Question 15 of 15Which of the following are characteristics of the graph of the square rootparent function? Check all that apply.A. It has a domain of all real numbers.B. It starts at the origin.C. It is in quadrant I.D. It has a range of y < 0.SUBMIT

Answer:

Step-by-step explanation:

Let a = tan⁻¹(x), so tan(a) = x,

\(\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},\)

Let b = tan⁻¹(y), so tan(b) = y,

\(\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},\)

sin( tan⁻¹(x) +  tan⁻¹(y)) = sin(a + b)

= sin(a) cos(b) + cos(a)sin(b)

= \(\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}\)

\(=\frac{x+y}{\sqrt{(1+x^2)(1+y^2)}}\)

Answer:

€4.20

Step-by-step explanation:

the have a 5 in 26 chance in winning so 26(letters in alphabet) - 5(vowels) =21

21÷5 =4.2

The three options given in the question are not the correct steps to solve the given quadratic equation.

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared (raised to the power of 2).

The three steps that Inga could use to solve the quadratic equation \(2x^2 + 12x - 3 = 0\) are:

1.Rewrite the equation in the form \(ax^2 + bx + c = 0\), where a, b, and c are constants: \(2x^2 + 12x - 3 = 0.\)

2.Use the quadratic formula x = [-b ± sqrt(\(b^2\) - 4ac)]/2a, where a = 2, b = 12, and c = -3, to find the values of x:

x = [-12 ± \(\sqrt{(12^2 - 4(2)(-3))\)]/(2*2)

x = [-12 ± \(\sqrt{(156)\)]/4

x = (-3 ± \(\sqrt{(39)\))/2

3.Simplify the roots if possible:

x = (-3 + \(\sqrt{(39)\))/2 or x = (-3 - \(\sqrt{(39)\))/2

Therefore, the three options given in the question are not the correct steps to solve the given quadratic equation.

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Answer:

AB = 28 , BC = 17.5 , X = 13.2

Step-by-step explanation:

since the figures are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{AB}{PQ}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{AB}{8}\) = \(\frac{14}{4}\) ( cross- multiply )

4 AB = 8 × 14 = 112 ( divide both sides by 4 )

AB = 28

and

\(\frac{BC}{QR}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{BC}{5}\) = \(\frac{14}{4}\) ( cross- multiply )

4 BC = 5 × 14 = 70 ( divide both sides by 4 )

BC = 17.5

similarly for the 2 similar figures

\(\frac{x}{6}\) = \(\frac{11}{5}\) ( cross- multiply )

5x = 6 × 11 = 66 ( divide both sides by 5 )

x = 13.2

Answer:

\(\overline{AB}=28\)

\(\overline{BC}=17.5\)

\(x=13.2\)

Step-by-step explanation:

If quadrilateral PQRS is similar to quadrilateral ABCD, their corresponding sides are in the same ratio:

\(\overline{PQ} : \overline{AB} = \overline{QR} : \overline{BC} = \overline{RS} : \overline{CD} = \overline{SP}:\overline{DA}\)

From inspection of the two quadrilaterals, the given side lengths are:

\(\overline{PQ} = 8\)

\(\overline{QR} = 5\)

\(\overline{RS} = 6\)

\(\overline{SP} = 4\)

\(\overline{DA} = 14\)

Substitute these into the ratio equation:

\(8 : \overline{AB} = 5 : \overline{BC} = 6 : \overline{CD} = 4:14\)

Solve for AB:

\(8 : \overline{AB} = 4:14\)

   \(\dfrac{8}{\overline{AB}}= \dfrac{4}{14}\)

 \(8 \cdot 14=4 \cdot{\overline{AB}}\)

   \(\overline{AB}=\dfrac{8 \cdot 14}{4}\)

  \(\boxed{\overline{AB}=28}\)

Solve for BC:

\(5 : \overline{BC} = 4:14\)

  \(5 \cdot 14=4 \cdot \overline{BC}\)

    \(\overline{BC}=\dfrac{5 \cdot 14}{4}\)

   \(\boxed{\overline{BC}=17.5}\)

\(\hrulefill\)

Assuming the two figures are similar, their corresponding sides are in the same ratio. Therefore:

\(x:6=11:5\)

   \(\dfrac{x}{6}=\dfrac{11}{5}\)

   \(x=\dfrac{11 \cdot 6}{5}\)

   \(x=\dfrac{66}{5}\)

  \(\boxed{x=13.2}\)

Answer:three-fourths

Step-by-step explanation:

because my dad said it was right

Answer:

0.6x = 6.6

Step-by-step explanation:

3.3x - 6.6 = 2.7x

3.3x - 2.7x - 6.6 = 0

0.6x = 6.6

x = 11

Answer:

i think the train would travel 3.125 in 1/2 an hour

Step-by-step explanation:

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

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h=20.4

Step-by-step explanation:

=> 7780.05 = 28.25 x 13.5 x h

multiply h by 13.5

=> 7780.05 = 28.25 x 13.5h

make h the subject of formula

=> 13.5h × 28.25 = 7780.05

Let's solve your equation step-by-step.

=> 13.5h(28.25)=7780.05

Step 1: Simplify both sides of the equation.

=> 381.375h=7780.05

Step 2: Divide both sides by 381.375.

=>\( \frac{381.375h}{381.375}= \frac{7780.05}{381.375}\)

divide the numerators by the denominators

=> h=20.4

Answer:

Example 1:

In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?

Solution:

Step 1: Assign variables :

Let x = red sweets

Write the items in the ratio as a fraction.

red/green

Step 2: Solve the equation

Cross Multiply

3 × 120 = 4 × x

360 = 4x

Isolate variable x

x=360/4

Answer: There are 90 red sweets.

Example 2:

John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?

Solution:

Step 1: Sentence: Jane has 20 marbles, all of them either red or blue.

Assign variables:

Let x = blue marbles for Jane

20 – x = red marbles for Jane

We get the ratio from John

John has 30 marbles, 18 of which are red and 12 of which are blue.

red/blue

We use the same ratio for Jane.

red/blue

Step 2: Solve the equation

Cross Multiply

3 × x = 2 × (20 – x)

3x = 40 – 2x

Isolate variable x

x=40/5

John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.

Answer: John has 4 more blue marbles than Jane.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The blood platelet count is an illustration of normal distribution,

Approximately 95% of the data lies within 2 standard deviations of the mean.

There are approximately 99.7% of women with platelet count between 65.2 and 431.8.

Given parameters are:

μ = 248.5

σ = 61.1

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7,

Start by calculating the z-score, when x = 126.3 and x = 370.7

Z = x-μ / σ

Therefore,

Z = 126.3-248.5/61.1

Z = -2

Also,

Z = 370.7-248.5/61.1

Z = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

Z = 65.2-248.5/61.1

Z = -3

And,

Z = 431.8-248.5/61.1

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8.

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Answer:

35

Step-by-step explanation:

just trust me its the total

Answer:

35

Step-by-step explanation:

25-5=20

20-10=10

10+15=25

25+10=35

The answers are given below.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given:

1) 2Sin(9θ).Cos(5θ)=1/2(Sin14θ+Sin4θ)

2) Sin(3θ)Sin(5θ)Cos(3θ)Cos(5θ)=1/2(Sin8θ+Sin2θ)

3)Cos6θ+Cos4θ=2Cos5θCosθ

4)Sin(13θ/2)+Sin9θ=2Sin(11θ/2)Sinθ

5)Cosθ=2√5/5

6)Cos2θ=23/2

7)Tan(π/12)=2-√3

8)Sin(165°)=√6-√2 /4

9)Cos(5π/18)Cos(2π/9)-Sin(5π/18)Sin(2π/9)=Cos(π/2)

                                                                      =0

Hence, these are the answers .

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The coefficient of the second term, 6x⁴, is 6.

The terms of the polynomial are:

-4y⁵, 6x⁴, 9w³, -4w, -1

The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.

The coefficient is 6.

Therefore, the list of terms is:

-4y⁵, 6x⁴, 9w³, -4w, -1

Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.

The coefficients indicate the scalar value by which each term is multiplied.

The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.

Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.

There is a 6 coefficient.

As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.

Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.

The scalar value by which each phrase is multiplied is shown by the coefficients.

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Answer:

Option e

Step-by-step explanation:

The type of test for this sticky is a two tailed test: (either up or down) from the severe storm class rating.

Thus, the null hypothesis would be that u is equal to 16.4 feet while the alternative hypothesis would be that u is not equal to 16.4 feet; and the p value area is on both sides of the mean since it is a two tailed test.

A formal power series that encodes the coefficients of a sequence of numbers is a generating function.

Here, the coefficients of the sequence {Sₙ} are encoded by the generating function S(x). where Sₙ is the number of lattice paths as described above.

Here we will use the fact that the generating function for a sequence satisfies a functional equation that relates the generating function to the sequence itself to prove that 1 + (x – 1)S(x) + xS(x)² = 0,

Here, the functional equation is

S(x) = 1 + xS(x) + xS(x)²

This equation implies that

The term 1 on the right-hand side corresponds to the fact that to reach the point (0,0) (the starting point), there is exactly one way which is to stay at the starting point.

The term xS(x) corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-1, n-1) we can reach any point (n,n)

The term xS(x)² corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-2, n-2), and then taking another step in the positive x-direction and following a path to (n-1, n-1) we can reach any point (n,n)

Thus, 1 + (x – 1)S(x) + xS(x)² = 0. Hence proved.

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Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Answer:

We need to determine 50% of 100 now and the procedure explaining it as such

Step 1: In the given case Output Value is 100.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 100 = 100%.

Step 4: In the Same way, x = 50%.

Step 5: On dividing the pair of simple equations we got the equation as under

100 = 100% (1).

x = 50% (2).

(100%)/(x%) = 100/50

Step 6: Reciprocal of both the sides results in the following equation

x%/100% = 50/100

Step 7: Simplifying the above obtained equation further will tell what is 50% of 100

x = 50%

Therefore, 50% of 100 is 50

Add to brainliest

\(\text{First term,}~ a = 8\\\\\text{Common ratio,}~ r= \dfrac{32}8 = 4\\\\\text{nth term} = ar^{n-1} \\\\\text{9th term} = 8\cdot 4^{9-1}\\\\\\~~~~~~~~~~~~~=8 \cdot 4^8\\\\\\~~~~~~~~~~~~~=524288\\\\\text{The 9th of the geometric sequence is 525288.}\)

Answer:

Step-by-step explanation:

LMAFOOOOOOOOOOOOOOOOOOOOOO

Answer:

a (5,0)

Step-by-step explanation:

2x + y = 10 substitute y= x - 5 into that first equation

2x+(x-5)=10

2x+x-5=10

3x - 5 = 10

3x = 10 + 5

3x = 15

\( \frac{3x}{3} = \frac{15}{3} \)

x=5

substitute the x into either the first or second equation

2(5) +y=10

10 + y = 10

y= 10 - 10

y = 0

therefore

x = 5 and y= 0

The probability of a randomly selected SAT score being between 1550 and 1575 is 0.2231. This means that approximately 22.31% of SAT scores are in this range.

The probability that a randomly selected SAT score is between 1550 and 1575 can be calculated using the standard normal distribution. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. We can convert the given SAT scores to the standard normal distribution by subtracting the mean of 1518 from the scores and then dividing by the standard deviation of 325. This gives us the values of 0.615 for 1550 and 0.769 for 1575. The probability of a randomly selected SAT score being between these two values can then be found using a z-table, which gives us the probability of 0.2231.In other words, the probability of a randomly selected SAT score being between 1550 and 1575 is 0.2231. This means that approximately 22.31% of SAT scores are in this range.

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Answer:

x=22°

Step-by-step explanation:

hopefully it is clear and understandable

:)

77 feet^2

Explanation:

Area of the wall is

8 2/5 × 18 1/3

42/5 × 55/3

14/5 × 55/1

14/1 × 11/1 = 154 feet^2

The area we want is half of this

77 feet^2

Hope this helps and answer you question

Answer:

5 Miles

Step-by-step explanation:

First, start with multiplying 1/2 by 10 (because we are using 1/10), and you get 10/2, which equals 5.

Answer: How many miles can he run in one hour?

six miles

But for a normal person it's one mile per 10 minutes or about six miles per hour.

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

Answer:

2

Step-by-step explanation:

2

Answer:c

Step-by-step explanation:because idnt know

Answer:

x + 80 =180 (Being sum of 180 degree)

or,x=180 -80

= 100