-
10. Which property is used in solving y + 3 = 11?
A Symm. Prop. of =
B Div. Prop. of =
C Mult. Prop. of =
D Subtr. Prop. of =

Answer:

(-1,4)

Step-by-step explanation:

Step 1) Change both equations to slope intercept form

3x+y=1 ---> y=-3x+1

5x+y=-1 ---> y=-5x-1

Step 2) Plot lines accordingly on graph

Lines intersect at (-1,4)

Answer:

0.630

Step-by-step explanation:

Simply evaluating, we get v (0) = 1, v (0.31831) = 0.630, v (2) = 1.566. Thus, the minimum velocity over the interval [ 0, 2] is 0.630.

The value of GJ and and JH will be 6.5 and 9.19 respectively

What is angle of elevation?

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Given data ,

The angle of elevation θ = 45°

The value of GH = 6.5

Now , the ΔJGH is a right triangle , so by Trigonometric relations

tan θ = JG / GH

tan 45° = 1

Therefore , 1 = JG / GH

1 = JG / 6.5

So , JG = GH = 6.5  

Now to calculate JH , we use the Pythagoras Theorem ,

where JH² = JG² + GH²

Substituting the values for JG and GH , we get

And JH² = 6.5² + 6.5²

              = 42.25 + 42.25

              = 84.5

taking square root on both sides

Therefore , JH = 9.19

Hence , The value of GJ and and JH will be 6.5 and 9.19 respectively

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There are 32,760 ways in which the teams can finish first, second, third, and fourth in the league.

To determine the number of ways the teams can finish first, second, third, and fourth in a league with 15 teams, we can use the concept of permutations.

For the first position, any of the 15 teams can finish first.

For the second position, there are 14 teams remaining that can finish second.

For the third position, there are 13 teams remaining that can finish third.

For the fourth position, there are 12 teams remaining that can finish fourth.

To calculate the total number of ways, we multiply the number of choices for each position:

Total number of ways = 15 * 14 * 13 * 12 = 32,760

Therefore, there are 32,760 ways in which the teams can finish first, second, third, and fourth in the league.

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The correct answer is option O: 5 V.

To determine the average voltage (Vavg) given a peak-to-peak voltage (Vpp) of 10 V, we need to consider the relationship between Vavg and Vpp in an alternating current (AC) waveform.

The average voltage of an AC waveform is related to its peak-to-peak voltage by the formula: Vavg = 0.5 * Vpp.

Applying this formula to the given Vpp of 10 V, we can calculate the Vavg as follows: Vavg = 0.5 * 10 V = 5 V.

The average voltage is equal to half of the peak-to-peak voltage, resulting in an average voltage of 5 V for a Vpp of 10 V.

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Step-by-step explanation:

heres tue answer. hope that helps

Answer:

x=5,y=6

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

Les deux nombres doivent avoir une différence de 3. Algébriquement, ce serait x + (x + 3) = 129. 2x est alors égal à 126. X est égal à 63 et x + 3 est à 66. Ces nombres sont des multiples consécutifs de 3 dont la somme est de 129.

Step-by-step explanation:

The two numbers must have a difference of 3. Algebraically, it would be x + (x + 3) = 129. 2x then is equal to 126. X equals 63 and x + 3 is 66. These numbers are consecutive multiples of 3 whose sum is 129.

The equation of the line that goes through the given points is y = -8x + 25.

Given the following points:

To determine the equation of the line that goes through the given points:

First of all, we would determine the slope of this line by using the following formula;

\(Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the points into the formula, we have;

\(Slope, \;m = \frac{1 - 9}{3 - 2}\\\\Slope, \;m = \frac{-8}{1}\\\\\)

Slope, m = -8

Now, we can determine the equation of the line by using this formula:

\(y-y_1 =m(x-x_1)\\\\y-9=-8(x-2)\\\\y-9=-8x+16\\\\y=-8x+16+9\)

y = -8x + 25

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Answer:

gas left after 3 hours = 4.75

gas left after t hours = 10-1.75t

Step-by-step explanation:

According to DeltaMath "Since Camila uses 1.75 gallons of gas per hour, she would use 1.75 x 5, or 5.25 gallons in 3 hours. Since Camila started with 10 gallons in the tank, the amount of remaining after 3 hours would be 10-5.25 or 4.75 gallons. "

We solve to find that the limit exists and is equal to 0: lim (x, y) → (0, 0) f(x, y) = 0. Therefore, the solution to the limit is 0.

To solve this limit, we need to use the definition of a limit and apply it to the function. The definition of a limit is:

lim (x, y) → (a, b) f(x, y) = L if and only if for every ε > 0 there exists a δ > 0 such that if (x, y) is in the domain of f and 0 < √((x-a)² + (y-b)²) < δ, then |f(x, y) - L| < ε.

We can apply this definition to the function f(x, y) = x^4 − (38y^2)/(x^2 + 19y^2) and the point (0, 0) to find the limit.

First, let's simplify the function:

f(x, y) = x^4 − (38y^2)/(x^2 + 19y^2) = x^4 − 38y^2/(x^2 + 19y^2)

Next, let's substitute the point (0, 0) into the function:

f(0, 0) = 0^4 − 38(0^2)/(0^2 + 19(0^2)) = 0

Now, let's apply the definition of a limit:

lim (x, y) → (0, 0) f(x, y) = 0 if and only if for every ε > 0 there exists a δ > 0 such that if (x, y) is in the domain of f and 0 < √((x-0)² + (y-0)²) < δ, then |f(x, y) - 0| < ε.

We can simplify this further:

lim (x, y) → (0, 0) f(x, y) = 0 if and only if for every ε > 0 there exists a δ > 0 such that if (x, y) is in the domain of f and 0 < √(x² + y²) < δ, then |x^4 − 38y^2/(x^2 + 19y^2)| < ε.

Now, we need to find a δ that satisfies this condition. Let's choose δ = √(ε/2). Then, if 0 < √(x² + y²) < δ, we have:

|x^4 − 38y^2/(x^2 + 19y^2)| < ε

|x^4| + |38y^2/(x^2 + 19y^2)| < ε

|x^4| + |38y^2|/(x^2 + 19y^2) < ε

Since 0 < √(x² + y²) < δ, we have:

|x^4| < (ε/2)^(4/2) = ε^2/4

|38y^2|/(x^2 + 19y^2) < 38(ε/2)^(2/2)/(ε/2)^2 + 19(ε/2)^(2/2) = 38ε/2ε + 19ε/2ε = 57ε/2ε = 57/2

Therefore, |x^4 − 38y^2/(x^2 + 19y^2)| < ε^2/4 + 57/2 < ε for all ε > 0.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The correct option is C, The given graph represents the rational function   \(\frac{1}{(x-1)(x-2)}\).

Mathematicians use graphs to variable logically depict or chart sentences or values in a visual way. Usually, a graph point shows the connection between two or more objects. A graph is a particular kind of non-linear side chain up of parts known as nodes as well as lines. The borders, also referred to as nodes, should be joined together with glue. The node numbers in this graph are 1, 2, 3, and 5.

Upon solving the given function,

\(\frac{1}{(x-1)(x-2)}\),

As, it is clear from the function that the value of x cannot be 1 or 2,

So,

The graph doesn't lie on x = 1 or x = 2.

So, it is the correct option.

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Answer:

(Part A) The formula for finding the area of a circle is πr². (Part B) The radius of that circle would be 5.27 m. 10.54 m cut in half would be 5.27 m. (Part C) The area of this circle would be approx. 87.21 m². Using the formula from Part A, first square 5.27. That will equal 27.7729. Now, multiply that by 3.14 (I used that value for π) to get 87.206906 m². However, we have to round to the nearest hundredth, so 87.21 m² is the answer.

To keep the cost per banana the same, the total cost must remain constant as the number of bananas changes. Therefore, for 4 bananas, the cost is $2, for 6 bananas, the cost is $3, for 7 bananas, the cost is $3.50, and for 10 bananas, the cost is $5.

To keep the cost per banana constant, we need to maintain the ratio of the total cost to the total number of bananas. In other words, the unit price (cost per banana) must remain the same regardless of the number of bananas purchased.

To fill out the table, we can use the formula:

Total cost = unit price × number of bananas

For example, for 4 bananas at a cost of $0.50 per banana, the total cost is:

Total cost = $0.50 × 4 = $2.00

To maintain the same cost per banana for 6 bananas, we need to adjust the unit price so that the total cost is the same as for 4 bananas:

Total cost = $2.00 = unit price × 6

Solving for the unit price, we get:

unit price = $2.00 ÷ 6 = $0.3333 ≈ $0.33 (rounded to two decimal places)

Similarly, for 7 bananas, the unit price must be adjusted so that the total cost is $2.00:

Total cost = $2.00 = unit price × 7

unit price = $2.00 ÷ 7 ≈ $0.29

For 10 bananas, the unit price must also be adjusted to maintain the same cost per banana:

Total cost = $2.00 = unit price × 10

unit price = $2.00 ÷ 10 = $0.20

Finally, for 16.5 bananas, we can use the same formula:

Total cost = $2.00 = unit price × 16.5

unit price = $2.00 ÷ 16.5 ≈ $0.12

Thus, we can fill out the table as follows:

number of bananas cost in dollars

unit price

(dollars per banana)

4 $

$0.50

6 $

$0.33

7 $

$0.29

10 $

$0.20

16.5 $

$0.12

So, we can see that by adjusting the unit price, we can maintain a constant cost per banana for different quantities of bananas.

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Answer: the measure of angle c is 28 degrees

Step-by-step explanation:

Answer:

DEA

Step-by-step explanation:

adjacent is next to and DEA is on line CF with CED

Answer:

x = -8

Step-by-step explanation:

The triangle is isosceles so the two angles are equal

Equation :

65 = x + 73

Subtract 73 from both sides

-8 = x

Check:

65 = -8 + 73

65 = 65

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

Each term in pattern B is 9 less than the corresponding term in pattern A.

The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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Answer:

Yes

Step-by-step explanation:

the factors of (x^ 2 +9x+20) are (x+4)(x+5)

The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1.  5x – 7 = 4x + 3.

To solve for x, we can add 7 to both sides of the equation and subtract 4x from both sides:

5x - 7 + 7 = 4x + 3 + 7

5x = 4x + 10

x = 10

2.  6 + 2x = 7x - 9

To solve for x, we can add 9 to both sides of the equation, subtract 6 from both sides and divide both sides by -1:

6 + 2x + 9 = 7x - 9 + 9

2x = -3

x = -3/2

3. 8x + 1 = -8 - x

To solve for x, we can add x to both sides of the equation and add 8 to both sides:

8x + 1 + x = -8 - x + x + 8

9x + 1 = 0

x = -1/9

4. -5 + 12x = 18x + 7

To solve for x, we can subtract 12x from both sides of the equation and add 5 to both sides:

-5 + 12x - 12x = 18x + 7 - 12x

-5 = 6x + 7

x = -6

5.  -4x + 3 = 5x - 13 - x

To solve for x, we can add x to both sides of the equation, subtract 3 from both sides and divide both sides by -1:

-4x + 3 + x = 5x - 13 - x + x + 3

-3x = -10

x = 10/3

The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3

That gives you the letters "joke"

Therefore, The letters corresponding to the solutions are: x = 10, x = -3/2, x = -1/9, x = -6, x = 10/3 That gives you the letters "joke"1.  5x – 7 = 4x + 3.

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Using Pythagorean Theorem, the length of the line segment from (-3, 10) to (4, -1) is 13 units.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

Let a = vertical distance between the two points

b = horizontal distance between the two points

c = distance between the two points / length of line segment

Hence, c² = (|y₂ - y₁|)² + (|x₂ - x₁|)².

Substitute the values of x and y and solve for c.

c² = (|y₂ - y₁|)² + (|x₂ - x₁|)²

c² = (|-1 - 10|)² + (|4 - -3|)²

c² = (|-11|)² + (|7|)²

c² = 11² + 7²

c² = 121 + 49

c² = 170

c = 13.04

length of line segment ≅ 13 units

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Answer:

12

Step-by-step explanation:

Answer:

3x^2-39x-6

Step-by-step explanation:

because math easy

Answer: 5x = 35 x 10-2. = 3.5 x 10-1. 3.5 x 10-¹. The exponent tells how many times 5 is multiplied to itself. Multiply the numbers and add the exponents.

Step-by-step explanation:

ZERO. Write the equation so one side of the equation is zero. ...

FACTOR. Factor the expression.

PROPERTY. Set each factor equal to zero and solve. ...

Check by substituting solutions into the original equation.

Answer:

11.3

Step-by-step explanation:

To find mean: All values added together divided by amount of values:

X: 11+12+13+14 = 50

50 / 4 (amount of values) = 12.5 (mean of x)

F: 8+3+17+12 = 40

40/4 (amount of values) = 10 (mean of f)

To find mean of x and f combined:

10 + 12.5 = 22.5

22.5 / 2 (amount of values) = 11.25 (mean of x and f combined)

To 1 dec pl.

= 11.3

Hope that makes sense

The annual interest rate of the bank account is 3.1%.

Given:

After 5 years there is $673.40 in the account.

After 8 years there is $737.90 in the account.

Let x and A be the annual interest rate and Amount at first.

A(1+x)^5 = 673.40

A(1+x)^8 = 737.99

A(1+x)^8 / A(1+x)^5 = 737.99/673.40

(1+x)^3 = 1.0959

1+x = \(\sqrt[3]{1.0959}\)

x = 0.3099

x ≈ 0.031

x = 3.1%

Therefore The annual interest rate of the bank account is 3.1%.

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