Question 6 (1 point)
Find m/RST.
(4x-24)
U
S/(3x)*
O a m/RST = 72°
Ob
mZRST 108⁰
Oc
mZRST = 156°
Od mZRST = 24°

Answers:

=========================================================

Explanation:

Problems 1, 2, and 5 are exponential functions of the form [tex]y = a(b)^x[/tex] where b is the base of the exponent and 'a' is the starting term (when x=0).

If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.

If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.

In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.

Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.

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Problems 3 and 4 are linear functions of the form y = mx+b

m = slope

b = y intercept

This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.

If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.

On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.

Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.

Answer:

Step-by-step explanation:

hello :

the system is : y = 5x + 1

                        y = –x + 7

put : x=1  you have y = 6

Answer:

1

Step-by-step explanation:

The factor (x³ - 1) is not repeated.

( f - g )(x) = 10x - 17 and ( f ° g)(-6)  = 60. The answers are option D and B

Different types of function demands different ways of solving them. Different types are simple function, function by substitution and function of function.

Given that

f(x) = [tex]x^{2}[/tex] + 9x - 14 and g(x) = [tex]x^{2}[/tex] - x + 3

( f - g )(x) will be the difference between f(x) and g(x)

( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - ( [tex]x^{2}[/tex] - x + 3)

( f - g )(x) =  [tex]x^{2}[/tex] + 9x - 14 -  [tex]x^{2}[/tex] + x - 3

( f - g )(x) = 10x - 17

Also, if f(x) = [tex]3x^{2}[/tex] - 15 and g(x) = 1 - 2/3 x

( f ° g)(-6) means that we will evaluate g at -6, then evaluate f at the result of g(-6)

g(-6) = 1 - 2/3 (-6)

g(-6) = 1 + 4

g(-6) = 5

f(g(-6)) = 3([tex]5^{2}[/tex]) - 15

f(g(-6)) = 3 x 25 - 15

f(g(-6)) = 75 - 15

f(g(-6)) = 60

Therefore, ( f - g )(x) = 10x - 17 and ( f ° g)(-6)  = 60

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Answer: 768

Step-by-step explanation:

3, 6 ,12 ,24, 48, 96, 192, 384, 768

12 x 2 = 48

48 x 2 = 96

96 x 2 = 192

192 x 2 = 384

384 x 2 = 768

Answer:

Step-by-step expl

2.73 A,16.3 V

Answer: C.

Step-by-step explanation:

The first number is a positive 4, which is your a1. Then the geometric sequence goes to a negative implying that it is multiplied by a negative. So the a1 = 4 and it is being multiplied by a negative 3.

Answer: C

[tex]\left \{ {{a_{1}=4 } \atop {a_{n}=a_{n-1}*(-3) }} \right.[/tex]

Step-by-step explanation:

The starting amount (a1) = 4

The rate is -3 because 4 * -3 = 12 and -12 and -12 * -3 = 36 etc.

The solution to the system of equations is x = 3 and y = 10

The system is given as:

2x-2y=-14

3x-y=-1

Multiply (1) by 1 and (2) by 2

So, we have:

1(2x-2y=-14)

2(3x-y=-1 )

This gives

2x - 2y=-14

6x - 2y=-2

Subtract the equations

-4x = -12

Divide by -4

x = 3

Substitute x = 3 in 3x-y=-1

3(3)-y=-1

Evaluate

9 - y = -1

Solve for y

y = 10

Hence, the solution to the system of equations is x = 3 and y = 10

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He needs to do 10 visits to earn a free ticket.

We know that he gets 30 points just for signing up, and he gets 8.5 points for each visit, then the amount of points as a function of v, the number of visits, is:

P(v) = 30 + 8.5*v

He will get a free movie ticket when he gets 115 points, then we need to solve the linear equation:

P(v) = 115 = 30 + 8.5*v

Solving for v:

v = (115 - 30)/8.5 = 10

He needs to do 10 visits to earn a free ticket.

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Answer:

Step-by-step explanation:

To find the inverse of a function [tex]f(x)[/tex], we let [tex]f(y)=x[/tex] and then solve again for y.

For example, using [tex]g(x)=-0.5x[/tex], we will let [tex]g(y)=x[/tex], giving [tex]x=-0.5y[/tex]. This means that [tex]y=-2x[/tex], and thus [tex]g^{-1}(x)=-2x[/tex].

Using similar logic, we see that:

There are 12 motorcycles in a company.

According to the statement

The ratio of cars, trucks, and motorcycles is 4:3:2.

The total number of cars and trucks is 42.

then

4x + 3x =42

7x = 42

x = 6.

now put these values in the ratio of vehicles.

Number of cars = 4*6 = 24

Number of truck = 3*6 = 18

Number of motorcycle  = 2*6 = 12

So, There are 12 motorcycles in a company.

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The total area of the square based prism is 413.7 square units

The given parameters are:

Base length, a = 10

Height, h = 11

The total surface area is calculated as:

[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2[/tex]

This gives

[tex]A = 10^2 + 2 *10\sqrt{\frac{10^2}{4}+11^2[/tex]

So, we have:

[tex]A = 100 + 20\sqrt{246[/tex]

Evaluate

A = 413.7

Hence, the total area of the square based prism is 413.7 square units

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Answer:

can you give the question?

Step-by-step explanation:

didnt ask a question

Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.

For Rectangle PQRS:-

By Pythagoras Theorem, in right triangle PQS,

SQ² = PQ² + PS²,

or, SQ² = 8² + 16² sq. inches,

or, SQ² = 64 + 256 sq. inches,

or, SQ = √320 sq. inches,

or, SQ = 8√5 inches.

Thus, the length of diagonal SQ, of rectangle PQRS is 8√5 inches.

For Square LMNO:-

By Pythagoras Theorem, in right triangle LMO,

OM² = LM² + LO²,

or, OM² = 8² + 8² sq. inches,

or, OM² = 64 + 64 sq. inches,

or, OM = √128 sq. inches,

or, OM = 8√2 inches.

Thus, the length of diagonal OM, of square LMNO is 8√2 inches.

We know that 2*OM ≠ SQ, as 2*8√2 ≈ 8√5.

Thus, Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.

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The following pairs of lines should be matched with their descriptions as follows:

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).

In Mathematics, the condition for perpendicularity of two lines is:

m₁ × m₂ = -1

Given the following equations:

y = 2x/3 + 4 and y = -3x/2 + 9; 2/3 × -3/2 = -1.

y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.

y = 5x/6 + 8 and y = 5x/6 + 2; 5/6 = 5/6.

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Answer:

A

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is 5.

[tex]y+1=5(x+6) \\ \\ y+1=5x+30 \\ \\ y=5x+29[/tex]

The value of n from the given expression is 35/36

Given the equation below expressed as:

1/5n+3/5n=7/9

Find the LCM

(n+3n)/5 = 7/9

4n/5 = 7/9

Cross multiply

4n * 9 = 5* 7

36n = 35

n = 35/36

Hence the value of n from the given expression is 35/36

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Answer:

17) 3

18) -5/4

19) 4/2 or 2

20) 1

21) 2/4 or 1/2

22) 4/7

23) -2/2 or -1

24) -1/3

Step-by-step explanation:

the easiest thing to do is go by rise over run and count the number of units, hope this helped!

Answer:

S₁₂ = - 654

Step-by-step explanation:

there is a common difference between consecutive terms , that is

- 14 - (- 5) = - 23 - (- 14) = - 32 - (- 23) = - 9

this indicates the series is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 5 and d = - 9 , then

S₁₂ = [tex]\frac{12}{2}[/tex] [ (2 × - 5) + (11 × - 9) ]

     = 6(- 10 - 99 )

    = 6 × - 109

    = - 654

The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.

The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;

(x²+3) (x³+4x) (x²+x-i-xi) = 0.

Hence, by further factorisation; we have;

x(x²+3) (x²+4) (x-i) (x+1) = 0.

The possible values of x are therefore;

x = 0;

x²+3 = 0; x = ±√3i

x² +4 = 0; x = ±2i

x -i = 0; x = i.

x +1 = 0; x = -1

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The average IQ test score would be 100.

What is a normal distribution?

A probability distribution that is symmetric about the mean or average is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the average value occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Average IQ Score

A score of 100 is regarded as the average IQ on various tests. The majority of results (68%) are within one standard deviation of the mean (that is, between 85 and 115). This indicates that the average result is within plus or minus 15 points for almost 70% of test takers.

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Answer: The figure changed size.

Step-by-step explanation:  Dilations change the sizes of shapes.  They can either make them bigger or make them smaller.

The data is significant at a significance level of 0.01 indicating that the average mass of apples in a farmer's orchard differs from 100g to a level of 0.01. Option C is correct.

Given as the farmer states that the average mass of an apple grown in his orchard is 100g, he measures the mass of 150 apples grown in his orchard and finds that the average mass per apple is 98g and the results are calculated as statistically significant at the 0.01 level.

The null hypothesis is:

H₀ = 100

Because of the farmer's claim.

The alternative hypothesis is:

H₁ ≠ 100

The alternative hypothesis tests the farmer's claim at a level of significance. Results are calculated as statistically significant at the 0.01 level.

This means that at the 0.01 level, the null hypothesis is rejected, i.e. H the average mass of the farmer's orchard differs from 100. Since it is significant at the 0.01 level, it will be significant at the 0.05, 0.1 and increasing levels.

Thus, at the significance level of 0.01, the average mass of apples grown in the farmer's orchard differs by 100 g. The correct answer is therefore given by option C.

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Answer:

680

Step-by-step explanation:

Answer:

104.607kph

Step-by-step explanation:

Conversion from mph to kph = 1.609mph

Answer:

If you have 6 chocolate and you have to divide that into 15 people than the answer will be 2 upon 5 or 0.4 for each.

Step-by-step explanation:

Look, you're taking these kinds of questions too serious and that's why you believe they're hard, now pay close attention:

the areas are defined in cm² but the radius is defined in cm, so you need find the positive root of cm².

[tex] \sqrt{ \frac{5500 {cm}^{2} }{220 {cm}^{2} } } = \frac{r}{5cm} = = > \\ 5 = \frac{r}{5} = = = > r = 25[/tex]

and the question wants the base area:

[tex]s = \pi {r}^{2} = = = > s = 3.14 \times {(25cm)}^{2} = = > 1963.5 {cm}^{2} [/tex]