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3 years ago

Solving a system of linear equations using the substitution method. 5x+4y=-26 5-x=-6y

2 answers:

5 0

Solve for x in 2nd equation
times -1 both sides
x-5=6y
add 5
x=6y+5

sub

5(6y+5)+4y=-26
30y+25+4y=-26
34y+25=-26
minus 25 both sides
34y=-51
divide both sides by 34
y=-3/2
sub back

x=6y+5
x=6(-3/2)+5
x=-18/2+5
x=-9+5
x=-4

(-4,-3/2) is solution

Naddik [55]3 years ago

5 0

We write x in terms of y in order to substitute using the second equation
-x=-6y-5
x= 6y+5

We substitute what we got above in the first equation
5(6y+5)+4y=-26

We solve for y
30y+25+4y=-26
34y+25=-26
34y=-51
y=-51/34

Then we plug what we got for y back in our first equation in order to get the value of x as well

x=6(-51/34)+5
x=-4

So the solutions are:
x=-4
y=-1.5

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Which expression represents the number 2i4−5i3+3i2+−81‾‾‾‾√ rewritten in a+bi form?

vichka [17]

Answer:

The expression $-1+14i$ represents the number $2i^4-5i^3+3i^2+\sqrt{-81}$ rewritten in a+bi form.

Step-by-step explanation:

The value of $i$ is $i=\sqrt{-1}[tex] or [tex]i^{2}=-1[\tex].Now [tex]i^{4}$ in term of $i^{2}[\tex] can be written as, [tex]i^{4}=i^{2}\times i^{2}$

Substituting the value,

$i^{4}=\left(-1\right)\times \left(-1\right)$

Product of two negative numbers is always positive.

$\therefore i^{4}=1$

Now $i^{3}$ in term of $i^{2}[\tex] can be written as, [tex]i^{3}=i^{2}\times i$

Substituting the value,

$i^{3}=\left(-1\right)\times i$

Product of one negative and one positive numbers is always negative.

$\therefore i^{3}=-i$

Now $\sqrt{-81}$ can be written as follows,

$\sqrt{-81}=\sqrt{\left(81\right)\times\left(-1\right)}$

Applying radical multiplication rule,

$\sqrt{ab}={\sqrt{a}}\sqrt{b}$

$\sqrt{\left(81\right)\times\left(-1\right)}={\sqrt{81}}\sqrt{-1}$

Now, $\sqrt{\left(81\right)=9$ and $\sqrt{-1}}=i$

$\therefore \sqrt{\left(81\right)\times\left(-1\right)}=9i$

Now substituting the above values in given expression,

$2i^4-5i^3+3i^2+\sqrt{-81}=2\left(1\right)-5\left(-i\right)+3\left(-1\right)+9i$

Simplifying,

$2+5i-3+9i$

Collecting similar terms,

$2-3+5i+9i$

Combining similar terms,

$-1+14i$

The above expression is in the form of a+bi which is the required expression.

Hence, option number 4 is correct.

5 0

3 years ago

How Many Close Confidants Do People Have? In a recent study,1 2006 randomly selected US adults (age 18 or older) were asked to g

yaroslaw [1]

Answer:

0.08065

Step-by-step explanation:

Given that in a recent study,1 2006 randomly selected US adults (age 18 or older) were asked to give the number of people in the last six months with whom you discussed matters that are important to you.

If X is random variable then X has mean 2.2 and s = 1.4

n=2006

Std error of mean = $\frac{1.4}{\sqrt{2006} } \\=0.03126$

For 99% since sample size is large, t and z distn almost coincide.

Hence we can take 2.58 as critical value

Margin of error at 99% = $2.58*0.03126\\=0.08065$

7 0

3 years ago

Which of the following values of r will result in a true statement when substituted into the given equation? -r + 5(r + 2) = -10

kramer

Answer:

Choice B is correct.

Explanation:

The given equation is -r+5(r+2)=-10

Put r=-5 into the above equation

-(-5)+5(-5+2)=-10

5+5(-3)=-10

5-15=-10

-10=-10

Right and left side of above equation is equal by putting r=-5 so it is true statement.

6 0

3 years ago

Read 2 more answers

In sweden, vat is at 25%. ella buys a hat in sweden for 50 sek( swedish krona). find the vat paid by ella.

V125BC [204]

If Ella buys a hat in Sweden for 50 SEK with 25% VAT, then the VAT paid by Ella is 12.5 SEK

A Value-Added Tax (VAT) is a consumption tax assessed on the value added in each production stage of a good or service

Given,

The price of hat = 50 SEK

VAT =25%

The amount paid as VAT= $50(\frac{25}{100})$

=12.5 SEK

Hence, If Ella buys a hat in Sweden for 50 SEK with 25% VAT, then the VAT paid by Ella is 12.5 SEK

Learn more about VAT here

brainly.com/question/20628016

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3 0

1 year ago

A shipping container is in the shape of a right rectangular prism with a length of 13

Lilit [14]

Answer:

371 pounds

Step-by-step explanation:

First you find how much space is in the container

length is 13

width is 15

height is 10

2 * (15 * 13 + 10 * 13 + 10 * 15)= 950

The total space in the container is 950

Then multiply it by 0.39 to find the weight

950 * 0.39 = 370.5

Round to the nearest pound

.5 rounded is rounded to a whole number

371 pounds

8 0

3 years ago