7+(-3+5)=7+(5+(-3)) communitive or associative! Pls help

Using the digits 0-9, the puzzle becomes:

To solve this puzzle, use the factoring pattern (a-b)(a+b) = a² - b² for the second equation.

First, the first blank in equation 1 must be either 1 or 3, since the two factors must have a difference of 1. Therefore, the first blank in equation 1 must be 1, and the second blank must be 2.

Next, use the factoring pattern in equation 2 to get:

x² - 1x + 1 = (x - 2)(x - 1)

This means that the missing number in the second set of blanks is 1, since the two factors have a difference of 1.

In equation 3, the second blank must be -3, since the two factors must have a difference of 5. Therefore, the first blank must be -1.

Finally, in equation 4, the missing number in the second set of blanks must be -4, since the two factors must have a difference of 2. Therefore, the missing number in the first set of blanks is 18.

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If x = (5,-5) and y = (8,-3), x•y is: 55.

The dot product (also called scalar product or inner product) of two vectors x = (x1, x2) and y = (y1, y2) is given by:

x•y = x1y1 + x2y2

Using the coordinates of the given vectors:

x = (5, -5)

y = (8, -3)

x•y = (5)(8) + (-5)(-3) = 40 + 15 = 55

Therefore, x•y = 55.

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Answer:

f(1.5) = 4.46

Step-by-step explanation:

f(x) = 5.97/x + 0.48                      f(1.5)

f(1.5) = 5.97/1.5 + 0.48

f(1.5) = 3.98 + 0.48

f(1.5) = 4.46

So, the answer is f(1.5) = 4.46

The volume of the pentagonal prism is 645 cubic millimeters.

We have,

The formula for the volume of a pentagonal prism is:

V = A x h

where A is the area of the pentagonal base and h is the height of the prism.

In this case, we are given the area of the base as 43 square millimeters and the height as 15 millimeters.

Therefore, we can calculate the volume as:

V = 43 x 15

V = 645 cubic millimeters

Therefore,

The volume of the pentagonal prism is 645 cubic millimeters.

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Answer:

We conclude that the value of the constant of proportionality.

Step-by-step explanation:

We know that if 'y' varies directly with 'x', we use the equation

y ∝ x

y = kx

where 'k' is called the constant of proportionality.

Given the equation

y = 14x

comparing with the equation

y = kx

Thus,

k = 14

Therefore, we conclude that the value of the constant of proportionality.

So, the matrix representation of the given system of linear first-order differential equations is: X' = [1 2; 3 0] X + [ -4e^(2t); 0 ].

To write the given system of linear first-order differential equations in matrix form, we can define the vector of variables X as X = [x, y].

The system can then be represented as:

X' = AX + B

where X' is the derivative of X with respect to the independent variable, A is the coefficient matrix, X is the vector of variables, and B is the vector of constant terms.

For the given system:

x' = x + 2y - 4e^(2t)

y' = 3x

The matrix form of the system becomes:

X' = [1 2; 3 0] X + [ -4e^(2t); 0 ]

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Answer:

\(-\frac{3}{5}\)

Step-by-step explanation:

so I like to think of slope as rise/run

the "rise" is the difference between the two y's and the run is the difference between the two x's. there isn't a particular order, but make sure that if you use the first coordinate's y first and then the second y, that you do the same for finding the difference between the x's because signs are important.

so, to solve this one:

\(\frac{10-13}{6-1} =\frac{-3}{5}\)

An angle of rotation is the measure of the amount that a figure is rotated about a fixed point called a point of rotation.

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Answer:

"A) 12n + 14m + 4" would be the standard form.

Step-by-step explanation:

the expression written correctly in standard form would be "A) 12n + 14m + 4"

10m + 3(n + 8) + 4(m - 5) + 9n you need to first clear the parenthesis by applying distributive property:

10m + 3(n + 8) + 4(m - 5) + 9n = 10m + 3n + 24 + 4m - 20 + 9n

After that you combine like terms

= 10m + 4m + 3n + 9n + 24 - 20 = 14m + 12n + 4

"A) 12n + 14m + 4" would be the standard form.

Answer:

(x-3)(x^2-7) = x^3 -3x^2 -7x + 21

just change the sign of the root and put x in front of it, then multiply the factors all together

(x-3)(x-sqr7)(x+sqr7)    roots come in conjugate pairs to eliminate irrational coefficients

(x-sqr7)(x+sqr7) = x^2-7.  similar to (a-b)(a+b) = a^2-b^2

Step-by-step explanation:

Answer:

43.6 (approximately)

Step-by-step explanation:

Diagonal measures of the screen is,

√(35²+26²)

= √(1901)

= 43.6 (approximately)

Answered by GAUTHMATH

We calculate the dioglonal using the Pythagorean theorem

\(\displaystyle\ C^2=A^2+B^2=> C=\sqrt{A^2+B^2} \ then \\\\C=\sqrt{26^2+35^2} =\sqrt{1225+676} =\sqrt{1901} \approx43.6\\\\Answer : the \:diagonal \:\:length is \:\underline{43.6}\)

Answer:

C

x-2 / x+6

Step-by-step explanation:

I did the math

(I am not 100% sure though, so if I am wrong, someone please mention it!)

The function f(x) . g(x) is a composite function, and the value of f(x) . g(x) is (x- 2)/(x + 6)

A composite function is a function formed by combining multiple independent functions

The functions f(x) and g(x) are given as:

\(f(x) = \frac{x + 12}{x^2 + 4x- 12}\)

\(g(x) = \frac{4x^2 - 16x+ 16}{4x+ 48}\)

The composite function f(x) . g(x) is calculated using:

\(f(x) \cdot g(x) =\frac{x + 12}{x^2 + 4x- 12} * \frac{4x^2 - 16x+ 16}{4x+ 48}\)

Expand the functions

\(f(x) \cdot g(x) =\frac{x + 12}{x^2 + 4x- 12} * \frac{4(x^2 - 4x+ 4)}{4(x+ 12)}\)

Cancel out the common factors

\(f(x) \cdot g(x) =\frac{1}{x^2 + 4x- 12} * \frac{x^2 - 4x+ 4}{1}\)

Further, expand

\(f(x) \cdot g(x) =\frac{1}{(x -2)(x + 6)} * \frac{(x - 2)(x - 2)}{1}\)

Cancel the common factors

\(f(x) \cdot g(x) =\frac{x- 2}{x + 6}\)

Hence, the value of f(x) . g(x) is (x- 2)/(x + 6)

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The value of the midsegment(PQ) of the Triangle DEF  is 5 , the correct option is  (5) .

The Mid Segment Theorem states that , the line segment that joins the mid points , of the the other two sides of the triangle is parallel to and half the length of the third side.

In the question ,

it is given that

In triangle DEF , PQ is the mid segment of the triangle DEF and DF is the base

So , by mid segment theorem ,

we get

PQ = (1/2)*DF

on substituting the value of DF , we get

PQ = (1/2)*10

PQ = 10/2

PQ = 5

Therefore , The value of the midsegment(PQ) of the Triangle DEF  is 5 , the correct option is  (5) .

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Answer:

\(\frac{2t-4}{3}\)

Step-by-step explanation:

\(\frac{2}{3}\)\((t-2)\\\)
=> \((\frac{2}{3} * t ) + (\frac{2}{3} * -2)\)
=> \(\frac{2t}{3} + (-\frac{4}{3})\)
=> \(\frac{2t-4}{3}\)

Hope you understood!!

Answer:

z=-58 bc 13-71= -58

Step-by-step explanation:

Answer:

Fraction Form:

c=79/34 also known as 2 11/34

Decimal Form:

c=2.32352941

9514 1404 393

Answer:

  √3 cm

Step-by-step explanation:

The square of a face diagonal is given by the Pythagorean theorem:

  (face diagonal)² = 1² + 1² = 2

Then the square of the space diagonal is ...

  (space diagonal)² = 1² +2 = 3

So, the length of the space diagonal is ...

  space diagonal = √3 cm

_____

In the attached diagram, AB and BC are edges of a face of the cube. AC is the diagonal of that face, a "face diagonal." That makes a right triangle with edge CD of the cube. The hypotenuse of that triangle is AD, the "space diagonal". As we have shown, the length of the space diagonal is ...

  AD² = CD² +AC² = 1² +(√2)² = 3

  AD = √3

We can use the integral test to determine the convergence of the series:

∫₂^∞ 1/(x^p ln(x)) dx

We integrate this using u-substitution with u = ln(x):

∫ln(2)^∞ 1/(u^p) du

This integral converges if and only if p > 1, so the given series converges if and only if p > 1.

Therefore, the series converges for all values of p > 1.

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Answer:

Step-by-step explanation:

5, 5, 5, 16, 16, 28, 29, 32, 35, 48

Mode: 5, 16

Median: 44/2 = 22

range: 48 - 5 = 43

mean: (5 + 5 + 5 + 16 + 16 + 28 + 29 +32 + 35 + 48)/10 = 219/10 = 21.9

The measure of angle ∠3 and angle ∠6, which are alternate interior angles formed between the parallel lines m and n are;

m∠3 = 60°, m∠6 = 60°

Alternate interior angles are angles formed in the inside part of two lines that have a common transversal, and on opposite sides of the transversal.

The information are;

Line m is parallel to line n (m ║ n)

m∠3 = 7·x - 10

m∠6 = 5·x + 10

From the possible diagram in a similar question, we get;

∠3 and ∠6 are alternate interior angles formed between parallel lines therefore;

∠3 ≅ ∠6

m∠3 = m∠6 (definition of congruent angles)

7·x - 10 = 5·x + 10 (substitution property of equality)

7·x - 5·x = 10 + 10 = 20

2·x = 20

x = 20 ÷ 2 = 10

x = 10

m∠3 = 7 × 10 - 10 = 60

m∠3 = 60°

m∠3 = m∠6

Therefore;

m∠6 = 60°

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(a) To find the maximum torque on the loop of wire, we can use the formula:

τmax = NABsinθ

where N is the number of turns, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the magnetic field and the normal to the plane of the loop.

Plugging in the given values, we get:

N = 150
A = (16.5 cm)^2 = 272.25 cm^2
B = 1.8 T
θ = 90° (since the maximum torque occurs when the loop is perpendicular to the field)

τmax = (150)(272.25 cm^2)(1.8 T)sin90°
τmax = 7338 N-cm or 0.7338 N-m (rounded to four significant figures)

Therefore, the maximum torque on the loop of wire is 0.7338 N-m.

(b) To find the torque when the angle between the field and the normal to the plane of the loop is 150°, we can again use the formula:

τ = NABsinθ

where θ is now 150°.

Plugging in the given values, we get:

N = 150
A = (16.5 cm)^2 = 272.25 cm^2
B = 1.8 T
θ = 150°

τ = (150)(272.25 cm^2)(1.8 T)sin150°
τ = -1999 N-cm or -0.1999 N-m (rounded to four significant figures)

Therefore, the magnitude of the torque in N-m when the angle between the field and the normal to the plane of the loop is 150° is 0.1999 N-m (since the negative sign just indicates the direction of the torque).
(a) To find the maximum torque on the loop of wire, we can use the formula:

τ_max = n * B * A * I * sin(θ)

where n is the number of turns (150), B is the magnetic field (1.8 T), A is the area of the loop, I is the current (46 A), and θ is the angle between the magnetic field and the normal to the plane of the loop.

Since the maximum torque occurs when sin(θ) = 1 (i.e., θ = 90°), we can calculate A by converting the side length to meters and squaring it:

A = (0.165 m)^2 = 0.027225 m^2

Now, we can calculate the maximum torque:

τ_max = 150 * 1.8 * 0.027225 * 46
τ_max ≈ 335.12 Nm

(b) To find the magnitude of the torque when the angle is 150°, we can use the same formula and plug in sin(150°):

τ = n * B * A * I * sin(150°)
τ = 150 * 1.8 * 0.027225 * 46 * sin(150°)
τ ≈ 167.56 Nm

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Let's begin by identifying key information given to us:

Numbers of apples = 35

Number of oranges = 30

Total number of fruits = 65

The ratio of apples to oranges is given by:

The odds that a carton of eggs will have at least one cracked egg is 97.5 %

The question has to do with probability

Probability is the likelihood for an event to occur. It is given by P(event) = number of required outcomes/total number of possible outcomes.

Given that the probability that a carton of eggs taken from the cooler at a store will have at least one cracked egg is 2.5%. Let the probability of at least one cracked egg be P(egg ≤ 1) = 2.5% = 0.025

Now, since we require the probability of  that a carton of eggs will have at least one cracked egg, that is the number of cracked is greater than 1.

Let the probability of cracked eggs greater than 1 be P(egg ≥ 1).

From the law of probability

P(egg ≤ 1) + P(egg ≥ 1) = 1

So,  P(egg ≥ 1) = 1 -  P(egg ≤ 1)

P(egg ≥ 1) = 1 -  0.025

P(egg ≥ 1) = 0.975

P(egg ≥ 1) = 0.975 × 100 %

P(egg ≥ 1) = 97.5 %

So, the odds that a carton of eggs will have at least one cracked egg is 97.5 %

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Answer:

Step-by-step explanation:

5x + 4y = 8   ⇒   4y = 8 - 5x  ⇒  y = (8 - 5x)÷4

2x − 3y = 17

2x - 3(8 - 5x)÷4 = 17    

          ×4            ×4    

8x - 3(8 - 5x) = 68

8x - 24 + 15x = 68

          +24       +24

           23x  =  92  

           ÷23      ÷23

               x = 4

Answer:

it is 4

Step-by-step explanation:

i did it on edge hope it helps.:)

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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Step-by-step explanation:

(1 ⅓ yd²) / (8/9 yd²)

(4/3 yd²) / (8/9 yd²)

(4/3) × (9/8)

3/2

1.5 / 1

Answer:

\(\qquad {:}\longrightarrow\tt 1\dfrac {1}{3}=\dfrac{4}{3}\)

\(\qquad {:}\longrightarrow\displaystyle\tt \dfrac {\dfrac {4}{3}}{\dfrac {8}{9}}\)

\(\qquad {:}\longrightarrow\tt \dfrac {4}{3}\times \dfrac {9}{8}\)

\(\qquad {:}\longrightarrow\tt \dfrac {36}{24}\)

\(\qquad {:}\longrightarrow\tt \dfrac {3}{2}\)

\(\qquad {:}\longrightarrow\tt 1.5 \:per\:unit\)

A result is called "statistically significant" when the p-value is less than the significant level, typically 0.05.

This means that there is less than a 5% chance that the results are due to chance alone, and suggests that there is a real effect present in the data.

The Null Hypothesis is the assumption that there is no significant difference between the measured phenomenon and a certain value or set of values. A statistically significant result means that the observed data are inconsistent with the assumption of no difference, or no effect.

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Answer:

9.6 days

Step-by-step explanation:

100 chickens, 12 days

find the days for 10 chickens: 1.2 days (to get 10 you have to divide 100 by ten, so divide 12 by ten too)

times by 8 to get the days for 80 chickens: 9.6 days

Answer: Let's assume that the bag of corn contains "C" units of corn. We know that this amount of corn can feed 100 chickens for 12 days.

To determine how long the same bag of corn would feed 80 chickens, we can use the following proportion:

(Corn units)/(chickens * days) = (Corn units)/(chickens * days)

We can set up two ratios, one for the original situation and one for the new situation, and then cross-multiply to solve for the unknown value:

C/100 * 12 = C/80 * d

where "d" is the number of days that the same bag of corn would feed 80 chickens.

Simplifying the equation, we get:

C/10 = C/80 * d

Multiplying both sides by 80, we get:

8C = Cd

Dividing both sides by "C", we get:

8 = d

Therefore, the same bag of corn would feed 80 chickens for 8 days.

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Answer:

The difference in price between a small pizza and a medium pizza is $0.81

Step-by-step explanation:

Small pizza

Side = 5inch

Area =  25 sq.in

Cost = $4 +0.04*25

        = 4 + 1.25  = $5.25

Medium pizza

Side = 8inche

Area = 64 sq.in

Cost = 3.50 + 0.04*64 = $6.06

Difference = Medium pizza - small pizza

                  = 6.06 - 5.25

                   = $0.81

Answer:

29 km < n < 43 km

Step-by-step explanation:

7,36,x

7+n>36 n>29

7+36>x 43>n

36+x>7 n>-29 don't use

29<n<43 29 km < n < 43 km