Rewrite the following equation in standard form

y = 4x + 2

Answer:

-2

Step-by-step explanation:

Given data

We have the expression

3(x+2) =0

open bracket

3x+6=0

3x=-6

divide both sides  by 3

x= -6/3

x= -2

Answer:

(3x)+2 or 3x + 6

Step-by-step explanation:

Trigonometry is the branch of geometry that gives the relationship between the angles and sides of a triangle.

c) proof. if cos∅ = \(\frac{x}{\sqrt{x^{2} + y^{2} } }\),  then x = adjacent, \(\sqrt{x^{2} + y^{2} }\) = hypotenuse

  To solve for opposite, since it is a right angle triangle

   \(hypotenuse^{2}\) = \(opposite^{2}\) + \(adjacent^{2}\)

  \((\sqrt{x^{2} + y^{2} }) ^{2}\) = \(opposite^{2}\) + \(x^{2}\)

  \(opposite^{2}\) = \(x^{2}\) +\(y^{2}\) -\(x^{2}\)

   opposite = y

xsin∅ = x\((\frac{y}{\sqrt{x^{2} + y^{2} } })\) = \(\frac{xy}{\sqrt{x^{2} } + y^{2} }\)

ycos∅ =  \(\frac{xy}{\sqrt{x^{2} } + y^{2} }\)

Therefore xsin∅ = ycos∅

d) 41 sin∅ = 40

   sin∅ = 40/41

   solving for adjacent = 9

    tan ∅ = opp/adj = 40/9

\(\frac{tan \alpha }{tan^{2}\alpha - 1 }\) = 40/9 ÷ \((\frac{40}{9} )^{2}\) - 1 = 40/9  ÷ 1600/81 - 1

                                         = 40/9  ÷ 1519/81 = 40/9 x 81/1519 = 360/1519

e) 1 - cos ∅ = 1/2

    cos ∅  = 1 - 1/2 = 1/2

   ∅ = cos inverse of 0.5 = 60°

   tan 60 = \(\sqrt{3}\)    \(tan^{2} 60\) = 3, sin 60 = \(\frac{\sqrt{3} }{2}\) \(sin^{2} 60\) = 3/4

      \(tan^{2} 60\) +  4\(sin^{2} 60\) = 3 + 4(3/4) = 3 + 3 = 6

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At this price. The cost to buy 8 magnets will be $26.67.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

A gift shop sells souvenir magnets. The store is selling 3 magnets for $10. At this price. The cost to buy 8 magnets will be

Let x be the cost of 8 magnets.

We know that the ratio of the cost and the number of magnets will be constant. Then we have

x / 8 = 10 / 3

x = $26.67

At this price. The cost to buy 8 magnets will be $26.67.

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To find the general solution of the differential equation y" - 7y' - 8y = 0, we can assume a solution of the form y(t) = e^(rt), where r is a constant to be determined.

Plugging this into the differential equation, we get: r^2e^(rt) - 7re^(rt) - 8e^(rt) = 0. Factoring out e^(rt), we have: e^(rt)(r^2 - 7r - 8) = 0.  For this equation to hold for all values of t, we must have: r^2 - 7r - 8 = 0.  Solving this quadratic equation, we find the roots to be r = -1 and r = 8. Therefore, the general solution to the given differential equation is: y(t) = C₁e^(-t) + C₂e^(8t).

Now, let's solve the given initial value problem y" + 7y' = 0 with the initial conditions y(0) = 15 and y'(0) = -63. Using the general solution, we can substitute the initial conditions into the equation and solve for the values of the constants C₁ and C₂. When t = 0, y(0) = C₁e^(0) + C₂e^(8(0)) = C₁ + C₂ = 15. When t = 0, y'(0) = -C₁e^(0) + 8C₂e^(8(0)) = -C₁ + 8C₂ = -63

Solving these two equations simultaneously, we find C₁ = -9 and C₂ = 24.

Therefore, the solution to the initial value problem y" + 7y' = 0, y(0) = 15, y'(0) = -63 is: y(t) = -9e^(-t) + 24e^(8t)

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9514 1404 393

Answer:

  g(x) = (x +1)^2 +3

Step-by-step explanation:

You know that the transformation ...

  g(x) = f(x -h) +k

moves the f(x) graph h units to the right and k units up. In this problem, we have h=-1 (1 unit left) and k=3 (3 units up), so the transformation is ...

  g(x) = f(x +1) +3

Since f(x) = x^2, the equation for g(x) is ...

  g(x) = (x +1)^2 +3

Answer:

41

Step-by-step explanation:

15+26=41

Answer:

41 minutes

Step-by-step explanation:

If she jogged 15 minutes more on Sunday than Saturday, we can find how many minutes she jogged on Sunday by adding 15 to Saturday's amount:

So, add 15 to 26:

15 + 26

= 41

So, she jogged 41 minutes on Sunday.

To prove AEB ≅ DEC by ASA (Angle-Side-Angle), the properties that can be used are:

So, the properties to use for proving AEB ≅ DEC by ASA are "Opposite angles are congruent" and "All sides are congruent."

\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}\)

Answer:

To prove AEB ≅ DEC by ASA (Angle-Side-Angle), the properties that can be used are:

1. Opposite angles are congruent: This property is necessary to establish that ∠AEB ≅ ∠DEC, as both angles are opposite each other in the square ABCD.

2. All sides are congruent: This property is necessary to establish that AE ≅ DE, as both sides are corresponding sides of the square ABCD.

So, the properties to use for proving AEB ≅ DEC by ASA are "Opposite angles are congruent" and "All sides are congruent."

Step-by-step explanation:

The opportunity cost of producing one ton of wheat in the US is 2 tons of corn.

The opportunity cost of producing one ton of wheat in the US can be determined by comparing the amount of corn that could have been produced instead.

In the US, workers can produce 10 tons of wheat per hour or 5 tons of corn per hour. Therefore, to produce one ton of wheat in the US, workers would have to forgo the production of 2 tons of corn (10 tons of wheat divided by 5 tons of corn).

Hence, the opportunity cost of producing one ton of wheat in the US is 2 tons of corn.

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The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.

To write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method

The digit 9 in the tenths place represents 9/10 or 0.9.

The digit 9 in the hundredths place represents 9/100 or 0.09.

The digit 9 in the thousandths place represents 9/1000 or 0.009.

Thus, the fractions are

0.9 = 9/10

0.09 = 9/100

0.009 = 9/1000

The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.

The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.

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The probability that EXACTLY three round of tosses are made is given as follows:

0.046875 = 4.6875%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Ann odd person is when a person has a different coin than the others, and the probability of no odd person is of:

Hence:

2 x 0.125 = 0.25.

Hence the probability of three round tosses is:

Hence the probability is of:

p = 0.25 x 0.25 x 0.75

p = 0.046875.

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From the given questions data the relation B and relation C is not a function.

What is the function?

A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, for a relationship to be a function, each input can only be associated with one output.

Using this definition, we can determine which of the given relations is not a function by checking whether each input is associated with exactly one output.

A. The inputs in relation A are 5, -2, 4, and -6. Each of these inputs is associated with exactly one output (4, 2, 1, and 2, respectively). Therefore, relation A is a function.

B. The inputs in relation B are -6, 4, -2, and 5. However, both -6 and 4 are associated with the output 4, so they violate the requirement that each input can only be associated with one output. Therefore, relation B is not a function.

C. The inputs in relation C are 4, -2, 4, and -6. The input 4 is associated with two different outputs (4 and 1), so relation C is not a function.

D. The inputs in relation D are -2, 4, 5, and -6. Each of these inputs is associated with exactly one output (4, 2, 1, and 5, respectively). Therefore, relation D is a function.

Therefore, the answer is relation B and relation C is not a function.

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Answer:

Andy :

36+35 = 71 cards.

- I hope this helps:)

Answer:

b

Step-by-step explanation:

To find the expected number of sixes appearing on three die rolls, we can calculate the probability of rolling a six on each individual roll and then multiply it by the number of rolls.

The probability of rolling a six on a single roll of a fair die is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a six.

Since the rolls are independent events, we can multiply the probabilities together to find the probability of rolling a six on all three rolls:

(1/6) * (1/6) * (1/6) = 1/216

Therefore, the probability of rolling a six on all three rolls is 1/216.

To find the expected number of sixes, we multiply the probability by the number of rolls:

Expected number of sixes = (1/216) * 3 = 1/72

So, the expected number of sixes appearing on three die rolls is 1/72.

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Answer:

y=4x-23

Step-by-step explanation:

y+3=4(x-5)

y+3=4x-20

y=4x-20-3

y=4x-23

Answer:

both are at the same distance

Step-by-step explanation:

Answer:

Austin and Devyn both have 1/3 of the way left on their way to school. They both also have walked the same amount.

Step-by-step explanation:

If Austin has to walk to his school, which could be said as 3/3 and Austin has already walked 2/3. Then if we conduct the equation 3/3-2/3=x. x=1/3. Now Devyn has already walked 4/6 of the way to school. If she has to walk a total of 6/6, then we can again make an equation 6/6-4/6=2/6. Now if we take the distance that they both have left to their school, its 1/3 and 2/6. These are both equavalent fractions because if you scale up 1/3, it equals to 2/6. Since they both have an equal amount of distance to travel, that must mean that they both have covered the same amount of distance already. We can double check to be sure. 2/3 *2/2=4/6. The reason we used 2/2 is because4/2=2 and 6/3=2.

Let's assume the total number of movies Aldo plans to watch each month is represented by the variable "M". To write an equation representing the total number of movies Aldo will watch in months, we can use the equation:

M = n * m

where "n" represents the number of months and "m" represents the average number of movies Aldo plans to watch per month.

This equation states that the total number of movies Aldo will watch (M) is equal to the number of months (n) multiplied by the average number of movies he plans to watch per month (m).

For example, if Aldo plans to watch an average of 5 movies per month and he plans to do so for 12 months, the equation becomes:

M = 12 * 5

which simplifies to:

M = 60

Therefore, Aldo plans to watch a total of 60 movies in 12 months.

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A standard normal random variable (Z) has a mean of 0 and a standard deviation of 1. The probability of Z being greater than 0 is equal to the area under the normal curve to the right of 0, which is exactly half of the total area under the curve (since the curve is symmetric around the mean of 0). Therefore, P(Z>0) is equal to 0.5.

A standard normal random variable, like Z in your question, follows a standard normal distribution, which is a special type of normal distribution with a mean of 0 and a standard deviation of 1. Now, you're asked to find the probability P(Z > 0).

Since the standard normal distribution is symmetrical around the mean (0), the probability of Z being greater than 0 is equal to the probability of Z being less than 0. In other words, half of the distribution is on the right side of the mean, and the other half is on the left side.

Therefore, P(Z > 0) = 0.5, which is your answer.

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Answer:28

Step-by-step explanation:7 x 4= 28

Answer:

28

Step-by-step explanation:

7, 14, 21, 28

Answer:

1 5/8 feet/year

Step-by-step explanation:

Height tree grew in 10 years

= 36 3/4-20 1/2

= 16 1/4 feet

Rate tree grew in a year

= 16 1/4÷10

= 1 5/8 feet/year

Answer:

length = 6m

Step-by-step explanation:

H=5m

V=180m^3

Here

V=l^2 ×H ( being a square)

180=a^2×5

a^2=36

a=6m

Answer:

below

Step-by-step explanation:

17/40 * 100 % = 42.5 %

Answer:

42.5%

Step-by-step explanation:

to get 40 (denominator) to 100, you need to multiply 40 by 2.5times.

so, multiply 17 (numerator) too: 17 times 2.5 = 42.5

42.5 percent is your answer

Answer:

d=-9

Step-by-step explanation:

you simplify both side of the equation

d/3-9=-12

1/3d+-9=-12

add 9 both sides

1/3d-9+9=-12+9

1/3d=-3

then you multiply 3 both sides

3 x (1/3d)=(3) x(-3)

d=-9

Hopes this helps  :)

Answer: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.)

Step-by-step explanation:  ???

Answer:

Step-by-step explanation:

1)  length = x m

breadth = x/2 m

Area of rectangular floor = 32 square m

\(length * breadth = 32\\\\x*\dfrac{1}{2}x = 32\\\\\\x^{2}=32*2\\\\\\x^{2} = 64\\\\x=\sqrt{64}=\sqrt{8*8}\\\\x = 8 \ m\)

Length = 8 m

Breadth =8/2 = 4 m

Perimeter = 2*(length + breadth) = 2*(8 + 4)

                = 2*12

                = 24 m

2) Perimeter of square = 12 cm

Side of a square = perimeter ÷ 4 = 12 ÷ 4 = 3 cm

Area =side *side = 3*3 = 9 cm²

3) Perimeter of square field = 60 m

Side = Perimeter ÷ 4 = 60 ÷4 = 15 m

Area of square = 15 * 15 = 225 m²

4) Perimeter of rectangle = 28 cm

breadth = (Perimeter ÷ 2) - length

             = (28 ÷2) - 8

             = 14 - 8

Breadth = 6 cm

Area of rectangle = 8 * 6 = 48 cm

\(\bold{\huge{\pink{\underline{ Solutions }}}}\)

We have,

Let the length of the rectangular field be x

So,

Breath of the rectangular field will be x/2

We know that,

\(\bold{\red{Area \: of \: rectangle = length}}{\bold{\red{\times{ Breath}}}}\)

Subsitute the required values,

\(\sf{32 = x }{\sf{\times{\dfrac{x}{2}}}}\)

\(\sf{32 = }{\sf{\dfrac{x^{2}}{2}}}\)

\(\sf{ 32}\sf{\times{ 2 = x^{2}}}\)

\(\sf{ 64 = x^{2}}\)

\(\bold{ x = 8 m}\)

Thus, The length of rectanglular field is 8m

Therefore,

Breath of the rectangular field will be

\(\sf{=}{\sf{\dfrac{8}{2}}}\)

\(\bold{ = 4 m }\)

We have to find the perimeter of the given rectangular field

We know that,

Perimeter of the reactangle

\(\bold{\blue{ = 2( L + W) }}\)

Subsitute the required values in the above formula :-

Perimeter of the rectangular field

\(\sf{ = 2( 8 + 4) }\)

\(\sf{ = 2}{\sf{\times{12}}}\)

\(\bold{ = 24 m}\)

Hence, The perimeter of the rectangular field is 24 m

We have

Let the side of the square be x

We know that,

\(\bold{\pink{ Perimeter\: of\: square = 4 }}{\bold{\pink{\times{ side}}}}\)

Subsitute the required values in the above formula :-

\(\sf{12 = 4 }{\sf{\times{ x }}}\)

\(\sf{\dfrac{ 12}{4}}{\sf{ = x }}\)

\(\bold{ x = 3 cm}\)

Thus, The length of the square is 3 cm

We have to find the area of square

We know that,

\(\bold{\red{Area \: of \: square = Side }}{\bold{\red{\times{ Side}}}}\)

Subsitute the required values,

Area of square

\(\sf{ = 3 }{\sf{\times{ 3 }}}\)

\(\sf{ = 9 cm^{2}}\)

Hence , The length and area of square is 3cm and 9 cm²

We have

Let the side of the square feild be x

We know that,

\(\bold{\pink{ Perimeter\: of\: square = 4 }}{\bold{\pink{\times{ side}}}}\)

Subsitute the required values,

\(\sf{60 = 4 }{\sf{\times{ x }}}\)

\(\sf{\dfrac{ 60}{4}}{\sf{ = x }}\)

\(\bold{ x = 15 m }\)

Thus, The side of the square feild is 15m

We have to find the area of square

We know that,

\(\bold{\red{Area \: of \: square = Side }}{\bold{\red{\times{ Side}}}}\)

Subsitute the required values,

Area of square

\(\sf{ = 15 }{\sf{\times{ 15 }}}\)

\(\sf{ = 225 cm^{2}}\)

Hence, The area of square feild is 225 cm²

We have,

Let the breath of the rectangle be x

We know that,

\(\bold{\blue{Perimeter\:of\: rectangle= 2( L + W) }}\)

Subsitute the required values,

\(\sf{ 28 = 2( 8 + x) }\)

\(\sf{ 28 = 16 + 2x }\)

\(\sf{ 28 - 16 = 2x }\)

\(\sf{ 12 = 2x }\)

\(\sf{\dfrac{ 12}{2}}{\sf{ = x }}\)

\(\bold{ x = 6 cm}\)

Thus, The breath of the rectangle is 6 cm

We have to find the area of rectangle

We know that,

\(\bold{\red{Area \: of \: rectangle = length}}{\bold{\red{\times{ Breath}}}}\)

Subsitute the required values,

Area of rectangle

\(\sf{= 8 }{\sf{\times{6}}}\)

\(\sf{ = 48 cm^{2}}\)

Hence, The breath and area of rectangle is 6cm and 48 cm² .

[ Note :- Kindly refer app for better understanding ]

The PERT expected activity time for this activity is 6 days.

To compute the PERT (Program Evaluation and Review Technique) expected activity time, we can use the formula:

Expected Time = (Optimistic Time + 4 * Most Likely Time + Pessimistic Time) / 6

Using the given values, we have:

Optimistic Time = 2 days

Most Likely Time = 5 days

Pessimistic Time = 14 days

Substituting these values into the formula:

Expected Time = (2 + 4 * 5 + 14) / 6

Expected Time = (2 + 20 + 14) / 6

Expected Time = 36 / 6

Expected Time = 6

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