Answer: |a|=−4
Step-by-step explanation:Divide each term in −|a|=4by −1 and simplify.
What is the distance between the points shown? Show your work.
Round your answer to the nearest tenth.
Answer:
8.3 units
Step-by-step explanation:
To find the distance between the two points, use the distance formula.
Distance = [tex]\sqrt{(x-x)^2+(y-y)^2}[/tex]
(x, y)
(-1.5, 4)
(-5, -3.5)
[tex]\sqrt{(x-x)^2+(y-y)^2}[/tex] - Formula
[tex]\sqrt{(-1.5--5)^2+(4--3.5)^2}[/tex] - Plug in values
[tex]\sqrt{(3.5)^2+(7.5)^2}[/tex] - Simplify parenthesis
[tex]\sqrt{12.25+56.25}[/tex] - Simplify
[tex]\sqrt{68.5}[/tex] = 8.27647267862 = 8.3
Quadrilateral NOPQ is dilated by a scale factor of to form
quadrilateral N'O'P'Q'. What is the measure of side Q'N'?
18
Z
20.1
20.1
18
0
K
The measure of side Q'N' after a dilation of quadrilateral NOPQ by a scale factor of 2/3 is 12 units
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Scale factor is the ratio of new side to original side. It is given as:
Scale factor = new side / original side
Given that the scale factor is 2/3 and the side QN is 18, hence:
QN * scale factor = Q'N'
Substituting:
18 * 2/3 = Q'N'
Q'N' = 12
The measure of side Q'N' is 12 units
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How much larger is a great white shark than a horn shark how many bamboo sharks would that equal
Answer: A great white shark can grow up to 20 feet in length, while a horn shark can grow up to 3 feet in length. Therefore, a great white shark is 17 feet larger than a horn shark.
Bamboo sharks can grow up to 5 feet in length. Therefore, to equal the length of a great white shark, you would need 4 bamboo sharks (since 4 x 5 = 20).
Step-by-step explanation:
The number of hours of daylight on a given day in City A is given by the following function, where x is the number of days after January 1.
a. The amplitude of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 4.
b. The period of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 365 days.
c. There are approximately 16 hours of daylight on the longest day of the year.
d. There are approximately 8 hours of daylight on the shortest day of the year.
e. The graph for the function is obtained.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function is given as y = 4 sin [(2π / 365)(x - 79)] + 12.
a. The amplitude of the function is the coefficient of the sine function, which is 4.
Therefore, the amplitude of the function is 4.
b. The period of the function is given by the formula: period = (2π/b), where b is the coefficient of x in the sine function.
In this case, b = (2π/365), so the period is -
period = (2π / (2π/365)) = 365
Therefore, the period value is 365 days.
c. The longest day of the year occurs on the summer solstice, which is around June 21.
On this day, x = 171 (assuming January 1 is x = 1). Plugging x = 171 into the function gives -
y = 4 sin [(2π/365)(171 - 79)] + 12 = 15.998 hours
Therefore, the number of hours for daylight is 16 hours.
d. The shortest day of the year occurs on the winter solstice, which is around December 21.
On this day, x = 355. Plugging x = 355 into the function gives -
y = 4 sin [(2π/365)(355 - 79)] + 12 = 8.002 hours
Therefore, the number of hours for daylight is 8 hours.
e. To graph the function for one period, we need to find the values of y for x ranging from 1 to 365.
We can use a graphing tool or software to plot the function.
The graph is plotted.
The x-axis represents the number of days after January 1, and the y-axis represents the number of hours of daylight.
The function oscillates between 8 and 16 hours of daylight over the course of one year, with the maximum occurring around day 171 and the minimum occurring around day 355.
The graph shows that the function is periodic, with a period of 365 days, as expected.
Therefore, the function is plotted.
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The elementary school in your town wants to replace its current playground. The space used for the new playground will be similar to that of the current playground. The current space is rectangular and has a length of 35 feet and a width of 45 feet. The length of the new space is 42 feet. Find the perimeter of the space used for the new playground. Perimeter: feet
By answering the above question, we may infer that Thus, the 159 feet that make up the perimeter of the area used for the new playground.
What is perimeter?A limit is a closed path that encircles, separates, or encompasses a one-dimensional length, a two-dimensional shape. A circle's or an ellipse's perimeter refers to its outermost region. Many practical uses may be made of the perimeter calculation. The radius of an edge is used to calculate a shape's perimeter. Get the circle's radius by multiplying the lengths of the sides of irregular shapes. Every form's perimeter may be determined by multiplying its side lengths. The area around an object is called its perimeter. Your home's walled garden serves as a wonderful example of this. A thing's perimeter is the area surrounding it. A 200 foot barrier will be needed to contain a 50 by 50 foot yard.
Current playground size is 1,575 square feet, or 35 feet by 45 feet.
The difference between the old and new playgrounds is 1,575 square feet.
New playground length = 1,575 square feet / 42 feet 37.5 feet, where new playground width equals new playground area.
We can calculate the perimeter now that we know the new playground's width is around 37.5 feet:
The new playground's perimeter is equal to 2 (length + width).
The new playground's perimeter is 2 (42 feet plus 37.5 feet).
2 is the new playground's perimeter (79.5 feet)
The new playground's perimeter is 159 feet.
Thus, the 159 feet that make up the perimeter of the area used for the new playground.
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What is the length of segment BC? A coordinate plane is shown. Point B is located at negative 3, negative 2, and point C is located at 0, 2. The points are connected by a line segment. Group of answer choices 5 7 6 4 Flag question: Question 3
Answer: 5
Step-by-step explanation:
Use the Formula d = √((x2 - x1)2 + (y2 - y1)2)
Find the difference between coordinates:
(x2 - x1) = (-3 - 0) = -3
(y2 - y1) = (-2 - 2) = -4
Square the results and sum them up:
(-3)2 + (-4)2 = 9 + 16 = 25
Now Find the square root and that's your result:
Exact solution: √25 = 5
Approximate solution: 5
ixl prediction! URGENT, PLEASE.
The expected number of not blue is 54
How to evaluate the expected number of valueFrom the question, we have the following parameters that can be used in our computation:
Spinner
Using the above as a guide, we have the following probability
P(Not Blue) = Not Blue/Total
So, we have
P(Not Blue) = 6/9
When it is spun 81 times, the expected number of times is
Times = 6/9 * 81
Evaluate
Times = 54
Hence. the number of times is 54
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find the vertex, y intercept, and x intercept to this quadratic function "y = x^2 + 2x - 3" pls show you work!
I need help fast, PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:hunger
Step-by-step explanation:
i hungry
For problems 7-12, consider the sets below, and indicate if each statement is true or false.
A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6} U = {numbers from 0 to 10}
7. 3 ∊ B 8. 5 ∊ C 9. B ⊂ A 10. C ⊂ A 11. C ⊂ B 12. C ⊂ U
Using the sets from above, and treating U as the Universal set, find each of the following:
13. A ⋃ B 14. A ⋃ C 15. A ⋂ C 16. B ⋂ C 17. A c 18. B c
The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U
13. A ⋃ B = {1, 2, 3, 4, 5, } 14. A ⋃ C = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = { 4 } 16. B ⋂ C = { }
17. [tex]A^{c}[/tex] = {6, 7, 8, 9, 10} 18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}
What are sets:
In mathematics, a set is a collection of distinct objects, which are called its elements or members. These objects can be anything - numbers, letters, people, animals, or other sets.
Sets are typically denoted using curly braces, and the elements of the set are listed inside the braces, separated by commas.
Here we have
A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6} and U = {numbers from 0 to 10}
=> U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
i. Indicate if each statement is true or false.
7. 3 ∈ B which means 3 belongs to set B
Since, set B = {1, 3, 5}
=> ∴ 3 ∈ B is true
8. 5 ∈ C which means 5 belongs to set C
The set C = {4, 6}
=> 5 ∈ C is false
9. B ⊂ A which means B is a subset of A and elements of B are belongs to set A.
Since elements of B are lies in set A
=> B ⊂ A is true
10. C ⊂ A which means C is a subset of A
Since all the elements of C are not lie in set A
=> C ⊂ A is false
11. C ⊂ B which means C is a subset of B
Since all the elements of C are not lie in set B
=> C ⊂ B is false
12. C ⊂ U which means C is a subset of U
Since all the elements of C are lies in U
=> C ⊂ U is true
13. A ⋃ B = {1, 2, 3, 4, 5} ∪ {1, 3, 5} = {1, 2, 3, 4, 5, }
14. A ⋃ C = {1, 2, 3, 4, 5} ∪ {4, 6} = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = {1, 2, 3, 4, 5} ⋂ {4, 6} = { 4 }
16. B ⋂ C = {1, 3, 5} ⋂ {4, 6} = { }
17. [tex]A^{c}[/tex] = The elements in the universal set but not in A = {6, 7, 8, 9, 10}
18. [tex]B^{c}[/tex] = The elements in universal set but not in B = {0, 2, 4, 6, 7, 8, 9, 10}
Therefore,
The correct statements are 7. 3 ∈ B, 9. B ⊂ A, 12. C ⊂ U
13. A ⋃ B = {1, 2, 3, 4, 5, } 14. A ⋃ C = { 1, 2, 3, 4, 5, 6}
15. A ⋂ C = { 4 } 16. B ⋂ C = { }
17. [tex]A^{c}[/tex] = {6, 7, 8, 9, 10} 18. [tex]B^{c}[/tex] = {0, 2, 4, 6, 7, 8, 9, 10}
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Jeremy is saving money for new tires for his car. What he saves
goes into his savings account. After one month, he has saved
$230. After four months, he has $329 saved.
According to the given information, Jeremy is saving approximately $20.56 per week for his new tires.
What is basic arithmetic?
Basic arithmetic refers to the fundamental operations of arithmetic, which include addition, subtraction, multiplication, and division. These operations are used to perform calculations with numbers, such as counting, computing sums, finding differences, calculating products, and determining quotients.
We can use this information to find Jeremy's weekly savings rate.
To find the weekly savings rate, we need to first find out how much Jeremy saves in a week.
For the first month, which is four weeks, Jeremy saves $230.
For the next three months, which is 12 weeks, he saves an additional $329 - $230 = $99.
Therefore, in total, Jeremy saves $230 + $99 = $329 in 16 weeks.
His weekly savings rate is then:
$329 / 16 weeks = $20.56 per week (rounded to the nearest cent)
So, Jeremy is saving approximately $20.56 per week for his new tires.
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This is the slope-intercept form for the equation of a line with slope m and y-intercept b.
y=mx+b
This is a formula for the slope of a line that passes through the points (x1,y1) and (x2,y2).
m=
change in y
change in x
=
y2–y1
x2–x1
solve
First, use the points (
–
4,
–
4) and (1,6) to find the slope of the line.
m
=
change in y
change in x
m
=
6–
–
4
1–
–
4
Find the changes in y and x from (
–
4,
–
4) to (1,6)
m
=
10
5
m
= 2
Next, use the slope and one of the points, such as (1,6), to find b, the y-intercept.
y
= mx+b
6
= 2(1)+b Substitute y=6, m=2, and x=1
6
= 2+b Multiply 2 by 1
4
= b Subtract 2 from both sides of the equation
The slope is 2, and the y-intercept is 4. Write the equation of the line in slope-intercept form.
y
= mx+b
y
= 2x+4
So the y-intercept is 4 the equation of the line in slope-intercept form is:
y = 2x + 4
What is in slope-intercept form?When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).
According to the given information:y = mx + b
m = (y2 - y1) / (x2 - x1)
Using the points (-4, -4) and (1, 6), we can find the slope of the line passing through them:
m = (6 - (-4)) / (1 - (-4)) = 10 / 5 = 2
So the slope of the line is 2. Let's use the point (1, 6):
y = mx + b
6 = 2(1) + b (substitute m = 2, x = 1)
6 = 2 + b
b = 6 - 2 = 4
So the y-intercept is 4 the equation of the line in slope-intercept form is:
y = 2x + 4
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[tex]P(x) = x^4 - x^3 - 11x^2 + 9x + 18[/tex]. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviours of the graph and where the company will break even (where P(x) = 0)
The graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
How did we arrive at this assertion?The function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 is a polynomial function of degree 4.
To sketch the graph of this function without using technology, we can start by analyzing the end behaviors of the function. As x approaches negative infinity, the leading term of the function, x^4, dominates and the function approaches positive infinity. As x approaches positive infinity, the leading term also dominates and the function again approaches positive infinity. This means that the graph will have a shape that rises on both ends.
Next, we can find the x-intercepts of the function, which are the values of x where P(x) = 0. We can use synthetic division or factorization to find that the function has three real roots: x = -2, x = -1, and x = 3. These values represent the points where the graph intersects the x-axis.
Finally, we can find the y-intercept of the function, which is the value of P(0). We can plug in x = 0 into the function to find that P(0) = 18. This means that the graph intersects the y-axis at the point (0, 18).
Putting all of this information together, we can sketch a rough graph of the function. The graph rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The function is positive between x = -2 and x = -1, and between x = 3 and positive infinity. The function is negative between x = -1 and x = 3.
To summarize, the graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
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Find the value of x.
Answer: x = 60 degrees
Step-by-step explanation:
As we see, there is a 90 degree angle formed the top left corner. You divided it by 2 and it is formed by both triangles and u get 45 degrees.
Now, according to angle sum property:
angle A + Angle B + Angle C = 180 degrees
therefore, 75 + 45 + angle c = 180
and by linear equation , angle c = 180 - [75 + 45]
= 180 -120
= 60
therefore, x = 60
Answer:
60 degrees
Step-by-step explanation:
A right triangle is 180 degrees. 60+75+a= 180degrees. It shows a right angle, with a line right at the middle. half of 90 is 45, so put that in the equation and you get 60+75+45=180 degrees. to solve for ? you want to take 45 + 75 + ? = 180 degrees 45 plus 74 is 135 so take 180-135 is 60. the ? will be 60 degrees.
I hope this helps : )
help with this please youll get 65 points
Answer:
105 or 40500
Step-by-step explanation:
you have too add or mutilple
The Boy Scout troop raised money
in a fundraiser. They donated $400 to
the food bank and half of the remaining
amount to the animal shelter. Malik and
Jacob wrote equations to represent y, the
amount of money donated to the animal
shelter based on x, the total money raised.
MALIK
*-400
2
y=.
JACOB
y=-400
Which equation is correct? Explain.
The equation deduced by Malik is the correct equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Given that, the Boy Scout troop raised money in a fundraiser. they donated $400 to the food bank and half of the remaining amount to the animal shelter, they both represented the amount donated for the animal shelter :-
Malik: y = (x-400) / 2
Jacob: y = x/2 - 400
So, if we consider y as the money donated for the animal shelter and x is the total-raised money,
Therefore, according to the question,
$400 donated to food bank, then the left amount = x-400
Half of the money donated to the animal shelter based = (x-400) / 2
Therefore, the equation will be:-
y = (x-400) / 2
Hence, the equation deduced by Malik is the correct equation.
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Please help me PLEASE HELPOP
Given - The expression as
[tex]\frac{3.07+2^4}{5.03-1.79}[/tex]
To find - the solution of the expression
Explanation To simplify the expression, we will simply the terms in the expression
[tex]\frac{3.07+2^4}{5.03-1.79} =\frac{3.07+16}{3.24} =5.885[/tex]
Hence the value of the expression is 5.885
Final answer- The value is 5.885
Three people spend money on a vacation. The expression −1,0263 represents the amount of money each person spends on the vacation. Which expression is equivalent to −1,0263 ?
Answer:-(-1,026/3
Step-by-step explanation:
Omar is going to eat a round lollipop that has a radius of 3 inches. What is the lollipop's
diameter?
Answer:
6
Step-by-step explanation:
radius is 1/2 the diamiter
Answer:
Step-by-step explanation:
Answer: 6 inches.
Explanation:
Since the radius is 3 inches, the diameter will be twice the size of the radius. The radius is half the width of a circular object. The diameter is the full width. Therefore Omar's lollipop has a diameter of 6 inches.
Tell whether the ordered pair is a solution of the equation.
7=y-5× (4,28)
Answer: No
Step-by-step explanation:
So you have to substitute the x and y with the numbers in the ordered pair.
y becomes 28.
x becomes 4.
So the equation 7 = y - 5x becomes 7 = 28 - 5(4).
Then, you solve.
7 = 28 - 5(4)
7 = 28 - 20
7 = 8
7 ≠ 8
So, the ordered pair is NOT a solution of the equation.
Hope this helps!!!
Help please due tonight
Select one,
{-3, -2,-1,0}
{-3,-2,2,3}
(-3,-2,-1,-0]
{-3, -2,-2,-3)
The domain of the function shown on the graph is {-3, -2, 2, 3 }.
What is the domain of the function on the graph?The domain of a function is the set of all possible input values (also known as the independent variable or x-values ) for which the function produces a valid output (also known as the dependent variable or y-values).
In other words, it is the set of values that can be plugged into the function to produce a meaningful result.
In this case, there are four (4) points on the graph.
The coordinates of the points are;
Point 1: x = -3 and y = 5Point 2: x = -2 and y = 5Point 3: x = 2 and y = 5Point 4: x = 3 and y = 5Since the domain are the set of the x-values, the domain of the function of the graph will be;
Domain : {-3, -2, 2, 3 }
Therefore, option B) {-3, -2, 2, 3 } is the correct answer.
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These lists show the ages of attendees in a yoga class and a dance class.
Yoga: 18, 31, 17, 44, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Which statement about attendees in the two classes is true?
A. The median age of the attendees in the yoga class is greater than the median age of
the attendees in the dance class.
B. The median age of the attendees in the dance class is greater than the median age of
the attendees in the yoga class.
C. The median age of the attendees in the yoga class is the same as the median age of the
attendees in the dance class.
D. The median age of the attendees in the yoga class is 44 years and the median age of
the attendees in the dance class is 47.
The true statement is the median age of the attendees in the yoga class is greater than the median age of the attendees in the dance class. (option A).
What is the true statement?
Median is the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.
Ages of Yoga students arranged in ascending order: 18, 17, 20, 31, 33, 36, 44
Median = 31
Ages of Dance students arranged in ascending order: 20, 23, 26, 30, 38, 42, 47
Median = 30
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How to determine the area of all faces in mm2
The surface area of all faces of the cube is found as in 150,100 mm².
Explain about the cube?A solid shape having six square faces is called a cube. Because every square face has an identical side length, each face is the same size.
A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex. A cube has twelve equal-length edges and six faces. Its faces are square-shaped. The cube's angles in the plane were right angles. The cube's faces are connected by four other faces.Area of the cube:
Area = 6*side²
Area = 6*(5)²
Area = 150 cm²
We know:
1 cm = 10 mm
Then,
Area = 150 x 100 mm²
Area = 150,100 mm²
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The complete question is-
The cube has the side length of 5 cm. How to determine the area of all faces in mm2
A square scarf has a side length of 34 yard on each side.
What is the area of the scarf?
Enter your answer in the boxes as a fraction in simplest form.
la surface de l'écharpe est de 1 1 56 cm² car la formule pour calculer l'air d'un carré est A= coté * coté soit coté²
donc : Aécharpe=34²=1156
Write the set using the roster method.
Set D is the set of positive two-digit even numbers greater than 74
that do not contain the digit 8
.
The set using Roster method is, D = {76, 90, 92, 94, 96}
What is Roster Method?The roster technique is defined as a method for displaying the elements of a set by listing the elements within brackets.
A roster method example is to write the set of numbers from 1 to 10 as
{1, 2, 3, 4, 5, 6, 7, 8, 9, and 10}.
Given:
Set D is the set of positive two-digit even numbers greater than 74
that do not contain the digit 8
First, Even numbers greater than 74 are
76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98.
Now, Even Number doe not contain 8 are 76, 90, 92, 94, 96.
Using Roster method the set is
D= {76, 90, 92, 94, 96}
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Problem 1: Mrs. Conrath bought
9 packages of lead pencils for
her classroom. Each package has
8 lead pencils. How many lead
pencils did she buy?
Problem 2: Mrs. Conrath saved
25 lead pencils for the Math Club.
How many lead pencils were
used for her classroom?
Each morning Dillion walks to the bus stop before school. It takes him 120 seconds to get there. Over the course of the school year (180 days), how many hours does Dillon spend walking to the bus stop in the morning?
Answer:
Step-by-step explanation:
95 hours
How far away from his was Liam after 15 minutes?
The requried, Liam is 24 blocks away from his house.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
A graph is shown, Liam left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Liam is x minutes after he left his house until he got back home.
In order to calculate Liam's distance after x = 15 minutes. Draw a perpendicular at x = 15 that intersects the curve. Since the line intersects the curve at y = 24. This implies that Liam is 24 blocks away from his house.
Thus, the requried Liam is 24 blocks away form his house.
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can someone help me please
The two solutions to the linear equation is given by the ordered pairs (0, 6) and (-4, 5).
How to graph the solution to this linear equation?In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point that lie on it;
y = 0.25x + 6.00
Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (-4, 5) and (0, 6).
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1 and 3/8 as the Sum of two fractions answer is
Answer:
Step-by-step explanation:
45