Find the solution(s) of the system of equations:
y = x2 + 6x + 9
y = 2x + 6


(–3,12) and (–1,8)


(3,12) and (1,8)


(3,0) and (1,4)


(–3,0) and (–1,4)

The rate of change of the volume is  9123 . 185   inches³/min.

What is volume of the sphere?

Volume of sphere is

   V = 4/3 π r³

differentiating with respect to time

[tex]\frac{dv}{dt} = \frac{4}{3} \pi . 3r^{2} . \frac{dr}{dt}[/tex]

[tex]\frac{dv}{dt} = 4\pi r^{2} . \frac{dr}{dt}[/tex]

now [tex]\frac{dr}{dt} = 6 inches/min ,[/tex]     when r = 11

[tex]\frac{dv}{dt} = 4\pi (11)^{2} . 6[/tex]

    = 2904 π      cubic inches per minute

    ≅ 9123 . 185   inches³/min

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Sum of the two separate equations.

The values satisfies the equation is 2430.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given that,

Equations for the two separate days :

125a +65 s = 1,200 - - - Friday

140a +50s = 1,230 - - - Saturday

Because, Inputting the solution, satisfied the equation:

a = 7 ; s = 5

265a+115s=2430

265(7) + 115(5) = 2430

1855 + 575 = 2430.

Therefore, The values satisfies the equation is 2430.

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For n= 4 the term = 1/18

A geometric sequence is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Here the sequence is in a geometric sequence, as there is a common ratio between the two-term of the sequence.

Common ratio= 2/12 = [tex]\frac{1}{3}[/tex]/2=1/6

To find the nth term of the geometric sequence we have a formula

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a = first term of the sequence

           r= common ratio

           n = number of term

To find the term where n= 4, we have,

[tex]a_{4}[/tex]= 12[tex]\frac{1}{6}^{4-1}[/tex]

   = 12[tex]\frac{1}{6}^{3} }[/tex]

   = 12/216

   =1/18

Therefore for n= 4 we have the term 1/18.

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The values of the variable x, y and z are x = 4; y = 3 and z = 25.

Now, as per the given question, the three equations are given below;

x = 2y - 2  .......eq 1

z = 5x + 3y - 4    .........eq 2

3y = 9       ...............eq 3

From equation , calculate y.

3y = 9

y = 9/3 = 3.

Substitute the value of y in eq 1.

x = 2y - 2

x = 2×3 - 2

x = 6 - 2

x = 4

Now, put the value of x and y in equation 2.

z = 5x + 3y - 4

z = 5×4 + 3×3 - 4

z = 20 + 9 - 4

z = 25

Thus, the values of the three variables are;

x = 4; y = 3 and z = 25.

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The true statements are as follows:

(6 ×3) ÷ (6 + 3) = 2

4 × 6 ÷ ( 3 × 8 )  = 1

3 × (3× 3) + 6 = 18

6 ÷ (4 - 3) + 8 = 14

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have the numbers 3, 4, 6, and 8 once in each exercise to make a true.

⇒ (6 ×3) ÷ (6 + 3) = 2

⇒ 4 × 6 ÷ ( 3 × 8 )  = 1

⇒ 3 × (3× 3) + 6 = 18

⇒ 6 ÷ (4 - 3) + 8 = 14

Thus, the required solution is shown above.

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There is need of total of 25 boxes of same size for the next lower level.

A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.

Some examples for sequence are :

2,4,6,8,10,12

3,9,27,81,243

The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.

In a sequence , first term always known as initial term.

and difference between two terms are known as common difference. It is denoted by d.

General form of sequence is :

[tex]a_1,a_2,a_3,----,a_n[/tex]

where , [tex]a_n[/tex] = last term in sequence.

According to question,

The boxes in each of successive levels make a sequence.

Also, number of boxes at level n = [tex]n^2[/tex]

As upto four level the number of boxes are 16.

at level 5 , n = 25

Thus, the total  boxes of equal or same size need for next lower level is 25.

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The complete question is :

Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.

a. How many boxes of same size would need for next lower level?

b. How many boxes of same size would need to add the 3 levels?

c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?

Answer:

0.714

Step-by-step explanation:

Argument

The total number of cards = 5 yellow. 3 blue and 7 red = 15 cards in all.

The probability of choosing a yellow card first is 5/15 = 1/3.

We are now down to 14 cards

There are 3 blue cards.

P(yellow then blue) = 1/3 * 3/14

P(yellow then blue) = 1/14 = 0.0714

The equation of the line in point-slope form, which passes through the pair of points located at (-1/2 , -1/2) and (-3 , -4), is y + 1/2 = 7/5(x + 1/2).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (-1/2 , -1/2) and (-3 , -4).

m = (y2 - y1)/(x2 - x1)

m = (-4 - -1/2)/(-3 - -1/2)

m = (-7/2)/(-5/2)

m = 7/5

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = 7/5 and (x1 , y1) = (-1/2 , -1/2)

(y - -1/2) = 7/5(x - -1/2)

y + 1/2 = 7/5(x + 1/2)

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Answer:

Step-by-step explanation:

yes the answer is correct 100 + 30 = 130

mark me brainliest

Answer:

it is correct

Step-by-step explanation:

100

+ 30

___

=130

___

Answer:

LCM = 27,720

Step-by-step explanation:

brainliest please

Answer:

No; 1,200 will cause her to exceed 1,500.

Step-by-step explanation:

Luna has,

→ consumed 900 cal

→ burned 500 cal

She wants to keep her daily calorie,

→ 1,500 cal/day

Calories she have left to consume,

→ 1500 - (900 - 500)

→ 1500 - 400

→ 1100 cal

Hence, she has to consume 1100 cal more to reach 1,500 cal/day.

He will owe a simple interest of $229.50

Simple interest is defined as the extra amount of money that is paid by the lender to the borrower for the amount of money that is taken on loan when returning the amount.

The simple interest on the principal is calculated by using the formula

I = P · R · T ,

Here I is the interest , P is the principal , R is the rate and T is the time.

Given in the question the amount of money loaned = $3600 , this is the principal (P) ,

Rate (R) = 4.25% = 0.0425

Time (T) is given  18 months which is equivalent to 1.5 years

Now the interest will be calculated by :

I = 3600 × 0.0425 × 1.5

I = 229.50

Therefore the interest earned is $ 229.50 .

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Question:✨Jin borrows $3,600 and plans to pay the loan off in 18 months. How much simple interest will he owe if it takes 18 months to repay the loan? Round to the nearest cent.

Answer: Ok took me a while to get the answer but

He will owe a simple interest of $229.50

Simple interest is defined as the extra amount of money that is paid by the lender to the borrower for the amount of money that is taken on loan when returning the amount.

The simple interest on the principal is calculated by using the formula

I = P · R · T ,

Here I is the interest , P is the principal , R is the rate and T is the time.

Given in the question the amount of money loaned = $3600 , this is the principal (P) ,

Rate (R) = 4.25% = 0.0425

Time (T) is given  18 months which is equivalent to 1.5 years

Now the interest will be calculated by :

I = 3600 × 0.0425 × 1.5

I = 229.50

Have an awesome night/day<3

Answer:

-30, -32 and -34

Step-by-step explanation:

-30 + -32 + -34 = -96

The value of the reverse permutation is F-¹(3) = 5.

An inverse permutation is one in which each number as well as the number of the place it occupies are swapped.

For, the given values in the question;

So, if you remove the last point, (5,3), the inverse is a function because it contains only the points.

F= {(2, 6), (3, 1), (4, 5), and (5,3)}.

Thus, it can be written as;

F: 2 → 3 → 4 → 5

F: 6 → 1 → 5 → 3.

Thus, F-¹(3); 3 →  5.

F-¹(3) = 5.

Therefore, the value of the reverse permutation is F-¹(3) = 5.

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Answer:

a₁ = 8 and r = 16

Step-by-step explanation:

the sequence has a common ratio r between consecutive terms and is therefore geometric , that is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2^{7} }{2^3}[/tex] = [tex]2^{(7-3)}[/tex] = [tex]2^{4}[/tex] = 16

r = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{2^{11} }{2^7}[/tex] = [tex]2^{(11-7)}[/tex] = [tex]2^{4}[/tex] = 16

r = [tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{2^{15} }{2^{11} }[/tex] = [tex]2^{(15-11)}[/tex] = [tex]2^{4}[/tex] = 16

the first term a₁ = 2³ = 8

The solution of the system of equations involving x + 3y = 5 and -2x - 4y = -5 is (-5/2 , 5/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 3y = 5     (equation 1)

-2x - 4y = -5     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

x + 3y = 5     (equation 1)

x = 5 - 3y

Substitute the equation of x to the second equation.

-2x - 4y = -5     (equation 2)

-2(5 - 3y) - 4y = -5

-10 + 6y - 4y = -5

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

-10 + 6y - 4y = -5

6y - 4y = -5 + 10

2y = 5

y = 5/2

Substitute the value of y in the equation of x.

x = 5 - 3y

x = 5 - 3(5/2)

x = 5 - 15/2

x = -5/2

Hence, the solution of the given system of equations is (-5/2 , 5/2).

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Answer:

Step-by-step explanation:

[5x+3x-(-2x)]+[-3-8]=9

10x+(-11)=9

10x=20

x=2

  The value of the geometric mean of the numbers 20 and 25 is.

Gm ( 20, 25) = 10√5

To solve this problem we define geometric mean.

   The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:

Gm (a,b,c) = √(a×b×c)

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (20, 25) = √20×25

Gm (20, 25) = √500

Gm (20, 25) = √5×100

Gm ( 20, 25) = 10√5

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The solution for f in expression 21 = 7e - 4f is (7e - 21) / 4

Given,

The expression: 21 = 7e - 4f

We have to solve this expression for f:

Then,

21 = 7e - 4f

Add 4f to both sides

21 + 4f = 7e - 4f + 4f

Then we will get,

21 + 4f = 7e

Add -21 to both sides

21 + 4f - 21 = 7e - 21

Then we will get,

4f = 7e - 21

Take 4 from left hand side to right hand side.

That is,

f = (7e - 21) / 4

Therefore, the solution for f in expression 21 = 7e - 4f is (7e - 21) / 4

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ N(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad Q(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +5}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\underset{midpoint}{\stackrel{\textit{\LARGE P}}{(3~~,~~-2)}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x+5}{2}=3\implies x+5=6\implies \boxed{x=1} \\\\\\ \cfrac{ y -3}{2}=-2\implies y-3=-4\implies \boxed{y=-1}[/tex]

The value of variable x for the given expression 2=x . 4/√3 is (√3 /2).

As given in the question,

Given expression :

2=x . 4/√3

To get the value of variable x

Multiply both the side of the expression by √3

2 × √3 =  ( x × 4 × √3 ) / √3

Divide both the side of the expression by 4

( 2 × √3 ) /4 = (x × 4 ) / 4

⇒ x = √3 / 2

Therefore, the value of variable x for the given expression 2=x . 4/√3 is

(√3 /2).

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Answer:

Tell what each power means but don't determine its value

Answer:

5 dollars a month

Step-by-step explanation:

There are 12 months in a year, so we divide the yearly amount by 12

60/12 = 5

5 dollars a month

The distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is o units .

Distance Formula : the distance between the line ax+by+c=0 and the point (p,q) is given by the formula

[tex]d=\frac{|ap+bq+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question the equation of line is [tex]y=\frac{1}{6} x+6[/tex]

taking LCM and solving further

[tex]y=\frac{x+36}{6} \\ \\ 6y=x+36\\ \\ x-6y+36=0[/tex] ⇒equation of the line .

Given point (-6,5)

from above values we found that a=1 , b = -6 , c=36, p=-6, q=5.

Substituting the values in distance formula we get

[tex]d=\frac{|1*(-6)-6*5+36}{\sqrt{1^{2} +(-6)^{2} } }[/tex]

[tex]=\frac{|-6-30+36|}{\sqrt{37} }[/tex]

[tex]=\frac{-36+36}{\sqrt{37} }[/tex]

[tex]=0[/tex]

Therefore , the distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is 0 units.

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The value of c so that cx-d=2x+4 has No Solution is c=2.

In the given question ,

we have

cx-d=2x+4       ....(i)

Given that d = 2 ,

We substitute the value of d=2 in equation (i)

On substituting we get

cx-2=2x+4

Simplifying further we get

cx=2x+4+2

cx=2x+6

cx-2x=6

x(c-2)=6

x=6/(c-2)

For x to have NO SOLUTION the denominator should be 0.

because when denominator becomes 0 the value becomes not defined , hence will have no solution.

Substituting the denominator = 0

we get c-2=0

c=2.

Therefore , the value of c so that cx-d=2x+4 has No Solution is c=2.

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Answer: 3.82x10^7

Step-by-step explanation:

Answer:

Step-by-step explanation

Height for time = 8 seconds

h = -4.9t^2 + 259t + 423

h = -4.9(8)^2 + 259(8) + 423

h = -313.6 + 2072 + 423

h = 2181.4 meters at 8 seconds

Heoght for time = 0 seconds

h = -4.9t^2 + 259t +423

h = -4.9(0)^2 + 259(0) + 423

h = 0 + 0 + 423

h = 423 meters at 0 seconds

4600 is the loan's future value, a, or the total amount due at time t.

What Is Simple Interest?

P=$4000

r=5%

t=3 years

Now we have to find th loans future value A.

So

Simple interest me I=prt=(4000)(.05)(3)=600

Total due is Principal + Interest =4000+600= 4600

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x less than or equal to 6 is the following is not a way to represent the solution of the inequality.

What is inequality in math?

2(x − 1) ≤ 10

2x - 2 ≤ 10

2x ≤ 10 + 2

2x ≤ 12

x ≤ 6

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