A scale drawing has a scale of 0.5 in =10 ft find the length

The measure of angle B where angle B is an acute angle by using the Law Of Sines is 61° .

What is an Acute Angle ?

The Acute Angle can be defined as an angles that measure less than 90° , the acute angle is smaller than Right Angle and also smaller than the Linear Angle ( measuring 180° ).

From the figure ,

we can see that the measure of the sides are given as a = 9 , b = 8 and

the measure of angle A is 79° .

By Applying the Law Of Sines ;

we get ,

[tex]\frac{SinA}{a} =\frac{SinB}{b}[/tex]

Substituting the values in the above equation ,

we get ;

[tex]\frac{Sin79\textdegree}{9} =\frac{SinB}{8}[/tex]

Simplifying further ,

we get ;

[tex]SinB = \frac{Sin79\textdegree}{9} \times 8[/tex]

substituting the value of Sin79° as 0.9816 ;

we get ;

[tex]SinB = \frac{0.9816}{9} \times 8[/tex]

[tex]SinB=0.8725[/tex]

So , B ≈ 61° .

Therefore , the measure of angle B is 61° .

The given question is incomplete , the complete question is

Find the measure of Angle B in the given figure .

Note that the angle B is acute . Round to the nearest degree .

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The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:

$60.

Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.

The amounts of each item are given as follows:

36, 48 and 24.

Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:

36 - 48 - 24|2

18 - 24 - 12|2

9 - 12 - 6|3

3 - 4 - 2

Hence:

gcf(36, 48, 24) = 2² x 3 = 12.

Which is the number of packages. As each package sells for $5, the amount earned is given as follows:

12 x 5 = $60.

Each package is composed by:

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The sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].

What is sine function?

The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.

The general sine function is

[tex]y = Asin(b(x+c)+D[/tex]

Where

Amplitude = A

Period = [tex]\frac{2\pi }{B}[/tex]

Phase shift = c

Vertical shift = D

Given:

A = 4 (amplitude)

[tex]\frac{2\pi }{B} = 4[/tex]  (period)

[tex]B = \frac{\pi }{2}[/tex]

Since midline: y = 1

And we know that graph of [tex]4sin(\frac{\pi }{2}x)[/tex], midline to be y = 1.

It must have vertical shift D = 1.

Since, y - intercept (0, 1)

⇒ x = 0, y = 1

⇒ It has no phase shift  ⇒ c = 0

Since it satisfy [tex]y = 4sin(\frac{\pi }{2}(x+c))+D[/tex]

The graph of the sine function is attached below.

Hence, the sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].

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Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.

Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

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Answer: 1/7

Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.

Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle divided by hypotenuse of the triangle.

sin is a trigonometric ratio.

If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.

sin Q = perpendicular / hypotenuse.

sin Q is the base of the trigonometry ratios and it is one of the ratio.

sine is an acute angle.

some formula of sine angle are ,

1- sine Q = 1/ cosec Q .

2- sin ^2 Q = 1- cos^2 Q .

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There are seven zeroes  located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/(2^5.5^8).

Terminating decimal is a decimal number which have a finite number of digits after the decimal point. Decimals like 3.45, 6.78, 1.987 are terminating decimals. Decimals which have 0 as the non terminating digit like 3.7800000.. are also called as terminating decimals.

Let P=1/(2^5.5^8)

Multiplying and dividing the numerator by 2^3

P= 2^3/(2^5.5^8.2^3)

P=8/(2^8.5^8)

P=8/10^8

P=0.00000008

The number of zeroes located to the right of the decimal point and before the first non-zero digit are seven.

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On solving the provided question we can say that - her in the equation  14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex]14w + 3p = 70.50 \\[/tex]

10w+7p = 62.50 ,

[tex]w = 12\\[/tex]

p = 18

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The value of m ∠ Q is 23°.

What are complementary angles?

Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary. We say two angles "Complement" one other when their sums equal 90 degrees.

Here, we have

Given: m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles.

The sum of the measures of two complementary angles is 90°.

So, m∠P + m∠Q = 90°

Substitute 12x+7 for m∠P and 6x−7 for m∠Q.

12x+7 + 6x−7 = 90°

18x = 90°

x = 5°

To find m∠Q, substitute 5 for x in 6x−7.

6×5 - 7 = 23°

m ∠ Q = 23°

Hence, the value of m ∠ Q is 23°.

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Answer:

the percentage is 62%

Step-by-step explanation:

Answer:

55 miles per hour

Step-by-step explanation:

The equation is:

R = d / s

We know

d = 495 miles

s = 9 hours

Let's solve

R = 495 / 9

R = 55 miles per hour

So, their driving rate is 55 miles per hour

Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

Pentagons are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."

Here,

we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.

Pentagonal prisms are pentagon-shaped if we look at them from the bottom.

When viewed from the side, a pentagonal prism would have a rectangular shape.

If we were to look at the pentagonal prism from the front, it would appear rectangular.

Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

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The fans at the semi final is less than the fans at the final .

The implementation of the away goals rule makes any goals scored away from home effectively count twice when the scores are tied, as is customary in matches with home and away legs, such as the knockout stage of the Champions League.

Champions League and Europa League, two of its premier club championships, starting in the 2021–22 season.

Semi final : 250*4/6+4 = 100

Final : 400*3/7+3= 120

Hence, The fans at the semi final is less than the fans at the final .

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The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

Given that,

We have to find the total surface area of the triangular prism in the given picture.

We know that,

First, we need to calculate the area of ​​the triangle

a = area of triangle

a = 1/2 ×15 cm × 8 cm

a = 60 cm²

Now,

We must determine the three rectangles' areas.

a₁ = 2cm × 17cm

a₁ = 34cm²

a₂ = 2cm × 15cm

a₂ = 30cm²

a₃ = 2cm ×8cm

a₃ = 16cm²

Now, we must multiply the triangle by two and sum all the estimated areas.

a₁ + a₂ + a₃ + 2a =60cm² + 34cm² + 30cm² + 2 × 16cm² = 156cm²

Therefore, The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

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The halfway between the number is -1/4 on the number line.We can find halfway by using midpoint formula.

If the given number is positive mark it on the right side of the origin. If it is a negative number mark it on the left side of zero.Then divide each unit into the values equal to the fraction's denominator.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.

Now

Using midpoint formula

[tex]x_{1}[/tex]+[tex]x_{2}[/tex]/2 =-5/6 +1/3 divide 2

Find common denominator and write the numerators above common denominator

-5+2/12 =-3/12

            =-1/4

Hence we find midpoint between numbers.

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Answer:

-33

Step-by-step explanation:

Plug 9 in for c, then simplify the resulting expression.

5c - 9c + 3

5(9) - 9(9) + 3

↓ execute multiplication

45 - 81 + 3

↓ simplify by adding 81 and 3

45 - 84

↓ execute subtraction

-33

Answer:

[tex] \sf \: - 33 \: (if \: c = 9)[/tex]

Step-by-step explanation:

Given expression,

→ 5c - 9c + 3

Now we have to use,

→ c = 9

Simplifying the given expression,

→ 5c - 9c + 3

→ 5(9) - 9(9) + 3

→ 45 - 81 + 3

→ -36 + 3

→ -33 => (answer)

Hence, required answer is -33.

Answer:

1/6

Step-by-step explanation:

There are 6 letters and the spinner lands on one at a time

Based on the description above, the individuals in this setting is option A: homes.

The website lists homes for sale in a suburban town and provides information such as neighborhood, selling price, number of bedrooms, and whether the home has a garage.

In this case each house is an instance or a data point of a "home" object, these objects have different attributes or features like neighborhood, selling price, number of bedrooms and garage, these attributes are used to describe the characteristics of the home, they are also called features.

Therefore, each home is an individual unit being sold on the market. Neighborhoods, selling prices, and bedrooms are attributes or characteristics of the homes, and they help provide more information about each individual home being listed.

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For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3

Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.

Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication

Given the polynomial:

p(x) = -3x² + 10 - 4x

Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:

p(x) = -3x² - 4x + 10

The degree is 2 (x²) and the leading coefficient is -3(-3x²)

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The statement that best represents the function must be identified by reading the graph.

A) When  x < 0, the function is negative.

This is accurate; as you can see, the function is negative for x < 0 because it is below the horizontal axis.

We shall see that choice A is the proper one. "When x < 0, the function is negative."

The function tends to infinity on the positive side at an x close to zero.

The function tends to negative infinity at x close to zero on the negative side.

The function tends to zero as x's absolute value grows.

So we can conclude that this is an inverse function similar to:

y = f(x) = 1/x

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Answer:The student needs to score 20 points

Step-by-step explanation:

? /50= 40/100Cross multiply:100*? = 40*50⇒? = 40*50/100= 20

Answer:

The surface area of this cuboid is 420 square inches.

Step-by-step explanation:

All we have to do is calculate each rectangle. For the width, we have 10 x 5 which is 50. Then we multiply it by 2 because we have two of those sides. Then we get 100. Then we have 11 x 5 which is 55. We multiply that by 2 and we get 110. Then we do that to the final two sides and we get 220. So the final answer if we add them all up is 420 square inches.

Answer: No

Step-by-step explanation:

Look at the 3 numbers in the sequence,

Geometric sequence means the ratio between two consecutive numbers in the sequence is a constant (eg. 10, 5, 2.5 is a geometric sequence as the ratio is a constant at 1/2)

However, for the sequence listed above

Looking at 1st and 2nd term,

Ratio = 110/120 = 11/12

Looking at 2nd and 3rd term,

Ratio = 105/110 = 21/22 which is not the same as 11/12.

Hence, since the ratio is not the same, this sequence is not a geometric sequence.

The area of the base of the bin is 9 ft^2.

The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.

Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.

We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.

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The volume of the cone is (2/3)π cubic feet. And the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft. The correct option is A.

Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.

Given:

Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown.

He used the same amount of concrete to construct a spherical barrier.

According to the information  given in the exercise, the height and the radius of the pylons are the following:

Height h = 2 ft

Radius r = 1 ft

So, the volume of the cone,

= (1/3)πr²h

= (1/3)π(1)²(2)

= (2/3)π cubic feet.

And the volume of the sphere is twice the volume of the cone.

So, the volume of the sphere,

4πr³/3 = 2π/3

2r³ = 1

r³ = 1/2 = 0.5

r = ∛0.5 = 0.8 ft.

Therefore, the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.

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The exponential equation that matches the number of zombies after 6 hours is the possible option;

Z = 14 × 4⁶

An exponential equation is one in which the argument is an index or power of a constant.

The initial number in the group of zombies = 14

The amount by which the group increases every hour = The group quadruples every hour

The required equation; The equation that matches the number of zombies after 6 hours

The information in the question indicates that the sequence is a exponential, which can be presented using the following equation;

Z = a·rⁿ

Where;

Z = The number of zombies after n hours

a = The first term = The initial number of zombies in the group = 14

r = The common ratio = The amount that multiplies members of the group every hour = 4

n = The number of hours after which the number in the group is evaluated

Therefore, after 6 hours, n = 6, and we get;

a₆ = 14 × 4⁶ = 14 × 4⁵ = 14336

The equation from the possible options, obtained from a similar question posted online, that matches the number of zombies after 6 hours is therefore;

Z = 14 × 4⁶

The possible options are;

Z = 4·(14)⁶

Z = 4·(1 + 14)⁶

Z = 14·(1 + 4)⁶

Z = 14·(4)⁶

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Answer:

you can use compass to make straight line

Answer:

Step-by-step explanation:

(9a⁴b⁷) x (6a³b⁸)

(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)

54 x a⁷ x b¹⁵ = 54a⁷b¹⁵

Answer:

(9a⁴b⁷).(6a³b⁸)

=54a⁷b¹⁵