Answers
The cost of filling the cone to its full capacity would be = 189.4 cents
What is a cone?A cone is a three-dimensional figure in geometry that tapers from a flat base (usually a circular base) to a point called a vertex or longitude (which forms an axis through the center of the base).
The formula for the volume of a cone = πr²h/3
Height (h) = 5 inches
Radius (r) = 3 inches
π = 3.14
volume = 3.14 × 3² × 5/3
= 3.15 × 9 × 1.67
= 47.35 in³
But 1 in³ = 4 cents
47.35 in³ = X
Make X the subject of formula;
X = 47.35 × 4 = 189.4 cents.
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Related Questions
How do you find the 3rd side of a triangle?
Answers
Answer:
a2 = b2 + c2 2bc cos(0)
Step-by-step explanation:
Joe the hiker decided to take a rest at the gas station before Kingston. While sitting at the picnic table, he noticed that there were many cars in the parking area. There were three times more silver colour cars than red cars. There were 2 more blue cars than red and silver cars together. There were twice more white cars than red. Joe counted 42 cars altogether in the parking lot.
How many white cars were there?
how many blue cars were ther?
how many red cars were there?
how many silvers were there
Answers
There are 7 white cars, 16 blue cars, 14 red cars and 5 silver cars.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let w represents white cars
b represent blue carr
r represents red cars
s represents silver cars
There were three times more silver colour cars than red cars
3s=r...(1)
There were 2 more blue cars than red and silver cars together
b+2=r+s..(2)
There were twice more white cars than red.
2w=r..(3)
42 cars altogether in the parking lot.
w+b+r+s=42
After solving the above equation we get
s=5, b=16, w=7 and r=14
Hence, there are 7 white cars, there are 16 blue cars, there are 14 red cars and 5 silver cars.
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How do you describe rational and irrational?
Answers
Rational and Irrational numbers can described as the number that can be expressed as [tex]\frac{p}{q}[/tex] are rational and which cannot be expressed are called as Irrational Numbers .
The Rational Numbers are defined as a number that can be represented in the form of [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex].
We can also , say that the fraction where the denominator and the numerator are integers and the denominator is not equal to zero are called as Rational Numbers .
For Example : [tex]\frac{2}{3} , \frac{4}{9}[/tex] represents a rational numbers .
The Irrational Numbers are defined as a real number that cannot be expressed as a ratio of integers .
For Example : [tex]\sqrt{2} , \sqrt{5}[/tex] represents a Irrational number .
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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
Answers
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
To maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Ultimately, the greatest possible quotient as required is; 25.
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Which function is shown on the graph?
of(x) = 1/2cos x
of(x) = -1/2cos x
Of(x) = -1/2sin x
Of(x) = 1/2sin x
Answers
The reasons and responses to the graphs in the question are as follows:
Graph 1.
The amplitude of the first graph is (1/2) which is the height from the midline to the peak
The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function
The period of the graph is 2·π, which is the period of the parent cosine function
Therefore, the correct option is
Graph 2: Please find attached the graph of the function g(x) = 2×cos(x)
Graph 3: The frequency of a sinusoidal function is given as follows;
The period of the graph = π
Therefore;
The frequency of the sinusoidal graph is 2
Graph 4. Required:
To find the equation that represents the function of the graph
Solution;
The period of the function, T = π
The graph of the function has a maximum at x = 0, therefore, the graph is similar to a cosine function, y = cos(B·x)
Where;
B = 2·π/T
Therefore;
B = 2·π/π = 2
Therefore;
The equation that represent the function in the graph is f(x) = cos(2·x)
Question 5. The given function is f(x) = cos(2·x)
The frequency factor in the given function, B = 2
The period, T = 2·π/B
Therefore, T = 2·π/2 = π
The period of the function, f(x) = cos(2·x), is 2
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the function f(x)=80(0.5)^ represents the distance after a pendulum begins swinging,where x is the number of swings
Answers
It looks like there may be a typo in the function you provided. It appears that you meant to write "f(x) = 80(0.5)^x", which would represent the distance after a pendulum begins swinging, where x is the number of swings.
This function indicates that the distance traveled by the pendulum decreases by half with each swing. For example, after the first swing, the distance traveled would be 80(0.5)^1 = 40 units. After the second swing, the distance traveled would be 80(0.5)^2 = 20 units. And so on.
The exponent x in the function represents the number of swings, so the distance traveled by the pendulum can be calculated by plugging in the desired value of x into the function. For example, to calculate the distance traveled after 10 swings, we can plug in x = 10:
f(10) = 80(0.5)^10 = 0.390625 units
This indicates that the pendulum has traveled a distance of approximately 0.39 units after 10 swings.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a Question 18 options: A) kite. B) trapezoid. C) hexagon. D) parallelogram.
Answers
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Option (d) is the correct choice.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
A parallelogram has the following qualities:
The opposing sides are equally spaced and parallel.
Angles on either side are equal.
The following or neighboring angles are supplemental.
All of the angles will be at right angles if any one of them is a right angle.
The two diagonals cut across one another.
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What is the degree of the polynomial of 5x²y 8xy² 9?
Answers
The polynomial is a mathematical expression containing variables and coefficients and can be written as a sum of terms of various degrees. In this case, the polynomial is composed of three terms of varying degrees: 5x²y, 8xy² and 9. The degree of this polynomial is the highest degree of the terms, which is 4.
1. Identify the terms of the polynomial: 5x²y, 8xy² and 9
2. Identify the degree of each term: 5x²y has degree 3, 8xy² has degree 4 and 9 has degree 0
3. Determine the highest degree among the terms: The highest degree is 4
4. The degree of the polynomial is then the highest degree among the terms, which is 4.
A polynomial is a mathematical expression consisting of variables and coefficients and can be written as a sum of terms of varying degrees. In this case, the polynomial consists of three terms: 5x²y, 8xy² and 9. To determine the degree of the polynomial, we must first identify the degree of each term. The term 5x²y has degree 3, the term 8xy² has degree 4 and the term 9 has degree 0. The degree of the polynomial is then the highest degree among the terms, which is 4. This means that the polynomial has a degree of 4, as the highest degree among its terms is 4. The degree of a polynomial is an important factor in solving equations and other mathematical problems, as it can determine the complexity of the equation.
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explain what the slope and intercept mean in each situation the amount of money y in a cash box after x tickets are purchased for carnival games. The slope of the line is 1/4 and the y intercept is 8
Answers
Answer:
The (1/4) slope is the prive per ticket. The y intercept is the money in the cash box before any tickets were sold.
Step-by-step explanation:
Let y be the money and x the numbers of tickets sold, as requested. We are told that the equation for this situation is:
y = (1/4)x + 8
Let's assume the money is in units of dollars. The slope of (1/4) would mean that each carnival game ticket cost $(1/4), or 25 cents. The y-intercept is the value of y when x=0, which means zero tickets have been sold. That means that the cash box had $8 before any sales were made. [perhaps to use for making change].
Solve 345°=
Please help me ASAP
the due date of my assignment is tomorrow
Answers
The answer to ur question is 1
A hockey team scored the following number of goals in their last 5 games:
2,3,5, 3,2
Which is the mean absolute deviation of the number of goals?
Hurry pls
Answers
The mean absolute deviation of the number of goals is 0.8 goals
What is Mean Absolute Deviation ?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.
The average distance between data points and a center point is referred to as mean absolute deviation. N is the number of words in the sample, where xi is the sample's individual value and x is the sample's mean or average.
Enter the numbers in the provided input box, separated by commas.To determine the mean absolute deviation for a set of data, click the "Calculate" button.To obtain the mean absolute deviation for the various figures, click the "Reset" option to clear the fields.The mean of the goals scored is = (2+3+5+3 +2)/5 = 3
The Mean Absolute Deviation is = [tex]\frac{1}{5}\{|(2-3)| + |(3-3)| + |(5-3)| + |(3-3)| + |(2-3)|}\}\\[/tex] = 4/5 = 0.8
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Because milk tea is flourishing in their town, Mathilda decided to sell Wintermelon milk tea (WMT) powder at Php 1 per gram and Okinawa milk tea (OMT) powder at Php 2 per gram. To increase her profit, she plans to mix the two milk tea powders. How much OMT should she mix with 300 grams of WMT so that she can sell the resulting mixture at Php 1.80 per gram?
Answers
So, Mathilda should mix 600 grams of OMT with 300 grams of WMT to sell the resulting mixture at Php 1.80 per gram.
Define the unitary method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What is a unit?A unit is a quantity with a fixed magnitude that is used to gauge the sizes of other quantities that behave similarly.
The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grams (g). Milliliter (ml) and liter are used to measure volume (L).
Let x be the amount of OMT powder in grams. We know that the total amount of powder in the mixture is x + 300 grams since Mathilda is mixing x grams of OMT with 300 grams of WMT.
(x * Php 2 + 300 * Php 1) / (x + 300) = Php 1.80
Solving for x, we can get the amount of OMT powder in grams:
x = (300 * Php 1.80 - 300 * Php 1) / (Php 2 - Php 1.80) = 300 * (Php 1.80 - Php 1) / (Php 2 - Php 1.80) = 600
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Please help with this question I’m confused on it
PLEASE HELPP
Answers
A. Triangle ABC is similar to triangle DEF.
B. The value of x is 21.
What are similar triangles?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are items that feature more than two figures that are the same shape but different sizes.
Here, we have
Given a triangle and we have to show both triangles are similar.
A. ABC will be similar to DEF if two sides along with their corresponding angle of ABC is equal to two sides and their corresponding angle of DEF. ABC will be similar to DEF if the corresponding ratios of all sides of both triangles are equal to each other.
Hence, triangle ABC is similar to triangle DEF.
B. By the property of similar triangles,
= AB/DE = AC/DF
= 14/x = 10/15
x = 21.
Hence, the value of x is 21.
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Help please! Thank you
Answers
Answer:
the answer is z^2-9. Using the box method line up equation. Then multiple numbers outside of the box and put numbers inside. Lastly combine like terms.
The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ?
(A) P(N = 8) (B) P(N > 8) (C) P(N < 8) (D) P(7 < N < 8) (E) P(N < 7) or P(N > 8)
Answers
The probability for all five answers is greater than 0.
The normal distribution is a type of continuous probability distribution, and probability can never equal 0 for a continuous distribution. The probability of a particular value (in this case, 8) is the area under the normal curve at that point. Since the area under a continuous distribution is always greater than 0, the probability of a specific value (A) is not 0.
The probability of a range of values (D) is calculated by subtracting the area under the normal curve to the left of the lower value, from the area under the normal curve to the right of the higher value. This calculation would produce a value greater than 0.
The probability of values greater than a given number (B) is calculated by subtracting the area under the normal curve to the left of the given number, from the area under the normal curve to the right of the given number. This calculation would produce a value greater than 0.
The probability of values less than a given number (C) is calculated by subtracting the area under the normal curve to the right of the given number, from the area under the normal curve to the left of the given number. This calculation would produce a value greater than 0.
Finally, the probability of values less than one number or greater than another number (E) is calculated by subtracting the area under the normal curve to the left of the lower number, from the area under the normal curve to the right of the higher number. Again, this calculation would produce a value greater than 0.
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Is x2 16 a perfect square trinomial?
Answers
No, x2 16 is not a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."
A perfect square trinomial is a polynomial of the form a2+2ab+b2, where a and b are constants. This trinomial does not have the same pattern of constant coefficients. It is simply the product of two linear expressions, x2 and 16.
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Find the value of x in the figure
Answers
Answer:
x=40º
Step-by-step explanation:
A straight line is 180º
180-40=140º
180-140=40º
x=40º
Hope this helps :)
Isabella is 30 miles into a 70-mile backpacking trip in the wilderness.
Isabella can hike 8 miles per day. How many more days does Isabella
need to finish?
Isabella needs how
more days.
Answers
Answer: Five Days
Step-by-step explanation:
Isabella can hike 8 miles per day. So:
[tex]\frac{30miles}{8miles} = 3.75 days[/tex]
It will take:
[tex]\frac{70 miles}{8 miles} = 8.75 days[/tex]
..in total to hike 70 miles.
So, subtracting the two values:
[tex]8.75 - 3.75 = 5[/tex]
She still needs to hike five days in order to finish the trail.
lamar bought v vanilla cupcakes and 8 chocolate cupcakes for the party write an expression that shows how many cupcakes lamar bought in all
Answers
Answer:
8 + v
Step-by-step explanation:
assuming Lamar didn't buy any other cupcakes outside of the chocolate and vanilla ones mentioned, the expression that gives you the total amount of cupcakes bought for the party is 8 + v. since you don't know the number of vanilla cupcakes Lamar bought, it is represented as the variable v in this problem. Then just add 8 and the variable v together. hope this helped :]
Recall that there are 2π radians in one full rotation and 360 degrees in one full rotation.
Suppose an angle has a measure of 2. 1 radians.
This angle (with a measure of 2. 1 radians) is what percent of a full rotation?
 %
Use your work in part (i) to determine the measure of the angle in degrees.
 degrees
Answers
If there are [tex]2\pi[/tex] radians and [tex]360 \textdegree[/tex] in one full rotation and an angle has a measure of [tex]2.1 radians[/tex] then the angle is 33.4 percent of a full rotation , and the measure of the angle in degrees is [tex]120.2\textdegree[/tex] .
we know that in 1 full rotation , the radians is 2π ;
and in 1 full rotation , the degree is 360 degree ;
We know that the relation between the degree and the radian measure is
⇒ [tex]1 radian = \frac{180\textdegree}{\pi }[/tex] ;
Part(i) ;
we have to express the 2.1 radians as a percent of full rotation ;
we get ; ⇒ [tex]\frac{2.1}{2\pi } \times 100\%[/tex]
on simplifying further ,
we get ; [tex]\approx 33.4\%[/tex] .
Part(ii) ;
we have to determine the measure of the angle in degrees.
from part(i) , we find the percent is [tex]33.4\%[/tex] ,
So , [tex]33.4\%\times 360\textdegree[/tex]
On simplifying ,
⇒ [tex]\frac{33.4}{100} \times 360\textdegree[/tex]
[tex]\approx 120.2\textdegree[/tex] .
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What is the equation of the function
shown in the graph, given that the
equation of the parent function is
f(x) = (-/-)² ?
(}})
Answers
The equation of the function shown in the graph is f(x) = (-2x)^2.
What is function?In mathematics a function is a relation between two states that assigned to each element of the first set exactly one element of the second set in order words it is the rule that is describe how unstead of values is related to another set a values function are used to model real voice scenario and to solve mathematical problems example of function include linear equation polynomials and trigonometric function.
This is based on the equation of the parent function, which is f(x) = (-/-)^2. The graph shows that the function has been shifted two units to the left, which is why the coefficient of x is -2 instead of -1.
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Find the centre focus,vertex,directrix and axis of each parabola and sketch the graph? (x-1)² = y+2
Answers
Answer:
Step-by-step explanation:
The equation for a parabola is of the form y = ax^2 + bx + c, where a, b, and c are constants. The graph of a parabola is a U-shaped curve that is symmetrical about a line called the axis of symmetry.
In the equation (x-1)^2 = y+2, we can rewrite it as y = (x-1)^2 - 2. This is the standard form of a parabola with a = 1, b = 0, and c = -2.
The vertex of the parabola is the point on the graph where the parabola reaches its highest or lowest point. For a parabola in standard form, the vertex is always of the form (h,k), where h and k are the values of x and y, respectively, at the vertex. The vertex of this parabola is (1,-2).
The axis of symmetry of the parabola is a line that divides the parabola into two mirror images. For a parabola in standard form, the axis of symmetry is always the line x = h, where h is the value of x at the vertex. The axis of symmetry of this parabola is the line x = 1.
The directrix of a parabola is a line that is used to define the parabola. For a parabola in standard form, the directrix is always the line y = k + p, where k and p are constants and p is the distance from the vertex to the directrix. The directrix of this parabola is the line y = -2 + p, where p is the distance from the vertex to the directrix.
The focus of a parabola is a point on the axis of symmetry that is used to define the parabola. For a parabola in standard form, the focus is always the point F(h,k+p), where h and k are the values of x and y, respectively, at the vertex, and p is the distance from the vertex to the directrix. The focus of this parabola is F(1,-2+p), where p is the distance from the vertex to the directrix.
To sketch the graph of this parabola, we can start by plotting the vertex at (1,-2). Then we can draw the axis of symmetry, which is the line x = 1. Next, we can choose a value for p and draw the directrix y = -2 + p. Finally, we can use the vertex and focus to plot points on either side of the axis of symmetry, and connect these points to form the U-shaped curve of the parabola.
[asy]
unit size(1cm);
real p = 1.5;
pair F, V;
F = (1,-2+p);
V = (1,-2);
draw((-2,0)--(4,0));
draw((0,-4)--(0,4));
draw((-2,V.y)--(4,V.y),dashed);
draw((F.x,p)--(F.x,-4),dashed);
label("$x$", (4,0), E);
label("$y$", (0,4), N);
label("$y = (x - 1)^2 - 2$", (4,-3), E);
a dot("$F$", F, NW);
a dot("$V$", V, S);
label
A certain United States flag has a perimeter of 58 feet. The length of the flag is 9 feet longer
than the width. What are the dimensions of the flag?
Answers
The dimensions of the flag are:
length = 19 feet and width = 10 feet
Let 'l' be the length of the flag and 'w' be the width of the flag.
The length of the flag is 9 feet longer than the width.
So, we get an equation
l = 9 + w ............(1)
The flag has a perimeter of 58 feet.
We know that the formula for the perimeter of rectangle:
P = 2(l + w) ..............(2)
Here, P = 58 feet
Substitute the value of P in equation (2)
58 = 2(l + w)
29 = (9 + w) + w ..........(from (1))
29 - 9 = 2w
2w = 20
w = 10
Substitute this value in equation (1),
l = 9 + 10
l = 19 feet
Therefore, length = 19 ft and width = 10 ft
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The points (14, –3) and (–10, –3) fall on a particular line. What is its equation in slope-intercept form?
Answers
y = -3
Step-by-step explanation:Slope intercept form is y = mx + c.
"m" is the slope and "c" is the y-interecept.
The slope is calculated by dividing the change in y values by change in x values. However, you can see from these two points that as the value of x changes, the value of y stays the same (-3). This means the slope is zero, as it doesn't move up in the y-direction at all.
This means y = 0x + c
You can substitute 14 for y and -3 for x from the first point to get:
-3 = 0(14) + c
-3 = c
y = 0x + -3
Which is the equation of the line in slope-intercept form.
This is the same as saying y = -3, as for every x value, y will always be -3.
There is no slope
Step by step
Find slope with y2 - y1 over x2 - x1
-3 - -3 over -10 - 14
0/-24 = 0 slope, so it’s a horizontal line at
Y = -3
Slope intercept form
Y-y1 = m (x-x1)
Y - -3 = 0 (x - -10)
Y + 3 = 0 (x + 10)
Y = -3
There is no slope
See attachment
Is 2 a happy number?
Answers
No, 2 is not a happy number because 2 can not become 1 after a series of stages in which each step 2 is replaced by the sum of its squares
Let's try to first comprehend what numbers are.
An arithmetic value that is calculated and utilized to represent a quantity is called a number. Numeral symbols, such as "3" are used in writing to represent numbers. A number system is a methodical technique to express numbers using digits or other symbols. The numerical system is a helpful collection of numbers that illustrates the number's algebraic and mathematical structure. presents an example that is typical.
Happy numbers If a number leads to 1 after a series of stages in which each step's number is replaced by the sum of its squares, it is said to be happy. For example, if we start with a happy number and keep replacing it with the sum of its squares, we eventually reach 1.
So 2 is not a happy number.
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Quadrilateral TEAMTEAMT, E, A, M i rotated -180^\circ−180
∘
minu, 180, degree about the origin
Answers
The quadrilateral's image points will be,A(3, 3) → A'(-3, 3) R(5, 7) → R'(-7, 5) M(7, 5) → M'(-5, 7) Y(5, 1) → Y'(-1, 5).
If a point (x, y) is rotated 180 degrees anticlockwise with respect to the origin, the rotational rule is:
(x, y) → (-y, x) (-y, x)
Consequently, the image point's coordinates following rotation will be (-y, x).
Using this guideline,
The quadrilateral's image points will be,
A(3, 3) → A'(-3, 3)
R(5, 7) → R'(-7, 5)
M(7, 5) → M'(-5, 7)
Y(5, 1) → Y'(-1, 5)
By graphing the image points we can get the graph of the image quadrilateral A'R'M'Y'.
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The question is incomplete, complete question:
Quadrilateral ARMY is rotated 180 degrees about the origin. Draw the image of this rotation.
A rigid body exists in an n-dimensional space. How many coordinates are needed to specify the position and orientation of this body in this space
Answers
The number of coordinates needed to specify the position and orientation of a rigid body in an n-dimensional space is n.
A rigid body is an object that maintains its shape and size while in motion. In order to specify the position and orientation of a rigid body in an n-dimensional space, we need to know its coordinates in each of the n dimensions. The coordinates describe the location of the body in the space and the orientation of the body relative to the space's coordinate system. Thus, n coordinates are required to fully specify the position and orientation of a rigid body in an n-dimensional space.
However, it is important to note that if the rigid body is placed in a space that's non-Euclidean, other parameters could be necessary to fully describe the rigid body position and orientation.
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A town has a population of 4000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 4500?
Answers
=========================================================
Work Shown:
x = number of years
y = population
y = 4000*1.02^x
4500 = 4000*1.02^x
4500/4000 = 1.02^x
1.125 = 1.02^x
log(1.125) = log(1.02^x)
log(1.125) = x*log(1.02)
x = log(1.125)/log(1.02)
x = 5.94784893412128
Rounding to the nearest year, it takes about 6 years for the population to reach 4500 people.
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Check:
Plug in x = 5
y = 4000*1.02^x
y = 4000*1.02^5
y = 4416.3232128
y = 4416
We come up a bit short. Now try x = 6
y = 4000*1.02^x
y = 4000*1.02^6
y = 4504.649677056
y = 4505
We go a bit over the target, but it's better to go over rather than come up short.
This confirms the answer is approximately 6 years.
Solve the following system of equations. Enter the y-coordinate of the
solution. Round your answer to the nearest tenth.
5x+2y=21
- 21+ 6v=-34
Answers
To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth: y = -2.2
What exactly does a coordinate system mean?system of coordinates, Arrangement of reference lines or curves for locating points in space The Cartesian (named for René Descartes) system is the most popular one in two dimensions.
To solve for y in the equation 5x + 2y = 21, we can start by isolating y on one side of the equation. To do this, we can subtract 5x from both sides of the equation:
5x + 2y = 21
5x - 5x + 2y = 21 - 5x
2y = 21 - 5x
To solve for y, we can then divide both sides of the equation by 2:
2y = 21 - 5x
y = (21 - 5x) / 2
To solve for y in the equation -21 + 6y = -34, we can start by isolating y on one side of the equation. To do this, we can add 21 to both sides of the equation:
-21 + 6y = -34
-21 + 21 + 6y = -34 + 21
6y = -13
To solve for y, we can then divide both sides of the equation by 6:
6y = -13
y = -13/6
y = -2.1666666666666665
To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth:
y = -2.2
So, the y-coordinate of the solution is -2.2.
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The endpoints of a line segment AB are (1, -6) and (5, -6). The equation of a line BC is
y=x-11. Is triangle ABC a right triangle? Justify your answer.
Answers
No, triangle ABC is not a right triangle. The equation of a line BC "y=x-11" is a line with slope of 1, which means it has an angle of 45 degrees with respect to the x-axis. The segment AB has a slope of 0, which means it is parallel to the x-axis. A right triangle's legs must be perpendicular, therefore a line with a slope of 1 and a line with a slope of 0 cannot be the legs of a right triangle.
A RIGHT TRIANGLEA right triangle is a triangle in which one of the angles is 90 degrees. In order for a triangle to be a right triangle, the two sides (or legs) that form the 90-degree angle must be perpendicular to each other. Perpendicular lines have slopes that are negative reciprocals of each other.
In this case, the equation of the line segment AB is "y = -6", which means it is parallel to the x-axis. The slope of a line parallel to the x-axis is 0. On the other hand, the equation of the line BC is "y = x - 11", which means it has a slope of 1. A slope of 1 means that the line is at a 45 degree angle with respect to the x-axis.
Since the slopes of the two lines are not negative reciprocals of each other (0 and 1), the legs of the triangle cannot be perpendicular. Therefore, triangle ABC cannot be a right triangle.
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