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3 years ago

One tank is filling at the rate of 3/4 gallon / 2/3 minute a second tank is filling at the rate of 3/8 gallon per 1/2 minute whi

ch tank is filling faster equation

Mathematics

1 answer:

eduard3 years ago

7 0

$\bf \cfrac{\quad \stackrel{gallons}{\frac{3}{4}}\quad }{\stackrel{minutes}{\frac{2}{3}}}\implies \cfrac{3}{4}\cdot \cfrac{3}{2}\implies \cfrac{9}{8}~g/m
\\\\\\
\cfrac{\quad \stackrel{gallons}{\frac{3}{8}}\quad }{\stackrel{minutes}{\frac{1}{2}}}\implies \cfrac{3}{8}\cdot \cfrac{2}{1}\implies \cfrac{3}{4}~g/m\\\\
-------------------------------$

$\bf \cfrac{3}{4}\cdot \cfrac{2}{2}\implies \cfrac{6}{8}\quad \textit{clearly then }\cfrac{9}{8}\textit{ is larger than }\cfrac{6}{8}
\\\\\\
\stackrel{\stackrel{tank's~volume}{gallons}}{y}=\cfrac{9}{8}\stackrel{minutes}{x}$

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Which expression is the factorization of x2 + 10x + 21?

LiRa [457]

<h2>Solution:</h2>

Equation: x² + 10x + 21

Step 1: Find two numbers that can add up to 10 and be multiplied to 21. We have: 7 & 3, in the sense that 7+3=10, and 7×3=21. Replacing 10 with 7+3, the equation is now → x² + 7x + 3x + 21

Step 2: Get the new equation bracketed → (x² + 7x) (+3x + 21)

Step 3: Use 'x' in the equation. For the first part, we have 'x'. x² = x × x so, bring out one x out side the bracket, divide 7x by = 7 → x (x +7). Do the same for the second part by dividing 21 by 3 = 7, and then bringing out 3 from the bracket → 3 (x + 7).

Bringing everything together, we have: x(x+7) +3(x+7) → (x+3) (x+7)

<h3>Final answer:</h3>

(x+3) (x+7)

<h3 />

4 0

1 year ago

One night a theater sold 186 movie tickets. an adults ticket cost $14, and a childs costs $10. in all, $2148 was taken in. How m

inna [77]

Answer:

72 adult tickets were sold and 114 child tickets were sold.

Step-by-step explanation:

x+y=186, 14x=10y=2148

x=186-y

14(186-y)+10y=2148

2604-14y+10y=2148

2604-4y=2148

-4y=-456

y=144

x=186-144 : x=72

3 0

3 years ago

polygon ABCD is defined by the points A(-4,2), B(-2,4), C(1,3), and D(2,2). match the coordinates of the points you f the transf

Tomtit [17]

Answer:

D' ..................> (-2,2)

C'' .................> (3,-1)

A''' ................> (4,-2)

B'' .................> (4,2)

Step-by-step explanation:

Before we begin, we should remember the rotation rules:

1- Rotation 90° clockwise:

Coordinates (x,y) become (y,-x)

2- Rotation 90° counter clockwise:

Coordinates (x,y) become (-y,x)

3- Rotation 180° clockwise:

Coordinates (x,y) become (-x,-y)

4- Rotation 270° counter clockwise:

Coordinates (x,y) become (y,-x) ...........> same as rotation 90° clockwise

Now, let's consider the given problem:

1- Coordinates of D' if polygon ABCD rotates 90° counter clockwise to create A'B'C'D'

Original coordinates of point D are (2,2)

Rotation 90° counter clockwise means that the new coordinates will be (-y,x) which is (-2,2)

2- Coordinates of C'' if polygon ABCD rotates 90° clockwise to create A''B''C''D''

Original coordinates of point C are (1,3)

Rotation 90° clockwise means that the new coordinates will be (y,x) which is (3,-1)

3- Coordinates of A''' if polygon ABCD rotates 180° clockwise to create A'''B'''C'''D'''

Original coordinates of point A are (-4,2)

Rotation 180° clockwise means that the new coordinates will be (-x,-y) which is (4,-2)

4- Coordinates of B'' if polygon ABCD rotates 270° counter clockwise to create A''B''C''D''

Original coordinates of point B are (-2,4)

Rotation 270° counter clockwise means that the new coordinates will be (y,-x) which is (4,2)

Hope this helps :)

5 0

2 years ago

Find the slope of each line

MissTica

1. -10/9
2. 2/5
3. -2/5
4. 3/5
5. 1/10
6. -10/3

3 0

2 years ago

Help me solve this problem 98+p=56

Arlecino [84]

p=-42

move 98 to the right side of the equal sign which becomes -98

p=56-98

do the math

p=-42

3 0

3 years ago

Read 2 more answers