Hello! I need help with question 50 please.

Answer:

The answer is -20 .

Step-by-step explanation:

You have to substitute x = -4 into the function :

\(f(x) = 3x - 8\)

\(f( - 4) = 3( - 4) - 8\)

\(f( - 4) = - 20\)

Answer:

Step-by-step explanation:

f(x) = 3x - 8

f(-4) = 3*(-4) - 8

f(-4)  = -12 - 8

f(-4) = - 20

-20 is what goes in the box.

Answer:

The equation that will represent the number of grams present after n hours is \(A(n) = 150(0.85)^n\)

3.035 grams will be left one day from now.

Step-by-step explanation:

Exponential equation for the amount of a substance:

The exponential equation for the amount of a substance is given by:

\(A(t) = A(0)(1-r)^t\)

In which A(0) is the initial amount and r is the decay rate, as a decimal, and t is the time period.

A radioactive isotope is decaying at a rate of 15% every hour.

This means that \(r = 0.15\)

Currently there are 150 grams of the substance.

This means that \(A(0) = 150\)

Write an equation that will represent the number of grams present after n hours.

\(A(n) = A(0)(1-r)^n\)

\(A(n) = 150(1-0.15)^n\)

\(A(n) = 150(0.85)^n\)

How much will be left one day from now?

One day is 24 hours, so this is A(24).

\(A(24) = 150(0.85)^{24} = 3.035\)

3.035 grams will be left one day from now.

The calculated value of Thomas's age based on the given parameters is 23 years

Let's use T to represent Thomas's age.

From the problem, we know that Huilan is 15 years younger than Thomas, so we can represent Huilan's age as T - 15.

The sum of their ages is given as 31, so we can write an equation:

T + (T - 15) = 31

Simplifying the left side of the equation, we get:

2T - 15 = 31

Adding 15 to both sides of the equation, we get:

2T = 46

Dividing both sides by 2, we get:

T = 23

Therefore, Thomas is 23 years old.

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when we take the number of vertices, subtract the number of edges, and add the number of faces we get the value of 2 as below:

From Euler's formula: V-E+F = 2

What is meant by Euler's formula?

The following formula is used for polyhedrons, according to Euler's formula, which is defined as follows:

F + V - E = 2

F is the face count, V is the vertices count, and E is the number of edges.

A polyhedron is a three-dimensional solid made by connecting polygons.

The flat surfaces that make up a polyhedron are referred to as its faces. Regular polygons make up these faces. The regions where the two flat surfaces connect to form a line section are referred to as the edges. The vertex is where the edges of the polyhedron come together. A vertex is a common term for a polyhedron's corner.

A soccer ball has 32 faces.

Out of which 20 are regular hexagons and 12 are regular pentagons.

Then,

Number of edges  = 20 * 6 + 12 * 5 = 180

But each edge is shared by 2 faces.

So the actual number of edges on the pentagon = 180/2 = 90

Now the number of vertices can be found using Euler's formula.

Euler's formula is as follows:

F + V = E +2

where

         F = 32

         E = 90

V = E + 2 - F = 90+2 - 32 = 60 = Number of vertices

Euler's formula can also be written as V-E+F = 2

Therefore when we take the number of vertices, subtract the number of edges, and add the number of faces we get the value of 2 as below:

From Euler's formula: V-E+F = 2

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The quadratic function represented by the graph for the given point  (3, -5) is y = x² - 2x - 8. The correct answer is option D.

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

Given that,

The point on the given graph for quadratic function is (3, -5).

From the graph, it is clear that it intersects x axis on -2 and 4 respectively.

Since the zeros of a quadratic function is given by the intersection of its graph on x-axis. The zeros of the given quadratic function are -2 and 4 respectively.

The equation of a quadratic function having zeros a and b is given as,

y = K(x - a)(x - b)

Substitute a = -2 and b = 4 to get the equation for given quadratic function as  y = K(x + 2)(x - 4)

In order to find the exact quadratic function substitute x = 3 and y = -5 in the above equation to get,

-5 = K(3 + 2)(3 - 4)

⇒ K = 1

Thus, the exact function is given as,

y = 1 × (x + 2)(x - 4)

y = (x + 2)(x - 4)

y = x² - 2x - 8

Hence, the quadratic function represented by the graph is y = x² - 2x - 8.

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Answer:

c 57

Step-by-step explanation:

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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Answer:

the proportion of days that are Sunny is 0.2

Step-by-step explanation:

Given the data in the question;

Using markov chain;

3 states; Sunny(1), Cloudy(2) and Rainy(3)

Now, based on given conditions, the transition matrix can be obtained in the following way;

\(\left[\begin{array}{ccc}0&0.5&0.5\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\)

so let the proportion of sunny, cloudy and rainy days be S, C and R respectively.

such that, from column 1

S = 0.25C + 0.25R   -------------let this be equation 1

from column 2

0.5C = 0.5S + 0.25R

divided through by 0.5

C = S + 0.5R ---------------------- let this be equation 2

now putting equation 2 into equation;

S = 0.25(S + 0.5R) + 0.25R

S = 0.25S + 0.125R + 0.25R

S - 0.25S = 0.375R

0.75S = 0.375R

S = 0.375R / 0.75

S = 0.5R

Therefore,

from equation 2; C = S + 0.5R

input S = 0.5R

C = 0.5R + 0.5R

C = R

Now, we know that, the sum of the three proportion should be equal to one;

so

S + C + R = 1

since C = R and S = 0.5R

we substitute

0.5R + R + R = 1

2.5R = 1

R = 1/2.5

R = 0.4

Hence, the proportion of days that are Rainy is 0.4

C = R

C = 0.4

Hence, the proportion of days that are Cloudy is 0.4

S = 0.5R

S = 0.5(0.4)

S = 0.2

Hence, the proportion of days that are Sunny is 0.2

The Definition of the Derivative correctly stated by

In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.

As, we know by definition of derivative

= \(\lim_{h \to 0}\) f(x+h)- f(x) / h

Also, the Derivative also shows the Slope of the secant line.

and, derivative is widely used to the rate of change then it also shows

Instantaneous rate of change.

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Answer:

70.434

Step-by-step explanation:

Answer:

Multiply 5.46 × 12.9 = ____

70.434

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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The cylinder's surface area is S = 452.4 cm²

Given data ,

Let the surface area of the cylinder with one base be S

Now , Surface area of cylinder = 2πr ( r + h )

To find the surface area of a cylinder, we need to calculate the sum of the areas of the curved surface (lateral surface) and the two circular bases.

where r = 8 cm

h = 5 cm

The formula for the lateral surface area of a cylinder is given by:

Lateral Surface Area = 2πrh

where r is the radius of the cylinder and h is the height.

The formula for the area of a circle is given by:

Base Area = πr²

Now , S = πr² + 2πrh

On simplifying , we get

S = π ( 8 )² + 2 ( π ) ( 8 ) ( 5 )

S = 64π + 80π

S = 452.389 cm²

Hence , the surface area is S = 452.4 cm²

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Answer:

2

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

Answer: 7.2

The 2 in the number 7.32 is in the tenths place.

We must move it to the hundredths place, 1 step forward.

You get a number of 7.2. The answer can be 7.2.

Hope this helps!

Answer:

  about 1.1%

Step-by-step explanation:

Given a moon has a diameter of 22% of the diameter its planet, you want the volume of the moon as a percent of the planet's volume.

The ratio of moon diameter to planet diameter is given as 22%. The ratio of moon volume to planet volume will be the cube of this scale factor:

  moon volume / planet volume = (0.22)³ ≈ 0.0106 = 1.06%

The volume of the moon is about 1.1% of the volume of the planet.

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Answer:

That is a quadrilateral good sir

-edge 2021

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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Answer:

d) 189.3 in²

Step-by-step explanation:

Area of rectangle is,

→ w × l

→ 10 × 15

→ 150 in²

Area of semi circle is,

→ (1/2)πr²

→ (1/2) × 3.14 × (5)²

→ 1.57 × 25

→ 39.3 in²

Now the total area will be,

→ 150 + 39

→ 189.3 in²

Thus, total area is 189.3 in².

The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

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Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

Which triangle is ​△abc​ similar to and why? responses △abc is similar to △ghi by ​aa similarity postulate. triangle a b c, is similar to , triangle g h i, by , ​, a a similarity postulate, ., △abc is similar to △jkl by ​aa similarity postulate​. triangle a b c, is similar to , triangle j k l, by , ​, a a similarity postulate, ​, . △abc is similar to △def by ​aa similarity postulate​. triangle a b c, is similar to , triangle d e f, by , ​, a a similarity postulate, ​, . ​△abc​ is not similar to any of the triangles given.

Point H is the ortho-center of our given triangle and option c is the correct choice.

We have been given an image of a triangle. We are asked to find the term that describes point H.

We can see that point H is the point, where, all the altitudes of our given triangle EFF are intersecting.

We know that ortho-center of a triangle is the point, where all altitudes of triangle intersect. Therefore, point H is the ortho-center of our given triangle and option c is the correct choice.

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Answer:

See below

Step-by-step explanation:

a)

\(2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }\)

\(\therefore x=\dfrac{4\pi }{3}\)

But note, as sine does represent the \(y\) value, \(\dfrac{5\pi }{3}\) is also solution

Therefore,

\(x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}\)

This is the solution for \(x\in[0, 2\pi ]\), recall the unit circle.

Note: \(\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)\)

b)

\(\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }\)

Once

\(\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}\)

As \(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)

\(\therefore x=-\dfrac{\pi }{6}\)

c)

\(4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}\)

Therefore,

\(\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}\)

\(\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}\)

The solutions are

\(x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}\)

Answer:

see explanation

Step-by-step explanation:

To find the first 3 terms substitute n = 1, 2, 3 into the formula

(a)= 25 - (3 × 1) = 25 - 3 = 22 = 25 - (3 × 2) = 25 - 6 = 19= 25 - (3 × 3) = 25 - 9 = 16

The first three terms are 22, 19, 16

Note the difference between consecutive terms is - 3

19 - 22 = 16 - 19 = - 3

Continuing this pattern

(b)16 - 3 = 13 13 - 3 = 10 10 - 3 = 7  7 - 3 = 4  4 - 3 = 1  1 - 3 = - 2

The first negative term is - 2

Answer: D

Step-by-step explanation:

Answer:

21km

Step-by-step explanation:

1km=100000cm

14x150000=2100000cm=21km

The distance in real life in kilometers by the given scale factor will be 21 kilometers.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

As per the given,

Scale factor = 1 : 150000

It means 1 cm will convert to 150000 cm.

In real life = 14 x 150000 = 2100000 cm

2100000 cm = 21000 m = 21 kilometer

Hence "The distance in real life in kilometers by the given scale factor will be 21 kilometers".

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Answer:

f

Step-by-step explanation:

I'll help.

\( \frac{1}{3}x = 9 \frac{1}{2} \)

\(x = ?\)

↓

\( \frac{1}{3} x = \frac{19}{2} \)

\(x = \frac{57}{2} \)

"How it can be 57 ?"

The number 19 is multiplied by the number 3 at the bottom left.

19 × 3 = 57.

Answer:

Step-by-step explanation:

tan(pi\4+A)tan(3pi\4+A) =-1

using the tangent sum of angle formula

Answer:

D

Step-by-step explanation:

DSADASD

Answer:

The answer is B.

Step-by-step explanation:

Given that the total angle in a triangle is 180°. So in order to find x, you have to subatract 95° and 57° from 180°

\(x + 95 + 57 = 180\)

\(x = 180 - 95 - 57\)

\(x = 28\)

Answer:

can u make. the question more clear how can I find the answer when both are in km?