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3 years ago

For what values of a are the following expressions true? |a+5|=−5−a

Mathematics

1 answer:

Fed [463]3 years ago

5 0

Answer:

a can be any real number less than equal to -5

Step-by-step explanation:

When a+5 is negative,

a + 5 = -(-5 - a)

a + 5 = a + 5

All values satisfy the equation

So a < -5

When a + 5 is greater than/equal to 0,

a + 5 = -a - 5

2a = -10

a = -5

a can be any real number less than equal to -5

You might be interested in

A carpenter wants to build a rectangular box with square sides in which to put round things. the material for the bottom costs $

alexira [117]

Answer: $1.627\times 1.627\times 1.88\ ft^3$

Step-by-step explanation:

Given

Suppose side face have a dimension of l\times l

and width of h

volume $V=l^2\cdot h$

$h=\frac{V}{l^2}$

volume $V=5 ft^3$

Area of side wall is $A_s=l^2$

Area of top Wall $A_t=l\times h$

Area of bottom $A_b=l\times h$

Cost of bottom wall $c_b=20\times l\times h=20lh$

Cost of top wall $c_t=50\times l\times h=50lh$

Cost of side walls $c_s=4\times l^2\times 10=40l^2$

total cost $C=c_s+c_t+c_b=20lh+50lh+40l^2$

$C=70lh+40l^2$

$C=70\times l\times \frac{5}{l^2}+40l^2$

differentiate C w.r.t l to get minima or maxima

$\frac{\mathrm{d} C}{\mathrm{d} l}=0$

$-\frac{350}{l}+80l^2=0$

$l^3=\frac{350}{80}$

$l=1.627 ft$

$h=\frac{5}{2.648}$

$h=1.88 ft$

Dimension of Box is $1.627\times 1.627\times 1.88\ ft^3$

5 0

3 years ago

The sum of two consecutive odd numbers is 88 find the numbers

Vesna [10]

Answer:

43,45

Step-by-step explanation:

43+45=88

7 0

3 years ago

Read 2 more answers

HELPPP

Bingel [31]

I'm not sure if it only wants you to find Equation 1 or go further and solve:

x = the number of 5c coins

y = the number of 10c coins

Equation 1: the total number of coins is 65

x + y = 65

total value of $3.80

0.05x + 0.1y = 3.8

<u>Simultaneous Equations</u>

Make one coefficient the same

10 * (0.05x + 0.1y = 3.80 = 0.5x + y = 38

x + y = 65

0.5x + y = 38

Subtract the equations

(x + y) - (0.5x + y)= 65 - 38

(x - 0.5x) + (y - y) = 65 - 38

0.5x = 27

x = 54

Substitute it into the original equation to find y.

x + y = 65

54 + y = 56

y = 65 - 54 = 11

Substitute it into the other equation to check it's right.

0.05x + 0.1y = 3.8

0.05(54) + 0.1(65) = 3.8

x = 54 5c coins

y = 11 10c coins

8 0

3 years ago

What fraction can not be simplified but has 24 as its bottom number

exis [7]

There are many different fractions that cannot be simplified with a 24 as the denominator! A few examples include:
1/24
5/24
7/24
33/24
107/24
Notice all of the numerators are prime.

3 0

3 years ago

Q1: Gabbi purchased a 30 lb. bag of dog food. Gabbi has 3 dogs that each eat 20 ounces of dog food per day. How many days will t

olya-2409 [2.1K]

Answer:

x=8

Step-by-step explanation:

First multiply 30 and 16 to find out how many ounces are in the 30 lb. bag of dog food.

30 x 16=480

Since the 3 dogs eat 20 ounces of food, we can make a equation.

3(20x)=480

20 x 3=60

60x=480

x=8

<u>Final answer</u>

8 days

3 0

3 years ago