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3 years ago

2(k+m) = 5, solve for m

Mathematics

1 answer:

Dovator [93]3 years ago

3 0

$2(k+m)=5\ \ \ \ | divide\ by\ 2\\\\
k+m=2,5\ \ \ \ | subtract\ k\\\\
m=2,5-k\\\\Solution\ is\ m=2,5-k.$

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etermine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 3 2 x

nata0808 [166]

Answer:

(32/15, -2/5)

Step-by-step explanation:

(1) ³/₂x - 2y = 4

(2) x + ⅓y = 2

(3) 3x - 4y = 8 Multiplied (1) by 2

(4) 3x + y = 6 Multiplied (2) by 3

5y = -2 Subtracted (3) from (4)

(5) y = -⅖ Divided each side by 5

x + ⅓(-⅖) = 2 Substituted (5) into (2)

x - ²/₁₅ = 2

x = 2 + ²/₁₅ Added ²/₁₅ to each side

x = 32/15

The system of equations has only one solution: (32/15, -2/5).

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3 years ago

The Tennessee Titans scored 22 points in week 5 and 35 points in week 6. Find the percent of increase.

Shalnov [3]

Answer:

59.09%

Step-by-step explanation:

35-22=13

13/2= .59090909=59.09%

3 0

3 years ago

Find the value of x such that the area of a triangle whose vertices have coordinates (6, 5), (8, 2) and (x, 11) is 15 square uni

Serjik [45]

Answer:

$x =12\ or\ -8$

Step-by-step explanation:

Given

$(x_1,y_1) = (6,5)$

$(x_2,y_2) = (8,2)$

$(x_3,y_3) = (x,11)$

$Area = 15$

Required

Find x

The area is calculated as thus:

$Area = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$

Substitute values

$15 = \frac{1}{2}|6*(2 - 11) + 8*(11 - 5) + x(5 - 2)|$

$15 = \frac{1}{2}|6*(-9) + 8*(6) + x(3)|$

$15 = \frac{1}{2}|-54 + 48 + 3x|$

$15 = \frac{1}{2}|-6 + 3x|$

Multiply through by 2

$2 * 15 = \frac{1}{2}|-6 + 3x| * 2$

$30 = |-6 + 3x|$

Remove absolute sign

$30 = -6 + 3x\ or\ -30 = -6 + 3x$

Add 6 to both sides

$36 = 3x\ or\ -24 = 3x$

Divide by 3

$12 = x\ or\ -8 = x$

$x =12\ or\ -8$

<em>So, the coordinates are (-8, 11) or (12,11)</em>

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3 years ago

Two rectangles are similar. The length and width of the first rectangle are 12

Masja [62]

Answer:

scale factor = 1.2

Step-by-step explanation:

To determine the scale factor, calculate the ratio of the length of the second rectangle to the length of the first rectangle. The corresponding ratio of widths should also equal the same ratio.

scale factor = $\frac{14.4}{12}$ = $\frac{6}{5}$ = 1.2

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3 years ago

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet a

Brrunno [24]

Answer:

Step-by-step explanation:

The student needs to check all algebraic and mathmatical calculations for errors and typos. I'm old and have been prone to making mistakes.

Cylinder A DIAMETER 12 ft and Height 13 ft

Cylinder B DIAMETER 10 ft and Height 16 ft

After pumping How much water remains in cylinder A

Volume of a cylinder = π(radius)²h is the normal form since they provided the diameter I will use Volume of a cylinder = π(diameter/2)²h

Water remaining in A = Volume of A - Volume of B =

VolA - VolB = π(D for A/2)²H of A - π(D for B/2)²H of B

writing if a little more condensed

VolA - VolB = π(D for A/2)²H of A - π(D for B/2)²H of B

Va - Vb = π(Da/2)²Ha - π(Db/2)²Hb

= π [(Da²/2²)Ha - (Db²/2²)Hb] factored out the π

= π/4 [ Da²Ha - Db²Hb] factored out the (1/2)²

I can't think of any other algebraic steps

Va - Vb = Water Remaining in Container A = π/4 [ Da²Ha - Db²Hb]

= π/4 [ (12²)(13) - (10²)(16)]

= π/4 [ (144)(13) - (100)(16)]

= π/4 [ 1872 - 1600 ]

= π/4 [272]

= π [ 272/4 ]

= π [ 136 / 2]

= π [ 68 ]

= π (68)

= 213.6 ft³ rounded to the nearest tenth

I checking my answer by using V = πr²h r = d/2

Va - Vb = π [ra²ha - rb²hb]

= π [6²(13) - 5²(16)]

= π [(36)(13) - (25)(16)]

= π [ 468 - 400]

= 68 π

= 213.6 ft³ I got the same answer

= π

test

8 0

3 years ago