(15 points)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the leg of each isosceles right triangle when the hypotenuse is of the given measure.
Given = 5√6
Answers
Answer:
Each of the legs of isosceles right triangle is 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Watch the attached figure for the isosceles right angled triangle
Looking at the figure we see that AB=5√6 and BC=CA
According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.
1) Applying the Pythagorean theorem to the isosceles right triangle, we have
[tex]BC^{2} + CA^{2} = AB^{2}[/tex]
2) Let BC=a and CA=a as they both are equal
So,
[tex]a^{2} + a^{2} = (5\sqrt{6} )^{2}[/tex]
=> [tex]2a^{2} = (5\sqrt{6} )(5\sqrt{6} )[/tex]
=> [tex]2a^{2} = 5*5*\sqrt{6}*\sqrt{6}[/tex]
=> [tex]2a^{2} = 25*6[/tex] (since √6*√6 = (√6)²= 6)
=> [tex]2a^{2} = 150[/tex]
3) Dividing both sides by 2, we get
[tex]\frac{2a^{2} }{2} =\frac{150}{2}[/tex]
4) Cancelling out the 2's on the left, we get
[tex]a^{2}[/tex] = 75
5) Taking the square root on both sides, we have
[tex]\sqrt{a^{2}} = \sqrt{75}[/tex]
=> a = 5[tex]\sqrt{3}[/tex]
So,
Each of the legs of isosceles right triangle is 5[tex]\sqrt{3}[/tex]
Answer:
Hi :) if you're coming from heritage and/or your answer needs a 2 in it, it would be 6 sqrt 2
Step-by-step explanation:
Related Questions
Which of the following is a trinomial with a constant term?
A. x3 + 12x2 + x
B. y - 426
C. -x + 42
D. x + 7y + 6
E. x7 - 6
F. y13
Answers
Choice A is a trinomial, but it doesn't have a constant term
Choice D is the only other trinomial. This has a constant term, which is 6. The constant is the term without any variables attached to it.
Answer: Choice D
Answer: D. [tex]x+7y+6[/tex]
Step-by-step explanation:
We know that a trinomial is a polynomial with three terms.
From all the given options, only option A. [tex]x^3+12x^2+x[/tex] and option D. [tex]x+7y+6[/tex] are trinomials having three terms .
But option A [tex]x^3+12x^2+x[/tex] does not have any constant term .
On the other hand option D. [tex]x+7y+6[/tex] has a constant term of 6.
Therefore, the option D. [tex]x+7y+6[/tex] represents a trinomial with a constant term.
You are in charge of buying the hamburgers and chicken for a party. The hamburgers cost $2 per pound and the chicken is $3 per pound, You have $60 to spend.
Answers
You can buy 15 hamburgers, and 10 chickens if you spend $30 on each.
$30 divided by $2 = 15 Hamburgers
$30 divides by $3 = 10 Chickens
30 + 30 = 60
(Please mark as Brainliest)
Carlos bought a snowboard for $24.99 and ice skates for $19.19 how much money did he spend all together
Answers
Answer: Carlos would owe in fact (Not including sales taxes) $44.18 (forty-four dollars and eighteen cents)
Step-by-step explanation:
Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?
Answers
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room.
Step-by-step explanation:
10 x 4 = 40$
Samuel earned $6.67 per hour.
Explanation:To calculate how much money Samuel earned per hour, we need to find the total number of hours he spent both mowing the lawn and cleaning his room.
Samuel spent 4 hours mowing the lawn and 2 hours cleaning his room, for a total of 6 hours.
He earned $40 for this time period.
To find how much he earned per hour, we divide the total amount earned by the total number of hours:
$40 divided by 6 hours = $6.67 per hour.
Therefore, Samuel earned $6.67 per hour.
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A survey of households revealed that 38% have a dog, 47% have a cat, and 15% have both a cat and a dog.
Given that a household owns a dog, what is the probability that it also owns a cat?
P(cat│dog)=
Since P(cat│dog)=39.47% and P(cat)=47%, are the events independent or not independent?
What is the probability of a household owning a cat or a dog?
P(cat or dog)=
Answers
Answer:
I) P(cat│dog) = [tex]\frac{0.15}{0.38}[/tex]
II) These events are not independent
III) P(cat or dog)= 0.7
Step-by-step explanation:
Given : Households have dogs = 38%
So, P(dog) = 0.38
Households have cats = 47%
So, P(cats) = 0.47
Households have both dogs and cats = 15%
So, P(both dog and cat ) = [tex]P(cat\cap dog)[/tex] = 0.15
solution :
i) By formula P(A│B) =[tex]\frac{P(A\cap B)}{P(B)}[/tex]
P(cat│dog)= [tex]\frac{P(cat\cap dog)}{P(dog)}[/tex]
P(cat│dog) = [tex]\frac{0.15}{0.38}[/tex]
ii) P(cat│dog)=39.47% = 0.39 and P(cat)=47% = 0.47, are the events not independent
Because condition for independent events in conditional probability is P(A|B)=P(A)
but P(cat│dog) ≠P(cat) i.e. 0.39≠0.47
So, these events are not independent
iii) P(cat or dog) = ?
"or" means union
Formula : [tex]P(A\cup B)= P(A) + P(B)-P(A\cap B)[/tex]
P(cat or dog) = [tex]P(cat\cup dog)= P(cat) + P(dog)-P(cat\cap dog)[/tex]
P(cat or dog)= 0.47 + 0.38 - 0.15
P(cat or dog)= 0.7
Answer:
Step-by-step explanation:
Cats are better (sorry, I just had to say it.)
Algebra 1 A Semester Exam
30. Write y=-3/4x-6 in standard form using integers. (1 point)
Answers
3x+4y= -24
Final answer:
To convert y = -3/4x - 6 to standard form with integers, multiply by 4 to remove the fraction and then arrange the equation as 3x + 4y = -24.
Explanation:
To write the equation y = -3/4x - 6 in standard form using integers, we need to rearrange the terms so that the x and y terms are on the left side of the equation and the constant is on the right side. Moreover, in standard form, the coefficients should be integers. The standard form is typically expressed as Ax + By = C.
Starting with the given equation:
y = -3/4x - 6
Multiply each term by 4 to remove the fraction:
4y = -3x - 24
Now, we need to move the x term to the left side of the equation:
3x + 4y = -24
This is the standard form of the equation, and all the coefficients are integers.
PLEASE HELP ME
27
What is the exact solution to the equation
e^3x+5=9 ?
x=3/5+in9
x=3/ln9−5
x=5+ln9/3
x=ln9−5/3
Answers
Answer:
[tex]x=\frac{-5+ln9}{3}[/tex] which appears to be from the list x=ln9-5/3
Step-by-step explanation:
We take the natural logarithm of both sides as the inverse operation to an exponent on e. This allows us to use log rules to rearrange the problem.
[tex]e^{3x+5}=9\\lne^{3x+5}=ln9 \\(3x+5)lne=ln9[/tex]
We know that as inverse operations, ln e =1.
[tex](3x+5)(1)=ln9\\3x+5=ln9\\3x=-5+ln9\\\frac{3x}{3}=\frac{-5+ln9}{3}[/tex]
[tex]x=\frac{-5+ln9}{3}[/tex]
Answer:
x = (ln (9)-5) /3
Step-by-step explanation:
e^3x+5=9
First we subtract 5 from each side
e^3x+5-5=9-5
e^3x=(9-5)
Then we take the natural log of each side
ln(e^3x) = ln(9-5)
3x = ln (9-5)
Then we divide by 3 on each side
3x/3 = ln (9-5) /3
x = ln (9-5) /3
PLEASE HELP ASAP 25 POINTS
Answers
Answer:
the answer is d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
To see if it is a solution substitute x in and see if it works for y
a. y>= x +2
-4 >= -2+2
-y> = 0 No
b y <= x+2
-4<=-2+2
-4 <0 True
keep going
y<= x-3
-4 <= -2-3
-4<=-5
No
c y> x+2
-4 >-2+2
-4 > 0
True
y< x-3
-4 <-2-3
-4 <-5
NO
d y <= x+2
-4 <= -2+2
-4<=0
True
-4 >= -2-3
-4>=-5
This is the solution
which of the following names a diameter of circle A?
Answers
Answer:
BC
Step-by-step explanation:
The diameter is the distance across the circle, going through the center
BC or CB is the diameter
Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 dollar bill. How much change should kelly get in return?
Answers
To get this answer, start by adding 16.79 and 28.49. The answer you should get is 45.28. Next, subtract 45.28 from 50 and your total should be 6.72. Hope this helped!
Use your knowledge of insulators and conductors to explain why
cooking pots are usually made of metal with some sort of plastic
handle
Answers
Cooking pots are made of metal because metals are good conductors of heat. Plastic is an insulator that is slow at conducting heat. That is why an insulator is used so that we don't burn ourselves.
The cooking pots are good conductor of electricity and sort of plastic
handle are insulator for safety purpose.
Conductors are materials that permit electrons to flow freely from particle to particle. Conductors allow for charge transfer through the free movement of electrons. Conductors are good conduction of electricity.Insulators are materials that does not allow the free flow of electrons from atom to atom and molecule to molecule.Insulator are bad conductor of electricity.Learn more:
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The price of an item has been reduced by 85% . The original price was 20 . What is the price of the item now?
Answers
Reduced by 85%,
So, 100-85 = 15% of 20,
[tex] \frac{15}{100} \times 20 \\ = \frac{15}{5} \\ = 3[/tex]
Prove of item is now 3.
!! Hope It Helps !!
Final answer:
The new price of the item is $3 after the 85% reduction from the original price of $20.
Explanation:
To find the new price of the item after an 85% reduction, we start with the original price and calculate 85% of that price to know how much is being subtracted. The original price is $20. Now let's calculate 85% of 20 dollars:
0.85 (85%) × $20 = $17
This means an $17 reduction from the original price. We subtract this from the original price to find the new price:
$20 - $17 = $3
The new price of the item is $3 after a reduction of 85%.
Enter the equations of the asymptotes for the function
Answers
Answer:
x = 7 and y = 2
Step-by-step explanation:
the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote
solve x - 7 = 0 ⇒ x = 7 is the asymptote
horizontal asymptotes occur as
[tex]lim( x → ± ∞), f(x) → c ( where c is a constant )
divide terms on numerator/ denominator by x
f(x) = (3/x/x/x -7/x ) + 2
as x → ± ∞, f(x) → 0 / 1 - 0 + 2 = 2
y = 2 is the asymptote
Answer: Vertical asymptote is x = 7
Horizontal asymptote is y = 2
Step-by-step explanation:
The vertical asymptote is the restriction on the domain (x-value). Since the denominator cannot be zero ⇒ x - 7 ≠ 0 ⇒ x ≠ 7 so the vertical asymptote is at x = 7.
The horizontal asymptote (H.A.) is the restriction on the range (y-value). There are three rules that determine the horizontal value which compare the degree of the numerator (n) with the degree of the denominator (m):
If n > m , then there is no H.A. (use long division to find the slant asymptote) If n = m , then the H.A. is the coefficient of n ÷ coefficient of mIf n < m, then the H.A. is y = 0In the given problem, n = 0 and m = 1 ⇒ n < m ⇒ H.A. is y = 0
Since there is a vertical shift of +2 units, the H.A. is y = 0 + 2 ⇒ y = 2
Simplify. -6i(5+3i) Enter your answer in standard form, in the box
Answers
Answer:
Pretty sure the answer is 18-30i
Step-by-step explanation:
-30i - 18i^2
-30i - 18 x (-1)
-30i +18
The expression -6i(5+3i) simplifies to 18 - 30i in standard form of a complex number.
Explanation:The problem asks us to simplify the expression -6i(5+3i). To simplify this, we multiply the complex number (-6i) with the complex number in the parenthesis. This results in (-6i * 5) + (-6i * 3i) which transforms into -30i - 18i^2. Since i^2 is -1, we can simplify further to -30i + 18. So the simplified form in standard form is 18 - 30i.
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People need to develop a financial plan to accomplish their retirement goals. True False
Answers
Answer:
True
Step-by-step explanation:
The reason I say this is because of the fact you can't go into retirement without knowing how much your going to get. You need to create a financial plan stating how much you will get and how much you have saved prior to this occurence.
Hope This Helps :)
Answer: True
Step-by-step explanation: People need to develop a plan to overcome the effects of taxation, inflation, and purchasing power risk. In addition, people need to coordinate their company benefits with a personalized financial plan. Because there are many complexities in dealing with the stock market and real estate, you need to have a properly constructed financial plan.
given : MN is an angle bisector of (angle)JMK
prove : m(angle)JMN=1/2m(angle)JMK
(i need all the reasons)
Answers
If the line MN is the angle bisector of ΔJMK, then it creates two angles of equal measure. Hence, m∠JMN is half of m∠JMK due to the property of an angle bisector.
Explanation:In the field of geometry, an angle bisector is a line or ray that divides an angle into two equal angles. This is given by the information provided that MN is an angle bisector of ΔJMK.
By definition, if MN is an angle bisector of ΔJMK, then it creates two angles, ∠JMN and ∠NMK, that are equal in measure. So, we have m∠JMN = m∠NMK. This is the definition of an angle bisector, which is the reason you are looking for.
Given this, if you want to find m∠JMN in terms of ∠JMK, keep in mind that MN bisects ∠JMK, creating the two equal angles we just mentioned. Therefore, m∠JMK = m∠JMN + m∠NMK. Since ∠JMN and ∠NMK are equal, m∠JMK = 2m∠JMN. Hence, m∠JMN = 1/2m∠JMK. This would be a consequence of the angle bisector property.
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It's 1:00 p.M. And I've driven 120 miles. At 3:00 p.M. I will have driven 208 miles. What is my speed?
Answers
From 1 pm to 3 pm is 2 hours.
208 miles - 120 mile = 88 miles
You drove 88 miles in 2 hours.
Speed = miles driven / time driven:
88 / 2 = 44 miles per hour
Answer:
44 miles/hour
Step-by-step explanation: since speed = distance/time
= 88miles/2hours
=44miles/hour
At the holiday valley ski resort, skis cost $16 to rent and snowboards cost $19. If 28 people rented on a certain day and the resort brought in $478, how many skis and snowboards were rented?
Answers
Answer:
[tex]18[/tex] skis and [tex]10[/tex] snowboards were rented.
Step-by-step explanation:
Let the number of skis rented be [tex]x[/tex] and the number of snowboards rented be [tex]y[/tex].
If a total of [tex]28[/tex] people rented on a certain day, then the total number of skis and snowboards rented that particular day is also [tex]28[/tex].
This gives us the equation
[tex]x+y=28...eqn(1)[/tex].
If skis cost $ [tex]16[/tex], then [tex]x[/tex] number of skis cost $ [tex]16x[/tex].
If snowboards cost $ [tex]19[/tex], then [tex]y[/tex] number of snowboards cost $ [tex]19y[/tex].
The total cost will give us another equation,
[tex]16x+19y=478...eqn(2)[/tex]
From equation (1),
[tex]y=28-x...eqn(3)[/tex].
We put equation (3) into equation (2) to get,
[tex]16x+19(28-x)=478[/tex]
We expand the brackets to obtain,
[tex]16x+532-19x=478[/tex]
We group like terms to get,
[tex]16x-19x=478-532[/tex]
This implies that,
[tex]-3x=-54[/tex]
We divide both sides by [tex]-3[/tex] to get,
[tex]x=18[/tex]
We put [tex]x=18[/tex] into equation (3) to get,
[tex]y=28-18[/tex]
[tex]y=10[/tex]
Therefore [tex]18[/tex] skis and [tex]10[/tex] snowboards were rented.
To solve this problem, you can set up a system of equations where one equation represents the total number of skis and snowboards rented, and the other represents the total cost of those rentals. By solving this system, you can determine the number of skis and snowboards rented.
Explanation:This problem is a classic example of a system of linear equations. Let's denote the number of skis rented as x and the number of snowboards rented as y. From the problem, we know that:
x + y = 28 (The total number of skis and snowboards rented is 28) 16x + 19y = 478 (The total income from skis and snowboard rentals is $478)
By solving these two equations, we can find the values of x and y which represent the number of skis and snowboards rented respectively.
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Write the linear equation in slope-intercept form: 5x - y = -17
a: y = -5x + 17
b: x = -1/5y - 17/5
c: y = 5x - 17
d: -5x - 17
Answers
In order to express the equation 5x - y = -17 in slope-intercept form (y = mx + b), we need to solve for y. After rearranging, it turns out the correct equation in slope-intercept form is y = 5x + 17.
Explanation:To write the equation 5x - y = -17 in slope-intercept form, we first need to solve the equation for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope, and b represents the y-intercept.
Let's rearrange the given equation: Start by adding 'y' to both sides to get 5x = y - 17. Add 17 to both sides, you will get y = 5x + 17. So, the correct answer is: y = 5x + 17. This aligns with option c.
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Comparing this with the answer choices, the correct option is c: y = 5x - 17.
To write the linear equation 5x - y = -17 in slope-intercept form, you must solve for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange the given equation:
Add y to both sides to isolate the y-variable on one side: 5x - y + y = -17 + y, which simplifies to 5x = y - 17.Now, subtract 17 from both sides to solve for y: y - 17 = 5x - 17.The equation in slope-intercept form is y = 5x - 17.Comparing this with the answer choices, the correct option is c: y = 5x - 17.
An extra large pizza has 12 slices. If there are four people at they table and they each get two slices, how many slices are left?
Answers
Answer:
there should be 4 slices left
Hope This Helped
Step-by-step explanation:
Answer:
The most accurate answer is:
*4*
I hope I helped you!
Step-by-step explanation:
Alright, lets examine the problem; *12* slices of pizza are given. We also have *4* guests at the table, and each are given *2* slices. Lets use subtraction to solve: 12 - 2 - 2 - 2 - 2- the *2*'s equal the amount of pizzas given, and the *12* represents our amount of slices of pizza. We also gave 4 people 2 slices, which is why we have *4* *2*'s
[SOLVE]
12 - 2 - 2 - 2 - 2 = 4
The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
Answers
i will give brainliest to best answer
Answers
Answer: B
Step-by-step explanation:
(x - 6) (x¹⁾²) (x + 3)
= (x¹⁾²) (x² - 3x - 18)
= x⁵⁾² - 3x³⁾² - 18x¹⁾²
= √x⁵ - 3√x³ - 18√x
********************************************
Answer: B
Step-by-step explanation:
[tex]\frac{f(x)}{g(x)} =\frac{(x+1)^{-1}}{x-2} = \frac{1}{(x+1)(x-2)}[/tex]
Since denominator cannot equal zero,
x + 1 ≠ 0 and x - 2 ≠ 0
x ≠ -1 and x ≠ 2
Interval Notation: (-∞, -1) U (-1, 2) U (2, ∞)
Hisaki is making sugar cookies for a bake sale he has 3 1/2 cups of sugar. The recipe calls for 3/4 cup of sugar for one batch of cookies how many total batches of sugar cookies can Hisaki make
Answers
Final answer:
Hisaki can make 4 1/3 batches of sugar cookies with the amount of sugar he has.
Explanation:
To find out how many total batches of sugar cookies Hisaki can make, we need to divide the total amount of sugar he has (3 1/2 cups) by the amount of sugar needed for one batch (3/4 cup).
We can convert the mixed number 3 1/2 into an improper fraction: 3 1/2 = 7/2.
Now, we divide 7/2 by 3/4: (7/2) ÷ (3/4) = (7/2) x (4/3) = 28/6 = 4 2/6 = 4 1/3.
Therefore, Hisaki can make a total of 4 1/3 batches of sugar cookies with the amount of sugar he has.
An ice block is melting so that the length of each side is changing at the rate of 1.5 inches per hour. How fast is the surface area of the ice cube changing at the instant the ice block has a side length of 2 inches?
Answers
Answer:
d SA /dt = 36 in ^2 / hour
Step-by-step explanation:
Surface area of a cube is 6s^2
We need to take the derivative with respect to t
d SA / dt = ds /dt * 12 s
We know ds /dt is 1.5 inches per hour
s = 2 for the particular instant we are looking at
d SA / dt =1.5 * 12 *2
d SA /dt = 36 in ^2 / hour
Answer:
-36 inches^2 per hour
Step-by-step explanation:
PLEASE HELP A store has sales of $500 in their first month. If sales increase at a rate of $10 each month, they can be modeled by this equation:an=500+(k-1)10 Use summation notation to model and evaluate the sales for the first ten years. Explain your steps.
Answers
Answer: 131,400$
Step-by-step explanation:
The sale for first month is $500.
The sale increases by $10 each month, as modelled by the equation:
a_k=500+(k-1)10
where, k = 1 (first month)
k = 2 (second month)
.... and so on.
we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)
Total sales = ∑ a_k
∑ a_k = ∑ (500+(k-1)10)
= 500k + ∑ (10k - 10)
= 500k + 10∑k - 10k
= 490k + 10∑k
= 490k + 10 {k*(k+1)/2}
= 490k + 5{k*(k+1)}
= 490k + 5k^2 + 5k
= 5k^2 + 495k
∴∑ a_k = 5k^2 + 495k
For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)
= 5*(120*120) + 495*120
= 72,000 + 59, 400
= 131,400$
Answer:
Distribute 10 to (k – 1) and simplify.
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used. The upper index is 10*12=120.
The values of the summations are 58,800 + 72,600. So, the total sales is $131,400.
Step-by-step explanation:
An account earns 1.5% interest compounded annually. The balance after 2 years is $8241.80. What is the principal?
Answers
I am not sure what did the problem mean by the principal but I guess It could be the valie invested initially
so,P=$8000
Jack can run a mile in 9, 1/3 minutes. How long will it take for him to run 3, 1/2 miles? What is the answer
Answers
Answer:
32, 2/3 minutes.
Step-by-step explanation:
Divide the original mile time by two to get what half a mile would be. Multiply the original mile time by 3, since he is running 3 miles. Add 4 and 2/3, half of a mile time, to that and you're left with 32 minutes and 40 seconds.
Identify the value of m in the diagram. HELP ASAP!!
Answers
Answer:
3
Step-by-step explanation:
The 'm' value stands for the slope in the context of a linear equation (y = mx + b). In the provided example, it was determined to be 3, i.e., for each unit movement along the x-axis, there will be a three units movement along the y-axis.
Explanation:The
value of m
in your diagram is representative of the slope in a mathematical equation, specifically in the context of a linear equation in the form y = mx + b. Here, 'm' describes how much the line on the graph moves up or down on the y-axis along the line's length. This usually means how much 'y' changes for each one-unit change in 'x'. According to the information provided, assuming that the equation is y = mx + b and b is set to 9, the m value has been determined to be 3. This indicates that for every step you move horizontally (along the x-axis), you would move three steps vertically (along the y-axis). Hence, in this case, the value of 'm' is 3.
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please help me with these please.
Answers
6. Answer: y = 5x - 11
Step-by-step explanation:
Parallel means "same slope". y = 5x - 2 is in the form y = mx + b,
so the slope (m) = 5
Next, input the point (x₁, y₁ = 2, -1) and slope (m = 5) into the Point-Slope formula:
y - y₁ = m(x - x₁)
y - (-1) = 5(x - 2)
y + 1 = 5x - 10
y = 5x - 11
*******************************************************************
7. Answer: [tex]\bold{y = \dfrac{1}{3}x + 4}[/tex]
Step-by-step explanation:
Perpendicular means "opposite reciprocal slope". y = -3x + 7 is in the form y = mx + b, so slope (m) = -3 ⇒ m⊥ = [tex]\frac{1}{3}[/tex]
Next, input the point (x₁, y₁ = 3, 5) and slope (m = [tex]\frac{1}{3}[/tex] ) into the Point-Slope formula:
y - y₁ = m(x - x₁)
[tex]y - 5=\dfrac{1}{3}(x - 3)[/tex]
[tex]y - 5 =\dfrac{1}{3}x - 1[/tex]
[tex]y=\dfrac{1}{3}x + 4[/tex]
Which expression are a factor of 36abc-9bcd+24abc
Answers
3bc ( 20a - 3d )
An expression which factorises 36abc - 9bcd + 24abc is:
3bc ( 20a - 3d )
STEP-BY-STEP EXPLANATION:
= 36abc - 9bcd + 24abc
= 60abc - 9bcd
= 3bc ( 20a - 3d )