can you please help me with number 4 please, I understand for the most part but need to make sure the answer is right

Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

Answer:

\(\frac{-7}{-5}\)

-7/-5

is the slope.

or -1 -2/-2  

you pick.

Step-by-step explanation:

Δy/Δx

-7-0 / 0-5

-7 / -5

-7/-5

is the slope.

change in y over change in x

y2-y1 over x2-x1

simplify if possible.

-1 -2/-2

it's negative.

Answer:

Slope = 1 2/5 or 1.4

Step-by-step explanation:

Using the y2 - y1/x2 - x1 format, you first replace the variables with the points (5 and 0 can be x1, y1, while 0 and -7 can be x2, y2)

-7 - 0/0 - 5

Now subtract: -7 - 0 = -7; 0 - 5 = -5

You would get -7/-5, which simplified: 1.4 or 1 2/5

:p

there you go!

The volume of the sphere is approximately 8181.510 cm³.

The volume of a sphere is the amount of space that is enclosed within the surface of a sphere.

It is a measure of the three-dimensional space that is contained within the sphere.

The volume of a sphere is used in a variety of fields, such as physics, engineering, and architecture, to calculate the space enclosed by a sphere or a spherical object, such as a planet or a ball.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. Substituting r = 12.5 cm and π = 3.14, we get:

V = (4/3) × 3.14 × (12.5 cm)³

V ≈ 8181.51 cm³

The volume of the sphere is approximately 8181.510 cm³.

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Answer: Neither since you are adding n, n+1, n+2 etc

Step-by-step explanation:

(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment

Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.

The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:

D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63

Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)

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Answer: It’s -1,-3

Step-by-step explanation:

got 100 on the test

Answer:

\(\frac{2}{\frac{1}{24} }\)

Step-by-step explanation:

2/x = 48

48x = 2

x = (2)/ (1/24)

\(\frac{2}{\frac{1}{24} }\) = 48

Answer:

120 T-Shirts

Explanation:

Let the number of t-shirts Arielle made = x

• Cost of making x t-shirts = $500

If she is planning to sell each for $25, then:

• Total Income from x t-shirts = 25x

Profit = Income -Expenses

=25x-500

Since she plans to make a profit of at least $2500, then:

We solve the inequality for x.

She must sell 120 t-shirts.

The surface areas of the figures are 336, 82 and 836

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

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

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The surface area of the prisms are

1. 336 cm²

2. 82 m²

3. 836 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as;

SA = 2B +pH

where B is the base area , p is the perimeter and h is the height.

1. SA = 2B +ph

B = 1/2 × 6 × 8

= 24 m²

p = 6+8+10 = 24m

h = 12m

SA = 2 × 24 + 24 × 12

= 48 + 288

= 336 cm²

2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)

= 2( 6+21+14)

= 2( 41)

= 82 m²

3. SA = 2πr( r +h)

= 2 × 3.14 × 7( 7 + 12)

= 44( 19)

= 836 cm²

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The value of the cash flows four years from today is $22,609.26.

The value of a set of cash flows can be calculated using the present value of an annuity formula. This formula takes into account the time value of money, which states that money has a different value at different points in time due to the opportunity cost of the money. In other words, the money you have today is more valuable than the money you will have in the future.

The present value of an annuity formula is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. In this example, the cash flows are $3,000, $4,040, $5,885, and $7,975, the interest rate is 5.4%, and the number of periods is 4. Plugging these numbers into the formula, the present value is $22,609.26. This is the value of the cash flows four years from today.

The value of the cash flows four years from today is $22,609.26.

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Specific individuals in a population are unfairly left out of a study, which is known as exclusion bias. When researchers design a study that inadequately represents specific segments of the community, undercoverage bias emerges.

When a sample is not chosen that accurately represents the full population of data, a statistical error known as sampling error arises. As a result, the sample's findings do not accurately reflect the outcomes that the complete population would produce.

When a sample is chosen from a population based on the idea of randomization, this practise is known as probability sampling.

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Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Using the midpoint formula we will see that the coordinates of B are (-9, 1)

We know that for two points (x, y) and (a, b) the midpoint is at:

( (x  + a)/2,  (y + b)/2)

In this case if the coordinates of B are (x, y), we can write the equation:

(-2, 4) = ( (x + 5)/2, (7 + y)/2)

We can solve these two equations to find the coordinates of point B, we will get:

(x + 5)/2 = -2

x + 5 = -4

x = -4 - 5 = -9

And:

(7 + y)/2 = 4

7 + y = 4*2 = 8

y = 8 - 7 = 1

The coordinates of B are (-9, 1)

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Answer:

it should be letter c

Step-by-step explanation:

I hope this help

Answer:

Step-by-step explanation:

One way of solution is to plot the lines and points and confirm the answer visually.

See attached.

Another way is to substitute the coordinates and verify if they satisfy both of the inequalities.

Each of the methods gives us the correct answer choice of D.

Answer: 166.72 \(ft^{2}\)

Step-by-step explanation: math

Step-by-step explanation:

All you have to do here is use the surface area, or SA, equation.

Sa=2lw+2lh+2hw
sa=2(8.5)(3.2)+2(8.5)(4.8)+2(4.8)(3.2)

Sa=54.4+81.6+30.72

Sa=166.72

Hope this helped!

Answer:

Step-by-step explanation:

A = Pe^rt

A = 1.4P

r = 0.02

t = ?

e^0.02t = 1.4

ln both sides

0.02t = ln(1.4)

t = ln(1.4)/0.02

t ~ 16.8 years

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.

To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.

Given:

∠A = 50°

∠C = 90°

CB = 16

We can start by finding the measure of ∠B:

∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)

50° + ∠B + 90° = 180°

∠B + 140° = 180°

∠B = 180° - 140°

∠B = 40°

Now, using Sine law

CB/ sin A = AB / sin C

16 / sin 50 = AB / sin 90

16 / 0.766044 = AB

AB = 12.25

Again 12.25 = AC/ sin B

12.25 = AC / sin 40

AC = 19.068

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Answer:

Step-by-step explanation:

The two given angles add to 180 if the 2 angles that look parallel are parallel.

That means that

17x + 14 + 4x - 2 = 180        Combine like terms

21x + 12 = 180                     Subtract 12

21x = 180 - 12                      Combine

21x = 168                             Divide by 21

x = 168 / 21

x = 8

Therefore 17x + 14 is the angle you want.

<B = 17*8 + 14 = 150.

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

There's another way to do this.

4x - 2 + <B = 180

4*8 -2 +<B = 180

32 -2 + <B = 180

30 + <B = 180

<B = 180 - 30

<B = 150

Answer:

Step-by-sTrue

tep explanation:

Answer:

1: False

2: True

3: True

4: True

5: False

Step-by-step explanation:

Answer:

35000

Step-by-step explanation:

35,007 to the nearest hundred would be 35000 because 7 is between both 0 hundred (000) and 1 hundred (100). However, because 7 is only 7 away from 000 and 93 away from 100, 000 is the nearest hundred.

Hope this helps :)

Answer:

To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.

Answer:

a) £58.5

b) £117

c) £438.75

Step-by-step explanation:

Mr Singh is paid £11.70 per hour after tax is deducted.

This means that for x hours of work, his earning are given by:

\(E(x) = 11.7x\)

a) How much does he earn if he works 5 hours?

This is E(5).

\(E(5) = 11.7*5 = 58.5\)

b) How much does he earn if he works 10 hours?

This is E(10).

\(E(10) = 11.7*10 = 117\)

c) He works 37.5 hours per week. How much does he earn in a week?

This is E(37.5).

\(E(37.5) = 11.7*37.5 = 438.75\)

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

Answer:

C

Step-by-step explanation:

On each linear pair, there is one of the Vertical angles and an angle shared between the two angles. This means we can use the fact that supplements of the same angle are congruent.

The basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

In the provided figure.

∠1 + ∠2 = 180 degrees ( linear pair of angles)...(i)

∠ 1 + ∠4 = 180 degrees ( linear pair of angles)...(ii)

According to transitive property, if a = b and b = c then a = c

Therefore,

∠1 + ∠2 = ∠1 + ∠4...(iii)

⇒∠2 = ∠4

Similarly, we can prove that

∠1 = ∠3

Therefore, we conclude that vertically opposite angles are always equal.

Hence, the basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Thus, statement c is correct.

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Answer:

The backpack weighs more

Step-by-step explanation:

9.5kg = 20.94391 lbs

Answer:

a backpack that weighs 9.5kg

Step-by-step explanation:

kilogram (kg) is stated to be 2.2 times heavier than a pound

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer: 288

Step-by-step explanation: 312 - 24 = 288

Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

Answer:

A. -1 and 1/3

Step-by-step explanation:

The number -1 and 1/3 is directly to the right of -1 and 2/3 because there is a -1/3 difference between them