Which expression is equivalent to ( 11 x − 8 ) + ( 7 − 4 x ) ?

Solve by graphing u=v and 6u=2v-24

Vadim26 [7]

Answer:

$u=-6 \\ \\ v=-6$

Step-by-step explanation:

In this exercise, we have two equations, namely:

$u=v \ and \ 6u=2v-24$

And we are asked to solve this problem by graphing. In this way, we can write a system of linear equations in two variables, but first of all, let's rewrite:

$u=y \\ \\ v=x$

Then:

$\left\{ \begin{array}{c}y=x\\6y=2x-24\end{array}\right.$

So here we have two lines.

The first one is:

$\boxed{y=x}$

This line passes through the origin and has a slope $m=1$

The second one is:

$6y=2x-24 \\ \\ \therefore y=\frac{2x-24}{6} \\ \\ \therefore \boxed{y=\frac{1}{3}x-4}$

This line has a slope $m=\frac{1}{3}$ and cuts the y-axis at $b=-4$

By using graph tools, we get the graph shown below, then:

$x=-6 \\ \\ y=-6 \\ \\ \\ Since \ u=y \ and \ v=x, then: \\ \\ u=-6 \\ \\ v=-6$

8 0

3 years ago

Which is greater or equal to 8/10 or 63/100

Elena L [17]

8/10 is greater than 63/100 because when 8/10 is turned into a percentage it is greater

8 0

3 years ago

Russell and Aaron can build a shed in 8 hours when working together. Aaron works three times as fast as Russel. How long would i

Whitepunk [10]

Answer:

32 hours.

Step-by-step explanation:

Let x represent the time taken by Russell and Aaron to build the shed.

We have been given that Russell and Aaron can build a shed in 8 hours when working together. Aaron works three times as fast as Russel.

Russell's work rate would be $\frac{1}{x}$ .

Since Aaron works three times as fast as Russel, so Aaron's work rate would be $\frac{3}{x}$ .

Part of work done by in one hour would be $\frac{1}{8}$ .

We can represent our given information in an equation as:

$\frac{1}{x}+\frac{3}{x}=\frac{1}{8}$

Let us solve for x.

$\frac{1}{x}*8x+\frac{3}{x}*8x=\frac{1}{8}*8x$

$8+3*8=x$

$8+24=x$

$32=x$

Therefore, it will take Russell 32 hours to build the shed working alone.

4 0

3 years ago

Original grade 80 New grade 100 Find the percent of increase

Taya2010 [7]

Answer: 20% increase

Step-by-step explanation: It’s out of 100 and you first got 80 and then you got 100. Since it’s out of 100 you could just subtract to numbers ex: 100-80=20. The answer is 20% increase

4 0

3 years ago

Read 2 more answers

PLEASE HELP!

sineoko [7]

The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here:[2]

exponents and roots 
multiplication and division 
addition and subtraction 

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations. 

It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 − 4 = 3 + (−4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 − 3 + 7 as the sum of 1, negative 3, and 7, and add in any order: (1 − 3) + 7 = −2 + 7 = 5 and in reverse order (7 − 3) + 1 = 4 + 1 = 5. The important thing is to keep the negative sign with the 3. 

The root symbol, √, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand. Other functions use parentheses around the input to avoid ambiguity. The parentheses are sometimes omitted if the input is a monomial. Thus, sin x = sin(x), but sin x + y = sin(x) + y, because x + y is not a monomial. Calculators usually require parentheses around all function inputs. 

Stacked exponents are applied from the top down, i.e., from right to left. 

Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws, also they can be removed if the expression inside the symbol of grouping is sufficiently simplified so no ambiguity results from their removal.

3 0

3 years ago