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Write the equation in slope-intercept form then change it to standard form with integer coefficients.

SCORPION-xisa [38]

Answer:

1. Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

2. Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

3. Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

Step-by-step explanation:

Slope intercept form: $y = mx + b$

where:

$y$ = y-coordinate
$m$ = slope
$x$ = x-coordinate
$b$ = y-intercept

Standard form: $Ax + By = C$

$\textsf{1. as} \ m=2: \ \ y = 2x + b$

$\textsf{at} \ (6, 8): \ \ 8 = 2(6) + b$

$\implies b = -4$

Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

$\textsf{2. as} \ \ m = \dfrac12: \ \ y = \dfrac12x + b$

$\textsf{at} \ (4, 1): \ \ 1 = \dfrac12(4) + b$

$\implies b = -1$

Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

$\textsf{3. as} \ \ m = \dfrac45: \ \ y = \dfrac45x + b$

$\textsf{at} \ (1,5): \ \ 5 = \dfrac45(1) + b$

$\implies b = \dfrac{21}{5}$

Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

7 0

2 years ago

Please help find mDF!!

Natalka [10]

9514 1404 393

Answer:

72°

Step-by-step explanation:

The external angle E is half the difference of subtended arcs CG and DF.

E = (CG -DF)/2

2E = CG -DF . . . . . . multiply by 2

DF = CG -2E = 160° -2(44°) . . . . . add DF-2E to both sides; substitute values

arc DF = 72°

4 0

2 years ago

A diver descends to a location of -50 1 over 4 meters relative to the surface of the water. He then descends another 10 1 over 2

Yanka [14]

Answer:

$-60\frac{3}{4}$ meters.

Step-by-step explanation:

To find diver's final location relative to the surface of water we will subtract $10\frac{1}{2}$ from $-50\frac{1}{4}$ because diver dives away another $10\frac{1}{2}$ from his previous location of $-50\frac{1}{4}$ .

$-50\frac{1}{4} -10\frac{1}{2}$

Now we will convert our mixed fraction into improper fraction and then we will find a common denominator.

$\frac{-201}{4} -\frac{21}{2} =\frac{-201-42}{4}$

$=\frac{-243}{4}$

Now let us convert our answer in mixed fraction.

$=\frac{-243}{4}=[tex]-60\frac{3}{4}$ [/tex]

Therefore, diver's final location relative to the surface of the water is $-60\frac{3}{4}$ meters.

3 0

3 years ago

Read 2 more answers

How do you evaluate an algebraic expression?

vodomira [7]

Answer:

follow the Order of Operations

Step-by-step explanation:

An algebraic expression cannot be evaluated unless all of its variables have been replaced by numerical values. (It can be simplified, but not evaluated if it contains variables.)

A collection of numbers and math symbols is interpreted according to the Order of Operations. This order reflects a precedence of operations that is generally agreed or understood to be applied to algebraic expressions. Operations with the highest precedence are performed first. Operations with equal precedence are generally performed in order, left to right. (There are exceptions.) Parentheses or other grouping symbols are used to modify the order of operations as may be necessary.

__

Here is a description of the most often seen operations in an algebraic expression, in order of precedence (highest to lowest).

1. Parentheses or Brackets -- any expression enclosed in parentheses or brackets is evaluated first. Evaluation is according to the order of operations. That means that if parentheses are nested, expressions in the innermost parentheses are evaluated first.

2. Exponents or Indices -- Expressions with exponents are evaluated next. In this context, roots are fractional exponents. If exponents are nested, they are applied right to left:

3^2^4 = 3^(2^4) = 3^16 = 43,046,721 . . . for example

Parentheses modify this order, so ...

(3^2)^4 = 9^4 = 6,561

The exponent is taken to be the first number immediately following the exponentiation symbol, so ...

9^1/2 = (9^1)/2 = 9/2 = 4.5

Again, parentheses alter this order, so ...

9^(1/2) = √9 = 3

3. Multiplication and Division -- These operations have the same precedence, so are performed in order of appearance, left to right. Of course, division is the same as multiplication by a reciprocal, and multiplication is a commutative and associative operation. Those features of these operations do not alter the "order of operations," but may alter your approach to actually doing an evaluation.

For example, 9*2/3 would be evaluated as (9*2)/3 = 18/3 = 6. However, recognizing that 9 = 3*3, you can rearrange the evaluation to ...

9/3*2 = 3*2 = 6

This rearrangement is allowed by the properties of multiplication, not by the Order of Operations.

You will also note that 9/3*2 is not the same as 9/(3*2). That is, the denominator in the division is only the first number after the division symbol. This is also true for expressions involving variables:

b/2a = (b/2)*a

If you want b/(2a), you must use parentheses.

Some authors make a distinction between the slash (/) and the symbol ÷ in their effect on an expression. The Order of Operations makes no such distinction, treating /, ÷, "over", "divided by" as all meaning exactly the same thing.

4. Addition and Subtraction -- These operations have the same precedence, so are performed in order of appearance, left to right. Of course, subtraction is the same as addition of an opposite, and addition is a commutative and associative operation. Those features of these operations do not alter the "order of operations," but may alter your approach to actually doing an evaluation.

__

Based on the first letters of these operations, several mnemonic "words" or phrases have been invented to help you remember the order. Some are ...

PEMDAS

Please Excuse My Dear Aunt Sally

BIDMAS

__

There are a number of tricky expressions floating around that test your understanding of the order of operations. Here is one of them:

10 × 4 - 2 × (4² ÷ 4) ÷ 2 ÷ 1/2 + 9

One of the things that makes this tricky is the distinction between ÷ and /, as discussed above. Here, the author of the expression intends for the / to indicate a fraction, so 2÷1/2 is intended to mean 2÷(1/2).

Working this according to the order of operations, we have ...

= 10 × 4 - 2 × (16 ÷ 4) ÷ 2 ÷ (1/2) + 9 . . . . . exponent inside parentheses

= 10 × 4 - 2 × 4 ÷ 2 ÷ (1/2) + 9 . . . . . division inside parentheses

= 40 - 2 × 4 ÷ 2 ÷ (1/2) + 9 . . . . . . first multiplication

= 40 - 8 ÷ 2 ÷ (1/2) + 9 . . . . . . second multiplication

= 40 - 4 ÷ (1/2) + 9 . . . . . first division

= 40 - 8 + 9 . . . . . . second division

= 32 . . . . . . first addition

= 41 . . . . . . second addition

7 0

2 years ago

Resource Allocation You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quar

vovikov84 [41]

Answer:

in order to use up all the eggs and cream, the number of quarts of each flavor that should be made is;

Creamy vanilla x = 200 quarts

Continental mocha y = 100 quarts

Step-by-step explanation:

Let x and y represent the number of quarts of Creamy Vanilla and Continental Mocha that should be made in order to use up all the eggs and cream respectively.

For Creamy Vanilla go 2 eggs and 3 cups of cream

For Continental Mocha go 1 egg and 3 cups of cream.

Total number of eggs = 500 eggs

Total number of cream cups = 900 cups.

For the eggs;

2 eggs × x + 1 egg × y = 500

2x + y = 500 .......1

For the cream cups;

3 cups × x + 3 cups × y = 900

3x + 3y = 900

Dividing through by 3

x + y = 300 .......2

Solving the simultaneous equation;

Subtracting equation 2 from 1

(2x + y) - (x+y) = 500-300

2x -x = 200

x = 200

Substituting x = 200 into equation 2;

200 + y = 300

y = 300 - 200

y = 100

Therefore, in order to use up all the eggs and cream, the number of quarts of each flavor that should be made is;

Creamy vanilla x = 200 quarts

Continental mocha y = 100 quarts

8 0

2 years ago