In the diagram above, <4 = 40 degrees find the measure of <1

Answer:

162√3.

Step-by-step explanation:

Area = 1/2 * p * q  where p and q are the diagonals.

Here p = 2*9 = 18 and we need to find q.

tan 60 = 0.5q/9

0.5q = 9 tan 60 = 9*√3

q = 18√3

So the area of this rhombus

= 1/2 * 18*18√3

= 162√3

=

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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The order of the number from the least to the greatest is -2 3/5, 10/3,3.9, 3 7/5, 20.

A rational number is a number that can be expressed as the fraction of two numbers in which the decimal is not zero. A rational number can be positive or negative. An example of a rational number is 3, -1.2.

An irrational number is a number that cannot be expressed as the fraction of two numbers. An example of a irrational number is 1/3, 22/7.

In order to order a number, all the numbers should have the same form. Thus, all the numbers would be converted to decimals where possible.

-2 3/5 = -2.6

10 /3 = 3.33

3 7/5 = 4.5

In order to order the numbers, note that the farther a negative number is from zero the smaller the number is and the farther a positive number is to zero, the greater the number is.

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The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.

To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:

h = 16t^2 + vt + s

Where:

h is the height of the flag,

t is the time in seconds,

v is the initial vertical velocity of the flag,

s is the initial height of the flag.

In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).

We can rewrite the equation as:

7 = 16t^2 + 30t + 5

To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.

The quadratic equation in this case is:

16t^2 + 30t + 5 - 7 = 0

16t^2 + 30t - 2 = 0

Now, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Applying the values from the quadratic equation, we have:

t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)

Simplifying further:

t = (-30 ± √(900 + 128)) / 32

t = (-30 ± √1028) / 32

Using a calculator, we find two solutions:

t ≈ -1.08 seconds or t ≈ 0.06 seconds

Since time cannot be negative in this context, we discard the negative solution.

Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.

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The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

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Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

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The simplified expression is \(-2x^2 - 2x - 5.\)

To simplify the expression, combine like terms:

\(3x^2 + 5x - 7x - 3 - 5x^2 - 2\)

Combine the \(x^2\) terms:

\((3x^2 - 5x^2) + 5x - 7x - 3 - 2\)

Simplify the \(x^2\) terms:

\(-2x^2 + 5x - 7x - 3 - 2\)

Combine the x terms:

\(-2x^2 - 2x - 3\)

This is the simplified form of the expression.

Therefore, the simplified expression is \(-2x^2 - 2x - 5.\)

We have grouped the terms with similar variables together and performed the necessary arithmetic operations to obtain the simplified form.

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Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x

Part B: width is 50 meters.

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that the variables are expressed as;

We then have that;

l = 2x + 10

Substitute the values

5500 = (2x + 10)(x)

expand the bracket

5500 = 2x² + 10x

2x² + 10x - 5500

x² + 5x - 2750

x² + 55x - 50x - 2750

x(x + 55) - 50(x + 55)

x = 50 meters

Length = 2(50) + 10

Length = 100 + 10 = 110 meters

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1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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12 tickets --

120/10= 12

Answer:

$12

Step-by-step explanation:

well 12 * 10 = 120 so 12 is 1 ticket

The angle m∠J  in the right angle triangle is 58.1 degrees.

One of the angle of a right tangle triangle is 90 degrees. The sum of

angles in a triangle is 180 degrees.

Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.

Hence,

tan ∠J = opposite / adjacent

tan ∠J = 15.1 / 9.4

∠J = tan⁻¹ 1.60638297872

∠J = 58.0909229196

Therefore,

m∠J = 58.1 degrees

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Answer:

graph y = 2/5 x - 3

shade everything bellow the line

Step-by-step explanation:

y <= 2/5 x - 3

graph y = 2/5 x - 3

shade everything bellow the line

We have the expression:

The first statement that is true about this expression is:

6a and 5a are like terms.

This is because like terms are terms that have the same variable or variables. In this case, 6a and 5a even though they have different coefficients (6 and 5) are like terms because they have the same variable "a".

The next statement that is true about the expression is:

2b is a term.

A term in an expression is each of the elements of the expression. For example, in the expression 10x+4y, 10x and 4y are terms.

And in the case of the expression we have 2b, 6a, 9 and 5a are all terms.

Thus, yes, 2b is a term.

The final statement that is true is:

9 is a constant.

This is because the term "9" does not have a variable, so it is called a constant.

The complete question is

find the slope of the tangent line and the equation of the tangent line at the given point, \(x^2y-5xy^2\)\(+6=0\) at the point (3,1).

Answer:

Tangent  = 1/23 , equation of tangent  = 23y - x = 20

Step-by-step explanation:

We are given the equation

\(x^2y-5xy^2\)\(+6=0\)

upon differentiation the given function we get

d (\(x^2y-5xy^2\)\(+6=0\)) /dt

= \(2xy +x^2dy/dx - 5y^2 -10xy dy/dx =0\)

upon substituting x=3 ,y=1 we will get

dy/dx = 1/23

now the equation of the tangent will be

y-1 = 1/23 (x-3)

23 (y-1) = x- 3

23y - 23 = x -3

23y - x = 20

The maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.

So, the minimum and maximum values when x are -1 and 3:

(1) When x = -1:

(2) When x = 3:

Therefore, the maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.

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Answer:

12) $540 donated

13) 96 miles in the past 2 weeks

14) $160 altogether

Answer:

12) 540

13)96

14)160

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It is C because you get the equivalent from the t and that t is the number 1 so 15×1 is 15

The solution is Option D.

The equation is d = ( 1/15 ) t

What is Speed?

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of Kiran be represented as = s

Let the distance traveled by Kiran be = d

Let the time taken by Kiran to travel d distance be = t

Now , the value of d = 1 mile

The time taken by Kiran t = 15 minutes

So , the speed of Kiran s is given by the formula

Speed = Distance / Time

Substituting the values in the equation , we get

s = d/t

s = 1 / 15 miles / minute

So , the speed is 1/15 miles / minute

Now , the equation to represent the distance d Kiran walks in t minutes is given by

Distance d = Speed s x Time t

d = ( 1/15 ) t

Therefore , the value of d = ( 1/15 ) t

Hence , The equation is d = ( 1/15 ) t

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Answer:2: 95/215, 3: 95/580, 4: 210/330 5: 365/580

Step-by-step explanation:probability=outcome in question/the total number in the given category

Answer:

y= 3/7x + 5 6/7

Step-by-step explanation:

6-3/5--2 = 3/7

y=3/7x+b

6=1/7+b

b=5 6/7

A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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Answer:

False

Step-by-step explanation:

Only six states have two syllables in their name.

No, only six states have at least two syllables.

Here,

We have to check the given statement '' All state names have at least two syllables'' is true or false.

What are states which have at least two syllables?

There are only 6 states have at least two syllables.

1. Georgia.

2. Kansas.

3. New York.

4. Texas.

5. Utah.

6. Vermont.

Now,

There are only 6 states have at least two syllables.

Hence,

The given statement '' All state names have at least two syllables'' is false.

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Answer:

Step-by-step explanation:

If A is 170 less than B, than the equation for that is:

A = B - 170 (1) where the word "is" means equals and less than is subtraction.

If the total of A + B is 1520, then

A + B = 1520 (2). Sub equation (1) into equation (2):

(B - 170) + B = 1520 and

2B - 170 = 1520 and

2B = 1690 so

B = 845. Building B is 845 feet tall and Building A is

A = 845 - 170 (this is equation (1) with the height of B subbed in) so

A = 675 feet

675 + 845 should equal 1520 according to our equation. And of course it does.

Answer: 675 + 845 should equal 1520 according to our equation. And of course it does.

Answer:

BE = 102 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other , so

DE = EB , that is

- 8x + 14 = 3 - 9x (add 9x to both sides )

x + 14 = 3 ( subtract 14 from both sides )

x = - 11

Then

BE = 3 - 9x = 3 - 9(- 11) = 3 + 99 = 102 units

Answer:

A

Step-by-step explanation:I've took the test

The annual interest rate is 7.5%.

What is Simple interest?

Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.

The formula for simple interest is:

I = P × r × t

where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.

In this case, we know I = $562.50, P = $1500, and t = 5 years.

we ca substitute values into the formula,

562.50 = 1500× r ×5

Simplifying, we get:

r = 562.50 / (1500 ×5)

r = 0.075

r = 7.5%

Therefore, the annual interest rate is 7.5%.

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Answer:

\(x - 3 = 13 \\ \\ x = 13 + 3 \\ \\ x = 16\)

-3 goes to other side and changes into +3

Answer:

x=−44

Step-by-step explanation:

Rewrite the equation as

−x11+43=47.−x11+43=47

Move all terms not containing

x

to the right side of the equation.

−x11=4

Multiply both sides of the equation by

−11.−11(−x11)=−11⋅4

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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