A proposition is a statement that is either true or false. In this case, the proposition states that if b does not divide ac, then b does not divide c.
To prove this proposition, we will assume that b does not divide ac and try to show that b does not divide c.
Let us begin by using the definition of divisibility.
If b divides ac, then there exists an integer k such that b = akc. We can rewrite this equation as b = (ak)c. Since a, b, and c are all integers, then (ak) is also an integer.
This means that if b divides ac, then b also divides c.
Now, let us assume that b does not divide ac.
This means that there does not exist an integer k such that b = akc.
We want to show that b does not divide c, so we will assume the opposite and show that it leads to a contradiction.
Suppose that b divides c.
Then there exists an integer m such that c = bm.
We can substitute this expression for c into the original equation and get b = a(bm). Since a, b, and c are all integers, then (bm) is also an integer.
This means that b divides ac, which contradicts our initial assumption.
Therefore, we have shown that if b does not divide ac, then b does not divide c.
This proposition is important in number theory and has applications in various fields of mathematics.
It is a useful tool for proving other propositions and theorems related to divisibility and prime numbers.
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The proposition you've provided is a statement about divisibility in the integers. Specifically, it states that if we have three integers a, b, and c, and b does not divide the product ac, then b also does not divide c.
This statement can be proven using a proof by contradiction. Suppose that b divides ac but does not divide c. Then we can write ac = bk and c = dj, where k and j are integers and d is the greatest common divisor of b and c (which we know exists by the Euclidean algorithm). Substituting the second equation into the first, we get ajd = bkd, which implies that b divides aj.
Now we can write aj = bl for some integer l, which implies that c = dj = (aj)/d = (bl)/d = (b/d)l. But this contradicts the assumption that b does not divide c, since b/d is a divisor of b. Therefore, we must conclude that if b does not divide ac, then b does not divide c.
Proposition: Suppose a, b, c ∈ Z (meaning a, b, and c are integers). If b does not divide ac, then b does not divide c.
Proof:
Step 1: Suppose b does not divide ac. This means that there is no integer k such that ac = bk.
Step 2: We want to prove that b does not divide c. To prove this, we will use a proof by contradiction. Let's assume the opposite, that b does divide c.
Step 3: If b does divide c, there exists an integer m such that c = bm.
Step 4: Since a, b, and m are all integers, we can multiply both sides of c = bm by a to get ac = abm.
Step 5: Now, we have ac = abm, which implies that b divides ac, as abm is a multiple of b.
Step 6: This contradicts our initial assumption that b does not divide ac. Therefore, our assumption that b divides c must be false.
Conclusion: If b does not divide ac, then b does not divide c.
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DECIDING WHETHER A FUNCTION IS INCREASING, DECREASING, OR CONSTANT
Some recent studies suggest that a teenager sends an average of 60 texts per day.[2] For each of the following scenarios, find the linear function that describes the relationship between the input value and the output value. Then, determine whether the graph of the function is increasing, decreasing, or constant.
The total number of texts a teen sends is considered a function of time in days. The input is the number of days, and output is the total number of texts sent.
A teen has a limit of 500 texts per month in his or her data plan. The input is the number of days, and output is the total number of texts remaining for the month.
A teen has an unlimited number of texts in his or her data plan for a cost of $50 per month. The input is the number of days, and output is the total cost of texting each month.
According to given data, we can prove that Statement 1 is increasing function, Statement 2 is Decreasing Function, and Statement 3 is Constant Function.
1. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts sent) is y = 60x, where y is the total number of texts sent and x is the number of days. The graph of this function is increasing because as the number of days increases, the total number of texts sent also increases at a constant rate of 60 texts per day.
2. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts remaining for the month) is y = 500 - 60x, where y is the total number of texts remaining for the month and x is the number of days. The graph of this function is decreasing because as the number of days increases, the total number of texts remaining for the month decreases at a constant rate of 60 texts per day.
3. The linear function that describes the relationship between the input value (number of days) and the output value (total cost of texting each month) is y = 50, where y is the total cost of texting each month and x is the number of days. The graph of this function is constant because the cost of texting is the same regardless of the number of days.
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Lisa worked 26 hours last month and earn seven dollars per hour she spent $17 on her earring since then how much money does she have left?
After spending $17 the amount of money left with Lisa is $165.
What is equation?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Lisa worked 26 hours last month.
For each hour she earns $7.
Total earnings of Lisa in last month is equated as -
Earning = 26 × 7
Earning = $182
She spent $17 dollars on earring.
The amount of money left with her is equated as -
Total Earning - Money spent
Money Left = 182 -17
Money Left = $165
Therefore, the money left with Lisa is $165.
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Can a triangle have three sides whose lengths are 3.2 cm 5.3 cm 9.4 cm?
A triangle can not have three sides whose lengths are 3.2 cm 5.3 cm 9.4 cm
We know that the triangle inequality theorem states that for any triangle the sum of any two sides of a triangle is greater than or equal to the third side.
Here, we have been given the three measurements.
Let a = 3.2 cm, b = 5.3 cm and c = 9.4 cm
Consider the sum of sides a and b,
a + b
= 3.2 + 5.3
= 8.5cm
< 9.4
= c
i.e., a + b < c
Acctording to triangle inequality theorem, a, b, c can not be the sides of triangle, as the sum of two sides that measure 3.2 cm and 5.3 cm is not greater than or equal to the third side which measures 9.4 cm
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(While doing this answer please, explain all of your steps! For 50 points and brainliest)
A company has a cost equation of
c= 0.925x² - 4x+ 20
and a profit equation of
p= -1.125x² + 6x+40.
Solve for the breakeven point. Show your work and explain the steps you used to solve. Round your answer to the nearest tenth.
Answer:2095.23
Step-by-step explanation:
In ΔEFG, e = 75 cm, mm∠G=141° and mm∠E=16°. Find the length of g, to the nearest centimeter.
if ΔEFG, e = 75 cm, m∠G=141° and m∠E=16° then length of g is 171.24 cm
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that ΔEFG, e = 75 cm, m∠G=141° and m∠E=16°
We need to find the length of g.
Because two angles are given, F = 180 – (141 +16 )
m∠F=180-157F=23
Now let us apply the sine rule
SinE/e=SinF/g
Sin16/75=sin23/g
g=171.24 cm
Hence, if ΔEFG, e = 75 cm, mm∠G=141° and mm∠E=16° then length of g is 171.24 cm
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What are the formulas for Class 8?
Algebra Formulas for Class 8
Some essential 8th-class formulas related to Algebra are:
Algebraic Identities For Class 8
(a + b)2 = a2 + 2ab + b2
(a − b)2 = a2 − 2ab + b2
(a + b) (a – b) = a2 – b2
(x + a) (x + b) = x2 + (a + b)x + ab
(x + a) (x – b) = x2 + (a – b)x – ab
(x – a) (x + b) = x2 + (b – a)x – ab
(x – a) (x – b) = x2 – (a + b)x + ab
(a + b)3 = a3 + b3 + 3ab (a + b)
(a – b)3 = a3 – b3 – 3ab (a – b)
I tried my best!
Question 3(Multiple Choice Worth 1 points)
(04.02 MC)
3
What is the y-intercept of the line perpendicular to the line y = -3/4x + 5 that includes the point (-3, -3)?
3/4
1
7
-21/4
Question
Answer: The y-intercept of the line perpendicular to the line y = -3/4x+5 that includes the point (-3,-3) is -21/4. Thus option D is correct.
Step-by-step explanation: The line is a general straight line y=mx+c where c is the y-intercept and m is the gradient or the slope.
In this equation, m= -3/4. Putting the value of m, y and x in the equation gives
-3=3/4(-3) + c
-3= 9/4 +c
solving for c we get,
c= -3-9/4
c = - 21/4
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Divide. Write your answer as a fraction or a mixed number in simplest form.
4\frac{2}{9} ÷ 1\frac{1}{3}
The solution of the division of 4 2/9 by the number 1 1/3 is
What are Mixed Fractions?Mixed fractions are type of fractions which consist of a whole number part and a fractional part.
Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.
The given fractions are 4 2/9 and 1 1/3.
First we have to change the mixed fraction into improper fraction.
4 2/9 = (4 × 9 + 2) / 9 = 38/9
1 1/3 = (1 × 3 + 1) / 3 = 4/3
Dividing these,
4 2/9 ÷ 1 1/3 = 38/9 ÷ 4/3
= (38/9) × (3/4)
= 38 / (3 × 4)
= 19/6
= 3 1/6
Hence the solution of the division of the mixed fractions given is 3 1/6.
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A customer uses a store credit card to purchase a boat for $10,500. The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years. If no payments are made for the two years, what will be the balance on the card, rounded to the nearest penny? $12,679.59 $12,695.85 $15,311.62 $15,350.92
The final balance on the card is $15350.92, rounded to the nearest penny.
The correct option is D.
What is continuous compound interest?Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to a period of time.
Formula of continuous compound interest rate;
P(t) = P₀[tex]e^{rt}[/tex], where P₀ is the principal amount, r is the interest rate and t is the time period.
Given:
A customer uses a store credit card to purchase a boat for $10,500.
The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years.
That means,
P₀ = $10500, r = 18.99 and t = 2.
So,
P(t) = P₀[tex]e^{rt}[/tex]
Substituting the values,
P(t) = (10500)[tex]e^{(0.1899)(2)}[/tex]
P(t) = (10500)(1.46199)
P(t) = 15350.917
P(t) = $15350.92
Therefore, the final amount is $15350.92.
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I need helppppppppppp
Answer:
$4.45
Step-by-step explanation:
First, we try to find the slope of the table. We can do this by doing the following- [tex]\frac{Change \ in \ y }{Change \ in \ x}[/tex]
When we do this, we find that the slope (or the change in y / change in x) is equal to 5.27
Now we subtract this from the slope of the price of steak at Store B which is 9.72
[tex]9.72-5.27 = 4.45[/tex]
You get 4.45 which is $4.45 or 4 dollars and 45 cents.
Madison put $463 in a 2% per year bank savings account. How much will be in the account at the
end of the year?
Located in Ennis, Montana, Madison Valley Bank provides services to residents of Madison County and the surrounding region. Madison deposited $463 into a bank savings account with a 2% annual interest rate.
Will inflation ever stop?Although inflation doesn't stop, it does get better. We don't want it to completely end, in fact. The Federal Reserve, the US central bank tasked with reducing the rate of inflation through a series of interest rate hikes, has set a target of about 2%. As a result, albeit not by as much, prices will still increase. At an interest rate of 8% compounded semi-annually, a $1,000 investment made now will be worth $1,480.24 after five years.
Calculator for future inflation in the US: In 2025, $106.09 is expected to be the same as $100 in terms of purchasing power. Future inflation of 3% per year is used as the basis for this computation. A 3.00% future inflation rate is predicted. when $54,855.74 is the same as $30
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Judy need 2/3/4 yard of flannel to ew a kirt. She obtain 3/8 yard of flannel from the local market. How much more fabric doe he need to titch the kirt?
Judy needs 1 5/8 yards area more of flannel to stitch the kirt.
To find how much more fabric Judy needs, we need to subtract the amount she already has from the amount she needs.
Judy needs 2/3 yard of flannel
Judy has 3/8 yard of flannel
To subtract these fractions, we first need to convert them to the same denominator.
2/3 yard = 4/6 yard
3/8 yard = 6/8 yard
4/6 yard - 6/8 yard = (24 - 24)/48 = 0/48
To simplify, 0/48 = 0
Therefore, Judy needs 0 yards more of flannel.
However, Judy needs 2/3 yard of flannel to stitch the kirt. Since she has 3/8 yard, we can subtract the two to find how much more fabric she needs.
2/3 yard - 3/8 yard = (16 - 12)/24 = 4/24
To simplify, 4/24 = 1/6
Therefore, Judy needs 1 1/6 yards area more of flannel to stitch the kirt.
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What are the 4 transformations of a function?
The four transformations of a function are translation, reflection, stretching/shrinking, and rotation.
What is function?Function is a group of related statements that perform a specific task. It is a block of organized, reusable code which can be used to perform a single, related action. Functions help make code more reusable and efficient. It also reduces the complexity of a program by breaking it down into smaller and simpler parts.
Translation involves shifting the graph of a function along a given axis; reflection involves flipping the graph of a function about a given axis; stretching/shrinking involves changing the scale of a graph along a given axis; and rotation involves rotating the graph of a function about a given point. All of these transformations can be used to modify the graph of a function, allowing for a variety of different outputs.
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what is a definition of a circle
Answer:
A round-shaped figure with no corners or edges.
Step-by-step explanation:
Answer: A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
Step-by-step explanation:
3/2(x-5)=-6 what is x equal to
Following the addition of both sides of the equation by 2/3, x is equivalent to 3/2(x-5)=-6.
what is equation ?An equation is a mathematical formula that joins two statements using the equal sign (=) to denote equality. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the terms 3x + 5 and 14 in the equation 3x + 5 = 14.
given
Add 2/3 to both sides of the equation.
(2/3(3/2⋅(x−5))=2/3⋅−6
Simplify the problem on both sides.
x − 5 = −4
Put all terms on the right side of the equation that don't contain x.
x = 1
Following the addition of both sides of the equation by 2/3, x is equivalent to 3/2(x-5)=-6.
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Abebi,bella and chuku hare $112. Abebi receive $x. Bella receive $12 le than Abebi. Chuku receive twice a much a bella
From an equation in x and olve it to find how much abebi receive
By solving the linear equation in x Abebi receives $37.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.
On identifying the information given in the problem we have:
Abebi, Bella, and Chuku share $112. Abebi receives $x. Bella receives $12 less than Abebi. Chuku receives twice as much as Bella.
On setting up an equation using the information given:
We know that the total amount shared is $112 and we want to find out how much Abebi receives, represented by x.
We know that:
Bella receives $12 less than Abebi =(x - 12)
Chuku receives twice as much as Bella =(2 * (x - 12))
So we can set up the equation as:
x + (x - 12) + (2 * (x - 12)) = 112
On simplifying the equation:
x + x - 12 + 2x - 24 = 112
Combining like terms:
4x - 36 = 112
On solving for x we get:
Add 36 to both sides:
4x = 148
Divide both sides by 4:
x = 37
On interpreting the solution we get:
By solving the linear equation in x Abebi receives $37.
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What is an example of the midpoint formula?
Mid-point formula is used to determine the mid-point of a line segment. An example of the mid-point formula is discussed below.
What is the mid-point formula?
The centre of a line segment is known as the midpoint. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
The formula used to find this mid-point of the line is called the mid-point formula.
[tex](x_{m},y_{m} ) =(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})[/tex]
where, [tex](x_{m} ,y_{m})[/tex] = mid-point coordinates
[tex](x_{1} ,y_{1})[/tex] = first point coordinates
[tex](x_{2} ,y_{2})[/tex] = second point coordinates
An example of mid-point formula is given below.
Find the mid-point of a line whose end coordinates are (3,5) and (6,10).
From the question, we can write,
[tex](x_{1} ,y_{1}) = (3,5)\\(x_{2} ,y_{2}) = (6,10)[/tex]
Then as discussed above, we can find the mid-point using the formula,
[tex](x_{m},y_{m} ) =(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})[/tex]
[tex]x_{m} = \frac{x_1 + x_2}{2} = \frac{3+6}{2} = 4.5[/tex]
[tex]y_{m} = \frac{y_{1} + y_{2}}{2} = \frac{5+10}{2} = 7.5[/tex]
Therefore the mid-point of the given line found using the mid-point formula is (4.5, 7.5).
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Which of the following is equivalent to 60^1/2?a. 60/2b. √60c. 1/60^2d. 1/√60
b. √60 is equivalent to 60^1/2
60^1/2 represents the square root of 60. The square root of a number is a value that when multiplied by itself, gives the original number. So in this case, √60 * √60 = 60. Therefore, the equivalent of 60^1/2 is √60.
Option a, 60/2 is not equivalent, because it is not the value that when multiplied by itself gives 60.
Option c, 1/60^2 is not equivalent, because it is not the value that when multiplied by itself gives 60.
Option d, 1/√60 is not equivalent, because it is not the value that when multiplied by itself gives 60.
It is important to note that 60^1/2 is not the same as (60^1)^1/2, the first one is finding the square root of 60 while the second one is finding the 1/2 power of 60 which is not the same thing.
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what is 3x times 6 times 2(-2+16)
Answer:
Step-by-step explanation: First we start by using the order of operations and do -2 + 16 which is 14. Then we do multiplication left to right, do 3 x 6 = 18x2 =36 +14 =50
How many solutions are there for 12x 1 3 4x 1 )- 2?
The equation have infinite solutions.
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
We can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.
12x + 1 = 3(4x + 1) - 2
12x + 1 = 12x + 3 - 2
12x + 1 = 12x + 1
The equation have infinite solutions.
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How many solutions exist for the given equation?
12x + 1 = 3(4x + 1) – 2
What's a substitution property?
Substitution property is a property in algebra that helps in substituting the value of a quantity/variable into an algebraic expression to solve a given mathematical problem.
The substitution property is a notion in algebra that is used for substituting the value of a given variable or a quantity into an expression to find the value of the unknown.
In other words, we can express that the substitution property is utilised to replace the value of a quantity in an equation or an expression to solve a mathematical problem.
For example, Using the substitution property of equality, find the value of the algebraic expression g(x) = sin x + cos x if x = 45°.
We will replace x with 45° in the expression. So we have
g(45°) = sin 45° + cos 45°
= 1/√2 + 1/√2
= 2/√2
= √2
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Drone sales for a New York based firm over the last 4 weeks are depicted in the table below Week Unit Sales 700 724 720 3 728 4 What is the equation of the trend line and the predicted sales for week 6? 0 718 + 10t and 798 730 + 8t and 778 O 734+10t and 774 698+8t and 746
The predicted sales for week 6 is 740
In the case of linear regression using excel formula, we can find the intercept and the slope value for the regression model.
The equation of linear regression is similar to the slope formula what we have learned before in earlier classes such as linear equations in two variables.
It is given by; Y= a + bXForecast[tex]$=\mathrm{A}+\mathrm{B}(\mathrm{x})$[/tex]
Where A is the intercept of the data, B is the slope, and X is the period.
Intercept [tex]=[/tex] INTERCEPT (Range Y, Range X)
Slope [tex]=[/tex] Slope (Range Y, Range X)The above data generates the equation.
Now the data corresponds to an intercept value of 698 and a slope of 8.
Therefore, for period [tex]$6, x=6$[/tex]
The equation [tex]$=698+(8 * 6)=746$[/tex]
The intermediate calculations are in the table below:
PERIODUNITSFORECAST
____________________
1 700 706
2 724 714
3 720 722
4 728 730
5 738
6 740
Therefore, the predicted sales for week 6 is 740.
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What is the process for converting 2D data to 3D data?
The process for converting 2D data to 3D data involves a few steps. First, a 3D model needs to be created, which is typically done using a 3D modeling software such as Blender or 3DS Max.
What is data?Data in math is information that can be used to draw conclusions or make decisions. It is typically collected, analyzed, and presented in the form of numbers, graphs, or tables. Data can be used to compare and contrast different scenarios, identify trends and patterns, or make predictions about the future. Data can also be used to help researchers develop hypotheses and develop models to explain phenomena.
Once the model is created, the data needs to be imported into the software in a format that can be used by the software, such as an .obj or .3ds file. The data can then be manipulated within the software to create the 3D model. Finally, the 3D model can be exported in a variety of file formats, such as .stl, .fbx, or .dae, that can be used for 3D printing, virtual reality, and other applications.
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An expression is shown.
5(−4)
-2
Create an expression that is equivalent to the expression shown.
If we expand the bracket, -20 -2 = -22.
So the equivalent expression would be -22.
How can this expression be shown?The expression 5(-4) means to take the number -4 and multiply it by 5.
Since multiplication is distributive, this is the same as -4 * 5 which results in -20.
And -20 -2 is -22.
So the equivalent expression is -22.
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Which of the following is a trinomial ?(а) -7z(b) z² – 4y²(c) x²y – xy² + y²(d) 12a – 9ab + 5b – 3.
As we know that Trinomial means a polynomial with three terms.
Therefore, option (c) x²y -xy² +y² is correct.
Given polynomials are:
(а) -7z
(b) z² – 4y²
(c) x²y – xy² + y²
(d) 12a – 9ab + 5b – 3.
To Find : Which one is Trinomial.
Monomial:
A monomial is defined as an expression with one non-zero term. It consists of various parts such as variables, coefficients and orders. A unary variable is the character it contains. A coefficient is a number that is multiplied by a monomial variable. The monomial degree is the sum of the exponents of all variables.
Binomial:
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each has a Boolean result of Success (probability p) or failure. A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.
Trinomial:
A ternary expression is an algebraic expression with three terms. An algebraic expression consists of variables and constants in one or more terms. These expressions use symbols or operations such as +, –, ×, and ÷ as separators. Trinomials fall into this algebraic expression, along with monomials, binomials, and polynomials.
In Short :
Monomial - A polynomial with single Term
Binomial - A polynomial with 2 terms
Trinomial - A polynomial with 3 terms
Based on the information:
(а) -7z only one term hence Monomial
(b) z² – 4y² Two terms Hence Binomial
(c) x²y – xy² + y² Three terms hence Trinomial
(d) 12a – 9ab + 5b – 3. Four terms hence quadrinomial.
So correct option is c) x²y – xy² + y²
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How do you write coordinates in quadratic form?
To write coordinates in quadratic forms,
Obtain the equation y = ax2 + bx + c.Determine -b / 2A. The vertex's x-coordinate is given here.Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate. The vertex's y-coordinate is given here.What is coordinate quadratic function?When a quadratic equation is written in standard form, the vertex's coordinates are (-b/2a, f(-b/2a)), where x = -b/2a and y = f(-b/2a). This suggests that the formula x = -b/2a should be used to determine the x-value of the vertex in the equation y = -3x2 + x + 1. The equation for a straight line, y = mx + c, is one of the key coordinate geometry formulas. The angle that the line makes with the positive x-axis is represented by the symbol, where m is the slope and c is the y-intercept (tan = m).When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point.To learn more about quadratic form refer to:
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Suppose that l is a tangent line to this circle which is parallel to the line y=5x+7 and has a negative y intercept. Then the point of tangency of l with this circle is.
A. The equation of a tangent line to the circle through the point (- 6 , 8) is y = 0.75x + 12.50
B. The point of tangency of L with the circle is (9.81 , - 1.96).
The full question is in the attachment. The equation of a tangent line to the circle with radius r centered at the origin through the point (p , q)
r = 10 p = - 6 q = 8px + qy = r²
- 6x + 8y = 10²
8y = 6x + 100
y = 6/8x + 100/8
y = 3/4x + 25/2
y = 0.75x + 12.50
The equation line y = mx + c has the slope or the gradient m. If two lines are parallel, the two lines have the same slope.
y = 5x + 7
m = 5m of L = 5 because parallelThe tangent line L to the circle with the gradient m and radius r
[tex]y \:=\: mx \pm r \: \sqrt{1 \:+\: m^2}[/tex]
[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 5^2}[/tex]
[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 25}[/tex]
[tex]y \:=\: 5x \pm 10 \: \sqrt{26}[/tex]
Because L has a negative y-intercept, it means when x = 0, y is negative. So the equation L
[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]
The point x of tangency of L with the circle
x² + y² = r²
x² + (5x - 10 √26)² = 10²
x² + 25x² - 100√26 x + 2,600 = 100
26x² - 100√26 x + 2,500 = 0
a = 26b = - 100√26c = 2,500[tex]x_{1.2} \:=\: \frac{-b \pm \sqrt{b^2 \:-\: 4ac}}{2a}[/tex]
[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{(- 100 \sqrt{26})^2 \:-\: (4 \times 26 \times 2,500)}}{2 \times 26}[/tex]
[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{260,000 \:-\: 260,000}}{52}[/tex]
[tex]x \:=\: \frac{100 \sqrt{26}}{52}[/tex]
[tex]x \:=\: \frac{50 \sqrt{26}}{26}[/tex]
x = 50/26 × √26
x = 9.81
The point y of tangency of L with the circle
[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]
[tex]y \:=\: 5 \times \frac{50 \sqrt{26}}{26} \:+\: 10 \: \sqrt{26}[/tex]
[tex]y \:=\: \frac{250 \sqrt{26}}{26} \:+\: \frac{260 \sqrt{26}}{26}[/tex]
[tex]y \:=\: \frac{- 10 \sqrt{26}}{26}}[/tex]
y = - 10/26 × √26
y = - 1.96
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Solve for x.
5.3 > x + 2/5
Responses
x < 5 7/10
x > 5 7/10
x < 4 9/10
x > 4 9/10
Answer:
your answer is D
Step-by-step explanation:
I literally just finished the quiz on edge
I need help with this question
Answer:
the answer is C should be
Step-by-step explanation:
the answer is C should be, I'm in middle school btw
Does 17 15 8 Make a right triangle?
It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 17 and 15.
17 + 15 > 8
32 > 8
Now we add 17 and 8
17 + 8 > 15
25 > 15
Now we add 15 and 8
15 + 8 > 17
23 > 17
It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.
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