Need help with math question

Answer:

Step-by-step explanation:

Please avoid use of " x " to indicate multiplication; instead, use " * " or " · "

P = ( 2 x l ) + ( 2 x w )  comes out as   P = ( 2 * l ) + ( 2 * w ).

This could be written in several different ways, e. g.,

P = ( 2 * l ) + ( 2 * w ),

P = ( 2 * w ) + ( 2 * l ),

P = ( l * 2 ) + ( w * 2), and so on.

The Distributive Property permits us to rewrite the formula P = (2 x l) + (2 x w) as P = 2(l + w). This factorization is an alternative mathematical representation of the same calculation.

Yes, you can utilize the Distributive Property to rewrite the formula P = (2 x l) + (2 x w) in a different way. The Distributive Property in mathematics is a fundamental property that states a(b + c) = ab + ac, which means you can distribute multiplication over addition. Applying this property to the formula P = 2l + 2w, we can factor out a common factor of 2 from both terms. So the formula can be written equivalently as P = 2(l + w).

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Answer:

6⃣

Step-by-step explanation:

3 + 24x² + 48x⁶; take the highest degree term possible.

Answer:

degree 6

Step-by-step explanation:

To obtain (f ￮ g(x) substitute x = g(x) into f(x)

f(4x³ + 1)

= 3(4x³ + 1)²

= 3(16[tex]x^{6}[/tex] + 8x³ + 1)

= 48[tex]x^{6}[/tex] + 24x³ + 3

The degree is determined by the term with the largest exponent.

In this case 48[tex]x^{6}[/tex] ← with exponent 6

Hence the polynomial is of degree 6

Answer:

L = 97, w = 27

Step-by-step explanation:

The perimeter formula is P = 2L + 2w.  We have too many unknowns simply to plug in, so we have to find a way to identify one in terms of the other.  The statement is that the length is 16 feet more than 3 times the width, so the length is in terms of the width and can be identified as

L = 3w + 16

and the width, then, is just w.  Now we can fill in those 2 values, both in terms of w, and set it to equal the perimeter value we were given of 248:

2(3w + 16) + 2w = 248 and

6w + 32 + 2w = 248 and

8w + 32 = 248 and

8w = 216 so

w = 27

That means that the width is 27.  Use that value of w now to find the length where

L = 3w + 16.

L = 3(27) + 16 and

L = 97

For the given rectangle, the width is 27 feet, and the length is 97 feet.

To find the dimensions of the rectangle, we start by representing the width as w. Given that the length is 16 feet more than three times the width, we represent the length as:
length = 3w + 16.

The formula for the perimeter of a rectangle is Perimeter = 2(length + width).
Setting up the equation, we get:

248 = 2(3w + 16 + w)

248 = 2(4w + 16)

248 = 8w + 32

216 = 8w

w = 27.

Now that we have the width, we can find the length:

Length = 3w + 16 = 3(27) + 16 = 81 + 16 = 97.

Thus, the dimensions of the rectangle are width = 27 feet and length = 97 feet.

Answer:

The surface area of the composite figure = 1172.08 inches²

Step-by-step explanation:

* Lets explain the figure

- There is a cylinder with diameter 8 inches and height 9 inches

- Rectangular prism with dimensions 16 , 11 , 11 inches

- The surface area of the cylinder will be the curved area and the

  top base

- The surface area of the prism will be the surface area of one base ,

 four side faces and top face which is the remaining from the subtraction

 of the rectangular base and the circular base

* Lets solve the problem

# The surface area of the cylinder

∵ The diameter of the base of the cylinder is 8 inches

∵ The diameter = twice the radius

∴ 8 = 2r ⇒ divide both sides by 2

∴ r = 4 inches

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π inches²

∵ π = 3.14

∴ The area of the base = 16(3.14) = 50.24 inches²

∵ The area of the curved surface = 2πrh

∵ r = 4 inches and h = 9 inches

∴ The area of the curved surface = 2(3.14)(4)(9) = 226.08 inches²

∴ The surface area of the cylinder = 226.08 + 50.24 = 276.32 inches²

# The surface area of the rectangular prism

∵ The dimensions of its base are 16 and 11 inches

∵ The area of the rectangle = length × width

∴ The area of the lower base = 16 × 11 = 176 inches²

∵ The area of the top face = area of the rectangle - area of the circle

∵ The area of the rectangle = 176 inches²

∵ The area of the circle = 50.24

∴ The area of the top face = 176 - 50.24 = 125.76 inches²

- There are two side faces with dimensions 16 and 11 inches

∴ The area of the two faces = 2 × 16 × 11 = 352 inches²

- There are two faces with dimensions 11 and 11 inches

∴ The area of the two faces = 2 × 11 × 11 = 242 inches²

∵ The surface area of the rectangular prism is the sum of the 6 faces

∴ The surface area of the prism = 176 + 125.76 + 352 + 242

∴ The surface area of the prism = 895.76 inches²

- The surface area of the composite figure is the sum of the surface

  area of the cylinder and the surface area of the prism

∵ The surface area of the cylinder = 276.32 inches²

∵ The surface area of the prism = 895.76 inches²

∴ The surface area of the composite figure = 276.32 + 895.76

∴ The surface area of the composite figure = 1172.08 inches²

Answer:

  y +2 = 2(x +3)

Step-by-step explanation:

The equation in point-slope form for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

The slope of your given line is the coefficient of x, -1/2. The slope of a perpendicular line will be the negative reciprocal of that: -1/(-1/2) = 2. So, you have m = 2, (h, k) = (-3, -2), and your desired equation is ...

  y -(-2) = 2(x -(-3)) . . . . . . which can be simplified to ...

  y +2 = 2(x +3)

Answer:

  from top to bottom: 1, 3, 2

Step-by-step explanation:

For chords and arcs, the "theorem that supports the statement" is essentially a restatement of the statement.

For the relationship to chords and diameters, the second statement on the right applies. A chord and the radii to its ends form an isosceles triangle. The altitude is the perpendicular bisector of the chord (triangle base). Of course, it is also a line segment that intersects the center of the circle (the apex of the isosceles triangle).

Answer:

1 matches with first statement, 2 matches with third statement and 3 matches with second statement i.e, 1,3,2.

Step-by-step explanation:

In circle, when two chords are equal , than their corresponding minor arcs are also equal. Converse is also true, if minor arcs are equal, than their corresponding chords are equal.So, when chords BC and DE are equal, than their minor arcs BC and DE are also equal. In converse, when arcs BC and DE are equal, than their chords BC and DE are also equal. for the third one, Perpendicular from the center bisect the chord, hence AX is ⊥ to BC than BX= XC.

We can say that diameters perpendicular to chord bisect the chord.

1 matches with first statement, 2 matches with third statement and 3 matches with second statement i.e, 1,3,2.

Final answer:

Two tangents meeting at opposite ends of a circle's diameter are parallel and cannot intersect outside the circle, since tangents are perpendicular to the radius at the point of tangency and parallel lines do not meet.

Explanation:

Two tangents that intersect a circle at opposite endpoints of the same diameter cannot intersect outside the circle. This is because a tangent to a circle is perpendicular to the radius at the point of tangency. In the case of tangents at the ends of a diameter, these tangents are parallel to each other since they are perpendicular to the same line (the diameter), which cannot intersect outside the circle by definition of parallel lines.

No, it is not possible for the two tangents to intersect each other outside the circle.

Let's consider the properties of tangents and diameters to a circle to explain why the two tangents cannot intersect each other outside the circle.

1. A tangent to a circle is a line that touches the circle at exactly one point. This point of tangency is perpendicular to the radius drawn to the point of tangency.

2. A diameter of a circle is a chord that passes through the center of the circle and has both endpoints on the circle. The center of the circle bisects the diameter, meaning it divides the diameter into two equal parts.

3. If a tangent intersects a circle at an endpoint of a diameter, then by the definition of a tangent, the tangent is perpendicular to the radius at that point. Since the radius is part of the diameter, the tangent is also perpendicular to the diameter at the point of tangency.

4. Now, consider two tangents, each intersecting the circle at opposite endpoints of the same diameter. Since each tangent is perpendicular to the diameter at its respective point of tangency, the two tangents are parallel to each other because they are both perpendicular to the same line (the diameter).

5. Parallel lines do not intersect. Therefore, the two tangents, being parallel, cannot intersect each other at any point, let alone outside the circle.

In conclusion, because the two tangents are parallel, they cannot intersect each other outside the circle, confirming that the scenario described in the question is not possible.

Answer:

15 races

Step-by-step explanation:

The team has competed in 45 and has won 30. So the success rate is:

Success rate is:

[tex]Sccess\ rate=r= \frac{30}{45}*100\\ =66.7\ percent[/tex]

We have to find the number of races the team needs to win for 75% success rate

Which means that

[tex]r = \frac{30+x}{45+x} = 0.75\\[/tex]

We have to solve the equation for x

[tex]\frac{30+x}{45+x}=0.75\\ 30+x = 0.75(45+x)\\30+x=33.75+0.75x\\x-0.75x=33.75-30\\0.25x=3.75\\x=\frac{3.75}{0.25}\\ x=15[/tex]

The team needs to win 15 races to get 75% success rate ..

Hello There!

The answer would be "I and III"

If Isabelle makes these changes, she will get charged an overdraft fee on 2 days. The days will be Thursday and Saturday.

Answer:

B

Step-by-step explanation:

2 x length + 2 x width = perimeter.

2(2s-5) + 2(4s-13) = 108

Simplify:

4s-10 + 8s-26 = 108

Combine like terms:

12s - 36 = 108

Add 36 to both sides:

12s = 144

Divide both sides by 12:

s = 144/12

s = 12

Now replace s with 12 in each equation:

2(12) - 5 = 24-5 = 19

4(12) - 13 = 48-13 = 35

The answer is d. 35,35, 19,19

Answer:

193

Step-by-step explanation:

We need to convert the decimal part of that number from years to days.  Do that like this:

.52895 × [tex]\frac{365days}{1year}[/tex].

The year label cancels and we are left to multiply .52895 by 365 to get 193.06675 days.

Final answer:

3.52895 years is approximately 3 years and 193 days when converted, using the average number of days in a year (365.2422) to calculate the days from the fractional part of the year.

Explanation:

To calculate the time in years and days when given a decimal of years, one must convert the fractional part of the year into days. Assuming that the initial figure 'If = 3.52895' represents 3.52895 years, we would have 3 complete years and a fraction of a year (0.52895). To find the number of days in this fractional year, we need to multiply it by the average number of days in a year. The average year contains 365.2422 days, accounting for the additional leap year day every four years.

To convert the 0.52895 of a year to days, the calculation would be:

0.52895 × 365.2422 = 193.215 (approximately).

Therefore, 3.52895 years is roughly 3 years and 193 days.

Answer:

1728 in³

Step-by-step explanation:

A 12-inch cube has a volume of (12 in)³ = 12³ in³ = 1728 in³.

The box will hold 1728 cubic inches.

To determine the volume of the box, which is the amount of space it can hold, one must calculate the product of its length, width, and height. Since the box measures 12 inches on each side, it is a cube. The volume ( V ) of a cube is given by the formula:

[tex]\[ V = a^3 \][/tex]

where a is the length of one side of the cube. In this case,  a = 12 inches. Plugging this value into the formula, we get:

[tex]\[ V = 12^3 \] \[ V = 12 \times 12 \times 12 \] \[ V = 144 \times 12 \] \[ V = 1728 \][/tex]

Therefore, the volume of the box, or the number of cubic inches it will hold, is 1728 cubic inches.

Answer:

  a.  y = -7cos(x) +7

Step-by-step explanation:

The middle level of the gum is 7 inches above the ground, and it oscillates 7 inches either side of that. Thus the offset of the cosine function (average height) is 7 and the multiplier (amplitude of oscillation) is also 7. The -7 on the cosine multiplier means the height of the gum is zero at x=0.

The cosine function that describes the height of the gum above the ground as a function of the angular distance, considering the diameter of the bike tire is 14 inches, is y = -7 cos x + 14.

The diameter of the bike tire is 14 inches which means that the radius is 7 inches. The maximum height the gum could reach would be the top of the wheel, or the diameter. The minimum height is when the gum is at the bottom of the wheel, touching the ground, or at 0. Thus, the range of the cosine function should be between 0 and 14. One pattern of the cosine function is that it starts from its maximum point, not from the middle of the range like the sine function. With this information, the correct answer is y = -7 cos x + 14. This starts at 14, dips to 0, and ranges back up to 14.

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Answer:

Two events are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't change the probability of the other. Two events are mutually exclusive when they cannot occur at the same time. For example, if we flip a coin it can only show a head OR a tail, not both. Independent event: The occurrence of one event does not affect the occurrence of the others.

Independent events do not affect each other's occurrence, while mutually exclusive events cannot occur at the same time. The concepts are distinct and significant in probability theory.

Independent vs Mutually Exclusive Events

Independent events and mutually exclusive events are not the same in probability theory. Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. The mathematical representation of this is P(A AND B) = P(A)P(B). On the other hand, two events are mutually exclusive if they cannot occur at the same time, meaning the events do not share any outcomes and the probability of both events occurring together, P(A AND B), is zero.

An example of independent events might be rolling a dice and flipping a coin. Whether the dice shows a six does not affect whether the coin shows heads. An example of mutually exclusive events would be drawing a heart or a club from a deck of cards as a single card cannot be both a heart and a club.

Answer:

Step-by-step explanation:

Let k represent the pounds of produce coming from Kelsey's garden. Then Doug's garden produces 5.8k pounds of produce, and the total weight of it is ...

  k + 5.8k = 102

  6.8k = 102 . . . . . . . . . . . simplify

  k = 102/6.8 = 15 . . . . . . pounds of produce from Kelsey's garden

  5.8k = 5.8·15 = 87 . . . . pounds of produce from Doug's garden

Answer:

4 1/8 inches

Step-by-step explanation:

7 1/4 - 3 1/8

(7-3) + (1/4 -1/8)

4 + (1/4 - 1/8)

4 + 1/8

4 1/8 inches

Answer:

  4 1/8 inches

Step-by-step explanation:

You apparently want to find the sum (in inches) ...

  5.5 + (1 3/4) - (3 1/8)

This can be done a number of ways. One is to use an appropriate calculator.

__

Another way to do this is to add the integer parts and fraction parts separately:

  = (5 +1 -3) +(1/2 +3/4 -1/8)

  = 3 + (4/8 +6/8 -1/8) = 3 + (4+6-1)/8 = 3 9/8

  = 4 1/8

__

Another way is to convert all the numbers to decimal, then add.

  = 5.500 +1.750 -3.125

  = 7.250 -3.125

  = 4.125 = 4 1/8

__

There were 4 1/8 inches of snow remaining Tuesday evening.

Answer:

120

Step-by-step explanation:

Angle ABC = 1/2 Arc ABC

Angle ABC = 1/2 *240

Angle ABC = 120

Answer:

1.08%

Step-by-step explanation:

When you solve problems like these you convert the percentages into fractions and multiply them together.

18%= 18/100 reduced------>     9/50

6% = 6/100 reduced------>  3/50

3/50 *  9/50 = 108/10000 reduced ------->  54/5000 reduced---->

27/2500.  The probability is 27/2500, or 1.08%

Answer:

No real solutions.

Step-by-step explanation:

We need to solve the following equation: 3x^2 + 6x + 6 = 0

First, we should divide the whole equation by 3:

3x^2 + 6x + 6 = 0 ⇒ x^2 + 2x + 2 = 0

Now, the equation has no real results. It happens because the polynomial never crosses the x-axis. (See graph attached).

The imaginary solution is:

x = -1 + i

x= -1 - i

Answer:

C. 55°

Step-by-step explanation:

Note the total measurement of angles for a triangle. The total measurement of all angles in a triangle = 180°

Note that m∠C is a right angle (as shown through the square), and that right angles = 90°

Subtract to find the measurement of the unknown angle (∠B)

∠B = 180 - (∠A + ∠C)

∠B = 180 - (35 + 90)

Simplify. Combine like terms. First, add (solve parenthesis), then subtract.

∠B = 180 - (125)

∠B = 55

m∠B = C. 55°

~

Answer:D

Step-by-step explanation:

125

Answer:

The equation can be used to find the value of x is 2.1 + 2x = 7.5 ⇒ D

Step-by-step explanation:

* Lets talk about the isosceles triangle

- The isosceles triangle has two equal sides

- The angle between the two equal sides is called the vertex angle

- The side opposite to the vertex angle is called the base of the triangle

- The end vertices of the base are called the base angles  

- The two base angles are equal in measure

- The perimeter of any triangle is the sum of the length of its  

 three sides

* Lets solve the problem

∵ The triangle is isosceles triangle

- The shortest side is opposite to the shortest angle  

∵ The two base angles are equal in measure

∴ The shortest angle is the vertex angle which opposite to the  

  base of the triangle

∴ The shortest side is the base of the triangle

∵ The length of the shortest side is y

∴ The length of the equal sides is x

∴ The lengths of the sides of the triangles are x , x , y

- The perimeter of the triangle is the sum of the length of its  

  three sides

∴ The perimeter of the triangle = x + x + y

∵ The perimeter of the triangle is 7.5 m

∴ x + x + y = 7.5 ⇒ add the like terms

∴ 2x + y = 7.5

∵ y = 2.1 ⇒ given

∴ 2x + 2.1 = 7.5

∴ 2.1 + 2x = 7.5

* The equation can be used to find the value of x is 2.1 + 2x = 7.5

Answer:

1/2 to land on heads

1/5 spinner

2/6=1/3 dice

10/16=5/3 marbles

32 out of 64

12/30

13 out of 39

125/200

Answer:

A'(-1,-3)

B'(-2,-2)

C'(-4,-3)

Step-by-step explanation:

The rotation by 90° counterclockwise about the origin has the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

So, the vertices of the triangle ABC have the images:

[tex]A(-3,1)\rightarrow A'(-1,-3)\\ \\B(-2,2)\rightarrow B'(-2,-2)\\ \\C(-3,4)\rightarrow C'(-4,-3)[/tex]

see attached diagram for details.

Answer:

56.02 dollars

Step-by-step explanation:

Wanted x, the price before taxes and tip.

sales tax: x * 0.11

+

tip on sales tax: x * 0.11 * 0.2

+

tip on price: x * 0.2

= 0.332x

= 18.6 (presumption)

Therefore,

x = 18.6/0.332 = 56.02

Answer:  $60

Step-by-step explanation:

Let the total price of Zoe dinner = x

According to question,

He paid 11 % sales tax  20% on tip.

Therefore,  he paid total extra charge = 11 + 20 = 31 %

That is, he paid 31 % extra in sales tax and tips for dinner.

But again according to the question,

Zoe paid $18.60 in sales tax and tips for her dinner.

⇒ 31 % of x = 18.60

⇒

⇒

⇒

⇒ x = 60

Thus, The total cost of Zoe's dinner before tax = $60

Answer:

14%

Step-by-step explanation:

If the selected student is a male, that reduces the population to consider, to 14 (4 + 6 + 2 + 2).

How many male juniors?  2

So, the chance for the random student to be a junior if he's a male, are 2 out of 14.

P = 2/ 14 = 1/ 7 = 14.29%

Rounded to the nearest whole percent: 14%

The first box has a total of 10 items ( 3 pencils + 7 pens = 10)

The probability of picking a pen would be 7/10

The second box has a total of 8 items ( 4 pencils  + 4 crayons = 8)

The probability of picking a crayon would be 4/18, which reduces to 1/2

To find the probability of doing both, multiply each probability together:

7/10 x 1/2 = 7/20

The probability is 7/20

Answer:

The answers 6

Step-by-step explanation:

haha buns

Answer:

D

Step-by-step explanation:

The 3 angles on the right form a straight angle, thus they sum to 180°

Subtract the 2 given angles from 180 to find measure of third angle ( which is the angle inside the triangle )

third angle = 180° - (70 + 60)° = 180° - 130° = 50°

The sum of the 3 angles in a triangle = 180°

Subtract the 2 known angles from 180 for measure of x

x = 180° - (50 + 60)° = 180° - 110° = 70° → D

Answer:

  cot(θ) = 5/6

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you the tangent relationship is ...

  Tan = Opposite/Adjacent

The cotangent function is the inverse of the tangent function, so ...

  Cot = Adjacent/Opposite

For your angle, the adjacent side of the triangle is the x coordinate, 5; the opposite side is the y coordinate; 6. Then the cotangent is ...

  cot(θ) = 5/6