What total length of ribbon is needed to line the two long sides of the hat? 10 in. 11 in. 20 in. 22 in.

On the number line the position of point F is at point 4.

According to the statement

We have a given that the on a number line , point D is at -3, and point E is at 6. The point F lies on the ratio of to is 2 : 3.

and we have to find the F point on the number line.

Firstly,

Number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations.

So, According to given information,

Point D is at -3, and point E is at 6.

Ratio of point E to F = 6*2/3

Then

Ratio of point E to F = 6*2/3

After solving it

The point F = 2*2

The point F = 4.

So, On the number line the position of point F is at point 4.

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1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)

2) [tex]\angle ABD[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ABD[/tex] and [tex]\triangle DEB[/tex] are right triangles (a triangle with a right angle is a right angle)

4) [tex]\triangle ABD \cong \triangle DEB[/tex] (HL)

5) [tex]\angle ACB \cong \angle DEB[/tex] (CPCTC)

There can be 36 combinations.

The total number of combinations of the dial can be found by using permutations without any number repeating.

There are four integers on the dial. They are 0, 1, 2, and 3.

It is also given that the numbers shouldn't repeat on the adjacent dial.

Therefore, we can say that there are 4 possible numbers on the first.

Similarly, on the second dial, only 3 numbers are possible since no two adjacent dials can have the same.

This is also the case for the third dial. It can also have 3 possible numbers.

Therefore, the total number of combinations is given by 4*3*3 = 36 combinations.

Therefore, we have found that there can be 36 combinations.

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By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.

In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 120

Reference angle = 60°.

For the coordinates, we have:

sin(-120) = -sin(60) = -1/2.

cos(-120) = -cos(60) = -√3/2.

By applying Pythagorean theorem, we have:

z² = x² + y²

z = √((-1/2)² + (-√3/2)²)

z = √(1/4 + 3/4)

z = √1

z = 1.

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The value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%

The equation is given as:

7000 = 20000(1-r)^10

The above equation is an exponential decay function.

So, we have:

7000 = 20000(1-r)^10

Divide both sides of the equation by 20000

0.35 = (1-r)^10

Take the 10th root of both sides

0.35^(1/10) = 1 - r

Evaluate the exponent

0.9 = 1 - r

Add r to both sides

0.9 + r = 1

Subtract 0.9 from both sides

r = 1 - 0.9

Evaluate

r = 0.1

Express as percentage

r = 10%

Hence, the value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%

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Step-by-step explanation:

I don't see any numbers, so I just give you an example :

11

every position in a number is worth 10 times the value of the position to its very right.

so, in e.g. 11

the left 1 is worth 10 times the value of the right 1.

The factorized expression using difference of squares is as follows,

9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

Difference of Squares

Difference of squares is a factorization method where an expression can be factored as (a + b) (a - b) when considered as the difference of two perfect squares,  a²-b². For instance, factoring x²-25 results in (x+5) (x-5). By enlarging the parentheses in (a + b) (a - b), the pattern (a + b) (a - b)=a²-b² is used as the foundation for this technique.

Factorization Using Difference of Squares

Given expression is,

36a⁴b¹⁰ - 81a¹⁶b²⁰

= (6a²b⁵)² - (9a⁸b¹⁰)²

Using square of differences, we have

a² - b² = (a + b) (a - b)

Here, a = 6a²b⁵ and b = 9a⁸b¹⁰

Thus, we get,

(6a²b⁵ + 9a⁸b¹⁰)(6a²b⁵ - 9a⁸b¹⁰)

Further Factorization

We can take out 3 common from both the bracket terms after applying difference of squares

3×3(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

= 9(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

Further, we can take out a²b⁵ as common from both the bracket terms

= 9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

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The extreme value of y = (x - h)² - c is the vertex of the equation.

The extreme values of a function are either the maximum or minimum values of the function.

The equation of a parabola in vertex form with vertex (h', k) is given by

y = a(x - h')² + k and its extreme values are

Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,

So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).

Now, since a = 1 > 0, (h, -c) is a minimum point.

So, the extreme value of y = (x - h)² - c is the vertex of the equation.

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Answer:

The lowest value is at (1, -8). H and C are equal to 1 and 8 in the equation y = (x - 1)2 - 8. Therefore, the minimum's x-coordinate corresponds to the equation's h-value, and its y-value is the opposite of the c-value.

Step-by-step explanation:

i re wrote it

Answer:

The water in pot X is hoter than that of pot Y

Answer:

A is the answer

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \:x = - \dfrac{ 9}{20} [/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:2(3x + 1) + 3(5x + 2) = x - 1[/tex]

[tex]\qquad❖ \: \sf \:6x + 2 + 15x + 6 = x - 1[/tex]

[tex]\qquad❖ \: \sf \:(6x + 15x - x) + (2 + 6 + 1) = 0[/tex]

[tex]\qquad❖ \: \sf \:20x + 9 = 0[/tex]

[tex]\qquad❖ \: \sf \:20x = - 9[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:x =- \cfrac{ 9}{20} [/tex]

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

________________________________

→ 2(3x + 1) + 3(5x + 2) = x – 1

→ 6x + 2 + 15x + 6 = x – 1

→ 21x + 8 = x – 1

→ 21x – x = – 1 – 8

→ 20x = – 9

→ x = –9/20

________________________________

Answer: [tex]f^{-1}(x)=\frac{x}{4}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex].

[tex]x=4y\\\\y=\frac{x}{4}\\\\\therefore f^{-1}(x)=\frac{x}{4}[/tex]

The volume of the cylinder having diameter 12 cm and height of 4 cm is 452 [tex]cm^{3}[/tex].

Given diameter of cylinder be 12 cm and height of cylinder be 4cm.

We are required to find the volume of cylinder.

Volume is the quantity of substance a container can hold in its capacity.

Diameter=12 cm

Radius=6 cm (Radius is always equal to half of diameter)

Volume of cylinder=π[tex]r^{2} h[/tex]

We have to just put the values of r, h and π in the formula to get the volume of the cylinder.

Volume=π[tex](6)^{2} 4[/tex]

=3.14*4*36

=452.57 [tex]cm^{3}[/tex]

After rounding off we will get 452 [tex]cm^{3}[/tex].

Hence the volume of cylinder is 452 [tex]cm^{3}[/tex].

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Question is incomplete as it should include height of cylinder be 4cm.

Answer:

x=1/3

Step-by-step explanation:

Answer:

In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .

Step-by-step explanation:

The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).

As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.

Calculation for the cosine function-

The given function is: cosine function, d = acos(bt).

As, the pendulum takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right.

The total time 't' by the pendulum is 2 sec.

Calculate the angular speed of the pendulum by-

ω = 2[tex]\pi[/tex]f

   = 2[tex]\pi[/tex]×(1/2)

ω = [tex]\pi[/tex] which is 'b' value of the given function.

As given, the distance of the pendulum from the centre is half of the total distance.

a = 12/2

a = 6

Substitute the obtained values in the cosine function, d = acos(bt),

d(t) = 6cos([tex]\pi[/tex]t)

Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is  d(t) = 6cos([tex]\pi[/tex]t).

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The complete question is -

Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).

Answer:

a=6

The period is 2 seconds.

b=pi

t=0.5

d=4.243

Step-by-step explanation:

Answer:

the correct answer is c (x+8)

Step-by-step explanation:

x+8=0

=x= -8

put x= -8 in the given polynomial

(-8)²+5(-8)-24

= 64-40-24

=24-24= 0

A. Up

Parabolas are graphs that make U-shapes and are formed from quadratic equations.

Vertical Parabolas

There are 2 different types of parabolas: vertical and horizontal.

If the x-value is squared, then the parabola is vertical. So, this graph must open up or down.

Positive A-Value

The a-value is the coefficient before the squared term. In a vertical parabola, the graph opens up if the a-value is positive. On the other hand, the graph opens down when the a-value is negative.

In this case, the graph is a vertical parabola that opens up. This means that the range will have a minimum value but no maximum.

Answer:

3.528

Step-by-step explanation:

the scale factor from the large triangle to the smaller triangle is 1/2.  All of the side lengths of the small triangle is 1/2 the side lengths of the large triangle.

A = 1/2 (bh)  The area of a triangle.  I need to know the base and the height of the little triangle to figure out the area.  If I use AC as the base, the length is given to me.  It is 4.2.  I do not have the height of the base, but I know that it is half of the height of the large triangle and that number is given to me.  It is 3.36, if I divide that by 2, I get 1.68.  Now I know all that I need to find the area.

A = 1/2(4.2)(1.68)

3.528Units^2

Answer:

a) x = 1.5 or x = -0.3

b) x = 5 or x = -8

Explanation:

Quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \:\: ax^2 + bx + c = 0[/tex]

Here given equation: 5x² - 6x  - 2 = 0

Identify variable constants: a = 5, b = -6, c = -2

Putting these values into equation:

[tex]\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}[/tex]

[tex]\sf x = \dfrac{ 3\pm \sqrt{76}}{5}[/tex]

[tex]\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}[/tex]

In one decimal point:

[tex]\sf x = 1.5 \quad or \quad -0.3[/tex]

b) Here use "middle term split" method

⇒ x² + 3x = 40

relocate

⇒ x² + 3x - 40 = 0

The factors of 40 are 8 and 5

⇒ x² + 8x - 5x - 40 = 0

factor common terms

⇒ x(x + 8) - 5(x + 8) = 0

collect into groups

⇒ (x - 5)(x + 8) = 0

set to zero

⇒ x - 5 = 0 or x + 8 = 0

relocate

⇒ x = 5 or x = -8

Step-by-step explanation:

a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] for a quadratic equation of the form [tex]ax^2+bx+c=0[/tex].

In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.

[tex]x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}[/tex]

This means that the value of x is both [tex]\frac{3+\sqrt{19}}5[/tex] and [tex]\frac{3-\sqrt{19}}5[/tex], since both values make x equal to 0. Putting both into the calculator, we get that [tex]x=1.5[/tex] or [tex]x=-0.3[/tex].

b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.

[tex]x^2+3x-40=0[/tex]

Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.

we can now make our factors x+8 and x-5

[tex](x+8)(x-5)=0[/tex]

If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.

[tex]x+8=0\\x=-8[/tex]    [tex]x-5=0\\x=5[/tex]

This makes our solutions x=-8 and x=5.

If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.

Answer:

Step-by-step explanation:

Answer:

Refer to the attached image!!

Hope it helps!

The volume of air inside the cube is 1887.376 cubic inches

The volume of a shape or an object is the amount of space in the object

The given parameters are:

The volume of the cube is calculated using

Volume = (Side length)^3

Substitute 12.6 for Side length

Volume = 12.6^3

Expand the exponent

Volume = 12.6 * 12.6 * 12.6

Evaluate the product

Volume = 2000.376

The volume of air inside the cube is calculated using

Volume of the air = Volume of the cube - Volume of the ball

So, we have

Air = 2000.376 - 113

Evaluate

Air = 1887.376

Hence, the volume of air inside the cube is 1887.376 cubic inches

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Answer:

y is equal to 24

Step-by-step explanation:

If y is directly proportional to x when x is equal to 5 and y is 12, then when you multiply 5 by 2 which is 10, y will be proportional to that when you multiply 12 by 2 which is 24

Answer:

b: 25

Step-by-step explanation:

The previous answer wowwubbzy13 uploaded is absolutely correct!

I'll set up a proportion.

If y = 12, then x = 5

--> 12:5

We want to find the y when x is 10

--> y:10

12:5 = y:10

5y = 120

y = 25

So B: 25 is the correct answer!

The volume of the prism would be enlarged by a factor of 8

The scale factor is given as:

k = 2

Let the initial volume be v and the final volume be V.

The relationship between both volumes is

V = k^3 * v

This gives

V = 2^3 * v

Evaluate

V = 8v

Hence, the volume of the prism would be enlarged by a factor of 8

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Any complex number [tex]z[/tex] can be written in polar/exponential form as

[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]

In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.

The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have

[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]

so (D) (the last option) is the correct choice.

Answer:39084620

Step-by-step explanation:

New questions in Mathematics

19 ft 4 ft l Find l. l = √ [?] ft

flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?

Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.

Solve the equation 7/4x-2=-5x+1

How to Convert 11010112 to base 10?

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)

Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)

The length of the wall = 125m

The area of the Playground = 10000[tex]m^{2}[/tex]

What is geometry?

A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.

Given data:

Perimeter of the playground=410m

length of the wall = 80m

The playground's width can be calculated as follows if its length is 80 meters:

(Formula of Perimeter of a rectangle)

P=2(L+B)              

410=2(80 +B)

410= 160 + 2B

2B= 410-160

2B= 250

B= 125 m

This results in a 125 m length for the playground.

The area of playground.

Area = Length x Width

Area = 80 x 125

area = 10000[tex]m^{2}[/tex]

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Answer:

A

Step-by-step explanation:

Area of the rectangle is 15*20=300

Area of the triangle is 8*17/2=68

Total area is 300+68=368

Perimeter is 15+20+20+8+17=80

Answer:

[tex]\rm {P = 80 \space\ feet,\space\ A = 360 \space\ square \space\ feet}[/tex]

Step-by-step explanation:

The perimeter of a shape is the sum of all the sides of the shape.

• Perimeter of the polygon = 15 + 20 + 17 + 8 + 20

                                            = 80 feet

To find the area of the polygon, we can separately find the areas of the triangle and the rectangle and then add them together.

• Area of rectangle = length × breadth

                                = 15 × 20

                                = 300 square feet

• Area of triangle = [tex]\frac{1}{2}[/tex] × base × height

As the height of the triangle is not provided, we have to calculate it.
Let the height of triangle = [tex]x[/tex]

Using Pythagoras's theorem:
[tex]x^2 + 8^2 = 17^2[/tex]

⇒  [tex]x^2 = 17^2 - 8^2[/tex]

⇒  [tex]x = \sqrt{17^2 - 8^2}[/tex]

⇒ [tex]x=\bf15[/tex]

Now using this value of height, we can find the area of the triangle:

Area of triangle =  [tex]\frac{1}{2}[/tex]  × 8 × 15

                          = 60 square feet

• Finally, we can add the areas of the triangle and rectangle together to find the area of the polygon:

Area of polygon = 300 + 60

                           = 360 square feet

Answer: 3/4

Step-by-step explanation:

Tangent is opp/adj

Therefore tan (x) = 18/24, which reduces to 3/4

Answer: y=-1/5x+ 8/5    (Third one down)