Which rules define the function graphed below? y=2x+3, y=-1/3x+3

The expression can be simplified to: [tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

We can simplify the expression as follows:

tan(x) + cot(x)/sec(x) = tan(x) + 1/tan(x) / 1/cos(x) = tan(x) + cos(x) / tan(x) * cos(x) = tan(x) + cos^2(x) / tan(x)

Using the identity: tan(x)^2 + 1 = sec^2(x), we can simplify further:

tan(x) + cos^2(x) / tan(x) = tan(x) + cos^2(x) / (sqrt(sec^2(x) - 1)) = tan(x) + cos^2(x) / sqrt(tan^2(x) + 1 - 1) = tan(x) + cos^2(x) / sqrt(tan^2(x))

Using the identity sin^2(x) + cos^2(x) = 1, we can simplify further:

[tex]tan(x) + cos^2(x) / \sqrt(tan^2(x)) = tan(x) + (1 - sin^2(x)) / \sqrt(tan^2(x)) = tan(x) + \sqrt(1 - sin^2(x)) / \sqrt(tan^2(x)) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

Therefore, the expression can be simplified to:

[tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

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Answer:

option

Step-by-step explanation:

f(x)=-3x²-4x+15

if (-3,-2) is substitute

x=-3 x=-2 is substitute in above given equation we get real zero.

Answer:

  (4, 0)

Step-by-step explanation:

You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.

When the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.

  (1, 0) ⇒ 4(1, 0) = (4, 0)

The image of the point is (4, 0).

Answer:

Step-by-step explanation:

To find the total distance traveled by the hikers to get home, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the straight line distance) is equal to the sum of the squares of the lengths of the other two sides.

Since the hikers traveled 3 km north and 4 km east, we can consider this as the sides of a right-angled triangle, with the hypotenuse being the straight line distance traveled to get home. So, the square of the distance traveled to get home is equal to the sum of the squares of the sides, i.e., 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us 5 km, so the distance traveled by the hikers to get home is 5 km.

Answer:

x = -5

Step-by-step explanation:

Since both horizontal lines are parallel, the marked angles are corresponding angles and are congruent. This, we can set them equal to each other:

47 = 10x + 97

Next, isolate “x” to find the value of “x”:

47 - 97 = 10x

-50 = 10x

-5 = x

How to determine this

Using product rule,

[tex]\frac{d}{dx}[/tex](u.v) = du/dx.v + dv/dx.u

where u = x-5

v = x+7

Using the rule,

d/dx = 1(3x + 7) + 3(x - 5)

d/dx = 3x +7 +3x - 15

d/dx = 6x - 8

Using the expanding, then differentiating,

d/dx = (x - 5)(3x + 7)

open bracket,

d/dx = 3x^2 + 7x - 15x - 35

Differentiating it,

d/dx = 6x + 7 - 15

d/dx = 6x - 8

Therefore, using different rule,it has been verified that both methods gave the same results.

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The graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and  a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x). Where it equals zero is where the quadratic equation finds its solutions. They are also known as the equation's roots.

Assuming the question is to graph the quadratic function y = 6x².

The x-intercept can be found by substituting y = 0

0 = 6x²

x = 0

x-intercept = (0,0)

y-intercept can be found by substituting x=0

y = 6 * 0

y = 0

y-intercept = (0,0)

The given quadratic equation is the equation of an upward parabola with the vertex as (0,0).

The axis of symmetry is x = 0 i.e y-axis.

Hence the graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

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well, let's take a looksie at both

[tex]~~~~~~ \stackrel{\textit{\LARGE Henry}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (5000)(0.042)(4) \implies I = 840 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\LARGE Ingrid}}{\textit{Simple Interest Earned}}[/tex]

[tex]I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.039)(6) \implies I = 1170 \\\\[-0.35em] ~\dotfill\\\\ 1170~~ - ~~840\implies \text{\LARGE 330}[/tex]

The solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

What is inequality?

An inequality is a mathematical statement that describes a relationship between two values or expressions, where one is greater than, less than, or not equal to the other.

To solve the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex], we can use the concept of interval notation and test each interval to see if it satisfies the inequality. Here are the steps:

Find the critical points of the expression, which are the values that make the expression equal to zero. In this case, the critical points are -5, -4, and -3.

Use these critical points to divide the number line into four intervals: (-∞, -5), (-5, -4), (-4, -3), and (-3, ∞).

Test a value in each interval to see if the inequality is true or false. We can use the sign of the expression to determine this:

For x < -5, all three factors are negative, so the product is negative. Therefore, this interval does not satisfy the inequality.

For -5 < x < -4, the first factor is positive and the other two factors are negative. The product is therefore negative. This interval does not satisfy the inequality.

For -4 < x < -3, the first and third factors are positive and the second factor is negative. The product is therefore positive. This interval satisfies the inequality.

For x > -3, all three factors are positive, so the product is positive. Therefore, this interval satisfies the inequality.

Write the solution set using interval notation. We have found that the solution set is (-4, -3) union ( -3, ∞).

Therefore, the solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

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The value of the angle is 120°.

The corresponding angle of a given angle refers to the angle in a congruent position in another figure. For example, if two lines intersect, the angle formed at one vertex of the intersection is called a vertex angle. The corresponding angle in the other figure is the angle in a congruent position, meaning that it has the same measure.

We are given two lines to be parallel

Hence the angle adjacent to x is 40°

Now Sum of All three angle is 180° (Angles in linear pair)

Hence we have

40 + x + 20 = 180°

x = 120°

Hence the measure of angle x is 120°

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Mr. Kazoo needs to buy 6 boards to complete his fencing as he can not buy exactly 5.71 boards.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables.

We can form numerical expressions from statements.

Given, Mr. Kazoo is planning to build a fence.

The gate is 40 inches wide.

Therefore, He needs to buy (40/7) = 5.71 boards.

But, He can not buy a board 0.71 part of the whole part, So he needs to buy 6 boards to complete his fencing.

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Answer:

im pretty sure it is 4/9

Step-by-step explanation:

From the question, we are to determine the probability of selecting two cards with D and D

From the formula for probability, we have that

P(D) = Number of favorable outcomes to D / Total number of possible outcomes

From the given information,

Number of favorable outcomes to D = 2

Number of possible outcomes = 3

Thus,

P(D) = 2/3

Then,

The probability of selecting two cards that have D and D with replacement is

P(D, D) = P(D) × P(D)

P(D, D) = 2/3 × 2/3

P(D, D) = 4/9

Hence, the probability is 4/9.

Answer:

1. 32 divided by 2 is 16

2.  2 x 16 = 36

Step-by-step explanation:

Answer:

4,233,000

Step-by-step explanation:

4,232,000                 4,4232,852                  4,233,000

4,4232,852 is between 4,232,000 and 4,233,000.  It is closer to 4,233,000.

The rule is to look a the digit in the hundreds' place.  That number is 8.  If the digit in the hundreds' place is 5 or larger, you round up.

Answer:

See the explanation below

6x8 is 48. You can't simplify 48/5, so that's your answer. If you wanted to create a mixed number, you could write 9 3/5

Answer: 753.98m³

Formula:V=πr2h3=π·62·203≈753.98224m³

The statement made by Diego is correct.

In order to determine the number of groups of 5/6 that are in 1, 1 would be divided by 5/6.

1 ÷ 5/6

= 1 x 6/5 = 6/5

6/5 is called an improper fraction because the numerator is greater than the denominator.

6/5 can also be rewritten as a mixed fraction. If it is rewritten as a mixed fraction, it becomes 1 1/5.

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Given question is incomplete , the complete question is given below:

Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? Explain or show your reasoning.

Answer: a) Mean and standard deviation of the sampling distribution:

The mean of the sampling distribution, also known as the expected value or the population mean, is equal to the proportion of U.S. residents who receive a jury summons each year, which is 15%. So, the mean of the sampling distribution is:

µ = 0.15

The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:

σ = √(p(1 - p) / n)

where p is the population proportion of U.S. residents who receive a jury summons each year (0.15), and n is the sample size (500).

σ = √(0.15 * (1 - 0.15) / 500)

σ ≈ 0.03

So, the standard deviation of the sampling distribution is approximately equal to 0.03.

b) Interpretation of the standard deviation:

The standard deviation measures the spread of the sampling distribution, or how much the sample proportions deviate from the population proportion. A smaller standard deviation indicates that the sample proportions are more likely to be close to the population proportion, while a larger standard deviation indicates that the sample proportions are more likely to be further from the population proportion.

In this case, the standard deviation of 0.03 indicates that the sample proportions are expected to be within 0.03 of the population proportion (0.15) about 68% of the time.

c) Justification for the approximate normality of the sampling distribution:

According to the central limit theorem, the distribution of the sample proportions will be approximately normal as long as the sample size is large enough. In this case, with a sample size of 500, we can assume that the sampling distribution is approximately normal.

Step-by-step explanation:

Answer: x=35

Step-by-step explanation:

The proof of congruence by SAS, then 2 corresponding sides and the corresponding included angles of both triangles are equal.

Angles who are of same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of same measure, then

[tex]m\angle A = m\angle B[/tex]is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

The SAS postulate , Two sides and the included angle of one triangle are identical to the corresponding two sides and the included angle of another triangle.

In the triangle, the angles mCAD and mACB are congruent.

m∠CAD ≅ m∠ACB

Since m∠CAD and m∠ACB are congruent, AD and BC must also be congruent.

As a result, the SAS Congruence postulate is proven.

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Answer:

=58%

Step-by-step explanation:

If rate of 5.8% = 1 day

than ? = 10 days

therefore 10/1 × 5.8%

= 10 × 5.8

= 58%

To the nearest whole number

= 58%

The surface area of cube will be 600 square units.

What exactly is a cube?

A Cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges in geometry. It is also described as a regular hexahedron. You've probably seen the 3 3 Rubik's cube, which is the most prevalent example in real life and is useful for improving brain capacity. Similarly, you will come across several real-life instances, such as 6 sided dice, etc. Solid geometry is concerned with three-dimensional objects and figures with surface areas and volumes. Other solid forms include cuboid, cylinder, cone, and sphere.

Surface area of cube=6*side²

Volume of cube=side³

Now,

As Side of cube=10 units

and Surface area of cube=6*side²

=6*10*10

=600 square units.

Hence,

           The surface area of cube will be 600 square units.

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Answer:

Step-by-step explanation:

18-5=13

18-9=9

Answer:

12th term = -61

Step-by-step explanation:

Given sequence,

→ 5, -1, -7, ...

Now we have to,

→ Find the 12th term of the sequence.

The common difference is,

→ d = a2 - a1

→ d = -1 - 5

→ [ d = -6 ]

Formula we use,

→ an = a1 + (n - 1)d

Then value of 12th term will be,

→ an = a1 + (n - 1)d

→ a12 = 5 + (12 - 1) × (-6)

→ a12 = 5 + 11 × (-6)

→ a12 = 5 - 66

→ [ a12 = -61 ]

Therefore, the 12th term is -61.

E1, E3, and E2, E3 are independent variables.

[tex]$& \mathrm{P}\left(\mathrm{E}_1\right)=\frac{1}{6} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_2\right)=\frac{1}{6} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_3\right)=\frac{2+4+6+4+2}{36}=\frac{1}{2} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_2 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_2\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]

Then,

[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_1\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right)=0 \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right) \equiv 0 \\[/tex]

Simplify,

[tex]$& \therefore \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right) \equiv \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right)[/tex]

E1, E3 are independent

E2, E3 are independent

The complete question is:

Let two fair six-faced dice A and B are thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

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The input is 8, the output of the function f(x) would be -5.

What is the function?

Function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet

To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:

f(x) = 8/x - 6

f(8) = 8/8 - 6

f(8) = 1 - 6

f(8) = -5

Hence, if the input is 8, the output of the function f(x) would be -5.

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The federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8 percent is around 39000 (which is 50000 - 11000).

Let's use f and p to denote the amounts of Josie's federal and private bank loans, respectively.

We know that the total amount of loans is 50000, so:

f + p = 50000

We also know that the interest on federal loans at 2.8% and the interest on private bank loans at 4.8% add up to 1600 per year. The interest on the federal loans is 0.028f and the interest on the private bank loans is 0.048p, so:

0.028f + 0.048p = 1600

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:

p = 50000 - f

Substituting this into the second equation, we get:

[tex]0.028f + 0.048(50000 - f) = 1600[/tex]

Simplifying and solving for [tex]f[/tex], we get:

[tex]f = \frac{1600 - 0.048 \cdot 50000}{0.02} \approx 11000[/tex]

Therefore, the federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8% is approximately 39000 (which is 50000 - 11000).

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Answer:

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Full surface area is the sum of areas of 4 triangles and the square base:

Find the height h of the pyramid, using slant height and the side of the base and Pythagorean:

Find the volume: