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3 years ago

Solve the system by substitution.

Mathematics

2 answers:

IgorLugansk [536]3 years ago

6 0

It would equal (8,3)

dsp733 years ago

4 0

Answer:

(x,y) = (8,3)

Step-by-step explanation:

3/4x - 3 = 1/4x +1

x = 8

y = 1/4 * 8 + 1

y = 3

(x,y) = (8,3)

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What's the difference between adding two rational number and get a negative number

nikklg [1K]

Comparing two rational numbers

Use fraction form:

Make the denominators the same and compare the numerators. The number with the smaller numerator is smaller. For example, to compare a/b and c/d, we rewrite

a/b=a*d/b*d

= ad/bd and c/d = c*b/d*b=bc/bd

Now just compare the numerators : "ad" and "bc"

Multiplying and Dividing Rational Numbers

Multiplying and dividing rational numbers in decimal form is the same as multiplying and dividing integers. The decimal place of the product is the same of all decimals of all multiplied numbers. For example, 3.12*2.4.

Solution => 3.12*2.4=7.488

When multiplying or dividing rational numbers in fractional form, you multiply the numerators (N*N) and then multiply the denominators (D*D).

When dividing rational numbers in fractional form, first take the reciprocal of the divisor, and then multiply the numerators and the denominators.

Example => 5/9 divided by 2/7 .

Solution => 5/9 * 7/2 = 35/18

Adding Rational numbers

Adding and Subtracting rational numbers in decimal form is the same as adding and subtracting integers.

Example => -3.54+2.79=-0.75

When adding or subtracting rational numbers in fractional form, first make the denominator equal, and then add or subtract the numerators.

6 0

3 years ago

Given: ΔАВС, m∠ACB = 90°,m∠ACD = 30°,AD = 8 cm. Find: CD, Perimeter ΔABC Please solve!

sukhopar [10]

If m ACD = 30 => m DCB = 60.
In triangle ACD:
$sin 30^{o}=sin \frac{AD}{AC} =\ \textgreater \ \frac{1}{2} = \frac{8}{AC} =\ \textgreater \ AC=16
$
$CD= 8 \sqrt{3}$
$BC= 16\sqrt{3}$
AC^{2}+CB^{2}=AB^{2} => AB= $\sqrt{1024}$ =32.
=> P=16+32+ $16 \sqrt{3}$ =48 + $16 \sqrt{3}$ .

8 0

4 years ago

Find the area. Show formulas, work, and label your answer.

egoroff_w [7]

Answer:

34.1

Step-by-step explanation:

8 4/5 is not needed. The other two will given you the answer.

Area = 1/2 * b * h

b = 12 2/5 = 12.4

h = 5 1/2 = 5.5

Area = 1/2 * 12.4 * 5.5

Area = 34.1 square feet.

6 0

3 years ago

Write 9,540,000 in expanded form using exponents to show powers of 10

krek1111 [17]

Answer:

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

Step-by-step explanation:

Given : 9,540,000

To find : Write 9,540,000 in expanded form using exponents to show powers of 10.

Solution : We have given 9,540,000

Here 9 is at million place 9000000

5 is at hundred thousand place = 500,000.

4 is at tens thousand place = 40,000

We expanded it as

9, 000,000 + 500,000+40,000.

In term of power of 10.

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

Therefore,

$9* 10^{6}+ 5* 10^{5}+4* 10^{4}$ .

6 0

3 years ago

Five distinct numbers are randomly distributed to players numbers 1 through 5. Whenever two playerscompare their numbers, the on

ad-work [718]

Answer:

Observe that the first and the second player have equal probability to get any of number. Using the principle of that symmetry, we have that

$P(X=0)=\frac{1}{2}$

Event X = 1 means that the first player has got greater number than the second player, but not than the third player. So, choose any three numbers out of five of them and say that the minimal number out of these three goes to the second player, mean number to the first one and the largest to the third one. Permute remaining two numbers on remaining two people. Hence

$P(X=1)=\frac{1}{6}$

Event X = 2 means that the first player has got greater number than the second and the third player, but not than the fourth player. So, choose any four numbers out of five of them and say that the minimal number and the next minimal out of these four go to the second and the third player (and permute them), third number to the first one and the largest to the fourth player. Give remaining number to the last person. Hence

$P(X=2)=\frac{1}{12}$

Event X = 3 means that the first player has got greater number than the second, the third, and the forth player, but not than the fifth player. So, permute these five numbers as follows: give the highest to the last person, the second highest to the first, and permute remaining numbers on the remaining people. Hence

$P(X=3)=\frac{1}{20}$

Event X = 4 means basically the first player has won all the battles i.e, he has got the greatest number. Hence

$P(X=4)=\frac{1}{5}$

7 0

3 years ago