sides of the equation by 2. And we will have the following expression:

(P-2L)/2 = W

(More to know: now, in this equation, if the value of P and L are given then we can use this equation to find the value of W.)

Hence, the equation to solve for W is W = (P-2L)/2.

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The number that represents Monica's balance at the end of the month, given the amount paid for the ingredients and the amount received, is 235, 000

The balance at the end of the month to Monica's ice cream parlor can be found by the simple formula:

= Amount received - Amount spent

The amount received is 550, 000.

The amount spent is:

= Purchase of ingredients + Equipment maintenance

= 210, 000 + 105, 000

= 315, 000

Monica's balance is therefore:
= 550, 000 - 315, 000

= 235, 000

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45 pieces can the dressmaker cut from 5 of these rolls of ribbon.

Mathematical expression:

When we validly combine numbers and variables, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

Here we have to find the number of 12-inch pieces can the dressmaker cut from 5 of these rolls of ribbon.

We are provided the length of the ribbon, which is 9 feet.

As we know that

1 feet = 12 inches

So rolls of 9 feet can make 9 pieces of 12 inches.

So 5 of these rolls of ribbon can make = 5 × 9 = 45 pieces.

Therefore we get 45 pieces.

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Answer:

2³⁰ > 30²

Step-by-step explanation:

Now the values of,

→ 2³⁰ = 1073741824

→ 30² = 900

Then the expression will be,

→ 2³⁰ ? 30²

→ 1073741824 > 900

→ 2³⁰ > 30²

Hence, answer is 2³⁰ > 30².