The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units.

A solid oblique pyramid has an equilateral triangle base with a base edge length of 14 units. The base triangle is triangle A C D. The apex is point B. The angles formed with the lateral sides are 45 degrees.

What is BC, the height of the pyramid?

7 units
7StartRoot 2 EndRoot units
14 units
14StartRoot 2 EndRoot units

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

It is important to always label your numeric answers with unit labels on order not to confuse others and to understand what it illustrates.

An example is when solving for the area of a shape abd the person writes cm³. This means volume and is incorrect.

A graph labelling is the process of assigning labels, which are often represented by integers, to the edges and/or vertices of a graph in the field of mathematics known as graph theory.

The information you need to obtain the answer must first be considered after you have determined what the challenge is asking for. You draw attention to certain aspects of the issue. After that, you label them so you can keep them organized and avoid becoming confused by them.

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Answer:

the prime factorization of 7850 is 2, 5, 5, 157

Answer:

See below

Step-by-step explanation:

Number of distinct variations:

3

[tex]\left[\begin{array}{ccc}1&5\\2&4\\3&3\end{array}\right][/tex]

The answer to x + y = 6 can pretty much be anything that equals 6 but in addition so for example 3 + 3!

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

I hope this helps or answers the question needed

Answer:

The result of [tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + \sqrt{45} - \sqrt{28} [/tex] is [tex]\tt{}6\sqrt{ 5} - 4 \sqrt{7}. [/tex]

Step-by-step explanation:

[tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + \sqrt{45} - \sqrt{28} [/tex]

[tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + 3\sqrt{5} -2 \sqrt{7}[/tex]

[tex]\tt{}6\sqrt{5} - 4 \sqrt{7}[/tex]

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

Answer:

11 times

Step-by-step explanation:

-99/-9=11

Answer:

Let's say you have a table with spots for 10 plates and each plate can hold 1 pie. But 7 plates are missing from the table. You place your pies in each spot anyway. Out of those 10 spots available, only 3 have both pies and plates.

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: -960... It seems like a really big answer but it's right!

Step-by-step explanation:

[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:

X+1

Step-by-step explanation:

x+1

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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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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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

Answer: 49 degrees

Step-by-step explanation:

130+99=229

229-180=49

49 degrees

180 degrees is a straight line

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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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 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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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 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.

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:

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!!