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fredd [130]
3 years ago
11

In the scale used on a blueprint, 141 inch represents 3 feet. On the blueprint, what is the length of a room with an actual leng

th of 24 feet.
Mathematics
1 answer:
natita [175]3 years ago
5 0
24÷3 =8
141×8=1128 inches
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Which equation represents the hyperbola in general form?
valina [46]

ANSWER

D.

9 {y}^{2}  - 4 {x}^{2}- 36y + 16x - 16 = 0

EXPLANATION

The standard equation of the hyperbola is

\frac{ {(y - 2)}^{2} }{4}  -  \frac{ {(x - 2)}^{2} }{9}  = 1

We multiply through by 36 to obtain:

9 {(y - 2)}^{2}  - 4( {x - 2)}^{2}  = 36

We now expand to get,

9( {y}^{2}  - 4y + 4) - 4( {x}^{2}  - 4x + 4) = 36

Expand :

9 {y}^{2}  - 36y + 36  - 4 {x}^{2}  + 16x - 16 = 36

To get the general form, we equate everything to zero to get,

9 {y}^{2}  - 4 {x}^{2}- 36y + 16x - 16 = 0

The correct choice is D.

7 0
3 years ago
Write the equation of circle b with center B(-2,3) that passes through (1,2)
professor190 [17]

Answer:

(x+2)^2 + (y-3)^2 = 10

Step-by-step explanation:

The standard equation for circle is

(x-a)^2 + (y-b)^2 = r^2

where point (a,b) is coordinate of center of circle and r is the radius.

______________________________________________________

Given

center of circle =((-2,3)

let r be the radius of circle

Plugging in this value of center in standard equation for circle given above we have

(x-a)^2 + (y-b)^2 = r^2    \ substitute (a,b) \ with (-2,3) \\=>(x-(-2))^2 + (y-3)^2 = r^2  \\=>(x+2)^2 + (y-3)^2 = r^2    (1)

Given that point (1,2 ) passes through circle. Hence this point will satisfy the above equation of circle.

Plugging in the point (1,2 )  in equation 1 we have

\\=>(x+2)^2 + (y-3)^2 = r^2    \\=> (1+2)^2 + (2-3)^2 = r^2\\=> 3^2 + (-1)^2 = r^2\\=> 9 + 1 = r^2\\=> 10 = r^2\\=>  r^2  = 10\\

now we have value of r^2 = 10, substituting this in equation 1 we have

Thus complete equation of circle is =>(x+2)^2 + (y-3)^2 = r^2\\=>(x+2)^2 + (y-3)^2 = 10

7 0
3 years ago
Find 4 consecutive even integers such that when three times the smallest of the intagers is added to twice the largest their sum
zhannawk [14.2K]
If x is the first of the integers then the statement is:

(x) , (x+2) , (x+4) , (x+6)

This means that the smallest is x and the largest is x + 6

so:
3(x) + 2(x+6) = 293
3x + 2x + 12 = 293
5x = 281
x = 56.2
This gives us a none integer (decimal)
What now?

Wait remember how x started as the lowest? what if x was the highest instead?

x, x-2, x-4, x-6
so:

3(x-6) + 2(x) = 293
5x = 315
x = 62.2

This is as close as have gotten to the answer
Cant seem to get an integer.
Maybe error in the question or some bad math on my part.


3 0
3 years ago
What number is a solution of the inequality y is greater than 1.9
hodyreva [135]
The question is, "<span>What number is a solution of the inequality y > 1.9?"


The answer can vary, one of them being 2.

Possible Answers: 2,3,4,5,6,7,8,9,10</span>
3 0
3 years ago
A teacher was interested in knowing the amount of physical activity that his students were engaged in daily. He randomly sampled
klasskru [66]

Answer:

The standard error of the mean is 4.5.

Step-by-step explanation:

As we don't know the standard deviation of the population, we can estimate the standard error of the mean from the standard deviation of the sample as:

\sigma_{\bar{x}}\approx\frac{s}{\sqrt{n}}

The sample is [30mins, 40 mins, 60 mins, 80 mins, 20 mins, 85 mins]. The size of the sample is n=6.

The mean of the sample is:

\bar{x}=\frac{1}n} \sum x_i =\frac{30+40+60+80+20+85}{6}=52.5

The standard deviation of the sample is calculated as:

s=\sqrt{\frac{1}{n-1}\sum (x_i-\bar x)^2} \\\\ s=\sqrt{\frac{1}{5}\cdot ((30-52.5)^2+(40-52.5)^2+(60-52.5)^2+(80-52.5)^2+(20-52.5)^2+(85-52.5)^2}\\\\s=\sqrt{\frac{1}{5} *3587.5}=\sqrt{717.5}=26.8

Then, we can calculate the standard error of the mean as:

\sigma_{\bar{x}}\approx\frac{s}{\sqrt{n}}=\frac{26.8}{6}= 4.5

6 0
3 years ago
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