Why is square a regular polygon?

Answer:

Step-by-step explanation:

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We can shown that the triangles are congruent by a translation of 2 units left and then a reflection over the y-axis.

Congruent triangles are triangles that have the same side lengths.

Transformations that keep  the congruence of a triangle are given as follows:

One vertex of the original triangle is given as follows:

A(8,8).

The equivalent vertex on the reflected and translated triangle is given as follows:

A'(6,-8).

Considering the reflection over the y-axis that we can see from the image, the complete rule is given as follows:

(x,y) -> (x - 2, - y).

Meaning that the translation was two units left.

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[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &\\ P=\textit{initial amount}\dotfill &2.5\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &13 \end{cases} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}} \end{array}} ~\hfill[/tex]

well, let's instead find when will there be 1 gram first off, then after that it's all downhill, so A = 1

[tex]\stackrel{A}{1}=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \cfrac{1}{2.5}=\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \log\left( \cfrac{1}{2.5} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{t}{13}} \right][/tex]

[tex]\log\left( \cfrac{1}{2.5} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]\implies \cfrac{\log\left( \frac{1}{2.5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]}=t\stackrel{\textit{after about 17 days and 5 hours}}{\implies 17.19\approx t ~\hfill }[/tex]

The mean can only be used with interval/ratio level data.

what is  ratio data ?

Ratio data is a form of quantitative (numeric) data. It measures variables on a continuous scale, with an equal distance between adjacent values. While it shares these features with interval data (another type of quantitative data), a distinguishing property of ratio data is that it has a 'true zero.

What are mean , median and mode?

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Hence, the mean can only be used with interval/ratio level data.

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The proportion of the class that scored higher than the student will be 0.0912.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The class normal is 85% and the standard deviation is 3%. Then the student from the class who earned 89% higher will be given as,

z = (0.89 - 0.85) / 0.03

z = 0.04 / 0.03

z = 1.3333

Then the probability is given as,

P(x > 89%) = P(z > 1.3333)

P(x > 89%) = 0.091211

The proportion of the class that scored higher than the student will be 0.0912.

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The exact length of the polar curve in this problem is given as follows:

320,597 units.

The definition of a polar curve is given as follows:

r(θ).

Then the length of the curve over an interval a ≤ θ ≤ b is given by the definite integral presented as follows:

[tex]L = \int_{a}^{b} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} d\theta[/tex]

The curve in this problem is given as follows:

[tex]r = e^{2\theta}[/tex]

The derivative is given as follows:

[tex]\frac{dr}{d\theta} = 2e^{2\theta}[/tex]

Then the arc length is given by the integral presented as follows:

[tex]L = \int_{0}^{2\pi} \sqrt{e^{4\theta} + 4e^{4\theta}} d\theta[/tex]

[tex]L = \int_{0}^{2\pi} \sqrt{5e^{4\theta}} d\theta[/tex]

[tex]L = \sqrt{5}(\int_{0}^{2\pi} e^{2\theta} d\theta)[/tex]

[tex]L = \frac{\sqrt{5}}{2}(e^{2\theta})|_{\theta = 0}^{\theta = 2\pi}[/tex]

Applying the Fundamental Theorem of Calculus to solve the double integral, the length of the arc is givena s follows:

[tex]L = \frac{\sqrt{5}}{2}(e^{4\pi} - 1)[/tex]

L = 320,597 units.

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Answer:

peanut butter jelly

Step-by-step explanation:

I love that!

The value of the expression 3 ¹/₅ ÷ 1/3 will be 9.6 or 48/5.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

3 ¹/₅ and 1/3

Convert the mixed fraction number into a fraction number. Then we have

3 ¹/₅ = 16 / 5

Then the division of the numbers 16/5 and 1/3 will be given by putting a division sign between them. Then we have

⇒ 16/5 ÷ 1/3

⇒ (16/5) / (1/3)

⇒ (16/5) x (3)

⇒ 48/5

⇒ 9.6

The value of the expression 3 ¹/₅ ÷ 1/3 will be 9.6 or 48/5.

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A negative result does not mean that you do not have the disease. It could be a false negative.

The reasons that could be there for a negative result when there is  actually the presence of the disease

The ELISA may not be sensitive enough to detect very low concentration  of the disease agent, as might occur when one is tested soon after infection before a proper immune response occurs.

As HIV buds from the surface of the host cell, it incorporates some of the host cell Human leukocyte antigen into its envelope. False negatives usually occurs during the window between infection and an antibody response to the virus which is known as seroconversion.

Therefore, if the sample gave a negative result for the disease-causing agent, it does not mean that you do not have the disease

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Answer: 12 miles

Step-by-step explanation:

Let y represent the cost and x represent the number of miles!

y = 1.25x + 3

Now put the $18 in for y

18= 1.25x + 3

15 = 1.25x

x = 12 miles

Answer:

Step-by-step explanation:

We can model the cost of a taxi trip with y = 1.25x + 3, where y is the total cost and x is the miles traveled. $1.25 is charged per mile, and the initial $3 is added to find the total cost. We know that the total cost is $18, so we can put 18 in for y and solve for x:

18 = 1.25x + 3

15 = 1.25x (subtracted 3 from both sides)

12 = x (divided each side by 1.25)

So, the trip was 12 miles

The required graph of the inequality has been shown and the solution is; 8 Nickels  and 12 dimes.

Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).

Let the number of nickels be x and let the number of dimes be y,

We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;

x + y = 20

x = 20 - y - - - - (1)

0.05x + 0.10y ≤ 1.60 - - - -(2)

We are also told that no less than 4 of the coins are dimes. Thus;

x ≥ 4

From the graph, one solution is given as 8 Nickels and 12 dimes.

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The measure of z in the polygon is (a) z = 15

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

Shape = 9-sided polygon

Parameter to calculate = the measure of z

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where n is the number of sides

In this case

n = 9

Substitute the known values in the above equation, so, we have the following representation

The sum of the interior angles = (9 − 2) × 180∘

Evaluate

The sum of the interior angles = 1260∘

So, the internal angle is

Angle = 1260/9

Evaluate

Angle = 140

This means that

5z + 65 = 140

So, we have

5z = 75

Divide by 5

z = 15

Hence, the angle is (a) z = 15

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Answer:

[tex]\textsf{1)} \quad x=\dfrac{y-b}{a}[/tex]

[tex]\textsf{2)} \quad x=\dfrac{y+b}{a}[/tex]

[tex]\textsf{3)} \quad x=2y-2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad &y & =xa+b\\\\&\textsf{Subtract $b$ from both sides}: \quad & y-b&=xa+b-b \\\\&\textsf{Simplify}: \quad &y-b&=xa \\\\&\textsf{Divide both sides by $a$}: \quad &\dfrac{y-b}{a} &=\dfrac{xa}{a} \\\\&\textsf{Simplify}: \quad &\dfrac{y-b}{a} &=x\\\\&\textsf{Switch sides}: \quad & x&=\dfrac{y-b}{a}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad &y & =xa-b\\\\&\textsf{Add $b$ to both sides}: \quad & y+b&=xa-b+b \\\\&\textsf{Simplify}: \quad &y+b&=xa \\\\&\textsf{Divide both sides by $a$}: \quad &\dfrac{y+b}{a} &=\dfrac{xa}{a} \\\\&\textsf{Simplify}: \quad &\dfrac{y+b}{a} &=x\\\\&\textsf{Switch sides}: \quad & x&=\dfrac{y+b}{a}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad & y&=\dfrac{x+2}{2} \\\\&\textsf{Multiply both sides by $2$}: \quad & 2 \cdot y&=2 \cdot \dfrac{x+2}{2} \\\\&\textsf{Simplify}: \quad & 2y&=x+2 \\\\&\textsf{Subtract $2$ from both sides}: \quad & 2y-2&=x+2-2 \\\\&\textsf{Simplify}: \quad & 2y-2&=x \\\\&\textsf{Switch sides}: \quad &x&=2y-2\end{aligned}}[/tex]

Answer:

z = 22

Step-by-step explanation:

Because we are given that angle measures TUW and VUW are the same, we can assume that both triangles are the same since they also have 90 degree angles and both their third angles are equal to 54. (I found that out by taking 180 degrees which is the total angle measure of all triangles, and subtracted it by 90 and 36).

Since they are the same, that means that side TW is the same length as side VW. With this information we can set up an expression:

2z = z + 22

Now, all we have to do is solve for z

2z = z + 22

-z   - z

z = 22

We know that the equation (B) 5+2(3+2x) = x+3 (x+1) has no solution.

The definition of equations in algebra is a mathematical statement that shows the equality of two mathematical equations.

For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Solve equations to find the equation which has no solution as follows:

(A) 4(x+3) + 2x= 6(x+2)

4(x + 3) + 2x = 6(x + 2)

4x + 12 + 2x = 6x + 12

6x = 6x

L. H. S = R. H. S

(B) 5+2(3+2x) = x+3 (x+1)

5 + 2(3 + 2x) = x + 3(x + 1)

5 + 6 + 4x = x + 3x + 3

11 + 4x = 4x + 3

L. H. S ≠ R. H. S

(We got our answer and so we don't need to solve further options)

Therefore, we know that the equation (B) 5+2(3+2x) = x+3 (x+1) has no solution.

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Correct question:

Which equation has no solution?

a 4(x+3) + 2x= 6(x+2)

b 5+2(3+2x) = x+3 (x+1)

c 5(x+3) + x = 4 (x+3) + 3

d 4 + 6(2+x) = 2(3x+8)

The polynomial of third degree whose zeros and degree are given, for zero of (-2), multiplicity 1 and for zero of (3), multiplicity 2 is [tex]f(x) = x^3 - 10x^2 - 15x + 18[/tex]

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

From the question statement, a third degree polynomial has a zero of (-2), multiplicity 1 and another zero of (3), multiplicity 2.

We need to determine the polynomial.

Since, (-2) is a zero of the polynomial, then (x+ 2) will be a factor of the polynomial. for zero of (-2), multiplicity is 1, means that the factor of (x + 2) is only multiplied once.

Similarly, (3) is another zero of the polynomial, then (x - 3) will be a factor of the polynomial.

For zero of (3), multiplicity is 2, this means that the factor of (x - 3) will be multiplied twice

Hence, our required polynomial is [tex]f(x) = x^3 - 10x^2 - 15x + 18[/tex]

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Answer:

8750 Rs

Step-by-step explanation:

Saves

12.5 : 100 = x : 10 000

x = 10 000 * 12.5 / 100

x = 100 * 12.5

x = 1250 Rs

Total he spends

10 000 - 1250 = 8750 Rs

The area is 0.25

What is a tangent line?

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.  A straight line has a slope of f'(c), where f' is the derivative of f, and is said to be tangent to a curve at a point x = c if it passes through the point (c, f(c)) on the curve. Space curves and curves in n-dimensional Euclidean space have a similar definition.

[tex]$$\begin{aligned}& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3-2 x\right] \\& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3\right]-\frac{\mathrm{d}}{\mathrm{d} x}[2 x] \quad \text { Sum } / \text { Rest rule } \\& f^{\prime}(x)=3 x^{3-1}-2 \quad \text { Power rule } \\& f^{\prime}(x)=3 x^2-2 \\&\end{aligned}$$[/tex]

Now finding tangent for a=-1,

[tex]\begin{aligned}& y=f^{\prime}(a)(x-a)+f(a) \\& y=f^{\prime}(-1)(x+1)+f(-1) \\& y=\left(3(-1)^2-2\right)(x+1)+(-1)^3-2(-1) \\& \mathbf{y}=\mathbf{x}+\mathbf{2}\end{aligned}$$[/tex]

For the first area,

[tex]$$\begin{aligned}& A_1: \int_{-2}^{-\sqrt{2}} x+2 d x=\frac{1}{2} x^2+\left.2 x\right|_{-2} ^{-\sqrt{2}} \\& A_1=\frac{1}{2}(-\sqrt{2})^2+2(-\sqrt{2})-\left(\frac{1}{2}(-2)^2+2(-2)\right) \\& A_1=\mathbf{3}-\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{1}} \approx \mathbf{0 . 1 7 1 5 7 2 8 7 6} \ldots\end{aligned}$$[/tex]

For the second area,

[tex]$$\begin{aligned}& A_2: \int_{-\sqrt{2}}^{-1} x+2-\left(x^3-2 x\right) d x=-\frac{1}{4} x^4+\frac{3}{2} x^2+\left.2 x\right|_{-\sqrt{2}} ^{-1} \\& A_2=-\frac{1}{4}(-1)^4+\frac{3}{2}(-1)^2+2(-1)-\left(-\frac{1}{4}(-\sqrt{2})^4+\frac{3}{2}(-\sqrt{2})^2+2(-\sqrt{2})\right) \\& A_2=-\frac{\mathbf{1 1}}{\mathbf{4}}+\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{2}} \approx \mathbf{0 . 0 7 8 4 2 7 1 2 4} \ldots .\end{aligned}$$[/tex]

Hence, required area is

[tex]$$\begin{aligned}& A=A_1+A_2 \\& A=3-2 \sqrt{2}-\frac{11}{4}+2 \sqrt{2} \\& \mathbf{A}=\frac{\mathbf{1}}{\mathbf{4}}=\mathbf{0 . 2 5}\end{aligned}$$[/tex]

The area is 0.25

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Answer:

120

Step-by-step explanation:

Let the unknown number be x.

Therefore, if 5.76 is 4.8% of x:

[tex]\boxed{\begin{aligned}4.8\%\; \textsf{of} \; x&=5.76\\\\\implies \dfrac{4.8}{100}x&=5.76\\\\4.8x&=576\\\\x&=\dfrac{576}{4.8}\\\\x&=120 \end{aligned}}[/tex]

So the unknown number is 120.

Answer:

7

Step-by-step explanation:

-57 decrease

In this equation.

The value of the function at x=0 is 17.78(4.86)^0 = 17.78(1) = 17.78.

ii. The ratio of output values ​​corresponding to an increment of 1 in input values ​​is (4.86)^1 = 4.86.

iii. A percent change of 1 unit is (4.86 - 1) × 100% = 286% increase.

For the function h(x) = 94.71(0.57)^x:

Thus, the value of the function at x=0 is 94.71(0.57)^0 = 94.71(1) = 94.71.

ii. The ratio of the output value corresponding to an increment of 1 in the input value is (0.57)^2 = 0.57.

iii. Percentage change of 1 unit is (0.57 - 1) × 100% = -57 reduction

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The equation is false (we can remove the dependence with the variable x) that is why the equation has no solutions.

Here we have the following linear equation:

5 - 4x - 7 - 10x = -8x - 4 - 6x - 10

We want to see why we don't have any solutions, to check that, we need to simplify both sides of the equation. Let's start by grouping like terms:

5 - 4x - 7 - 10x = -8x - 4 - 6x - 10

(5 - 7) + (-4x - 10x) = (-4 - 10) + (-8x - 6x)

-2 - 14x = -14 - 14x

Notice that now we can add 14x in both sides of the equation, then we will get:

-2 -14x + 14x = -14 - 14x + 14x

-2 = -14

So we have a false equation, this happens because the equation does not truly depend of the value of x.

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Answer:

Check below/above

Step-by-step explanation:

A) The graph passes through the point (0,1).

The domain is all real numbers.

The range is y>0.

B) it would be a linear equation that shifts the graph vertically.

C) the slope of an exponential function continues to increase, while the slope of a linear function stays the same.

The Correct answer is A. (-4,1) ordered pair generated by this model should be discarded because the values are unreasonable.

In algebra, a quadratic equation (from Latin quadratus 'rectangular') is any equation that can be rearranged in well-known form as ax²+bx+c=0 Where x represents an unknown value, and a, b, and c constitute recognized numbers.

One supposes usually that a ≠ zero; the one's equations with a = zero are taken into consideration degenerate because the equation then will become linear or even simpler. The numbers a, b, and c are the coefficients of the equation and can be prominent with the aid of calling them, respectively, the quadratic coefficient, the linear coefficient, and the consistent or loose time period.

The values of x that satisfy the equation are referred to as answers to the equation, and roots or zeros of the expression on its left-hand aspect. A quadratic equation has at most two answers. If there is handiest one solution, one says that it's miles a double root. If all the coefficients are real numbers, there are both actual solutions, a single actual double root, or two complicated answers which can be complicated conjugates of each other.

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Complete Question:

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?

The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:

$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$

We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:

$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$

Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.

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By the information provided in the question, we got to know that - there are 2598960 ways.

Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.

[tex]^nC_{r} = \frac{n!}{r!(n - r)!}[/tex]

You are choosing a subset of size 5 from a set of size 52.

[tex]Note that the order you are dealt these 5 cards is irrelevant.[/tex] Thus, order doesn’t matter.

Thus, this is a combination problem. The formula for this is:

[tex]Comb(52,5) = \frac{52!}{5! 13!} = 2598960.[/tex]

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Answer: 43 small tanks

Step-by-step explanation:

First, take 900 - 212 = 688 fish in small tanks

Then take 688 divided by 16 fish in each tank = 43

So there are 43 smaller tanks

The measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.

What is an isosceles triangle?

An isosceles triangle, therefore, has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg)

In an isosceles triangle, the two base angles are equal. Therefore, the measure of each base angle is (4x + 5)°.

An exterior angle of a triangle is supplementary to one of the base angles if it forms a straight line with the base angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two base angles.

Therefore, the measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.

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Answer: A, B, C, E

Step-by-step explanation:

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R

Full question is:

Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7e(xyz) at a specified point (0, 0, 7)

If we have a level surface, then it will give us

f(x,y,z) = x+y+z = 7e(xyz). where f is the function of the x, y, and z coordinates.

Now let us calculate the ∇ gradient of f at point (0,0,7):

∇ = (fx,fy,fz) = (1−7yz,1−7xz,1−7xy)

= (1, 1, 1)

We get the equation for the tangent plane A:

A: 1(x−0) + 1(y−0) + 1(z−7)=0

This can also be written as:

x+y+z = 7 ------------------------------------------------------------------(a)

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)

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The bacteria culture has an initial size of 79.7409

Given,

The count in a bacteria culture;

After 10 minutes is 400

After 30 minutes is 2000

Assume that the count grows exponentially;

We have to find the initial size of the culture;

Here,

The growth of population can be calculated using;

P = P₀ (1 + r)^t

Here,

Count of bacteria, P = 400 and 2000

Time period, t = 15 and 30

Initial size =  P₀

So,

400 = P₀ × (1 + r)¹⁰

2000 = P₀ × (1 + r)³⁰

Take P₀ common.

Then,

400/(1 + r)¹⁰ = 2000/(1 + r)³⁰

(1 + r)³⁰/ (1 + r)¹⁰ = 2000/400

(1 + r)¹⁰ = 5

1 + r = 1.175

r = 0.175

Now,

The value of P₀ should be determined from the above equation;

That is,

400 = P₀ × (1 + 0.175)¹⁰

P₀ = 400/ (1 + 0.175)¹⁰

P₀ = 79.7409

Therefore,

The initial size of the bacterial culture is 79.7409

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