Lines L and K are parallel; what is the value of a + b?

Answer:

The amount of money that Alex has is $47.4

Step-by-step explanation:

Let

x----> amount of money that Alex has

y----> amount of money that Jennifer has

z----> amount of money that Jennifer Shannon has

we know that

x+y+z=91 ----> equation A

x=3y -----> equation B

y=z-12 -----> z=y+12 -----> equation C

substitute equation B and equation C in equation A and solve for y

(3y)+y+(y+12)=91

5y=91-12

y=79/5

y=$15.8

Find the value of x

x=3y ----> x=3(15.8)=$47.4

Answer:

Solution (-2, 7)

Step-by-step explanation:

2x + 3y = 17      (1)

5x + 6y = 32    (2)

Using elimination method

Multiply (-2) to the equation (1)

-4x - 6y = -34  

Now you have 2 new equations

-4x - 6y = -34

5x + 6y = 32

----------------------------Add

x = -2

Substitute x = -2 into 2x + 3y = 17

2(-2) + 3y = 17

- 4 + 3y = 17

3y = 21

 y = 7

Solution (-2, 7)

Final answer:

The solution to the system of equations 2x + 3y = 17 and 5x + 6y = 32 using the elimination method is x = -2 and y = 7.

Explanation:

To solve the system of equations using the method of elimination, we manipulate the equations to make the coefficients of either x or y the same, and then subtract one equation from the other to eliminate that variable. Let's consider the given equations:

2x + 3y = 17 (Equation 1)

5x + 6y = 32 (Equation 2)

We can see that the coefficients of y are in the ratio of 3:6 or 1:2. To use elimination, we want the coefficients to match, so we can multiply Equation 1 by 2:

(2)(2x) + (2)(3y) = (2)(17)

4x + 6y = 34 (New Equation 1)

Now we can subtract the new Equation 1 from Equation 2:

(5x + 6y) - (4x + 6y) = 32 - 34

5x - 4x + 6y - 6y = -2

x = -2

Now that we have a value for x, we can substitute it back into one of the original equations to solve for y. Let's substitute x into Equation 1:

2(-2) + 3y = 17

-4 + 3y = 17

3y = 17 + 4

3y = 21

y = 7

The solution to the system of equations is x = -2 and y = 7.

Let the base = x

Then the height would be 2x ( twice the length of the base.

Now using the given formula you get:

25 = 1/2 * 2x *x

Multiply 2x by 1/2:

1/2 * 2x = 2x/2

25 = 2x/2 * x

2x/2 = 1x, now you have:

25 = x *x

Multiply x by x:

25 = x^2

Take the square root of both sides:

x = √25

x = 5

Answer:

Approximately 68%

Step-by-step explanation:

The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2, that is to say:

X ∼ N(µ, σ2) ⇒ X ∼ N(71, 4).

Now, to find the percentage of bags that contain between 69 and 73 potatos we need the help of a calculator.

Pluging the data into a calculator we get that the percentage of bags that contain between 69 and 73 potatos is 68.27% ≈ 68%.

The solution is: Approximately 68%

Answer:

Approximately 68% percent of bags contain between 69 and 73 potato chips.

Step-by-step explanation:

Number of chips in a bag is normally distributed.

Mean = 71

Standard deviation = 2

We know that in normal distribution, 34.1% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34.1 + 34.1 = 68.2 % of bags will fall.

A table of normal distribution about mean is attached for better understanding.

Our range is:

69 to 73

71 - 2 to 71 + 2

71 ± 2

mean ± standard deviation

Our range is within 1 standard deviation. Hence, Approximately 68% of bags contain between 69 and 73 potato chips.

Answer:

No Solution

Step-by-step explanation:

Substitution means to replace the variable with the one provided, in this problem we have been given y = 2x, so we would simply replace the y variable in the second equation with 2x.

Review over what we have been given

y = 2x

-6x + 3y = 16

As explained above, substitute the y value in the second equation with the contents of the first equation.

-6x + 3(2x) = 16

In this step, you can solve for the value of x.

-6x + 6x = 16

Since both of the x variables cancel out, we cannot find the value of x since it equals to zero, which also means we cannot find the value of y.

0 = 16

Generally, we find the value of our x, then we would input that into the first equation to find the value of y.

But as stated above, there is no value of x, therefore there is no solution.

[tex]12\dfrac{1}{3}-6\dfrac{9}{10}=12\dfrac{10}{30}-6\dfrac{27}{30}=6+\left(-\dfrac{17}{30}\right)=5\dfrac{13}{30}[/tex]

Answer:

Option D is correct.

Step-by-step explanation:

We need to find the pattern in the values as the exponents increase.

First value is 1/3

if we multiply 3 with 1/3 i.e. 1/3*3 we get 1

The next value is 1 in the table.

Now, if we multiply 1 with 3 i.e. 1*3 we get 3

The next value is 3 in the table.

Now, if we multiply 3 with 3 i.e 3*3 we get 9

So, the next value is 9 in the table.

So, if we multiply 3 with the previous value we get the next value in the table.

Hence Option D multiply the previous value by 3 is correct.

Answer:

x = 5

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{2}[/tex](3x - 7) = 3, then

3x - 7 = 2³ = 8 ( add 7 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

The required solution of logarithmic expression  log2 (3x - 7) = 3 is x = 5. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To solve for x in the equation log2 (3x - 7) = 3, we first use the definition of a logarithm to change the logarithmic form to the exponential form.

log2 (3x - 7) = 3

2³ = 3x - 7

Next, we solve for x by adding 7 to both sides of the equation:

8  + 7= 3x - 7 + 7

15 = 3x

Finally, we divide both sides of the equation by 3:

x = 5

So, the solution of log2 (3x - 7) = 3 is x = 5.

Learn more about simplification here:

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Answer: If [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex]

Step-by-step explanation:

Let be "a", "b", and "c" all real numbers, the Transitive property of equalities states that :

If [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex]

You can observe that if two numbers are equal to the same number, then all this numbers are equal to each other.

For example, applying the Transitive property of equalities to:

[tex]x+3=5[/tex] and [tex]2x+1=5[/tex]

You can equate them:

[tex]x+3=2x+1[/tex]

And solve for "x":

[tex]3-1=2x-x\\\\x=2[/tex]

Answer:

The correct answer option is: If a = b and b = c, then a = c.  

Step-by-step explanation:

The Transitive Property of Equality states that if one value, lets say [tex] a [/tex] is equal to another value, call it [tex] b [/tex], which is equal to another value, call it [tex] c [/tex], then the very first value [tex] a [/tex] would be equal to the third value [tex] c [/tex].

So from the given answer options, the correct option is: If a = b and b = c, then a = c.  

Answer:

35° and 105°

Step-by-step explanation:

Sum of all the angles of triangle is 180°

One angle = 40°

35° + 105° + 40° = 180°

Answer:

35° and 105°

Step-by-step explanation:

I had this question trust me its correct.

There are 50 states in the U.S. so to find the states that don't have a store operator by company A you must subtract the states that do by the total number of states:

50 - 38 = 12

12 stores do not have a store operator by company A

To find the fraction you must do [tex]\frac{part}{whole}[/tex]

Part is the number of states that don't have a store operator by company A

Whole is the total number of states in the U.S.

You get the fraction:

[tex]\frac{12}{50}[/tex]

^^^This fraction can be simplified to...

[tex]\frac{6}{25}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

12 states do not have a store operator by company A

6/25 is the fraction of states do not have a store operator by company A​

Step-by-step explanation:

50 - 38 = 12

12/50 = 6/25

The answer is:

The fourth graph.

We are given the following equation:

[tex]f(x)=x[/tex]

Then, we need to find the graph of f(x+2) that will be equal to:

[tex]f(x+2)=x+2[/tex]

[tex]y=x+2[/tex]

Now, finding the x-axis interception, making "y" equal to 0, we have:

[tex]0=x+2[/tex]

[tex]-2=x[/tex]

Therefore, the x-axis interception point is located at (-2,0), it matches with the fourth graph.

Now, finding the y-axis interception, making "x" equal to 0, we have:

[tex]y=x+2[/tex]

[tex]y=0+2=2[/tex]

Therefore, the y-axis interception point is located at (0,2), it matches with the fourth graph.

Hence, we have that the graph of f(x+2) is the fourth graph since the second graph function cuts the x-axis at -2 and the y-axis at 2.

Have a nice day!

Answer: 717,000

Step-by-step explanation:

716,773 rounded to the nearest thousand is 717000 because the 7 is closer to 10 than it is to 0

Hello There!

716,772 rounded to the nearest thousand would be 717,000

772 is closer to 717,000 than 716,000

Answer:

The correct answer is first option

512 cubic mm

Step-by-step explanation:

Points to remember

Volume of hexagonal pyramid = Base area * height

To find the volume of hexagonal pyramid

It is given that, base area = 64 square mm and

height = 8 mm

Volume = Base area * Height

 = 64 * 8

 = 512 cubic mm

Therefore the correct answer is first option

512 cubic mm

Answer:

f(3) = 9

Step-by-step explanation:

Wherever you see an x on the right, put a 3 in for that x

f(x) = 2x^2 + x - 12

f(3) = 2*(3)^2 + 3 - 12

f(3) = 2*9 + 3 - 12

f(3) = 18 + 3 - 12

f(3) = 9

Answer:

c

Step-by-step explanation:

The best first step to solve the equation -2(x+3)=-10 is to distribute the -2 across the parentheses, simplify the equation, and then solve for x.

Checking the answer by substituting the value of x back into the original equation ensures the solution is correct.

When solving the equation -2(x+3)=-10, the best first step to simplify the equation is to distribute the multiplication of -2 across the parentheses.

This is done to eliminate the parentheses and simplify the equation into its simplest form. After distribution, you would then have the simplified equation -2x - 6 = -10.

From there, you can proceed to solve for x by adding 6 to both sides of the equation to isolate the term with x, then dividing both sides by -2 to find the value of x.

Here are the basic problem-solving steps:

Once you've calculated the value of x, it's important to check the answer to ensure it is reasonable.

You can do this by substituting the value of x back into the original equation.

Answer:

The Building's tall and wide ratio is 90 : 45 = 2 : 1

now the wide is 3, let's say that tall is a.

2 / 1 = a / 3

a = 2 x 3

a = 6

So the picture will be 6 feet tall.

Answer:

B is le answer

Step-by-step explanation:

To find the values of the variables in each equation, isolate the variable on one side by performing operations. The solutions for the variables are 4, -1, 2, 6, no solution, and 10.8 for the respective equations.

To find the value of the variable in each equation, we need to isolate the variable on one side of the equation. Let's solve each equation step by step:

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Answer:

8

Step-by-step explanation:

–16 • 1/8 • 4 + 32 ÷ 2

Using PEMDAS, we multiply and divide from left to right since there are no parentheses or exponents.

-2 • 4 + 32 ÷ 2

-8 +32 ÷ 2

-8 + 16

Now we add and subtract from left to right

8

Answer:

C 40

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

y+10 + 2y + 50 = 180

Combine like terms

3y + 60 =180

Subtract 60 from each side

3y+60-60 = 180-60

3y = 120

Divide by 3

3y/3 = 120/3

y = 40

The sum of all the angles of a triangle is 180 degrees. To solve for y you can make a formula of the sum of the angles equal to 180 like so...

y + 10 + 2y + 50 = 180

Now you must combine like terms. This means that first numbers with the same variables (y) must be combined...

(y + 2y) + 10 + 50 = 180

3y + 10 + 50 = 180

Combine like terms 10 and 50...

3y + 60 = 180

Now bring 60 to the left side by subtracting 60 to both sides (what you do on one side you must do to the other). Since 60 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

3y + 60 - 60 = 180 - 60

3y + 0 = 120

3y = 120

Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.

3y / 3 = 120 / 3

y = 40

C. 40

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

5

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

1/cosecx = sin(x)

cosec(x) = 1/sin(x)

1/sec(x) = cos(x)

sec(x) = 1/cos(x)

1/sin(35) - 1/cos(55)

1.74344 - 1.7344  isn't that something?

0

Answer:

14/3

Step-by-step explanation:

Simplify the following:

48/6 - 10/3

Hint: | Reduce 48/6 to lowest terms. Start by finding the GCD of 48 and 6.

The gcd of 48 and 6 is 6, so 48/6 = (6×8)/(6×1) = 6/6×8 = 8:

8 - 10/3

Hint: | Put the fractions in 8 - 10/3 over a common denominator.

Put 8 - 10/3 over the common denominator 3. 8 - 10/3 = (3×8)/3 - 10/3:

(3×8)/3 - 10/3

Hint: | Multiply 3 and 8 together.

3×8 = 24:

24/3 - 10/3

Hint: | Subtract the fractions over a common denominator to a single fraction.

24/3 - 10/3 = (24 - 10)/3:

(24 - 10)/3

Hint: | Subtract 10 from 24.

| 2 | 4

- | 1 | 0

| 1 | 4:

Answer:  14/3

Answer:

Your answer is 4 and 2/3

Step-by-step explanation:

Hope this helps have a good day!

Answer:

It is known that 1 pint equals 16 ounces

Step-by-step explanation:

It is known that 1 pint equals 16 ounces. Then we use this data to transform a number of ounces into pints.

Suppose we have x ounces. We want to know how many pints are these x ounces. Then we perform the following operation

[tex]x\ ounces*\frac{1\ pint}{16\ ounces}=z\ pints[/tex]

Where z pints is the amount equivalent to x ounces

Monarch butterflies flap their wings 12 times per second. Over the course of one hour, which is 3600 seconds, they flap their wings approximately 43,200 times.

Monarch butterflies flap their wings about 12 times per second. To figure out how many times they flap their wings in 1 hour, we need to calculate the total number of seconds in an hour and then multiply that by the flapping rate.

Step 1: Calculate the number of seconds in one hour.

Step 2: Multiply the number of seconds by the flapping rate.

So, Monarch butterflies flap their wings approximately 43,200 times in one hour.

ANSWER

The correct answer is D

EXPLANATION

The given quadratic expression is

[tex]3 {x}^{2} + 8x = - 1[/tex]

Divide through by 3

[tex]{x}^{2} + \frac{8}{3} x = - \frac{1}{3} [/tex]

We now add the square of half the coefficient of x because the coefficient of the quadratic term is now unity.

The constant we would add is

[tex] {( \frac{4}{3} )}^{2} = \frac{16}{9} [/tex]

The correct answer is D

Answer: Option D.

Step-by-step explanation:

Given the quadratic equation [tex]3x^2+8x=-1[/tex], you can observe that the leading coefficient is not 1, then you have to divide both sides of the equation by 3:

[tex]\frac{3x^2+8x}{3}=\frac{-1}{3}\\\\x^2+\frac{8}{3}x=\frac{-1}{3}[/tex]

Now, you can observe that the coefficient of the x-term is [tex]\frac{3}{8}[/tex], so you must divide it by 2 and square it. Then you get:

[tex](\frac{\frac{8}{3}}{\frac{2}{1}})^2=\frac{16}{9}[/tex]

Therefore, you must add [tex]\frac{16}{9}[/tex] to both sides of the equation.

Answer:

it is the second one because 1/2 divided by 3 equals 1/6 3 times

Answer:

Step-by-step explanation:

Use Basic Proportionality Theorem (look at the picture).

Therefore we have the equation:

[tex]\dfrac{3x-2}{50}=\dfrac{6}{30}\qquad\text{cross multiply}\\\\30(3x-2)=50(6)\qquad\text{use the distributive property}\\\\(30)(3x)+(30)(-2)=300\\\\90x-60=300\qquad\text{add 60 to both sides}\\\\90x=360\qquad\text{divide both sides by 90}\\\\x=4[/tex]