The dimensions of a rectangles are 8cm and 12cm. What is the ratio of its length to its perimeter?

2/25

Step-by-step explanation:

\(\begin{aligned}\tt\left(\frac{4}{25}\right)\cdot\frac{1}{2}&=\tt\frac{4}{50}\to(\div~2)\\&=\tt\frac{2}{25}\end{aligned}\)

Answer:

X' = (-12,3)

Y' = (-10,5)
Z' = (-9,-2)

Explaination:

Please check image

Based off the x = -4 , I think that means that our x axis is no longer x = 0 but on the x = -4 line

Ex;

if point X is 8 units to the left of x=0, now point X' should be 8 units to the left of x=-4 making point X' = (-12,3)

The simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x  + 3

The side lengths are given as:

2x^2 + 5x + 3, 2 + 2x and 3x - 2

Add these lengths to determine the perimeter (P)

P = 2x^2 + 5x + 3 + 2 + 2x + 3x - 2

Collect like terms

P = 2x^2 + 5x + 2x + 3x  + 3 + 2 - 2

Evaluate the like terms

P = 2x^2 + 10x  + 3

Hence, the simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x  + 3

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The proportion of infants with birth weights under 95 ounces is approximately 0.1587 or 15.87%.

We are given a normal distribution with mean µ = 110 and standard deviation σ = 15. We want to find the proportion of infants with birth weights under 95 ounces, i.e., P(X < 95).

To solve this, we need to find the z-score for 95 ounces, which is given by:

z = (X - µ) / σ = (95 - 110) / 15 = -1

Using a standard normal distribution table, we can find the probability of a z-score being less than -1. This is the same as the probability of an infant having a birth weight less than 95 ounces.

From the standard normal distribution table, the probability of a z-score being less than -1 is 0.1587.

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Answer:

X=10

Step-by-step explanation:

71+50=121

180-121=59

So (6x-1)=59

(6x-1)=59

    +1   +1

6x=60

6x/6=60/6

x=10

The equation of the tangent plane to z=x**2−y**2 at the point (x,y)=(2,1) is z = 4x - 2y - 5 and to z=3x-2y at (x,y)=(4,3) is z = 3x - 2y + 6.

The partial derivatives of z with respect to x and y must first be found in order to determine the equation of the tangent plane to the surface z=x**2-y**2 at the point (x,y)=(2,1):

Z/Y = -2Y, and Z/X = 2X.

After that, we can use the expression for a plane's point-normal form, which is given by:

z - z0 Equals n · (x - x0, y - y0) (x - x0, y - y0)

where n is the plane's normal vector and (x0, y0, z0) is a location on the plane. We know the normal vector is given by because we want the tangent plane: n = <∂z/∂x, ∂z/∂y, -1>

The normal vector is therefore n = 4, -2, -1> at the location (2,1). Also known is the equation z0 = f(2,1) = 22 - 12 = 3. Consequently, the expression of the tangent plane's solution is:

z - 3 = <4, -2, -1> · (x - 2, y - 1) (x - 2, y - 1)

z - 3 = 4(x - 2) (x - 2) - 2(y - 1) (y - 1) - (x - 2) (x - 2)

z = 4x - 2y - 5

(b) We must first determine the partial derivatives of z with respect to x and y in order to obtain the equation of the tangent plane to the surface z=3x-2y at (x,y)=(4,3):

∂z/∂x = 3 ∂z/∂y = -2

Then, we can use the point-normal form of the equation of a plane, which is denoted by the formula: z - z0 = n (x - x0, y - y0), where (x0, y0, z0) is a point on the plane and n is the normal vector to the plane. Due to our desire for the tangent plane, we are aware that the normal vector is given by: n = z/x, z/y, -1.

The normal vector is therefore n = 3, -2, -1> at the location (4,3). Additionally, we are aware of the fact that z0 = f(4,3) = 3(4) - 2(3) = 6 for the given number (4). In light of this, the tangent plane equation is

z - 6 = <3, -2, -1> · (x - 4, y - 3)

z - 6 = 3(x - 4) - 2(y - 3) - (x - 4)

z = 3x - 2y + 6

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Answer:

(-infinity, 1)

Step-by-step explanation:

According to the graph, the largest value y can take on is +1.  

Thus, the range of this function is (-infinity, 1)

Answer:

Step-by-step explanation:

121+7x-4=180

7x-4=180-121=59

7x=59+4=63

x=63/7

x=9

It will be nice if you give me brainliest. Good luck!

Answer:

804.25 m^2

Step-by-step explanation:

diameter= 36m

radius=36/2=18m

Area= πr^2

= π*18*18

=256π

=804.25 m^2

Answer:

Area equals to 1017.88

Step-by-step explanation:

A=1/4πd 2=1/ 4·π·362≈1017.87602

I WILL USE THE REASONS CORRESPONDING ANGLES AND ANGLES ON THE STRAIGHT LINE. SINCE THE DIAGRAM LACKS FULL LABELLING THAT MAKES ME UNABLE TO EXPLAIN MORE USING DEMONSTRATION

\(3x - 3 + (4x - 6) = 180 \\ 3x + 4x - 3 - 6 =180 \\ 7x - 9 = 180 \\ 7x = 180 + 9 \\ 7x = 189 \\ \frac{7x}{7} = \frac{189}{7} \\ x = 27\)

ATTACHED IS THE SOLUTION x=27°

Answer:

x = 27

Step-by-step explanation:

3x - 3 and 4x - 6 are same- side exterior angles and sum to 180° , that is

3x - 3 + 4x - 6 = 180

7x - 9 = 180 ( add 9 to both sides )

7x = 189 ( divide both sides by 7 )

x = 27

The coordinate of the y-intercept of the given quadratic graph is: (0, -3)

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The general form of quadratic equations is expressed as:

y = ax² + bx + c

Now, from the term y-intercept, we know that it is the point where the graph crosses the y-axis and as such, we have the coordinate from the graph as:

(0, -3)

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Answer:

You can try the last one by yourself. If you need help on that I will help you, but remember that plug in all the answer choices, so that you can know if it has one solution, infinite solution, or no solution. Hope this helps, thank you !!

The equation provided is: ρ²(sin²(φ)sin²(θ) + cos²(φ)) = 16, This equation is in spherical coordinates,

where ρ represents the radial distance from the origin, φ is the polar angle (or the angle between the positive z-axis and the vector), and θ is the azimuthal angle (or the angle between the positive x-axis and the projection of the vector onto the xy-plane).

Now, let's analyze the equation further: 1. Divide both sides of the equation by 16 to isolate ρ²: ρ² = 16 / (sin²(φ)sin²(θ) + cos²(φ)) 2. Take the square root of both sides to find ρ: ρ = √(16 / (sin²(φ)sin²(θ) + cos²(φ))).

From this, we can see that the surface is defined by the radial distance ρ, which depends on the angles φ and θ. This indicates that the given equation represents a 3-dimensional surface in spherical coordinates.

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Answer:

8.94 inches

Step-by-step explanation:

Solve for hypotenuse.

Answer:

k - 8.1 > 24

Step-by-step explanation:

difference = subtraction

greater than 24 = > this sign

Answer:

5.17

Step-by-step explanation:

just at 10 pecent

Answer:

I think that the third one is the correct answer , $4.94 i mean .

Answer:

The equation of the line in slope-intercept form is  \(y=0.4x+2.2\)

Step-by-step explanation:

The equation of the line in slope-intercept form can be calculated as follows ?

The first step is to find the slope-intercept form of the given line by the point-slope form formula as follows

\(y-y_{1}=m(x-x_{1})\)

Where \(m\) is the slope of the line

Write the given value of the slope

\(m=\frac{2}{5}\)

Convert the value of the slope into decimal

\(m=0.4\)

The second step is to substitute \(0.4\) for \(m\), \(1\) for \(y_{1}\), \(-3\) for \(x_{1}\) in the point-slope form formula

\(y-1=0.4(x-(-3))\)

Take out the inner bracket on the right side of the equation

\(y-1=0.4(x+3)\)

Expand the right side of the equation

\(y-1=0.4x+1.2\)

Add \(1\) to both sides of the equation

\(y-1+1=0.4x+1.2+1\)

Simplify the equation

\(y=0.4x+2.2\)

Hence the equation of the line in slope-intercept form is

\(y=0.4x+2.2\)

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The main task for members during the final session is to put into words what has transpired from the first to the final session.

The group's goals should be discussed during the first few meetings, then each member's personal goals should be covered. Even small toddlers can follow and take part in these dialogues. They must be aware that the emphasis will be on defining and exploring particular issues and themes.

Over the years, I've discovered that assisting customers in comprehending what will occur during their initial meeting (often referred to as the "intake session") can be extremely beneficial in putting them at ease and beginning our partnership on a cordial and inviting note.

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Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

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

Explanation:

The old dimensions of the rectangle were 30 by 15.

The new dimensions are 30+x by 15+x, where x is some positive number.

The new rectangle dimensions multiply to 1000

(30+x)(15+x) = 1000

Use the FOIL rule to expand out the left side like so

(30+x)(15+x) = 1000

450+30x+15x+x^2 = 1000

450+45x+x^2 = 1000

x^2+45x+450

Then lets get everything to one side

x^2+45x+450 = 1000

x^2+45x+450-1000 = 0

x^2+45x-550 = 0

---------------------

From here we use the quadratic formula

Plug in a = 1, b = 45, and c = -550.

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(45)\pm\sqrt{(45)^2-4(1)(-550)}}{2(1)}\\\\x = \frac{-45\pm\sqrt{4225}}{2}\\\\\)

\(x = \frac{-45\pm65}{2}\\\\x = \frac{-45+65}{2} \ \text{ or } \ x = \frac{-45-65}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-110}{2}\\\\x = 10 \ \text{ or } \ x = -55\\\\\)

Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.

The only practical answer is x = 10.

So each dimension is increased by 10 feet.

--------------------------

If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25

Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.

--------------------------

Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet

Answer:

-6

cuz I'm smart. big brain time

Answer:

Andre's equation: y=5x+100

Elena's equation: y=20x+10

Step-by-step explanation:

total money (y) = (amount per week) times number of weeks (x) + (starting amount)

to solve number 3, plug in 4 for x in both equations and solve for y.

then find the difference between the two values.

to solve number 4, because both equaions are already set equal to y, you can set them equal to each other so you have 5x+100=20x+10

then solve for x to find number of weeks and plug this value into one of the equations for y to find how much money they have in their bank account.

Step-by-step explanation:

a diameter is always twice the radius.

the only pairs in this list, where one number is twice the other, is :

2.5 and 5

7.6 and 15.2

so,

2.5 is the radius of A

5 is the diameter of A

7.6 is the radius of B

15.2 is the diameter of B

15.7 is then the circumference of A (as the smaller of the remaining 2 numbers).

47.7 is the circumference of B.

this is also proven by the formula for the circumference of a circle : c = 2×pi×r

Yes, 1212 divided by 3 = 404.

Answer:

Step-by-step explanation:

Sum the digits. The result must be divisible by 3.

1+2+1+2=6

6:3=2

YES

The initial population of the bacteria culture is 200 bacteria.

The initial population of the bacteria culture can be determined using the equation for exponential growth: P(t)=P0(1+rt), where P(t) is the population after time t, P0 is the initial population, and r is the relative growth rate.

In this case, after 2 hours, the population is 600 and after 8 hours the population is 75,000. Plugging in the values, we get P0 = 600/(1+2*r), or P0 = 600/3. Thus, the initial population of the bacteria culture is 600/3 = 200 bacteria.

Exponential growth is a function of time and rate of growth. It is often used to model population growth or decay, such as in this case. The equation for exponential growth states that the population at any time is equal to the initial population multiplied by the rate of growth at each unit of time.

In this case, the rate of growth (r) is constant over the time period, so the population can be determined by putting in the values for P(t) and P0 and solving for r. Then, using the same equation, the initial population (P0) can be determined.

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Answer:

y = -1/2x + 6.

Step-by-step explanation:

The line perpendicular to y = 2x + 3 has slope of - 1/2 so we can write it as

y = -1/2x + c

When x = -4, y = 8 so we substitute:

8 = -1/2 (-4) + c

8 = 2 + c

c = 8-2 = 6

So, the answer is

y = -1/2x + 6.

Answer:

y = -1/2x + 6.

Step-by-step explanation:

Answer:

25 feet in one second

Step-by-step explanation:

125 divided by 5 is 25

Answer:

25 feet per second

Step-by-step explanation: