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2 years ago

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On a state map, a cartographer plots Texmath at coordinates (2, 2) and Lonestar Village at coordinates (9, 16). How far is it fr

om Texmath to Lonestar Village?

2 answers:

Digiron [165]2 years ago

7 0

Since two points are given, we can use the distance formula in order to know hpw far is it from Texmath to Lonestar Village. Distance formula is written as

Distance = $\sqrt{ ( x_{2} - x_{1} )^{2} +(y_{2} - y_{1} )^{2} }$

Substituting the values, we have:

Distance = $\sqrt{ ( 9-2 )^{2} +(16-2)^{2} }$

= $\sqrt{7^2 +14^2}$

= √245 = 15.65 units

andrew11 [14]2 years ago

6 0

Answer:

the answer is:

7[5

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At an archeological site, the remains of two ancient step pyramids are congruent. If ABCD~=EFGH, find AD

worty [1.4K]

Answer: 300ft

Step-by-step explanation:

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1 year ago

A vertical plane intersects the three-dimensional object in the image and divides the object into equal halves. What is the shap

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2 years ago

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Solve the system of linear equations using multiplication.

Anna71 [15]

Answer:

$(8,-1)$

Step-by-step explanation:

The given system is:

$3x+3y=21$

$6x+12y=36$

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

$x+y=7$

$x+2y=6$

We could solve the first equation for $x$ and replace the second $x$ with that.

Let's do that.

$x+y=7$

Subtract $y$ on both sides:

$x=7-y$

So we are replacing the second $x$ in the second equation with $(7-y)$ which gives us:

$(7-y)+2y=6$

$7-y+2y=6$

$7+y=6$

$y=6-7$

$y=-1$

Now recall the first equation we arranged so that $x$ was the subject. I'm referring to $x=7-y$ .

We can now find $x$ given that $y=-1$ using the equation $x=7-y$ .

Let's do that.

$x=7-y$ with $y=-1$ :

$x=7-(-1)$

$x=7+1$

$x=8$

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

$3x+3y=21$ with $(x,y)=(8,-1)$ :

$3(8)+3(-1)=21$

$24+(-3)=21$

$21=21$ is a true equation so the "solution" looks promising still.

$6x+12y=36$ with $(x,y)=(8,-1)$ :

$6(8)+12(-1)=36$

$48+(-12)=36$

$36=36$ is also true so the solution has been verified since both equations render true for that point.

5 0

2 years ago

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A pair of fair dice is cast. what is the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one

WITCHER [35]

If a pair of fair dice is cast, the probability that the <span>sum of the numbers falling uppermost is 9, given that at least one of the numbers falling uppermost is a 3 is given by:

$\frac{P(sum\, of\, 9\, \cup\,3)}{P(3)}$

The number of outcomes of sum of 9 where at last one is 3 is (3, 6) and (6, 3) = 2.

</span>The number of outcomes of last one of the numbers falling uppermost is a 3 is (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (1, 3), (2, 3), (4, 3), (5, 3) and (6, 3) = 11.

Therefore, <span>the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one of the numbers falling uppermost is a 3 is 2 / 11.</span>

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2 years ago

the daily profit in dollars of a specialty cake shop is described by the function P(x)=-3x^2+168x-1920. Where x is the number of

forsale [732]

Answer:

28

Step-by-step explanation:

We have the following function:

$f(x)=-3x^{2} +168x-1920$

where a=-3, b=168 and c=-1920

In order to calculate the maxium profit for the company, and how many cakes should be prepared in order to reach it, we have to calculate where the parabola's vertex is ubicated. To do so, we use the following formula:

$Xv= \frac{-b}{2a}$

$Xv= \frac{-168}{2.(-3)}$

$Xv= \frac{-168}{2.(-3)}$

$Xv= 28$

So 28 cakes should be prepared per day in order to maximize profit.

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2 years ago

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