Jack is 14 years old. In 2032 to Jack will be twice his age. What year is it​

Answer:

64

Step-by-step explanation:

Important angle relationships that will help us answer this question :

For more clarification kindly view the attached images :)

Using these angles relationships, we can easily find the answer two different ways.

First way :

Creating an equation : We want to find the measure of angle MPN. It's important to note that this angle falls on a line made up of other angles ( angle mpe and angle npe ) forming a straight line ( line e )

Using our angle relationships we know that angles that form a straight line are supplementary and add up to 180 degrees.

So we can say angle mpe + angle npe + angle MPN = 180. ( we can use this equation to solve for angle MPN )

Here we are given that angle mpe is a right angle ( indicated by the little square ) meaning it has a measure of 90 degrees.

So we can further simplify our equation saying that angle npe + 90 + angle MPN = 180 ( by plugging in angle mpe = 90 )

Now if you didn't know we can solve an equation ( find the missing angle ) if there is a single variable ( in this case we want the variable to be angle MPN ). This means that in order to solve for angle MPN we just find the measure of the other angle, angle npe.

Finding angle npe

The angle under "x" is corresponding to angle mpE so we can say the angle under x = angle npe.

The angle under x also appears to be supplementary to the angle with a measure of 153 degrees. So we can say that angle under x + 154 = 180

Subtracting both sides by 153 we get that angle under x = 180 - 154 = 26 degrees.

Because the angle under x and angle npe are corresponding and equal to each other, angle npe also has a measure of 26 degrees.

Finishing creating the equation and solving for angle MPN : So we have angle npe + angle mpe + angle MPN = 180

We know angle mpe = 90 and angle npe = 26

So we can say 90 + 26 + angle MPN = 180

Now we can solve for angle MPN

90 + 26 + angle MPN = 180

==> combine like terms

116 + angle MPN = 180

==> subtract 116 from both sides

angle MPN = 64 degrees

Second way :

We can also solve for angle MPN using the angle relationship " opposite interior angles "

The angle with a measure of 154 degrees and angle ePN are opposite exterior angles meaning they are congruent. ( so angle ePN = 154 )

Angle ePN is made up of angle mpe and angle MPN. This means that angle mpe + angle MPN = 154

We've already identified that angle mpe = 90 degrees because it's a right angle so we can say angle angle MPN + 90 = 154

Subtracting both sides by 90 we get that angle MPN = 154 - 90 = 64 degrees

And we are done!

Answer:

The volume of the cylinder is approximately 1570.8 cm³.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume Formula [Cylinder]:
[tex]\displaystyle V = \pi r^2 h[/tex]

Step-by-step explanation:

Step 1: Define

Identify given variables.

h = 5 cm

r = 10 cm

Step 2: Find Volume

∴ the volume of a cylinder whose height is 5 cm and radius is 10 cm is approximately 1570.8 cm³.

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Topic: Geometry

The pair of angles that share a ray as a common side in the given diagram is: ∠FAB and ∠FAD.

Adjacent angles are angles that lie adjacent or next to each other sharing a common vertex and have the same ray as a common side.

In the diagram attached below, ∠FAB and ∠FAD share a common vertex, A, and a ray FA as a common side.

Therefore, the pair of angles is: ∠FAB and ∠FAD.

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Answer:

the cords for a should be (-3,0) and the cords for b should be (7,15) sorry if im incorrect

The equation that is not necessarily true is that PQ = AB.

The perpendicular bisector of any line segment can be drawn by opening the compass more than half, by putting the nib of the compass at one end of a line segment, and by marking an arc on both sides of the line segment from both the ends of the segment.

The following Property that the perpendicular bisector PQ follows when it bisects the line segment AB include:

Therefore, PQ is Perpendicular Bisector of Line Segment AB is not true.

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Answer:

Yes x = 9/2 is the correct solution.

Step-by-step explanation:

You have substituted x = 9/2 into both sides of the equation and they have both simplified to the same value.

Answer:

x=70+30-60

Step-by-step explanation:

Word to my mother

Hello, detailed answer is given below.

If you have any question(s), then feel free to ask in comments!

Check the picture below.

Answer:

B, C, D

Step-by-step explanation:

Square roots are not in polynomials

The relationship between the corresponding sides of similar triangles indicates that the height of the tree is 60 feet. The correct option is therefore;

Similar triangles are triangles in which the ratio of the corresponding sides of the triangles are equivalent for the three sides of the triangle.

The location of the tree divides the hypotenuse side and the base of the triangle formed by the building into two parts of the same length, therefore;

The length of the hypotenuse side to the building = 2 × 108 ft = 216 ft

The length of the base to the building = 2 × 90 ft = 180 ft

The ratio of corresponding sides of similar triangles and the trigonometric ratio of sines, indicates that we get;

Height of the tree/108 = 120/216

Height of the tree = 108 × (120/216) = 60 feet

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Answer:

(a^2)+4a-5

Step-by-step explanation:

(3+a+2)(a+2-3)

(a+5)(a-1)

use FOIL or box method

5a-5+(a^2)-a simplifyes to

(a^2)+4a-5

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ 2^3~~ = ~~8\implies \log_2(8)~~ = ~~3[/tex]

The value of (26 - 7) and (5 - 24) when they're multiplied will be -399.

From the information given, we are told to multiply (26 - 7) and (5 - 24). This goes thus:

= (26 - 7) × (5 - 24)

= 21 × -19

= -399

In this case, value of (26 - 7) and (5 - 24) when they're multiplied will be -399.

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Answer: rectangle

Step-by-step explanation:

From the options, it is implied that it is a parallelogram.

From inspection, we can tell that not all the sides are congruent, so it is not a rhombus or a square.

To determine if it is a rectangle, we can use the slope formula to see if there is a pair of perpendicular sides (if this is the case, then this will be a parallelogram with a right angle, making it a rectangle)

[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC} \text{ because} \left(m_\overline{AB} \right) \left(m_{\overline{BC} \right)=1[/tex]

So, the most specific classification is a rectangle.

Step 4 is the reason SSS

Answer:

however dc =20 cm is

Step-by-step explanation:

so this isnt contrary to 50

Answer:

If it's all about trapezoid and FE is the median:

SOLUTION:

m = \frac{1}{2}

2

1

[(20) + (38)]

m = \frac{1}{2}

2

1

(58)

m = \frac{58}{2}

2

58

m = 26

ANSWER: 26 cm

Step-by-step explanation:

Answer:

pls write your answer in order i dont know if they are together or separate

Answer:

Option C, The volume of the length cube is 3 times the volume of the smaller cube

Step-by-step explanation:

21.8 / 7.8 = 2.8

the volume of the larger would be 21.8^3 = 10360.23

the volume of the larger would be 7.8^3 = 474.55

Answer: attached image

Answer:

a) x = 1

Step-by-step explanation:

Given: 2x + 3 = 5

1. Subtract 3 from both sides:

2x + 3 - 3 = 5 - 3

⟹ 2x = 2

2. Divide both sides by 2:

2x ÷ 2 = 2 ÷ 2

⟹ x = 1

3. Check your work:

2(1) + 3 = 5

2 + 3 = 5

⟹ 5 = 5 ✔

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Answer:

Least 8.06, 8.295, 8.3, 8.31 Greatest

Answer:

  A, C, F

Step-by-step explanation:

The first figure is drawn using 8 squares. The next uses 11 squares, and the one shown in Step 3 uses 14 squares. The numbers of blocks follow the sequence ...

  8, 11, 14

which begins with 8 and increases by 3 from one step to the next. This constant increase from one term to the next makes it an arithmetic sequence.

__

The general term, an, of an arithmetic sequence can be written in terms of its first term, a1, and its common difference, d, as ...

  an = a1 +d(n -1)

When the first term is a1=8, and the common difference is d=3, this becomes ...

  an = 8 +3(n -1)

which simplifies to

  an = 8 +3n -3 = 3n +5

Written in functional form, these explicit equations are ...

  f(n) = 8 +3(n -1) . . . . . matches choice A

  f(n) = 3n +5 . . . . . . . . matches choice F

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The recursive form of the definition of a sequence starts with the first term, then tells you how to obtain the next term from that. Here, the first term is ...

  f(1) = a1 = 8

and each term is 3 more than the last:

  f(n) = 3 +f(n-1) . . . . . . . . . 3 is added to the previous term

Together, this is ...

  f(n) = 8, f(n) = 3 +f(n -1) . . . . . matches choice C

Answer:

B: Save $10

Step-by-step explanation:

A: $14.80, B: $12, C:$18.70, D: $16.50

Answer:

About 61 cartons with a reminder with a remainder of 10

Step-by-step explanation:

12 * 61 = 732 → 742 - 732 = 10 eggs

hope this helps

Answer:

B

Step-by-step explanation:

the absolute value function always gives a positive result

However, the value inside can be positive or negative, that is

5x + 30 = 10x or - (5x + 30) = 10x

solving both

5x + 30 = 10x (subtract 5x from both sides )

30 = 5x ( divide both sides by 5 )

6 = x

or

- (5x + 30) = 10x

- 5x - 30 = 10x ( add 5x to both sides )

- 30 = 15x ( divide both sides by 15 )

- 2 = x

As a check

substitute these values into the equation and if both sides are equal then it is a solution.

x = 6

left side = | 5(6) + 30 | = | 30 + 30 | = | 60| = 60

right side = 10(6) = 60

Then x = 6 is a solution

x = - 2

left side = | 5(- 2) + 30 | = | - 10 + 30 | = | 20 | = 20

right side = 10(- 2) = - 20 ≠ 20

Thus x = - 2 is an extraneous solution

Answer:

You add 33 on both sides to solve for the variable.

Step-by-step explanation:

Answer:

range is 515, mode:All values are equal, Median is 243 and the mean is  311.18

mean:to find the mean you need to add up all you numbers so all of these add up to be 3423 and then you divide by the amount of numbers which it 11 so 11 / 3423 = 311.18  so the answer is the mean is 311.18

median: to find it you need to put all the numbers smallest to biggest so it would be in the order 155, 175, 190, 210, 213, 243, 340, 380, 390, 457, 670 and then you pick the one in the middle and that would be 243

mode:All values appeared just once so there is not one

range: to find the range to need to find the differences in the smallest to the biggest number so smallest one is (155) biggers (670) so 155 - 670 = 515 so the range is 515

Hope This Helped