Find the sum of E = [3 4 7] and the additive inverse of G = [-2 0 5].

1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

In this question,

a small pool hold 1500 gallons of water.

When there's is 5 gallons of water in the pool, the person decided

that not to stand outside and watch the pool fill.

This means, from the time he had decided, the amount of water in the pool = 5 gallons.

the water was filling the pool at a rate of 2.

Let t be the time in minutes.

So, the amount of water in the pool after 't' minutes would be,

f(t) = 2t + 5

We get an mathematical model for given situation,

f(t) = 2t + 5, where t is the time in minutes

We need to find the amount of water in the pool after 50 minutes

For t = 50 minutes

f(50) = 2(50) + 5

f(50) = 100 + 5

f(50) = 105 gallons

Also, we need to find the amount of time required to fill the pool.

1500 = 2t + 5

1495 = 2t

t = 747.5 minutes

t = 12 hours 46 minutes

Therefore, 1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

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Answer:

The values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.  

Step-by-step explanation:

In this question we need to solve the given equation that is 5x² - 9x - 10 to obtain the value of x using the complex solution method.

Now, the given equation is 5x² - 9x - 10 in which we need to apply the quadratic formula to find the solution;

So, the quadratic formula is => -b ± √(b² - 4ac) / 2a

Now, on comparing the equation 5x² - 9x - 10 we get the values;

a = 5

b = -9

c = -10

Further, on substituting the values given above in the quadratic formula to obtain the value of x.

=> -(-9) ± √((-9)² - 4(5×(-10)) / 2×5

=> 9 ± √(81 +200) / 10

=> 9 ± √(281) / 10

After simplifying the above equation we obtained the value of x that is;

=> x = 9 ± √(281) / 10

Now, the final values of x from the above condition are;

=> x = 9 + √(281) / 10  

and

=> x = 9 - √(281) / 10

It can be further represented in the decimal form;

=> x = 2.57630546...

and

=> x =  −0.77630546...

Thus, the values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.  

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Answer:

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

Given inequality:

Simplify and collect like terms:

Answer:

12%

Step-by-step explanation:

Odds in favor means number of favorable outcomes : number of unfavorable outcomes

Here favorable outcome is selecting a left-handed person

So odds of 3:22 means that the ratio of selecting  left-handed person to right-handed person is [tex]\frac{3}{22}[/tex]

P(left) = [tex]\frac{3}{3+22} = \frac{3}{25}[/tex]

P(left) as percent = [tex]\frac{3}{25}\cdot100[/tex] = 12%

Answer:

The solution to this equation is (9t)^(12) / (4a)^(6).

Step-by-step explanation:

It is given that [(4a³t²)/(9at^6)]^-3 which is to be simplified and solved to get the final answer.

Now,

let us have a look at the equation and observe the powers given;

=> [(4a³t²)/(9at^6)]^-3

So, let us convert the powers using the rules;

=> [(4a²)/(9t^4)]^-3

Further, we will apply the rule known as product of powers and we get an equation that is;

=> (4a)^(-6) / (9t)^(-12)

Now, after reciprocating both the powers as per the rules we get;

=> (9t)^(12) / (4a)^(6)

Therefore, the solution to this equation is (9t)^(12) / (4a)^(6).

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A real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

It should be noted that an equation is used to show the relationship between the variables that are illustrated.

In this case, a real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

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Answer:

34

Step-by-step explanation:

I really don't know I just wanted to answer for points

If the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.

Given that the concentration of hydrogen ions in household dish detergent is 10⁻¹² .

We are told to find the pH level of household dish detergent.

pH is basically a measure of how acidic/basic water is. The range of pH ranges from 0 - 14, with 7 being neutral.

We have to find the negative value of log value of concentration level to find pH of the solution.

pH=-log ([tex]10^{-12}[/tex])

pH=-(-12)log (10)          [We know that [tex]log a^{b}[/tex]=b log a]

pH=12*1

pH=12

Hence if the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.

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The inverse function returns the original value for which the output of a function was given.

The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3)

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.

A function's inverse is not always a function! To ensure that the inverse function is also a function, the original function must be a one-to-one function. A one-to-one function is one in which each second element corresponds to exactly one first element. (Each x and y value is only used once).

The inverse of a function is thought to be a reflection of the original function along the line y = x. Simply put; the inverse function is obtained by swapping the original function's (x, y) values.

Let the function be y = 4 - 3x

f(x) = 4 - 3x

y = 4 - 3x

simplifying the value of x, we get

x = 4 - 3y

x - 4 = -3y

x - 4/-3 = y

[tex]f^{-1[/tex]= - (x - 4/3)

The inverse of this function is [tex]f^{-1[/tex](x) = -(x - 4/3).

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Answer:

mean is the sum of all the values divided by the total values.

Step-by-step explanation:

so total values are 6, and the sum of all the values is: 1+29+27+28+30+27

                                                                                         = 142

so now the mean is 142÷6=   23.67

The Solution for equation 2 ln x=4 is 7.4088.

2 ln x=4

( [tex]x^{2}[/tex]) = [tex]e^{4}[/tex]

[tex]x^{2}[/tex] = 54.598

x = √54.598

x = 7.4088

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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Answer: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number =x

So, x*12*2=144

=12x=144/2

=12x=72

=x=72/12

=x=6

So the answer is 6 because 6*12=72 and doubling 72 gives us 144.

Have a great day!!!

After rotating a parallelogram 270° counterclockwise points of D will be (2,7).

There are 4 types of translation they are, translation, rotation, and dilation.

We know when we rotate a shape 270° counter-clockwise the coordinates (x,y) becomes (y, -x) that is we switch x and y and make x negative.

Given a parallelogram with points C(-4,6), D(-7,2), E(6,6) and F(3,2).

Assuming point D when rotated 270° becomes D'.

∴ The points of D will switch which is (2,-7) and then we will make x negative.

So, D' becomes (2,7).

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Classification of each of the listed as rational or irrational are done below

What is a rational numbers?

This is a term used in mathematics to refer to some set of numbers that are fractions where the numerator and the denominator are non zero digits. Rational numbers can be expressed as fractions.

Irrational numbers refers to numbers that cannot form a fraction

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The given equation in logarithmic form is 7^5 =16807

As given to us, the function is log₇16807=5

Let us write this function in exponential form using the definition of logarithm

logₐx=b

a^b=x

here the logarithm is log₇16807=5

thus 7^5=16807

hence the given equation in logarithmic form is 7^5 =16807

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Answer:7 and a half

Step-by-step explanation:

Simple enough, if it seven inches and grows half an inch a week than after a week it grows half an inch, so its just 7 + a half, your awnser is 7 and a half

Answer:since the bottom is 10cm and both tops are the same length that means its 5cm

Step-by-step explanation:YOU can divide 10 by 2

Answer:

[tex] \sf \fbox{46.296 British Pounds}[/tex]

Step-by-step explanation:

1 shower job requires 3 hours of work,

plumber will fix only 1 shower that means he will work for 3 hours,

Charges of 1 hour = 25$

Charges of 3 hour = 25× 3 = 75$

The currency that plumber accept is British pound (£),

1 British pound (£) = 1.62 dollar ($)

x British pound = 75 dollar

[tex] \frac{1}{x} = \frac{1.62}{75} [/tex]

taking reciprocal both the side,

[tex] \frac{x \cancel £}{1\cancel£} = \frac{75 \: \cancel\$ }{1.62 \:\cancel \$} [/tex]

[tex]x = 46.296[/tex]

Jamar need to pay 46.296 British Pounds to plumber for the shower job.

The two units that were cancelled was Dollar & Pound.

It is required to cancel units because, mathematical operation does not work for different units. For e.g. If I have given two measurement one is volume(cm³) & another is length(cm) so I cannot add them.

[tex] \sf Volume + Length = Not \: possible [/tex]

Same thing happens with division Operation of two different units, the magnitude gets cancelled but unit still remains there.

[tex]\sf \small \pink{Thanks }\: \green{for} \: \blue{joining} \: \orange{brainly } \: \red{community}![/tex]

Answer:

[tex]\frac{1}{y^9}[/tex]

Step-by-step explanation:

Exponent rule → [tex]a^{-b}=\frac{1}{a^b}[/tex]

Using exponent rule → [tex]y^{-9}=\frac{1}{y^9}[/tex]

Final result → [tex]=\frac{1}{y^9}[/tex]

The solution for equation ln (3 x+5)²=4 is 0.796.

ln (3 x+5)²=4

2 ln (3x + 5)= 4

3x + 5 = [tex]e^{2}[/tex]

3x = 7.389-5

x = 0.796

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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An absolute value equation that has the given solution is  mathematically given as

I3 + xI - 7 = 0 where the solutions (or roots) are in X= 4 and X= -10

This is further explained below.

Generally, in this case, we want an absolute value equation that has the solutions x = 4 and x= -10.

A cheap way to do this is to look for a number N that:

N + 4 = -(N - 10)

then, isolating N we get:

2N = 6 + 10 = 6

N = 6/2 = 3

then

=N +4  

= 3 + 4

= -8

and

=N - 10

= 3 - 10

= -7

In conclusion,  we know that I-7I = I7I = 7

now we can write our equation as:

I3 + xI - 7 = 0

where the solutions (or roots) are in X= 4 and X= -10

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Answer:

y=6x-3

Step-by-step explanation:

6 is the slope bur (0,-3) is the y-intercept. Therefore, you just need to plug in the y-intercept and slope into y=mx+b which will give you y=6x-3.

The equation to find the nth term of the sequence is aₙ = 4n - 17

The equation of the sequence can be represented as follows;

a₃ = - 5, a₄ = - 1, a₅ = 3, a₆ = 7, a₇ = 11

Therefore, let's find the equation of the nth term.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

d = 11 - 7 = 4

Hence, let's find the first term using 7th term

11 = a + 6(d)

11 = a + 6(4)

11 - 24 = a

a = - 13

Therefore, the equation to find the nth term of the sequence is as follows:

aₙ = -13 + (n - 1)4

aₙ = - 13 + 4n - 4

aₙ = - 13 - 4 + 4n

aₙ = 4n - 17

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Answer:

[tex] \sf \: x=0.4[/tex]

Step-by-step explanation:

-0.5x-3.69=x-1.9-2.39

Step 1: Simplify both sides of the equation.

−0.5x−3.69=x−1.9−2.39

−0.5x+−3.69=x+−1.9+−2.39

−0.5x−3.69=(x)+(−1.9+−2.39)(Combine Like Terms)

−0.5x−3.69=x+−4.29

−0.5x−3.69=x−4.29

Step 2: Subtract x from both sides.

−0.5x−3.69−x=x−4.29−x

−1.5x−3.69=−4.29

Step 3: Add 3.69 to both sides.

−1.5x−3.69+3.69=−4.29+3.69

−1.5x=−0.6

Step 4: Divide both sides by -1.5.

−1.5x/−1.5 = −0.6/−1.5

x=0.4

The value of x will be 0.4.

In mathematics, an equation is a connection of two expressions that is expressed as an equality on all sides of the corresponding sign.  A statement that uses the equal sign to show that both of the expressions possess the same value is called an equation. Mathematical equations are made up of figures, an equal sign, and an optional variable in the position of an unknowable value.

-0.5x-3.69=x-1.9-2.39

-0.5x - x = -1.9 - 2.39+3.69

Simplifying the given equation:

-1.5 x = - 0.6

x = 0.6 / 1.5

x = 0.4

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