factor the trinomial 2xsquared + 5x -42

The exponential function to model the predicted value of Bruce's investment account is

y = 6225 * 2^x.

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

here, we have,

we know that,

An exponential function is written in the form - y=a*(b)^x

Here, y is the function, a is the base value b is the rate and x is time period.

now, we have,

from the given information, we get,

This equation uses the initial value of the account (6225)

and the base of the exponent (2) representing the account will double in value every decade.

if, we have,

the predicted value of Bruce's investment account is y.

time period is, x decades after starting the account.

So, the exponential equation will be -

y = 6225 * 2^x.

Therefore, the exponential equation is .

y = 6225 * 2^x.

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In positive exponents, the simplified form of the above polynomial is s⁷/t¹¹.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here,

=4s⁵*t⁻⁷/-2s⁻²*-2t⁴

=s⁷/t¹¹

The simplified form of given polynomial is s⁷/t¹¹ in positive exponents.

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To find the values of b and c, we can use the quadratic formula:

[tex]x = (-b ± \sqrt{ (b^2 - 4ac)}) / 2a[/tex] which will give us the value B = -6 & C = -4

A quadratic equation is a second-order polynomial equation in one variable using the formula [tex]x = ax2 + bx + c = 0[/tex] and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

So the equation that she get is [tex]x^{2} -6x-4[/tex]

this means that x=3+√13 or 3-√13

which also equals to x=3+√13 & x-3-√13=0 and

x=3-√13

x-3+√13=0

which if you try to find the quadratic equation for this. you need to do it by this

(x-3+√13)(x-3-√13)

which will get you

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It will cost $4 for 45 minutes and for 2 hours it will cost $8. If parked for 3 to 4 hours it will cost $16 for garage at BWI Airport.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

Graphs can be used to determine the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis because the term "domain" refers to the set of potential input values. The possible output values that make up the range are shown on y-axis.

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The equation which describes the nth term for the sequence 3/5,1/5,1/15,1/45,\cdots2 is  an = 3/5 (1/3)n-1 , which is option C.

We use the formula an=a1+(n−1)d an = a1 + (n−1)d , to calculate the nth term of a given sequence. The 'n' here  represents a number.

Using the nth term we can any number on the sequence which allows us to locate any term in a series.

By substituting different values for the term number, we can create a series utilizing the nth term (n).

To find the tenth term we use the sequence formula and substitute a random number in place of n.

Example if we need to find the first 50 term then we will substitute n as 50.

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Therefore , the solution of the given problem of function comes out to be 4 log2  + 3/4 is the are required.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=>  f(x) = x.2ˣ

=>A = [tex]\int\limits^2_{-1} x.2^{x}[/tex]dx

=> A = [tex]2^{x} \int\limits^2_{-1} x. + x\int\limits^2_{-1} 2^{x}[/tex]

=>  [ xlog2 + x²/2 +  x²log2 ]₋₁²

=>  log2 + 3/4 + 3log2

=> 4 log2  + 3/4

Therefore , the solution of the given problem of function comes out to be 4 log2  + 3/4 is the are required.

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Answer:

The answer is D) 5, the number of eggs on the charts never exceeds that number.

We can solve this equation using the distributive property. First, we will use the distributive property to multiply the 3y by 2.

The distributive property is a mathematical rule that allows you to multiply a single number by a group of numbers by multiplying the single number by each number in the group individually. This rule can be expressed in two ways. The first way is a(b + c) = ab + ac. The second way is a(b - c) = ab - ac.

This will give us 2x * 3y = 2(3y). Then, we will subtract 6 from both sides of the equation, which gives us 2x * 3y - 6 = 2(3y) - 6. We can then divide both sides of the equation by 6, which gives us 2x * 3y / 6 = 2(3y) / 6. Finally, we can divide both sides of the equation by 3y, which gives us 2x = -2. Therefore, the solution to 2x 3y = -6 is 2x = -2.

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The value of p for the given logarithmic function  -log(2.1x10^12) is, -8.678  

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function [tex]x = a^y[/tex].

Formulae for logarithmic function are,

LogAB = LogA + LogB         .................(i)

Logₐaᵇ = b                             ................(ii)

Given expression,

p = -log(2.1x10^12)

p = -log2.1 + log10^12  (by applying formula i )

p = -log2.1 + 12             (by applying formula ii )

p =  -(-3.322) + 12        (log2.1 = -3.322)

p =  -8.678

Hence, the value of p is equal to -8.678

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The amount of cherries bought by the Harrison is 62.5 pounds.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

The amount of cherries bought by the Harrison should be more than the cherries bought by the Liam which is 5/8. Thus, The amount of cherries bought by the Harrison is more than the 5/8 or 62.5 pounds of cherries percent.

The cherries bought by the Liam is 5/8 pounds

The cherries bought by the Harrison is more than the Liam.

As in the problem the number of cherries bought Harrison (let) should be more than the cherries bought by the Liam (let ). Therefore,

H > L

As we know that the number of cherries bought by the Liam is 5/8 pounds. Keep the value of  in the above equation, we get,

H > 5/8

This equation can be rewritten in the percentile form as,

h > (5/8) * 100 %

h > (5/2) * 25 %

h > 62.5 %

Hence, The amount of cherries bought by the Harrison is more than 5/8 pounds or 62.5 pounds of cherries percent.

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The area of quadrilateral BEFD is 15.32units²

Let the area of  ∆ABC be A

Let the area of ∆AFE be X

Let the area of ∆AFC be Y

Let the area of ∆DFC be Z

Using Ladder theorem:

1/A + 1/Y = 1/(X+Y) + 1/(Y+Z)

Since X = 4, Y = 9 and Z = 7, we have:

1/A + 1/9 = 1/(4+9) + 1/(9+7)

1/A + 1/9 = 1/13 + 1/16

1/A = 1/13 + 1/16 - 1/9

1/A = 53/1872

A = 1872/53

A = 35.32

area of  ∆ABC = area of ∆AFE + area of ∆AFC + area of ∆DFC + area of quadrilateral BEFD

35.32 = 4 + 9 + 7  + area of quadrilateral BEFD

35.32 = 20 + area of quadrilateral BEFD

area of quadrilateral BEFD = 35.32 - 20

area of quadrilateral BEFD = 15.32unit²

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Answer:

L' = (-1,2)

M' = (1,2)

L'M' = 2

The slope of the original segment and dilated segment are both zero

Step-by-step explanation: just did it on edge!

Answer:

C. 94

Step-by-step explanation:

|A| = [tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]

det(A) = a * [tex]\left[\begin{array}{ccc}e&f\\h&i\\\end{array}\right][/tex] - b * [tex]\left[\begin{array}{ccc}d&f\\g&i\\\end{array}\right][/tex] + c * [tex]\left[\begin{array}{ccc}d&e\\g&h\\\end{array}\right][/tex]

OR

det(A) = aei - afh - bdi + bfg + cdh - ceg

|A| = [tex]\left[\begin{array}{ccc}-2&-2&-5\\2&7&-3\\8&9&9\end{array}\right][/tex]

det(A) = -2 * [tex]\left[\begin{array}{ccc}7&-3\\9&9\\\end{array}\right][/tex]  - (-2) * [tex]\left[\begin{array}{ccc}2&-3\\8&9\\\end{array}\right][/tex] + (-5) * [tex]\left[\begin{array}{ccc}2&7\\8&9\\\end{array}\right][/tex]

OR

det(A) = (-2)(7)(9) - (-2)(-3)(9) - (-2)(2)(9) + (-2)(-3)(8) + (-5)(2)(9) - (-5)(7)(8)

det(A) = 94

Answer:

216

Step-by-step explanation:

first multiply 4by6 to get that area we will call that a

then 12 by 20 to get that area we will call that b

the shaded area is a's area minus B's area

(12*20)-(4*6)

240-24

216

Answer:

216 in²

Step-by-step explanation:

(12)(20) - (4)(6) = 240 - 24 = 216

The Quotient of Powers was used to simplify this expression is By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents

We have given that,

2 to the fifth power, over 8 = 22

The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form or to rewriting the same algebraic expression with no like terms and in a compact manner.

By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.

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Answer:

26 - 11√5

Step-by-step explanation:

(4√5-3)(√5-2)

= 4√5 (√5-2) -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3√5 -3 ⋅ -2

= 26 - 11√5

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Answer: C= 30

Step-by-step explanation:

A^2+B^2=C^2

C= √(B²+A²)

C= √(18²+24²)

C=30

The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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Solving provided question, we can say that the given linear equation is  y = -2x + 4 and -x -x +3(-2x + 4 ) + 9 = x = 7/3

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

the given linear equation is

y = -2x + 4 and -x +3y = -9

now,

-x +3(-2x + 4 ) + 9

-x - 6x - 12 +9 = 0

-7x = -3

x = 7/3

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Answer:

Mr. Hurd received a discount of 57% on the trampoline. The cost of the trampoline was $699.99 and he got it for $429.99, resulting in a discount of 57% when rounded to the nearest percent.

Step-by-step explanation:

The triangle given is similar to using SAS. Sharon is wrong and the value of KL is 14.

there are three types of triangle similarity criteria known. those are

Given, two Triangle ΔGHI and ΔKLJ. Also, we can see in the figure That ratio of there two known sides is equal and they both have a similar angle.

the ratio of two sides of given triangles

4/8 and 5/10

hence, the ratio of both the side is equal that is 1/2

from the SAS theorem:

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

thus, given triangles are similar.

Since the Ratio of all three sides would be equal.

hence, HI / KL = 1/2

the third side of the triangle JKL, KL is 14.

Therefore, The given triangle is comparable to using SAS. Sharon is mistaken; The value of KL is 14.

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According to the following graph, we have identified that if the demand is for 35 units then the predicted price per unit is $27.

The term graph in math is defined as pictorial representation of algebraic equation.

Here we have given the following graph and here  we also know that the scatter plot shows a regression line of units demanded and price.

Here we need to know the definition of regression line, which means the relationship between two variables. And it is applied in scenarios where the change in the value of the independent variable causes changes in the value of the dependent variable.

Based on these definition, here we have the relationship between the units demanded and the price of those units.

Now, by looking into the given graph, we have identified that if the demand is for 35 units, then the units price is $27.

Therefore, option (c) is correct.

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The XYZ axis is called as X-axis, Y-axis, and Z-axis, respectively.

The term axis in math is defined as  a line with respect to which a curve or figure is drawn, measured, rotated, etc.

Here we have given that XYZ axis, in math are no standard names for the coordinates in the three axes

Based on these the coordinates are often denoted by the letters X, Y, and Z, or x, y, and z.

And these axes may then be referred to as the X-axis, Y-axis, and Z-axis, respectively.

Here in the graph x-axis and y-axis represent the first two dimensions where as the z-axis, the third dimension. Which is also defines the x and y denote width and height and the z denotes depth.

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1) The best approximation for the area of this figure is 21+14. 5π units².

2) The total area of the closed figure is 10.5 + 19.63 = 30.13 square units.

3) This is a hexagon with vertices at the specified coordinates on a coordinate plane.

1) The best approximation for the area of this figure is 21 + 14.5π units². The area of a semicircle with a radius of 7 is 14.5π units², and the two segments form a rectangle with an area of 21 units². Adding these two values together gives 21 + 14.5π units².

2) This closed figure can be divided into two parts: a triangle and a quarter of a circle. The area of the triangle can be found using the formula for the area of a triangle (base times height divided by 2). The base of the triangle is the length of the segment from negative 5 comma negative 2 to negative 5 comma 1, which is 3 units. The height of the triangle is the length of the segment from negative 5 comma negative 2 to 2 comma 1, which is 7 units. So the area of the triangle is (3*7)/2 = 10.5 square units.

The area of the quarter of a circle can be found using the formula for the area of a circle (pi times the radius squared). The radius of the semicircle is the length of the segment from 2 comma 1 to negative 5 comma negative 2, which is 5 units. So the area of the quarter of the circle is (pi*5²)/4 = 19.63 square units.

So the total area of the closed figure is 10.5 + 19.63 = 30.13 square units.

3) A hexagon is a polygon with six sides and six angles. In this case, the hexagon is placed on a coordinate plane, with each of its vertices (or corners) located at specific x and y coordinates.

The coordinates provided are: (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2). These coordinates correspond to six points on the plane, and the hexagon is formed by connecting these points in the specified order.

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the statement that "you walk at a constant rate" tells us that the relationship is indeed proportional, namely, there's a value in the input that's consistent or common yielding the output.

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, for the distance "from school" table, let's use those two points in that table

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{0.5})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{1.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1.5}-\stackrel{y1}{0.5}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{10}}}\implies \cfrac{1}{20}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0.5}=\stackrel{m}{\cfrac{1}{20}}(x-\stackrel{x_1}{10})\implies y-0.5=\cfrac{1}{20}x-\cfrac{1}{2} \\\\\\ y=\cfrac{1}{20}x-\cfrac{1}{2}+0.5\implies y=\cfrac{1}{20}x-\cfrac{1}{2}+\cfrac{1}{2}\implies \boxed{y=\cfrac{1}{20}x}[/tex]

The order from greatest to least is -3/8> -2/5>-0.44>-0.5

To compare all the numbers, we first convert the numbers to their fractional equivalent.

Therefore, -0.44= -44/100

And -0.5= -5/10

Now, we covert all the numbers to get the same denominator in all the numbers, therefore, let the denominator be 100

Therefore, we multiply -3/8 with 12.5 in both numerator and denominator to get, -37.5/100

Then, we multiply -2/5 with 20 in both numerator and denominator to get, -40/100

and, we multiply -5/10 with 10 in both numerator and denominator to get -50/100

Therefore, with these resultant value we can say that, -37.5/100> -40/100 >-44/100> -50/100

Thus, -3/8> -2/5>-0.44>-0.5

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The upper bound of a is 3.13.

The smallest amount that would round up to the following anticipated value is the upper bound.

The number of digits that contribute to a value's level of precision is known as significant figures and is typically found in measurements. As soon as a digit is non-zero, we begin calculating significant numbers.

Given in the question

v = 37. 6

u = 11. 3

t = 8. 4

To find:- a = (v - u)/t

Solution: -

Since finding the upper boundary for a

Upper boundary =  (upper v - lower u) / (lowest t)

So putting the value values of v, u, t in we get the value

a = (37.6 - 11.3) / 8.4

Therefore the value of a = 3.13

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first expression = 1×2, 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2 and second expression = 1×9

In mathematics, an expression is a statement that represent the method of mathematical operation in a symbolic form. An expression is developed based on numerical terms or both numerical and variable terms along with operator or signs.

it is stated that one factor is a two-digit number between one and ten.

the multiplication expression can be 1×2 , 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2

In the next, the multiplication expression for 2nd statement:

one factor is a two-digit number between one and ten and their product is greater than 8 and less than 10

1×9

the above is greater than 8 and less than 10.

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Answer:legs

Step-by-step explanation: I cannot give a explanation since it is simply math, anything adjacent to a right angle is called a leg.

Answer: the legs? or opposite and hypotenuse.

Step-by-step explanation:

a) The coordinates of the center is (2 ,-3)

b) The radius of the circle is 3

c) The diameter of the circle is twice the radius = 2(3) = 6

Now, According to the question:

a) The equation of a circle is given by

[tex](x-h)^2 + (y-k)^2 =r^2[/tex]

where (h, k) is the center and r is the radius

(x - 2)² + (y+3)² = 9

(x - 2)² + (y- -3)² = 3^2

The coordinates of the center is (2 ,-3)

b) The radius of the circle is 3

c) The diameter of the circle is twice the radius = 2(3) = 6

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The complete question is this:

For the circle with equation (x - 2)² + (y+3)² = 9 , answer each question.

(a) What are the coordinates of the center?

(b) What are the radius of the circle?

(c) What is the diameter of the circle?

15%

If you take fiction plus non fiction it equals 10k books. 1500/10000 is 15%