Use inductive reasoning to predict the next line in this sequence of computations. Then use


a calculator or perform the arithmetic by hand to determine whether your conjecture is


correct.


9.3+5 = 32


99.3 + 5 = 302


999. 3+5 = 3002


9999.3+5 = 30002


Make a conjecture by predicting the correct numbers in the line below.


0-3+5 -0


Is the conjecture correct?


O A. Yes


OB. No

Answer:

107.76

Step-by-step explanation:

We are told in the above question that:

He flew 3,610 miles in 33.5 hours. If he flew about the same number of miles each hour, how many miles did he fly each hour?

We solve the above question by:

33.5 hours = 3610 miles

1 hour = x miles

Cross Multiply

33.5 hours × x miles = 3610 miles × 1 hour

x miles = 3610 miles × 1 hour/33.5 hours

x miles = 107.76119403 miles

Approximately = 107.76 miles per hour

Therefore, he flew 107.76 miles each hour

Answer:

[tex]\:x=55^{\circ \:\:}[/tex]

Therefore, option 'b' is correct.

Step-by-step explanation:

Let x be the angle

determining the [tex]\tan ^{-1}\left(1.4281\:\right)[/tex]

[tex]\:\tan \:x\:=1.4281\:[/tex]

[tex]x=\tan ^{-1}\left(1.4281\:\right)[/tex]

[tex]\:x=55^{\circ \:\:}[/tex]

Therefore, option 'b' is correct.

Answer:

[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The cosine ratio is defined as:

[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]

Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:

[tex]\displaystyle \cos A=\frac{17}{38}[/tex]

[tex]\cos A=0.4474[/tex]

Using a scientific calculator, we get the inverse cosine:

[tex]A=\arccos(0.4474)[/tex]

[tex]A\approx 63^\circ[/tex]

Since A+B+C=180°, we can solve for C:

C = 180° - A - B

C = 180° - 63° - 90°

C = 26°

Thus:

[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]

In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.

To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:

1. Sine (sin): [tex]\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)[/tex]

2. Cosine (cos): [tex]\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)[/tex]

3. Tangent (tan): [tex]\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)[/tex]

Given:

AC = 38

AB = 17

To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.

1. For m∠A:

[tex]\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]

2. For m∠C:

[tex]\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]

Let's calculate the angles:

[tex]1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)[/tex]

Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).

To know more about right triangle, refer here:

https://brainly.com/question/31613708

#SPJ2

Answer:

4.36

8.23

Step-by-step explanation:

Answer:

4.36

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the total number of miles Rex can travel be x;

If a cab company charges $0.85 per mile, then x miles will cost $0.85x

If the flat rate rate charge is $3.10, the total price for x miles will be;

0.85x + 3.10

Since Rex has no more than $15 to spend on a ride, the inequality to represent the equation will be;

0.85x + 3.10 ≤ 15 (less than or equal to means that the total value cannot exceed $15)

Next is to solve for x

Given

0.85x + 3.10 ≤ 15

subtract 3.10 from both sides

0.85x + 3.10-3.10 ≤ 15-3.10

0.85x ≤ 15-3.10

0.85x ≤ 11.90

x ≤  11.90/0.85

x ≤ 14

This means that Rex can travel 14 miles without exceeding his limit

Answer:

[tex]3.10 + 0.85m \leq 15[/tex]

[tex]m \leq 14.0[/tex]

Step-by-step explanation:

Given

[tex]Flat\ Rate = \$3.10[/tex]

[tex]Addition = \$0.85[/tex] (per mile)

[tex]Maximum\ Amount = \$15[/tex]

Required

Determine the inequality that represents the scenario and solve

Let the number of miles be represented by m.

The company's charges can be calculated using:

[tex]Flat\ Rate + Additional\ Charges * m[/tex]

Substitute values

[tex]\$3.10 + \$0.85 * m[/tex]

Rex can't exceed $15 implies that the company's charges can't exceed Rex's budget.

This is expressed as:

[tex]\$3.10 + \$0.85 * m \leq \$15[/tex]

[tex]\$3.10 + \$0.85m \leq \$15[/tex]

[tex]3.10 + 0.85m \leq 15[/tex] ---- The inequality

Solving for m: Collect Like Terms

[tex]0.85m \leq 15 - 3.10[/tex]

[tex]0.85m \leq 11.9[/tex]

Divide through by 0.85

[tex]m \leq 11.9/0.85[/tex]

[tex]m \leq 14.0[/tex] ---- The solution

Answer:

1092 is divisible into 1, 7, or 1092.

Step-by-step explanation:

Step-by-step explanation:

1092 / 1 = 1092

1092 / 2 = 546

1092 / 3 = 364

1092 / 4 = 273

1092 / 6 = 182

1092 / 7 = 156

1092 / 12 = 91

1092 / 13 = 84

1092 / 14 = 78

1092 / 21 = 52

1092 / 26 = 42

1092 / 28 = 39

1092 / 39 = 28

1092 / 42 = 26

1092 / 52 = 21

1092 / 78 = 14

1092 / 84 = 13

1092 / 91 = 12

1092 / 156 = 7

1092 / 182 = 6

1092 / 273 = 4

1092 / 364 = 3

1092 / 546 = 2

1092 / 1092 = 1

Answer:

10111

Step-by-step explanation:

Answer:

♡ hi again, queen! ♡

- It's 10111.

have a great day!

✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

I take it that x is somewhere near the end of the diagonal line, so you want to know the value of 3x + 1???

We know that (3x + 1) + (2x + 4) = 90 degrees. That's because AEF = 90 degrees.

So begin by removing the brackets.

3x + 1 + 2x + 4 = 90                 Combine the like terms.

5x + 5 =90                               Subtract 5 from both sides.

5x + 5 - 5 = 90 - 5                   Combine  

5x = 85                                    Divide by 5

x = 17

3x + 1  = 3*17 + 1 = 51 + 1 = 52

Answer:

x=10 and y= 8.

Step-by-step explanation:

Given that the cost of 1 banana = $0.60

Cost of 1 mango = $1.50.

Total cost= $ 18  

Here, x be the number of bananas and y be the numbers of mangos,

As the number of bananas is 2 more than the number of mangos,

So, x=y+2

[tex]\Rightarrow y=x-2 \cdots(i)[/tex]

Cost of x bananas [tex]=\$ 0.60 \times x[/tex]

Cost of y mangos [tex]=\$ 1.50 \times y[/tex]

Total cost = 0.6x+1.5y

[tex]\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).[/tex]

Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.

Both the graphs intersect at the point (10,8) as shown in the graph.

So, the solution of both the equations is, (x,y)=(10,8). i.e

The number of bananas = x= 10 and

the number of mangos = y = 8.

Answer:

23) 53/100

24)2/5

25)3/5

26)11/50

27)17/50

28)19/1000

29)4/5

30)1/250

31)9/25

32)1 3/10

33)11 1/2

34) 7 3/40

Step-by-step explanation: Hope this helps!

Answer:

Step-by-step explanation:

Equations

Subtract the second equation from the first one side-by-side:

The answer is 2

Answer:

Image point → (6, 1)

Step-by-step explanation:

Given point → (-3, 3)

Transformation to be done → [tex]R_{180}0T_{-3,-4}[/tex]

Transformations to be done,

Step - (1). Translation of the given by 3 units left and 4 units down.

Step - (2). Followed by the rotation counterclockwise 180° about the origin.

Rule for step (1),

(x, y) → (x - 3, y - 4)

By this rule,

(-3, 3) → [(-3 - 3), (3 - 4)]

         → (-6, -1)

Rule for step -2,

(x, y) → (-x, -y)

(-6, -1) → (6, 1)

Therefore, following these two steps coordinates of the image point → (6, 1)  

Answer:

D

Step-by-step explanation:

We have the equation:

[tex]x+9=4(x-1)^2[/tex]

To convert this to standard form, we can simply expand.

First, expand the right-hand side:

[tex]x+9=4(x^2-2x+1)[/tex]

Distribute the right:

[tex]x+9=4x^2-8x+4[/tex]

Subtract 9 from both sides:

[tex]x=4x^2-8x-5[/tex]

Finally, subtract an x from both sides:

[tex]0=4x^2-9x-5[/tex]

Flip:

[tex]4x^2-9x-5=0[/tex]

Hence, our answer is D.

Answer:

0

Step-by-step explanation:

m= y2-y1/x2-x1

=0-0/-3-5

=0/-8

=0

Answer:

Slope = 0

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

Every triangle has a measure of 180, so if we know two of the angles we can find the last one easily. To find angle 1, we first must find angle 2. 2 must be equal to 42 because it is vertical to the other angle that is equal to 42 degrees. Then to find angle 1 do the operation 180-(50+42). This equals 88, which is the measure of angle 1.

Answer:

Plz I don't understand everything

Answer:

hope this is not to hard to understand

Answer: Thanks for the points

Step-by-step explanation:

Answer:

Step-by-step explanation:

step 1. 4y+9x=18

step 2. 4y=-9x+18

step 3. idk

Answer:

(2,0)

plug 0 for y and solve

Answer:

D. If M does not divide AB into two congruent segments, then M is not the midpoint of AB.

Step-by-step explanation:

A conditional statement is one that include 'if'. Thus it is also referred to as an 'if' statement.

Given a conditional statement:

If M is the midpoint of AB, then M divides AB into two congruent segments.

The converse of the given statement is done by interchanging the two parts of it. So that we have:

If M divides AB into two congruent segments, then M is the midpoint of AB.

Then, the inverse can be obtained by getting the negative of both parts of the converse. Therefore, the inverse is:

If M does not divide AB into two congruent segments, then M is not the midpoint of AB.

The correct option is D.

Answer:

Step-by-step explanation:

We are given the sequence

[tex]15, 29, 49, 75, 107\\15->29 = 14\\29 -> 49 = 20\\49->75 = 26\\75 -> 107 = 32\\14, 20, 26, 32\\14 -> 20= 6\\20 -> 26 = 6\\26 -> 32 = 6\\\\6, 6, 6\\6->6 = 0[/tex]

Since we had to find the differences twice, it is a second degree polynomial

[tex]y = an^2 + bn + c\\plugging \: in \: n = 1, 2, 3...\\the \: sequence \: is \\a+b+c, 4a + 2b + c, 9a + 3b + c...\\the \: diff \: under \: is \\3a + b, 5a + b, 7a + b...\\the \: diff \: under \: is \\2a, 2a, 2a...\\so, \\2a = 6\\a = 3\\3(3) + b = 14\\b = 5\\\\a +b + c = 15\\3 + 5 + c = 15\\c = 7\\[/tex]

so,

[tex]y = 3n^2 + 5n + 7[/tex]

Answer:

f

klllllllllk

Step-by-step explanation:

Answer:

-19=-2/3x

3*-19=-2x

-57=-2x

-57/-2=x

57/2=x

x=28.5

Step-by-step explanation:

Answer:

x = [tex]\frac{57}{2}[/tex]

Step-by-step explanation:

Given

- 19 = - [tex]\frac{2}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )

- 57 = - 2x ( divide both sides by - 2 )

[tex]\frac{-57}{-2}[/tex] = x , that is

x = [tex]\frac{57}{2}[/tex]

Answer:

107

Step-by-step explanation:

The two angles would make a linear pair, which means they're supplementary to each other. Supplementary angles add up to 180.

This allows us to do 180 - 73 = 107

x would be 107.

Answer:

Answer is at the bottom!

Step-by-step explanation:

Cherry juice=5+5+5+5+5+5=30

Lime juice =3+3=6

6 cherry slushes and 2 lime slushes were sold.

Hope this helps!!

Answer:

6 cherry slushes and 2 lime

Step-by-step explanation:

add them all up or Mutiply and Divide all together I think

Answer:

The T shirt choice

Step-by-step explanation:

Both values increase at the same rate therefore is proportional.

Answer:

The mean of C is 170 households

The standard deviation of C, is approximately 5 households

Step-by-step explanation:

The given parameters are;

The percentage of households in the United States that had a computer in 2014 = 85%

The size of the randomly selected sample in 2014, n = 200

The random variable representing the number of households that had a computer = C

Therefore, we have;

The probability of a household having a computer P = 85/100 = 0.85

Let

Therefore;

The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;

μₓ = 200 × 0.85 = 170

The mean of C = μₓ = 170

The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5

Therefore;

The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05

The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)

The mean and the standard deviation of C are 170 and 5.05 respectively

The given parameters are:

[tex]\mathbf{n = 200}[/tex] -- the sample size

[tex]\mathbf{p = 85\%}[/tex] -- the proportion of household that had a computer

(a) The mean

This is calculated as:

[tex]\mathbf{\bar x = np}[/tex]

So, we have:

[tex]\mathbf{\bar x = 200 \times 85\%}[/tex]

[tex]\mathbf{\bar x = 170}[/tex]

(b) The standard deviation

This is calculated as:

[tex]\mathbf{\sigma = \sqrt{np(1 - p)}}[/tex]

So, we have:

[tex]\mathbf{\sigma = \sqrt{170 \times (1 - 85\%)}}[/tex]

[tex]\mathbf{\sigma = \sqrt{170 \times 15\%}}[/tex]

[tex]\mathbf{\sigma = \sqrt{25.5}}[/tex]

Take square roots

[tex]\mathbf{\sigma = 5.05}[/tex]

Hence, the mean and the standard deviation of C are 170 and 5.05 respectively

Read more about mean and standard deviation at:

https://brainly.com/question/10729938

Answer:

x = −2 or x = 10

Step-by-step explanation:

for the explanation see the image