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2 years ago

The length of a rectangle is six times its width.

Mathematics

1 answer:

svlad2 [7]2 years ago

6 0

Do 600 divided by 6 and it will equal 100 so you answer is 100

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21. In 4 + In(4x - 15) = In(5x + 19)

Alexxx [7]

Answer:

$x=-30;\quad \:I\ne \:0$

Step-by-step explanation:

$In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)$

$\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\$

$\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\$

$\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:$

$\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0$

3 0

3 years ago

2/5 (x-4) =2x. Solve for x

Bess [88]

$\dfrac{2}{5}(x-4)=2x\ \ \ \ |multiply\ both\ sides\ by\ 5\\\\2(x-4)=10x\ \ \ \ |use\ distributive\ property:a(b-c)=ab-ac\\\\2x-8=10x\ \ \ |add\ 8\ to\ both\ sides\\\\2x=10x+8\ \ \ \ |subtract\ 10x\ from\ both\ sides\\\\-8x=8\ \ \ \ |divide\ both\ sides\ by\ (-8)\\\\\boxed{x=-1}$

7 0

3 years ago

10. Mr. Sanchez goes to the movies every 18 days. His brother goes to the

mestny [16]

90 days.

For this question you just need to find the least common multiple of 18 and 30. That can be found by first finding the prime factorization of each number. 18 = 2 * 3 * 3 and 30 = 2 * 3 * 5. Then you multiply the 2 * 3 * 3 * 5, you ignore the 3 from 30 because 18 has more 3s. The answer is 90.

5 0

2 years ago

Ashley began a new fitness and wellness program. After 30 days she weighed 124 pounds.

Pie

Ashley lost approximately 0.53 pounds per day. After 30 days, she lost 16 pounds and 16/30=0.53

8 0

2 years ago

Rectangular prism A measures 2 inches by 7 inches by 8 inches. Rectangular prism B measures 1 inches by 5 inches by 10 inches.

satela [25.4K]

The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³

Surface Area to Volume Ratio = 43/28

<h3>Mensuration of Solids</h3>

Given Data

Rectangular prism A

Length = 2 inches

Width = 7 inches

Height = 8 inches

Surface Area

A=2(wl+hl+hw)

A=2(7*2+8*2+8*7)

A=2(14+16+56)

A= 172 inches²

Volume

Volume = L*W*H

Volume = 2*7*8

Volume = 112 inches³

Surface Area to Volume Ratio

= 172/112

= 43/28

Learn more about Mensuration of Solids here:

brainly.com/textbook-solutions/q-7-composite-figures-use-diagram-backpack-right

#SPJ1

7 0

1 year ago