Graph the line 3x + 6y =12.

9514 1404 393

Answer:

  x = 19

Step-by-step explanation:

The two marked angles are corresponding angles, so have the same measure.

  6x -9 = 5x +10

  x = 19 . . . . . . . . . add 9-5x

Answer

1/3

Step-by-step explanation:

Answer:

1/2 is bigger than 1/3 by a little bit

Answer:

14 month

Step-by-step explanation:

Lets create equations for these two gyms. I believe this is an algebra 1 problem.

Community Gym: y=70x+50

Workout Gym: y=60x+190

Because both gyms are equal to y, we can set them together and solve for x.

70x+50=60x+190

10x=140

x=14

You can find the cost by plugging in 14 into both of the equations. You get a cost of $1030 after 14 months

Therefore, after 14 months you will have paid the same amount for both gyms.

Answer:

x = 14 months, $1030

Step-by-step explanation:

The expressions are,

→ 70x + 50

→ 60x + 190

Forming the equation,

→ 70x + 50 = 60x + 190

Now required value of x will be,

→ 70x + 50 = 60x + 190

→ 70x - 60x = 190 - 50

→ 10x = 140

→ x = 140/10

→ [ x = 14 months]

The amount of money will be,

→ 70(14) + 50 = 60(14) + 190

→ 980 + 50 = 840 + 190

→ $1030 = $1030

Hence, it will take 14 months.

Answer:

30.9 is your answer

Step-by-step explanation:

Answer:

$110

Step-by-step explanation:

=0.15(x-200)+20

=0.15(800-200)+20

=0.15(600)+20

=90+20

=$110 paid

Answer:

44

Step-by-step explanation:

hi! we can plug in 7 for each x in this equation.

f(7)=5(7)+7+2

=35+7+2

=35+9

=44

Answer:

Step-by-step explanation:

Simplifying

3x = 5 + 2(3 + 4x)

3x = 5 + (3 * 2 + 4x * 2)

3x = 5 + (6 + 8x)

Combine like terms: 5 + 6 = 11

3x = 11 + 8x

Solving

3x = 11 + 8x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8x' to each side of the equation.

3x + -8x = 11 + 8x + -8x

Combine like terms: 3x + -8x = -5x

-5x = 11 + 8x + -8x

Combine like terms: 8x + -8x = 0

-5x = 11 + 0

-5x = 11

Divide each side by '-5'.

x = -2.2

Simplifying

x = -2.2

Answer:

x = -11/5

Step-by-step explanation:

3x = 5 + 2(3 + 4x)

~Distribute left side

3x = 5 + 6 + 8x

~Combine like terms on the left side

3x = 11 + 8x

~Subtract 8x to both sides

-5x = 11

~Divide -5 to both sides

x = -11/5

Best of Luck!

9514 1404 393

Answer:

  cos θ = 2/3

Step-by-step explanation:

We presume you want the value of the cosine for

  sin θ = √5/3 ≈ 0.745356

__

There are several possible approaches you can take to this problem.

1) Using the trig identity:

  cos = √(1 -sin²)

  cos θ = √(1 -(√5/3)²) = √(1 -5/9) = √(4/9)

  cos θ = 2/3

__

2) Another approach you can take is to use a calculator to find the angle, then use the calculator to find the cosine of the angle.

  cos θ = cos(arcsin(√5/3)) = cos(arcsin(0.745356)) = cos(48.19°) ≈ 0.666667

  cos θ = 2/3

__

3) Yet another approach is to check the answer choices for reasonableness.

You are given sin θ = 0.745356. This is more than 0.707107, the value where sine and cosine are equal, so the cosine value must be less than 0.707. The answer choices are ...

  2/3 ≈ 0.667

  3/2 . . . greater than 1; not a viable cosine value

  2√5/5 ≈ 0.894 . . . too large

  √5/2 . . . greater than 1; not a viable cosine value

  3√5/5 . . . greater than 1; not a viable cosine value

So, just looking at the values of the offered answer choices, you can choose the correct one. It is the only value with the appropriate magnitude.

  cos θ = 2/3

Answer:

18

Step-by-step explanation:

count

The number of students measured in this sample is 18.

The number of students measured is the number of heights that were acquired for the sample.

Looking at the question, the number of heights acquired were 18 which means that there were 18 students.

Knowing the number of students is important as it can help you calculate things such as mean:

Mean = Sum of heights / Number of students

= (75 + 72 + 72 + 73 + 74 + 65 + 69 + 74 + 70 + 70 + 71 + 75 + 71 + 75 + 69 + 75 + 78 + 70) / 18

= 72.11

In conclusion, the number of students measured is 18.

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Answer:

About 780 plants

Step-by-step explanation:

195 flowers*4 volenteers=780 plants

Answer:

900 people

Step-by-step explanation:

.36x=324

×=324÷.36

x=900

900 people were in the survey.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

324 indicated that they regularly work more than 45 hours a week.

and  36% of those surveyed.

let the total people surveyed be x

36% of x= 324

36 x/100 = 324

36 x = 32400

x= 32400 / 36

x= 900

Hence, total 900 people are surveyed.

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Answer: Either 8 dimes and 6 nickles, or 4 quarters and 10 pennies. Both combinations add up to $1.10.

Have a nice day

The 14 coins can be:

- 8 dimes and 6 nickels

Or

- 10 pennies and 4 quarters

Given,

14 coins make up $1.10

We need to find what are the 14 coins.

We have,

100 pennies = $1

20 nickels = $1

10 dimes = $1

4 quarters = $1

Find the coins that are worth $1.10

We have

10 dimes = $1

So,

1 dime = $0.10

8 dimes = $0.80 _____(1)

20 nickels = $1

So,

1 nickels = $0.05

6 nickels = $0.30 _____(2)

100 pennies = $1

10 pennies = $0.1 _____(3)

4 quarters = $1 ______(4)

From (1) and (2)

8 dimes + 6 nickels = $0.80 + $0.30

14 coins = $1.10

From (3) and (4)

10 pennies + 4 quarters = $0.1 + $1

14 coins = $1.10

Thus the 14 coins can be:

- 8 dimes and 6 nickels

- 10 pennies and 4 quarters

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Answer:

16

Step-by-step explanation:

5x + 2y - 7z    

(x = 2, y = 10, z = 2)

First things first you would want to take the letters that the numbers are equal to and replace them with the numbers.

5(2) + 2(10) - 7(2)

Then you multiply the number that's beside the parentheses, 5(2) is the same as 5 x 2.

5(2) = 10

2(10) = 20

7(2) = 14

so now you have

10 + 20 - 14

10 + 20 = 30

30 - 14 = 16

and 16 is your final answer!

Given:

Expression is

[tex]3r^2-2r+4[/tex]

To prove:

If r is any rational number, then [tex]3r^2-2r+4[/tex] is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.  

Let r be any rational number.

We have,

[tex]3r^2-2r+4[/tex]

It can be written as

[tex]3(r\times r)-2r+4[/tex]

Now,

3, -2 and 4 are rational numbers by property 1.

[tex]r^2=r\times r[/tex] is rational by Property 3.

[tex]3r^2\text{ and }-2r[/tex] are rational by Property 3.

[tex]3r^2+(-2r)+4[/tex] is rational by property 2.

So, [tex]3r^2-2r+4[/tex] is rational.

Hence proved.

We want to prove that if r is rational, then:

[tex]3*r^2 - 2r + 4[/tex]  Is also rational.

The proof is below:

Remember that a rational number is any number that can be written as a quotient of two integer numbers.

Then we have:

[tex]r = \frac{a}{b}[/tex]

Where a and b are integers.

If we replace that in our equation, we get:

[tex]3*(\frac{a}{b}) ^2 - 2*(\frac{a}{b}) + 4\\\\\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}[/tex]

Note that if a is an integer, then 3*a^2 is also an integer.

If b is an integer, then b^2 is also an integer.

Now we can perform the sum of these fractions to get:

[tex]\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}\\\\\frac{3a^2 - 2ab + 4b^2}{b^2}[/tex]

And because integers are closed under the addition, then the numerator of that fraction is also an integer, then we have that the given expression can be written as a quotient of two integers, thus, it is a rational number.

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Answer:

−5x+13y=84

Step-by-step explanation:

I hope this is good :)

Answer:

157

Step-by-step explanation:

You just have to take 73+84, and here is the equation.

73+84=157

OR

First, add the numbers in the ones place.

3+4=7

Now you know that the ones place is 7, we find the tens place.

7+8=15

Since only a 1-digit number can fill up a place, we bring the one over to the hundreds place.

Hence, the answer 157.

Answer:

A

Step-by-step explanation:

A is correct! How have a great day!

Answer

Can someone help

Step-by-step explanation:

Complete Question:

1. Classify the data of the heights of ladders produced by a tool company.

Group of answer choices :

Statistics

Qualitative

Classical

Quantitative

Answer:

The data of the heights of ladders produced by a tool company is:

Quantitative

Step-by-step explanation:

The heights of ladders are stated in numbers.  Quantitative data give information about quantities or numbers.  They can be measured with certainty.  They are not like qualitative data which are descriptive and cannot be easily measured unless classified in some ways.  Quantitative measurements associate measurement units to data, e.g. meters and feet. For example, the heights of persons, buildings, or things like ladders can be measured quantitatively in meters and feet.  Another feature of quantitative data is that arithmetic operations can be performed on the data.

Answer:

A) Categorical

B) Nominal

Step-by-step explanation:

 As we can see from the data that the question only had two answers i-e Yes or no so therefore they were categorical rather than quantitative in which he would have asked the user for how much money they were willing to pay more.

It's nominal because he asked in terms of more or less rather than some specific number

Answer:

296 minutes

Step-by-step explanation:

18,000 - 300 = 17,700.

17,700 ÷ 60 = 296.

It will take 296 minutes to drain the whole pool.

Answer:

.15,.2,.39,.7

Step-by-step explanation:

Answer:

9y

Step-by-step explanation:

since the symbols are the same you just add and keep the symbol.

Answer:

The answer is D.

Step-by-step explanation:

-24+24=0

Answer:

congruent angles

Step-by-step explanation:

Answer:

1 x 11

10 + 1

Step-by-step explanation:

Answer:

$15,000 was invested in CDs.

$40,000 was invested in bonds.

$75,000 was invested in stocks.

Step-by-step explanation:

Let C be the amount invested for CDs, B be the amount invested for bonds, and S be the amount invested for stocks.

We know that the total amount invested must be $130,000 because that was the amount given to the Scholarship Fund. So:

[tex]C+B+S=130000[/tex]

We know that CDs pay 2% or 0.02 interest; Bonds pay 2.9% or 0.029 interest; and Stocks pay 9.9% or 0.099 interest. In total, the investment earned $8,885. So:

[tex]0.02C+0.029B+0.099S=8885[/tex]

Let's remove the decimals by multiplying everything by 1000. This yields:

[tex]20C+29B+99S=8885000[/tex]

Now, we know that $25000 more was invested in bonds than CDs. So:

[tex]B=25000+C[/tex]

We have a triple system of equations. We can solve this using substitution. Let's substitute our third equation into the second equation. This yields:

[tex]20C+29(25000+C)+99S=8885000[/tex]

We want to isolate the C variable. Here, we removed the B but we still have an S.

So, to remove the S, we can go back to our first equation. We have:

[tex]C+B+S=13000[/tex]

Subtract C and B from both sides:

[tex]S=130000-C-B[/tex]

We can now substitute this for S:

[tex]20C+29(25000+C)+99(130000-C-B)=8885000[/tex]

We got a B again. But, we already know what B is. Substitute:

[tex]20C+29(25000+C)+99(130000-C-((25000)+C))=8885000[/tex]

So, our equation is now in terms of C. Solve for C. Distribute on the far right:

[tex]20C+29(25000+C)+99(130000-C-25000-C)=8885000[/tex]

Combine like terms:

[tex]20C+29(25000+C)+99(105000-2C)=8885000[/tex]

Distributive Property:

[tex]20C+725000+29C+10395000-198C=8885000[/tex]

Combine like terms:

[tex](20C+29C-198C)+(725000+10395000)=8885000[/tex]

Add:

[tex]-149C+11120000=8885000[/tex]

Subtract 1112000 from both sides:

[tex]-149C=-2235000[/tex]

Divide both sides by -149:

[tex]C=15000[/tex]

So, a total of $15,000 was invested in CDs.

Since $25,000 more was invested in bonds than in CDs, this means that a total of $25000+$15000 or $40,000 was invested in bonds.

To find out how much was invested in stocks, we can use our first equation again:

[tex]C+B+S=130000[/tex]

Substitute 15000 for C and 40000 for B:

[tex]15000+40000+S=130000[/tex]

Add:

[tex]55000+S=130000[/tex]

Subtract 55000 from both sides:

[tex]S=\$75000[/tex]

So, $15,000 was invested in CDs, $40,000 was invested in bonds, and $75,000 was invested in stocks.

And we're done!

Answer:

$15,000 was invested in CDs.

$40,000 was invested in bonds.

$75,000 was invested in stocks.

Step-by-step explanation:

The number of yards Martin needs to rope off the perimeter of the garden is: 320 yards.

Perimeter of any figure is the total length of the surrounding of the figure or shape.

Given:

A unit on the grid = 10 yards

From the diagram given, the figure is surrounded by 32 units

Thus:

Perimeter of the garden = 32 units × 10 = 320 yards.

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