Answer:
y = -2/3x + 2
Step-by-step explanation:
Hey there!
Well since we already got the y-intercept to find slope we'll use the points,
(3,0) and (0,2).
Formula: [tex]\frac{y^2 - y^1}{x^2 - x^1}[/tex]
Plug in the given points,
[tex]\frac{2 - 0}{0 - 3}[/tex]
Slope = -2/3
Slope-intercept: y = -2/3x + 2
Hope this helps :)
Answer:
y = -2/3x + 2 or
2x + 3y = 6 (standard form).
Step-by-step explanation:
I am assuming you want the equation of the straight line that passes through these 2 points.
The 2 points are (3, 0 ) and (0, 2).
The slope of the line = (2 - 0) / (0 - 3)
= -2/3.
The equation is y = -2/3x + 2 ( as 2 is the y-intercept).
In standard form this is :
3y = -2x + 6
2x + 3y = 6.
A 6 foot tall man makes a shadow that is $ 3\frac{1}{2} $ feet long. How tall is a building that makes a $ 14\frac{7}{8} $ foot shadow?
the building is twenty feet
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
Petra deposits 278.16 in a savings account that earns 2.1% simple interest. What is Petra’s account balance after nine years
Answer:
The answer is $330.73.
Step-by-step explanation:
The answer is $330.73.
Step 1. Calculate simple interest: I = ?
Step 2. To get account balance add simple interest to the principal amount:
I + P = ?
Step 1. Calculate simple interest.
I = P * r * t
P - principal
r - rate
t - time period
We have:
P = $278.16
r = 2.1% = 2.1/100 = 0.021
t = 9
I = 278.16 * 0.021 * 9 = 52.57
Step 2. To get account balance add simple interest to the principal amount:
I + P = ?
52.57 + 278.16 = 330.73
You are playing monopoly with your friends. You just landed on a site
where your friend owns four houses. The rent for each house is 20 coins.
You have 50 coins. How many coins will you have after paying the total
rent?
Answer:
You wont have any coins left. You will have a negative number of coins because 20 x 4 = 80. 80 - 50 = 30. You will need to owe 30 coins
What is the value of the bisecting angle, x, marked on this square?
The four corners of a square are 90 degrees.
They are evenly split by the diagonal lines, so each corner is now two 45 degree angles.
The lines form triangles, which have 3 angles that need to equal 180 degrees.
Two of the angles are 45, so 45 + 45 = 90 degrees.
X = 180 -90 = 90 degrees.
Answer:
90 degrees
By 90 * 4 is 360
Step-by-step explanation:
For each problem, find the missing value using the Pythagorean Theorem
Answer:
b = √2
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
a = Leg₁
b = Leg₂
c = Hypotenuse
Step 1: Plug in variables
3² + b² = (√11)²
Step 2: Solve
9 + b² = 11
b² = 2
b = √2
And we have our answer!
Please Help. Most helpful answer and explanation would be very appreciated. I don't understand this.......Write each of the following equations in slope-intercept form.
1.) y − 1 = 4x − 4
2.) 3x = 2 − y
Answer:
1.) y = 4x - 3
2.) y = -3x + 2
Step-by-step explanation:
I'm not really sure how to explain it super well, but I do know the answers
Find any real numbers for which the rational expression is undefined. x+8/x-3 select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
x = 3
Step-by-step explanation:
What you wrote, x + 8/x - 3 means [tex] x + \dfrac{8}{x} - 3 [/tex].
I assume you didn't mean that, but instead, you mean
[tex] \dfrac{x + 8}{x - 3} [/tex], so I'll use this expression in the problem.
A fraction cannot have zero in the denominator since division by zero is undefined and not allowed. The denominator of the fraction is x - 3.
We need to find which value of x makes the expression x - 3 have a value of zero. Then that is the value of x that must be excluded from the domain.
We set the denominator equal to zero, and we solve for x.
x - 3 = 0
Add 3 to both sides.
x = 3
A value of 3 used for x makes the denominator equal zero, so the real number for which the expression is undefined is
x = 3.
The entire graph of the function g is shown in the figure below. Write the domain and range of g as intervals or unions of intervals.
Answers:
Domain = [tex][-5, -2] \cup [1,5)[/tex]
Range = [tex](-4,4][/tex]
=============================================
Explanation:
The domain is the set of allowed x value inputs. We note that the left-most point is when x = -5, and this point has a closed or filled in endpoint, so we're including this x value in the domain.
The left piece has its other endpoint at x = -2, so the interval [tex]-5 \le x \le -2[/tex] is part of the domain. We write that as [tex][-5,-2][/tex]is part of the domain's answer. The other part is [tex][1, 5)[/tex]. We include x = 1 but exclude x = 5 as there's a hole here.
Use the union symbol to glue the two intervals together and we end up with [tex][-5, -2] \cup [1,5)[/tex] as the full domain.
----------------------------
The range is the set of possible y values. The lowest point is when y = -4, but we exclude this endpoint since there's an open hole here. The highest point is when y = 4. The range is [tex]-4 < y \le 4[/tex] which we write as [tex](-4, 4][/tex]
Since there are no gaps in the range, we don't use any union symbols here. Any y value between -4 and 4 is possible, other than y = -4 itself.
The third side is described in relation to one of the equal sides, so let x = the length of one of the equal sides. Which equation models the problem? x + x + (5 – 2x) = 23 x + x + (2x – 5) = 23 x + x + (2x + 5) = 23 x + (2x – 5) + (2x – 5) = 23
Answer:
its b
Step-by-step explanation:
tta be just trust me
Answer:
It's B and the length of the third side of the triangle is 9cm.
Step-by-step explanation:
One of the two equal sides S. Both of them 2S. The third side is 2S5. The perimeter is 2S2S5 and that's 23. So 4S5 23, then 4S28, and S7. The third side is 2S5, and that's 9.
How to find x intercept with y=4x+15
Answer:
The x intercept is (-15/4 ,0)
Step-by-step explanation:
To find the x intercept, set y = 0 and solve for x
y = 4x+15
0 = 4x+15
subtract 15 from each side
-15 = 4x+15-15
-15 = 4x
Divide by 4
-15/4 = 4x/4
-15/4 = x
The x intercept is (-15/4 ,0)
1. for the equation 17h+6=40 select the appropriate property of equality to move the constant term to the right side of the equation
Ok so there are two ways to do this kind of pre-algebra.
I'm going to do it the way I learned it, and the way they teach you in schools.
Ok so you want the variables on one side and the constant term (normal numbers) on the other side (of the equation).
So to do that you have to bring the 6 to the right side.
17h=40+6
Except when you move it to the other side you have to change the sign in front of it.
+ → -
- → +
× → ÷
÷ → ×
In this case, there is an addition sign in front of the 6.
So + → - and the final equation is...
17h=40-6
If you want to do it the way they do it in schools, then you have to remove 6 from both sides (so it will still be equal).
17h+6=40
You have to subtract 6 from (17h+6), which would be 17h.
Then you have to subtract 6 from (40), which would be 40+(-6) or 40-6
The final equation is 17h=40-6
Ok so 40-6=34.
So 17h=34
Divide 34 by 17 or divide each side by 17.
h=34/17 or 2
♡ Hope this helped! ♡
❀ 0ranges ❀
Answer:
40-6=34.
So 17h=34
Divide 34 by 17 or divide each side by 17.
Step-by-step explanation:
Hope this helps!
how's yalls day going? 2nd day of school for me and I'm feeling great! stay safe people
I just got my g mail and I went in during the middle of the class
Answer:
hi :)
Step-by-step explanation:
Can someone please proof check it . If I am wrong, please tell me. thank you
Answer:
2b - 2a
Step-by-step explanation:
AB = AO + OB
= - 2a + 2b = 2b - 2a
WILL GIVE BRAINLIEST AND 35 POINTS Solve this system of equations. [tex]\left \{ {{3x+y=-21} \atop {y=4x}} \right.[/tex]
Answer:
[tex](-3,-12)[/tex]
[tex]x=-3, y=-12[/tex]
Step-by-step explanation:
So we have the system:
[tex]3x+y=-21\\y=4x[/tex]
To solve this, we can do some substitution. Substitute the y in the first equation for the 4x in the second:
[tex]3x+y=-21\\3x+(4x)=-21[/tex]
Combine like terms:
[tex]7x=-21[/tex]
Divide both sides by 7. The left side cancels:
[tex](7x)/7=(-21)/7\\x=-3[/tex]
So we determined that x is -3. Now, plug this number back into the second equation:
[tex]y=4x\\y=4(-3)=-12[/tex]
So the solution is:
[tex](-3,-12)[/tex]
Answer:
[tex]\Large \boxed{x=-3 \ } \\ \\ \Large \boxed{y=-12}[/tex]
Step-by-step explanation:
3x + y = -21
y = 4x
Substitue y = 4x in the first equation.
3x + 4x = -21
Combine like terms.
7x = -21
Divide both sides by 7.
x = -3
Let x = -3 for the second equation.
y = 4(-3)
Multiply.
y = -12
The solution for the system of equations is x = -3 and y = -12.
If g(x) = -3x^2 +4x+5 find g(3)
Answer:
-10
Step-by-step explanation:
g(x) = -3x^2 +4x+5
Let x = 3
g(3) = -3*(3)^2 +4*3+5
= -3*9 +12+5
= -27+12+5
= -10
Answer:
g(3) = -10
Step-by-step explanation:
g(x) = -3x^2 + 4x + 5
g(3) = -3(3^2) + 4(3) + 5
g(3) = -3(9) + 12 + 5
g(3) = -27 + 12 + 5
g(3) = -15 + 5
g(3) = -10
how many solution this equation have 3r-5=3r-5
Answer:
infinite solutions
Step-by-step explanation:
Hello!
Since 3r - 5 is on both sides of the equation we can put any number in for r and it would still be true so the answer is infinite solutions
The answer is infinite solutions
Hope this helps!
The point A (2,-3) is reflected onto A' (-3,2). What was the line of reflection?
f(x)=1-3x and g(x)=x+4 calculate f(-1/3)
For f function, we don't need to us the value of g function. So, 1-3x = 1-3.-1/3 =2
Answer : 2
f(-⅓) = 2
Step-by-step-explanation :
[tex]f(x) = 1 - 3x \\ f( \frac{ - 1}{3} ) = 1 - 3( \frac{ - 1}{3} ) \\ f( \frac{ - 1}{3} ) = 1 + \frac{3}{3} = 1 + 1 = 2[/tex]
Evaluate the expression for the given value of the variable(s). 5a + 5b; a = −6, b = −5
Answer:
- 55
Step-by-step explanation:
a = −6, b = −5
5a + 5b = 5 * (a + b) = 5 * (- 6 - 5) =5 * (- 11) = - 55Find −3a2 − b3 + 3c2 − 2b3 if a = 2, b = −1, and c = 3.
Answer:
18
Step-by-step explanation:
-3a² - b³ + 3c² - 2b³
= -3(2)² - (-1)³ + 3(3)² - 2(-1)³
= -3(4) - (-1) + 3(9) - 2(-1)
= (-12 + 1 )+ (27 + 2)
= -11 + 29
= 18
Answer:
18
Step-by-step explanation:
a = 2, b = -1, c = 3
-3a^2 - b^3 + 3c^2 - 2b^3
-3(2^2) - (-1^3) + 3(3^2) - 2(-1^3)
-3(4) - (-1) + 3(9) - 2(-1)
-12 + 1 + 27 + 2
-12 + 30
18 <===
Can someone help me or explain it bc this is rlly hard and this type of Math confuses me...
===========================================================
Explanation:
Parallel lines never cross, so we can rule out choices B, C, and D. These choices all have segments that cross or meet somehow. Segments AB and OC don't intersect, and their extended lines do not appear to intersect either.
---------
We don't really need to use a diagram for this problem even though a diagram is handy. The reason we don't need a diagram is simply look at the letters to see if there's any repeated letters.
For instance, with choice B, the letter O shows up twice. So that must mean the two segments intersect at point O. But we can't have parallel lines intersect, which allows us to rule out choice B. The other answer choices we rule out will follow the same idea.
Only AB and OC have letters that don't show up twice.
Answer:
A) AB and OC
Step-by-step explanation:
Ok, so basically, when two lines are parallel, t means they will never touch each other no matter how long they are
for example, these two l‘s are parallel
l l
in this problem, we just have to find the lines that are parallel
finsing the lines are quite easy, just look for the first letter, in this case, A, then find the other lettter, here it is B, and there is your line!
here all the lines are marked in red, whch makes finsing each line easier
proving our answer is correct...
BO and CO makes an upside down V shape ( like a roof )
CO and CD make a v Shape
and
CD and DO make an upside down L
i hope this helped!
List three ordered pairs that represent solutions to the equation x - y = 5.
Answer:
2x-y=3
Step-by-step explanation:
x & y intercept for 4x+6y=12
Answer:
x- intercept at (3, 0)
y- intercept at (0, 2)
Step-by-step explanation:
x-intercept occurs at y=0.
4x +6y= 12
when y=0,
4x +6(0)= 12
4x= 12
x= 12 ÷4
x= 3
Thus, x-intercept occurs at x=3, at the point (3, 0).
y- intercept occurs at x=0.
4x +6y= 12
when x=0,
4(0) +6y= 12
6y= 12
y= 12 ÷6
y= 2
Thus, y- intercept occurs at the point (0, 2).
Solve for x
Picture is above
Answer:
x = 10
Step-by-step explanation:
a² + b² = c²
6² + 8² = c²
36 + 64 = 100
√100 = ±10
x = 10
Answer:
10
Step-by-step explanation:
We can use the Pythagorean Theorem to find the value of x.
It states that in a right triangle, [tex]a^2 + b^2 = c^2[/tex].
A and b are the sides, while c is the hypotenuse.
We already know the measure of a and b, so we can find the measure of c easily.
[tex]6^2 + 8^2 = c^2\\\\36+64=c^2\\\\100=c^2\\\\10=c[/tex]
Hope this helped!
IF YOU SOLVE I WILL BE YOUR BEST FRIEND I SWEAR. ALSO WILL AWARD THE BRAINLIEST THING. PLEASE. I NEED THESE GRADES SO I WONT BE A DISSAPOINTMENT TO MY MY MOM!
Answer:
see below
Step-by-step explanation:
x⁵ - 8x⁴ + 22x³ - 26x² + 21x - 18 = 0
x = 2, x = ± i, x=3 with multiplicity 2
-----------------------------------------------------
x⁴ - 5x³ + 7x² - 5x + 6 = 0
x = 2, x=3, x = ± i
--------------------------------------------------------
-1 + 4i = 4 + i
i
--------------------------------------------------------
x³ - 26x² + 21x - 18 = 0
x = ± 2i, x = 3/2
--------------------------------------------------------
(1 + i) (-3 - 4i)
= 1 - 7i
--------------------------------------------------------
6.
(-5 + 2i) + (3 - 6i)
= -2 -4i
--------------------------------------------------------
7.
x⁴ + 5x² + 4 = 0
x = ± i , x = ± 2i
--------------------------------------------------------
8.
(7 - i) - (-5 + 6i)
= 12 - 7i
--------------------------------------------------------
9.
(4 - i) (4 + i)
= 17
--------------------------------------------------------
10.
(3 + 8i) (4 - 3i)
= 36 + 23i
*PLEASE HELP, DIFFICULT QUESTION* What is the total volume of snow used to make the snowman if the head is 12 inches wide, the middle is 16 inches wide, and the bottom is 18 inches wide? (Use 3.14 for pie)
Answer:
6103.07 inches ^ 3
Step-by-step explanation:
Step 1: Find the volume of the head
d = 12
r = d/2
r = 6
[tex]=\frac{4}{3} (3.14)6^{3} \\=904.78 inches^{3}[/tex]
Step 2: Find the volume of the body
d = 16
r = d/2
r = 8
[tex]=\frac{4}{3} (3.14)8^{3} \\=2144.66inches^{3}[/tex]
Step 3: Find the volume of the legs
d = 18
r = d/2
r = 9
[tex]=\frac{4}{3} (3.14)9^{3} \\=3053.63 inches^{3}[/tex]
Step 4: Add the volumes together
[tex]904.78 +2144.66+3053.63=Volume[/tex]
[tex]6103.07=Volume[/tex]
Therefore the volume of the snowman is 6103.07 inches ^ 3
Some friends want to see a movie that is showing at two different theaters in town. They plan to share three tubs of popcorn during the movie.
Movie theatre prices. Theatre A: ticket price 14 dollars 50 cents, popcorn 5 dollars 75 cents. Theatre B: ticket price 13 dollars, popcorn 6 dollars 75 cents.
Answer:
Let's call x as the number of friends, now, in Theatre A we have:
Price for x tickets = x*$14.50
price for 3 tubs of popcorn = 3*$5.75 = $17.25
Total price:
Pa(x) = $14.50*x + $17.25
Now, for Theatre B we have:
Price for x tickets = $13*x.
Price for 3 tubs of popcorn: = 3*$6.75 = $20.25
Total price:
Pb(x) = $13*x + $20.25.
Now, we can find the number of friends x in such case that they will pay the same in each theater by:
Pa(x) = Pb(x)
$14.50*x + $17.25 = $13*x + $20.25.
Now we solve this for x:
($14.50 - $13)*x = $20.25 - $17.25 = $3
$1.50*x = $3
x = $3/$1.50 = 2.
Then, if there are 2 friends, they will pay the same in both theatres
If there are more tha 2 friends, the cheaper place will be Theatre B, because the slope is smaller, which means that for each additional ticket the total price will increase less.
find a quadratic polynomial each with the given number as the sum and product of its zeroes respectively
[tex] \sqrt{2} \: \: \: and \ \frac{1 }3[/tex]
Answer:
[tex] \alpha + \beta = \sqrt{2} [/tex]
[tex] \alpha \beta = \frac{1}{3} [/tex]
The quadratic equation is given by
[tex]y = {x}^{2} - ( \alpha + \beta )x + \alpha \beta [/tex]
[tex]y = {x}^{2} -x \sqrt{2} + \frac{1}{3} [/tex]
The ratio of the areas of two similar
parallelograms is 4:9. Find the height of the
bigger one if the smaller is of height 4cm.
Answer: 6 cm
Step-by-step explanation:
Given: The ratio of the areas of two similar parallelograms is 4:9.
To find : The height of the bigger one if the smaller is of height 4 cm.
Let h be the height of the bigger one.
Since the areas of similar figures are proportional to the square of their corresponding sides.
Then, [tex]\dfrac{4^2}{h^2}=\dfrac{4}{9}[/tex]
[tex]\dfrac{16}{h^2}=\dfrac{4}{9}\\\\\Rightarrow\ h^2=\dfrac{9}{4}\times16\\\\\Rightarrow\ h^2=36\\\\\Rightarow\ h= 6\ cm\ \ \ \ \text{[ height cannot be negative.]}[/tex]
Hence, the height of bigger parallelogram = 6 cm
PDF attached below All questions are related to each other
1. The first option is represented by a linear function, ∴ y = 50x + 150. The y intercept here is 150, as the first week is 200 dollars, not the 0th week. 200 - 50 = 150.
Given the domain here is 1 - 6 (6 weeks) we can plug in x as 1,2,3 etc and solve for y, completing the table.
Option A :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 250 | 300 | 350 | 400 | 450 |
And for option b we have an exponential function. 1 + 10% = 1 + 0.1 = 1.1. Therefore we have the function ∴ y = 200( 1.1 )^x-1 that models this situation. Remember that we have " x - 1 " as the exponent rather than x, as the first week begins with 200 dollars, not the 0th week.
That gives us the following table,
Option B :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 220 | 242 | 266.2 | 292.82 | 322.102 |
2. (a) We already calculated the " iterative rules " for each sequence in the first part. For your explanation on that behalf, just include the explanation above. Rule of Option A : y = 50x + 150. Rule of Option B : [tex]y = 200( 1.1 )^{x-1}[/tex].
(b) Let's take an example week and substitute into our equations to help clarify our friend's doubt. Say week 2...
y = 50(2) + 150 = 100 + 150 = 250 ✓
y = 200( 1.1 )^2-1 = 200( 1.1 )^1 = 200( 1.1 ) = 220 ✓
3. (a) A function is an equation that represents the relation between x and y, which is exactly the purpose of the rules y = 50x + 150, and y = 200( 1.1 )^x-1.
(b) I disagree with my friend. These particular examples do have y - intercepts, but just because a rule is a function, doesn't make it have a y - intercept. There are some exceptions, such as y = 1 / x.
(c) An input such as 18.5 is meaningless, as x represents the weeks. An employer doesn't provide the payments at half weeks.
4. Let's substitute 20 as x,
y = 50 * 20 + 150 = 1,000 + 150 = $1,150
y = 200( 1.1 )^x-1 = 200( 1.1 )^20-1 = 200( 1.1 )^19 = $1,223.1818
The first payment option will provide the greatest total income.