Suppose that 14 inches of wire costs 70 cents. At the same rate, how many inches of wire can be bought for 50 cents?

The exact solutions of the given equation in the interval are;

A: x = 0, π/2, π, ³/₂π

We are given the equation as;

sin 4x = –2sin 2x

Writing the equation in standard form gives;

sin 4x + 2sin 2x = 0

Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;

2sin 2x cos 2x + 2sin 2x = 0

Factorize to get;

2sin 2x(cos 2x + 1) = 0

A. sin 2x = 0

The unit circle will give us 3 solutions for 2x as follows;

2x = 0

Thus; x = 0

2x = π

Thus; x = π/2

2x = 2π

Thus; x = π

B. cos 2x = - 1

The unit circle gives 2 solutions for 2x as;

2x = π

Thus; x = π/2

2x = 3π

Thus; x = ³/₂π

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Complete question is;

How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?

Answer:

2x-2y=4 that is the best way u can write it

A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

example :

y=4+2x+x

y = 3x + 4

y = 3x + 4 is a polynomial that has exponent equal to 1.

Therefore A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

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The probability that George will win is 1/10 and the probability that Julia will win is 1/20.

So, calculate the probability as follows:

We know,

(A) George's probability of winning:

(B) Julia's probability of winning:

Therefore, the probability that George will win is 1/10 and the probability that Julia will win is 1/20.

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Using mathematical operations, the amount that would be saved by buying 3 dresses instead of buying per piece is $3.40.

The mathematical operations include the following basic operations: addition, subtraction, division, and multiplication.

Mathematical operations determine the results of mathematical expressions and problems.

Cost of a dress = $6.20

Cost of 3 dresses = $15.20

Cost per dress if 3 dresses were bought = $5.067

Amount saved for buying 3 dresses instead of one = $3.40 ($6.20 x 3 - $15.20)

Thus, mathematically, the customer would save $3.40 by buying 3 dresses for $15.20 instead of buying at $6.20 per unit.

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Answer:

D. 3 3/7 ft²​

Step-by-step explanation:

A = LW

A = 4 ft × 6/7 ft²

A = 24/7 ft²

A = 3 3/7 ft²

The missing reasons used in solving the given inequality are;

Reason 2; Subtraction property

Reason 3; Subtraction property of order

Reason 5; Division property of order.

There are different properties of algebra such as distributive property, commutative property, associative property, addition property, division property e.t.c

We are given the inequality as;

−2(x + 3) − 4 > 4x + 30

Step 1;

-2x - 6 - 4 > 4x + 30

Reason 1; Distributive property

Step 2; -2x - 10 > 4x + 30

Reason 2; Subtraction property

Step 3; -6x - 10 > 30

Reason 3; Subtraction property of order

Step 4; 6x > 40

Reason 4; Addition property of order

Step 5; x < -20/3

Reason 5; Division property of order.

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Answer: i am not positive but i think 2.5 on x and 9, and 27 on y

Step-by-step explanation: just want to help asap

Answer: 5q-5r               -5q+5r

The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10

Let the number of cups be represented by x.

This will be expressed as:

2/3 = x/4.62

Cross multiply

3x = 2 × 4.62

3x = 9.24

Divide

x = 9.24 / 3

x = 3.08

Therefore, 3.08 cups are needed.

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Answer:

The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.

Step-by-step explanation:

Answer:

5:6

Step-by-step explanation:

The entire class is 11/11.

Girls: 5/11 of the class.

Boys: 11/11 - 5/11 = 6/11

Ratio of girls to boys:
5/11 / 6/11 = 5/11 × 11/6 = 5/6

Answer: 5:6

Answer:

$420

Step-by-step explanation:

multiple 10.50 by 40 to get 420

The mistakes that Claire made in solving the equation are;

1) She did not use distribution property correctly in step 1 as 2(8) = 16 and not 10.

2)  - (2+5x) should have been simplified to -2 - 5x and not -2 + 5x

3) 10 + 56x = 8x - 2 should have been 12 = -64x and not 12 = 64x

We want to solve the equation 8(2 + 7x) = 3x - (2 + 5x)

Step 1; Expand the bracket on the left hand side and right hand side to get; 16 + 56x = 3x - 2 - 5x

Step 2; Simplify the right hand side to get;

16 + 56x = -2x - 2

Step 3; Rearrange to get;

16 + 2 = -58x

Step 4; Add up the left hand side to get;

18 = -58x

Step 5; Divide both sides by -58 to get;

x = -9/29

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Complete question is;

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It

turns out Clare's work has three mistakes!

find all three mistakes explain the below

8(2 + 7x) = 3x - (2+5x)

10 + 56x = 3x - 2 + 5х

10 + 56x = 8x - 2

10 = 64x - 2

12 = 64x

x = 3/16

The area of the plot is 193 sq.yd.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, A developer buys an empty lot to build a small house.

To find the area, we need to be divided the figure into triangles and rectangles

Area of the first triangle = (1/2) * base * height

base = 17 unit and height = 10 unit

= (1/2) * 17 * 10

= 17*5=85 sq. unit

Area of the second triangle = (1/2)* 9* 8

=36 sq. unit

Area of the rectangle = base * height

base = 9 unit and height = 7 unit

Area = 9*7= 63 sq. unit

Area of the last triangle = (1/2) * 2*9

= 9 unit

Adding all the areas to get the area of the plot = 85+36+63+9

Hence, Area of the plot = 193 sq.yd.

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Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters

information given in the question

Mia stands at a horizontal distance of 15 meters from the building

The angle of elevation from her eyes to the roof ((point AA)) is 18

the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^

her eyes are 1.75 meters from the ground

The direction of movements describes a right angle triangle of

opposite = height of antenna + height of the building

adjacent = 15 meters

The  distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The  the height of the antenna is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only

tan 53  = opposite / 15

opposite = 15 * tan 53 = 19.906 meters

opposite = 15 * tan 18 = 14.266 meters

Height of the antenna

= 19.606 - 14.266

= 5.34 meters

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The set of information that is true about the relation is:

Domain: {3, 4, 5, 6}

Range: {-8, -1, 2, 7}

The relation is not a function.

A relation that represents a function will have each of its domain elements related to exactly one range element.

All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,

Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.

Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:

The domain of the relation is: {3, 4, 5, 6}

The range of the relation is: {-8, -1, 2, 7}

The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.

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Answer:

x ≥ 6

Step-by-step explanation:

|-3x| - 7 ≥ 11     The absolute value of -3x is 3x

3x - 7 ≥ 11        Cancel the 7 by adding it on both sides

3x ≥ 18            To get x by itself divide 3 on both sides

x ≥ 6

Answer: $78.75

Step-by-step explanation:

You have to multiply the price by tax and add

Answer:

B

Step-by-step explanation:

the two angles lies on the same lines and they have the same vertex

The simplified expression of the expression given as -3x+16+5x+8 is 2(x + 12)

From the question, the equation is given as

-3x+16+5x+8

To start with, we need to rewrite the expression

So, we have the following representation

-3x + 16 + 5x + 8

The above expression is not an equation

Instead, it is an expression

This is so because there is no equality symbol i.e. = in the expression

So, we collect the like terms

-3x  + 5x + 8 + 16

Solving further, we need to evaluate the like terms

So, we have the following equation

-3x  + 5x + 24

Evaluate the like terms again

So, the equation becomes

2x + 24

The above expression cannot be further simplified, however, it can still be factored

Factor out 2 from the expression

This gives

2(x + 12)

Hence, the solution is 2(x + 12)

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Answer:

1024

Step-by-step explanation:

8 times 2 to the 7th power

2 by the 7th power 128 times 8 1024

Patrick is vegetarian and Thelma is non vegetarian.

What are vegetarian?

The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.

Main Body:

As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.

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The straight line y = x -1 is shown figure  

To plot straight-line graphs we need to take values of x and y values to make a value table and to work out the graph.

Take x values as -1, 0, 1, etc. to make our work easy and clearer, and from that find the values of y.

After calculating the coordinates, use the resultant points to plot the line as a graph.  

Here we have a line

y = x -1  

To sketch the graph we need to make a value table as given below

First take x values as, -1,  0, 1 from that find the values of y  

At  x = -1 => y = -1 - 1 = -2

At  x = 0 => y = 0 - 1 = -1

At  x = 1 =>  y = 1 - 1 = 0  

From the above calculations, the value table is

        x   -1   0   1

        y   -2  -1  0      

Use the above value and Sketch the graph

[ the resultant graph is shown below ]

The straight line y = x -1 is shown figure    

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The percent of error is 15%. The correct option is B.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Alton estimated that 230 people attended the band concert.

The actual count for attendance was 200 people.

To find the percent of error:

230 - 200 / 200

= 30 / 200

= 0.15

0.15 decimal to the percentage is 15%.

Therefore, the error is 15%

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The fraction in their simplest form will be:

9. 12/15 = 4/5

10. 6/8 = 3/4

11. 25 / 100 = 1/4

12. 5 / 40 = 1/8

13. 7/77 = 1 / 11

14. 4 / 36 = 1/9

15. 18/20 = 9/10

16. 100/1000 = 1/10

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

It should be noted that in order to divide a fraction in their simplest form, the equivalent numbers must be used.

For example, 100/1000 will be:

(100 ÷ 100) / (1000 ÷ 100)

= 1 / 10

25 / 100 has a common factor of 25 as.this gives 1/4.

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answer:

10

step-by-step explanation:

easy: 100 ÷ 10 = 10. you need 10

explanation: you need 100 (on the left side) to equal the right side. each weight on the right side weighs 10, but you don't know how many you need. use x for the unknown amount. now, you have:

100 = 10x. solve by dividing each side by 10.

10 = x. verify by doing 10 x 10 = 100

By solving a system of equations, we will see that the equation is:

-4*x - 3*y = -18

We know that the linear equation:

A*x + B*y = -18

We know that this linear equation passes through the points (-3, 10) and (6, -2), then replacing these values in the equation we will get two equations:

A*-3 + B*10 = -18

A*6 + B*-2 = -18

So we have a system of equations:

-3A + 10B = -18

6A - 2B = -18

if we add the two times the first equation and the second one we get:

2*(-3A + 10B) + 6A - 2B = 2*(-18) - 18

18B = -3*18

B = -3

by replacing that value of B in one of the equations we will be able to solve it for A.

6*A - 2*(-3) = -18

6*A + 6 = -18

6*A = -18 - 6 = -24

A = -24/6 = -4

The equation is:

-4*x - 3*y = -18

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The area of left over wrapping paper is 380 square inches

The given dimensions are:

The surface area of the box is calculated as

Surface area = 2(lw + lh + wh)

This gives

Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches

The surface area of the wrapping paper is calculated as

Wrapper = lw

This gives

Wrapper = 2 * 3 = 6 square feet

Express the area in square inches

Wrapper = 864 square inches

The area left is the difference between the areas calculated above

i.e.  Amount left = Wrapper - Box

So, we have

Amount left = 864 square inches - 484 square inches

= 380 square inches

Hence, the amount left is 380 square inches

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