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2 years ago

Negative one-half x + 3 = 4 minus one-fourth x

Mathematics

2 answers:

Maurinko [17]2 years ago

5 0

The answer is x = -2

nadya68 [22]2 years ago

4 0

the answer is n equals -4

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10) The scale of a map is 1 inch represents 4 miles. How many miles does 0.5 inches represent?

scoundrel [369]

Answer:

2 miles

Step-by-step explanation:

1 in=4miles

0.5 in=2miles

so divide by two on each side

7 0

2 years ago

Read 2 more answers

A rectangular piece of metal is 15 in longer than it is wide. Squares with sides 3 in long are cut from the four corners and the

ziro4ka [17]

Answer:

The original dimensions of the piece of metal are

Length: 36 inches

Width: 21 inches

Step-by-step explanation:

Let

x ----> the original length pf the piece of metal

y ----> the original width pf the piece of metal

we know that

$x=y+15$ ----> equation A

The volume of the box is equal to

$V=LWH$

we have

$V=1,350\ in^3$

$L=(x-3-3)=(x-6)\ in\\W=(y-3-3)=(y-6)\ in$

$H=3\ in$

substitute in the formula of volume

$1,350=(x-6)(y-6)(3)$ ----> equation B

substitute equation A in equation B

$1,350=(y+15-6)(y-6)(3)$

solve for y

$450=(y+9)(y-6)$

$y^2-6y+9y-54=450\\y^2+3y-504=0$

Solve the quadratic equation by graphing

using a graphing tool

The solution is y=21

Find the value of x

$x=21+15=36$

therefore

The original dimensions of the piece of metal are

Length: 36 inches

Width: 21 inches

5 0

2 years ago

Find the smallest positive integer solution to the following system of congruences: x = 0 (mod 5) x = 8 (mod 11) The solution is

igomit [66]

Answer:

The smallest positive integer solution to the given system of congruences is 30.

Step-by-step explanation:

The given system of congruences is

$x=0(mod5)$

$x=8(mod11)$

where, m and n are positive integers.

It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as

$x=5m$

$x=11n+8$

$5m\cong 11n+8$

Now, we can say that m>n because m and n are positive integers.

For n=1,

$5m=11(1)+8=19$

$5m=19$

19 is not divisible by 5 so m is not an integer for n=1.

For n=2,

$5m=11(2)+8$

$5m=30$

$m=6$

The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is

$x=5(6)=30$

Therefore the smallest positive integer solution to the given system of congruences is 30.

8 0

3 years ago

)Robert is using the following data samples to make a claim about the house values in his neighborhood:

Dafna11 [192]

The answer would be A. He should use the mean because it is in the center of the data. I hope this helped ^^

4 0

3 years ago

√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q.

frutty [35]

Answer:

The smallest value of p+q is 11

It happens when p = 6 and q = 5.

=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

180 = 9*20

180 = 36*5

Those factorizations then lead to the following

$\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\$

Then we have

p+q = 2+45 = 47

p+q = 3+20 = 23

p+q = 6+5 = 11

The smallest value of p+q is 11 and it happens when p = 6 and q = 5.

Side note: p+q is smallest when we go with the largest perfect square factor.

6 0

1 year ago