f(x) = (x + 2)²
What is f(4)?
21
36
13
89

If the rate of decay is proportional to the amount of the substance present at time t, then the amount remaining after 24 hours is 57.7 milligrams

Now we need to find the value of k. We know that the mass decreased by 5% after 6 hours, which means that the amount remaining is 95% of the initial amount. We can substitute these values into our formula and solve for k:

0.95 initial amount = initial amount x (1 - k x initial amount)⁶

Simplifying this equation, we get:

1 - [tex](0.95)^{(1/6)})[/tex] = k x initial amount

Solving for k, we get:

k = (1 - [tex](0.95)^{(1/6)})[/tex]) / initial amount

Now we can use this value of k to find the amount remaining after 24 hours:

Amount remaining = 100 x (1 - k x 100)²⁴

Plugging in the value of k, we get:

Amount remaining = 100 x (1 - (1 - [tex](0.95)^{(1/6)})[/tex] * 100)²⁴

Evaluating this expression, we get:

Amount remaining = 57.7 milligrams

Therefore, after 24 hours, there will be approximately 57.7 milligrams of the radioactive substance remaining.

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The measures of the angles are m∠1 = 74° and m∠2 = 74°.

Given,

[tex]m\angle1 = 2x^\circ[/tex]

[tex]m\angle2 = (x + 69)^\circ[/tex]

We need to find the measure of these angles.

The straight line angle is 180 degrees.

If the angle is split the sum must be equal to 180 degrees.

We have,

[tex]m\angle1 = 2x^\circ[/tex]

[tex]m\angle2 = (x + 69)^\circ[/tex]

The figure is at a straight-line angle.

So we have,

[tex]m\angle1 + m\angle2 = 180^\circ[/tex]

[tex]2x^\circ + (x + 69)^\circ = 180[/tex]

[tex]2x + x + 69 = 180[/tex]

[tex]3x + 69 = 180[/tex]

[tex]3x = 180 - 69[/tex]

[tex]3x = 111[/tex]

[tex]x = 111\div3[/tex]

[tex]x = 37[/tex]

Now,

[tex]- m\angle1[/tex]

[tex]= 2x[/tex]

[tex]=2 \times 37[/tex]

[tex]= 74[/tex]

[tex]- m\angle2[/tex]

[tex]= x + 37[/tex]

[tex]= 37 + 37[/tex]

[tex]= 74[/tex]

Thus the measures of the angles are m∠1 = 74° and m∠2 = 74°.

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Answer:

103.6ft

Step-by-step explanation:

21ft + 18ft + 17.6ft + 29ft + 18

Answer:

SOHCAHTOA

Step-by-step explanation:

Sine=Opposite/hypotenuse

Cosine= Adjacent/hypotenuse

Tangent: Opposite/adjacent

You can use SOHCAHTOA to memorize all the basic functions.

SOH for sine

CAH for cosine

TOA for tangent    

Answer:

Sin= opp/hyp

Cos=adj/hyp

Tan=opp/adj

Step-by-step explanation:

I will assume the candle burns 1 inch per hour  ( you left that out of your post)

Length of candle remaining = 9 - 1 x      where 'x' = hours

     amount of candle remaining =   0   =  9 - x

                                           x = 9 hrs  

If it is NOT one inch per hour ....put that number where '1' is and solve for x

Equations B and C match the tape diagram.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

The tape diagram shows 1 part of 8 and 6 parts of x, with a total of 35.

Equation B, 35 = 8 + 6x, represents the total of 35 as the sum of the 1 part of 8 and 6 parts of x.

Equation C, 6 + 8x = 35, represents the total of 35 as the sum of the 1 part of 6 and 8 times x, which also matches the tape diagram.

Equations A, D, E, and F do not match the tape diagram because they do not accurately represent the given parts and total.

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If y varies directly as x then the value of y is (-15) when x = (-3).

It is given that y varies directly as x. It means y is proportional to x.

y ∝ x

y = kx

{Where k is constant of proportionality.}

It is given that y=25 when x=5. Put x=5 and y=25 in the above equation to find the value of k.

25 = k(5)

Divide both sides by 5.

The value of k is 5.

The relation between x and y is defined by the equation: y = 5x.

Put x = (-3) in the above equation.

Thus, y = 5(-3)

 y = (-15)

Therefore the value of y is (-15) when x = (-3).

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—-------- Correct question format is given below —--------

(Q). If y varies directly as x, and y=25 when x=5, find y when x=(-3).

a) Sienna's page is now [tex]\frac{1}{3}[/tex] full after giving [tex]\frac{1}{3}[/tex] of her cards to Daniel.

b) Daniel can fit all the cards on one page in his binder since his binder page can hold up to 30 cards and he has a total of 70 cards after receiving [tex]\frac{1}{3}[/tex] of Sienna's cards.

a) Sienna's page was [tex]\frac{6}{9}[/tex] full, which can be simplified to [tex]\frac{2}{3}[/tex]. We know that she gave [tex]\frac{1}{3}[/tex] of her cards to Daniel, so the fraction of cards she has left is:

[tex]\frac{2}{3} - \frac{1}{3} =\frac{1}{3}[/tex]

Therefore, Sienna's last page is now [tex]\frac{1}{3}[/tex] full.

b) To determine whether Daniel can fit all the cards on one page in his binder, we need to know how many cards he has and how many cards his binder pages can hold.

Let's assume that Daniel's binder page can hold 30 cards, and he has 2 full pages plus the [tex]\frac{1}{3}[/tex] of Sienna's cards that she gave him, which is approximately 10 cards.

Therefore, he has a total of 2 x 30 + 10 = 70 cards.

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The complete question is:

Sienna also collects baseball cards in a binder just like Daniel's. Her page was 6/9 full, but she gave ⅓ of those cards to Daniel.

a What fraction of Sienna's last page is full now? Use numbers, labeled sket or words to model and solve the problem.

b Can Daniel fit the cards from his first page, his second page, and the cards Sienna gave him all on one page in his binder? Use labeled sketches, numbers or words to show your thinking.

The width is 3………..

………..

The section of the research report that may have the information about the statistical parameter used and the findings of statistical tests is the "Results" and ''Reference" section.

The results section usually comes after the introduction and literature review sections of the research report.

A research report is a document that outlines the results of a study conducted by an individual or a group. The research report is a written record of the study and includes information about the research design, data collection, data analysis, and findings. A research report can be written in different formats, depending on the discipline and audience.

Statistics refers to the collection, analysis, interpretation, presentation, and organization of data. Statistics help researchers to draw conclusions from data and make informed decisions. Statistical tests are used to determine whether the results of a study are statistically significant, which means that the results are unlikely to have occurred by chance. Statistical tests are an essential part of the research process, and the findings of these tests are reported in the results section of a research report.

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The numbers that would make the inequalities given true are 3 (first inequality) and 5 (second inequality).

To begin, an inequality is a mathematical expression that uses symbols such as < less than or > greater than. In the case presented, we need to find two numbers.

Based on this, some possible numbers are:

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Answer:

BC ≈ 17.8 cm

Step-by-step explanation:

An HTML (Hypertext Markup Language) element consists of several parts that work together to define its behavior and appearance on a webpage. The basic structure of an HTML element includes:

Opening tag: The first part of an HTML element is the opening tag, which is enclosed in angle brackets ("<" and ">") and indicates the beginning of the element. It includes the name of the element, such as "p" for a paragraph or "img" for an image.

Attributes: After the name of the element, you can specify one or more attributes that modify the element's behavior or appearance. Attributes consist of a name and a value, separated by an equal sign. For example, the "src" attribute specifies the source URL of an image element.

Content: The content of an HTML element is the information that appears between the opening and closing tags. For example, the content of a paragraph element would be the text that appears within it.

Closing tag: The closing tag is similar to the opening tag but includes a forward slash ("/") before the element name to indicate the end of the element. For example, the closing tag for a paragraph element would be "</p>".

Here's an example of a complete HTML element:

<p class="intro">This is a paragraph element with a class attribute.</p>

In this example, "p" is the name of the element, "class" is an attribute that specifies the CSS class of the element, and "This is a paragraph element with a class attribute." is the content of the element.

By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

We can start by determining the common factor between the two terms in order to factor the phrase 0.15c - 0.072. The common factor in this situation is 0.006, which we may factor out to obtain:

0.15c - 0.072 = 0.006(25c - 12) (25c - 12)

As a result, factoring the expression 0.15c - 0.072 gives 0.006 (25c - 12).

It is possible to utilise this factored form to further simplify calculations or to resolve equations that contain this statement. If we needed to find c in the equation 0.15c - 0.072 = 0, for instance, we could use the factored form to obtain:

0.006(25c - 12) = 0

25c - 12 = 0

c = 12/25

In conclusion, factoring the expression 0.15c - 0.072 involves finding the common factor between the two terms, which is 0.006. By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

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Answer: <PFY and <YFP

Step-by-step explanation:

Answer:

<PFY and <YFP

Step-by-step explanation:

The first four terms of the sequence defined by n+5 are 6, 7, 8, and 9, and the tenth term of the sequence is 15.

To find the first four terms of the sequence defined by n + 5, we simply substitute n = 1, 2, 3, and 4, respectively

When n = 1: 1 + 5 = 6

When n = 2: 2 + 5 = 7

When n = 3: 3 + 5 = 8

When n = 4: 4 + 5 = 9

Therefore, the first four terms of the sequence are 6, 7, 8, and 9.

To find the tenth term of the sequence, we substitute n = 10

When n = 10: 10 + 5 = 15

Therefore, the tenth term of the sequence is 15.

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The newer energy star washing machines uses less water compare to older models is equals to 25%.

Newer Energy Star washing machines use approximately 25% less water than older models.

Energy Star-certified washing machines are designed to use less water.

And energy while still providing the same or better washing performance compared to traditional models.

According to Energy Star, certified models use about 25% less energy and 33% less water than non-certified models.

Therefore, the percent of less water used by newer energy star washing machine than older modals is equals to 25%.

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The points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

The coordinate plane is a two-dimensional space formed by two perpendicular lines called the x-axis and y-axis. The point where the two axes intersect is called the origin. Each point in the plane is identified by a pair of numbers called its coordinates, where the first number represents its position along the x-axis and the second number represents its position along the y-axis. Coordinates are typically written as (x, y), with the x-coordinate listed first and the y-coordinate listed second. The coordinate plane is commonly used in mathematics to graph and analyze equations, functions, and geometric shapes.

Let x be the number of bags of popcorn and y be the number of bags of cotton candy. Then the cost constraint is:

3x + 7y ≤ 56

We also have the constraint that Chris needs at least 7 bags of popcorn:

x ≥ 7

To graph these constraints, we can rewrite them in slope-intercept form:

y ≤ (-3/7)x + 8

x ≥ 7

The first inequality has a slope of -3/7 and a y-intercept of 8, and the second inequality is a vertical line at x = 7.

To plot the points that are part of the solution set, we can simply plug them into the two inequalities and see if they are true. The points that satisfy both inequalities are part of the solution set.

(3, 7) satisfies both inequalities:

7 ≤ (-3/7)(3) + 8

3 ≥ 7

(2, 2) does not satisfy the first inequality:

2(7) > 3(2) + 7

(8, 1) satisfies both inequalities:

1 ≤ (-3/7)(8) + 8

8 ≥ 7

(10, 2) satisfies both inequalities:

2 ≤ (-3/7)(10) + 8

10 ≥ 7

(5, 5) does not satisfy the first inequality:

5(7) > 3(5) + 7

Therefore, the points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

To graph these on the coordinate plane, we can plot the vertical line x=7 and the line y= (-3/7)x + 8, and then shade in the feasible region below the line and to the right of the vertical line.

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Answer:

100 - 25π cm²

Step-by-step explanation:

Area of Square = 10 × 10 = 100 cm²

Area of Circle = πr² = r² × π = 25π cm²

Area of Shaded Regions = 100 - 25π cm²

Answer:

B. Compound event

Step-by-step explanation:

An event where two or more things happen at the same time is called a compound event.

Thus, the cost of each balcony tickets and general admission floor tickets are 24 and 55.

Equations linear in two variables: It is a mathematical formula with the notation ax+by+c=0. X and Y are variables, whereas a, b, and c are real numbers. It is possible to state that a and b do not equal zero. When the same integer is added towards both sides, multiplied by the same number, or divided by the same number, a linear equation can be solved. X and Y stand for two-variable linear equations.

For the given query:

Let 'x' be the price of each balcony tickets.

Let 'y' be the price of each floor tickets.

Then, system of linear equation are:

27x + 82y = 3453 ...eq1

90x + 93y = 7182 ..eq2

Using substitution method:

27x + 82y = 3453

x = (3453 - 82y)/27  ...Put in eq 2

90( (3453 - 82y)/27 ) + 93y = 7182

10/3 *(3453 - 82y)) + 93y = 7182

10 *(3453 - 82y)) + 279y = 21546

34530 - 820y + 279y = 21546

541y = 12984

y = 24

Now,

x = (3453 - 82y)/27

x = (3453 - 82(24))/27

x = 55

Thus, the cost of each balcony tickets and general admission floor tickets are 24 and 55.

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Answer:

1/10

Step-by-step explanation:

Just 6 and 16, so there are 2/20 numbers simplified is 1/10.

:)

The number of days that the race lasted is five days and the correct formula is 1/16(4^5 - 1)/4 - 1. Option B

Geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed non-zero number called the common ratio. In other words, each term is a constant multiple of the term that precedes it. The first term in the sequence is denoted by "a" and the common ratio is denoted by "r".

The common difference of the progression is;

1/4/1/16 = 1/4 * 16/1 = 4

Using the formula

a(r^n -1)/r - 1

1/16(4^5 - 1)/4 - 1

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Alpha value of 0.80 would cause exponential smoothing to respond the most slowly to forecast errors.

What is exponential smoothing?

Exponential smoothing is a method for estimating time series data in statistics. This method of forecasting is widely used in the estimation of the business cycle and other data with a linear trend. Exponential smoothing predicts the next time period by combining the most recent value of the series with a fraction of the prior forecast. The quantity of smoothing is determined by the alpha parameter.

Exponential smoothing can be described as follows:

[tex]$$S_t=\alpha y_t + (1-\alpha)S_{t-1}$$[/tex]

Where

S_t is the predicted value for time t,

α is the smoothing constanty is the actual value for time t−1

(1−α)S_{t−1} is the forecasted value for time t−1

Based on the equation, it is evident that the larger the value of α, the greater the contribution of the current period to the forecast. In the same way, the lower the value of α, the less significant the role of the current period in the forecast. As a result, it can be concluded that the smaller the value of α, the more slowly exponential smoothing reacts to forecast errors.

Therefore, the answer to this question is alpha value of 0.80 would cause exponential smoothing to respond the most slowly to forecast errors.

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The area of this triangle was 18 square units.

Let's use the given information to set up some equations. We are told that the sum of the lengths of the three sides of the triangle is 18. Let's call the lengths of the two shorter sides a and b, and the length of the hypotenuse c. Then, we have a + b + c = 18.

We are also told that the sum of the squares of the lengths of the three sides is 128. Using the Pythagorean theorem, we know that a² + b² = c². So, we can rewrite this equation as a² + b² + c² = 128.

Now we have two equations with three variables. We need to find a way to eliminate one of the variables. We can do this by using the first equation to solve for one of the variables in terms of the other two. Let's solve for c:

c = 18 - a - b

Now we can substitute this expression for c into the second equation:

a² + b² + (18 - a - b)² = 128

Expanding and simplifying, we get:

2a² + 2b² - 36a - 36b + 144 = 0

Dividing by 2, we get:

a² + b² - 18a - 18b + 72 = 0

We can rewrite this equation as:

(a² - 18a + 81) + (b² - 18b + 81) = 38

Completing the square, we get:

(a - 9)² + (b - 9)² = 5

So we have:

(a - 9)² = 1

(b - 9)² = 1

This gives us four possible solutions:

a = 8, b = 10, c = 18 - a - b = 0 (not possible)

a = 10, b = 8, c = 18 - a - b = 0 (not possible)

a = 9, b = 9, c = 0 (not possible)

a = b = c = 6√2

The only valid solution is the last one, where all three sides have the same length of 6√2. To find the area of the triangle, we can use the formula:

Area = (base x height)/2

Since this is a right triangle, one of the sides is the base and the other is the height. So we can choose any two sides to use as the base and height. Let's choose a and b:

Area = (a x b)/2

Substituting the values a = 6√2 and b = 6√2, we get:

Area = (6√2 x 6√2)/2

Area = 36/2

Area = 18

Therefore, the area of the right triangle with sides of length 6√2 is 18 square units.

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Answer:

-5

Step-by-step explanation:

The equation of the first circle is (x + 2)² + (y - 4)² = 16, and the equation of the second circle is x² + y² = 64.

What is equation of circle?

The equation of a circle is a mathematical representation of the geometric shape of a circle. It defines the relationship between the coordinates of the points on the circle and the center of the circle. There are different forms of the equation of a circle, but the most commonly used form is the standard form, which is:

(x - a)² + (y - b)² = r²

Where (a, b) are the coordinates of the center of the circle, and r is the radius of the circle.

The equation can be written in different forms depending on the information given. For example, if the center of the circle is at the origin (0,0), then the equation becomes x² + y² = r²

Here,

Centre of first circle is (-2,4) and radius is 4 unit and centre of second circle is (0,0) and radius is 8 unit.

We can write the equations of the two circles as follows:

First Circle:

Center: (-2, 4)

Radius: 4 units

So, required equation of first circle is (x + 2)² + (y - 4)² = 16

Second Circle:

Center: (0, 0)

Radius: 8 units

So, required equation of second circle is x² + y² = 64

Thus, the equation of the first circle is (x + 2)² + (y - 4)² = 16, and the equation of the second circle is x² + y² = 64.

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Answer: W=10pi

Step-by-step explanation:

The required matrices are:

[tex]A= \begin{bmatrix}1 & 1 & 0\\1 & -1 & 0\end{bmatrix}[/tex] and [tex]B= \begin{bmatrix}1 & 1\\1 & -1\\0 & 1\end{bmatrix}[/tex]

letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.

A matrix is a rectangular array of numbers or other mathematical objects (such as complex numbers, polynomials, or functions) arranged in rows and columns. The size or dimensions of a matrix are given by the number of rows and columns it has, and a matrix with m rows and n columns is said to be an m × n matrix.

Let A be the 2×3 matrix:

[tex]A= \begin{bmatrix}1 & 1 & 0\\1 & -1 & 0\end{bmatrix}[/tex]

and let B be the 3×2 matrix:

[tex]B= \begin{bmatrix}1 & 1\\1 & -1\\0 & 1\end{bmatrix}[/tex]

Then, for any vector x in [tex]R^2[/tex], we have:

[tex]T(U(x)) = A(Bx) = A(x_1 + x_2, x_1 - x_2, x_3)[/tex]

             [tex]= (x_1 + x_2 + x_1 - x_2, x_1 - x_2 - x_1 - x_2, 0)[/tex]

             [tex]= (2x_1, -2x_2, 0)[/tex]

To show that this is a reflection over the line y=x, we can verify that T(U(x)) is equal to its own inverse. That is, we want to show that:

[tex]T(U(T(U(x)))) = x[/tex]

Substituting T(U(x)) for y, we have:

[tex]T(U(T(U(x)))) = T(U(y)) = A(By) = A(2y_1, -2y_2, 0)[/tex]

                        [tex]= (2y_1 + (-2y_2), 2y_1 - (-2y_2), 0)[/tex]

                        [tex]= (4y_1, 4y_2, 0)[/tex]

To see that this is equal to x, we note that the first and second components have been swapped, which corresponds to a reflection over the line y=x. Thus, T(U) is indeed a reflection over the line y=x.

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The complete question is:

Find an example of a 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.

Answer: A. x = 3

Step-by-step explanation:

       I have graphed x = 8 and the point (3, 6). See attached.

       We know that options C and D are incorrect because they are y = equations and not x = equations like the one given, so they will not be parallel to x = 8.

       Lastly, our point is (3, 6) with a value of x = 3. This gives us a parallel equation that goes through that point (I have added x = 3 to the graph attached as well);

        x = 3