3. When using set builder notation, what does it mean to 'Define a set'?

Based on the altitudes of both the airplane and the helicopter, the number of minutes until they are at the same altitude is 20 minutes.

Assuming the minute both will be on the same altitude is x, the altitude that the airplane would be at that point is:

= 30,000 - 1,000x

The helicopter's altitude would be:

= 0 + 500x

Putting them together gives:

30,000 - 1,000x = 500x

30,000 = 1,500x

x = 30,000 / 1,500

= 20 minutes

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Answer:

20x + 8

Step-by-step explanation:

5*4x + 5*5 -17

20x +25 -17

20x + 8

Step-by-step explanation:

You need to attach the table in order to get an answer.

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

[tex]\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;[/tex]

it is clear, the required constant is 12 (12 per hour).

To find the point of intersection for two lines, we can use substitution to solve for the coordinates.

We're given:

With these two equations, we can:

Isolate x in the second equation:

[tex]x+2y=7\\x =7-2y[/tex]

Substitute the second equation into the first:

[tex]3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5[/tex]

Solve for y:

[tex]21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2[/tex]

Solve for x:

[tex]x+2y=7\\x+2(2)=7\\x+4=7\\x=3[/tex]

The point of intersection of the lines is (3,2).

It can be modeled by an exponential function because each time x increases by 1, f(x) is multiplied by 4.

This means the base of the exponential function is 4, and since f(x)=3 when x=0, [tex]f(x)=3(4)^{x}[/tex]

Answer: 1, -2, 1

Step-by-step explanation:

[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]

Answer:

y = 4x - 5

Step-by-step explanation:

y = mx + b

By putting above values in equation (i)

-1 = 4 (1) + b

-1 = 4 + b

-5 = b

b = -5

y = 4x - 5

Answer:

power of a power

Step-by-step explanation:

the power of a power law says that, "if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same."

for example, for this problem, you would do:

[tex](x^4)^9\\= x^4^*^9\\= x^3^6[/tex]

Answer:

4 kg

Step-by-step explanation:

so 1.6 * 4 is 6.4 so you just double check if you want

4 + 1.6 which is 1/4 of 6.4 will be 5.6 (matches with the question)

4 + (1.6*4) (indicates it's full) = 10.4( also Matches with the question)

there is another way by setting up an equation. let me know in comments if you want to see it that way

If  tank weighs 5.6kg when it 1/4 filled with water. If it weighs 10.4kg when it is full , then weight when it is empty is 0.93kg

Two or more expressions with an Equal sign is called as Equation.

Given,

A tank weighs 5.6kg when it 1/4 filled with water

Tank weighs 10.4kg when it is full

We need to find the weight when it is empty.​

Let weight of the tank “x” and the weight of the water in the full tank “y”.

From the problem statements, we deduce the following equations:

x + y/4 = 5.6kg => x = 5.6kg - y/4

x + y = 10.4kg => y = 10.5kg - x

y = 10.5kg - (5.6kg - y/4)

3y/4 = 4.9

Thus y = 6.53kg; x = 0.93kg

Hence, weight of the tank when it is empty is 0.93kg.

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[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].

We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).

This set is {3, 4, 11, 13, 14, 15, 17, 24}

Answer:

[tex]3 \frac{7}{8}[/tex]

Step-by-step explanation:

Answer:

Option B :39 degrees is the correct.

The nearest degree is 39°

Step-by-step explanation:

Laws of cosines relates each side with its opposite angle.

Formula for this is :

[tex]c^{2} =a^{2} +b^{2} - 2abcosC[/tex]

[tex]a^{2} = b^{2}+c^{2} - 2bccosA[/tex]

[tex]b^{2} =a^{2}+c^{2} -2accosB[/tex]

in figure a=28

              b=18

              c=25

Here we have to find angle between a and c that is B

So [tex]18^{2} = 25^{2} +28^{2} -2*25*28cosB[/tex]

324 = 625 + 784 - 1400cosB

1400cosB =  625 + 784 - 324

1400cosB = 1085

cosB = 0.775

∠B = 39.195° ≈ 39°

The boat change 39°  when it made its first turn.

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Answer:

B 39 degrees

Step-by-step explanation:

The person above me is correct and I got proof for the people with trust issues. :  )

Answer:

127 degrees = x

Step-by-step explanation:

A six sided polygon has interior angles that sum to

(n-2)(180) =  (6-2)(180 = 720

so all of the angles in the question add to 720

 98 + 133 + x + x + 155 + 80 = 720

  solve for x = 127 degrees

Answer:

x = 127

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6 , then

sum = 180° × 4 = 720°

sum the interior angles and equate to 720

x + x + 155 + 80 + 98 + 133 = 720 , that is

2x + 466 = 720 ( subtract 466 from both sides )

2x = 254 ( divide both sides by 2 )

x = 127

Answer:

$41269.983

rounded:

$41,269.98

Step-by-step explanation:

well you begin with the equation a=p(1+r/n)[tex]^{nt}[/tex]

so 30,000(1+0.08/12)to the power of 4 times 12

when you plug all of that in a calculator your receive $41269.983

[tex]1) \text{ } f(-2)=8(-2)^{2}-3(-2)+2=\boxed{40}\\\\2) \text{ } f(-1)=8(-1)^{2}-3(-1)+2=\boxed{13}\\\\3) \text{ } f(0)=8(0)^{2}-3(0)+2=\boxed{2}\\\\4) \text{ } f(1)=8(1)^{2}-3(1)+2=\boxed{7}\\\\5) \text{ } f(2)=8(2)^{2}-3(2)+2=\boxed{28}[/tex]

Answer:

3 cakes

Step-by-step explanation:

just flow by the formula then ignore the remainder and take the whole number which is 3 then that becomes your answer good day.

Answer:

5 lbs 1 oz

Step-by-step explanation:

This year Lucille weighs 106 lb 13 oz. A

year ago she weighed 101 lb 12 oz. How

much has she gained in the year?

16oz = 1 lb

13 oz = 13/16 = .8125

12 oz = 12/16 = 3/4 = .75

106.8125 - 101.75

106.8125

-101.7500

---------------

   5.0625 =

5.0625 = 5 1/16

1/16 of a pound is 1oz

5 lbs 1 oz

Answer:

The answer will be 63%.

Step-by-step explanation:

they have all ready mentioned that.

Answer:

Angle 1: 55 degrees
Angle 2: 55 degrees
Angle 3: 70 degrees

Step-by-step explanation:

Finding angle 1: We know that in a triangle, all three angles must add up to 180 degrees. In the triangle on the left, 2 of the angle measures are already given to us. Therefore, we can simply do 180 - 40 - 85, thus the measure of angle 1 is 55 degrees.
Finding angle 2: We know that opposite angles are congruent. Therefore, angle 2 and angle 1 have the same measure.
Finding angle 3: Using the same thought process as we used when finding the measure of angle 1, we can subtract the other 2 angles. 180 - 55 - 55 is equal to 70.

Answer:

first, we take the first triangle( the right one), since a triangle is equal to 180 we add 85 and 40 which gives us 125, we then subtract 125 with 180 getting 55 so (1) =55

to find (2) we put 55 the same number as no. (1) because of the property VERTICALLY OPPOSITE ANGLES.

then to find (3) we do the same steps as (1), we add 55 and 55 and subtract by 180. 55+55=110

             =110 - 180

             =70

There u go, please mark me as brainless

Answer:

C

Step-by-step explanation:

The slope is -1/3, so it will go down and to the right. Down 1, to the right 3 (rise over run!)

The y intercept is 2.

(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as

[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]

Expand the right side and match up coefficients:

[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]

Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that

[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]

and

[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]

(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then

[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]

Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].

(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is

[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]

which expands to

[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]

Reusing the identity from (a-i) and the result from part (b), we have

[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]

We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].

So, the simplest quadratic that fits the description is

[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]

To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].

The total surface area of the cone is 3π + 10 cm².

A cone is a three-dimensional object that consists of a circular base and a vertex.

Total surface area = πr (r + l)

Where:

π x 3 + (3 + 7)

3π + 10 cm²

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Answer:

C

Step-by-step explanation:

A and B are wrong because 37 is prime. 31 is prime and 33 is divisible by 11 and 3 so C

Answer:

CI = $182.25

Step-by-step explanation:

Compound interest formula:

[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex]  ,

where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).

Using formula:

CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]

CI = $182.25

Step-by-step explanation:

1/2 represents every fraction, where the denominator (bottom part) is twice the numerator (top part).

like 4/8 or 6/12 or 128/256 or ...

what do we need in the denominator to calculate with 15/16 ?

the same : 16.

and what is half of 16 ? 8.

so, we need the 1/2 based on 16th = 8/16.

so, the dog ate 8/16 (1/2) of the original 15/16.

what was left was

15/16 - 8/16 = 7/16 pound

Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:

1.053x = 30.8.

x = 30.8/1.053

x = 29.2.

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Answer:

[tex]\sf 1. \quad \tan(B)=\dfrac{4}{3}[/tex]

[tex]\sf 2. \quad \tan(A)=\dfrac{7}{2}[/tex]

[tex]\sf 3. \quad \angle A[/tex]

Step-by-step explanation:

Acute angle: an angle less than 90°

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Question 1

Refer to the first attached diagram.

If tan(A) = 3/4 then the side opposite ∠A is 3 units, and the side adjacent ∠A is 4 units.

Therefore:

[tex]\implies \sf \tan(B)=\dfrac{4}{3}[/tex]

Question 2

Refer to the second attached diagram.

If tan(B) = 2/7 then the side opposite ∠B is ,and the side adjacent ∠B is 7.

Therefore:

[tex]\implies \sf \tan(A)=\dfrac{7}{2}[/tex]

Angle A would be bigger (see second attachment).