The slopes formed by each of the pairs of points are given as follows:
(2,11.9),(4,10.5): -0.7.(2,8) , (4,7.5): -0.25.(2,6) , (4,1.5): -2.25.(2,0.5) , (4.-1): -0.75.(2,-1) , (4,-1): 0.(-2.8,-5.0) , (-3.6,-5.9): 0.89.SlopeThe slope is equivalent to the rate of change, hence, given two points, the slope is calculated as the change in y, also called rise, of these two points divided by the change in x, also called run.
For the first case, the points are:
(2, 11.9) and (4, 10.5)
Hence:
The change in x is of 4 - 2 = 2.The change in y is of 10.5 - 11.9 = -1.4.The slope is:
m = -1.4/2 = -0.7.
The other slopes are calculated as follows:
(2,8) , (4,7.5): m = (7.5 - 8)/(4 - 2) = -0.25.(2,6) , (4,1.5): m = (1.5 - 6)/(4 - 2) = -2.25.(2,0.5) , (4.-1): m = (-1 - 0.5)/(4 - 2) = -0.75.(2,-1) , (4,-1): m = (-1 - (-1))/(4 - 2) = 0. (no change in the output).(-2.8,-5.0) , (-3.6,-5.9): m = (-3.6 - (-2.8))/(-5.9 - (-5)) = 0.89.More can be learned about slopes at https://brainly.com/question/28954211
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The difference between two-fifth of a number and 9 is 7. Find the number.
Answer:
The number is 40.
Step-by-step explanation:
Step 1: Assume your variables
Consider the 'number' to be [tex]x[/tex].
Step 2: Create an equation(s)
The information in the question states that the difference between [tex]\frac{2}{5}[/tex] of [tex]x[/tex] and [tex]9[/tex], is [tex]7[/tex].
Representing this mathematically gives us:
[tex](\frac{2}{5}\times x) -9=7[/tex]
Step 3: Solve the equation
The equation we have is:
[tex](\frac{2}{5}\times x) -9=7[/tex]
So, let's solve it:
[tex](\frac{2}{5}\times x) -9=7\\\\\text{Add 9 to both sides:}\\(\frac{2}{5}\times x) -9+9=7+9\\\\\text{Simplify:}\\(\frac{2}{5}\times x)=16\\\\\text{Multiply by}~\frac{5}{2}~\text{on both sides:}\\\frac{5}{2}\times\frac{2}{5}\times x=16\times \frac{5}{2}\\\\\text{Simplify:}\\1\times x=\frac{80}{2}\\\\\text{Calculate:}\\x=40[/tex]
If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c. Write an absolute value equation to represent the definition of betweenness.
The absolute value equation to represent the definition of betweenness is
AB + BC = AC ↔ B ∈ A,C
Absolute value equation:
An absolute value equation is a function that contains an algebraic expression within absolute value symbols.
Given,
Here we have the statement "If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.".
Here we need to find the absolute value function for this statement.
In order to find the absolute value equation,
First we have to identify the symbols for the terms mentioned in the statement they are,
between = ∈
if and only if = ↔
sum = +
Now, we have to divide the statement as two parts.
First one is, "c lie on the same line, then b is between a and c"
It can be written as,
B ∈ A,C
Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."
Which can be written as
AB + BC = AC
When we combine it, the we get the absolute value equation as,
B ∈ A,C ↔ AB +BC = AC
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The area of a rectangle is 110 square units. Its length measures 11 units. Find the length of its diagonal. Round to the nearest tenth of a un
it
The length of the diagonal of the Triangle is 14.86 units
What is Diagonal?
When two polygonal vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.
Given,
Area of Rectangle = 110square units
Length = 11units
Breadth = ?
Area of Rectangle = length x breadth
Breadth = Area of Rectangle / length
Breadth = 110 / 11
Breadth = 10units
Length of diagonal (Pythagoras Theorem)
H^2 = P^2 + B^2
H^2 = (11)^2 + (10)^2
H^2 = 121 + 100
H^2 = 221
H = [tex]\sqrt{221}[/tex]
H = 14.86 units
Hence, The length of its diagonal is 14.86 units
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Multiply by applying the commutative and/or associative property. (−310)(4.2)(−100) What is the product?
The product of the given expression is 1,30,200.
Given expression:-
(−310)(4.2)(−100)
We have to find the solution of the given expression by using either the commutative property or the associative property.
We will use the associative property of multiplication to find the product.
(−310)(4.2)(−100) = (-310)*(4.2*(-100)) = (-310)*(-420) = 1,30,200
Associative property
The associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result.
Hence,
(a*b)*c = a*(b*c) , where a, b and, c are real numbers.
Commutative property
Commutative property In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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WILL GIVE BRAINLIEST!!! solve the problem fill in the blanks to show your work
By performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The four mathematical operations are functions that take input values, or numbers, and turn them into output values, or yet another number. They are multiplication, division, addition, and subtraction.So, the values in the blank will be:
= - 1.2(2/5) ÷ -2= -1.2(0.4) ÷ -2= - 0.48 ÷ -2= 0.24Therefore, by performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
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Hi, can you help me to solve this problem, please !!!
Remember that
The y-intercept is the value of y when the value of x=0
In this problem
we have the equation
y=7x^2+4
For x=0
substitute
y=7(0)^2+4
y=4
the y-intercept is (0,4)Find the coordinates of the vertices of each figure after a reflection over the given axis.
triangle ABC with vertices A(2,3)B(4,-5), and C(-1,2); x-axis
The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)
Given,
A triangle ABC with vertices A(2,3) , B(4,-5), and C(-1,2)
To find the coordinates of the vertices of each figure after a reflection over the given axis.
Now, According to the question:
We should know that:
You should know that you can predict changes in coordinates after translations without a graph or anything like that.
(x, y) reflected over the x axis = (x, -y)
(x, y) reflected over the y axis = (-x, y)
(x, y) rotated 90 degrees around the origin = (y, -x)
(x, y) rotated 180 degrees around the origin = (-x, -y)
(x, y) rotated 270 degrees around the origin = (-x, y)
So here's our set of points.
A(2,3) , B(4,-5), and C(-1,2)
Here's those points reflected over the x axis.
A' (2, -3) B' (4, 5) and C' (-1, -2)
Hence, The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)
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Hey!
New question 4 today
Nadia is walking a 3.4-mile trail. She stops to take a break after walking 1.6 miles. Which explains whether the distance Nadia already walked is greater than, less than, or equal to the distance she has left to walk?
!PLEASE!
Don't give wrong answers. (its not very nice)
Only use one of the answer options. (other answers are wrong)
Based on the distance walked by Nadia when she took her break, the statement that explains the distance already walked is C. The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8.
How to find the distance?Nadia had already walked 1.6 miles by the time she took her break. This means that the distance she was still left to walk in the mile trail was:
= 3.4 - 1.6
= 1.8 miles
The distance that Nadia had already walked was 1.6 miles and yet she was left to walk 1.8 miles.
We can therefore conclude that the distance that Nadia already walked is less than the distance still to be walked.
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The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8 which is the correct answer would be an option (C).
What is the distance?Distance is calculated as the product of a person's movement and time.
Nadia took a rest after covering 1.6 miles of walking.
This indicates that she had the following distance to cover on the mile trail:
⇒ 3.4 - 1.6 = 1.8 miles
Nadia had already walked 1.6 miles, but she still had another 1.8 miles to go.
Therefore, the distance Nadia has already traveled is less than the distance that needs to be covered.
Hence, the correct answer would be an option (C).
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Marty graphs the hyperbola (y+2)2/36−(x+5)2/64=1 .
How does he proceed?
Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Marty first identifies the center of the hyperbola as Response area, and that the hyperbola opens Response area. Since a = Response area, the coordinates of the vertices are Response area.
The slopes of the asymptotes of this parabola are ± Response area, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Response area.
Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes.
To construct the graph of the hyperbola, the procedure is as follows:
Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).Equation of an hyperbolaThe equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:
(y - y*)²/a² - (x - x*)²/b² = 1.
A vertical hyperbola opens up and down.
In this problem, the equation is:
(y + 2)²/36 - (x + 5)²/64 = 1.
Hence the center is:
(-5, 2).
The value of coefficient a is:
a² = 36 -> a = 6.
Then the vertices of the hyperbola are:
(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).The slopes of the asymptotes of the parabola are given as follows:
±a/b.
Hence:
a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.Since the asymptotes pass through the center, the equation is:
y - 2 = ± 3/4(x + 5).
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What is the solution to the inequality?
17<9+x
OA. x<8
OB. x>8
OC. x > 26
OD. x< 26
SUBMIT
Answer:
B) x > 8
Step-by-step explanation:
1-Step: Combine like terms by subtracting 9 on both sides : 17-9 < X
8 < X
2- Step: flip the signs (Since 8 is less than X, Then X is greater than X)
X > 8
3 points
Simplify the following expression
I WILL USE THE LAWS OF EXPONENTS
[tex] {x}^{n} \times {x}^{m} \\ = {x}^{n + m} [/tex]
AND
[tex] \frac{{x}^{n}}{ {x}^{m} } \\ = {x}^{n - m} [/tex]
[tex] \frac{3 {x}^{ - 2 + 5} }{ {x}^{8} } \\ = \frac{3 {x}^{3} }{ {x}^{8} } \\ = 3 {x}^{3 - 8} \\ = 3 {x}^{ - 5} [/tex]
ATTACHED IS THE SOLUTION.
Answer:
i hope this one is good for you
A store sells 3 T-shirts for 28.14
Answer:
Step-by-step explanation:
1 T shirt = 28.14
There are 2 methods this can be done.
Method `1
Adding 3 times
28.14 + 28.14 + 28.14 = $84.42
Method 2
Multiplying 28.14 by 3
28.14 times 3 = $84.42
Therefore answer is 84.42
I'll give brainliest
6. A calculator screen shows the following numbers in Scientific Notation. Rewrite the numbers in proper Scientific Notation and then in Standard Form:
a) 3.6E-5
proper scientific notation: 3.6 x 10⁻⁵
standard form: 0.000036
Write a multiplication problem with two fractions that has a simplified product of 4/5.
A problem that consists of the multiplication of two fractions, and in which the simplified product is 4/5 is presented as follows;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
What is a fraction in mathematics?A fraction consists of a number that is expressed as a quotient, such that the numerator is being divided by the value in the denominator.
The multiplication problem with two fractions that ha a simplified product of 4/5 is found as follows;
let the fractions be [tex] \displaystyle \frac{a}{b} [/tex] and [tex] \displaystyle \frac{c}{d} [/tex]
The multiplication product is therefore;
[tex] \displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b\cdot d} = \frac{4}{5}[/tex]
The lowest common multiple of a and c is 4, while the lowest common multiple of b and d is 5
Taking b as 15, and a as 14 and c as 6, while d is taken as 7, such that we have;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} =\frac{2 \times 7}{5 \times 3} \times \frac{2 \times 3}{7} = \frac{2 \times 2}{5 \times 1} =\frac{4}{5} }[/tex]
The multiplication problem is therefore;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
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help me plssssssssssssss
Answer:)0.3 I Think
Step-by-step explanation:
1.8/6
The answer is:
10.8 cm
Explanation:
6 × 1.8 = 10.8
- firstly, remove the decimal point
- Secondly, multiply regularly 6 by 18
- You'll get 108 as an answer
- Take back the decimal point one to the left because you took it one to the right before, so you will have to do the inverse of the previous action
Good luck
I need this answered please
Answer:
240 copies of the standard version.
Step-by-step explanation:
See attached worksheet.
Bonus: Since 240 standard copies were downloaded, we know that 3 times that number is the number of high quality versions downloaded.
Copies Size(MB) Total MB
Standard 240 2.6 624
High 720 4.4 3168
Total (MB) 3792 {This matches the data]
factor this polynomial completely[tex]10 {x}^{2} - 11x + 3[/tex]
Given:
There are given the equation:
[tex]10x^2-11x+3=0[/tex]Explanation:
According to the question:
we need to find the factor of the given equation:
So,
From the equation:
[tex]\begin{gathered} 10x^{2}-11x+3=0 \\ 10x^2-6x-5x+3=0 \\ (2x-1)(5x-3)=0 \end{gathered}[/tex]Final answer:
Hence, the factor of the given equation is shown below:
[tex](2x-1)(5x-3)=0[/tex]A square has approximately 300 square feet . The length of each side of the square is between which two whole numbers?
Area = 300 ft^2
Formula
Area = length of a side x length of a side
Substitution
300 = length of a side ^2
[tex]\sqrt{300}[/tex][tex]\sqrt{300}\text{ = 17.32}[/tex]The length of a side is between 17 and 18
Answer:
The length of the side of the square is approximately [tex]17.32[/tex] feet, which lies between the whole numbers [tex]17[/tex] and [tex]18[/tex].
Step-by-step explanation:
Step 1: Assume your variable
Since all the sides of a square are the same, let's consider the side to be the variable: [tex]x[/tex].
Step 2: Create an equation
The formula for the area of a square is:
[tex]\text{Area}=\text{Side}^{2}[/tex]
We have assumed the side to be [tex]x[/tex], and the area is said to be [tex]300[/tex], so substitute these values into the formula:
[tex]\text{Area}=\text{Side}^{2}\\300=x^{2}[/tex]
Step 3: Solve the equation
Using the formula for the area of a square, we came to find an equation:
[tex]x^{2}=300[/tex]
Now, let's find the value of [tex]x[/tex]:
[tex]x^{2}=300\\\\\text{Square root both sides of the equation:}\\\sqrt{x^{2}}=\sqrt{300}\\\\\text{Simplify:}\\x=\sqrt{300}\\\\\text{Calculate:}\\x\approx 17.32[/tex]
The length of the side of the square is approximately [tex]17.32[/tex] feet.
As we know, this number lies between [tex]17[/tex] and [tex]18[/tex].
Kala earns 45 dollars each week working part-time at a bookstore. She earns one additional dollar for each book that she sells.
Let A be the amount (in dollars) that Kala earns in a week if she sells
B books.
Write an equation relating to A to B Then use this equation to find the amount of money Kala earns if she sells 21 books.
The equation relating to A to B is A = 45 + b and the amount is $66.
What is an equation?An equation is used to show the relationship between the variables that are illustrated.
In this case, Kala earns 45 dollars each week working part-time at a bookstore and she earns one additional dollar for each book that she sells.
Let the books be represented as b. The equation will be:.
A = 45 + 1b
A = 45 + b
where A = amount earned.
The amount earned when 21 books are sold will be:
A = 45 + b
A = 45 + 21
A = 66
The amount is $66.
This illustrates the concept of equations.
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given the domain {-2,2,4} what is the range for relation 3x+y=3a (-9,3,9)b (9,-3,-9)c (-3,9,15)d (0,5,7)
the relation is 3x + y = 3
so,
y = 3x - 3
the domain is the values of x
so, substitute with each value of {-2,2,4} at the last equation of y
when x = -2 , y = 3*-2 - 3 = -6 - 3 = -9
when x = 2 , y = 3 * 2 - 3 = 6 - 3 = 3
when x = 4 , y = 3 * 4 - 3 = 12 - 3 = 9
so, the range will be {-9 , 3 , 9}
The correct answer is option a. (-9,3,9)x
The surface area S(r) in square units of a cylinder with a volume of 18 cubic units is a function of its radius r in
units where S(r) = 2rr²+36. What is the surface area of a cylinder with a volume of 18 cubic units and a
radius of 3 units
The surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 68.52 units².
How to calculate the surface area?The volume of a cylinder is calculated as:
= πr²h
In this case, the volume is given as 18 units³. The computed height is 0.637 units.
The surface area will be:
= 2πr² + 2πrh
= 2(3.14 × 3²) + (2 × 3.14 × 3 × 0.637)
= 56.52 + 12
= 68.52 units²
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Alberto's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 6 adult tickets and 14 student tickets for a total of $84. The school took in $105 on the second day by selling 12 adult tickets and 7 student tickets. What is the price each of one adult ticket and one student ticket?
Answer:
Adult: $7
Student $3
Step-by-step explanation:
Hello!
We can use a system of linear equations to find the solution.
Let the price of adult tickets be x, and the price of student tickets are y.
The price of Day 1 can be represented by 6x + 14y = 84, and the second day can be represented by 12x + 7y = 105.
We can solve the system by graphing both equations on a coordinate plane and finding the point of intersection.
The point of intersection happens at x-coordinate 7 and y-coordinate 3. Recall that x is assigned to the price of adult tickets, and y is assigned to student tickets.
The price of adult tickets is $7, and the price of student tickets is $3.
What is the slope of a line perpendicular to the line whose equation is 3x+18y=108. Fully simplify
The slope of the line which is perpendicular to the given line 3x+18y=108 is (6).
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
We already know the equation of a line in slope intercept form y = mx + b and we also know that perpendicular lines that have slopes which are negative reciprocals of each other.
Given a line 13x + 18y=108, this slope intercept form can be written as,
3x + 18y = 108
18y = 108 - 3x
y = (108 /18) - (3/18)x.
y = (6) - 1x/6.
y = -(1/6)x + 6.
∴ The slope of the given line is (-1/6), thus the slope of the line which is perpendicular is (6).
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19) f(x) = -x +3
g(x)= x - 4
Find f(x) · g(x)
Answer:
-8x + (3x - 12)
Step-by-step explanation:
f(x) · g(x)
(-x + 3) · (x - 4)
(-2x · 4x) + (3x - 12)
-8x + (3x - 12)
Pls mark brainliest
PLEASE PLEASE PLEASE HELP ME I WILL MARK BRAINLY
Answer:
pretty sure its WZX
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
54°
(7x+1)°
The value of x according to the complete task content as given is; 5.
Sum of interior angles in a triangle.It follows from the complete task content that a right angled triangle is given(in which case one of the angles is a right angle = 90°).
Hence, the required value of x can be determined from the; sum of interior angles of a triangle as follows;
90° + 54° + 7x + 1° = 180°
7x = 180° - 90° - 54° - 1°
Evaluate the right side of the equation;
7x = 35°
Divide both sides by; 7;
x = 35°/7
x = 5.
Ultimately, the value of x according to the task content is; 5.
Remark:
The completed task content is; The measures of the angles of a triangle are shown in the figure below. Solve for x. The figure is a right triangle with the other two interior angles 54° and (7x + 1)°.
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please answer also this will give u 100 points
Answer:
Step-by-step explanation:
Slope is gradient which is, change in y
change in x
so, on the graph, change in y = 10-2.5 = 7.5
change in x = 5-0 =5
so, gradient is, 7.5/5
= 3/2
A construction crew is lengthening a road that originally measured 10 miles. The crew is adding one mile to the road each day.Let L be the length (in miles) after D days of construction.Write an equation relating L to D. Then graph your equation using the axes below.
Let:
L = length of the road
D = Days of construction
We can write a linear equation in the slope-intercept form:
[tex]y=mx+b[/tex]Where:
m = Slope = rate = 1 mile per day
b = y-intercept = Initial value = 10 miles
Therefore:
[tex]\begin{gathered} L=1D+10 \\ L=D+10 \end{gathered}[/tex]The graph is:
Write the equation in slope intercept form: x-3y=12
Answer:
[tex]\\ y = \frac{1}{3} x - 4[/tex]
Step-by-step explanation:
Hope this helps! :))
Two cars are initially 10 miles parat on the same straight road and are moving towards each other. One car is going 30 miles per hour and the other car is going 36 miles per hour. How far apart are the two cars 2 minutes later?
Answer:
Let's break down the given information.
Car A
Speed - 30 mph
Hence the distance traveled per minute would 30/60 mph which is 0.5 Miles every minute.
Car B
Speed - 36 mph
The distance traveled per minute would 36/60 mph which is 0.6 Miles every minute.
Initial distance between the cars is 10 Miles
Car A travels 1 miles in 2 minutes and Car B travels 1.2 miles in 2 minutes.
Hence to calculate the distance between the 2 cars we need to calculate
Initial distance - Distance travelled by Car A - Distance traveled by Car B
Which is
10 - 1 - 1.2
7.8 Miles distance between the 2 cars
