Final answer:
The statement about cubic polynomial functions rising to the left and falling to the right is false; the behavior of a cubic function's graph depends on the sign and magnitude of its coefficients, particularly the leading coefficient.
Explanation:
The statement that a graph of a cubic polynomial function that rises to the left must necessarily fall to the right is false. While this behavior is common for many cubic functions, it's not a definitive rule. Cubic functions are defined by the equation f(x) = [tex]ax^3 + bx^2[/tex] + cx + d, where a, b, c, and d are constants, and a ≠ 0. The sign and magnitude of these constants, especially the leading coefficient 'a', influence the end behavior of the function.
For example, if 'a' is positive, the right end of the cubic function's graph will rise, and depending on the signs and magnitudes of the other coefficients, the left end might also rise or fall. Similarly, if 'a' is negative, the right end will fall, and the left end's behavior can vary. Cubic graphs can also exhibit turning points where the function's direction changes, which is dictated by the local minima and maxima.
Therefore, while many cubic polynomials may display the behavior of rising to the left and falling to the right, others with different coefficients could have a completely different end behavior or shape, such as rising on both ends or falling on both ends. Two-dimensional (x-y) graphing tools and learning about graphing polynomials can provide visual understanding of these concepts.
Number 28 plz?????!!?!???
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. (1 point) 4, -14, and 5 + 8i
The required polynomial function is x⁴ - 67x² + 1450x - 4984 = 0 with 4 degrees with real coefficients.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The zeros are given in the question as 4, -14, and 5 + 8i
The required polynomial function of minimum degree with real coefficients whose zeros include those listed above.
For the zero 4, you can write (x-4)
For the zero -14, you can write (x+14)
For the zero 5+8i since it is complex it will be accompanied by its conjugate 5-8i
So, you can write (x-(5+8i) and (x-(5-8i)) =(x²-10x+89)
(x - 4)(x + 14)(x² - 10x + 89)
Expanding the expression, we get
x⁴ - 67x² + 1450x - 4984 = 0
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Tom went to his car in the morning and saw that a car or truck had bumped into it during the night, causing a lot of damage. What is the most likely outcome of this situation?
His finance company will reduce his interest.
His insurance company will lower his monthly payments.
His insurance company will pay for damages.
His finance company will increase his interest.
Answer:
His insurance company will pay for damages.
Step-by-step explanation:
An insurance is a form of contract that permits an individual to transfer the responsibilities of a financial loss to an insurance company. The company bears the risk of the financial loss. Small amount of money are collected from their clients and summed together to pay for losses that the client may encounter in the future. Insurance safeguards an individual and his property from losses, misfortune, hazards or theft. Covered losses are paid for by the insurance company thereby reducing the financial costs for the individual. Examples include auto insurance , health insurance, disability insurance, and life insurance.
graph and solve the system
3x+6y-12= 0
x + 2y = 8
Martin drives to work at a speed of 45 miles per hour. It takes him about 2 hours and 15 minutes to get to work. If gas costs $2.75 per gallon and Martin’s car gets 25 miles per gallon, about how much does Martin spend on gas to get to work?
2.25 * 45 = 101.25 miles to work
101.25 / 25 = 4.05 gallons of gas
4.05 * 2.75 = $11.14 total cost of gas
Find a formula for the sum of the first n even positive integers.
b.prove the formula that you conjectured in part (a)
(a) The formula for the sum of the first n even positive integers is n(n+1) and (b) the formula has been proved with an example.
What is an arithmetic progression?Arithmetic progression is the sequence of numbers that has a fixed common difference between any two consecutive numbers.
For the given situation,
Part (a):
The sum of even numbers formula is obtained by using the sum of terms in an arithmetic progression formula.
Sum of Even Numbers Formula = n(n+1),
where n is the number of terms in the series.
Part (b):
Let us consider the even positive numbers,
2,4,6,8,10,.......
Now take first 5 positive numbers 2,4,6,8,10
By using the formula, n=5
Sum of n even positive integers = [tex]n(n+1)[/tex]
⇒ [tex]5(5+1)[/tex]
⇒ [tex]5(6)[/tex]
⇒ [tex]30[/tex].
Now add the first 5 positive numbers without the formula,
⇒ [tex]2+4+6+8+10=30[/tex]
Hence we can conclude, that the formula for the sum of the first n even positive integers is n(n+1) and the formula has been proved with an example.
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The formula for the sum of the first n even positive integers is S = n(n+1). This was derived by recognizing the pattern of the series and using the formula for the sum of an arithmetic series. The proof by induction confirms the validity of our formula.
Explanation:The problem asks us to find and prove a formula for the sum of the first n even positive integers. To find the formula, we recognize that the first n even integers can be represented as 2, 4, 6, ..., 2n. Hence, the sum S of the first n even integers can be written as S = 2 + 4 + 6 + ... + 2n. This is an arithmetic series with the first term a = 2 and the common difference d = 2. The sum of an arithmetic series can be given by the formula S = n/2 [2a + (n-1)d], substituting a = 2 and d = 2, we get S = n/2 [2*2 + (n-1)2] = n[2 + 2(n-1)], which simplifies to S = n(n+1).
To prove this formula, we use induction. For n=1, the sum is 2, which matches our formula 1(1+1) = 2. Assuming the formula holds for n = k, for n = k+1, the sum would include one more term, 2(k+1), so the new sum is S + 2(k+1) which upon simplification, verifies our formula for all n.
If it takes Ashley 3 seconds to run from the batters box to first base at an average speed of 6.5 m/sec, what is the distance that she covers in that time?
The height of a rocket a given number of seconds after it is released is modeled by h (t) = 6t2 + 32t + 10. What does t represent?
Answer: t represents the the number of seconds after rocket is released.
Step-by-step explanation:
Given: The height of a rocket a given number of seconds after it is released is modeled by [tex]h (t) = 6t^2 + 32t + 10[/tex].
Here h (height) is the dependent variable , which depends on the number of seconds after rocket is released (independent variable).
Since the independent variable in the function is t, then t must represents the the number of seconds after rocket is released.
The variable t represents the number of seconds that have passed since the rocket was released.
How to identify what a variable represents?Here we know that the height of a rocket a given number of seconds after it is released is modeled by:
h(t) = 6*t^2 + 32*t + 10
So this is a function that relates height with time in seconds, we know that the function models the height, so we must have that:
[h(t)] is equivalent to height.
This means that the other variable, t, must be related to time in seconds.
Then we can conclude that the variable t represents the number of seconds after the rocket has been released.
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What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? 20.6 units 22.7 units 25.6 units 27.6 units
we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have a triangle
so
the polygon has three sides
Let
[tex]A(-5,4)\\B(1,4)\\C(3,-4)[/tex]
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AB
[tex]A(-5,4)\\B(1,4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(4-4)^{2}+(1+5)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAB=6\ units[/tex]
Step 2
Find the distance BC
[tex]B(1,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3-1)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{68}[/tex]
[tex]dBC=8.25\ units[/tex]
Step 3
Find the distance AC
[tex]A(-5,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3+5)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{128}[/tex]
[tex]dAC=11.31\ units[/tex]
Step 4
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
substitutes the values
[tex]P=6+8.25+11.31=25.56\ units=25.6\ units[/tex]
therefore
the answer is
[tex]25.6\ units[/tex]
At a charity bike rally, 2/3 of the student population of Heartsworth Middle School participated. If there are 1,200 students in Heartsworth, how many participated?
800 students participated at a charity bike rally
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
It is given that :
there are 1200 students population of Heartsworth Middle School.
and, 2/3 of the student participated in a charity bike rally That is :
(2 x 1200)/ 3 = 2400/3 = 800 students
Therefore, 800 students participated at a charity bike rally.
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prove that x-s-t is a factor of x^3 - s^3 -t^3 -3st(s+t)
To prove that (x-s-t) is a factor of the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we applied the factor theorem which states that (x-c) will be a factor of a polynomial if f(c) equals zero. By substituting x with (s+t) into the polynomial, we got a value of zero, confirming that (x-s-t) is indeed a factor.
Explanation:To prove that (x-s-t) is a factor of $x^3 - s^3 -t^3 -3st(s+t)$, we can use the factor theorem. According to the factor theorem, a polynomial f(x) has a factor (x-c) if and only if f(c) equals zero.
Given the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we substitute (x = s + t) into the polynomial, thus:
$f(s + t) = (s + t)^3 -s^3 -t^3 - 3st(s + t)$.
After simplifying the equation, we obtain:
$s^3 + 3s^2t +3st^2 + t^3 - s^3 - t^3 - 3st^2 - 3s^2t$.
When we cancel out the like terms, the result is 0. Therefore,
$(x - s - t)$ is a factor of the given polynomial $x^3 - s^3 -t^3 -3st(s+t)$. This proves our result according to the Factor theorem.
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89.87 is 215% of what number
89.87 is 215% of approximately 41.8. This is found by converting 215% to a decimal (2.15) and dividing the given number (89.87) by this decimal.
Explanation:
The student's question relates to an application of percentages. To work out this problem, we must first understand that in this context, 215% is equivalent to 2.15 when transformed into a decimal. We then divide the given number, 89.87, by 2.15 to find the original value. The calculation would be as follows: 89.87 ÷ 2.15, which equates to approximately 41.8. Therefore, 89.87 is 215% of the number 41.8.
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: A bookstore owner is conducting market research to forecast sales for the coming year. The bookstore is open 360 days a year and out of the 1,200 people who pass the store each day, 8% of them enter the store and make a purchase. The average amount of each sale is $18. What is the estimated amount of sales for the coming year?
Answer:
622,080
Step-by-step explanation:
thanks me later
which overlapping triangles are congruent by ASa
What is h(10) equal to?
the total cost of a bus ride and a ferry ride is $8.00. in one month, bus fare will increase by 10% and ferry fare will increase by 25%. the total cost will then be 9.25. how much is the current bus fare?
On a particular road map 1/2 inch represents 18 miles about how many miles apart are 2 towns that are 21/2 inches apart on this map
PLEASE HELP ME :( I DONT UNDERSTAND! A teacher already had a certain number of canned goods for the food drive. Each day of the food drive, the class plans to bring in 10 cans. The total number of canned goods for 10 is 205. Assume the relationship is linear. Find and interpret the rate if change and the initial value.
Ricardo is constructing a line through point P that is perpendicular to line m. He has already constructed the arc shown.
He places his compass on point X to construct an arc.
What must be true about the width of the compass opening when Ricardo draws the arc?
It must be less than 1/2XY.
It must be equal to XY .
It must be equal to PX .
It must be greater than 12XY.
Answer:
It must be greater than 1/2XY.
Step-by-step explanation:
We draw an arc from point X below the arc that passes through X and Y. Keeping our compass the same width, we will draw another arc from point Y below, intersecting the first arc.
If the width of the compass is not set to more than 1/2XY, then the two arcs will not intersect and we will not complete our construction.
Perpendicular lines are lines that meet at 90 degrees.
The true statement about the width of the compass is that: (d) It must be greater than 1/2XY.
From the question, we understand that he has drawn arc XY already.
The next step is to draw an arc less than the width of XY, but greater than half width XY.
This will ensure that the arcs bisect one another.
Hence, the true option is (d).
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1. What is the area of a parallelogram whose vertices are A(−1, 12) , B(13, 12) , C(2, −5) , and D(−12, −5) ?
2.
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.
Which combination of loaves of bread and batches of muffins could Helena bake?
Answer:
Helen can make 2 loaves of bread and 4 batches of muffins.
Step-by-step explanation:
Let x be the number of loaves of bread
Let y be the number of batches of muffins
As per the given requirement of flour, the equation becomes:
[tex]3.5x+2.5y=17[/tex] .......(1)
As per the given requirement of sugar, the equation becomes:
[tex]0.75x+0.75y=4.5[/tex] .....(2)
Multiplying equation (1) with 0.3 and subtracting (2) from (1)
[tex]1.05x+0.75y=5.1[/tex] now subtracting (2) from this we get
=> [tex]0.3x=0.6[/tex]
So, x = 2
And as [tex]3.5x+2.5y=17[/tex] ; so substituting x = 2 here we get
[tex]3.5(2)+2.5y=17[/tex]
[tex]7+2.5y=17[/tex]
[tex]2.5y=17-7[/tex]
[tex]2.5y=10[/tex]
So, y = 4
Hence, there will be 2 loaves of bread and 4 batches of muffins.
What is m∠JNM?
Enter your answer in the box.
°
we know that
Vertical angles are a pair of opposite and congruent angles formed by intersecting lines
In this problem
m∠JNM=m∠KNL -------> by vertical angles
so
[tex](4x+6)\°=(7x-21)\°[/tex]
Solve for x
[tex]7x-4x=6+21\\3x=27\\x=9\°[/tex]
Find the value of m∠JNM
m∠JNM=[tex](4x+6)\°[/tex]
substitute the value of x
m∠JNM=[tex](4*9+6)\°[/tex]
m∠JNM=[tex]42\°[/tex]
therefore
the answer is
m∠JNM=[tex]42\°[/tex]
A club with 15 women and 12 men need to form a committee that consists of a president, a vice president, a secretary, and a treasurer. how many committees are possible…
a. if the committee must have two women and two men?
PLEASE HELP ASAP: A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t = 0 sec is 1 meter right of zero, that is, s(0) = 1.
The average velocity over the interval 0 to 8 seconds
The instantaneous velocity and speed at time 5 secs
The time interval(s) when the particle is moving right
The time interval(s) when the particle is
going faster
slowing down
Find the total distance the particle has traveled between 0 and 8 seconds
Answer:
1) Average velocity = 10/3 m/s
2) Instantaneous velocity = -2 m/s
Speed = 2 m/s to the left
3) (0, 3) ∪ (6, 8]
4) Going faster: (3, 4.5) ∪ (6, 8]
Slowing down: (0, 3) ∪ (4.5, 6)
5) Total distance = 35.67 m (nearest hundredth)
Step-by-step explanation:
The relationships between position (displacement), velocity and acceleration are:
[tex]\boxed{\boxed{\begin{array}{c}\textbf{POSITION (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]
Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its position s(t) we can integrate v(t):
[tex]\begin{aligned}\displaystyle s(t)=\int v(t)\;\text{d}t&=\int(t^2-9t+18)\;\text{d}t\\\\&=\dfrac{t^{2+1}}{2+1}-\dfrac{9t^{1+1}}{1+1}+18t+C\\\\&=\dfrac{t^{3}}{3}-\dfrac{9t^{2}}{2}+18t+C\end{aligned}[/tex]
As s(0) = 1, then:
[tex]\begin{aligned}s(0)=\dfrac{(0)^{3}}{3}-\dfrac{9(0)^{2}}{2}+18(0)+C&=1\\0-0+0+C&=1\\C&=1\end{aligned}[/tex]
Therefore, the position function s(t) is:
[tex]\large\boxed{s(t)=\dfrac{t^3}{3}-\dfrac{9t^2}{2}+18t+1}[/tex]
Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its acceleration a(t) we can differentiate v(t):
[tex]\begin{aligned}a(t)=\dfrac{\text{d}}{\text{d}t}[v(t)]&=2\cdot t^{2-1}-1\cdot9t^{1-1}+0\\&=2t-9\end{aligned}[/tex]
Therefore, the acceleration function a(t) is:
[tex]\large\boxed{a(t)=2t-9}[/tex]
[tex]\hrulefill[/tex]
Question 1To find the average velocity over the interval [0, 8], use the formula:
[tex]\textsf{Average Velocity}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]
In this case:
t₁ = 0t₂ = 8Calculate the position at t₁ and t₂ by substituting t = 0 and t = 8 into s(t):
[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1}=1[/tex]
[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1}=\dfrac{83}{3}[/tex]
Therefore:
[tex]\textsf{Average Velocity}=\dfrac{s(8)-s(0)}{8-0}=\dfrac{\frac{83}{3}-1}{8}=\dfrac{10}{3}\; \sf m/s[/tex]
Therefore, the average velocity is 10/3 m/s.
[tex]\hrulefill[/tex]
Question 2To find the instantaneous velocity at t = 5 seconds, substitute t = 5 into v(t):
[tex]\begin{aligned}v(5)&=(5)^2-9(5)+18\\&=25-45+18\\&=-2\end{aligned}[/tex]
So, the instantaneous velocity at t = 5 seconds is -2 m/s.
Speed is a scalar quantity that measures how fast an object is moving regardless of its direction. Therefore, speed is the magnitude of velocity:
[tex]\textsf{Speed}=|v(5)|=|-2|=2\;\sf m/s[/tex]
Therefore, the speed at t = 5 is 2 m/s to the left.
[tex]\hrulefill[/tex]
Question 2The particle changes direction when v(t) = 0.
[tex]\begin{aligned}v(t)&=0\\\implies t^2-9t+18&=0\\t^2-6t-3t+18&=0\\t(t-6)-3(t-6)&=0\\(t-3)(t-6)&=0\\\\t-3&=0\implies t=3\\t-6&=0\implies t=6\end{aligned}[/tex]
Therefore, the particle changes direction at t = 3 and t = 6.
We know that the position of the particle at t = 0 is 1 meter right of zero. Therefore:
It is moving to the right in the interval (0, 3).It is moving to the left in the interval (3, 6).It is moving to the right in the interval (6, 8].Therefore, the time intervals between 0 ≤ t ≤ 8 when the particle is moving right is:
(0, 3) ∪ (6, 8][tex]\hrulefill[/tex]
Question 4When a(t) > 0:
[tex]\begin{aligned}a(t)& > 0\\2t-9& > 0\\2t& > 9\\t& > \dfrac{9}{2}\\t& > 4.5\; \sf s\end{aligned}[/tex]
When a(t) < 0:
[tex]\begin{aligned}a(t)& < 0\\2t-9& < 0\\2t& < 9\\t& < \dfrac{9}{2}\\t& < 4.5\; \sf s\end{aligned}[/tex]
Therefore:
Velocity is positive in the interval (0, 3) and (6, 8].Velocity is negative in the interval (3, 6).Acceleration is positive in the interval (4.5, 8].Acceleration is negative in the interval (0, 4.5).(Refer to the attachment).
If velocity and acceleration have the same sign, it means the object is speeding up.
If velocity and acceleration have opposite signs, it means the object is slowing down.
Therefore, the time intervals when the particle is going faster and slowing down are:
Going faster: (3, 4.5) ∪ (6, 8]Slowing down: (0, 3) ∪ (4.5, 6)[tex]\hrulefill[/tex]
Question 5To find the total distance the particle has traveled between 0 and 8 seconds, we need to consider the distance traveled between the intervals when it changes direction.
To do this, find the position of the particle at t = 0, t = 3, t = 6 and t = 8.
[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1=1[/tex]
[tex]s(3)=\dfrac{(3)^3}{3}-\dfrac{9(3)^2}{2}+18(3)+1=23.5[/tex]
[tex]s(6)=\dfrac{(6)^3}{3}-\dfrac{9(6)^2}{2}+18(6)+1=19[/tex]
[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1=\dfrac{83}{3}\approx27.67[/tex]
Therefore, in the interval 0 ≤ t < 3, the particle travels:
[tex]|s(3)-s(0)|=|23.5-1|=22.5\; \sf meters\;(to\;the\;right)[/tex]
In the interval 3 < t < 6, it travels:
[tex]|s(6)-s(3)|=|19-23.5|=4.5\; \sf meters\;(to\;the\;left)[/tex]
In the interval 6 < t ≤ 8, it travels:
[tex]|s(8)-s(6)|=|27.67-19|=8.67\; \sf meters\;(to\;the\;right)[/tex]
So the total distance the particle has traveled between 0 and 8 seconds is:
[tex]\textsf{Total distance}=22.5+4.5+8.67=35.67\; \sf meters[/tex]
A scuba diver descends at a rate of 40 feet per minute. How many feet will the scuba diver move in 2 minutes?
What is the Solution of the following system?
{-3x -2y = -12
{9x + 6y= -9
Imagine those two bracket things are one big one connecting both equations, and the answers are A (2,1) B No Solutions C (-2, -1) D Infinitely Many Solutions
@Emma11234
(Fill in the blank )
Zero pairs are two numbers that ______ to get zero.
A. Subtract
B. Add
C. Divide
D. Multiply
Which set of statements always have the same truth value
A) Conditional and Converse
B) Conditional and Inverse
C) Inverse and Contrapositive
D) Conditional and Contrapositive
The set of statements always have the same truth value will be Conditional and Contrapositive i.e. Option [tex](D)[/tex] .
What is Conditional and Contrapositive?
Conditional and Contrapositive : If the conditional statement is “If P then Q.” Then converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.”
So,
As per given options,
Option [tex](B)[/tex] and [tex](C)[/tex] have inverse, so they have nothing to do with inverse.
Now,
So, according to the above mentioned definition,
Option [tex](D)[/tex] Conditional and Contrapositive is the correct option.
Hence, we can say that the set of statements always have the same truth value will be Conditional and Contrapositive Option [tex](D)[/tex] .
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Kesia knows that 1/4=0.25. Explain how she could use this fact to determine the decimal equivalent of 5/8
Answer:
0.625
Step-by-step explanation:
We are given that
Kesia knows =[tex]\frac{1}{4}=0.25[/tex]
We have to determine the decimal equivalent to [tex]\frac{5}{8}[/tex] using given decimal value.
[tex]\frac{5}{8}[/tex] can be written as
[tex]\frac{5}{8}=\frac{2}{8}+\frac{2}{8}+\frac{\frac{1}{4}}{2}[/tex]
[tex]\frac{5}{8}=\frac{1}{4}+\frac{1}{4}+\frac{\frac{1}{4}}{2}[/tex]
[tex]\frac{5}{8}=0.25+0.25+\frac{0.25}{2}[/tex]
[tex]\frac{5}{8}=0.50+\frac{0.25}{2}[/tex]
[tex]\frac{5}{8}=0.625[/tex]
Hence,[tex]\frac{5}{8}=0.625/tex]
Write the equation in the slope-intercept form. 7x − 4y + 8 = 0
Final answer:
To convert the equation 7x - 4y + 8 = 0 to slope-intercept form, solve for y to get y = (7/4)x + 2, with a slope of 7/4 and a y-intercept of 2.
Explanation:
To write the equation 7x − 4y + 8 = 0 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we want to solve for y. The steps are as follows:
Subtract 7x and 8 from both sides of the equation to isolate terms involving y: -4y = -7x - 8.Divide every term by -4 to solve for y: y = (7/4)x + 2.Thus, the equation of the line in slope-intercept form is y = (7/4)x + 2. Here, the slope is 7/4 and the y-intercept is 2.