Determine whether the binomial is a factor of x³+4 x²+x-6 . x+2 .
Answers
The Remainder Theorem is a result in algebra that provides a relationship between a polynomial function and the remainder obtained when dividing that polynomial by a linear factor.
The given expression is x³+4x²+x-6. We need to determine whether the binomial x+2 is a factor of this expression.
To check if x+2 is a factor, we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by x-a and the remainder is 0, then (x-a) is a factor of f(x).
In this case, we want to check if x+2 is a factor of x³+4x²+x-6. To do this, we need to substitute -2 for x in the expression and see if the result is 0.
When we substitute -2 for x in the expression x³+4x²+x-6, we get (-2)³+4(-2)²+(-2)-6 = -8+16-2-6 = 0.
Since the result is 0, we can conclude that x+2 is indeed a factor of x³+4x²+x-6.
Therefore, x+2 is a factor of x³+4x²+x-6.
To know more about Remainder Theorem visit:
https://brainly.com/question/30242664
#SPJ11
The binomial x+2 is not a factor of the polynomial x³+4x²+x-6.
To determine whether the binomial x+2 is a factor of the polynomial x³+4x²+x-6, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by a binomial x-a and the remainder is zero, then (x-a) is a factor of f(x).
To apply the Remainder Theorem, we need to perform polynomial long division.
Here's how you can do it step-by-step:
1. Write the dividend, which is the polynomial x³+4x²+x-6, and the divisor, which is the binomial x+2.
_____________________
x+2 | x³ + 4x² + x - 6
2. Divide the first term of the dividend by the first term of the divisor. In this case, (x³ ÷ x) gives us x².
x²
_____________________
x+2 | x³ + 4x² + x - 6
3. Multiply the divisor (x+2) by the quotient (x²) and write the result underneath the dividend. In this case, (x+2)(x²) gives us x³ + 2x².
x²
_____________________
x+2 | x³ + 4x² + x - 6
- (x³ + 2x²)
2x²
4. Subtract the result from step 3 from the dividend. In this case, (x³ + 4x²) - (x³ + 2x²) gives us 2x² + x.
x²
_____________________
x+2 | x³ + 4x² + x - 6
- (x³ + 2x²)
___________
2x² + x
5. Bring down the next term from the dividend, which is -6.
x² + (2x² + x)
_____________________
x+2 | x³ + 4x² + x - 6
- (x³ + 2x²)
___________
2x² + x
- 6
6. Divide the first term of the new dividend (2x²) by the first term of the divisor (x). This gives us 2x.
x² + (2x² + x)
_____________________
x+2 | x³ + 4x² + x - 6
- (x³ + 2x²)
___________
2x² + x
- 6
- (2x²)
- 5x
7. Multiply the divisor (x+2) by the quotient (2x) and write the result underneath the new dividend. In this case, (x+2)(2x) gives us 2x³ + 4x².
x² + (2x² + x)
_____________________
x+2 | x³ + 4x² + x - 6
- (x³ + 2x²)
___________
2x² + x
- 6
- (2x²)
_________
- 5x
8. Subtract the result from step 7 from the new dividend. In this case, (2x² + x) - (2x² + 4x²) gives us -5x.
x² + (2x² + x)
_____________________
x+2 | x³ + 4x² + x - 6
- (x³ + 2x²)
___________
2x² + x
- 6
- (2x²)
_________
- 5x
9. Since there are no more terms to bring down, we have reached the end of the division. The final remainder is -5x.
10. Now, let's analyze the remainder. Since the remainder is not zero, we can conclude that the binomial x+2 is not a factor of the polynomial x³+4x²+x-6.
Learn more about binomial from the given link:
https://brainly.com/question/9325204
#SPJ11
Related Questions
Evaluate. Then interpret the result in terms of the area above and/or below the x-axis. | (x3 - 2x) dx 2 [ = ] (x3 - 2x) dx = 1 (Type an integer or a simplified fraction.) 2
Answers
We evaluate the integral using the Fundamental theorem of Calculus, by using and antiderivative of the funtion in the integrand;
An antiderivative of x^3 - 2 x is = 1/4 x^4 - x^2
So we evaluate this antiderivative at the two limits of integration:
At x = 1 the antiderivative becomes: 1/4 (1) - 1 = - 3/4
At x = - 1/2 the antiderivative becomes: 1/4 (-1/2)^4 - (-1/2)^2 = - 15/64
Now we subtract the evaluation at the upper limit minus the evaluation at the lower limit:
- 3/4 - (-15/64) = - 33/64
Allow me to show you the actual area we have calculated in a graph for the integration:
The curve in blue is the original function you provided : f(x) = x^3 - 2x
You can see that there is an area above the x axis that has been integrated and that gives as a result a positive number.
The area below the x axis is the part of the integral that provides the negative part which as you see is dominant in this calculation, therefore resulting in a negative final result.
Please, make sure you type -33/64 in the box provided.
5-4c-2-9c
evaluate the expression
Answers
Answer:
-13c + 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
5 - 4c - 2 - 9c
Step 2: Simplify
Combine like terms (c): -13c + 5 - 2Combine like terms (Z): -13c + 3Answer:
-13c + 3
Step-by-step explanation:
Can someone please help me find the answer to this question
Answers
Answer:
2,-2
you just have to look at the "menu" of choices and determine which one of the choices
fits the question... the f(-4) says you have to see which one of the three
choices has -4 in it ...
the middle one does -4≤x≤1 -4 is for sure in the range
this question #1 answer is "2" because the result is always a 2 for that choice...
the next question put in 3 ... three is greater than 1 (that is the third choice)
so the result is -(3) + 1 = -2
your answers are 2, and -2
Step-by-step explanation:
Chelsea is making a necklace she uses 6 blue beads for every 1 silver bead complete the table to show the ratio of blue beads to silver beads?
Answers
Answer: 12:2, 18:3, 24:4
Step-by-step explanation: You can multiply 6 by 2, 3, and 4 because the graph has 4 columns. Then multiply the top by 2, 3, and 4,
Please help me! Thank youuu
Answers
Answer: 3,600
dont quote me on it doing it the way i learned how to lol
Step-by-step explanation: Volume = length x width x height.
Answer:
917.33
Step-by-step explanation:
Top conic volume formula: ⅓ r²h=⅓(16/2)²*(18-12.5)
=⅓8²*5.5
=⅓352
=117.33
Volume formula of a cylinder: V=r²h
=8²*12.5
=800
117.33+800=917.33
A sampling frequency of 10 pixels per millimeter would produce how much spatial resolution?
A. 1 line pair per millimeter B. 5 line pairs per millimeter C. 10 line pairs per millimeter D. 20 line pairs per millimeter
Answers
A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).
A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:
1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.
So, the answer is B. 5 line pairs per millimeter.
learn more about spatial resolution:https://brainly.com/question/31759884
#SPJ11
determine the angle of rotation at the point z0 = 2 i when w = z 2
Answers
The angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\),\) which is approximately 1.107 radians or 63.43 degrees.
To determine the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\),\) we can follow these steps:
1. Express \(\(z_0\)\) in polar form: To find the polar form of \(\(z_0\)\), we need to calculate its magnitude \((\(r_0\))\) and argument \((\(\theta_0\))\). The magnitude can be obtained using the formula \(\(r_0 = |z_0| = \sqrt{\text{Re}(z_0)^2 + \text{Im}(z_0)^2}\)\):
\(\[r_0 = |2i + 1| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}\]\)
The argument \(\(\theta_0\)\) can be found using the formula \(\(\theta_0 = \text{arg}(z_0) = \arctan\left(\frac{\text{Im}(z_0)}{\text{Re}(z_0)}\right)\)\):
\(\[\theta_0 = \text{arg}(2i + 1) = \arctan\left(\frac{2}{1}\right) = \arctan(2)\]\)
2. Find the polar form of \(\(w\)\): The polar form of \(w\) can be expressed as \(\(w = |w|e^{i\theta}\)\), where \(\(|w|\)\) is the magnitude of \(\(|w|\)\) and \(\(\theta\)\) is its argument. Since \((w = z^2\)\), we can substitute z with \(\(z_0\)\) and calculate the polar form of \(\(w_0\)\)using the values we obtained earlier for \(\(z_0\)\):
\(\[w_0 = |z_0|^2e^{2i\theta_0} = \sqrt{5}^2e^{2i\arctan(2)} = 5e^{2i\arctan(2)}\]\)
3. Determine the argument of \(\(w_0\):\) To find the argument \(\(\theta_w\)\) of \(\(w_0\)\), we can simply multiply the exponent of \(e\) by 2:
\(\[\theta_w = 2\theta_0 = 2\arctan(2)\]\)= 1.107 radians
Therefore, the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\).\)
Learn more about exponent here: https://brainly.com/question/29277932
#SPJ11
The complete question is:
"Determine the angle of rotation, in radians and degrees, at the point z0 = 2i + 1 when w = z^2."
Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let x represent the number
of slushies sold.
a. Write a linear function for cost.
C(x) =
Write a linear function for revenue.
R(x)=
c. Find C(50). Show your work.
• Write C(50) as an (x, y) coordinate point. ——-
• Write a sentence that explains the meaning of the point in the context of the problem.
D. Find R(50).
Represent R(50) as an (x, y) coordinate point. ———
Write a sentence that explains the meaning of the point in the context of the problem?
e. If the students sell 50 slushies, do they make a profit? Use mathematical work to help explain your answer. Complete the sentence below.
If the students sell 50 slushies, do they make——- a profit? Because——-
F. How many slushies do the students need to sell to break even? Use complete sentences to explain your problem solving strategy and your conclusion.
G. How many slushies do the students have to sell to make a profit of $1250? Use complete sentences to explain your problem solving strategy and your conclusion.
Answers
The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
What is a function?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable
solution:
The linear function:
C(x) = 1.25x + 500
For revenue function:
R(x) = 3.50x
R(50) = 3.50(50)
= $175
Using the C(x) and revenue function we can find the number of slushies and profit.
Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
Hence the linear and revenue functions are C(x) = 1.25x + 500 and R(x) = 3.50x
Learn more about the function here:
https://brainly.com/question/17043948
#SPJ1
20
7
i need help with this
Answers
Answer:
Do you want it typed or handwritten
what have you observed on the two table?
Answers
Answer:
i. x and a are increasing while y and b are reducing
Identify explicit formula for the sequence 3, 6, 9, 12, 15, ...
Answers
Answer:
This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 to the previous term in the sequence gives the next term. In other words, an=a1+d(n−1) a n = a 1 + d ( n - 1 ) . This is the formula of an arithmetic sequence.
Step-by-step explanation:
I hope it's useful for you.
Thank you...
An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.
We have the Sequence,
3, 6, 9, 12, 15.......
Here the common difference
d = 6-3
d = 3
So, the Explicit formula is
a(n) = a(1) + (n-1)d
a(n) = 3 + (n-1)3
Learn more about Explicit Formula here:
https://brainly.com/question/18069156
#SPJ2
Create a right triangle, in which a is the right angle, and m∠c is approximately 60°. what is the approximate measure of angleb? mangleb = ° what is the sum of manglea, mangleb, and manglec? °
Answers
For a right triangle, the approximate measure of ∠b is 30°. The sum of the angles m∠a, m∠b, and m∠c is 180°.
A right triangle is a triangle that has one angle that measures 90°. In this case, we are told that ∠a is the right angle, so m∠a = 90°. We are also told that m∠c is approximately 60°. To find the approximate measure of ∠b, we can use the fact that the sum of the angles in a triangle is 180°. Therefore, we can write the equation:
m∠a + m∠b + m∠c = 180°
Substituting the known values for m∠a and m∠c, we get:
90° + m∠b + 60° = 180°
Simplifying and solving for m∠b, we get:
m∠b = 180° - 90° - 60°
m∠b = 30°
So the approximate measure of ∠b is 30°.
The sum of m∠a, m∠b, and m∠c is simply the sum of the three angle measures:
m∠a + m∠b + m∠c = 90° + 30° + 60° = 180°
So the sum of the angles is 180°.
Learn more about Right triangle:
https://brainly.com/question/2217700
#SPJ11
√x-3 +3=x
is it extraneous or not?
Answers
Answer:
extraneous
Step-by-step explanation:
extraneous
Can y’all please help ASAP.
A fish is located 5 feet below sea level.
A bird is flying 10 feet above sea level.
A shark is swimming at 18 feet below sea level.
A balloon is floating at 7 feet above sea level.
What is the furthest from sea level (zero)?
Answers
Answer: A shark is swimming at 18 feet below sea level.
Step-by-step explanation: because it just asked that which one is the furthest from sea level it don’t say above zero or below zero!
A, B and C lie on a straight line segment.
A, E and D lie on a straight line segment.
BE = 1.75m, CD = 7m and BC = 1.5m.
Work out the length of AB.
A
E
B
D
С
Answers
The value of AB id 0.5 unit.
What is AAA similarity ?The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.
What are corresponding angles?Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal are called corresponding angles and they are always equal.
According to the given question.
A, B and C lie on the straight line segment. and A, E, and D are also lie in the straight line segment.
Also, BE = 1.75m, CD = 7m and BC = 1.5m
Now, in ΔAEB and ΔADC
EB is parallel to BC
So,
∠AEB ≅ ∠ADC (corresponding angles)
∠ABE ≅ ∠ACD (corresponding angles)
∠EAB ≅ ∠DAC (common angle to the both triangle)
Hence, by AAA Similarity rule
ΔAEB is similar to ΔADC
Therefore,
\(\frac{AE}{AD} =\frac{BE}{CD} =\frac{AB}{AC}\) (sides of the similar triangles are in proportion)
So,
\(\frac{BE}{CD} =\frac{AB}{AC} \\\implies \frac{AB}{AC} =\frac{1.75}{7} ....(i)\)
Now, AC = AB + BC (as, A, B, and C lie on a straight line)
\(\implies \frac{AB}{AB+BC} =\frac{1.75}{7}\) (from (i))
\(\implies \frac{AB}{AB+1.5} =\frac{1.75}{7}\)
\(\implies 7AB = 1.75AB + 1.75(1.5)\)
\(\implies 7AB -1.75AB = 2.625\)
\(\implies 5.25AB = 2.625\)
\(\implies AB = \frac{2.625}{5.25} = 0.5\)
Hence, the value of AB id 0.5 unit.
Find out more information about AAA similarity and corresponding angles here:
https://brainly.com/question/11222402
#SPJ3
The cone below has radius 3 cm and slant height l cm. The total surface area, including the base, is 24 pi cm^2 Work out the length l
Answers
The slant height of the cone whose total surface area is 24π cm² and radius is 3 cm is 5cm
Total surface area of cone = πr(r +l)
r = radius of the cone
l = slant height of the cone
The total surface area of Cone = 24π cm²
The radius of the cone = 3 cm
By putting the value in the equation we get
24 π = π × 3 ( 3 + l )
24 π / π = 3 ( 3 + l )
24 = 3 ( 3 + l)
24/3 = 3 + l
8 = 3 + l
8 - 3 = l
l = 5 cm
The slant height of the cone = 5 cm
To know more about slant height click here
https://brainly.com/question/19863050
#SPJ4
Solve for the inverse of the following function:
f(x)=4x-16
Answers
(−45)(158)(73)(−1)
QUICK
Answers
Answer:
If you are multiplying (-45)(158)(73)(-1) your answer is 519,030.
Step-by-step explanation:
Yolanda has quarters, Q, and dimes, D, in her coin jar. She has a total of 31 coins.
The total amount of money in the jar is $4.75\$4.75$4.75 . Write two equations that could be used to find the number of quarters and the number of dimes in the jar.
Solve the equations to find out how many quarters and
how many dimes Yolanda has in her jar.
Answers
Answer:
11 Quarters 20 Dimes
Step-by-step explanation:
Q+D=31
25Q +10D = 475 (miltiplied all by 100 to avoid decimals)
Multiply the first by -10(to eliminate D)
-10Q - 10D = - 310
25Q+10D = 475
ADD BOTH( D will cancel)
15Q = 165
Q= 11
31-11 =20 (dimes =20)
11x0.25 = 2.75
20x0.10=2
2.75+2 = $4.75
A plane intersects only one nappe of a double-napped cone such that it is parallel to a generating line. Which conic section is formed?.
Answers
When a plane intersects only one nappe of a double-napped cone such that it is parallel to a generating line, it forms a parabola.
When a plane intersects only one nappe of a double-napped cone parallel to a generating line, it forms a conic section known as a parabola. This is because a parabola is defined as the set of all points that are equidistant to a fixed point (known as the focus) and a fixed line (known as the directrix).
When a plane intersects a double-napped cone parallel to a generating line, it intersects all the generatrices at the same angle, resulting in a curve that is symmetric and opens in one direction. This curve is a parabola, and it is commonly found in nature, such as the path of a thrown ball, the shape of a satellite dish, or the reflector of a car's headlights.
The properties of a parabola make it useful in various fields, including optics, physics, and engineering, where it is used to model and analyze a wide range of phenomena, such as the trajectory of projectiles, the behavior of lenses and mirrors, and the design of antennas and reflectors.
To know more about parabola:
https://brainly.com/question/21685473
#SPJ4
Which system of inequalities is represented by the graph? A. {y≥1y−x 0 C. {y≤1y−x 0
Answers
Answer:
y≤1
y−x>0
Step-by-step explanation:
I just took the quiz
A graph can be used to represent a system of inequality.
The system of inequality, the graph represents is:
\(y \ge 1\) and \(y - x > 0\)
The attached graph has two lines.
A thick horizontal lineA dotted slant lineThe thick horizontal line
Below this line, is a shaded region; and it passed through \(y = 1.\)
This means that the horizontal line represents all values of y starting from 1.
So, the inequality is:
\(y \ge 1\)
A dotted slanted line
First, calculate the slope of the line
\(m =\frac{y_2 - y_1}{x_2 - x_1}\)
The line passes through (0,0) and (1,1).
So, we have:
\(m =\frac{1-0}{1-0}\)
\(m =1\)
The equation is:
\(y = m(x - x_1) + y_1\)
\(y = 1(x - 0) + 0\)
\(y = x + 0\)
\(y = x\)
The left part of the dotted line is shaded. This represents >.
So, we have:
\(y> x\)
Subtract x from both sides
\(y - x > 0\)
Hence, the system of inequality, the graph represents is:
\(y \ge 1\)
\(y - x > 0\)
Read more about system of inequalities at:
https://brainly.com/question/19526736
find the perimeter of the figure 13cm 6cm 8cm 15cm
Answers
The perimeter of the figure with sides of lengths 13 cm, 6 cm, 8 cm, and 15 cm is 42 cm.
To find the perimeter of a figure, we need to add up the lengths of all its sides. In this case, we have four sides with lengths of 13 cm, 6 cm, 8 cm, and 15 cm.
To calculate the perimeter, we simply add these lengths together:
Perimeter = 13 cm + 6 cm + 8 cm + 15 cm
Adding these values, we get:
Perimeter = 42 cm
Therefore, the perimeter of the given figure is 42 cm.
It's important to note that the figure's shape or arrangement of sides is not specified in the question. The given lengths could correspond to any type of polygon or closed figure. Without further information about the shape or angles of the sides, we can only calculate the sum of the lengths.
If the figure is a quadrilateral, the given lengths may represent the lengths of its sides. However, the angles and shape of the figure are unknown, so we cannot determine the exact type of quadrilateral or calculate any other properties of the figure based on the given information.
For more such questions on perimeter visit:
https://brainly.com/question/19819849
#SPJ8
A sum amounts Rs. 720 is divided into two parts in the ratio 3:5. How much will be the amount in second part?) Ans: Rs. 450
Answers
ATQ
\(\\ \rm\rightarrowtail 3x+5x=720\)
\(\\ \rm\rightarrowtail 8x=720\)
\(\\ \rm\rightarrowtail x=90\)
Second part:-
5x=5(90)=450
Can someone help? I need to see work so i can write it on the screenshot and i need the answer
Answers
Answer:
y=12 .
180-106=74
74+3y+22+4y=180
96+7y=180
7y=84
y=12
4×12 = 48
Step-by-step explanation:
Good luck dear ;)
this is a sat practice. need help
Answers
Answer:
The answer is A) -1 + 12i
Step-by-step explanation:
(7 + 3i) + (-8 + 9i)
(7 - 8) + (3 + 9)i
7 - 8 = - 1
3 + 9 = 12
- 1 + 12
(7+3i)+(-8+9i)
You go ahead and rewrite it like this
7-8+3i+9i
And then combine like terms
-1+12i
So your answer is A
Logan has 68 points in a trivia game. He answers a question correctly for 35 points. Then he
answers a multi-part question incorrectly and loses 225 points. What equation can Logan use to
find his final point total?
Answers
If m3 + m1 =230, find m6
Answers
Answer:
m6 is 65 degrees
Step-by-step explanation:
Since angle 3 and angle 1 are congruent, they are the same degree. The problem said that the sum of their angles is 230, so to find the individual angles of each, divide by two to get 115. Angle 3 and angle 6 add up to 180 degrees since they are adjacent to each other (that's an important rule you need to know). If angle 3 is 115 and you need to find angle 6, subtract 180 from 115 and you will get 65.
"Number line from minus five to five by increment of one from left to right and each tick mark is labeled. The shaded part on the number line is from open circle at minus one to close circle at four."/>
Answers
The number line represents the inequality -1 < x ≤ 4 .
A number line is a graphical representation of all the real numbers .
A number line can be used to plot rational and irrational numbers.The absolute value of a real number represents the distance of the real number from zero. A number line is graduated and every point on the number line represents a particular real number.Given the statement "The shaded part on the number line is from open circle at minus one to close circle at four." which means that a particular range for a variable is given.
The value of the variable is more than -1 but less than or equal to 4.
So the statement can be represented as an inequality also such as
-1 < x ≤ 4 or x ∈ [ -1 , 4 )
To learn more about number line visit:
https://brainly.com/question/13189025
#SPJ1
Write an equation in slope intercept form for a line that passes through (10,-1) and a y intercept of -6
Answers
The equation in slope intercept form for a line that passes through (10,-1) and a y intercept of -6 is y = -1/10x - 6.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions that are separated by an equals sign (=), and the equation is true if and only if both expressions have the same value.
Slope intercept form is a way to express a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y intercept. In this equation, m is equal to -1/10 (the slope of the line between the two given points) and b is equal to -6 (the given y intercept). This equation can be used to describe the line that passes through (10,-1) and has a y intercept of -6.
To know more about equation click-
https://brainly.com/question/2972832
#SPJ1
if $x$ and $y$ are positive integers such that $5x+3y=100$, what is the greatest possible value of $xy$?
Answers
The greatest possible value of $xy$ is $17\times5=\boxed{85}$. To get the greatest possible value of $xy$, we need to maximize the values of $x$ and $y$. We can start by rearranging the equation $5x+3y=100$ to solve for one of the variables in terms of the other:
$5x+3y=100 \implies 5x=100-3y \implies x=\frac{100-3y}{5}$
Since $x$ must be a positive integer, $100-3y$ must be divisible by 5. The largest multiple of 3 less than 100 is 99, so we can try values of $y$ starting from 1 and working up to 33 (because if $y\geq34$, then $5x\leq0$, which is not positive).
When $y=1$, we get $x=\frac{100-3}{5} = 19.4$, which is not an integer.
When $y=2$, we get $x=\frac{100-6}{5} = 18.8$, which is also not an integer.
When $y=3$, we get $x=\frac{100-9}{5} = 18.2$, still not an integer.
When $y=4$, we get $x=\frac{100-12}{5} = 17.6$, still not an integer.
When $y=5$, we get $x=\frac{100-15}{5} = 17$, which is an integer.
From here, we can continue to increase $y$ and see that the values of $x$ will only decrease. Thus, the greatest possible value of $x$ is 17 and the corresponding value of $y$ is 5.
Learn more about possible value here, https://brainly.in/question/12676364
#SPJ11