expand and simplify 4(3a+2b)+3(2a-3b) - (a+2b)

Step-by-step explanation:

d(v)=1.1(45)+0.6(45)²

=1.1(45)+0.6(2025)

=49.5+1215

=1264.5

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.

Let a, b, c, d be the four numbers, then

if a : b = c : d then (a + b) : b :: (c + d) : d.

If a : b :: c : d then (a - b) : b :: (c - d) : d.

Given equation,

\($\Rightarrow \frac{a}{b}=\frac{p}{q}$$\)

Adding 1 on both sides of the equation, we get

\($&\Rightarrow \frac{a}{b}+1=\frac{p}{q}+1 \\\)

\($&\Rightarrow \frac{a+b}{b}=\frac{p+q}{q}\)

This rule exists also comprehended as the Componendo property of fractions.

Therefore, \($\frac{a+b}{b}=\frac{p+q}{q}$$\) then a = pb + q but the hypothesis says that

a = (p+b) / q.

If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.

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Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Answer:

20

Step-by-step explanation:

\(\frac{32}{1.6} =\frac{32}{\frac{16}{10}} =32*\frac{10}{16} =\frac{320}{16} =20\)

So the answer is 20

The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

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The tangents of the acute angles in the right triangle gives:

tan(G) = 2

tan(H) = 1/2

It should be noted that tangent is the ratio of opposite over adjacent. Thus:

tan(angle) = opposite/adjacent

So for reference angle G, we say,

tan(G) = JH/GJ = 2/1 = 2

We'll treat tan(H) in a similar fashion, but the opposite and adjacent sides swap roles. That means we'll apply the reciprocal to the result above to get 1/2 for tan(H)

So we have this interesting property where

tan(G)*tan(H) = 2*(1/2) = 1

In general,

tan(A)*tan(B) = 1 if and only if A + B = 90 degrees

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The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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fisrt we are going to find the delivery fee. for this we can use the information in teh table to have two equations with two incognitas:

With the second row we can have, where p is the variable for the pizza and f is the variable of the fee:

This ecuation says that one pizza plus the fee is going to be $20. now with the 3 row we can made the same procedure:

Now we have two incognitas and 2 equations. for solving this I solve the first equation for p:

and I replace p in the second equation:

So the fee is $8.

For the price or the pizza we can use any of the two equation above, and replace the value of the fee. In this case I use the first equation:

Now for the final question: ¿How many pizzas can someone order if they had 120 dollars?

first we can take out the cost of the fee:

And the customer will have 112 dollar for the pizzas, so we can divide the total amound of money by the unitary cost of the pizza:

So he will be able to buy 9 pizzas.

Answer:

Step-by-step explanation:

\(p(x)=2x^2-ax+1\\\\p(1)=3\times 1^2-a\times1+1=4-a\\\\\text{but } p(1)=2 \text{ So,}\\\\4-a=2 \rightarrow a=2\)

Answer:2

Step-by-step explanation:

p(x)--->p(1)

means you should write 1 instead of every x and then make whole equation equal ro 2:

3*1^2-a*1+1=3-a+1=2

-a+4=2

-a=-2

a=2

Your problem → (x^8+2x^4+1)+(2x^4+x^2+1)

(x^8+2x^4+1)+(2x^4+x^2+1)

=x^8 + 2x^4 + 1 + 2x^4 + x^2+1

=x^8+2x^4+2x^4+x^2+1+1

=x^8+4x^4+x^2+2

The side AC is 10 units long.

Measurement of length can be done in a variety of methods, including using handspan, foot span, metres, or other units including millimetres, inches, and metres. There are two types of length measurement units: There are both conventional and nonstandard length measurement units.

The Pythagorean theorem can be used to determine the length of side AC in the triangle ABC given:

AC² = AB² + BC²

AC² = 6² + 8²

AC² = 36 + 64

AC² = 100

AC = 10

As a result, the side AC is 10 units long.

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Answer:

The answer to this question should be D. 0.67

Hope this helped.

The completed table of values for the equation 4x + 2y = 64 is provided .

To complete the table of values for the equation 4x + 2y = 64, we can assign different values to x and solve for y. Let's choose a range of values for x and calculate the corresponding values of y.

Table of Values:

x y

0 32

4 28

8 24

12 20

16 16

20 12

24 8

28 4

32 0

To find the values of y, we substitute each x-value into the equation and solve for y. For example, when x is 0, we have 4(0) + 2y = 64, which simplifies to 2y = 64 and y = 32. Similarly, for x = 4, we have \(4(4) + 2y = 64\), which simplifies to \(16 + 2y = 64\) and\(y = 28.\)

By continuing this process for the remaining values of x, we can complete the table of values for the equation 4\(x + 2y = 64.\)

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Answer:

(-2,0)

Step-by-step explanation:

remember the rule for 90 degree clockwise is (-y,x) opposite y and x

the negative in there DOES NOT mean it will always be negative it means opposite but in this case yes it's negative because the opposite of positive is negative

Hope this helps dude, I'm also learning this in online school lol. ^-^

The image of point (0,2) after a rotation of 90° counterclockwise about the origin is (-2, 0).

The given coordinate point is (0, 2).

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

The rule of 90° counterclockwise rotation: (x, y) becomes (-y, x), here

(-2, 0)

Therefore, the image of point (0,2) after a rotation of 90° counterclockwise about the origin is (-2, 0).

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The standard deviation of the restaurant profits in 2021 is given by $71181.

Restaurant profit for outcome 'move to A' = $ 260000

Restaurant profit for outcome 'move to B' = $ 120000

Restaurant profit for outcome 'stay in C' = $ 100000

The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.

Standard deviation of the restaurant profits in 2021 is given by

= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)

= $ √(((100000)² + (40000)² + (60000)²)/3)

= $ √(15200000000/3)

= $ √5066666667

= $ 71181 (rounded to the nearest dollar)

Hence standard deviation of the restaurant profits in 2021 is given by $71181.

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The question is incomplete. The complete question will be -

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

Step-by-step explanation:

Let :

Equations

Subtract : (2) - (1)

Finding y

Plain Wrapping Paper : $10

Holiday Wrapping Paper : $23

Answer:

Cost per roll of plain wrapping paper = $10

Cost per roll of holiday wrapping paper = $23

Step-by-step explanation:

Let p = cost of a roll of plain wrapping paper

Let h = cost of a roll of holiday wrapping paper

Given:

⇒ 2p + h = 43

Given:

⇒ 7p + h = 93

System of Linear Equations

Equation 1:   2p + h = 43

Equation 2:   7p + h = 93

To solve, subtract Equation 1 from Equation 2 to eliminate h:

⇒ 5p = 50

⇒ 5p ÷ 5 = 50 ÷ 5

⇒ p = 10

Substitute found value of p into Equation 1 and solve for h:

⇒ 2(10) + h = 43

⇒ 20 + h = 43

⇒ 20 + h - 20 = 43 - 20

⇒ h = 23

Cost per roll of plain wrapping paper = $10

Cost per roll of holiday wrapping paper = $23

Answer:

-1.5x + 3

Step-by-step explanation:

The Y-intercept is visible, wherever the line is touching the Y-Axes is the intercept. Use this formula to solve for slope:

200.60 interest does andy’s account earn.

Let x be the amount of interest earned by Andy's account.

According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:

x = 200 + 0.3% of 200

Simplifying the right-hand side of the equation, we get:

x = 200 + 0.003 × 200

x = 200.60

Therefore, the answer is option 1: 200.60.

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Sebastian's basis in the two assets are: $42,389 and $66,611

The computation of the Sebastian's basis in these two assets is shown below:

= Market value of the first piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment

= ($76300 ÷ $(76300 + 119900)) × $109,000

= $42,389

= Market value of the second piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment

= ($119,900 ÷ $(76300 + 119900)) × $109,000

= $66,611

The Total market value of two pieces of equipment

= $(76300 + 119900)

= $196,200

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Answer: 186 cubic in

Step-by-step explanation:

Answer:

at ∠A     sin Ф = 180 + (2 / \(\sqrt{22}\) )

at ∠B     cos Ф = 180 + (3\(\sqrt{2}\)  / \(\sqrt{22}\) )

at ∠C     tan Ф = 180 + (2 / 3\(\sqrt{2}\)  )

Step-by-step explanation:

let (a) = 3\(\sqrt{2}\)

let (b) = 2

let (c) = r

to get the value of hypotenuse (r) use pythagorean theorem

a² + b² = c²

2² + (3\(\sqrt{2}\) )² = c²

c = \(\sqrt{22}\)

use the law of sines to get the value of angle A (point origin)

sin Ф = opp / hyp

cos Ф = adj / hyp

tan Ф = opp / adj

at ∠A

sin Ф = 180 + (2 / \(\sqrt{22}\) )

at ∠B

cos Ф = 180 + (3\(\sqrt{2}\)  / \(\sqrt{22}\) )

at ∠C

tan Ф = 180 + (2 / 3\(\sqrt{2}\)  )

The length of portion BC of the cloth is approximately 5.8709 inches.

To find the length of portion BC of the cloth, we need to use trigonometric functions.

In this case, we can use the cosine function.

Given that the adjacent side to angle B is labeled BC and the hypotenuse is labeled 7 in, we can apply the cosine function, which is defined as the adjacent side divided by the hypotenuse:

cos(angle) = adjacent / hypotenuse

In this scenario, the angle we are considering is 33 degrees.

Therefore, we have:

cos(33°) = BC / 7 in

To isolate BC, we can rearrange the equation:

BC = 7 in \(\times\) cos(33°)

Calculating this expression, we find:

BC ≈ 7 in \(\times\) 0.8387 (rounded to four decimal places)

BC ≈ 5.8709 in.

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Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

d)

\( {i}^{740} \)

Step-by-step explanation:

i¹= i

i²= -1

i³= -i

i⁴= 1

i¹²⁴= i^(124 +0)

i^124 . i^0

i^(4×31) . i^0 = 1³¹. i^0

1.i^0= i^0

= 1

a) i^179= i^(176+3)

i^176 . i³ = i^(4×44) . i³

1⁴⁴. i³ = 1. i³

= -i

b) i^582 = i^(580 + 2)

i^580 . i²= i^(4×145) . i²

1^145 . i²= 1.i²

= -1

c) i^165= i^(164+1)

i^164 . i¹ = i^(4×41) . i¹

1⁴¹ . i¹ = 1.i

= i

d) i^740= i^(740+0)

i^740 . i^0 = i^(4×185) . i^0

1^185 . i^0 = 1. i^0

= 1

i¹²⁴= i^740 = 1