MATHEMATICS HIGH SCHOOL

A set of equations is given below:Equation E: a = 5b + 1
Equation F: a = 3b + 4

Which statement describes a step that can be used to find the solution to the set of equations?

Equation F can be written as 5b + 1 = 3b + 4.
Equation F can be written as b + 1 = 3b + 4.
Equation F can be written as a = 3(a − 1) + 4.
Equation F can be written as a = 5(a − 4) + 1.

Answers

Answer 1

Answer:

Answer:

Equation F can be written as 5b + 1 = 3b + 4

Step-by-step explanation:

A set of equations is given below:

Equation E: a = 5b + 1

Equation F: a = 3b + 4

In substitution method we solve the equation for a variable and substitute it in other equation

Given a= 5b +1

Also equation F : a= 3b+4

both equation have 'a' on the left hand side

So we substitute 5b+1 for 'a' in second equation

Substitute 5b+1 in the place of 'a' in Equation F

Equation F can be written as 5b + 1 = 3b + 4

Answer 2

Answer: the answer is A because they are equal to eachother

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Answers

Answer:

1/5 · 1/5 · 1/5 · 1/5

Step-by-step explanation:

One way of interpreting exponents is as repeated multiplication. When you see (1/5)⁴, you can read that as "4 copies of 1/5, multiplied together." That expansion looks like (1/5)⁴ = 1/5 · 1/5 · 1/5 · 1/5

Answer:

Step-by-step explanation:

I took a long look at my answer and this was the one that made more sense. :)

300,000 to nearest 100,000?

Answers

Answer:

The answer is 3

Step-by-step explanation:

100,000 times 3 equal 300,000.

hope this helps you :)

Final answer:

When rounding 300,000 to the nearest 100,000, the result is 300,000 because it’s already a multiple of 100,000.

Explanation:

The question is asking to round the number 300,000 to the nearest 100,000. When rounding numbers, you look at the digit immediately to the right of the digit place you're rounding to. If this digit is 5 or greater, you round up; if it's less than 5, you keep the original number. In the case of 300,000, there are no digits to the right of the 100,000's place because it's already a multiple of 100,000. Therefore, 300,000 rounded to the nearest 100,000 is 300,000.

Learn more about Rounding Numbers here:

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In the process oif finding the difference quoitent for the function f(x)=π,Joan writes f(π+h)-f(π)/h

Answers

Joan's expression for the difference quotient is incorrect. The correct form is [f(π+h) - f(π)] / h, where f(x) = π, indicating the difference between two function values divided by h.

Joan's expression, f(π+h) - f(π) / h, is written incorrectly. The correct expression for the difference quotient for the function f(x) = π should be:

[f(π+h) - f(π)] / h

So, the correct expression is to subtract f(π) from f(π+h) and then divide the result by h. Joan made an error in the placement of the brackets, and the corrected expression accurately represents the difference quotient for this function.

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--The given question is incomplete, the complete question is given below " In the process oif finding the difference quoitent for the function f(x)=π,Joan writes f(π+h)-f(π)/h is it correct or incorrect"--

ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)

Answers

we have that
Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2)
y - 3x = – 8-----> y=3x-8------> the slope m=3

we know that
if two lines are perpendicular
then
m1*m2=-1
m1=3
so
m2=-1/3

with m=-1/3 and point (3, 2) find the equation of the line
y=mx+b
2=(-1/3)*3+b------> 2=-1+b-----> b=3

the equation of the line is
y=(-1/3)x+3

the answer is
y=(-1/3)x+3

see the attached figure

Last week you worked the following hours: Monday, 5½ Wednesday, 6¾ Friday, 4½ How many hours did you work in all last week? A. 16¾ B. 17½ C. 17¾ D. 18½

Answers

Answer:

A. 16¾

Step-by-step explanation:

We will convert all the mixed fractions to improper fractions.

Monday, 5½ = $(11)/(2)$

Wednesday, 6¾ = $(27)/(4)$

Friday, 4½ = $(9)/(2)$

Now, we will add all these fractions by taking the LCM of denominator.

The LCM of 2,4 and 2 is 4.

We get the following result after addition.

$(11)/(2) +(27)/(4) +(9)/(2)$

= $(22+27+18)/(4)$

= $(67)/(4)$ hours

In mixed fraction it becomes 16¾ hours.

Express Fx and Fy in terms of the length of the vector F and the angle θ, with the components separated by a comma.

Answers

Fx, Fy = F cos θ, F sin θ

Further explanation

This is a fundamental problem with vector components.

A vector quantity is some quantities that have the magnitude and a direction. For example, all forces or momentums are vectors.
Whereas, a scalar quantity only has magnitude. For example, all forms of energy are scalars.

The list below shows some recognized methods to represent a vector. i.e., a force.

$\boxed{ \ \textit{\textbf{F}}, \vec{F}, \bar{F} \ }$

It is possible to split one vector into two vectors. This process is called resolving and the vectors that we get are called the components of the original vector.

Vector problems can always be solved by using the mathematics of trigonometry, i.e., the functions of sine or cosine. This is particularly appropriate when resolving.

By using the cartesian coordinate system, see the attachment on how to calculate the values of either these components.

Horizontal component: $\boxed{ \ F_x = \textit{\textbf{F}}\ cos \ \theta \ }$
Vertical component: $\boxed{ \ F_y = \textit{\textbf{F}} \ sin \ \theta \ }$

Here, the angle between the vector F and the horizontal axis we call θ (theta).

As a reminder:

$\boxed{cos \ \theta = (adjacent)/(hypotenuse)} \rightarrow cos \ \theta = (F_x)/(F) \rightarrow \boxed{F_x = F cos \ \theta}$
$\boxed{sin \ \theta = (opposite)/(hypotenuse)} \rightarrow sin \ \theta = (F_y)/(F) \rightarrow \boxed{F_y = F sin \ \theta}$

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Keywords: express Fx and Fy, in terms of the length of the vector F, and the angle θ, with the components, separated by a comma, resolving, split, horizontal, vertical, angle, theta, sine, cosine, trigonometry, cartesian coordinate system

The components of the vector F are $\fbox{\begin\nF\cos\theta\end{minispace}}$ and $\fbox{\begin\nF\sin\theta\end{minispace}}$ .

Further Explanation:

A physical quantity can be defined as the physical property that can be measured and have some value in numbers.

For example- mass, amount of substance, length, time, electric current, temperature, force, light intensity, density, velocity, speed etc.

A quantity is said as a vector if it has some magnitude and direction in order to give the details regarding the quantity.

For example- Force, velocity, current density, electric field, magnetic field, displacement, acceleration, momentum etc.

A quantity is said as a scalar if it has only the magnitude in order to give the details regarding the quantity.

For example- speed, distance, current, volume, density, mass, energy, time, temperature etc.

Given:

The resultant vector is $F$ .

The horizontal component is ${\vec F_x}$ .

The vertical component is ${\vec F_y}$ .

Concept:

Let a vector have some length $F$ and making an angle $\theta$ with horizontal axis.

The triangle rule of resultant vector state that when two vector is denoted by the two sides of the triangle and the magnitude and the direction is taken in the same direction then the third side of the triangle denoted by resultant vector with some magnitude and direction.

The diagram is drawn as shown in the Figure 1.

The vertical component is along y-axis and the vertical component of the vector $\vec F$ is expressed as: