The set of complex numbers is the set of all numbers of the form a + bi, where a and b are real numbers and i=

Answer:

Possible length range of third side is between 3<x<21.

Step-by-step explanation:

Sum of two sides of triangle cannot be equal or less than third side. Therefore, one side length of a triangle must be between subtract and sum of other two sides. Than, range of third side is:

[tex](12-9)<x<(12+9)\\3<x<21[/tex]

original height was 5" and it was enlarged to 30"

 find the ratio by dividing 30 by 5

30 / 5 = 6

 so ratio would be 1/6 meaning for every 1 inch of the original the new one is 6 inches

now you need to multiply the original width by 6 to find the new width

7" x 6 = 42"

 new width = 42"

The mathemtical expression for the word expression  5 less than twice x "  is 2x - 5 option (A) 2x -5 is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The  word expression is:

5 less than twice x

Twice the x  = 2x

5 less than twice the x:

= 2x - 5

Thus, the mathematical expression for the word expression  5 less than twice x "  is 2x - 5 option (A) 2x -5 is correct.

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Answer:   -1.9

Step-by-step explanation:just add up the values for the weight change

(-1.8)+(0.9)+(-1.4)+(0.4)

-1.9

Answer:

750

Step-by-step explanation:

for others

750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity

We need to find how many gallons of 80%

8x, since we don't know how many gallons

mixed with 250 gall of 40%: 0.40(250)

and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:

8x+0.4(250)=0.7x+0.7*250

Multiply on both sides of the equation

0.8x+100= 0.7x+175 Subtract 100 on both sides

0.8x= 0.7x+75

Subtract 0.7 on both sides

0.1x= 75

Divide both sides by 0.1

x= 750

You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

Hence,  750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.

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From the information, A is a right triangle, B is an acute triangle and C is an acute angle.

A polygon with three sides, angles, and vertices is called a triangle.

Given that, triangle side lengths, we need to identify the triangle as acute, right or obtuse,

How to solve the triangle?

It will be a right triangle if a² + b² = c², It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².

1) a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25

25 = 25

This is a right triangle.

2) a² + b² = 5² + 6²

= 25 + 36 = 61

c² = 7² = 49

61 > 49 = аcute triangle.

3) a² + b² = 8² + 9²

= 64 + 81 = 145

c² = 12² = 144

145 > 144 = аcute triangle.

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q, and p

you don't show the options but it should look something like this:

195 +15d = 360

answer:

subtract 195 from each side

15d = 165

d = 165/15  =11

 he needs to walk 11 dogs

The equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and number of dogs is 11.

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.

Frank needs a total of $360 to cover his expenses of the week. He earns $195 a week working at a restaurant and also walks dogs to supplement his income, frank charges $15 per dog that he walks.

The equation, which can be used to find the number of dogs d that frank needs to walk to cover his expenses,

[tex]15d+195=360[/tex]

Solve it further to find the number of dogs d,

[tex]15d+195=360\\15d=360-195\\d=\dfrac{165}{15}\\d=11[/tex]

Thus, the equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and the number of dogs is 11.

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To solve the problem, two equations were set up based on the conditions given. After substitution and simple algebraic operations, the larger number was found to be 38 and the smaller number to be 29.

The question involves finding two numbers where the sum is 67, and the smaller number is 9 less than the larger number.

Let's define the larger number as x and the smaller number as y. According to the problem:

Substitute Equation 2 into Equation 1:

x + (x - 9) = 67

2x - 9 = 67

2x = 67 + 9

2x = 76

x = 38

Now, we can find y using Equation 2:

y = x - 9

y = 38 - 9

y = 29

Therefore, the larger number is 38 and the smaller number is 29.

Answer:

- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).

- m∠BAC = 130°.

- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).

Explanation:

We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.

1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.

Therefore, m∠DCB = 30°.

2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.

3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.

4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.

5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,

we find m∠BAC = 180° - 25° - 25° = 130°.

Answer:  [tex]\frac{1}{3}[/tex]

Explanation:

let y = [tex]log_{8} (2)[/tex]

whenever we transfer base from  log from one side to other it will remain be base after shifting to the other side.

Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]

here we have n = y, m=2, x=8    by substituting the values

we will get

[tex]8^{y} = 2[/tex]          (1)

we can write 8 in power of 2 that is [tex]2^{3}[/tex]

we will rewrite the above equation (1) as

[tex]2^{3y} = 2[/tex]

we can equate the power when base is same then we will get

3y = 1

then

[tex]y=\frac{1}{3}[/tex]

The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3

Let the given logarithmic function be x to have:

[tex]log _82=x[/tex]

This can be transformed into indices to have:

[tex]8^x = 2[/tex]

Solve the resulting indices for "x" a shown:

[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]

Cancel the base and equate the power to have:

[tex]3x = 1\\x = \frac{1}{3}[/tex]

Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3

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Answer:

y − 100 = -12.5 (x − 4)

Step-by-step explanation:

Pick two points on the line to calculate the slope:

m = (y₂ − y₁) / (x₂ − x₁)

m = (100 − 125) / (4 − 2)

m = -12.5

Next, use point-slope form to write the line equation.

y − y₁ = m (x − x₁)

y − 100 = -12.5 (x − 4)

To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. Given that the side length of the tile is 12 inches, the length of the diagonal is approximately 17 inches when rounded to the nearest inch.

To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the right triangle are the sides of the square tile, and the hypotenuse is the diagonal. Given that the side length of the tile is 12 inches, we can calculate the length of the diagonal as follows:

Square the length of one side: 12 x 12 = 144

Multiply the result by 2: 144 x 2 = 288

Take the square root of the result: √288 ≈ 16.97 inches

Rounded to the nearest inch, the length of the diagonal of the square tile is 17 inches.

Final answer:

The length of the diagonal of the square, rounded to the nearest inch, is 17 inches.

Explanation:

The length of the diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the square are both 12 inches long. So, we have:

hypotenuse² = side1² + side2²

hypotenuse² = 12² + 12²

hypotenuse² = 144 + 144

hypotenuse² = 288

To find the length of the hypotenuse (or the diagonal), we take the square root of both sides:

hypotenuse = √(288)

hypotenuse = 16.97 inches (rounded to the nearest inch)