Examples of irrational numbers

Answer:

Option A

Step-by-step explanation:

If you take a look at the translation described in option A, the x value is increased by 1 (from -2 to -1), and the y value is decreased by 5 (from -5 to -10), meaning that you have made this jump with just one translation. Hope this helps!

Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = (x - 2)² + k ← is in vertex form

with (h, k) = (2, 4)

Thus the minimum value is 4 when x = 2 → B

Answer:

-0.75968791285

Step-by-step explanation:

To find cos(-15°), we recognize that cosine is an even function, so cos(-15°) = cos(15°). Utilizing the cosine angle subtraction formula and known cosine and sine values, we find that cos(15°) = (√6 + √2) / 4, thus cos(-15°) = (√6 + √2) / 4.

Finding Cosine of -15 Degrees:

To find cos(-15°), we can use the cosine angle addition formula. This is particularly useful as we can break down -15° into simpler angles:

cos(-15°) = cos(15°) because cosine is an even function: cos(-θ) = cos(θ).

Next, we utilize the angle subtraction formula for cosine:

cos(15°) = cos(45° - 30°) = cos(45°)cos(30°) + sin(45°)sin(30°)

We know that:

cos(45°) = √2 / 2    

cos(30°) = √3 / 2

sin(45°) = √2 / 2

sin(30°) = 1 / 2

Substituting these values into the formula, we get:

cos(15°) = (√2 / 2) × (√3 / 2) + (√2 / 2) × (1 / 2)

Simplify the expression:

cos(15°) = (√6 / 4) + (√2 / 4)

Thus:

cos(15°) = (√6 + √2) / 4

Therefore, cos(-15°) = (√6 + √2) / 4.

Answer:

D)

9 units

Step-by-step explanation:

[tex]distance = 6 - ( - 3) = 6 + 3 = 9 \: units[/tex]

Answer:

A) -9 units is the distance between -3 and 6

Answer:

4a+6

Step-by-step explanation:

To find the answer to this problem, you need to combine the like terms. (3a+7)+(a-1)=(3a+a)+(7-1)=4a+6. Hope this helps!

The of the given expression is 4a+6.

An algebraic expression is formed by using integers, constants, variables, and arithmetic operations. Variables and constants can be combined in an algebraic expression through mathematical operations.

Given that, an expression (3a+7)+(a−1), we need to find sum,

So,

(3a+7)+(a−1)

Opening the brackets,

3a+7+a-1

Combining the like terms,

3a+a+7-1

= 4a+6

Hence, the of the given expression is 4a+6.

Learn more about expression click;

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Answer:

P = 0.0909

Step-by-step explanation:

To know the number of ways or combinations in which we can select x elements from a group of n elements, we can use the following equation:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, if you sat down at your computer and randomly loaded 4 of the 12 problems, there are 495 different possibilities and it is calculated as:

[tex]12C4=\frac{12!}{4!(12-4)!}=495[/tex]

Then, from 495 different possibilities, there are 45 possibilities that both this problem and Richard Rusczyk's problem were among the four you loaded. This 45 possibilities are calculated as:

[tex](1C1)*(1C1)*(10C2)=(\frac{1!}{1!(1-1)!})*(\frac{1!}{1!(1-1)!})*(\frac{10!}{2!(10-2)!})=45[/tex]

Because you need to select: this problem and there is only one, the problem that Richard Rusczyk wrote and there is only one, and 2 problems from the other 10.

Finally, the probability that both this problem and Richard Rusczyk's problem were among the four you loaded is equal to:

[tex]P=\frac{45}{495}=0.0909[/tex]

We can't see any choices but it doesn't matter.  That's the factorization of the difference of two squares.  It's important to recognize either side when you see it; the usual next move is to replace it with the other side.

(x + y)(x – y) = x² - y²

Answer: x² - y²

Answer:

B (it's kinda cut off)

Step-by-step explanation:

Use the acronym SOHCAHTOA to determine which trigonometric function to use. We'll use cosine since we have the hypotenuse and the adjacent length.

Set up an equation:

cos(41)=x/18

cos(41)*18=x

13.585=x

So your best choice would be B

Answer:

81

Step-by-step explanation:

9*7 = 63

6*3 = 18

63 + 18 = 81

Answer:

1/9

Step-by-step explanation:

There are 30 pens in total, 1/3 of the pens are each the following colours: blue; black; red.

This will result in a one in three chance of picking up a red pen. As Mr.Lopez puts the pen back, the fractions stay the same as it's the same possibility both times.

As it's again a one in three chance, we just have to multiply it for the possibility of him picking a blue pen, which is 1/3.

1/3 * 1/3 = 1/9

Final answer:

The slope-intercept form of the equation 9x - y = 9 is y = 9x - 9, which shows a slope of 9 and a y-intercept of -9, corresponding to option b).

Explanation:

The slope-intercept form of the equation 9x - y = 9 can be found by solving for y. We want to rearrange the equation to get y by itself on one side, which allows us to see the slope and y-intercept more clearly. The standard slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

To solve for y, we perform the following steps:

Add y to both sides of the equation: 9x - y + y = 9 + y, resulting in 9x = 9 + y.

Next, we subtract 9 from both sides to get y by itself: 9x - 9 = y.

The resulting equation is y = 9x - 9, which matches option b).

This shows the slope of the line is 9 and the y-intercept is -9. The values correspond to the terms in the slope-intercept form where the coefficient of x is the slope, and the constant term is the y-intercept.

Answer:

d. 4 ft

Step-by-step explanation:

1/2h(b1+b2)

1/2h(10)=20

multiply both sides by 2

h(10)=40

divide both sides by 10

h=4

Answer:

[tex]\pi \: {r}^{2} \\ \pi \: {6}^{2} \\ = 36\pi[/tex]

Step-by-step explanation:

P(t) = 12,000 (2)^(-t/15)

9,000 = 12,000 (2)^(-t/15)

0.75 = 2^(-t/15)

ln(0.75) = ln(2^(-t/15))

ln(0.75) = (-t/15) ln(2)

-15 ln(0.75) / ln(2) = t

t = 6.23

The time it would take for Sawyerville's population to decrease to 9000 can be calculated by setting the population function equal to 9000 and solving for 't'. After a series of algebraic transformations, you can isolate 't' and calculate its value with a scientific calculator.

To find the amount of time it will take for Sawyerville's population to fall to 9000 people, we can set up the equation: P(t) = 9000. Therefore, we have 9000 = 12,000 - 2-t/15.

To solve this equation, we first need to isolate the exponential term by subtracting 9000 from both sides, getting 3000 = 2-t/15. Then, we take the natural logarithm (ln) of both sides to remove the exponential term, resulting in ln(3000) = -t/15*ln(2). Divide both sides by -ln(2) and multiply them by 15 to find 't'. The final equation is: t = -15*ln(3000)/ln(2).

In this particular problem, you may need the help of a scientific calculator to compute the value of 't'.

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Simplify the radical by breaking the radicand up into a product of known factors.

Therefore the answer would be 2! Hopefully this helps.

Answer: I believe the volume is 4188.79 cm^3.

Step-by-step explanation: The equation for the volume of a sphere is (4/3)(pi)(r^3) = (4/3)(pi)(1000) = 4188.79 cm^3.

Answer:

50

Step-by-step explanation:

Unknown number = x

32% = 0.32

Write an equation

0.32(x) = 16

Simplify

0.32x = 16

Divide both sides of the equation by 0.32

x = 50

50

Hope this helps :)

Answer:

25.9666 m

Step-by-step explanation:

The 4 arches combine to for a circle, so then you can find the area of the shaded region by subtracting the area of the square from the area of the circle.

The formula for area of a circle is A=[tex]\pi[/tex]r^2

Since the radius of the circle would be 11/2 or 5.5, the area if the circle would be [tex]\pi[/tex] x 5.5^2. This equals 95.0334.

The area of the square would be 11 x 11 = 121.

The 121-95.0334= 25.9666 m

Answer:

For the green one the answer is 8 square units

For the red one the answer is 9 square units

Hope this helps

The area of the shaded green polygon is equal to 8 square units.

The area of the shaded red polygon is equal to 9 square units.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle = 1/2 × b × h

Where:

Note: When the green polygon is dissected, three triangles would be formed.

By substituting the given side lengths into the formula for the area of a triangle, we have the following;

Area of triangle = (1/2 × 1 × 1) + (1/2 × 3 × 1) + (1/2 × 3 × 4)

Area of triangle = 0.5 + 1.5 + 6

Area of triangle = 8 square units.

In order to determine the area of the shaded red polygon, we would have to apply Pick's theorem;

Area of polygon = (b/2 + i) - 1

where:

By substituting the number of lattice points, we have the following;

Area of polygon = (b/2 + i) - 1

Area of red polygon = (4/2 + 8) - 1

Area of red polygon = 10 - 1

Area of red polygon = 9 square units.

Answer:

8.64 feet squared

Step-by-step explanation:

The formula for calculating the area of a triangle is 1/2(bh) or base * height divided by 2,

So first multiply 4.8 and 3.6

(4.8) (3.6) = 17.28

Then divide that by 2

17.28/2 = 8.64

Answer:

A. 8.64 feet squared

Step-by-step explanation:

A = 1/2bh

A = 1/2(4.8 x 3.6)

A = 1/2(17.28)

A = 8.64 feet²

Answer:

The volume of the cone is equal to 1000π in³  in terms of π  or  is approximately equal to 3140 in³

Step-by-step explanation:

To find the volume of a cone with a height of 30 in. and diameter of 20 in., we will follow the steps below;

First write down the formula for finding the volume of a cone

V = πr²[tex]\frac{h}{3}[/tex]

where v is the volume of the cone, r is the radius of the cone and h is the height of the cone.

From the question given, the height h of the cone is 30 in and the diameter is given to be 20 in. but radius is half of diameter, this implies that r=d/2=20/2=10 in., that is radius r = 10 in

We can proceed to inert the values into the formula

V = πr²[tex]\frac{h}{3}[/tex]

   =π×10²×[tex]\frac{30}{3}[/tex]

   =π×100×10

  =1000π

v =1000π in³  in terms of π

substituting π = 3.14

v ≈1000(3.14)

v≈3140 in³

Therefore the volume of the cone is equal to 1000π in³  in terms of π  or  is approximately equal to 3140 in³

The approximate volume of the cone is [tex]\(\frac{10000\pi}{3}\)[/tex] cubic inches.

To find the volume of a cone, the formula used is:

[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

Given that the diameter of the cone is 20 inches, we can find the radius by dividing the diameter by 2:

[tex]\[ r = \frac{diameter}{2} = \frac{20 \text{ in}}{2} = 10 \text{ in} \][/tex]

Now we can substitute the values of r and h into the volume formula:

[tex]\[ V = \frac{1}{3} \pi (10 \text{ in})^2 (30 \text{ in}) \][/tex]

[tex]\[ V = \frac{1}{3} \pi (100 \text{ in}^2) (30 \text{ in}) \][/tex]

[tex]\[ V = \frac{3000\pi}{3} \text{ in}^3 \][/tex]

The approximate volume of the cone is [tex]\(\frac{10000\pi}{3}\)[/tex] cubic inches.

There will be 1.095kg of cashews.

Step-by-step explanation:

Peanut = 1.78kg

Almonds = 0.625kg

If the total mass of the nuts should be 3.5kg then the cashew will be,

Cashew = 3.5 - 1.78 - 0.625

= 1.095 kg

There will be 1.095kg of cashews.

Answer:

There will be 1.095kg of cashews.

Step-by-step explanation:

Peanut = 1.78kg

Almonds = 0.625kg

If the total mass of the nuts should be 3.5kg then the cashew will be,

Cashew = 3.5 - 1.78 - 0.625

= 1.095 kg

There will be 1.095kg of cashews.

Answer:

$5.00 per pound

Step-by-step explanation:

12oz = $3.75

12(1.33333333) = 16

3.75(1.33333333) = 4.9 repeating

so the answer is $5.00

For this case we have that by definition, the volume of a cone is given by:

[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]

Where:

r: It is the radius of the cone

h: Is the height of the cone

We must find the radius knowing that the circumference of the base of the cone is[tex]19.1 \ ft[/tex]

[tex]2 \pi * r = 19.1\\r = \frac {19.1} {2 \pi}\\r = 3.04 \ ft[/tex]

Thus, we substitute in the formula:

[tex]V = \frac {1} {3} * \pi * (3.04) ^ 2 * 5.3\\V = \frac {1} {3} * \pi * 9.25 * 5.3\\V = \frac {1} {3} * 154.0165\\V = 51.34[/tex]

Thus, the volume of the cone is: [tex]51.34 \ ft ^ 3[/tex]

Answer:

[tex]51.3 \ ft ^ 3[/tex]

Answer:

51.3 ft^3

Step-by-step explanation:

Marvin would need 6.25 cans of paint for square 1.

Using ratio of paint used

We are given that it takes 4 cans of paint to paint square 3 and 5 cans of paint to paint square 2.

This suggests a possible ratio between the amount of paint needed for different squares. Let's assume this ratio remains constant.

If the ratio between squares 2 and 3 is r, then:

Paint needed for square 2 = 5 cans = r * Paint needed for square 3

Paint needed for square 3 = 4 cans

Solving for r: r = 5 cans / 4 cans = 1.25

Assuming the same ratio applies to square 1 and 2:

Paint needed for square 1 = r * Paint needed for square 2

Paint needed for square 1 = 1.25 * 5 cans = 6.25 cans

Therefore, Marvin would need 6.25 cans of paint for square 1.

Complete question:

Marvin is painting three squares shaped like the one below. If it takes him exactly four cans of paint to paint square 3 and five cans of paint to paint square 2, how many cans of paint should he need to paint square 1?

Answer:

A. [tex](x+5)^2+(y-8)^2=100[/tex]

Step-by-step explanation:

1. The standard form of the equation of a circle is [tex](x-h)^{2} + (y-k)^2=r^2[/tex]

2. To find the center we require the  midpoint   of the  2 given points

center =[tex][\frac{1}{2}(-4-6),\frac{1}{2}(11+5)][/tex]

=(-5,8)

3. The radius is the distance from the centre to either of  the 2 given points calculate the radius using the  distance formula

d= [tex]\sqrt{(x_{2}+x_{1})^{2} +(y_{2}-y_{1})^{2}[/tex]

let [tex](x_{1},y_{1})= (-5,8) \\[/tex] and [tex](x_2,y_2)=(-4,11)[/tex]

r=[tex]\sqrt{(-4+5)^2+(11-8)^2} =\sqrt{81+9}=10[/tex]

--> [tex](x-(-5)^2+(y-8)^2=10^2[/tex]

--> [tex](x+5)^2+(y-8)^2=100[/tex]

Answer:

The anser is B 100% willing to put $100 on it.

Step-by-step explanation: