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3 years ago

The sum of two numbers is 56. Their difference is 18.

Mathematics

1 answer:

IrinaVladis [17]3 years ago

8 0

Let one number be x and the other be y.
x+y=56
x-y=18
2x=74
x=37
y=19
Hope this helped!

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How many solutions does the system have? \begin{cases} 5y =15x-40 \\\\ y = 3x-8 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 5y=15x−40 y=3x−8 C

Ksenya-84 [330]

Answer:

Step-by-step explanation:

Converting the lines into the from $ax+by+c=0$

$5y=15x-40\\\Rightarrow 15x-5y-40=0$

$y=3x-8\\\Rightarrow 3x-y-8=0$

$\dfrac{a_1}{a_2}=\dfrac{15}{3}=5$

$\dfrac{b_1}{b_2}=\dfrac{-5}{-1}=5$

$\dfrac{c_1}{c_2}=\dfrac{-40}{-8}=5$

So, $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$ .

Hence, these lines have infinitely many solutions.

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3 years ago

Demerol 45mg and atropine 400mcg/ml give how much per ml to total volume to inject demerol contains 50mg/ml, atropine contains 4

OverLord2011 [107]

Answer:

Volume injected = 1.65 ml

Step-by-step explanation:

mass of Demerol =45 mg.

density of pre-filled in syringe = 50 mg/ml

Volume = 45/50 = 0.9 ml

For atropine mass = 0.3 mg

density= 400 mcg/ml [ Note : 1 mcg = 0.001 mg]

volume filled = 0.3/400(0.001) = 0.75 ml

So, the total volume filled = 0.75+0.9 = 1.65 ml

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3 years ago

how many cubic blocks of side length 1/6 inch would take to fill a rectangular prism with a length, width, and height of 1/3 inc

borishaifa [10]

Volume of one cubic block = (1/6)^3 = 1/216 cu ins

Volume of the prism = 1/3 * 2/3 * 2/3 = 4/27 cu ins

Number of blocks to fill prism = 4/27 / 1/216 = (216*4) / 27 = 32

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3 years ago

Read 2 more answers

A book costs $ 25.00. You have a coupon for 30 % off. Calculate the final price of the book with a 5% GST. (Begin by finding the

guapka [62]

Answer:

$18.375 or rounded = $18.38 (brainliest if correct)

Step-by-step explanation:

25.00- 7.5 = $17.5

5% of 17.5 = 0.875

17.5 +0.875 = 18.375

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3 years ago

Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)

Mnenie [13.5K]

One way would be to find the distance from the point to the center of the circle and compare it to the radius

for
$(x-h)^2+(y-k)^2=r^2$
the center is (h,k) and the radius is r

and the distance formula is
distance between $(x_1,y_1)$ and $(x_2,y_2)$ is
$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

r=radius
D=distance form (8,4) to center

if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle

so
$(x+2)^2+(y-3)^2=18$
$(x-(-2))^2+(y-3)^2=(\sqrt{18})^2$
$(x-(-2))^2+(y-3)^2=(3\sqrt{2})^2$

the radius is $3\sqrt{2}$
center is (-2,3)

find distance between (8,4) and (-2,3)

$D=\sqrt{(8-(-2))^2+(4-3)^2}$
$D=\sqrt{(8+2)^2+(1)^2}$
$D=\sqrt{10^2+1}$
$D=\sqrt{100+1}$
$D=\sqrt{101}$

$r=3\sqrt{2}$ ≈4.2
$D=\sqrt{101}$ ≈10.04

do r<D

(8,4) is outside the circle

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4 years ago