Suppose we are given the following.
Line 1 passes through (-2,2) and (2,-8).
Line 2 passes through (0,-1) and (5,6).
Line 3 passes through (4,-7) and (2,-2).
(a) Find the slope of each line.
Slope of Line 1 = 08
Slope of Line 2 =
Slope of Line 3 =
(b) For each pair of lines, determine whether they are
parallel, perpendicular, or neither.
Line 1 and Line 2: OParallel OPerpendicular
Line 1 and Line 3:
Line 2 and Line 3:
Parallel
OParallel
Neither
OPerpendicular Neither
OPerpendicular
Neither
Answers
The slope of the line passing through (-2,2) and (2,-8) is -5/2
The ratio of the "vertical difference" to the "vertical change" between (any) two unique points on a line is used to compute slope.
The ratio can also be written as a quotient ("rise over run"), which produces the same number for every 2 different points on same line. A declining line has a negative "rise." The line might be useful, as determined by the slope, or it might appear in a diagram that represents a road or a roof as a narrative or a design.a)The slope of the line passing through (0,-1) and (5,6) is 7/5 .
The slope of the line passing through (4,-7) and (2,-2) is -5/2 .
b) line 1 and line 2 are perpendicular.
line 3 and line 2 are perpendicular.
line 1 and line 3 are parallel .
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Related Questions
Simplify as far as possible without a calculator.
5
√
3
(
2
√
3
−
3
√
7
)
Answers
After simplification this 5√3(2√3−3√7) we get, -38.71
5√3(2√3−3√7) is a linear equation.
What is linear equation?
An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.
Let's simply this 5√3(2√3−3√7)
=> 5√3 * 2√3 - 3√7 * 5√3
=> 5*2*√3*√3 - 3 * 5 √7 * √3
=> 10 * 3 - 15 * 1.732 * 2.645
=> 30 - 68.717
=> -38.717 or -38.71
Therefore, the value of 5√3(2√3−3√7), after simplification we get -38.71
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Choose four rational numbers at least two of your numbers should be between -1 and 1 one of which should be written as a decimal and the other should be written as a fraction
Answers
Any number that can be written as a fraction and in which the numerator and denominator are both integers is referred to as a rational number. In other words, p/q can be used to represent a rational number when p and q are both integers and q is 0. It will be 0.25 and 0.5.
Explain about the rational numbers?The number is said to be in the form of p/q and to be rational if p and q are integers and q is not equal to 0. Examples of rational numbers are 1/3, 2/4, 1/5, 9/3, etc.A rational number is any number that can be written as the difference between two integers. For example, any integer is a rational number. The number one can be written as 10,000/10000, -2 over -2, or 1/1. This includes both ordinal and decimal fractions. A decimal fraction is one that has a denominator that is a power of 10. An example would be 0.25Hence, the rational numbers will be 0.25 and 0.5.
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The perimeter of the rectangle is
A) 9.49
B) The p
C) 18.97
The area of the rectangle
A) 18.5
B) 20
C) 40
Please answer ASAP
Answers
The area and the perimeter of the rectangle is found as 13.12 sq. unit and 21.77 units respectively.
What is termed as the rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and all four vertices that are 90 degrees apart. degrees. As a result, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal as well as parallel, it is also known as a parallelogram.For the given question;
To find the perimeter of the rectangle ABCD, first find the length of the sides.
Using the distance formula, find the length DA and DC,
DA = √(x2 - x1)² + (y2 - y1)²
Put the coordinate of the point D and A.
DA = √(8 - 1)² + (2 - 0)²
DA = √49 + 4
DA = √53 units.
Now, length DC
DC = √(3 - 1)² + (3 - 0)²
DC = √4 + 9
DC = √13 units.
For the rectangles;
DA = CB = √53 units.
DC = AB = √13 units.
Perimeter = DA + CB + DC + AB
Perimeter = 2√53 + 2√13 units
Perimeter = 2(√53 + √13) units.
Perimeter = 21.77 units.
Area = (1/2) base × height
Area = (1/2) CB × CD
Area = (1/2) × √53 × √13
Area = 26.24/2
Area = 13.12 sq. unit.
Thus, the area and the perimeter of the rectangle is found as 13.12 sq. unit and 21.77 units respectively.
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A nurse mixes 40 cc of a 70% saline solution with a 10% saline solution to produce a 26% saline solution. How much of the 10% solution should he use?
Answers
ANSWER :
He should use 110 cc of 10% solution
EXPLANATION :
Note that the percent solution is the amount of salt divided by the total volume or quantity.
From the problem, 40 cc of a 70% saline solution.
The amount of salt is 0.70(40) = 28 cc
Another solution is "x" cc of 10% saline solution.
The amount of salt is 0.10x cc
When added together, the total volume is 40 + x
and the amount of salt is 28 + 0.10x
The resulting solution is 26% saline solution.
So we can have :
[tex]\frac{\text{ amount of salt}}{\text{ total volume}}=0.26[/tex]Substitute the results :
[tex]\begin{gathered} \frac{28+0.10x}{40+x}=0.26 \\ \text{ Cross multiply :} \\ 28+0.10x=0.26(40+x) \\ 28+0.10x=10.4+0.26x \\ 0.10x-0.26x=10.4-28 \\ -0.16x=-17.6 \\ x=\frac{-17.6}{-0.16}=110 \end{gathered}[/tex]Max loves fishing. He and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an average speed of 10 km/hour. Some time later a cruise ship left traveling in the same direction but at an average speed of 14 km/hour. After traveling for ten hours the cruise ship caught up with the fishing boat. How long did the fishing boat travel before the cruise ship caught up?
Answers
The fishing boat traveled for 14 hours before the cruise ship caught up.
In this question, we have been given Max and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an average speed of 10 km/hour.
After some time, a cruise ship left traveling in the same direction but at an average speed of 14 km/hour.
The cruise ship caught up with the fishing boat after traveling for 10 hours.
Let a cruise traveled 'm' km after 10 hours.
Using the formula of speed,
speed = distance / time
14 = m / 10
m = 14 * 10
m = 140 km
This means, a cruise traveled 140 km in 10 hours.
Now, we find the time needed for a fishing boat to cover 140 hours.
speed = distance / time
10 = 140/t
t = 140 / 10
t = 14 hours
Therefore, the fishing boat traveled for 14 hours before the cruise ship caught up.
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The cost of a banquet is represented by the equation C = 14p + 90, where C is the cost
and p is the number of people attending. What is the price per person attending?
Answers
The price per person attending is 104 .
What are linear equations?If a variable's highest power is always 1, an equation is considered to be linear. As a one-degree equation, it also goes by that name. An equation with one variable that has the usual form Ax + B = 0 is a linear equation. A coefficient, B is constant, and x is a variable in this situation. An equation with two variables that has the usual form Ax + By = C is a linear equation. Both a B are factors, C is a standard, and the variables in this solution are x and y. Linear equations are defined as equations with the maximum degree of 1. A linear equation cannot have a variable with an exponent greater than 1, according to this rule. A straight line is formed on the linear equation graph.
C = 14p + 90
Here p = 1 cause per person
So,
C = 14 (1) + 90
C = 104
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i need to know if they are functions, please say
function A:(function or not a function)
function B:(function or not a function)
Answers
Answer:
First one is a function, second one is not, since it assigns more than one y value for x values.
Step-by-step explanation:
A function means for every x value, at most 1 y value exists. This is clearly not the case for the bottom figure. You can test it with an imaginary vertical line. There should be zero or one intersections.
if y=-2 when x=4, find y when x =7
Answers
As x and y vary inversely as each other , if x=7 then y = -8/7.
in the question ,
it is given that
x and y vary inversely ,
So , x * y = k
given that , when x = 4 , the value of y = -2 .
Substituting , 4 * (-2) = k
k = -8
so , the constant of variation (k) = -8 .
in order to find value of y when x = 7 ,
we substitute x=7 and k = -8 in the relation xy = k
we get , 7 * y = (-8)
Dividing both sides by 7 we get
7y/7 = -8/7
on simplifying we get ,
y = -8/7
Therefore , as x and y vary inversely as each other , if x = 7 then y = -8/7 .
The given question is incomplete , the complete question is
If y varies inversely as x, and y = -2 when x = 4 find y when x = 7 .
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At a particular restaurant, each pizza roll has 55 calories and each mini hotdog has 70 calories. A combination meal with pizza rolls and mini hotdogs is shown to have 910 total calories and 12 more pizza rolls than mini hotdogs. Determine the number of pizza rolls in the combination meal and the number of mini hotdogs in the combination meal.
Answers
There are 14 pizza rolls in the combination meal and 2 mini hotdogs in the combination meal.
In the above question, it is given that
At a particular restaurant,
Number of calories in Pizza roll = 55 calories
Number of calories in mini hotdogs = 70 calories
A combination meal with pizza rolls and mini hotdogs is shown to have total = 910 calories
We need to find , the number of pizza rolls and number of mini hotdogs in the combination meal
Let the number of mini hot dogs be x
Then number of pizza roll be x+12 ( given )
The following equation is generated from the given information as
55( x + 12) + 70x = 910
55x + 70x + 660 = 910
125x = 910 - 660
Then, number of hotdogs are x = 2
and, number of pizza rolls = x + 12 = 2+12 = 14
Hence, there are 14 pizza rolls in the combination meal and 2 mini hotdogs in the combination meal
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This Stem-and-Leaf Plot shows the number of books sold daily by a bookstore in the previous month. What is the mode of the data set?A.) 45 booksB.) 13 booksC.) 21 booksD.) 53 books
Answers
As you can see in the stem-and-leaf plot, the box with the most numbers is
[tex]\rightarrow2|00111122\leftarrow[/tex]And in this box, the number that is repeated the most is 1. So that, the data that is repeated the most is 21.
Therefore, the mode of the data set is 21.
Question 13 of 20
ƒ(x) = 2x³ +7x² − 4x − 5
-
g(x) = 3x - 2
Find (ƒ – g)(x).
Answers
Answer:
(f - g)(x) = 2x³ + 7x² - 7x - 3
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 2x³ + 7x² - 4x - 5 - (3x - 2) ← distribute parenthesis by - 1
= 2x³ + 7x² - 4x - 5 - 3x + 2 ← collect like terms
= 2x³ + 7x² - 7x - 3
Jane is going to purchase a home that is $180,000, she makes the standard down payment (20%), then she is going to obtain a mortgage for the rest. How much will Jane have paid total for the house if she does a 30-year mortgage (360 months)? Interest rate for both is 4%(.04) How much will she have paid total for the house if she does a 15-year mortgage? Worth 5 points
Answers
Answer:
36000
Step-by-step explanation:
I think its that because the 20% of 180000 is 36000
given r(x)= 11/(x-4)^2 which repress the domain restriction on r(x) and the corresponding inverse function?
Answers
A function that "undoes" another function is referred to as an inverse in mathematics. To put it another way, if f(x) yields y, then y introduced into the inverse of f yields x. A function that can be inverted has an inverse, which is denoted by the symbol f1. The solution is: x>4;r-1(x)=4-(root of (11/x)
Explain about the inverse function?Something that is opposite or reversal in nature or quality. The inverse of "if A then B" is "if not-A then not-B" — compare contrapositive. 2: a proposition or theorem constructed by opposing both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem.
reciprocal, inverse multiplicative. (Mathematics) One of two numbers whose product is 1: the multiplicative inverse of 7 is 1/7, while the reciprocal of 2/3 is 3/2. type: antagonism, oppositeness. the connection between seemingly opposing parties.
If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function. The term "f inverse" is widely used to refer to this particular inverse function, which is singular.
The solution is: x>4;r-1(x)=4-(root of (11/x)
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2(2x - 7) = 22 solve for x and simplify your answer as much as possible
Answers
Answer: 9
Step-by-step explanation:
2(2x-7) = 22
4x - 14 = 22
4x = 36
x = 36/4
x = 9
Distribute the two to the 2x-7 in parentheses
Add 14 to 22
Divide 36 by 4
Find the LCM of 4 and 14
Answers
Mia, this is the solution:
4 = 2 * 2
14 = 2 * 7
Therefore, we have:
2 = two ocurrences (the higher number)
7 = one ocurrence
LCM = 2 * 2 * 7
LCM = 28
Please find X
I will give brainly to the best
Answers
Answer:
x = 25°
Step-by-step explanation:
Hello!
If the angles are vertical, the measures of the angles are equal.
Vertical angles are formed by the intersection of two lines, and are non-adjacent angles. The measures of the two angles are equal to each other.
We can set up an equation for x, and solve for it.
Solve for x75° = 4x - 25° => add 25 to both sides75° + 25° = 4x => Simplify100° = 4x => Isolate the variable25° = xThe value of x is 25°.
Direct VariationInverse VariationNeither21 pointTell whether x and y show direct variation, inverse variation, or neither y = x - 2
Answers
Given:
Given the equation y = x - 2
Required: Classify it as direct variation, inverse variation or neither.
Explanation:
Two variables x and y show direct variation when they satisfies y = ax or y/x = a, where a is non-zero.
Similarly, two variables x and y show inverse variation when they satisfies y = a/x or xy = a, where a is non-zero.
Here, the equation y = x - 2 is in neither of the form y = ax or y = a/x.
So, y = x - 2 show neither direct nor inverse variation.
Final Answer: y = x - 2 show neither direct nor inverse variation.
Rewrite 8-1/2 as an improper fraction.
Answers
Answer:
[tex]\frac{15}{2}[/tex]
Step-by-step explanation:
8 - [tex]\frac{1}{2}[/tex]
= [tex]\frac{16}{2}[/tex] - [tex]\frac{1}{2}[/tex]
= [tex]\frac{15}{2}[/tex]
Answer:
The answer is 17/2
Step-by-step explanation:
You get that by multiplying the whole number 8 by the denominator of the fraction, and that will be equal to 16 and the 1 from the numerator of the fraction 1/2, so the equation will look like 16+1=17. Your new numerator 17.
Which step shows the result of applying the subtraction property of equality? one-fourth (12 x 8) 4 = 3 step solution 1 3 x 2 4 = 3 2 3 x 6 = 3 3 3 x = negative 3 4 x = negative 1 step 1 step 2 step 3 step 4
Answers
The step 3 follow the subtraction property of equality.
Given,
The Equation is : 1/4 (12x + 8) + 4 = 3
There is some steps:
Step Solution
1 3x + 2 + 4 = 3
2 3x + 6 = 3
3 3x = -3
4 x = -1
To find the which step shows the result of applying the subtraction property of equality?
Now, According to the given steps:
From the table, we can know
From Step 2: 3x + 6 = 3
Subtract 6 on both sides
3x + 6 - 6 = 3 - 6
3x = -3
Hence, The step 3 follow the subtraction property of equality.
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What is the length of segment SR?
Answers
Applying the midsegment theorem, the length of segment SR is: 6 units.
What is the Midsegment Theorem?The Midsegment theorem states that if a segment is draw to connect the two midpoints of two sides of a triangle together, it is parallel to the third side of the triangle and also has a length measure that is half of the length of the third side of the triangle.
Segment SR is the midsegment of the triangle given and is parallel to the third side, FD.
SR = 2x - 14
FD = x + 2
Therefore:
SR = 1/2(FD) [midsegment theorem]
Substitute
2x - 14 = 1/2(x + 2)
2(2x - 14) = x + 2
4x - 28 = x + 2
4x - x = 28 + 2
3x = 30
x = 30/3
x = 10.
Length of SR = 2x - 14 = 2(10) - 14
Length of SR = 6 units
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Answer:
12 units
Step-by-step explanation:
Where should you plot the ordered pair (3,4) in relation to the origin?
CLEAR CHECK
4 spaces to the right and 3 spaces up
3 spaces to the right and 4 spaces up
3 spaces to the right, 4 times
3 spaces up and 4 spaces to the right
Answers
Answer:
3 spacesto the right and 4 spaces up
Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks. Write an equation that represents the relationship between the dollar amount in her bank account and the number of weeks of saving.
Answers
Answer: d=50+20w
D(deposit) = 50(starting amount)+20(added amount)w(multiply 20 by the amount of weeks, 12, and this is your equation.)
Write an equasion of the line that passes through (0,-2) and (4,10)
Answers
Answer:
12.649
Step-by-step explanation:
we can use Pythagoras to solve this; simply by forming a triangle of the difference between the x and y values. (I added a lil-sketch of it).
So, we just need to find the length of the two sides:
Vertical side: 12
Horizontal side: 4
Thus;
[tex]4^{2} + 12^{2} = c^{2} \\160 = c^{2}\\Side c is equal to 12.649 (in whatever unit given)[/tex]
You have a function that takes in an X value and produces a Y value. The x value equals 7 times the y value, plus 18 more. What's the x value when the y value equals 6?
Answers
The value of x from the given function is 60.
Given that, the x value equals 7 times the y value, plus 18 more.
What is the function?A function in math means a correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to outputs.
Now, the x value equals 7 times the y value, plus 18 more
x=7y+18
Put y=6 in the obtained function, that is
x=7(6)+18
⇒ x = 42+18
⇒ x = 60
Therefore, the value of x from the given function is 60.
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hi help please thanks
Answers
∠1 and ∠3 are a pair of corresponding angles.
What are corresponding angles?The angles created when a transversal intersects two parallel lines are known as corresponding angles. Typical examples of corresponding angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks. Angles that correspond to parallel lines have equal measures. The lines are parallel if the corresponding angles are equal.Eight angles are created when two parallel lines cross a transversal. Four pairs of corresponding angles will be created from all eight angles. One of the pairs consists of angles 1 and 5.So, in the given image ∠1 and ∠3 are the pair of corresponding angles.
Therefore, ∠1 and ∠3 are a pair of corresponding angles.
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Solve for x and then give the m∠G?
Enter your answer in the box.
Answers
first the sum of all angles of in triangle is 180 degree.
x+(3x+25)+(x-5)=180
x+3x+25+x-5=180
4x+25+x-5=180
4x+x+25-5=180
5x+20=180
5x=180-20
5x=160
x=32 degree and
the angle of G is 3(32)+25=121 degree
Calculate and interpret the residual for the woman who had a lean body mass of 50.6 k and a metabolic of 1502
Answers
The women with mass of 50.6 Kg burns 85 calories more per day then predicted.
What is Residual?A residual is defined as something that remains after other items have been used, taken away, or discarded. The paint that is left over after every room in a house has been painted is an example of residue.
Residuals are crucial in assessing a model's quality. Remainings can be investigated in terms of their size and/or if they exhibit a pattern. When all of the residuals are 0, the model makes perfect predictions. The model is less accurate the further the residuals are from 0.
Given:
body mass= 50.6 Kg
Metabolic rate= 1502
Now, residual
= 1502 - 1416.8806
= 85.1194
Hence, the women with mass of 50.6 Kg burns 85 calories more per day then predicted.
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Jerrod brought 48 cupcakes to school. At school, he gave 3 cupcakes to
each student in his class. He has 6 cupcakes remaining. How many
students are in Jerrod's class?
Answers
it should be 14 students i think
Hope this help you
My number is a multiple of 4. My number has 8 factors, including 2 and 3. My number is less than 30. My number is
Answers
Answer:
24
Step-by-step explanation:
mutiples of fours under 30 leave 7 possible numbers
but the only number w 8 factors under 30 is 24
(if you're too lazy to read all of the below im about to say then because it is divisible by 2,3,4 and less than 30 the number is 2 x 3 x 4 = 24)
First, we exclude 0 cause it has more than 8 factors (literally)
Since 2 and 3 are 2 of the number's factors, it must be divisible by 6.
Therefore, we have 4 options : 6,12,18,24 (30 does not count)
Since it is divisible by 4, we are left with 2 : 12 and 24.
(here's something extra which is how to identify the number of factors a number has, not necessary in this case cause we can just count, but it's useful anyways)
We do the prime factorization of that number :
For example : 120
The prime factorization of 120 is 2^3 x 3 x 5.
Now, we take the index number of every single one of the prime numbers in the factorization, add each of them by 1 and multiply them
So, the index number of 2 is 3, 3 is 1 and 5 is 1 (2^3 x 3^1 x 5^1)
-> 120 has (3+1)(1+1)(1+1) = 16 (factors).
Applying it to this case, only 24 would work, as :
24 = 3 x 2^3
So, it has (3+1)(1+1) = 8 (factors), just as it says.
Suppose n represents an integer. Then the next integer can be represented by the expression n+1. Write a linear expression that represents the sum of any two consecutive integers. Then use the expression to make an argument about whether the sum of any two consecutive integers is even or odd. Explain your reasoning.
Answers
The expression 2n + 1 will produce both odd and even numbers based on the choice we have made.
Expression:
An expression is a mathematical expression consisting of numbers, operations, and one or more variables.
Given,
Suppose n represents an integer. Then the next integer can be represented by the expression n+1.
Here we need to write the linear equation for these two consecutive integers.
Then we have to use the expression to make an argument about whether the sum of any two consecutive integers is even or odd.
Let n represents the first integer and n+1 is the second integer.
Then the linear equation for these two consecutive integer is
=> n + (n + 1)
=> 2n + 1
Now we have to take the value of n and n + 1 as, 2 and 3,
Then we apply the value to the expression,
=> 2(2) + 3
=> 4 + 3
Similarly, if we take the value as 5 and 6,
Then we get,
=> 2(5) + 6
=> 10 + 6
=> 16
So, based on the given details the equation givens both odd and even number based on the number our choices.
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