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3 years ago

In the standard equation of a circle (x – h)2 + (y – k)2 = r2, h and k are...

Mathematics

1 answer:

olchik [2.2K]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

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julsineya [31]

Answer:500 miles

Step-by-step explanation:

186 dollars minus 36 because it is a daily rate and you get 150 which divided by 0.30 is 500 miles

4 0

3 years ago

Tristan had 1/3 lb of grapes at home he went to the store and bought 3/8 lb of grapes what fraction of a pound of grapes does Tr

Black_prince [1.1K]

Answer:

Tristan has a 17/24 lb fraction of a pound of grapes now.

Step-by-step explanation:

Given

The number of grapes Tristan had at home = 1/3 lb

The number of grapes Tristan had at the store = 3/8 lb

To determine

What fraction of a pound of grapes does Tristan have now?

In order to get the total fraction of a pound of grapes, all we need is to add the number of grapes Tristan had at home and the number of grapes Tristan had at the store.

i.e.

Current number grapes = 1/3 + 3/8

Least Common Multiple of 3, 8: 24

Adjust fractions based on L.C.M

= 8/24 + 9/24

Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

= (8 + 9) / 24

= 17/24 lb

Therefore, Tristan has a 17/24 lb fraction of a pound of grapes now.

3 0

3 years ago

Solve for X and Y show work

ale4655 [162]

Answer:

X=5.66 or 5.65685424949

Y=4

Step-by-step explanation:

Since this is a 45,45,90 triangle, the y is also 4.

Then the x is y^2+4^2.

That means that it is 16+16=32

Now you have to square 32 which gives you 5.66

3 0

3 years ago

HELPP MEEE PLEASEEEEE!

snow_lady [41]

Let $a=x+\tfrac{5}{2}$. Then the expression $(x+1)(x+2)(x+3)(x+4)$ becomes $\left(a-\tfrac{3}{2}\right)\left(a-\tfrac{1}{2}\right)\left(a+\tfrac{1}{2}\right)\left(a+\tfrac{3}{2}\right)$.

We can now use the difference of two squares to get $\left(a^2-\tfrac{9}{4}\right)\left(a^2-\tfrac{1}{4}\right)$, and expand this to get $a^4-\tfrac{5}{2}a^2+\tfrac{9}{16}$.

Refactor this by completing the square to get $\left(a^2-\tfrac{5}{4}\right)^2-1$, which has a minimum value of $-1$.

Similar to Solution 1, grouping the first and last terms and the middle terms, we get $(x^2+5x+4)(x^2+5x+6)+2019$.

Letting $y=x^2+5x$, we get the expression $(y+4)(y+6)+2019$. Now, we can find the critical points of $(y+4)(y+6)$ to minimize the function:

$\frac{d}{dx}(y^2+10y+24)=0$

$2y+10=0$

$2y(y+5)=0$

$y=-5,0$

To minimize the result, we use $y=-5$. Hence, the minimum is $(-5+4)(-5+6)=-1$, so $-1+2019 = \boxed{\textbf{(B) }2018}$.

Note: We could also have used the result that minimum/maximum point of a parabola $y = ax^2 + bx + c$ occurs at $x=-\frac{b}{2a}$.

Solution 4

The expression is negative when an odd number of the factors are negative. This happens when $-2 < x < -1$ or $-4 < x < -3$. Plugging in $x = -\frac32$ or $x = -\frac72$ yields $-\frac{15}{16}$, which is very close to $-1$. Thus the answer is $-1 + 2019 = \boxed{\textbf{(B) }2018}$.

Solution 5 (using the answer choices)

Answer choices $C$, $D$, and $E$ are impossible, since $(x+1)(x+2)(x+3)(x+4)$ can be negative (as seen when e.g. $x = -\frac{3}{2}$). Plug in $x = -\frac{3}{2}$ to see that it becomes $2019 - \frac{15}{16}$, so round this to $\boxed{\textbf{(B) }2018}$.

We can also see that the limit of the function is at least -1 since at the minimum, two of the numbers are less than 1, but two are between 1 and 2.

5 0

3 years ago

Given the following data for resting heartrate among college students, what is the IQR? 57, 59, 60, 62, 62, 63, 64, 68, 70, 70,

aev [14]

Answer:

Step-by-step explanation:

The inter-quartile range (IQR) is the difference between the third and first quartile. The data gathered is:

57, 59, 60, 62, 62, 63, 64, 68, 70, 70, 71, 71, 73, 79, 87, 89, 90

The data set has 17 values, the first quartile is the average between the 4th and 5th values, while the third quartile is the average between the 13th and 14th values:

$Q_1 = \frac{62+62}{2}=62\\Q_3 = \frac{73+79}{2}=76$

The IQR is:

$IQR = Q_3 - Q_1 = 76 -62\\IQR = 14$

8 0

3 years ago