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3 years ago

A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?

2 answers:

4 0

"They have different slopes but the same y-intercept, so they have one solution" is the statement which best describes the two lines.

Answer: Option D

Step-by-step explanation:

Given equations:

$y=\left(\frac{1}{2} \times x\right)-3$

$y=\left(-\frac{1}{2} \times x\right)-3$

As we know that the slope intercept form of a line is

y = m x + c

So, from equation 1 and equation 2 we can see that

$m_{1}=\frac{1}{2} \quad \text { and } c_{1}=-3$

$m_{2}=-\frac{1}{2} \text { and } c_{2}=-3$

So, from the above expressions, we can say that both lines have different slopes but have same y – intercept with one common solution when x = 0.

olga55 [171]3 years ago

4 0

Answer: D

Step-by-step explanation:

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Using a property of operations, what can you say about the sums of (-13.2) + 8.1 and 13.2 + (-8.1)

Wewaii [24]

They are opposites of each other.
-13.2 + 8.1 = -5.1
13.2 - 8.1 = 5.1

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3 years ago

Sample Response: You would graph the equation f(x) = –x + 3 for input values less than 2. There would be an open circle at the p

fgiga [73]

Answer:

Step-by-step explanation:

What did you include in your response? Check all that apply.

There would be an open circle at (2, 1). Yes

There would be a closed circle at (2, 3). Yes

There would be an open circle at (4, 3). Yes

There would be a closed circle at (4, −4). Yes

Endpoints that are not included in the domain of a particular piece of a function are represented by an open circle. Yes

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2 years ago

Riangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.

DochEvi [55]

Answer:

Step-by-step explanation:

1. Part A: We know parts of our triangle since the cosine of X is given. XY = 2.5 and XZ = 5.59 and since it is a scale factor of 2, ABC is most likely similar to XYZ by angle measures and the special relationship is, that they are all equal, because with a scale factor of two, all the ratios in triangle ABC will simplify to the ratios of triangle XYZ.

Part B: Because triangle XYZ was dilated with a scale factor of 2 to create triangle ABC, just multiply the sides by 2 to get the sides AC and CB, which is AB = 2 times XY and CB = 2 times XZ.

2. We can first find the hypothenuse by adding squaring 8 and 6 to have 100. Then square root it to have 10 as our hypothenuse

Now we can use sin x = 6/10 and cos y = 6/10

3. Since this is using the angle of elevation, we can say that the length of side AB is perpendicular from the perspective of angle of elevation, and the hypotenuse's length is known, so in this case, we can use a sine or cosecant ratio.

Sin(40 Degrees) = AB/100

AB = 100 x sin(40 Degrees) ft

AB ~ 64.28 ft which can be rounded to 64 ft

The triangle I drew was a right triangle with points A, B, and C. 40 is on point C while 100 ft was on the hypotenuse. The kite was near A and the ground was between segment B and C.

4. Since the angle and Adjacent line is given and it is asking us to find H which is the opposite, we well try and be using Tangent = opposite/adjacent

500 ft Multiply by tan39 = 405 (Estimated after rounding to nearest hundreth 404.892).

To be honest, I didn't know so much about these questions but this might give a better understanding and if I'm wrong then I apologize.

7 0

2 years ago

What is the midpoint of AC

Elina [12.6K]

the answer is........ B

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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