Two trains leave stations 240 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80
miles per hour. How long will it take for the two trains to meet?

Answer:

x= 2/7

Step-by-step explanation:

Multiply both sides by the common denominator

3x^2 +6x−2=3x^2 −x

Move everything to the left side.

3x^2+6x-2-3x^2+x=0

Simply.

7x-2=0

Separate the cosntants and variables.

7x=0+2

Add or subtract zero

7x=2

Then divide both sides by 7.

7x/7=2/7

Cancel out common factors in the numerator and denominator

x=2/7

Answer:

  x = 2/7

Step-by-step explanation:

You want to solve the equation 3x/(3x-1) + 2/x = 1.

It works nicely to subtract 1 from both sides, then simplify.

  [tex]\dfrac{3x}{3x-1}+\dfrac{2}{x}=1\\\\\dfrac{3x}{3x-1}\cdot\dfrac{x}{x}+\dfrac{2}{x}\cdot\dfrac{3x-1}{3x-1}-\dfrac{x(3x-1)}{x(3x-1)}=0\\\\\dfrac{3x^2+6x-2-3x^2+x}{x(3x-1)}=0\qquad\text{combine terms}\\\\\dfrac{7x-2}{x(3x-1)}=0\qquad\text{simplify}\\\\7x-2=0\qquad\text{expression is 0 when numerator is 0}\\\\\boxed{x=\dfrac{2}{7}}\qquad\text{add 2, divide by 7}[/tex]

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Additional comment

The values x=0 and x=1/3 would make the denominator zero, so are excluded from the domain of the equation. By working the problem this way, we ensure that extraneous solutions do not present themselves.

By using simple rule of three, a period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

One year on Earth is equivalent to 365.3 days and one year on Venus is equivalent to 224.7 days, the equivalent terrestrial time of 9.5 years on Venus is found by simple rule of three:

x = 9.5 yr × (224.7 days / 1 yr)

x = 2134.65 days

A period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

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Answer: Sym. Prop. of ≅

Step-by-step explanation:

no explanation

Answer:

Step-by-step explanation:

Y-3x=13+3x

The domain of the graph in set builder notation is; x ≤ -2 or x ≥ 1

The range of the graph in set builder notation is; y ≥ -2 or y ≥ 1

Domain refers to the set of all possible input values and Range refers to the set of all possible output values generated by the function.

Now, from the given graph, we can see that there are two lines. Thus;

Domain of left graph line is; x ≤ -2

Domain of right graph line is; x ≥ 1

Thus, the domain of the graph in set builder notation is;

x ≤ -2 or x ≥ 1

Similarly, the range is as follows;

Range of the left graph line is; y ≥ 1

Range of the right graph line is; y ≥ -2

Thus, the range of the graph in set builder notation is;

y ≥ -2 or y ≥ 1

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Answers are in bold

======================================================

Explanation:

The x is a placeholder for a number.

When we say f(5), we mean f(x) when x = 5

So we'll replace every copy of x with 5 like so...

[tex]f(\text{x}) = -3\text{x}^2 - 2\\\\f(5) = -3(5)^2 - 2\\\\f(5) = -3(25) - 2\\\\f(5) = -75 - 2\\\\f(5) = -77\\\\[/tex]

Notice how I used the order of operations PEMDAS after x = 5 was plugged in.

A similar situation happens with g(-4). We'll plug x = -4 into g(x) to get the following:

[tex]g(\text{x}) = 2\text{x} +4\\\\g(-4) = 2(-4) +4\\\\g(-4) = -8 +4\\\\g(-4) = -4\\\\[/tex]

You can use a graphing calculator or graphing software (eg: Desmos or GeoGebra) to confirm these answers quickly.

Assets of respondents in a survey is a quantitative data and the level of measurement is a ratio scale.

Qualitative properties are properties that are observed and can generally not be measured with a numerical result.

Examples of quantitative data include, number of students in a class, weight of students in a class, etc.

Quantitative data is the value of data in the form of counts or numbers where each data set has a unique numerical value. This data is any quantifiable information that researchers can use for mathematical calculations and statistical analysis to make real-life decisions based on these mathematical derivations.

Examples of qualitative data include hair color, religion, nationality, etc.

Thus, assets of respondents in a survey is a quantitative data and the level of measurement is a ratio scale.

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The name of the metric system prefix are :  10^-6: micro , 1/100: centi , 0.001: milli, 1000: kilo

In mathematical exponents, prefixes are referred to as the alphabetic names related to the mathematical factors, such as 10⁻⁹:  it nano ,10⁻¹²: Pico and so on.In order to identify the prefixes of the metric system, we first convert from factor to exponent form.

such :

10^-6  is micro  

1/100 = 0.01x 10^2: centi

0.001 = 1x 10 ^-3 : milli

1000 =  1x 10^3 : kilo

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Write the name of the metric system prefix associated with each mathematical factor. Do not use any hyphens in your answers and do not abbreviate the prefixes. Spelling counts.

10^-6 ______________

1/100 ______________

0.001 _____________

1000 ______________

Answer:

128 feet²

Step-by-step explanation:

48 = x + x + 2x + 2x = 6x

x = 8

x × 2x = 8 × 16 = 128

the answer for given expression is 54

How do you define expression in math?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

the given expression is

[tex]-k^2 - (4k-7n)+3n\\-k^2 -4k +7n+3n\\put k = -2 and n=5\\-( -2)^2 - 4(-2) + 10 *5\\-4 +8+50\\54the answer for given expression is 54[/tex]

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The weights that are significantly low z₁ = 5.361308 grams and significantly high z₂ = 5.48057 grams  

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

z -score = (z₁ - μ₀) / σ

where μ₀  is the mean and σ the standard deviation.

Consider a value to be significantly low if its z score is less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.

Here μ₀ = 5,37215 and σ = 0.05421

Substitute z -score = -2

⇒ -2  = (z₁ - 5,37215)/0.05421

⇒ (-2)(0.05421) = z₁ - 5.37215

⇒ -0.10842 = z₁ - 5.37215

⇒ z₁ = 5.37215 - 0.010842

⇒ z₁ = 5.361308

And if z = 2

Here μ₀ = 5,37215 and σ = 0.05421

Substitute z -score = 2

⇒ 2(0.05421) = z₂ -  5.37215

⇒ 0.10842 = z₂ - 5.37215

⇒z₂ = 5.37215 + 0.10842

⇒ z₂ = 5.48057  

Therefore, the weights that are significantly low z₁ = 5.361308 grams and significantly high z₂ = 5.48057 grams

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Your question is incomplete, probably the complete question is:

A data set lists the weights​ (grams) of a type of coin. Those weights have a mean of 5.37215 g and a standard deviation of .05421 g. Identify the weights that are significantly low or significantly high.

Consider a value to be significantly low if its z score is less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.

Light is about 874052.5 times faster than sound

From the question, we are to determine the magnitude by which light is faster than sound

From the given information,

The speed of light is about 2.998 x 10⁸ meters per second.

and

The speed of sound is about 343 meters per second.

To determine how many rimes faster the speed of light is than the speed of sound, we will divide the speed of light by the speed of sound

That,

The magnitude by which light is faster than sound = (2.998 x 10⁸) / 343

The magnitude by which light is faster than sound = 874052.5

Hence, light is about 874052.5 times faster than sound

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1.545 is  the riemann sum of the function .

What does Riemann sum do?

f(x) = x

p = { 1, 1.2 , 1.7 , 2}

c = { 1.1, 1.45,2}

fpr the interval  ( 1, 1.2) Δx = 0.2

                          ( 1.2, 1.7 ) Δx = 0.5

                           ( 1.7 , 2 )  Δx = 0.3

R(f, p,c ) = f(1.1) 0.2 + f( 1.45)0.5 +  f(0)0.3

             = (1.1) × 2  + ( 1.45) ×( 0.5) +  2 × 0.3

             = 0.22 + 0.725 + 0.6

             = 1.545

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The quadratic function given the roots (4, 0) and (-2, 0) and the point (3, -3) = 1/3(x-4)(x-2)

A quadratic function is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can expand up or down, and their "width" or "steepness" can vary, but they all share the same basic "U" shape.

The quadratic function given the roots (4, 0) and (-2, 0) and the point (3, -3)

We utilize equation when p and q are the roots.

y = a(x- p)(x-q)

We are given with roots 4  and -2

y = a(x- 4)(x-(-2))

y = a(x- 4)(x + 2)

Now we use the given point (3,-3) to find out 'a'

3 = a(3- 4)(3 + 1)

3= a(-1)(-2)

3= 1a

a = 1/3

Replace the value of 'a'

f(x) = 1/3(x-4)(x-2)

The quadratic function given the roots (4, 0) and (-2, 0) and the point (3, -3) = 1/3(x-4)(x-2)

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Answer:

3a + (5b + 7c)

Step-by-step explanation:

The answer cannot be 3a(5b +7c) because when the number is immediately before the brackets, it signifies multiplication. therefore the 3a(5b+7c) would be equivalent to 15ab+21ac

the answer cant be 7c(5b+3a) because of the same explanation as the one above, therefore 7c(5b+3a) would be equivalent to 35cb+21ca

the answer finally cant be 8ab+7c because it means that one added 3a and 5b giving you 8 but it cannot be ab because ab is equivalent to a×b, hence, one cant put a multiplied algebraic expression with an added number

The equation equivalent to the the expression (3a + 5b) + 7c is 3a + (5b+7c). Hence, the first option is the correct one.

In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.

For instance, the equation x + y has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.

The first option is correct because it does not affect the main equation rest are not the same as the equation.

For example, let's take the second equation :

3a (5b + 7C)

After solving this option we get 15ab + 21 ac so it is incorrect because it changed the main expression.

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Answer:

64 and 13 I hope this helps

Step-by-step explanation:

Answer:

6 trust me

Step-by-step explanation:

Answer: 7.49%

Step-by-step explanation: i got it right on edg

Answer:

7.49%

Step-by-step explanation:

Answer:

3-x^2-20

Step-by-step explanation:

That is how you convert it from word form to standard form.

Answer:

down below

Step-by-step explanation:

Top left: X is greater than or equal to 3. Top right: X is less than or equal to 3. Bottom left: X is greater than 3. Bottom right: X is less than 3.

The greater than or equal to sign and the less than or equal to sign has a closed circle because it is marking the point and moving forward or back. Ex: less than or equal to 3. It would be a closed circle because it is the specific point and what ever is beyond or behind it. The less than or greater than sign would have a closed circle because it is only what is beyond or behind the certain number.

Hope this helps! :)

(x+3i)(x-3i)

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = √-1 and both a and b are real numbers.

Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.

Using complex numbers,

x²+81 = x² - (-9i)²

           = (x²- 9²i²)

           = (x+3i)(x-3i)

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Answer:

y=4x-1

Step-by-step explanation:

to find the slope you use this equation

(y2-y1) / (x2-x1)

you also need y=mx+b to write in your final equation for the slope,

m is the slope and b is the y intercept (where the point meets the y axis, horizontal line that goes like this | )

first, you got lucky this equation gave you the b value( remember, b is the y intercept) , which you can find when x is 0.

to find the slope we choose any two coordinates (x,y) from the table

i choose (0,-1) and (5,19)

and we put this in this formula

(y2-y1) /

(x2-x1)

(19+1) it’s plus because subtracting a negative - - makes it positive

so

(19+1)/

(5-0)

= 20/5 which is 4. so m( the slope) m=4

now that we have b=-1 and m=4 we can write the final answer equation

which is

y=4x-1

Answer:

An infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, ...}. Examples of infinite sequences are N = (0, 1, 2, 3, ...) and S = (1, 1/2, 1/4, 1/8, ..., 1/2 n , ...)