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By apply the law of cosine, the shortest length of wire needed is 180 feet.

In order to determine the shortest length of wire needed, we would apply the law of cosine because a mental image of the scenario described produces a right-angled triangle.

In Trigonometry, law of cosine (cos) is given by this mathematical expression:

C² = A² + D² - 2(A)(D)cosD

Note: Angle D = 90° + 32° = 122°

Substituting the given parameters into the formula, we have;

C² = 55² + 145² - 2(55)(145)cos122°

C² = 3,025 + 21,025 - 2(7,975)(-0.5299)

C² = 24,050 - (-8,451.905)

C² = 24,050 + 8,451.905

C² = 32,501.905

C = √32,501.905

C = 180.28 ≈ 180 feet.

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The region common  to both the graphs as shown is the solution set.

A system of equations is a collection of two or more equations with a same set of unknowns

Given are the following  quadratic inequalities -

x² - 6x - 7 < 0

3x² - 28x + 32 ≤ 0

We have the following quadratic inequalities -

x² - 6x - 7 < 0

3x² - 28x + 32 ≤ 0

We will plot both of them. The common region be the possible set of solutions to the given inequalities. Refer to the graph attached. The region common to both the graphs is the solution set.

Therefore, the region common  to both the graphs as shown is the solution set.

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Answer: 60 degrees

Step-by-step explanation: Because all sides are equilateral, and in an equilateral triangle all angles are 60 degrees, hope that helps.

Answer:26.5

Step-by-step explanation:

Answer:

see the attachment photo!

Answer:

18X^2 + 18XY + 12YX + 12Y^2

Step-by-step explanation:

you have to moltiplicate the first term with the other two and the same thing for the second term of the first moltiplication

Step-by-step explanation:

what is the question you need an answer for ?

I assume you only need the result of the multiplication of both terms.

remember, when multiplying summary terms, we need to multiply every part of one term with every part of the other term.

(3x + 2y)(6x + 6y) = 18x² + 18xy + 12xy + 12y² =

= 18x² + 30xy + 12y²

The time taken to reach the maximum height is 1.25 seconds.

The maximum height is 32 feet.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

h(t) = -16t² + 40t + 7

Differentiating with respect to t.

h'(t) = -16 x 2t + 40

0 = -32t + 40

32t = 40

t = 40/32

t = 1.25

The maximum height.

h(t) = -16t² + 40t + 7

h(1.25):

= -16 x 1.25 x 1.25 + 40 x 1.25 + 7

= -25 + 50 + 7

= 32 feet

Thus,

The time taken to reach the maximum height is 1.25 seconds.

The maximum height is 32 feet.

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The value of x in the remote angles of the triangle  is 22.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.  

In other words the sum of the remote interior angle is equals to the external angle.

Therefore,

110 = 3x + 2x

110 = 5x

divide both sides by 5

110 / 5 = 5x / 5

x = 22

Therefore, using exterior angle theorem, the value of x is 22.

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Answer: (X^3)*y

:) Hope this helps, I spent a lot of time on it!

Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).

As given in the question,

Focus of the parabola is equal to (-3, -3)

Directrix of the parabola is given by x = 5

Let (x, y) be the point on the parabola.

Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5

⇒√(x +3)² + (y +3)² = | x -5|

⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²

⇒x² +6x +y² +6y +18 = x² -10x +25

⇒y² +6y -7 = -16x

⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.

Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by  x = (-1/16)(y² +6y -7).

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A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.

The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.

Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.

Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.

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The amount of water after x minutes is equal in both pools.

What is a Linear equation in one variable?

A univariate linear equation is an equation of the form ax + b = 0, where a and b are two integers, x is a variable, and there is only one solution.

For example, 2x+3=8 is a linear equation in one variable.

The given equation is 5000 - 50x = 4800 - 30x.

solving for 'x',

                        5000 - 50x = 4800 - 30x

                        5000 - 4800 = 50x - 30x

                        200 = 20x

                        x = 200/20

                        x = 10

The amount of water after 10 minutes in Pool A will be = 5000 - 50(10)

                                                                                           = 5000 - 500                                                                                                                                              

                                                                                           = 450 liters

The amount of water after 10 minutes in Pool B will be = 4800 - 30(10)

                                                                                           = 4800 - 300                                                                                                                                              

                                                                                           = 450 liters.

Hence, the amount of water will be the same in both pools.

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Answer:

answer in the picture step by step

The probability of more than $225 is 0.35197.

Here we need to find the probability of more than $225.

We need to calculate the z-score associated with x = $225

Z(score) = 225 - 204 / 55

= 0.381818

z(score) = 0.38

For z = 0.38 the corresponding probability is P(z < 0.38) = 0.64803.

Here we have to find the values greater than this value:

P(z > 0.38) = 1 - P (z < 0.38)

P( z > 0.38) = 0.35197

So the probability that a hotel room costs 225 or more per night is P (x > 225) = 0.35197 and the percentage is 35.197%.

Therefore the probability is 0.35197.

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The value of angle with x, given the equation on the circle, is 4) 3.

The angle is given by the expression:
31x + 3

The same angle is shown to be a right angle with the line EF being straight and therefore a right angle. Right angles have a total measure of 90 degrees.

The value of x can therefore be found by equating the expression to 90 degrees:
31x + 3 = 90

31 x = 90 - 3

x = 87 / 31

x = 2.8

x = 3

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Answer:

(-1,4) (-3,0)

picture below (im assuming you meant x^2.)

if you meant x2, please look at the second image

FIRST PHOTO = y=x^2 + 6x + 9 & y=2x+6

SECOND PHOTO = y=x2 + 6x + 9 & y=2x+6

The reduced fraction is 7 using GCF method.The GCF is also known as the Highest Common Factor (HCF)

The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

The fraction = 14/66

The factors of 14 = 2×2×2×3

The factors of 28 = 11*3*2

The gcf is 2 × 2 = 4

Divide the denominator and numerator by 4

14 ÷2 = 7

14÷ 2 = 7

We get,

The fraction = 14/2 =7

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Answer:

x=-5/2

Step-by-step explanation:

x=-5/2

Answer:

12x+4=20x+24

Add negative 4 to both sides

6x+9=4x-3

Add -9 to both sides

-5x/4=4 Multiply both sides by 04

-4(5x-7)=-18 Distribute -4 on the left side

Step-by-step explanation:

12x+4=20x+24

Add negative 4 to both sides

6x+9=4x-3

Add -9 to both sides

-5x/4=4 Multiply both sides by 04

-4(5x-7)=-18 Distribute -4 on the left side

The distance between the points (5, 7) and (8,-5) is √13.

The length of the path joining two points determines their distance from one another. It's crucial to know how to calculate the distance between two points when working with graphs. This makes it possible for a learner to estimate how long the line is, which is useful in a variety of circumstances. Using the distance formula is the most typical method of determining the distance.

Points (5, 7) and (8,-5)

Formula:

AB² = (x₂ - x₁)² + (y₂ + y₁)²

AB² = (8 - 5)² + (-5+7)²

AB² = (3)² +(2)²

AB² = 9 + 4

AB² = 13

AB = √13

The distance between the points (5, 7) and (8,-5) is √13.

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Answer:

x = 6

Step-by-step explanation:

Given equation,

→ 3x - (2/3)x = 14

Now the value of x will be,

→ 3x - (2/3)x = 14

→ (9/3)x - (2/3)x = 14

→ ((9 - 2)/3)x = 14

→ (7/3)x = 14

→ 7x = 14 × 3

→ x = 42/7

→ [ x = 6 ]

Hence, the value of x is 6.

Yes, it is correct. (a) congruent by SSS

                             (b) congruent by SAS

                             (c) congruent by ASA

(a) Given in figure,

    MN = OP

    ∠MNO = ∠NOP

    ON = ON (Common)

   Hence, ΔMNO ≅ ΔNOP by SAS.

(b) Given in figure,

     UV = XY

    ∠UVW = ∠XYZ

    UW = XZ

   Hence, ΔUVW ≅ ΔXYZ by SAS.

(C) Given in figure,

     ∠ABC = ∠EDF

     BC = DE

    ∠ACB = ∠DEF

   Hence, ΔABC ≅ ΔDEF by ASA.

Therefore, all are congruent.

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The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64

The formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.

Simple interest formula is given as:

S.I = P(1 + rt)

Substituting the values into the formula

S.I = 600(1 + 0.08 * 16)

S.I = 664

The interest generated is $64

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Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?

Linear Regression analysis has three key applications:

(1) evaluating predictor strength, (2) anticipating an effect, and as well (3) trend forecasting.

Linear regression is a fundamental and widely used method of predictive analysis. The overall goal of regression is to investigate two things:

Regression analysis has three key applications:

The formula y = c + b*x defines the simplest form of the regression equation with one dependent so one independent variable,

where,

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The equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18.

The equation will be written as,

C = T - 3

18 = T-3

T = 18 + 3

T = 21 years

Therefore, the equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.

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Answer:

Step-by-step explanation:

You want to know the number of vases of each type of flower if there are 36 vases containing 125 flowers, with 3 daisies or 4 lilacs in a vase.

Let x and y represent daisy and lilac vases, respectively. The problem statement gives two relations:

  x +y = 36 . . . . . total number of vases

  3x +4y = 125 . . . total number of flowers

Substituting for x, we have ...

  x = 36 -y

  3(36 -y) +4y = 125

  108 +y = 125

  y = 13

  x = 36 -13 = 23

There are 23 vases of daisies and 13 vases of lilacs.

For 8 pounds of weight, the charges be the same for both the companies.

Given, that To ship an overnight package

Shipping Company A charges $14 plus $2.25 per pound

Shipping Company B charges $20 plus $1.50 per pound

Let, the weight be w

And the cost of shipment by company A & B be A(w) & B(w) respectively.

According to the question,

A(w) = 14 + 2.25w

B(w) = 20 + 1.50w

Now, when charges be the same

A(w) = B(w)

14 + 2.25w = 20 + 1.50w

On subtracting 1.50w on both the sides, we get

14 + 2.25w - 1.50w = 20 + 1.50w - 1.50w

14 + 0.75w = 20

Now on subtracting 14 on both the sides, we get

14 + 0.75w - 14 = 20 - 14

0.75w = 6

On dividing both the sides by 0.75, we get

0.75w/0.75 = 6/0.75

w = 8

Hence, weight = 8 pounds.

For 8 pounds of weight, the charges be the same for both the companies.

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Answer:

  A)  n > 0

Step-by-step explanation:

You want the solution and graph for -8n +18 > -6(3n -3).

Eliminating parentheses, we have ...

  -8n +18 > -18n +18

Subtracting 18 gives ...

  -8n > -18n

Adding 18n, we have ...

  10n > 0

Finally, dividing by 10 gives ...

  n > 0

The graph is attached.