two sides of a triangle are 18 ft and 23 ft. Find the range for the measure of the third side.

Answer:

see explanation

Step-by-step explanation:

(a)

common ratio r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{14}{28}[/tex] = [tex]\frac{1}{2}[/tex] = 0.5

(b)

to find the next term, multiply the previous term by r = 0.5

14 × 0.5 = 7

7 × 0.5 = 3.5

3.5 × 0.5 = 1.75

the next 3 terms in the sequence are 7 , 3.5 , 1.75

⇒In a geometric sequence to find the common ratio(r) we use the formula

[tex]r=\frac{T_{2} }{T_{1} }[/tex]

But in general we use the formula is [tex]r=\frac{T_{n+1} }{T_{n} }[/tex]

In this case we are going to use

[tex]r=\frac{14}{28} \\r=\frac{1}{2}[/tex]

⇒The common ratio of the sequence is [tex]\frac{1}{2}[/tex], to get the 3 consecutive terms you are going to multiply the current term by the common ratio which in this case is [tex]\frac{1}{2}[/tex]

[tex]T_{3} =T_{2} * r\\\\T_{3}=14(\frac{1}{2} )\\T_{3} =7[/tex]

[tex]T_{4} =T_{3} *r\\T_{4}=7(\frac{1}{2} )\\T_{4}=\frac{7}{2}[/tex]

[tex]T_{5}=T_{4} *r\\T_{5}=\frac{7}{2} *\frac{1}{2} \\T_{5}=\frac{7}{4}[/tex]

If you have any questions ask me as soon as possible.

GOODLUCK!!

Answer: Every 15 minutes he runs a mile. 60 / 4 = 15

I hope this helps or answers the question needed

Using the equation of motion, it can be determined that Alexander travels at an average speed of 37.73 m/s while operating a bike.

Equations of motion are equations that explain how a physical system behaves in terms of how its motion changes over time.

The three equations are,

For the initial 5.98 seconds, initial velocity = 0, acceleration = 10.3 m/s and time taken = 5.98 s

Using first equation of motion,

v = u + at

v = 0 + 10.3(5.98) = 61.594 m/s

He then kept this speed up for 7.92 seconds.

For the last 4.33 seconds, final velocity = 0, initial velocity = 61.594 m/s

Acceleration = (0-61.594)/4.33 = -14.224 m/s

Distance travelled in 5.98 seconds is given as follows:

s = u t + 1/2(at²)

= 0 + 1/2(10.3)(5.98)²

= 184.16 m

Distance travelled in 7.92 seconds = 61.594 × 5.98 = 368.33 m

Distance travelled in 4.33 seconds is given as follows:

s = u t + 1/2(at²)

s = 61.594(4.33) + 1/2(-14.224)(4.33)²

= 133.35 m

Total distance travelled = 184.16 + 368.33 + 135.35 = 687.84 m

Average speed = Total distance/Total time = 687.84/(5.98+7.92+4.33)

= 37.73 m/s

Therefore, average motion speed for Alexander while riding a bike is 37.73 m/s which is calculated by using the equation of motion.

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ok it literally shows on the figure the length of the side AC is 6x + 7.

Answer:

AC = 25 units

Step-by-step explanation:

since ∠ A and ∠ C are congruent then the 2 legs BC and AB are congruent

BC = AB ( substitute values )

7x - 1 = 5x + 5 ( subtract 5x from both sides )

2x - 1 = 5 ( add 1 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Then

AC = 6x + 7 = 6(3) + 7 = 18 + 7 = 25

Using the triangle inequality theorem the range of measures of the third side is 5 < x < 41

The triangle inequality theorem states that any side of a triangle must be shorter than the other two sides added together.

In other words, the triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Therefore, for a triangle that has the sides a, b and c will follow the principle below:

c < a + b

b < a + c

a < b + c

Therefore, the triangle has two sides as 18 ft and 23 ft. The range of the third side is as follows:

x < 23 + 18; x < 41

18 < 23 + x

23 < x + 18

Therefore, base on the first and third inequality.

x < 41

x > 5

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (1500)(0.07)(8) \implies I = 840[/tex]

Answer:

11 times

Step-by-step explanation:

-99/-9=11

The solution to the equation is x = 5.24

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

(x - 3)^2 = 5

Take the square root of both sides

So, we have

x - 3 = 2.24

Add 3 to all sides of the equation

So, we have

x = 5.24

Hence, the solution is x = 5.24

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Answer: 49 degrees

Step-by-step explanation:

130+99=229

229-180=49

49 degrees

180 degrees is a straight line

Answer:

195 feet? (I know the answer but I'll leave the rest to you about typing it either cm2 or those stuff.

Step-by-step explanation:

To work this out so, congruent means identical. We already have the answer to EF so 13 x ? But BC = 15 feet. And BC = FG So,

13 x 15 = 195.

Hope this helps

The temperature in salt lake city will be 0° Celsius.

Temperature tells us about the degree of hotness or coldness of a body. According to the thermodynamics, temperature is a measure of the average kinetic energy of the atoms or molecules in the system.

Given is Salt Lake City where it is 8˚ colder than it is in Houston.

The degree of coldness on Celsius scale increase as the temperature tends to negative values and degree of hotness on Celsius scale increase as the temperature tends to positive values. The temperature in Houston is 8° Celsius. Since, the temperature is 8 degrees colder, we will subtract 8° from the temperature value in Houston. Therefore, temperature in salt lake city will be -

T[S] = + 8 - 8 = 0° Celsius

Therefore,  the temperature in salt lake city will be 0° Celsius.

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Given,

Total distance [tex]=2\frac{1}{2}[/tex] miles

You run 1/3 of that distance on a hill.

Distance on a hill[tex]=\frac{1}{3} * 2\frac{1}{2}[/tex] miles

You run down a slope for the last 1/2 of the hill=[tex]\frac{1}{3} * 2\frac{1}{2}*\frac{1}{2}[/tex] miles[tex]=\frac{5}{12}[/tex] miles

Distance you run down the slope [tex]=\frac{5}{12}[/tex] miles

The domain of a function f(x) is the set of values of the variable x for which the function is defined (has a defined finite value).

In the case of rational functions like this one, the function becomes undefined when the denominator is 0, so we can write:

As the square root will only give positive values or zero, there is no value of x that will make the square root be equal to -5. Then, this condition does not give us any discontinuity for f(x).

We have now to consider that the square root of (20-x) will not accept negative arguments in order to be in the realm of real numbers. So then, we have the condition:

Then, f(x) will not be defined for x that do not satisfy this condition.

We can conclude that f(x) is defined for all values of x that are equal or less than 20.

Answer: The domain is {x: x<=20}

Then

Answer:

[tex]23+4x(2+5)<15-5x(8-7)]2^5[/tex]

Answer:

X+1

Step-by-step explanation:

x+1

The probability of a head and an even number is 1/4.

Probability is the occurrence of a certain event out of the total events than can occur in a given context.

Given event is a coin is tossed and then a die is rolled.

∴ The sample space (S) is = (H,1), (T,1), (H,2), (T,2), (H,3),(T,3), (H,4), (T,4), (H,5), (T,5), (H,6), (T,6).

So, the number of sample spaces N(S) = 12.

The number of heads and an even number N(H,E) = 3.

∴ The probability of a head and an even number is = N(H,E)/N(S).

= 3/12.

= 1/4.

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The given parameters did not satisfied the conditions. Therefore, it is not a right angle triangle.

What is triangle?

In mathematics, the triangle is a closed polygon shape which has three vertex as well as three sides. It consist of three forms depending upon the sides. If all the sides are different then it is scalene otherwise equilateral triangle.

According to the question, the given triangle parameters are as follows:

AC = 6 cm; AB = 15 cm; BC = 9 cm;

Using Pythagoras theorem, the right angle property can be checked:

Let us assume the triangle ABC, with three sides:

AB² + BC² = AC² ⇒ (15)² + (9)² = (6)²

The given parameters did not satisfied the right angle triangle conditions. Therefore, it is not a right angle triangle.

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Answer:

  not a triangle

Step-by-step explanation:

You want to know if side lengths AC=6 cm, AB = 15 cm, and BC = 9 cm will define a right triangle.

The triangle inequality requires the sum of the two shortest sides of a triangle exceed the length of the longest side. Here the requirement for the given lengths to form a triangle is ...

  6 cm + 9 cm > 15 cm . . . . . . . . false

The given side lengths do not satisfy the triangle inequality, so do not form any kind of triangle.

__

Additional comment

Side lengths of a right triangle will satisfy the Pythagorean theorem, so that would be the test for a right triangle. We used the triangle inequality here, because we noticed the short sides add up to the long side. We need go no further, because these lengths do not even form a triangle.

The value of sin ∠A in the right triangle is 3 / 5

A right triangle is a triangle that has one of its angles as 90 degrees.

Base on the angles, the side of a right triangle can be named as follows:

Using trigonometric ratio, sin ∠A can be found as follows:

sin ∠A = opposite / hypotenuse

Hence,

opposite side = 3

hypotenuse side = 5

Therefore,

sin ∠A = 3 / 5

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The first step to solve this question is to find the values of h(-5) and g(-2)

In order to do that, you need to use the value of x=-5 in the function h(x) and x=-2 in the function g(x).

So we have that:

Now we can calculate the product of h(-5) and g(-2):

So the value to fill the blank is -68.

The correct answer is 0.4834

There can only be one tornado every year on the calendar. This indicates that there are only two conceivable outcomes of the event: either there will be one tornado or none at all.

The likelihood of a tornado in any given year is 0.14. This indicates that an event's chance of occurring is fixed. p = 0.14

The frequency of tornadoes in one year is unrelated to the quantity in other years. This indicates that the incidents are unrelated to one another.

The likelihood that there won't be more than two tornadoes in a 12-year period has to be calculated. This indicates that the number of trials, n, is set at 12.

p = 0.14

q = 1 - p = 1 - 0.14 = 0.86

n = 12

x = 2

We need to find: P( x < 2)

Fewer than 2 tornadoes means either 1 or 0 tornado. So,

P(x < 2) = P(x=0) + P(x=1)

the likelihood of less than two tornadoes occurring in a 12-year period is 0.4834

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The probability that the father and son will obtain a kill if they both fired at an animal the same time is 0.9

The probability of an event is the likelihood of the occurrence of event.

The average number of animals the father kills every 5 shots he takes = 2

The average number of animals the son kills every 2 shots he takes = 1

[tex]Probability = \dfrac{Number \ of \ required \ items}{Number \ of \ possible \ outcomes}[/tex]

Which gives:

The probability that the father kills an animal = [tex]P(F) = \dfrac{2}{5} = 0.4[/tex]

The probability that the son kills an animal is; [tex]P(s) = \dfrac{1}{2} =0.5[/tex]

The probability that if the father and the son fires at the same animal, the probability that they will obtain a kill, which is the probability that the animal is killed , P(A) = The probability that the father kills the animal + The probability that the son kills the animal

Which gives: P(A) = 0.4 + 0.5 = 0.9

The probability that the animal will be killed is approximately 0.9

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Hello!

To evaluate h(3)

 ==> must plug '3' into x's position in the equation:

    [tex]h(3)=3^2-4(3)+5\\h(3)=9-12+5=2[/tex]

Hope that helps!

Answer:

2

Step-by-step explanation:

substitute 3 for the x

3²-4(3)+5

9-12+5

2

Answer:

Jenny owes her sister 9.3 dollars.

Step-by-step explanation:

23.63 - 16.33 = 9.3

The value of the absolute value expression given; | 1.1n | for n > 1 as required in the task content can be classified as; Choice B; >1.

It follows from the task content that the best classification of the expression | 1.1n | for n > 1 be determined.

Since the domain of variable n is such that n > 1, it follows that 1.1 × n > 1.1.

There, it follows that; 1.1n > 1.1 > 1.

By definition; The absolute value |n| of any real number n is the non-negative value of x irrespective of its sign. For instance, the absolute value of 15 is 15, and also the absolute value of −15 is also 5.

Hence, the absolute value sign; | 1.1n | indicates positive values.

Ultimately, the correct classification of.the expression is; Choice B; > 1.

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Given that of the new books the new books the new liberian ordered;

-1/3 are science

-2/5 are biography

Let s, b and f represent the fraction of science, biography and fiction of the new book.

substituting the values of s and b given;

That's it, do you have any question about the answer? my ple