The additive inverse of 6 /- 13 is -6 /+ 13, which means that the two numbers have the same magnitude but opposite signs.
The additive inverse of a number is the number that needs to be added to the original number to get a result of zero. In other words, the additive inverse of a number is the opposite of the number in terms of sign. To find the additive inverse of 6 /- 13, we must multiply the negative sign of -13 by -1 to change it to a positive. This means that the additive inverse of 6 /- 13 is -6 /+ 13. This means that the two numbers have the same magnitude but opposite signs. To verify this, we can add the two numbers together. 6 /- 13 + -6 /+ 13 = 0. Therefore, the additive inverse of 6 /- 13 is -6 /+ 13.
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Two factories, National Food Inc. and Anderson's Mill, produce canned food. There is a proportional relationship between the amount of time each factory runs and the amount of food it produces.
The number of the cans that is produced is 5832.
What is a direct proportion?
We know that the term direct proportion has to do with a case in which one of the variables is increasing and the other is also increasing along side. This implies that the two variables can be seen to increase at the same time.
We have that the relationship of the process can be given as shown in question in simple format as; y = 243x where;
x = Number of hours
y = Number of cans
After 24 hours, we have;
y = 243(24)
y = 5832
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What are the 5 common geometric shapes?
Circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
Thus, circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.
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Circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.
Define geometric shapes.Any building, whether open or closed, with a specific shape and characteristics composed of lines, curves, and points is referred to as a geometric shape. Squares, rectangles, circles, cones, cylinders, spheres, and so on are a few examples of well-known geometric forms. Each of these forms has specific characteristics that set them apart from other shapes.
Figures enclosed by a boundary created by combining a specific number of curves, points, and line segments are referred to as geometric forms. Every shape has a distinctive name like a circle, square, triangle, or rectangle, for example. In everyday life, we are surrounded by a variety of fundamental geometric forms, such as the triangle-shaped pizza slice, rectangle-shaped doors and windows, and many more.
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Can 7 cm 5 cm and 3 cm form a triangle?
Yes, the triangle can be easily formed for the sides 7 cm, 5 cm and 3 cm.
According to the side side side rule of triangle, if the sum of the any two sides of triangle is more than third side, it will form a triangle. Let us check the same by assuming side a to be 7 cm, side b to be 5 cm and side c to be 3 cm.
Side a + side b > side c
7 + 5 > 3
Add the digits in Left Hand Side of the equation
12 > 3
Side b + side c > side a
5 + 3 > 7
Add the digits in Left Hand Side of the equation
8 > 7
side c + side a > side b
3 + 7 > 5
Add the digits in Left Hand Side of the equation
10 > 5
We see that the two sides of the triangle are greater than third side, hence, it is possible to form the triangle.
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75% of the ticket old at an amuement park were dicount ticket. If the park old 68 ticket in all, how many dicount ticket did it ell?
Total discount ticket at the amusement park were 51. If 75% of the sold ticket were discounted tickets and if the amusement park sold 68 tickets in all.
Total number of ticket sold = 68
75% of them were discount tickets, = 75 × 68/100
= 51 tickets
So 51 tickets were discount tickets and (68-51) = 17 tickets were without discount tickets. We can also calculate the without discount ticket by a different method. Remaining 25% tickets were the without discount tickets. So,
= 25 × 68/100
= 17 Tickets
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please help with this question in the screenshot !!!
The Volume of shape Q is 25,600 cm³.
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared.
Let z be the scale factor
x be the surface area of shape Q
and, y be the surface area of shape P
So, z²=x/y
we have,
x = 2880 cm², y= 720 cm²
z² = 2880/720
z² = 4
z = 2
Now, If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
z³ = x/y
We have z= 2 and y = 3200 cm³
So, 2³ = x/3200
x = 8×3200
x = 25,600 cm³
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Element X decays radioactively with a half life of 6 minutes. If there are 220 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 26 grams?
where
h (t) = 5+40t - 16t²
. tis in seconds after being thrown in the air
• height is measured in feet above the ground.
We can use this model to answer some questions like how high the ball will reach.
As a reminder, the velocity of the ball at time t is v(t) = h' (t) and the acceleration is at a (t) = h" (t).
(Side note on projectile motion: there are variations on this model, for example, if the ball is not thrown st
will not focus on those in this example.)
Question 1
1 point possible (graded)
When is the ball the highest?
To obtain how fast the ball traveling 2 seconds after it is thrown, we differentiate the position equation with respect to time once;
dh(t) = d (-16[tex]t^{2}[/tex] + 40t +5 )
dt dt
dh(t) = -32t + 40
dt
with t= 2:
h'(2) =-32 (2) +40
h'(2) =-24 ft/s.
What is velocity?Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time . The standard unit of velocity magnitude (also known as speed ) is the meter per second (m/s). Alternatively, the centimeter per second (cm/s) can be used to express velocity magnitude. The direction of a velocity vector can be expressed in various ways, depending on the number of dimensions involved.Velocity is relative. Consider a car moving at 20 m/s with respect to the surface of a highway, traveling northward. If you are driving the car, the velocity of the car relative to your body is zero. If you stand by the side of the road, the velocity of the car relative to you is 20 m/s northward. If you are driving a car at 15 m/s with respect to the road and are traveling northward, and another car moving 20 m/s with respect to the road passes you in the same direction, that other car's velocity relative to you is 5 m/s northward. But if that other car passes you going the opposite way on the road, its velocity relative to you is 35 m/s southward.To learn more about Velocity refer to:
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The functions approximate the velocities (in meters per second) of an object
dropped from a height of x feet right before it hits the ground on Earth and Venus.
What is the velocity of an object dropped from a height of 100 feet right before it
hits the ground on Venus?
Earth: E(x) = 4.4√x
Venus: V(x) = 0.9 x E(x)
The velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: V(x)=0.9×4.4√x
Thus if x=100feet or 30.47 m putting this value in the equation we get
V(30.47)=0.9×4.4√30.47
= 21.86 m/sec
Hence, the velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec
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which is an appropriate estimate for the following 3,844 divide by 75
need answer asap <3 ! thank you so much to anyone that answers !
Answer:
A. -1
Step-by-step explanation:
imma human calculator and no one can stop me
Two students can eat 4 doughnuts in 6 minuts. At this rate, how many doughnuts will be eaten by 8 students sin 9 minutes?.
By using the ratio formula, the number of doughnuts that will be consumed of 8 students in the time period of 9 minutes is 24 doughnuts.
The ratio formula compares the connection between two quantities or numbers. In this case, we are given that:
2 students can eat 4 doughnuts in 6 minutes
By using the ratio formula, 1 student can eat = 4/2 = 2 doughnuts in 6 minutes
It takes an average student about 3 minutes to consume a doughnut using the formula= 6/2 = 3 minutes
In one minute, the amount of doughnut can be consumed by a student is 1/3 of a doughnut
This method can be used to predict how many doughnuts 8 students can consume in 9 minutes:
X = 8 x 9 x (1/3) = 24 doughnuts
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If the scale factor of figure A
too figure B is 7:2 find the perimeter of figure A
The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.
What is perimeter?
A boundary is a closed path that encompasses, encircles, or delimits a two-dimensional shape or a one-dimensional length. A circle's or an ellipse's perimeter is its outermost portion. Numerous applications in real life involve the perimeter calculation. The radius of a shape's edge is known as the perimeter. By summing the lengths of the sides of various forms, discover how to calculate the perimeter. By multiplying the lengths of the sides, one can always get a shape's perimeter. The area surrounding an object is called its perimeter. An enclosed garden is one example at your home. The distance around anything is called its perimeter. A 200-foot fence will be needed for a yard that is 50 feet by 50 feet.
Ratio factor of A to B = 7:2
Proportion between the perimeters = 7/2
We now understand that a shape's perimeter equals the sum of all its sides. Consequently, using the values from the provided figure, enter the following expression:
A1 / 9+5+9+12 = 7/2
A1 = (7*35)/2
A1 = 122.50 units.
The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.
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Is root 1 and 1 are equal?
No, the square root of 1 is 1, but 1 is not equal to the square root of 1. The square root of a number, represented by the symbol √, is a value that, when multiplied by itself, gives the original number.
For example, the square root of 4 is 2, because 2 x 2 = 4. In the case of 1, the square root is also 1, because 1 x 1 = 1.
In mathematics, the square root of a number is always non-negative, real number. It is positive for positive numbers and zero for zero. So, in short, the square root of 1 is 1, but 1 is not equal to the square root of 1. It is just a value that gives 1 when multiplied with itself.
It's important to note that the square root is not a number but an operator, an action which you perform on a number. The square root of a number is a value that, when multiplied by itself, gives the original number.
In this case, the square root of 1 is 1, which means that 1 multiplied by 1 is 1.
Also, it's worth mentioning that there are two types of square roots: principal square root and non-principal square roots. Principal square root is the positive value of the square root and non-principal square roots are the negative value of the square root.
In this case, the square root of 1 is 1, which is the positive value of the square root.
In conclusion, the square root of 1 is 1, and it is the positive value of the square root, but 1 is not equal to the square root of 1, as the square root is a value that gives the original number when multiplied by itself.
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Write a paragraph proof of the corollary interior angles theorem.
A corollary is a theorem that connects to an established theorem in mathematics with a brief proof. As opposed to statement or theorem, the term "corollary" is inherently arbitrary.
Explain about the corollary interior angles theorem?A corollary may be unquestionably true if the idea or theory it is founded on is correct. Any triangle's internal angles, for instance, add up to 180 degrees in all cases. Each interior angle of an equilateral triangle is 60 degrees, which is a corollary of the aforementioned theorem.
A triangle is equiangular if it is equilateral, which is a corollary to the Base Angles Theorem. Converse of Base Angles Theorem Corollary: If a triangle is equiangular, it is also equilateral.
The sum of the measurements of the two distant interior angles determines how large an exterior angle of a triangle must be. the triangle's angle-sum Corollaries: A right triangle's acute angles are complimentary. A theorem whose proof naturally follows from another theorem is called a corollary.
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The corollary interior angles theorem is a mathematical result that relates to the number of sides in a polygon and the sum of the interior angles of that polygon.
What is corollary interior angles theorem?The corollary interior angles theorem states that if a polygon has n sides, then the sum of its interior angles is equal to (n-2) times 180 degrees. This theorem is a direct result of the interior angle theorem, which states that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees. To prove the corollary interior angles theorem, we first consider a triangle with three sides. The sum of the interior angles of a triangle is equal to 180 degrees, which confirms that the interior angle theorem holds for a triangle. We can then use this result to extend the theorem to polygons with more sides by induction. If we add one more side to the polygon, the sum of the interior angles increases by 180 degrees. By continuing this process and adding sides to the polygon, we can conclude that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees. This confirms the corollary interior angles theorem.
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if In = 5 x" (1+x)0.5 dx ,n= 0,1,2....
where the integral is for x e [0,1].
By first finding a bound on the integrand, which of these is an upper bound on In?
Pick ONE option
O 1/(n+1)
O 1/2(n+1)
O 1/(n+1) + 1/(n+2)
O N^N
The correct option is 1/(n+1).The upper bound for the integral is 1/(n+1).
To determine the upper bound, we can use the fact that the integrand is bounded by its maximum value on the interval. The maximum value of the integrand on the interval [0, 1] is:
f(x) = 5x(1 + x)^(0.5)
At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.
Therefore, an upper bound for the integral is:
In ≤ 5√2∫x^n dx
0
Using integration by parts, we obtain:
In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1
= 5√2/ (n + 1)
Therefore, the upper bound for the integral is 1/(n+1).
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can someone show mw how to do liner programming on desmos :)?
2 large solar panels can charge an electric car
in the same time as 6 small solar panels.
If 2 large solar panels can charge a car in
240 minutes, how many minutes would it take
for 5 large solar panels and 3 small solar
panels to charge the car?
The time taken by 5 large solar panels and 3 small solar panels to charge a car, found using the unitary method, is 576 minutes.
What is unitary method?The unitary approach is a method for problem-solving that involves first determining the value of a single unit, and then determining the necessary value by multiplying the single unit value.
Given
Time taken by 2 large solar panels to charge a car = 240 minutes
Time taken by 2 large solar panels to charge a car
= Time taken by 6 small solar panels to charge a car = 240 minutes
The unitary method can be used to find the charging times of 1 large and 1 small solar panel.
The time taken by 1 solar panel is greater than time taken by 2 large and 6 small solar panels.
Time taken by 1 small solar panel = 240 * 6 = 1440 minutes
Time taken by 1 large solar panel = 240 * 2 = 480 minutes
Therefore the time taken by 5 large solar panels and 3 small solar panels to charge a car = (480/5)+ (1440/3) =96 + 480= 576 minutes.
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Explaining How to Write a Quad
Explain how you could write a quadratic function in
factored form that would have a vertex with an x-
coordinate of 3 and two distinct roots.
y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.
what is function ?The study of mathematics covers numbers and their variations, equations and related structures, shapes and their locations, and locations where they can be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)
Vertex form of a quadratic equation: (h,k) is vertex
y = a(x-h)^2 + k
The x of the vertex needs to equal 3
y = a(x-3)^2 + k
y = (x-3)^2 - 1
y = x^2 -6x + 8
y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.
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When Angel left his house in the morning, his cell phone battery was partially charged. Let
B
B represent the charge remaining in Angel's battery, as a percentage,
t
t hours since Angel left his house. A graph of
B
B is shown below. Write an equation for
B
B then state the
x
x-intercept of the graph and determine its interpretation in the context of the problem.
B =
The x intercept of the function is
Which represents
1.the charge of the battery when Angel woke up
2.the charge of the battery when Angel left his house
3.the number of hours until Angel’s phone dies
4.the percentage charge that Angel’s phone loses each hour
The slope of -6 means that the battery reduces by 6% each hour
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
The slope of -6 means that, the battery reduces by 6% each hour and the equation is B = -6t + 48
The points
The points on the graph are represented using the following ordered pair (1, 42) and (5,18)
The slope
Start by calculating the slope (m) using:
m = (B2 - B1)/(t2 - t1)
So, we have:
m = (18 -42)/5-1
m = -24/4
m = -6
The equation
The equation is then calculated as:
B = m(t - t1) + B1
This gives
B = -6(t - 1) + 42
B = -6t + 6 + 42
B = -6t + 48
Hence, The slope of -6 means that the battery reduces by 6% each hour
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NEED HELP ASAP - Algebra 2
Identify the first step that shows an error in the problem below.
Answer: The exponential form should be 10⁵=9x+1 instead of 9x+1=10⁵
Step-by-step explanation:
The exponential form of a logarithm should be the other way around.
If the bu travel more than 28 mile, how much dieel i left? Expre your anwer in the form of an inequality
The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.
If a vehicle uses diesel fuel, the amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality by saying that the diesel remaining will always be greater than or equal to 0.
diesel remaining ≥ 0
The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.
The amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality, which states that the diesel remaining will always be greater than or equal to 0. This means that no matter how far the vehicle has traveled, there will always be some diesel left in the tank.
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What are the 3 types of 3D modeling?
Polygonal Modeling: a type of 3D modeling that uses points, lines, and polygons to create a 3D object. NURBS Modeling: a type of 3D modeling that uses mathematical equations to create smooth curves and surfaces. Subdivision Modeling: a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes.
1. Polygonal Modeling: This type of 3D modeling uses points, lines, and polygons to create a 3D object. The polygons are connected together to create the 3D shape, and then textures and colors can be applied to the shape. This type of modeling is often used to create characters and environments for video games and animations.
2. NURBS Modeling: NURBS stands for Non-Uniform Rational B-Splines. This type of 3D modeling uses mathematical equations to create smooth curves and surfaces. NURBS modeling is often used for creating organic shapes such as cars and furniture.
3. Subdivision Modeling: Subdivision modeling is a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes. This type of modeling is often used for creating characters and creatures for video games and animations.
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Write an equation of the perpendicular bisected of the segment with endpoints (3,7) and (-1,-5)
The equation of perpendicular line that bisects the line segment is y = - (1 / 3) · x + 4 / 3.
How to find the equation of the perpendicular line that bisects a line segment
In this problem we must determine the equation of the line that is perpendicular to a line segment and partitions the line segment in two parts of equal length, it happens when the perpendicular line passes through the midpoint of the line segment.
The equation of the line in explicit form is shown below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableIn addition, two lines are perpendicular to each other when the following relationship is observed:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.Besides, the slope of a line can be determined by secant line formula:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.And lastly, the midpoint of a line segment is determined by this formula:
M(x, y) = 0.5 · A(x, y) + 0.5 · B(x, y)
First, find the midpoint of the line segment:
M(x, y) = 0.5 · (3, 7) + 0.5 · (- 1, - 5)
M(x, y) = (1.5, 3.5) + (- 0.5, - 2.5)
M(x, y) = (1, 1)
Second, determine the slope of the line related to line segment:
m = (- 5 - 7) / (- 1 - 3)
m = (- 12) / (- 4)
m = 3
Third, calculate the slope of the perpendicular line:
3 · m' = - 1
m' = - 1 / 3
Fourth, find the intercept of the equation of perpendicular line:
b = y - m · x
b = 1 - (- 1 / 3) · 1
b = 1 + 1 / 3
b = 4 / 3
Fifth, write the equation of perpendicular line:
y = - (1 / 3) · x + 4 / 3
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Higher Order Thinking Hugo needs a total
of 22.23 square feet of terry cloth to make a
beach towel and a beach bag. The beach bag
requires 5.13 square feet of cloth. What is the
length of the beach towel? Explain.
The length of the beach towel is 4.135 feet.
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape
Given that
Hugo needs a total of 22.23 square feet of terry cloth to make a beach towel and a beach bag.
Total area of the terry cloth = 22.23 square feet
The beach bag requires 5.13 square feet of cloth.
Area of cloth for beach bag = 5.13 square feet
Area of the cloth for beach towel = 22.23 - 5.13 = 17.1
Area of the beach towel is 17.1 square feet.
Assuming the towel is square shape,
(Length of the towel)² = 17.1
Length of the towel = √(17.1) = 4.135
Hence the length of the beach towel is 4.135 feet.
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Find the value of each variable in the following parallelogram
So on solving the provided question we can say that we know that all angles of Quadrilateral is 90, 4x - 2 = 90; x = 22
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
we know that all angles of Quadrilateral is 90
4x - 2 = 90
4x = 88
x = 22
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Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.
a. In words, define the random variables X and .
b. Which distribution should you use for this problem? Explain your choice.
c. Construct a 95% confidence interval for the population mean length of engineering conferences.
i. State the confidence interval.
ii. Sketch the graph.
iii. Calculate the error bound.
The random variable X represents the length of each engineering conference, and is measured in days.
The normal distribution should be used for this problem, as the underlying population is normal. The normal distribution is a continuous probability distribution that is characterized by a symmetric bell-shaped curve. It is a useful model for events that follow a normal or Gaussian pattern, such as the lengths of engineering conferences.
c. i. The 95% confidence interval for the population mean length of engineering conferences is (3.38, 4.50) days.
ii. The graph of the 95% confidence interval for the population mean length of engineering conferences is shown below.
iii. The error bound for the 95% confidence interval is 0.77 days. This can be calculated using the formula: Error Bound = 1.96*(standard deviation/√sample size). In this case, the error bound is calculated as: 1.96 * (1.28/√84) = 0.77.
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What is a 3-dimensional vector?
A 3-dimensional vector is a line segment running from a point called head to the point called tail in 3-Dimensional space.
Vectors are mathematical or geometrical quantity that has two independent properties i.e., direction and magnitude. There are many types of vectors like unit vectors, equal vectors, etc.
The magnitude of the vector is the length of the line segment without it the direction has no power, Similarly unit vectors help us to find the direction of vectors and their magnitude is 1.
A 3-dimensional vector has majorly 3 components i.e., it has projections in the x, y, and z axes. For a three-dimensional vector A(a1,a2,a3), the formula for its magnitude is ∥a∥=√a21+a22+a23.
Along with magnitude and directions, the 3-D vectors also have angles and they are formed from the vector directly to each of the 3 positive axes.\ i.e., x, y, z axes. The formula used to calculate angle is θ = cos-1 [ (a · b) / (|a| |b|) ]
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WILL GIVE BRAINLEST, DUE TODAY, A system of linear equations is shown in the graph. How many solutions does the system have?
a coordinate plane with one line that passes through the points 0 comma 4 and 3 comma 5 and another line that passes through the points 0 comma negative 1 and 6 comma 1
No solution
One solution at (0, −1)
One solution at (3, 0)
Infinitely many solutions
The number of solutions which the system of equations has is: A. no solution.
How to determine the number of solutions?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (0, 4), a linear equation of the first line can be calculated in slope-intercept form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 4 = (5 - 4)/(3 - 0)(x - 0)
y = x/3 + 4
For the second line, we have:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 1 = (1 + 1)/(6 - 0)(x - 0)
y = x/3 + 1
In conclusion, the system of linear equations has no solution because it represents parallel lines.
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6 x. _. = 3 what is the missing number
Answer:
1/2
Step-by-step explanation:
6 x __ = 3
We divided by 6 into both sides
x = 3/6 = 1/2
So, the missing number is 1/2
Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS)
The grouping symbols commonly used in mathematics are the following:
( ), [ ], { },Parentheses: ( )Brackets: [ ]Braces: { }Bar:Now, According to the question:
What are the 4 types of grouping symbols?
The grouping symbols commonly used in mathematics are the following:
( ), [ ], { },Parentheses: ( )Brackets: [ ]Braces: { }Bar:The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
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