When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x ?

Answer:

24 cm³

Step-by-step explanation:

V = LWH = 2 × 3 × 4 cm³ = 24 cm³

Answer: (8,10)

Step-by-step explanation:

To go from A to C, we go right 2 units and up 6 units.

So, if we let the fourth vertex be D, then to go from B to D, we must also go right 2 units and up 6 units from B.

Therefore, the answer is (8, 10).

The ship captain should be turned 129.49 so it's heading straight for Island B.

Given Island A is 160 miles from Island B and the captain of a ship travels 170 miles from Island A and then discovers that he is off course and 200 miles from island B.

So we gave it

a = 200 feet

b = 170 feet

c = 160 feet

We need to find angle C which goes directly to island B.

We apply the "cosine law":

[tex]\begin{aligned}\cos C&=\frac{a^2+b^2-c^2}{2ab}\\ &=\frac{(200)^2+(170)^2-(160)^2}{2\times 200\times 170}\\ &=\frac{40000+28900-25600}{68000}\\ &=\frac{43300}{68000}\\ &=0.636\end[/tex]

Now we multiply both sides by cos⁻¹, we get

cos⁻¹(cos C)= cos⁻¹(0.636)

C = 50.51

The interior angle is 50.51°

We need to find the outer angle to find the bearing the captain needs to turn

Applying the additional angle ruler:

The outside angle = 180 - 50.51 = 129.49°

Therefore, he must turn so as to head directly for Island B, where Island A is 160 miles from Island B and the captain is sailing 170 miles.

from Island A and then discovers that it is off-road and 200 miles away

Island B is 129.49.

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The triangle is illustrated below.

The first thing you should find are the new vertices:

(x, y) ---> (2x, 2y) ---> (x', y')

(0, 0) ---> (2 (0), 2 (0)) ---> (0, 0)

(-4, 4) ---> (2 (-4), 2 (4)) ---> (-8, 8)

(-4, -2) ---> (2 (-4), 2 (-2)) ---> (-8, -4)

Then, you must join the ordered pairs and graph the new triangle.

See the attached graph.

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Answer:

sin(x - y) = 0.21

Step-by-step explanation:

we have the sin values which we need to get cos values

sin (A-B) = sin A cos B - sin B cos A

sin² A + cos² A = 1

sin x = 4/9

cos² x = 1 - sin² x = 1 - 16/81 = 65/81

cos² x = 65/81

cos x = √65/9

sin y = 1/4

cos² y = 1 - sin² y = 1 - 1/16 = 15/16

cos² y = 15/16

cos y = √15/4

sin(x − y) = sin x cos y - sin y cos x

sin(x - y) = 4/9 √15/4 - 1/4 √65/9

sin(x - y) = (4√15-√65)/36

sin(x - y) = 0.21

socratic Narad T

Answer: C

Step-by-step explanation:

on edg

Step-by-step explanation:

The simplification of the polynomial expression will give 3x² - 20x + 8.

The polynomial expression is given as:

(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)

= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7

Then collect like terms

= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19

= 3x² - 20x + 8.

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Answer:

[tex]\frac{\sqrt{3} }{6}[/tex]

Step-by-step explanation:

using the 30- 60- 90 triangle for exact values , then

tan60° = [tex]\sqrt{3}[/tex] , and

cot60° = [tex]\frac{1}{tan60}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]

cos60° = [tex]\frac{1}{2}[/tex]

cot60° cos60°

= [tex]\frac{1}{\sqrt{3} }[/tex] × [tex]\frac{1}{2}[/tex]

= [tex]\frac{1}{2\sqrt{3} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= [tex]\frac{1}{2\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= [tex]\frac{\sqrt{3} }{6}[/tex]

The answer is [tex]\boxed {\frac{1}{2\sqrt{3}}}[/tex]

The needed trigonometric values :

Hence, the value of the expression is :

There are 9 positive integers with 1 digit (1 - 9).

There are 90 integers with 2 digits (10 - 99).

There are 900 integers with 3 digits (100 - 999).

There are 9000 integers with 4 digits (1000 - 9999).

And so on. It stands to reason that there are [tex]9\times10^{n-1}[/tex] integers with [tex]n[/tex] digits.

Now,

1000 = 9 + 900 + 91

so the 1000th positive integer with an odd number of digits is the 91th number with 3 digits, which is 190.

Answer:

1. 4x²-6x-4

2. 8x³+4x²-8x-4

3. x⁵-x⁴+3x³+x²+12

Step-by-step explanation:

1. (4x+2)(x-2)

apply foil method (a+b)(c+d)=ac+ad+bc+bd

(4x+2)(x-2)=4x.x + 4x(-2) + 2x + 2(-2)

2. (4x²-4) (2x+1)

apply the same method as question no.1

(4x²-4) (2x+1)=4x².2x + 4x².1 + -4.2x-4.1

3. (x²+3) (x³-x²+4)

Distributive parentheses

(x²+3) (x³-x²+4)= x².x³ + x²(-x²) + x².4+ 3x³+3(-x²) +3.4

Answer:1.166 reams of paper.

Step-by-step explanation:

Just use simple division and divide 7/6.

Each classroom will get  [tex]\dfrac{7}{6}[/tex]  paper when there are 6 fifth grade classrooms that share 7 packs of paper.

A fraction is defined as a part of a whole. The upper part of the fraction is called the numerator, and the lower part is called the denominator.

Given that:

Number of fifth grade classrooms = 6

Number of packs of paper = 7

The number of paper each classroom get in fractions can be obtained by dividing the number of packs of paper by the number of fifth grade classrooms.

Each classroom get = [tex]\dfrac{Number \ of \ packs \ of \ paper}{ \ Number \ of \ fifth \ grade \ classrooms}[/tex]

Each classroom get = [tex]\dfrac{7}{6}[/tex]

Each classroom will get  [tex]\dfrac{7}{6}[/tex]  paper.

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Answer:

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle

Answer:

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Hi

How are you?

Kya kar rahi hoo?

The transformations that are applied to pentagon ABCDE to create A"B"C"D"E" are:

1) Translation (x, y) → (x + 8, y + 2)

2) Reflection across the x-axis (x, y) → (x, -y)

So, the overall transformation given in the graph is (x, y) → {(x + 8), -(y + 2)}.

The transformation rules are:

The pentagons in the graph have vertices as

For the pentagon ABCDE: A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), and (-2, 4)

For the pentagon A"B"C"D"E": A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), and E"(6, -6)

Consider the vertices A(-4, 5) from the pentagon ABCDE and A"(4, -7) from the pentagon A"B"C"D"E".

Applying the Translation rule for the pentagon ABCDE:

The rule is (x, y) → (x + a, y + b)

So, the variation is

-4 + a = 4

⇒ a = 4 + 4 = 8

5 + b = 7

⇒ b = 7 - 5 = 2

So, the pentagon ABCDE is translated by (x + 8, y + 2).

Applying the Reflection rule for the translated pentagon:

The translated pentagon has vertices (x + 8, y + 2).

When applying the reflection across the x-axis,

(x + 8, y + 2) → {(x + 8), -(y + 2)}

Therefore, the complete transformation of the pentagon ABCDE to the pentagon A"B"C"D"E" is (x, y) → {(x + 8), -(y + 2)}

Verification:

A(-4, 5) → ((-4 + 8), -(5 + 2)) = (4, -7)A"

B(-6, 4) → ((-6 + 8), -(4 + 2)) = (2, -6)B"

C(-5, 1) → ((-5 + 8), -(1 + 2)) = (3, -3)C"

D(-2, 2) → ((-2 + 8), -(2 + 2)) = (6, -4)D"

E(-2, 4) → ((-2 + 8), -(4 + 2)) = (6, -6)E"

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Answer:

2 face cards

Step-by-step explanation:

By definition, there are 12 face cards (Kings, queens, and jacks) and 36 numbered cards (2's through 10's) in a standard deck of 52 cards.  Aces are not considered face cards (no face on the card).

The ratio of face cards in a full deck is (12/52) or slightly over 23%.

The likelihood of a face card in a hand of 8 cards is:

(8 cards)*(12 face cards/52 cards) = 1.85 cards.  We need to round to the nearest whole card, so the expected number of face cards in a hand of 8 is 2 cards.  

Answer: 433.33 cm^3

Step-by-step explanation: Since the base is a square, volume = base area × height / 3

10*10 = 100,  100 * 13 = 1300, divided by 3 = 433.33 cm^3

The  appropriate display to show the spread of 150 test scores for Mrs. Hansen's last science test is: b.  box and whisker plot.

Box and whisker plot which is also called box plot can be defined as the plot that show a graphical presentation of data set by helping to display the data set or data score .

Hence a graphical presentation display to show the spread of 150 test scores for Mrs. Hansen's last science test is option B which is Box and whisker plot .

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The arc length of [tex]y=2\cos(3x)[/tex] on the interval [tex][a,b][/tex] is

[tex]\displaystyle \int_a^b \sqrt{1 + (y')^2} \, dx = \int_a^b \sqrt{1 + (-6\sin(3x))^2} \,dx = \boxed{\int_a^b \sqrt{1+36\sin^2(3x)} \, dx}[/tex]

p→r

The law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost  similar to the transitive property.

now if we want to define general case then we can say tha

a→b

and

b→c  => a→c

now according to statements given in the problem

p→q and q→r ⇒ p→r

which completes the syllogism.

hence ,  p→r is the required answer.

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Evaluating the given expressions and inequalities, we have;

[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]

12) (8•a - 5•b) - 2•(a + b) = 4

[tex] 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]

[tex] 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]

[tex] 16) \: x \geq 11\frac{2}{3} [/tex]

17) k > 9

18) v > 9

20) m ≤ 16

The given expressions are;

[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right)[/tex]

Where x = 4, and y = 6, we have;

[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4[/tex]

Therefore;

[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]

12) (8•a - 5•b) - 2•(a + b)

Where a = 3 and b = 2, we have;

(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4

Therefore;

[tex]13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} [/tex]

Where a = 7, and p = 6, we have;

[tex] \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 [/tex]

Therefore;

[tex] \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]

[tex]14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } [/tex]

Where m = 5, and n = 6, we have;

[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 [/tex]

Therefore;

[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]

[tex]16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} [/tex]

Which gives;

[tex] \frac{7}{6} \times 10 \leq x [/tex]

[tex] \mathbf{ \frac{35}{3} }\leq x [/tex]

[tex] x \geq 11\frac{2}{3} [/tex]

17) 20 < k + 11

Therefore;

k > 20 - 11 = 9

18) 6•v > 54

v > 54 ÷ 6 = 9

Therefore;

[tex]20) \: 8 \geq \mathbf{ \frac{m}{2}} [/tex]

Therefore;

2 × 8 = 16 ≥ m

Which gives;

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The expression that is not equivalent to (1 - sin²(x)) tan(-x) is D. (cos²x - 1)(cot -x).

It should be noted that (cos²x - 1)(cot -x). is not equivalent to the given expression.

This is illustrated as:

(cos²x - 1)(cot -x)

= (-sin²x) × (-cot x)

= sin²x × cosx/sin x = sinxcosx

In conclusion, the correct option is D.

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The expression _______ is not equivalent to (1 − sin2(x)) tan(-x).

a. (1 - cos^2(x)) cot(-x)

b. (cos^2(x) - 1) cot(x)

c. (sin^(x) - 1) tan(x)

d. (cos^2(x) - 1) cot(-x)

The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

According to the statement

we have to give the terms which explain the sin (pi/3) perfectly.

And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.

And Now we explain all terms below

So,

"Right Triangle is a triangle whose one of the angle measures 90° "

And "The hypotenuse is a longest side of the right triangle.

And"Unit Circle is a circle with radius 1."

For given question,

We have been  given a unit circle.

So, We need to find the sin (pi/3)

We know, in a right triangle for any angle , θ

Sinθ = Opposite side of angle / Hypotenuse

So, for , Sin(pi/3) = Opposite side of angle / 1

Sin(pi/3) = Opposite side of angle

Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

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Mark up = $66

Mark up on selling price = 37%

Selling price = 37%

Selling price x Mark up percentage = Mark up

Selling price x 37% = 66

Selling price = $178.38

Cost = Selling price - Mark up

= 178.38-66

= $112.38

Cost as a percentage of selling price = Cost / Selling price

= 112.38/178.38

= 63%

The selling charge is how much a purchaser pays for a product or service. it is able to range relying on how tons consumers are inclined to pay, how a whole lot the seller is inclined to just accept, and the way competitive charge is in comparison to other businesses inside the marketplace.

A sale rate is the discounted rate at which goods or services are being offered. This rate is normally offered for a restrained period of time, usually to spur income all through a slow duration or to sell off excess stock. the discount is advertised as a percentage discount from the ordinary listing charge.

Fee rate: the quantity paid to purchase a piece of writing or the fee at which an editorial is made is known as its cost charge. The value fee is abbreviated as C.P. selling price: The rate at which an editorial is sold is called its selling rate. The promoting price is abbreviated as S.P.

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The equation that is represented by the graph below is y = e^x - 4.

From the graph, it can be seen that the only exponential function n to hat intercept the function at equal to 3 is y = e^x - 4.

Let's equate y to 0.

y = e^x - 4.

e^x - 4 = 0

e^x = 4

In(e^x) = In(4)

x = 1.386

The x intercept is located at (1.386, 0).

In conclusion, the correct option is D.

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Answer: b

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Answer:

there should have been names of every line and joining parts

Answer: 120 hr

Step-by-step explanation: 15$ every hr so for 120 hrs it would be 1,800$ plus the signing bonus of 200$ would total 2,000$ but with out the bonus she would have to work 134 hrs for 2,010$

i. The number of people who like banana only is 20.

ii. The number of people who like none of the fruits is zero.

iii. The number of people who like at most one fruit is 30.

The question has to do with sets.

A set a collection of well ordered items

Since we have 55 people, 3x + 5 people like banana and x + 5 people like apple. If all the people who like apple also like banana and if 2x + 15 people like at least one of fruit then, we have that

3x + 5 + x + 5 + 2x + 15 = 55

3x + 2x + x + 5 + 5 + 15 = 55

6x + 30 = 55

6x = 55 - 25

6x = 30

x = 30/6

x = 5

Since the number of people who like banana only is 3x + 5.

So, number of people who like banana only is n = 3x + 5

= 3(5) + 5

= 15 + 5

= 20

So, the number of people who like banana only is 20.

Since from the question, a person likes at least one fruit, either banana, apple or both. No one likes none of the fruits.

So, the number of people who like none of the fruits is zero.

To like at most one fruit, the person either likes apple or banana.

So, their sum is n = 3x + 5 + x + 5

= 4x + 10.

Since x = 5, we have n = 4x + 10.

= 4(5) + 10

= 20 + 10

= 30

So, the number of people who like at most one fruit is 30.

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Answer:

4

Step-by-step explanation:

If the probability of drawing a yellow jelly beans is 1/4, the box is has 1/4 yellow jellybeans.

1/4b=6

b=24

14+6+x=24

20+x=24

x=4

Answer:

36 blue jelly beans

Step-by-step explanation:

We can find the total number of jelly beans by adding all red, yellow, and blue jelly beans together.

14+6+x

This simplifies to 20+x

For probability, it is (the number of things you want)/(the total number of things there are).

If the probably of drawing a yellow jelly bean is 1/4, we can set up this equation:

[tex]\frac{14}{20+x}=\frac{1}{4}[/tex]

We can cross multiply:

[tex]20+x=14(4)\\x+20+56\\x=36[/tex]

There are 36 blue jelly beans.