Determine whether each pair of expressions is equivalent. Show your work.
2(x-y) and 2x - 2y

Answer:

√29

Step-by-step explanation:

You would use the distance formula in this case to solve the problem:

(8-3)^2+(1-3)^2=29

Now square root 29, leaving you with √29.

Answer:

5.39

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(3 - 8)² + (1 - 3)²

√(-5)² + (-2)²

√25 + 4

√29

= 5.39

Answer:

x = -1/3 or x = -4

Step-by-step explanation:

Answer:

x= \(\frac{-1}{3}\)

x= -4

Step-by-step explanation:

\(6x^2+28x-2=2x-10\)

Subtract 2x - 10 from both sides.

\(6x^2+26x+8=0\)

\(x= \frac{ -(26) +/ \sqrt{(26)^2-4(6)(8)} }{2(6)}\)

x= \(\frac{-26 +/\sqrt{676-4(6)(8)} }{2(6)}\)

x= \(\frac{-26 +/ \sqrt{676-192} }{2(6)}\)

x= \(\frac{-26+/\sqrt{484} }{2(6)}\)

x= \(\frac{-26+/22}{12}\)

x= \(\frac{-26+22}{12}\)  = -0.33333333333333 = -1/3

x= \(\frac{-26-22}{12}\)= -4

The area of a parallelogram, whose vertices are (−4,−2),(−2,6),(10,6) and (8,−2) is (c) 72.

To find the area of the parallelogram, we can use the formula A = base × height, where the base is the distance between two parallel sides and the height is the perpendicular distance between the base and the other parallel side.

We can take the vectors formed by the coordinates of the parallelogram's adjacent sides, then take the cross product of those vectors to find the area.

Using the coordinates given, the vectors formed are (-2+4, 6+2) = (2,8) and (8-10, -2-6) = (-2,-8). Taking the cross product of these vectors, we get |(2,-8,0) x (-2,8,0)| = 72.

Therefore, the area of the parallelogram is 72 square units.

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Answer:

\(y = -\frac{1}{5}x + 7\)

Step-by-step explanation:

Find the perpendicular slope:

\(-\frac{1}{5}\)

-- The y-intercept is given to you: 7

Slope-intercept form:

\(y = -\frac{1}{5}x + 7\)

Answer:

1. acd=35 and d=105

2. 4

3. 3

Step-by-step explanation:

sorry if im wrong

Answer:

1. 105˚

2. 18

3. 7.79

Step-by-step explanation:

1. Alternate interior angles are the same (Within this shape)

∠ACD = 40˚

Sum of angles in any triangle = 180˚

∠D = 180˚ - 40˚ - 35˚ = 105˚

2. Perimeter of ABCD

Find ∠B (Equilateral triangle of BC=CP=BP=4) ≅60˚

4+1 = CD = BA

CD+BA = 10

4 = BC=AD

BA+AD+DC+CB = 5+5+4+4 = 18

3. Find BN

AB = DC = 6

AD = BC = 9

∠ cos 30 = BN / 9

∠ cos 30 * 9 = BN

BN ≈ 7.79

Answer:

6n-2 = 22

Step-by-step explanation:

n = 4

6(4)-2

24-2

22

Answer:

24 sq ft

Step-by-step explanation:

Its simple! multiply length x width

length x width = area in sq ft

8 x 3 = 24 sq ft

The square feet of blanket 3 feet wide and 8 feet long is 24 sq ft.

When we multiply the length, width, and height of a cuboid, we obtain its volume.

Volume of Cuboid = Length x Width x Height

In other words, the capacity or volume of a cuboid or any rectangular box can be estimated if we multiply these three dimensions together.

Volume of rectangle = length x width

Area in square feet = length \(*\) width

= 8 \(*\) 3

= 24 sq ft

Therefore, 24 square feet are there in a blanket 3 feet wide and 8 feet long.

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Answer:

1.

A- about 43.98

B- about 17.59

C- 32.99

Step-by-step explanation:

Answer:

1) 43.98

2) 17.59

3) 32.99

Step-by-step explanation:

hopefully they’re all right

Given the function f(x)=sin(2πx), with x = 0.3, f(x) = 0.951057. The objective is to approximate the value of f(0.2) using the first two terms in the Taylor series and Vx=0.1.

We know that the Taylor series for a function f(x) can be written as:f(x)=f(a)+f′(a)(x−a)+f′′(a)2(x−a)2+…+f(n)(a)n!(x−a)n+…The first two terms of the Taylor series are given by:f(x)=f(a)+f′(a)(x−a)The first derivative of f(x) is given by:f′(x)=2πcos(2πx)On substituting x = a = 0.1, we get:f′(0.1) = 2πcos(2π * 0.1) = 5.03118603447The value of f(x) at a=0.1 is given by:f(0.1) = sin(2π * 0.1) = 0.587785252292With a=0.1, the first two terms of the Taylor series become:f(x)=0.587785252292+5.03118603447(x−0.1) = 0.587785252292+0.503118603447x−0.503118603447×0.1Using x=0.2 and substituting the values of a and f(a) in the equation above, we get:f(0.2)=0.587785252292+0.503118603447*0.2−0.503118603447×0.1=0.712261After approximating the value of f(0.2) using the first two terms in the Taylor series,

we can conclude that the value of f(0.2) = 0.712261 with a = 0.1, with an error of approximately 0.012796.

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Answer: 68 mph

Step-by-step explanation:

Answer : The expression will be

( c - 7 ) / 3

Step-by-step explanation:

Let's say Adam has c pieces of candy

He took ten pieces for himself which means we can write this as c-7

He then divided this amount between his 3 children (c-7)/3

Answer:

mean  is 16

Step-by-step explanation:

to find the mean of the data set u add up all the numbers and then u see how many number there are in total and u divided the solution of the sum and divided it by the total number of numbers.

17+21+14+17+12+15+16 = 112

then u see how many number there are and there are 7

112/7= 16

Answer: 1/50

Step-by-step explanation:

Step 1: We need to multiply the numerator and denominator by 100 since there are 2 digits after the decimal.

0.02 = (0.02 × 100) / 100

= 2 / 100 [ since 0.02 × 100 = 2 ]

Step 2: Reduce the obtained fraction to the lowest term

Since 2 is the common factor of 2 and 100 so we divide both the numerator and denominator by 2.

2/100 = (2 ÷ 2) / (100 ÷ 2) = 1/50

Answer:

the solutions are {1, -3/2}

Step-by-step explanation:

The given equation 2x^2 + x - 1 = 2 simplifies to 2x^2 + x - 3 = 0 if we subtract 2 from both sides.

We are told that -3/2 is a solution and must find the other solution   To do this, use synthetic division; if the remainder is zero, that tells us that -3/2 is actually a solution, and we can obtain the second solution easily, as follows:

-3/2     /     2       1        -3

                         -3        3

           -------------------------

                 2      -2        0

Since the remainder is 0, we have verified that -3/2 is a solution.  The coefficients of the other factor of the original equation are 2 and -2, and so this other factor is 2x - 2, or 2(x - 1).  Setting this result equal to zero yields x = 1.  

Thus the solutions are {1, -3/2}.

Answer:

1

Step-by-step explanation:

Took the Test edge 2021

Thus, The P-value is 0.0386. Reject the null hypothesis that there is no difference in the GPAs.

Based on the given information, the university is comparing the grade point averages of theater majors with the grade point averages of history majors.

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Answer:

Step-by-step explanation:

.

Answer:

thxxxxxxxxxx for the points

Step-by-step explanation:

The correct equation to represent the given scenario for each cupcake sold is option a. y - 3x - 110.

The bake sale requires $110 in supplies, which means there is an initial cost involved before any profit can be made. This is represented as a constant (-110) in the equation. Each cupcake is sold for $3, and this price represents the amount of money earned per cupcake sold (3x). The variable 'x' stands for the number of cupcakes sold, and 'y' represents the total profit made.

In the equation y - 3x - 110, the term '3x' denotes the money earned from selling 'x' number of cupcakes at $3 each, and the term '-110' accounts for the initial supplies cost. Therefore, the equation shows the profit 'y' made from selling cupcakes after subtracting both the money earned from cupcake sales (3x) and the initial supplies cost (110). Hence, the correct answer is Option A.

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If the height of a regular tetrahedron is 20 inches,  the length of each edge of the tetrahedron is  10√2 inches. This can be found by using the Pythagorean theorem.

This can be found by using the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. In this case, the hypotenuse of the right triangle is the height of the tetrahedron or 20 inches. The other two sides of the triangle, the base and the height of the triangle, will be equal since the triangle is equilateral, so each side is 10 inches.

The Pythagorean theorem can then be applied as follows: 10^2 + 10^2 = 20^2, or 100 + 100 = 400. This simplifies to 200 = 400, so the length of each side of the triangle is 10√2 inches.   For a more visual explanation of this, imagine the height of the tetrahedron is a diagonal line going down the center of the triangle, dividing it into two equal right triangles. Since the triangle is equilateral, the base of each triangle will be 10 inches, and the height of the triangle will also be 10 inches.

This creates the right triangle that the Pythagorean theorem can be applied. The Pythagorean theorem will then tell us that the hypotenuse of the triangle is 10√2 inches. Since the hypotenuse of the right triangle equals the height of the tetrahedron, the length of each edge of the tetrahedron is 10√2 inches.

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Answer:

48

Step-by-step explanation:

3 ⋅ 2^t

3 * 2^4

3*16

48

Answer: -3/2

Step-by-step explanation:

There are two methods to find the slope

METHOD 1. Rise/Run

Rise: the y-axis value

Run: the x-axis value

In the graph, rise/run=3/2

The line is going down, so it should be negative

-3/2

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

131

Step-by-step explanation:

Hope it helps ;)

Answer:

36 and 108

Step-by-step explanation:

the red lines indicate the sides are equal making it an isosceles triangle the angles opposide the sides are equal so x^2=5x+6 with guess and check I got x=6 and 6x6 is 36 and 5(6)+6 is 36 now to find the last angle, angle f just do 180- (36+36) you get 108

Answer:

$21

Step-by-step explanation:

We have here a case of a linear situation. We have that:

1. We have a fixed cost of $4.99.

2. And we need to add $0.30 for every ounce the package weighs.

The equation that represents the total cost of the shipping is:

We can see that per every ounce, we need to multiply it by $0.30 to obtain the total cost (plus the fixed cost of $4.99).

We expressed the equation in the slope-intercept form (y = mx +b).

Step-by-step explanation:

hey the answer is 12 I'll take a picture of it

Answer:

90+100+110+3x+2x=360

300+5x=360

5x=360-300

5x=60

x=12

The polyhedron with 26 faces, consisting of 20 triangles and 6 quadrilaterals, has 42 edges and 30 vertices.

To find the number of edges, we can use Euler's formula for polyhedra: F + V - E = 2, where F represents the number of faces, V represents the number of vertices, and E represents the number of edges. In this case, F = 26

Given that 20 faces are triangles, each triangle has 3 edges, so the triangles contribute 20 * 3 = 60 edges. Similarly, since 6 faces are quadrilaterals, each quadrilateral has 4 edges, resulting in 6 * 4 = 24 edges. Therefore, the total number of edges is 60 + 24 = 84.

Now, substituting the values into Euler's formula, we have: 26 + V - 84 = 2. Solving for V, we find that V = 60.

Thus, the polyhedron has 42 edges and 30 vertices.

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Answer:B

Step-by-step explanation: To solve this, we first need to find the ratio of concenrate to water for each mixture. A is 2:3.5, B is 5:8, and C is 0.5:2. Now, we can roughly estimate them. C is .25, B is around .6, and A is around .57. This means that B is the most lemony.

Answer:

80%

Step-by-step explanation:

96.3 - 53.5 = 42.8

42.8 / 53.5 = 0.8

0.8 × 100 = 80%