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3 years ago

Solve the system using substitution: y = -6x + 7 3x – 2y = 16 helppp

Mathematics

2 answers:

bearhunter [10]3 years ago

7 0

Answer:

x=-6 y=-1

Step-by-step explanation:

// Solve equation [2] for the variable y

[2] y = -x - 7

// Plug this in for variable y in equation [1]

[1] 3x - 2•(-x -7) = -16

[1] 5x = -30

// Solve equation [1] for the variable x

[1] 5x = - 30

[1] x = - 6

// By now we know this much :

x = -6

y = -x-7

// Use the x value to solve for y

y = -(-6)-7 = -1

Solution :

{x,y} = {-6,-1}

marissa [1.9K]3 years ago

6 0

Answer: 1 .x=-1/6y+7/6 (2.x=2/3y+16/3

Step-by-step explanation:

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1. Find the digit that makes 3,71_ divisible by 9.

KiRa [710]

QUESTION 1

We want to find the digit that should fill the blank space to make

$3,71-$

divisible by 9.

If a number is divisible by 9 then the sum of the digits should be a multiple of 9.

The sum of the given digits is,

$3 + 7 + 1 = 11$

Since

$11 + 7 = 18$

which is a multiple of 9.

This means that

$3,717$

is divisible by 9.

The correct answer is B

QUESTION 2

The factors of the number 30 are all the numbers that divides 30 exactly without a remainder.

These numbers are ;

$1,2,3,5,6,10,15,30$

The correct answer is A.

QUESTION 3.

We want to find the prime factorization of the number 168.

The prime numbers that are factors of 168 are

$2,3 \: and \: 7$

We can write 168 as the product of these three prime numbers to obtain,

$168={2}^{3}\times 3\times7$

We can also use the factor tree as shown in the attachment to write the prime factorization of 168 as

$168 ={2}^{3}\times 3\times7$

The correct answer is B.

QUESTION 4.

We want to find the greatest common factor of

$140\:\:and\:\:180$

We need to express each of these numbers as a product of prime factors.

The prime factorization of 140 is

$140={2}^{2}\times 5\times7.$

The prime factorization of 180 is

$180={2}^{2} \times{3}^{2}\times5.$

The greatest common factor is the product of the least degree of each common factor.

$GCF={2}^{2}\times5$

$GCF=20$

The correct answer is A.

QUESTION 5.

We want to find the greatest common factor of

$15,30\: and\:60.$

We need to first find the prime factorization of each number.

The prime factorization of 15 is

$15=3\times5.$

The prime factorization of 30 is

$30=2\times 3\times 5.$

The prime factorization of 60 is

$60={2}^{2}\times3 \times5$

The greatest common factor of these three numbers is the product of the factors with the least degree that is common to them.

$GCF=3 \times5$

$GCF=15$

The correct answer is C.

QUESTION 6

We want to determine which of the given fractions is equivalent to

$\frac{3}{8}.$

We must therefore simplify each option,

$A.\: \: \frac{15}{32}=\frac{15}{32}$

$B.\:\:\frac{12}{32}=\frac{4\times 3}{4\times8}=\frac{3}{8}$

$C.\:\:\:\:\frac{12}{24}=\frac{12\times1}{12\times 2}=\frac{1}{2}$

$D.\:\:\frac{9}{32}=\frac{9}{32}$

The simplification shows that

$\frac{12}{32}\equiv \frac{3}{8}$

The correct answer is B.

QUESTION 7.

We want to express

$\frac{10}{22}$

in the simplest form.

We just have to cancel out common factors as follows.

$\frac{10}{22}=\frac{2\times5}{2 \times11}$

This simplifies to,

$\frac{10}{22}=\frac{5}{11}$

The correct answer is C.

QUESTION 8.

We were given that Justin visited $25$ of the $50$ states.

The question requires that we express $25$ as a fraction of $50.$

This will give us

$\frac{25}{50}=\frac{25\times1}{25\times2}$

We must cancel out the common factors to have our fraction in the simplest form.

$\frac{25}{50}=\frac{1}{2}$

The correct answer is C.

QUESTION 9.

We want to write

$2\frac{5}{8}$

as an improper fraction.

We need to multiply the 2 by the denominator which is 8 and add the product to 5 and then express the result over 8.

This gives us,

$2 \frac{5}{8}=\frac{2\times8+5}{8}$

this implies that,

$2\frac{5}{8}=\frac{16+5}{8}$

$2\frac{5}{8}=\frac{21}{8}$

Sarah needed

$\frac{21}{8}\:\:yards$

The correct answer is D.

QUESTION 10

See attachment

QUESTION 11

We wan to write

$3\: and\:\:\frac{7}{8}$

as an improper fraction.

This implies that,

$3+\frac{7}{8}=3\frac{7}{8}$

To write this as a mixed number, we have,

$3\frac{7}{8}=\frac{3\times8+7}{8}$

This implies that,

$3\frac{7}{8}=\frac{24+7}{8}$

This gives

$3\frac{7}{8}=\frac{31}{8}$

The correct answer is B.

QUESTION 12

We want to find the LCM of $30$ and $46$ using prime factorization.

The prime factorization of 30 is $30=2\times 3\times 5$

The prime factorization of 46 is $40=2\times 23$ .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times \times3 5\times 23$

$LCM=690$

The correct answer is D.

QUESTION 13

We want to find the least common multiple of 3,6 and 7.

The prime factorization of $3$ is $3$ .

The prime factorization of 6 is $6=2\times 3$ .

The prime factorization of 7 is $7$ .

The LCM is the product of the common factors with the highest degrees. This gives us,

$LCM=2\times3 \times7$

$LCM=42$ .

The LCM is 42, therefore 42 days will pass before all three bikes will at the park on the same day again.

The correct answer is B.

See attachment for continuation.

6 0

3 years ago

Read 2 more answers

I really need help please help me

hram777 [196]

Answer:

i11, i26, i20, i21

Step-by-step explanation:

Alright, so there's an order to imaginary numbers. At the 1st power, it's i. At the second, it's -1. At the 3rd, it's -i. At the 4th, it's 1. And at the 5th, it restarts.

5 0

3 years ago

Peter has a dozen sticks of butter.He needs 1/6 of a stick to make an omelet.How many omelets can peter make

PilotLPTM [1.2K]

Answer:

72 omelets

Step-by-step explanation:

If the whole stick of butter is cut into 6 pieces, and you can use one of those 6 pieces of butter per omelet, you can make 6 omelets with one stick of butter. Now, you have 12 sticks of butter, and you can make 6 omelets with each. 12 x 6= 72. I believe u can make 72 omelets in all.

Hope this helps dear!!

5 0

3 years ago

Saul has 130 baseball cards. How many bags of 10 baseball cards does he need to get so that he will have 200 baseball cards in a

kolezko [41]

Answer:

6 bags of baseball cards

Step-by-step explanation:

3 0

2 years ago

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean

iogann1982 [59]

Answer:

0.1469

Step-by-step explanation:

Given from the question;

Mean=8.4 hrs=μ

Standard deviation=1.8 hrs=δ

Sample size, n=40

Let x=8.7

z=(x-μ)÷(δ÷√n)

Find z(8.7)

z=(8.7-8.4)÷(1.8÷√40)

z={0.3×√40}÷1.8=1.05409

z=1.0541

Read from the standard normal probabilities table

P(z>1.0541)

=0.1459

3 0

3 years ago