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3 years ago

A cleaners recommend 1 1/2 cup of cleaner to 12 cups of water what is the ratio of cleaner to water in simplest form

Mathematics

1 answer:

Evgen [1.6K]3 years ago

6 0

Answer:

8 cups of water : 1 cup of cleaner

Step-by-step explanation:

To find the ratio, divide one value by the other. 12÷1½=8, so the ratio is 8 cups of water : 1 cup of cleaner.

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Find the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4)

Zolol [24]

Answer:

y = 8

Step-by-step explanation:

Two triangles are said to be congruent if all the three sides and three angles of both triangles are equal.

The distance between two points on the coordinate plane is given as:

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\$

In triangle ABC:

$|AB|=\sqrt{(2-8)^2+(6-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|AC|=\sqrt{(5-8)^2+(0-4)^2}=5\\\\|BC|=\sqrt{(5-2)^2+(0-6)^2 }=\sqrt{45}$

In triangle MNO:

$|MN|=\sqrt{(1-7)^2+(2-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|MO|=\sqrt{(4-7)^2+(y-4)^2}\\\\|NO|=\sqrt{(4-1)^2+(y-2)^2 }$

Since triangle ABC and triangle MNO are congruent, hence:

|AB| = |MN| = 2√10, |AC| = |MO| = 5, |BC| = |NO| = √45

$|AC|=|MO|=5\\\\\sqrt{(4-7)^2+(y-4)^2}=5\\\\(4-7)^2+(y-4)^2=25\\\\9 +(y-4)^2=25\\\\(y-4)^2=16\\\\square\ root\ of\ both\ sides:\\\\y-4=4\\\\y=4+4\\\\y=8$

Hence O = (4, 8)

3 0

3 years ago

What is the determinant of the coefficient matrix of the system

Ad libitum [116K]

$\left[\begin{array}{ccc}-3&0&-2\\9&0&5\\6&0&-12\end{array}\right] \\D(system)= |-3|\left[\begin{array}{ccc}0&5\\0&-12\\\end{array}\right]-0 \left[\begin{array}{ccc}9&5\\6&-12\\\end{array}\right] +|-2| \left[\begin{array}{ccc}9&0\\6&0\\\end{array}\right] \\=3*0-0+0=0\\
determinant of system is 0$

8 0

3 years ago

Read 2 more answers

the radius of a battery is 16.5 meters and is 56.3 tall what is the volume of the battery round to the nearest tenth

horrorfan [7]

Answer:

48153.3

Step-by-step explanation:

π x 16 x 52 x 56 x 3

if π = 3.14, then multiply 3.14 with the other multipliers.

5 0

3 years ago

Example 3:

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

5!/(3!(5-3)!)

5!/(3!x2!)

120/12

7 0

3 years ago

Reduce 12/20 to lowest term

skelet666 [1.2K]

Answer:

3/5

Step-by-step explanation:

12/20

(divide both by 2)

12/2= 6

20/2=10

6/10

(divide by both by 2)

6/2= 3

10/2= 5

3/5

7 0

3 years ago