100 points
What is the equation for the line in slope-intercept form?

The following triangles are congurent

Yes SAS

Answer:

x=2.3

Step-by-step explanation:

Isosceles triangle means both sides are the same length, triangle is also right meaning you can plug values into Pythagorean theorem ([tex]a^2+b^2=c^2[/tex])

[tex]x^2+x^2=\sqrt{11}^2 \\2x^2=11\\x=\sqrt{\frac{11}{2} } \\x=2.345...\\x=2.3[/tex]

Assuming all my math is right, this is your answer

A 90-degree tan is referred to as infinity. Thus, 90 degrees is the value for tan-1.

It is given that, tan⁻¹∞

We have to find the value of tan⁻¹∞.

Now,

The value of tan⁻¹∞ is π/2.

By using the trigonometric concepts, we can find the value of tan⁻¹∞

we already know that, tan π/2 = ∞

we have to apply tan⁻¹ on both sides

we get,

              tan⁻¹ tan π/2 = tan ∞

                             π/2 = tan⁻¹∞

Hence, the value of tan⁻¹∞ is  π/2.

The trigonometric function "tangent" is represented by the inverse function "inverse tan." The opposing side of the right triangle is divided by the adjacent side, and this relationship is utilized to compute the angle by using the tangent ratio of the angle. All inverse trigonometric functions must be named with the prefix "arc," so inverse tangent is abbreviated as "arctan."

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The expression 2x2 3x 9 area of the garden is a quadratic polynomial.

2x2 contains a power value and 3x contains the constant x and 9 is the integer so this is the Quadratic Polynomial. When a variable term in the polynomial expression has a highest power of 2, the polynomial is said to be quadratic.

Only the exponent of the variable is taken into account when determining a polynomial's degree. It is not taken into account how strong a coefficient or constant term is.

A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0. The roots or zeros of the quadratic equation are the name given to the solutions of such an equation.

The capability to derive a number of significant inferences from the analysis of the discriminant is an additional advantage of this approach.

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Full Question: What is the type of polynomial 2x^2-3x-9 expressing area of the garden?

(a) linear polynomial

(b)Quadratic polynomial

(c) cubic polynomial

(d) constant polynomial​

Order of addends has no bearing on the amount according to the commutative property of addition. 6 added value.

The machine below produces a different number when a number is entered. 9 is produced if 3 is inserted. If 6 is put in, 12 will come out. If 7 is put in, 13 will come out. ​

Order of addends has no bearing on the amount according to the commutative property of addition.

Changing the addends' order does not alter the amount, according to the commutative property of addition.

Every output number, as we can see, adds a value of 6 to the corresponding input number.

3 + 6 = 9.

6 + 6 = 12.

7 + 6 = 13.

The Complete Question.

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The element will be gone in approximately 10.9 minutes.

We can calculate this by using the formula:

Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))

Time = (log(300 / 110)) / (log(1 - 0.054))

Time = 10.9 (rounded to the nearest tenth of a minute)

Therefore, The element will be gone in approximately 10.9 minutes.

A logarithmic function is a mathematical function that relates the logarithm of a number to its argument. The logarithm of a number (base 10) is represented by the log symbol (log 10) and the number being used as the argument. The inverse of this function is an exponential function, which relates the exponential of a number to its argument. Logarithmic functions are often used in mathematics and science to simplify and solve equations involving large exponents. They are also commonly used in finance, engineering, and other fields that involve large numbers.

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Time = (log(Initial mass / Final mass)) / (log(1 - decay rate))

Time = (log(300 / 110)) / (log(1 - 0.054))

Time = 10.9 (rounded to the nearest tenth of a minute)

You can solve 2 equations with 2 variables using calculator in equation mode.

To solve a system of two equations with two variables using a scientific calculator, you can use the following steps (based on CASIO fx-991ES PLUS):

First press the 'mode' button and then press '5' corresponding to equations.

Now press '1' corresponding to a linear equation in two variables of format anX + bnY = cn. Now a matrix appears, each row correspond to each equation. The first column represent the coefficient of X, second column represent the coefficient of Y and third column, the coefficient. Note that the equation should be of the format mentioned before.

Now press '=' to get the solution. On the first press you get X and on second press, you get the value of 'Y'.

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The given expression x² + 2x + 3 is a polynomial.

In the math term expression is defined as an expression that is made up of variables and constants, along with algebraic operations

Here we have given the expression that can be written as x² + 2x + 3 and here we need to identify the given expression is polynomial or not.

AS we all know that the term polynomial means  an expression that consists of variables (or indeterminate), terms, exponents and constants

And we have also know that the polynomials can be identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

And the non-polynomial expressions will be the expressions which contain other operations.

Based on these rule we have identified that the given expression is an polynomial.

Complete Question:

Is the expression x² + 2x + 3 is polynomial or not?

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Answer:

Where is the statement?

Step-by-step explanation:

Un equipo de cuatro personas participó en una carrera de relevo de 400 yardas, lo que significa que cada miembro del equipo corrió una distancia de 400 yardas. El equipo completo completó la carrera en 53.2 segundos. Para calcular el tiempo promedio que cada persona corrió, debemos dividir el tiempo total de la carrera entre el número de personas en el equipo. En este caso, se divide 53.2 segundos entre 4 personas, lo que da un tiempo promedio de 13.3 segundos por persona.

The perimeter of the pentagon is 76 units. The solution is obtained using tangent to circle.

What is tangent to a circle?

A line that touches a circle only once is said to be tangent to it. A point to circle can only have one tangent.

In the figure, the circle is circumscribed by the pentagon.

We are given QZ = 10, YX = 9, WX = 9, UW = 17, and US = 10

VW = WX = 9   (tangent of circle)

So, VU = UW - VW

VU = 17-9= 8

Since, VU and UT are tangents of circle, therefore

UT = 8

US = UT + TS

⇒10 = 8 + TS

⇒TS = 2

Now, TS and SR being tangents, therefore

TS = SR = 2

Also, RQ and QZ are tangents, therefore

RQ = QZ = 10

Similarly, ZY and YX are tangents, therefore

ZY = YX= 9

Thus, Perimeter = SQ + QY + YW + WU + US

⇒Perimeter = SR+ RQ+ QZ+ ZY+ YX+ XW+ UW+ US

⇒Perimeter = 2+ 10+ 10+ 9+ 9+ 9+ 17+ 10

⇒Perimeter = 76 units

Hence, the perimeter of the pentagon is 76 units.

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The length of BD and CD are 15 units and 20 units respectively

By the Angle Bisector Theorem, we have:

BD/DC = AC/BC = 21/28

We can use the Pythagorean Theorem to find AC:

AC² + BC² = AB²

21² + 28² = AB²

AB = 35 units

Now we can use the Angle Bisector Theorem to find BD:

BD/DC = 21/28

BD + DC = AB

BD = (21/49) × AB

BD = (21/49) × 35

BD = 15 units

To find CD, we can use the fact that BD + DC = AB:

CD = AB - BD

CD = 35 - 15

CD = 20 units

Therefore, the length are BD = 15 and CD = 20 units.

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Using the given information, we can calculate the z-score as z = (56.4 - 67.6) / 3.5, which gives us a z-score of -2.3. This means that 2.3 standard deviations below the mean of adult men's heights is the doorway height of 56.4 inches. Since the area under the normal curve from -∞ to -2.3 is 16%, this means that 84% of adult men can fit through the door without bending.

Using the given information and the desired percentage, we can calculate the z-score as z = (x - 67.6) / 3.5, where x is the doorway height. Solving for x, we get x = 57.6 inches. Therefore, a doorway height of 57.6 inches would allow 40% of adult men to fit through without bending.

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The 2 equations will have infinitely many solutions if k equals 10.

Here we have

10x + 5y − (k−5) = 0 and 20x + 10y − k = 0

Since these 2 are already in the standard form

a₁x + b₁y + c₁ = 0

and

a₂x + b₂y + c₂ = 0

we don't have to make any changes to them

According to the law, an equation has infinitely many solutions if

a₁/a₂ = b₁/b₂ = c₁/c₂

here,

a₁ = 10,  b₁ = 5, and c₁ = - k + 5

and,

a₂ = 20, b₂ = 10, and c₂ = - k

Hence, we get

10/20 = 5/10 = ( - k + 5)/(-k)

or, (k - 5)/k = 1/2

or, 2k - 10 = k

or, k = 10

Hence the 2 equations will have infinitely many solutions if k is equal to 10.

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Complete Question

For what value of k does the following pair of linear equations have infinitely many solutions?

10x + 5y − (k−5) = 0 and 20x + 10y − k = 0

For a quadratic of the form px^2 + 40x + 16 to be a perfect square, it must be able to be written in the form (mx + n)^2 for some real numbers m and n.

Expanding (mx + n)^2 gives:

(mx + n)^2 = m^2x^2 + 2mnx + n^2

Comparing this to the given quadratic, we can see that:

m^2 = p

2mn = 40

n^2 = 16

Solving for m and n, we find that:

m = ±√p

n = ±4

Therefore, in order for the quadratic to be a perfect square, the square root of p must be rational, and the value of p must be one of the following:

p = 0, 1, 16

So the possible values of p that make the quadratic a perfect square are 0, 1, 16.

Answer:

Step-by-step explanation:

Set up a ratio: 150/100 = 210/x, or your investment gave you a return of 36% of the 150 you invested.

The investment's initial value is subtracted from its current value, which is then divided by the investment's original value to determine a simple rate of return.

The calculation is as follows in light of the facts above:

The entire sum should be

30 × 15

= $450

= 210 - 6

= $204

The total amount should be because it was sold for $210 plus a $6 commission.

Right now, rate of return is

= (204 - 450) ÷ 204×100

= 16.58%

You spent $150 to purchase 10 shares at a price of 15%, or 36%. You made 54$ after subtracting the commission of $6 and selling it for 210$.

Set up a ratio: 150/100 = 210/x, or your investment gave you a return of 36% of the 150 you invested.

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Answer:

115

Step-by-step explanation:

Answer:

x=83

Step-by-step explanation:

All angles of a triangle add up to 180 so:

53+44=97

180-97=83

Answer:

[tex]\huge\boxed{\sf x = 83\°}[/tex]

Step-by-step explanation:

So,

x + 53 + 44 = 180

x + 97 = 180

x = 180 - 97

[tex]\rule[225]{225}{2}[/tex]

You are a parabola with vertex at (x,y) = (-4,0) and a focus at (x,y) = (-4,3).

A parabola is a mathematical curve that is symmetrical in shape and is often described as an upside-down U. It is a two-dimensional, closed curve and is an important part of conic section geometry. A parabola has a single vertex, which is the highest or lowest point of the parabola. It can also be thought of as the focus of the parabola.

The zeros you have listed are the x-intercepts, which means that your equation is of the form y = ax^2 + bx + c, and your a value is negative because your parabola opens downwards. You can determine the other coefficients by looking at the vertex and focus coordinates.

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Answer:

A fruit bouquet artist charges $1.50 for each piece of fruit in a bouquet, x, plus an additional $17 for the basket and decorations. Customers receive free delivery when their order is over $40.

Step-by-step explanation:

$1.50 represents the cost of each piece of fruit, but we don't know how many fruits are included in the basket, so let x be the number of fruit. That total must be added to the cost of the basket.

If consumers receive free delivery for orders over $40, then 17+1.50x must be greater than $40.

[tex]\it tan60^o=\dfrac{AB}{BC} \Rightarrow \sqrt3=\dfrac{AB}{50} \Rightarrow AB=50\sqrt3\approx50\cdot1,732\approx87\ m[/tex]

The value of the acute angle theta is 59.99 degrees

From the question, we have the following parameters that can be used in our computation:

tan theta equals1.73205

Express teh equation properly

So, we have the following representation

tan theta = 1.73205

Take the arc tan of both sides

theta = tan^-1(1.73205)

Evaluate

theta = 59.99

HEnce, the acute angle is 59.99

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Answer:50

Step-by-step explanation:

The example of a linear equation in two variables in standard form is 3x + 2y = 6

A linear equation in two variables in standard form is of the form:

Ax + By = C

where A, B, and C are constants and x and y are variables.

An example of a linear equation in two variables in standard form is:

3x + 2y = 6

This equation can be written in standard form by first subtracting 6 from both sides,

3x + 2y -6 = 0

and then dividing both sides by the greatest common factor of the coefficients,

(3/1)x + (2/1)y = 6/1

This gives the standard form of the equation:

3x + 2y = 6.

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The value for a in quadratic function a(x-1)²+3 is obtained as a = 2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The vertex of the quadratic function is (1,3).

The line passes through the points (3,5).

The equation is in the form - a(x-1)²+3

It is known that the vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex of the parabola.

So it can be written -

f(x) = a(x-1)² + 3

Substitute the value of (1,3).

f(1) = a(1-1)² + 3 = 3

And for the point (3,5) the equation will be -

f(3) = a(3-1)² + 3 = 5

Set up a system of equations -

a(1-1)² + 3 = 3

a(3-1)² + 3 = 5

Solving for a in these equations -

a = 2

Therefore, the value of a is obtained as 2.

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The difference between the largest 8-digit number and the smallest 7-digit number is 98999999.

The aim is to find the smallest 7-digit and largest 8-digit numbers, and then we need to determine the difference between these two values.

Let's start by finding the smallest 7-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 therefore it  can be used in the highest place value.

Thus, we can create the required 7-digit smallest number with 0 and 1.

Hence, the smallest 7-digit number is 1000000.

Now, we will discover the largest 8-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 8-digit number with the digit 9.

Thus, the largest 8-digit number is 99999999.

Now, find the difference between these two values.

So, we can determine the difference between the smallest 7-digit and the largest 8-digit numbers by subtracting the smallest from the largest.

Thus, we get,

⇒99999999−1000000

⇒98999999

Hence, 98999999 is the difference between the smallest 7-digit and the largest 8-digit numbers.

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For least integer function,

domain :  set of all real numbers

range : set of all integers

We know that the least integer function of any real number p is the least integer which is greater than or equal to the given number p.

The mathematical definition of ceiling function is :

f(x) = minimum { a ∈ Z ; a ≥ x }

where Z is the set of integers.

A least integer function is also known as the ceiling function.

The symbol to represent least integer function is ⌈ ⌉.

We can write least integer function for x as:

⌈x⌉ or ceil (x)

From above definition of ceiling function we can say that the domain of least integer function is the set of all real numbers whereas the range of  is the set of all integers.

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