The rectangular frame is made from 5 straight pieces of metal.
The weight of metal is 1.5kg per metre.
Work out the total weight of the metal in the frame.

The given system of equations has no solution.

The given system of equations are A-B =2 and A+2= B.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here,

A-B =2 --------(I) and A+2= B --------(II)

From equation (II) substitute B=A+2 in the equation (I), we get

A-(A+2)=2

⇒ A-A-2=2

⇒ 0-2=2

Hence, the given system of equations has no solution.

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Explanation:

x = number of weeks

y = height of the plant (inches)

The first sentence of "plant is 4 inches tall on week 8" gives us the point (x,y) = (8,4)

The second sentence gives us the point (32,16)

To find the growth rate, compute the slope.

[tex](x_1,y_1) = (8,4) \text{ and } (x_2,y_2) = (32,16)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{16 - 4}{32 - 8}\\\\m = \frac{12}{24}\\\\m = \frac{1}{2}\\\\m = 0.5\\\\[/tex]

The slope of 0.5 means the plant grows 0.5 inches per week.

Put another way, the plant grows 1 inch per every 2 weeks.

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Another approach:

The plant goes from 4 inches to 16 inches. It has grown 16-4 = 12 inches over the timespan of 24 weeks (since 32-8 = 24).

So its growth rate is 12/24 = 0.5 inches per week.

Notice how these values and calculations were mentioned in the previous section.

The velocity of the sign are given as follows:

a) Relative to the car: 60 kilometers an hour.

b) Relative to the ground: 0 kilometers an hour.

The relative speed of one object towards another is given by the rate of change in the position of each these objects relative to each other in regard to time.

Relative to the car, the sign gets 60 kilometers closer every hour, hence the relative speed of the sign will be of 60 kilometers. an hour.

Now, for the ground, the distance between the sign and the ground will always be the same, that is, there is no change in the distance. Hence, the velocity of the sign relative to the ground is of 0 kilometers and hour.

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Answer: 2a+5

5a-2-3a+7

First gather together the like terms

5a-3a  and  -2+7

then solve

5-3=2   and -2+7=5

answer = 2a+5

The set of values for Rents lesser than $700. So, rent 700 <y<0

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The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.

A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.

A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.

In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.

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Answer:

Option D

Step-by-step explanation:

This is because it contains the sum of the same variable to different powers.

Friday hope that this helps

The domain of y equals two divided by the quantity x minus three squared all minus one [y = (2)/(x - 3)² - 1] is: all real numbers.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.

Translating the word problem into an algebraic equation, we have;

y = (2)/(x - 3)² - 1

When x = 3, we have:

y = (2)/(3 - 3)² - 1

y = 2/-1 = -2

When x = 1, we have:

y = (2)/(1 - 3)² - 1

y = 2/3

In conclusion, the domain of this function is all real numbers.

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Step-by-step explanation:

15t + 30 = 20t | -15t

30 = 5t

t = 30/5 = 6

20 + 5t = -6t + 86 | + 6t

20 + 11t = 86 | -20

11t = 66

t = 6

18t + 20 = 24t + 50 | -18t

20 = 6t + 50 | -50

-30 = 6t

t = -30/6 = -5

18t - 2 = 10t + 54 | -10t

8t - 2 = 54 | +2

8t = 56

t = 56/8 = 7

7t - 5 = 15t + 91 | -7t

-5 = 8t + 91 | -91

-96 = 8t

t = -96/8 = -12

Answer:

(x+8)(x-9)

Step-by-step explanation:

1. Use the sum-product pattern

x²-x-72

x²+8x-9x-72

2. Find the common factor from the 2 pairs

x²+8x-9x-72

x(x+8)-9(x+8)

3. Rewrite in factored form

x(x+8)-9(x+8)

(x-9)(x+8)

Solution to problem: (x-9)(x+8)

Answer:

x = 135

Step-by-step explanation:

You need to find the supplementary angle of x.

To find x, use the supplementary angle theorem. (The angles "lie" on a straight line, so they add up to 180°, or a straight line.)

45+x = 180

x = 135

7 i do not feel like explaining tbh

Answer: 110°

Step-by-step explanation:

Looks like a bit more than 100°.

2(-x - 5) = 12

Step 1 : Expand the bracket.

=> -2x - 10 = 12

Step 2 :Add both side by 10.

=> -2x - 10 + 10 = 12 + 10
=> -2x = 22

Step 3 : Divide both side by -2.

=> -2x : (-2) = 22 : (-2)
=> x = -11

Therefore, x = -11.

Answer:

x = - 11

Step-by-step explanation:

2(- x - 5) = 12 ( divide both sides by 2 )

- x - 5 = 6 ( add 5 to both sides )

- x = 11 ( multiply both sides by - 1 )

x = - 11

The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

The quadratic function is

f(x) = [tex]-3x^2[/tex] + 18x + 3

The general form of the quadratic function is

y = [tex]ax^2[/tex] + bx + c

If a < 0, the quadratic function has maximum value

Here the value of a = -3

Therefore the function has maximum value.

Maximum value will be at x = -b / 2a

= -18 / 2(-3)

= -18 / -6

= 3

The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a

Substitute the value in the equation

(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3

= (-36 - 324 / -12

= -360 / -12

= 30

Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

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Answer:

875 square feet.

Step-by-step explanation:

Multiply 350 square feet by 2.5 gallons.

The solution for the given polynomial are x = -9, 9 and -10.

What is polynomial?

Polynomials are algebraic expressions that contain coefficients and variables. Variables are sometimes known as indeterminates. Mathematical operations like addition, subtraction, multiplication, and positive integer exponents can be performed on polynomial equations but division by variables cannot.

Given polynomial:

(x+9)(x-9)(x+10)

Equating it wit zero,

we get solutions as:

x = -9, 9, -10

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Answer:

  a. 3/2 meters

  b. 15/4 times as great

Step-by-step explanation:

You want the width of a rectangle that is 3/5 m² in area and 2/5 m long. You also want to know the factor by which the length is greater than the width.

The formula for the area of a rectangle is ...

  A = LW

Filling in the known values, we can solve for the length:

  3/5 m² = (2/5 m)·L

  L = (3/5)/(2/5) m = 3/2 m . . . . . . divide by the coefficient of L

The length of the rectangle is 3/2 meters.

The ratio of length to width is ...

  length/width = (3/2 m)/(2/5 m) = (15/10)/(4/10) = 15/4

The length is 15/4 times greater than the width.

When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

So, the equations are graphs are:

Now, graph both equations as follows:

Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

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The value of the given expression is 9/2 when substituting the values of m = -3, n = 2, and p = -1 in the expression.

The value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.

Given that m = -3, n = 2, and p = -1

The expression is given in the question

⇒ m(p -n)²/ 3p +m

Substitute the values of m = -3, n = 2, and p = -1 in the expression

⇒ -3(-1 -2)²/( 3(-1) +(-3))

⇒ -3(-3)²/(-3-3)

⇒ -3(9)/(-6)

⇒ 27/6

⇒ 9/2

Given that x = 3, y = 2, and z = 4

The expression is given in the question

⇒ (3z + 2x + y)/(4y - 2x + z)

Substitute the values of x = 3, y = 2, and z = 4 in the expression

⇒ (3×4 + 2×3 + 2)/(4×2 - 2×3 + 4)

⇒ (12 + 6 + 2)/(8 - 6 + 4)

⇒ 20/6

⇒ 10/3

Thus, the value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.

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Answer:

x=10

Step-by-step explanation:

4x+5x+angle g should equal 180 degrees total.

with this in mind, we can subtract angle g from 180, as it is know,. (180-90)

so 4x+5x=90. 9x=90, x=10.

hope this helps.

Check the picture below.

After ≈16.61 years the population will increased by  times it's original amount.

What do you mean by population?

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.

Given: If a population doubles every 5  years.

Assume,  'A' is the starting population, and 't' is the passing time in years.

Given the fact that a population doubles every five years, our population is growing exponentially, as per the question.

Here, the equation can be written as follows: [tex]A(t) = A(2)^{\frac{t}{5} }[/tex]                    (1)

We now need to determine when the population will have multiplied by 10 by that time.

Let's substitute [tex]A(t) = 10A[/tex]  in the above equation.

[tex]10A = A(2)^{\frac{t}{5} }[/tex]

[tex]10 = (2)^{\frac{t}{5} }[/tex]

Taking the natural log of both sides we get:

[tex]ln10 = \frac{t}{5} \times ln2[/tex]                        {[tex]ln(a)^n= nln(a)[/tex]}

2.3025 x 5 = t x 0.6931

[tex]t = \frac{2.3025}{0.6931}\\t = 16.6096[/tex]

Therefore, After ≈16.61 years the population will increased by  times it's original amount.

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The length of the base when the height is 6 cm is 21 cm .

In the question ,

it is given that ,

the length of the base(b) of the triangle varies inversely with the height(h) ,

which is represented as

b ∝ 1/h

b = k/h

where k is the constant of variation

given that when b = 18 , h is = 7

18 = k/7

k = 18 × 7

k = 126

Substituting , the value of k = 126  in the equation b = k/h  ,

we get ,

b = 126/h

So, the length of the Base When h = 6,

b = 126/6

b = 21

Therefore, the length of the base when the height is 6 cm is 21 cm .

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Answer:

[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]

hopefully this will u...^⁠_⁠^

Answer:

324 cm²

Step-by-step explanation:

area of a square = L x L = L²

L = 18cm

(18cm)² = 18cm x 18cm = 324 cm²

The required equation of slope is y = x/2 + 6

Given : y = 3x + 6

this is of the form y = mx + c

thus on comparing we get

the slope or m = 3

And the y intercept = 0, 6

It is also given that we have to find the equation of the slope which passes through the point ( -2, 5 )

thus the two points are:

( -2, 5 )  and ( 0,6 )

Thus the slope or m = y2 - y1/ x2 - x1

=> m = 6 - 5 / - ( -2 )

m = 1/ 2

Thus the equation of the slope is

y - y₁ = m ( x - x₁ )

₁Substituting the value of m from above we get

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

this implies 2y - 10 = x + 2

x - 2y = - 12

or we can also write this as

y = x/2 + 6

Refer to the graph given below for further understanding.

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Answer:

Step-by-step explanation:

Answer:

I don't know if this what you want but...

Step-by-step explanation:

2x+y=17

2x= 17-y

x= 17-y

     2