The equation of the first circle is (x + 1)^2 + (y - 1)^2 = r^2 and the equation of the second circle is (x + 1)² + (y - 1)² = 16
The equation of the perpendicular bisectorThe points are given as:
P(3, 0) and Q(0, 5)
The midpoint of PQ is
Midpoint = 0.5(3 + 0, 0 + 5)
Midpoint = (1.5, 2.5)
Calculate the slope of PQ
m = (y2 - y1)/(x2 - x1)
m = (5 - 0)/(0 - 3)
m = -5/3
A line perpendicular to PQ would have a slope (n) of
n = -1/m
This gives
n = -1/(-5/3)
n = 0.6
The equation is then calculated as:
y = n(x - x1) + y1
Where
(x1, y1) = (1.5, 2.5)
So, we have:
y = 0.6(x - 1.5) + 2.5
y = 0.6x - 0.9 + 2.5
Evaluate the sum
y = 0.6x + 1.6
Hence, the equation of the perpendicular bisector of PQ is y = 0.6x + 1.6
The center of the circleWe have:
y = x + 2
Substitute y = x + 2 in y = 0.6x + 1.6
x + 2 = 0.6x + 1.6
Evaluate the like terms
0.4x = -0.4
Divide
x = -1
Substitute x = -1 in y = x + 2
y = -1 + 2
y = 1
Hence, the center of the circle is (-1, 1)
The circle equationWe have:
Center, (a, b) = (-1, 1)
Point, (x, y) = (0, 5) and (3, 0)
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where r represents the radius.
Substitute (a, b) = (-1, 1) in (x - a)^2 + (y - b)^2 = r^2
(x + 1)^2 + (y - 1)^2 = r^2
Substitute (x, y) = (0, 5) in (x + 1)^2 + (y - 1)^2 = r^2
(0 + 1)^2 + (5 - 1)^2 = r^2
This gives
r^2 = 17
Substitute r^2 = 17 in (x + 1)^2 + (y - 1)^2 = r^2
(x + 1)^2 + (y - 1)^2 = r^2
Hence, the circle equation is (x + 1)^2 + (y - 1)^2 = r^2
The value of a and bThe equation of the second circle is
2x² + y² + ax + by - 14 = 0
Rewrite as:
2x² + ax + y² + by = 14
For x and y, we use the following assumptions
2x² + ax = 0 and y² + by = 0
Divide through by 2
x² + 0.5ax = 0 and y² + by = 0
Take the coefficients of x and y
k = 0.5a k = b
Divide by 2
k/2 = 0.25a k/2 = 0.5b
Square both sides
(k/2)² = 0.0625a² (k/2)² = 0.25b²
Add the above to both sides of the equations
x² + 0.5ax +0.0625a² = 0.0625a² and y² + by + 0.25b² = 0.25b²
Express as perfect squares
(x + 0.25a)² = 0.0625a² and (y + 0.5b)² = 0.25b²
Add both equations
(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²
So, we have:
2x² + ax + y² + by = 14 becomes
(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14
Comparing the above equation and (x + 1)^2 + (y - 1)^2 = r^2, we have:
0.25a = 1 and 0.5b = -1
Solve for a
a = 4 and b = -2
This means that the value of a is 4 and b is -2
Show that the second circle is in the firstWe have:
a = 4 and b = -2
Substitute these values in (x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14
This gives
(x + 0.25*4)² + (y - 0.5*2)² = 0.0625*4² + 0.25*(-2)²+ 14
(x + 1)² + (y - 1)² = 16
The equation of the first circle is
(x + 1)² + (y - 1)² = 17
The radii of the first and the second circles are
R = √17
r = √16
√17 is greater than √16
Since they have the same center, and the radius of the first circle exceeds the radius of the second circle, then the second circle lies inside the first circle.
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Help with geometry similar triangles. ABC ~ ___ by ___ with a scale factor of ___
Answer choices ADE, AED, DEA, EDA, or None. Side Side Side, Side Angle Side, Angle Angle, or None. 1:2, 2:1, 3:2, 7:3, or N/A.
Triangle ABC and Triangle DEF are congruent, as stated, of 7:3 with scale factor of isocellus triangle.
Find scale factor?
According to the scale factor, the ratio obtained by dividing the equivalent side lengths of like figures.
Triangle ABC and Triangle DEF are congruent, as stated.
Similar figures have equivalent angles and sides that are equal.
To determine the scale factor,
You must ascertain the ratio between the triangle's corresponding sides.
In order to obtain the sides of the other triangle, multiply each side of the first triangle by the same number.
What we're looking for is the scale factor, which is represented by the number.
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Which ratios have a unit rate less than 1? Choose ALL that apply.
According to our answer to the given question of ratio, Holly earns 4 share at $5 every, for a maximum of $20, and Jasmin receives just as, or
$ten (2 x $5).
What is a ratio?An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equation two ratios. If there were one boy and three girls, the ratio could be shown as 1:3. 1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.
Here,
There is a total of $30.
Gertie shares out $30 in such a 2:4 proportion.
The maximum number of outstanding shares is 6, which is 2 plus 4.
$5 per share is the result of dividing $30 by six.
Two parts, or $ten (2 x $5), go to Jasmine.
Holly will receive four $5 shares, for a totaling of $20.
According to our answer to the given question, Holly earns 4 share at $5 every, for a maximum of $20, and Jasmin receives just as, or $ten (2 x $5).
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He radiu of the un i about 96,600,000 kilometer. The radiu of Earth i about 6370 kilometer. A. Write each radiu in cientific notation. B. The urface area S of a phere with radiu r i given by S = 4 π r 2 S=4πr 2. Aume the un and Earth are perfect phere. Find their urface area. Write your anwer in cientific notation. C. What i the ratio of the urface area of the un to the urface area of Earth? What doe the ratio tell you?
A. The radius of the sun in scientific notation is 9.66 x 10^8 kilometers and the radius of Earth is 6.37 x 10^3 kilometers.
B. To find the surface area of a sphere with a given radius, we can use the formula S = 4πr^2.
The surface area of the sun is 4π(9.66 x 10^8)^2 = 1.4 x 10^18 square kilometers.
The surface area of Earth is 4π(6.37 x 10^3)^2 = 5.1 x 10^10 square kilometers.
C. To find the ratio of the surface area of the sun to the surface area of Earth, we can divide the surface area of the sun by the surface area of Earth.
The ratio of the surface area of the sun to the surface area of Earth is: 1.4 x 10^18 / 5.1 x 10^10 = 2.7 x 10^7.
This ratio tells us that the surface area of the sun is 2.7 x 10^7 times larger than the surface area of Earth.
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Determine which of the lines,if any are parallel. Explain
How do you find the sides of a 3 4 5 triangle?
The 3-4-5 rule is a rule that states that in any right triangle, the ratio of the length of the two shorter sides will be 3:4 if the length of the hypotenuse is 5.
To determine if a triangle is a 3-4-5 triangle, you can use the following steps:
Identify the hypotenuse (the longest side of the triangle)Divide the length of the hypotenuse by 5.Multiply the result by 4 to find the length of the side opposite to the right angle.Multiply the result by 3 to find the length of the side adjacent to the right angle.For example, if the hypotenuse of a triangle is 10 units, you can use the 3-4-5 rule to determine if it is a 3-4-5 triangle:Divide the length of the hypotenuse by 5: 10 / 5 = 2
Multiply the result by 4: 2 x 4 = 8
Multiply the result by 3: 2 x 3 = 6
So, the triangle has sides of 6, 8, and 10 units, which is a multiple of 3-4-5 triangle and it is a right triangle.
Note that not all triangles that have sides in the ratio 3:4:5 will be a right triangle, only those that have a 90-degree angle are considered as a right triangle.
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Are multiples of 2 prime numbers?
No, not all the multiples of 2 are not prime numbers only 2 itself is prime number other multiples of 2 are composite numbers.
As given in the question,
Given number is equal to :
2
Prime numbers are defined as the number which represents only two factors one and the number itself.
Multiples are defined as the given number when multiply by any integer.
Multiples of 2 are as follow :
2 × 1 = 2
2 × 2 = 4
2 × 3 = 6
2 × 4 = 8
2 × 5 = 10 ................ so on.
2 × n = 2n where 'n' belongs to any integer.
Only 2 has two factors.
other multiples of two has more than two factors.
Minimum number of factors of other multiples are :
One, two , and the number itself.
Other multiples represents composite number.
Only 2 is representing the prime number.
Therefore, in the multiple of 2 only 2 is the prime number other are composite number.
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Evaluate the following integral : Integral of x^3 + 1/x^0.5 dx
The value of the integration of the expression [tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex] will be [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]
[tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex]
Split the single integral into multiple integrals.
We will get: [tex]$$\int x^3 d x+\int \frac{1}{x^{0.5}} d x$$[/tex]
By the Power Rule, the integral of x^3 with respect to x is (1/4)x^4.
[tex]\frac{1}{4} x^4+C+\int \frac{1}{x^{0.5}} d x[/tex]
Let u=x^{0.5}.
Then [tex]d u=\frac{0.5}{x^{0.5}} d x[/tex],
So [tex]$\frac{x^{0.5}}{0.5} d u=d x$[/tex].
Now, we will rewrite the above using u and du.
Let u=x^{0.5}.
Finding the value of (du/dx)
Differentiate x^{0.5}.
[tex]\frac{d}{d x}\left[x^{0.5}\right][/tex]
Differentiate using the Power Rule which states that [tex]$\frac{d}{d x}\left[x^n\right]$[/tex] is n x^{n-1} where n=0.5.
We will get: 0.5 x^{-0.5}
Simplify.
Rewrite the expression using the negative exponent rule
[tex]b^{-n}=\frac{1}{b^n}\\0.5 \frac{1}{x^{0.5}}[/tex]
Combine 0.5 and [tex]\frac{1}{x^{0.5}}[/tex] we will get [tex]\frac{0.5}{x^{0.5}}[/tex]
Rewrite the problem using u and du.
We will get it as:
[tex]\frac{1}{4} x^4+C+\int 2 d u[/tex]
Apply the constant rule, we will get: [tex]\frac{1}{4} x^4+C+2 u+C[/tex]
Simplifying we will get it as: [tex]\frac{1}{4} x^4+2 u+C[/tex]
Replace all occurrences of u with x^{0.5}.
We will get it as: [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]
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Which of the following lines has a y-intercept of (0,3) and a slope of ?
A y= 1/2x+3
B y= 1/2x-3
C y= 3x+1/2
D y= 3x-1/2
Comparing the provided equations in the options with the slope-intercept form y = mx + c and with the intercept value given , The answer is option A and B.
What is a equation?An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.
What is slope and intercept?In a linear equation, the slope (also called the gradient) is a measure of the steepness of the line, and the y-intercept is the point at which the line crosses the y-axis. The slope of a linear equation can be represented as m in the form of y = mx + b, where m is the coefficient of x, and b is y-intercept. The y-intercept is the point where the line crosses the y-axis, which can be represented by the value of b in the form of y = mx + b.
intercept (c) = 3units
option A also has 3 as c
option B also has 3 as c
when compared with y= mx + c
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Mr. Ramiriz i making pie to ell at the local farmer’ market. It cot her $5 to make each pie, plu a one-time cot of $30 for baking upplie. She plan to ell the pie for $12 each. Which equation can be ued to find the number of pie he need to ell to break even?
5x – 12x = 30
5x 12x = 30
5x 30 = 12x
12x 30 = 5x
The equation can be used to find the number of pie he need to sell to break event.
c. 5x + 30 = 12x
Given :Mrs. Ramirez is making pies to sell at the local farmer’s market. It costs her $5 to make each pie, plus a one-time cost of $30 for baking supplies. She plans to sell the pies for $12 each.
To Find: Which equation can be used to find the number of pies she needs to sell to break even.
Solution:
Let no. of pies be x
It cost her $5 to make each pie
So, cost of making x pies = 5x
Since there is a one-time cost of $30 for baking supplies.
So, total cost for her is 5x+30
If she sells each pie for $12
Then cost of pies = 12x
Now,
The equation can be used to find the number of pies she needs to sell to break even:
c) 5x+30=12x
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If the frequency of a fm wave is 8.85 × 107 hertz, what is the period of the fm wave? a. 2.58 × 10–8 seconds b. 1.13 × 10–8 seconds c. 1.25 × 10–7 seconds d. 5.82 × 10–7 seconds
The time period of fm wave is found to be 1.13 x 10⁻⁸ sec.
Define the term frequency of the wave?The quantity of waves that pass a fixed point in a unit of time is referred to as frequency in physics.
A body in periodic motion undergoes how many cycles or vibrations in one unit of time, according to this definition.The rate at which current changes direction each second is known as frequency. It is expressed in hertz (Hz), a unit of measurement that is used internationally. One hertz is equal to one cycle per second. One hertz (Hz) is equivalent to one cycle per second. A complete alternating current or voltage wave is referred to as a "cycle.".For the given frequency of a fm wave = 8.85 × 10⁷ hertz.
Time period = 1 / frequency
T = 1 / 8.85 × 10⁷
T = 0.112 x 10⁻⁷ sec
T = 1.13 x 10⁻⁸ sec
Thus, the period of the fm wave is found to be 1.13 x 10⁻⁸ sec.
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Evaluate each expression.
(Examples)
4 7. |10|= ?
Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.
Mean = 2 Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.
We can determine that at least
100 (1-1k2)% = 100 (1-1/4)% = 75%
is within 2 standard deviations of the mean using Chebyshev's Rule with
k = 2. The percentage times the sample size yields the equivalent number of households:
75% x 40 = 30 Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
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On solving the provided question, we can say that the expression, we have here is 4 7. |10|= 470 or -470
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
the expression, we have here is
4 7. |10|= 470 or -470
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What is -1.2 x (-1.2)?
The product of the operation -1.2 x (-1.2) is 1. 44
What is multiplication?Multiplication is simply described as one of the four primary mathematical operations of arithmetic, other are;
additionsubtractiondivision.The result of any multiplication operation is called a product.
Also, to multiply simply means to add equal group of numbers or variables.
It is also important to note the following multiplication of mathematical signs, we have;
- × - = ++ × + = ++ × - = -- × + = -From the information given, we have that;
-1.2 x (-1.2)
To find the product, expand the bracket, we get;
- 1.2 × - 1.2
Multiply the values, we get;
1. 44
Hence, the value is 1.44
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true or false? i need help
g-9=24;g=35 is this true or false
Answer: no
Step-by-step explanation:
35 -9 = 26
you add 1+1 =2
then you look at the equal and that is your answer
If a quadratic function has a turning point of (-3, 2)
then where does the quadratic function defined by
g(x) = 2f(x-4) + 5.
a) Describe the transformations(s).
b) State the turning point of g(x).
a) The quadratic function g(x) = 2f(x-4) + 5 is defined as a transformed version of the original quadratic function f(x). The transformation applied to f(x) is a horizontal shift of 4 units to the left and a vertical shift of 5 units upward. This can be observed from the fact that x is replaced with (x-4) in the function g(x). The function is also scaled by a factor of 2.
How does a quadratic function work?
f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.
b) The turning point of the quadratic function f(x) is (-3, 2). To find the turning point of g(x), we must first apply the horizontal shift of 4 units to the left to the x-coordinate, and then apply the vertical shift of 5 units upward to the y-coordinate.
The turning point of g(x) is (-3+4, 2+5) = (1,7)
So, the turning point of the transformed function g(x) is (1,7)
We can see that the transformation of g(x) moves the turning point of f(x) to the right and up, as expected from the transformation.
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Work out the value of x
Answer:
3
Step-by-step explanation:
trust lil bru
What is another name for ∠ XYZ?
This means that the solution to the triangle issue is ABC, which is equivalent to XYZ.
What's the triangle all about?Any shape with 3 sides and three points is a polygon. The fundamental form of geometry is this. The corners of the triangular Triangle ABC are A, B, and C. When four parts are not collinear in a geometric shape, a single plane plus triangle are produced. As triangles have three sides as well as a top right corner, they are included in polygons.
Here.
Thus,
To prove : ABC and XYZ are similar
hence ∠A = ∠X.
The definition of ∠B and ∠Y is the same.
Because ∠Z = ∠C,
Similar to xy, line ab shares the same value.
There is no difference between lines bc and yz.
XZ corresponds to line ac.
To come up with a solution, Cpct was used.
Triangle segments that match each other are congruent.
The solution to the triangle problem is ABC is proportional with XYZ as a result.
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Answer: it's Y because i took the test, also when doing this type of math problem you wouldn't start from X or Z because they are starting points
Step-by-step explanation: I TOOK the test
I’ll give brainliest if correct
Which equation represents a nonlinear function
y = x^2 represents a nonlinear function.
A linear function has the form of y = mx+b where m and b are constants and x is variable, the graph of a linear function is always a straight line. A nonlinear function is any function that is not linear, the graph of a nonlinear function is not a straight line.
y = x^2 is nonlinear because the variable x is squared, a quadratic function and its graph is a parabola.
y=2x is a linear function and its graph is a straight line, increasing linearly with x.
y = x is also a linear function and its graph is also a straight line, increasing linearly with x.
y = x+2 is a linear function and its graph is also a straight line with a y-intercept of 2, increasing linearly with x
So, y = x^2 represents a nonlinear function, and it is the correct answer.
1. find the value of 3x 4y - 10 if x = 3 and y =5
2. find the value a cubed + 5a if a = 2
3. 6ab + 4bc - 2ac if a = 1, b = 2, c = 3
4. subtract 2x squared + 3x - 2 from 5x squared - 9x + 11
5. find the difference of 2x squared + 4xy squared 5xsquared y - 2
-x squared 4xy squared 3xsquared y - 10
Step-by-step explanation:
3×4(5)-10
12(5)-10
60-10
50
HELPP PLEASE. What is the equation of the line that passes through the point (-6,-3) and had a slope of -1/6?
PLEASE HELP GEOMETRY FINAL
What is the sequence of transformations that maps A ABC to
A A'B'C'?
Select from the drop-down menus to correctly identify each step.
Step 1: Choose…
rotate 90° clockwise about the origin.
reflect across the line y = x
reflect across the Y axis.
rotate 180° about the origin.
Step 2: Choose..
translate 1 unit right.
Translate 2 units right.
Translate 4 Units down.
Reflect across the x-axis.
Answer:
I believe… ( it might be wrong… )
Reflect across the line y = x.
translate 1 unit right.
Step-by-step explanation:
i took the same test before but i believe i had a question just like this and got it right soooo….. ye
Is a triangle possible with length of the sides as 10.2 cm 6.8 cm and 4.6 cm?
It is not possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 10.2 and 6.8
10.2 + 6.8 > 4.6
17 > 4.6
Now we add 10.2 and 4.6
10.2 + 4.6 > 6.8
14.8 > 6.8
Now we add 6.8 and 4.6
6.8 + 4.6 > 10.2
11.4 > 10.2
It is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.
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write a new equation 6x+2y=12
Is △fhk similar to △ghj? if so, which postulate or theorem proves these two triangles are similar? responses △fhk is similar to △ghj by the sss similarity theorem. , , triangle f h k, , , , is similar to , , , , triangle g h j, , , , by the , , , , s s s similarity theorem, , . △fhk is similar to △ghj by the ssa similarity theorem. , , triangle f h k, , , , is similar to , , , , triangle g h j, , , , by the , , s s a similarity theorem, , . △fhk is similar to △ghj by the sas similarity theorem. , , triangle f h k, , , , is similar to , , , , triangle g h j, , , , by the , , , , , , s a s theorem, , . △fhk is not similar to △ghj.
No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.
Similar triangles are triangles that have the same angle measures and the same side lengths. In order to determine if two triangles are similar, it is necessary to compare the sides and angles of the triangles.
In this case, the sides and angles of △fhk and △ghj are not the same, so they are not similar. Therefore, there is no postulate or theorem that can prove these two triangles are similar. No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.
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jimmy pays 3.69 for every gallon of gas he puts in car. draw a graph which models the change in amount of money Jimmy has.
Therefore , the solution of the given problem of equation comes out to be 3.69x = y.
What is the equation?Equ is the translation of the Latin word for equivalent. Latin roots can be found in the base words of many English language words that are subject to modification, such as adequate, moderate, and equality. As both sides of either an equation are, in essence, "same" to one another, the Latin root term equ enters our variable quite easily.
Here,
Given : Jimmy spends $3.69 per gallon of fuel he puts in his vehicle.
Thus,
To find the equation for the amount of money:
Let x be the number of times he refuel his gallon of fuel:
So,
Here y represents the total amount of money.
3.69x = y
Therefore , the solution of the given problem of equation comes out to be 3.69x = y.
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y = -x + 2
y = 3x + 6
Graph each line in the system shown below. What is the point of intersection? Does more than one exist? How do you know for sure?
The solution of the system of linear equations is (-1,3) and thus has unique solution as shown in the graph attached.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The linear equations here as y = -x + 2 & y = 3x + 6
For a system of two linear equations and two variables, there can be no solution, exactly one solution, or infinitely many solutions (just like for one linear equation in one variable). An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
But clearly the two equations are not coincident and also not parallel
Thus the system of equations must have exactly one unique solution.
Therefore solving for the equations
y = -x + 2
y = 3x + 6
Substracting the two equations we get -4x-4=0 or x=-1
∴ y=1+2
=3
Hence, The solution of the system of linear equations is (-1,3) and thus has unique solution as shown in the graph attached.
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Which of the following ordered pair is a solution of 2x +3y ≤ 6?A. 1-1,4) B. (-21) C. 11,2) D. (3.3)
(0,2) and (3,0) are the required two solutions of the given equation in an ordered pairs .
The given equation is 2x+3y<=6.
When, x=0,y=2
When, y=0,x=3
Hence,
(0,2) and (3,0) are the two solutions of the given equation
in order to determine the x x and y y values to form the ordered pair.
An ordered pair, is a pair of elements in which it have a specific importance for the order of their required placements. Ordered pairs are mainly used in coordinate geometry in order to represent a point on a coordinate plane and it is also used to represent elements of a relation .
An ordered pair is defined as pair formed by two elements which are separated by a comma and written inside the parentheses. example, (x, y) represents an ordered pair, where 'x' is called the first element and 'y' is called the second element of the ordered pair. These elements which have specific names according to that context they are being used and that can be either variables or constants. The order of the elements which has a certain importance in an ordered pair. It means that (x, y) may not be equal to (y, x)at all the time.
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How do you find the value of N example?
N! also called N factorial is the product of all positive non-integers equal to or less than N or simply is the product of the Nth integer and all integers below it.
N! is represented as 1x2x3x4.......x n which is also equivalent to n x (n-1_x(n-2w)x(n-3)......x1. Therefore the formula for N factorial is N! = n × (n - 1)!. For whole numbers, the factorial is a product of natural numbers till 1 of the values is equal to or less than whole numbers.
N is also used to represent the set of natural numbers up to infinity. Natural numbers include the values from till infinity, they can be represented like N=[1,2,3,4,5,6........].
Examples of N! are:-
4!= 4x3x2x1=24 here we take the product of values equal to or less than 4 upto 112= 12x11x10x9x...... x2x1=479001600 here we calculate the product of 12 and lesser natural numbers(N+3)!= (N-3)X(N+2)X(N+1)X......X1To know more about factorials visit:
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URGENT!
Prove that in the isosceles triangle the heights removed from the vertices of the base on the side edges are congruent
Therefore ,consider that the divided congruent triangle corresponding bases are equivalent as proof.
How do triangles work?Given that it contains three sides & three vertices, a triangle qualifies as a polygon. It is a fundamental characteristic in geometry. Triangle ABC is the name given to a triangle with vertices A, B, & C. When the three components are not collinear, Euclidean geometry reveals an unique plane and triangle. The polygonal shape of a triangle has 3 components and three corners. The points where three sides touch each other end to end are referred to as the triangle's corners. The sum of the three triangle angles is 180 degrees.
Here,
Given :
This RHS theorem can be employed to demonstrate the equality of the respective.
bases of all those split congruents as well as the congruency of two independents that are produced by the altitude of such an isosceles from every given vertex.
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a triangle has 3 sides x+4, x+6, and x. Write an expression to find the perimeter
An expression to find the perimeter of this triangle is P = 3x + 10.
How to calculate the perimeter of this triangle?Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:
P = a + b + c
Where:
P represents the perimeter of a triangle.a, b, and c represents the length of sides of a triangle.Given the following parameters:
Side a = x + 4Side b = x + 6side c = xSubstituting the given parameters into the perimeter of a triangle formula, we have the following;
Perimeter of triangle, P = x + 4 + x + 6 + x
Perimeter of triangle, P = 3x + 10
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hurry up please!!!!!!
The approximate annual cost of raising a child born in 2013 at age 17 is 15230.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
a) Plot (2, 12,940), (5, 12,970), (8, 12,800), (11, 13,600) 1nd (14, 14420) on graph.
b) (8, 12800) and (14, 14420)
Here, slope m=(14420-12800)/(14-8)
= 1,620/6
= 270
Substitute m=270 and (x, y)=(8, 12800) in y=mx+c, we get
12800=270(8)+c
12800=2160+c
c=10640
Substitute m=270 and c=10640 in y=mx+c, we get
y=270x+10640
c) Now, substitute x=17 in y=270x+10640, we get
y=270×17+10640
y=15230
Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is 15230.
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