Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
2 similar triangles. Triangle 1 has side lengths 14, 21, blank. Triangle 2 has side lengths 18, 27, blank.
a.
StartFraction 14 Over 27 EndFraction = StartFraction 21 Over 28 EndFraction = StartFraction 14 Over 27 EndFraction
b.
StartFraction 14 Over 18 EndFraction = StartFraction 21 Over 27 EndFraction = StartFraction 7 Over 9 EndFraction
c.
StartFraction 14 Over 21 EndFraction = StartFraction 18 Over 27 EndFraction = StartFraction 2 Over 3 EndFraction
d.
StartFraction 27 Over 14 EndFraction = StartFraction 28 Over 21 EndFraction = StartFraction 27 Over 14 EndFraction

The correct value that equates to this expression is q¹⁰

.

To solve this expression, just:

[tex]{ = \large \sf (q {}^{5} ) {}^{2} } [/tex]

[tex]{ = \large \sf q {}^{5 \times 2} } [/tex]

[tex] \pink{ \boxed{ = \large \sf q {}^{10} } } \\ [/tex]

Therefore, the answer will be q¹⁰

Answer:

Q¹⁰

Step-by-step explanation:

Given that,

Solution:

Well,there is a law of exponents,which states that:

Same case is here as well.

Just multiply both powers given.

5*2 = 10

Hence, the expression equivalent to (Q⁵)² is (Q)¹⁰

The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6

Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.

Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.

Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.

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By following the pattern the next image in the pattern is (b) since the correct option is (b).

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers is arranged in a particular way, the arrangement is referred to as a pattern.

From the pattern given: In pattern one, the first column contains 2 blocks and the second column contains 1 block. In pattern second, the first column contains 3 blocks, the second column contains 2 blocks and the third column contains 1 block. In pattern third, the first column contains 4 blocks, the second column contains 3 blocks, the third column contains 2 blocks and the fourth column contains 1 block.

∴ You can observe that block the ks are arranged in descending numbers.

Hence, option (b) is correct.

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The measure of angle XYZ in the parallelogram is: 71°.

In a parallelogram, the angles that are opposite each other are congruent.

Find m∠XWZ using the triangle sum theorem:

m∠XWZ = 180 - m∠WXZ - m∠WZX

m∠XWZ = 180 - 81 - 28

m∠XWZ = 71°

m∠XWZ = m∠XYZ [opposite angles are congruent]

m∠XYZ = 71°

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Answer:

71°

Step-by-step explanation:

I got it right on Edmentum

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Step-by-step explanation:

[tex] = {i}^{31} [/tex]

[tex] = {i}^{28} \times {i}^{3} [/tex]

[tex] = {( {i}^{4} )}^{7} \times ( {i}^{2} \times i)[/tex]

[tex] = ( {i}^{2} \times {i}^{2} ) {}^{7} \times {i}^{2} \times i[/tex]

[tex] = ( - 1 \times ( - 1)) {}^{7} \times ( - 1) \times i[/tex]

[tex] = {1}^{7} \times ( - i)[/tex]

[tex] = 1 \times ( - i)[/tex]

[tex] = - i[/tex]

The answer is D.

Answer:

y=2x-8

or

f(x)=2x-8

Step-by-step explanation:

To write in slope-intercept form using this information, first use the point slope formula.

y-y1=m(x-x1)

m is slope.

y+4=2(x-2)

Use distributive property on the right side.

y+4=2x-4

Now, subtract 4 from both sides.

y+4-4=2x-4-4

y=2x-8

Written using function notation:

f(x)=2x-8

Hope this helps!

If not, I am sorry.

33333333333333333333333333333333333

The molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

From the question, we are to determine the molarity of the resulting solution

From the given information,

Number of moles = 5.99 × 10⁻⁶ mol

Volume = 1.50 × 10⁻² L

Using the formula,

Molarity = Number moles / Volume

∴ Molarity = (5.99 × 10⁻⁶) / (1.50 × 10⁻²)
Molarity = 3.99 × 10⁻⁴ M

Hence, the molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

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Answer:

The answer is 3.99 × 10–4 M

Step-by-step explanation:

I just did the assignment on Edge :)

Step-by-step explanation:

The translations of the typical functions are

[tex]y = a(bx + c) + d[/tex]

Where a is the vertical translation,

If a is greater than 1 or less than -1, we have a vertical stretch

If a is between -1 and 1 , we have a vertical compressions or shrink.

If a is negative, we have a negative reflection across the x axis.

If b is greater than 1 or less than -1, we have a horizontal compression or shrink

If b is between -1 and 1, we have a horizontal stretch

If b is negative, we have a reflection about the y axis,

If c is negative, we have a translation to the right c units

If c is positive, we have a translation to the left c units

If d is positive, we have a translation upward d units

If d is negative, we have a translation downward d units.

Here in this problem, our parent function is x^3.

So I would do the following transformations.

The degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.

The degree of the polynomial is defined as the highest power of the variable of the given polynomial or it is the maximum power of the polynomial.

The degree of the given expressions are shown as follows:-

(x-9)                 →  degree 1,

(-4x²-6x+9)      → degree 2,

(x²-2x+9)         → degree 2,

(-3)                   → degree 0,

(3x-2)               → degree 1,

(6x+2)              → degree 1

(5)                    → degree 0.

Therefore the degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.

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Answer:

I think it's 1.17 - -3.85

Answer:

x = 27, y = 6

Step-by-step explanation:

x - 2y = 15

x - 4y = 3 (rearranged the orginal equation)

  x - 2y = 15

-  x - 4y = 3

___________

2y = 12

y = 6

Plug this value in any original equation

x - 2(6) = 15

x = 27

x and y of the simultaneous equation are 27 and 6 respectively.

Given,

x - 2y = 15

x - 3 = 4y

Here,

Equations:

x - 2y = 15

Rearranged the original equation

x - 4y = 3

Now subtract both equations,

x - 2y = 15

x - 4y = 3

⇒2y = 12

y = 6

Plug this value in any original equation

x - 2(6) = 15

x = 27

Thus the solution of system of equation is x = 27 and y = 6.

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The table that correctly identifies the sample of spinning the spinner and then selecting a card is Option A.

A sample is a random element that belongs to a population. Another way to state it is that, it is a set of all the outcomes that are possible from a given set of events.

Table A accurately depicts each potential result. Along the column on the left is where you'll see the card outcomes.

The spinner's output is shown along the top row. The intersection of the left and top results appears in each cell.

For instance, row 1, and column 3 include "red, purple" to show that you received a card with the color "purple" and the color "red" on the spinner.

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Answer: Since they have the some points in common we can just plot them and seeing ang. DBC would just be a straight line and angle ABC would be 90 degrees and half of that angle so they would be equal

[tex]7a³ (8a² + a)²-4a³ \\ \\ 7 {a}^{3}(8 { {a}^{2} + a)(8 {a}^{2} + a )} - 4 {a}^{3} \\ \\ 7 {a}^{3} ( {8a}^{2} (8 {a}^{2} + a ) + a(8 {a}^{2} + a ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 8{a}^{3} + 8 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 16 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 448 {a}^{7} + 112 {a}^{6} + 7 {a}^{5} - 4 {a}^{3} \\ \\ {a}^{3} (448 {a}^{4} + 112 {a}^{3} + 7 {a}^{2} - 4).[/tex]

The inequality is 100*[tex]3^{t}[/tex]≤ 656100.

The correct option is (B).

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

From the table attached below:

a=300, r= 900/300 = 3

As, it is GP

Now,

f(t) = [tex]ar^{t-1}[/tex]

f(t) = [tex]300*3^{t-1}[/tex]

f(t) = 300/3 *[tex]3^{t}[/tex]

f(t) = 100*[tex]3^{t}[/tex]

Inequality is used to determine greater than or equal to 656100

100*[tex]3^{t}[/tex]≤ 656100

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The missing side and angles are 16.8 , 23.33 degree and 123.7 degree respectively.

Triangle is a polygon with three sides , three angles and three vertices.

Given is triangle ABC , with sides  a = 8, c = 11, and m∠C=33 degree

The missing angle and side is given by Cosine rule of triangle

c² = a² + b² - 2ab cosC

11² = 8² + b²  - 2* 8 * b * cos 33

57 = b² -13.42 b

b²  -13.42b -57 = 0

b = 16.8

By sine rule

a / sin A = b/sin B = c/sinC

8 / sin A = 11 / sin 33

A = 23.33 degree

Similarly

B = 123.7 degree

Therefore the missing side and angles are 16.8 , 23.33 degree and 123.7 degree respectively.

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Answer:

1. 3/14

2. 2/7

3. 1/7

4. 5/14

5. 11/14

6. 9/14

Step-by-step explanation:

first get the total number of pens

3 red pens + 4 blue pens + 2 black pens + 5 green pens =

14 total number of pens

1. What is the probability that the pen chosen red?

3 red pens out of a total of 14 pens = 3/14

2. What is the probability that the pen chosen is blue?

4 blue pens out of a total of 14 pens = 4/14 -> simplified -> 2/7

3. What is the probability that the pen chosen is black?

2 black pens out of a total of 14 pens = 2/14 -> simplified -> 1/7

4. What is the probability that the pen chosen is green?

5 green pens out of a total of 14 pens = 5/14

5. What is the probability that the pen chosen is NOT red?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

4 blue pens, 2 black pens and 5 green pens are NOT red

4 blue pens + 2 black pens + 5 green pens =

11 total number of pens that are NOT red

11 total number of pens that are NOT red out of a total of 14 pens = 11/14

6. What is the probability that the pen chosen is NOT green?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

the 3 red pens, 4 blue pens, 2 black pens are NOT green

3 red pens + 4 blue pens + 2 black pens =

9 total number of pens that are NOT green

9 total number of pens that are NOT green out of a total of 14 pens = 9/14

gathmath.com

Given :-

>> Total no. of outcomes = 3 + 4 + 2 + 5

>> Total no. of outcomes = 3 + 4 + 7

>> Total no. of outcomes = 10 + 4

>> Total no. of outcomes = 14

Solution 1 :-

We know,

As there are three red pens. Therefore,

Solution 2 :-

We know,

As there are four blue pens. Therefore,

Solution 3 :-

We know,

As there are two black pens. Therefore,

Solution 4 :-

We know,

As there are five green pens. Therefore,

Solution 5 :-

We know,

As there 11 pens that are not red (Green + black + blue).

Solution 6 :-

We know,

As there are 9 pens that are not green (Red + blue + black).

If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.

Given 95% confidence level, standard deviation=0.05.

We know that margin of error is the range of values below and above the sample statistic in a confidence interval.

We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data  near the mean are more frequent in occurence than data far from mean.

We know that margin of error for a confidence interval is given by:

Me=[tex]z/2* ST/\sqrt{N}[/tex]

α=1-0.95=0.05

α/2=0.025

z with α/2=1.96 (using normal distribution table)

Solving for n using formula of margin of error.

[tex]n=(z/2ST/Me)^{2}[/tex]

n=[tex](1.96*0.05)^{2} /(0.01)^{2}[/tex]

=96.4

By rounding off we will get 97.

Hence the sample size required will be 97.

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The given question is incomplete and the full question is as under:

If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?

Answer:

Eric´s mom had:

31 years 11 months

Step-by-step explanation:

1 year = 12 months

40 years = 39 years + 12 months

40 years 3 months = 39 years + 12 monts + 3 monts = 39 years 15 months

Then:

 40 years 3 months

-   8 years 4 months

it´s equivalent to:

 39 years 15 months

-   8 years  4 months

= 31 years  11 monts

Usando proporciones, en conjunto con multiplicación cruzada, encontra-se que el valor de p es de 6.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

En este problema, relación es dada por:

[tex]\frac{p}{p+2} = \frac{6}{8}[/tex]

Aplicando multiplicación cruzada:

8p = 6(p + 2)

8p = 6p + 12

2p = 12

p = 12/2

p = 6.

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The sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

We have a sandbox:

The length of the sandbox = 4 feet

The width of the sandbox = 6 feet

The height of the sandbox = 2 feet

Amount of sand can hold = volume of the sandbox

= 4×6×2

= 48 cubic feet

Thus, the sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.

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The form of controls that are effective in eliminating, reducing, or minimizing hazards is called; Engineering controls

Engineering controls are defined as strategies that are designed to protect workers from hazardous conditions by placing a barrier between the worker and the hazard or by removing a hazardous substance through air ventilation.

Now, the reason why this is effective in eliminating, reducing, or minimizing hazards is because they are designed to remove the hazard at the source, before it comes in contact with the worker.

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Answer:

2

Step-by-step explanation:

When a function and its inverse are composed, the output is equal the input.

The value of the WZ will be 28.18. The given figure is quadrilateral.

It is concerned with the geometry, region, and density of various 2D and 3D shapes.

In ΔZXY

∠Z+∠X+∠Y=180

∠Z+34°+90°=180°

∠Z = 56°

In Δ WZY

sin Θ = WZ/ZY

sin 56° = WZ/34

WZ= 28.18

Hence, the value of the WZ will be 28.18.

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The side WZ = 30.4.

The angles which lie on the alternate side of the line between two parallel lines.

Given a geometry in which ZY = 34, WY = 38, and ∠ZXY = 34°

In this geometry, opposite sides are equal.

WZ = XY and WX = ZY.....................(1)

The diagonal are perpendicular to each other.

∠XVY = 90°

Diagonal form four right angle triangles. Take ΔXVY

VY = WY/2

VY = 38/2

VY = 17

Using trigonometric property,

sin X° =  VY / XY

sin 34° = 17/XY

XY = 30.4

From equation 1, we have

WZ = 30.4

Thus, the value of WZ is 30.4.

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Answer:

A) 37, 34, 22, 28, 19, 25

E) 55, 43, 49, 61, 58, 54

Step-by-step explanation:

The range of a set of data is the largest number minus the smallest number

A) 37, 34, 22, 28, 19, 25

37 - 19 =18

Range is 18

B) 34, 22, 18, 19, 31, 33

34 - 18 =16

Range is 16

C) 95, 79, 83, 88, 81, 99

95 - 81 =14

Range is 14

D) 17, 26, 17, 18, 26, 31

31-17 =14

Range is 14

E) 55, 43, 49, 61, 58, 54

61 - 43 =18

Range is 18

Answer:

-69

Step-by-step explanation:

inches:-69

-5 9/12 (-5 3/4 clearer) feet

Explanation in detail:

Write the equation down and distribute it.

3x - 1 = 2(x + 34)

3x - 1 = 2x + 68

Remove the variable on one side first (it makes solving the equation less complicated.)

3x - 1 = 2x + 68

-3x -3x

-1 = -x + 68

On all sides, subtract 68.

-1 = -x + 68

-68 -68

-69 = x

I'm guessing the answer in feet and inches is...

inches:-69

-5 9/12 (-5 3/4 simplified) feet

Answer:

A five units right and three units up

Step-by-step explanation:

take coordinate C for example and count how many spaces you need to go either right or left and then up and down for the two triangles to be in the same place