I have a question, what is 71.5 - 28.742

An exponential function can represent growth or decay

Graph (a) represents an exponential decay

From the graphs, we have the following highlights

The first highlight is the behavior of an exponential decay

Hence, graph (a) represents an exponential decay

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Answer:

the first graph

Step-by-step explanation:

cuz i took da test

The solution (X = 8, Y = 16) represents a minimum because the second partial derivatives are both positive.

The quadratic equation's roots 32

+6x+8=0 utilises the quadratic formula to determine. x = is the quadratic formula.

where the quadratic equation's coefficients are a, b, and c. Here, an equals 1, b equals 6, and c equals 8. We obtain the quadratic formula's result by entering these values: x =

x = (-6 ± √(36 - 32)) 2 x = (-6 to 4) 2 x = (-6 to 2) 2 x = (-3 to 1) 1 x = (-2 to 4)

Generally, any quadratic equation of the form may be solved using the quadratic formula to get the roots.

Whereas a, b, and c are real numbers, + bx + c=0. One effective method for tackling a wide range of physics and maths issues is the quadratic formula.

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The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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The required integer to represent the loss on each play is -5m-5.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

During a football game, a team lost 10 yards on its first play and 20 yards on its third play.

To write an integer to represent the loss on each play:

Use -10 to represent losing 10 yards.

Use -20 to represent losing 20 yards.

Add both of the expression,

(-10) + (-20)

= -10 -20.

Whenever we add two negative values, the sum is negative.

(-10) + (-20) = -10 -20 = - 30

Let m be the required integer.

So, -5m-5  is the loss on each play.

Where m is the number of play.

Therefore, the required integer is -5m-5.

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Answer:

\(Solution,\\Area(A)=441m^{2} \\Now,\\Length=\sqrt{Area} \\Length=\sqrt{441m^{2} } \\Length=21m\)

Step-by-step explanation:

Hope it will help you a lot.

Answer:

20

Step-by-step explanation:

the area of a triangle is 1/2 base times hight (a=1/2bh)

Answer:

20 cm squared

Step-by-step explanation:

The formula is Area equals (base times height) divided by 2, so (5*8)/2=20

We can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

The function f(x) = -x³ + 6x² -10x + 4 is a polynomial function, which means that it is defined for all real values of x. Unlike some functions (such as square roots or logarithms) which have restrictions on their input values, a polynomial function can take any real number as an input.

To express the domain of the function in interval notation, we use the notation (-∞, ∞), which represents all real numbers. The symbol ∞ stands for infinity, and the open interval notation with the parentheses indicates that there are no specific endpoints for the domain; it extends indefinitely in both directions along the real number line.

Therefore, we can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.

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Answer:

Difference in weight is 24 once

Step-by-step explanation:

got it right

Answer:

x intercept: (-8,0)

y intercept: (0,2)

The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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Functions can either be discrete or continuous.

The function is given as:

\(\mathbf{y = 35x}\)

Where x represents the number of blankets

x can only take whole numbers (i.e 0, 1, 2....)

A discrete function is such that can only non-decimal values.

Hence, the function is discrete

(b) The domain

In (a), we listed the values of x to be: (0,1,2...)

This means that, the domain is: \(\mathbf{[0,\infty)}\)

(c) The range

When x = 0, we have:

\(\mathbf{y = 35x}\)

\(\mathbf{y = 35 \times 0 = 0}\)

This means that, the range is: \(\mathbf{[0,\infty)}\)

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Point located at each location: 1) A  2) I 3) W 4) H 5) X 6) G 7) J 8) N 9) U 10) M 11). Ordered pairs are:  B(2,8) 12) E(0,0) 13) T(3,3) 14) Q(8,7)  15) Y(7,6) 16) R( 9,8) 17)  F(9,0) 18) S(3,6) 19) C(6,7)

Describe Ordered pair?

An ordered pair is a pair of mathematical object elements, such as numbers or other mathematical elements, where the order in which the object elements are listed is important. The ordered pair is usually written in the form (a, b), where 'a' represents the first element or coordinate, and 'b' represents the second element or coordinate.

In the context of the Cartesian coordinate system, an ordered pair represents a point in two-dimensional space, where the first element or coordinate represents the horizontal position on the x-axis and the second element or coordinate represents the vertical position on the y-axis. The order of the elements in an ordered pair is crucial because (a, b) is different from (b, a) and represents a different point in two-dimensional space.

Point located at each location is:

1) A

2) I

3) W

4) H

5) X

6) G

7) J

8) N

9) U

10) M

The ordered pair for given points is:

11) B(2,8)

12) E(0,0)

13) T(3,3)

14) Q(8,7)

15) Y(7,6)

16) R( 9,8)

17)  F(9,0)

18) S(3,6)

19) C(6,7)

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Answer:

a

Step-by-step explanation:

Answer:

The inequality representation is :   x + y ≥ $400

Step-by-step explanation:

Inequality is the comparison and boundary for two non equal values. So inequality compares the non equal values.

As the owner wants to make $400 and sets boundary that;

                   Least amount to make = $400

                   Highest amount to make= infinite

This introduces relation in inequality as $400 or greater than $400.

The money made is counted combine from child tickets and adult tickets. If x is the made made through child tickets and y is from the adult then,  

                                           x + y ≥ $400

Answer:

Step-by-step explanation:

as much as I think I know this I don't I just need the points

The required value of h, representing the height of the three-dimensional rectangle, is 12.

The diagonal of a three-dimensional rectangle is defined by the equation d² = x² + y² + h². To solve for h, we can rearrange the equation as follows:

h² = d² - x² - y²

Given the values d = 13, x = 3, and y = 4, we can substitute them into the equation:

h² = 13² - 3² - 4²

h² = 169 - 9 - 16

h² = 144

Taking the square root of both sides, we find:

h = 12

Therefore, the value of h, representing the height of the three-dimensional rectangle, is 12.

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Answer:

-3

Step-by-step explanation:

For a 2 by 2 matrices such as B =  [a b c d], the determinant is expressed as;

ad - bc

Given the matrices

[A] = [5 -4 3 -3]

Determinant of A  = 5 (-3) - -4(3) (if you compare with the original matrices)

Determinant of A  = -15 + 12

Determinant of A  =-3

Hence the Determinant of A  is -3

Answer:

1102.85

Step-by-step explanation:

Bank:

beginning balance - outstanding checks + deposits in transit

1011.18 - 225.50 - 388.10 + 705.27 = 1102.85

Checkbook:

beginning balance + account earned - service charge

1024.34 + 88.51 - 10.00 = 1102.85

Answer:

  (i)  (x√x)/3 -(√x)/2

  (ii)  f(x) = x³/27 +3x -5

Step-by-step explanation:

You want the value of the integral in each case. One integral is indefinite, the other has conditions specified.

In each case, the power rule applies:

  \(\displaystyle \int{x^n}\,dx=\dfrac{x^{n+1}}{n+1}\)

The integral can be rewritten as the sum of two integrals involving half powers.

  \(\displaystyle \int{\dfrac{2x-1}{4\sqrt{x}}}\,dx=\dfrac{1}{2}\int{x^{\frac{1}{2}}}\,dx-\dfrac{1}{4}\int{x^{-\frac{1}{2}}}\,dx=\dfrac{x^{\frac{3}{2}}}{2\left(\dfrac{3}{2}\right)}-\dfrac{x^{\frac{1}{2}}}{4\left(\dfrac{1}{2}\right)}\\\\=\boxed{\dfrac{1}{3}x\sqrt{x}-\dfrac{1}{2}\sqrt{x}}\)

You are given the derivative and three conditions:

Together with the integral, the conditions give rise to three equations in the three unknown coefficients.

  \(\displaystyle f(x) = \int{ax^2+b}\,dx=\dfrac{a}{3}x^3+bx+c\)

Then the equations we can write for a, b, c are ...

  f'(3) = 4   ⇒   a(3²) +b = 4

  f(3) = 5   ⇒   (a/3)(3³) +b(3) +c = 5

  f(0) = -5   ⇒   a(0³) +b(0) +c = -5

The last equation gives the value of c = -5, so the remaining equations become ...

  9a +b = 4

  9a +3b = 10

Subtracting the first from the second, we have ...

  (9a +3b) -(9a +b) = (10) -(4)

  2b = 6

  b = 3

Using this in the first equation, we find 'a' to be ...

  9a +3 = 4

  a = 1/9

Then f(x) is ...

  \(\boxed{f(x)=\dfrac{1}{27}x^3+3x-5}\)

Graph C:This graph intersects the x-axis at only one point, so the equation it represents has only one solution. Therefore, the answer is Graph C.

In order to identify which graph has only one solution, we need to understand what it means for an equation to have only one solution. In algebra,

a solution is a value of the variable that makes the equation true. So, if an equation has only one solution, it means that there is only one value of the variable that makes the equation true.

There are several ways to determine the number of solutions an equation has, but one common method is to graph the equation and look at the intersection of the graph with the x-axis. If the graph intersects the x-axis at only one point,

then the equation has only one solution. If the graph intersects the x-axis at two or more points, then the equation has two or more solutions. If the graph does not intersect the x-axis at all, then the equation has no solutions.

With this in mind, let's examine each of the given graphs to determine which one has only one solution.

Graph A:This graph intersects the x-axis at two points, so the equation it represents has two solutions.

Graph B:This graph does not intersect the x-axis at all, so the equation it represents has no solutions.

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The area of the polygon is 14 units².

We have,

We can see that,

The polygon has two triangles.

One triangle:

Base = 4 units

Height = 2 units

Area = 1/2 x 4 x 2 = 4 units²

Another triangle.

Base = 4 units

Height = 5 units

Area = 1/2 x 4 x 5 = 10 units²

Now,

Area of the polygon.

= 4 + 10

= 14 units²

Thus,

The area of the polygon is 14 units².

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Answer:

$147

Step-by-step explanation:

she has 6 Gran children

Spends $24.50 on each

on six children $24.50. multiplied by 6

Answer:

Step-by-step explanation:

(a) To find the N-intercept, we set t to 0 in the equation N = -0.3t + 250:

N = -0.3(0) + 250

N = 250

Therefore, the N-intercept is (0, 250).

(b) The N-intercept is the point on the graph where the tuition is $0 and represents the number of students who would enroll in the basketball camp if it were free. In this case, if the tuition was $0, 250 students would enroll in the basketball camp.

(c) To find the t-intercept, we set N to 0 in the equation N = -0.3t + 250 and solve for t:

0 = -0.3t + 250

0.3t = 250

t = 250/0.3

t ≈ 833.33

Therefore, the t-intercept is approximately (833.33, 0).

(d) The t-intercept is the point on the graph where the number of students who enroll in the basketball camp is zero and represents the tuition that would need to be charged for no students to enroll. In this case, if the tuition was approximately $833.33, no students would enroll in the basketball camp.

Answer:

= \(\frac{25}{6}\)

Step-by-step explanation:

\(\frac{2}{6\sqrt{8} } \sqrt{2} = \frac{1}{6}\)

\(-(-\frac{18}{\sqrt{-81} } -2) = 4\)

= \(\frac{1}{6} + 4\)

= \(= \frac{1}{6} + \frac{24}{6}\)

= \(\frac{25}{6}\)

Answer:

here you go I hope this helps:)

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

Step-by-step explanation:

Answer:

) A (3, 5)            

(ii) B (-2, 7)          

(iii) C (-5, -8)      

(iv) D (9, -4)

Solution:

When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.

(i) The new position of the point A (3, 5) will be A' (-3, -5)

Answer:

i don't see what are you talking about . honestly

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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The solutions to the matrices are

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

The matrices

The dimensions of the matrices are

A = 2 by 3 i.e 2 rows and 3 columns

B = 3 by 2 i.e 3 rows and 2 columns

For the positions of the matrices, we have

A₂₁ = 4

B₁₂ = 8

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The laplace transform of f(t) is

F (s) =  2/s³ - 2e^{-2s}/s³ + e^{-2s}/s²  + 2e^{-2s}/s  -  3e^{-3s}/s²  + 7e^{-3s}/s

Since f(t) = t² 0 < t < 2,

= t - 1 for 2 < t < 3 and

= 7 for t > 3

Since f(t) has discontinuities at t = 0, t = 2, t = 3, expressing f(t) in terms of unit step, we have

t² = t²u(t) - t²u(t - 2)

t - 1 = (t - 1)u(t - 2) - (t - 1)u(t - 3)

=  (t - 1 + 1 - 1)u(t - 2) - [(t - 1 + 3 - 3)u(t - 3)]

=  (t - 2 + 1)u(t - 2) - [(t - 3 + 2)u(t - 3)]

= (t - 2)u(t - 2) + u(t - 2) - (t - 3)u(t - 3) + 2u(t - 3)

f(t) = 7 = 7u(t - 3)

So, f(t) =  t²u(t) - t²u(t - 2) + (t - 2)u(t - 2) + u(t - 2) - (t - 3)u(t - 3) - 2u(t - 3) +  7u(t - 3)

\(L[u(t - c)f(t - c)}] = e^{-cs} F(s)\)

and \(L[t^{n}] = \frac{n!}{s^{n + 1} }\)

Taking the laplace transform, we have

L{f(t)} = L{t²u(t)} - L{t²u(t - 2)} + L{(t - 2)u(t - 2)} + L{u(t - 2)} - L{(t - 3)u(t - 3)} - L{2u(t - 3)} +  L{7u(t - 3)}

\(F(s) = \frac{2!}{s^{3} } - \frac{e^{-2s} 2!}{s^{3} } + \frac{e^{-2s} 1!}{s^{2} } + \frac{e^{-2s} 1!}{s } - \frac{e^{-3s} 1!}{s^{2} } - \frac{2e^{-3s} 1!}{s^{2} } + \frac{7e^{-3s} 1!}{s} \\= \frac{2!}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{e^{-3s}}{s^{2} } - \frac{2e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

\(F (s) = \frac{2}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{e^{-3s}}{s^{2} } - \frac{2e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

So, the laplace transform of f(t) is \(F (s) = \frac{2}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{3e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

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