The rectangle below has an area of 12y^2+21y^5.
The width of the rectangle is equal to the greatest common monomial factor 12y^2 and 21y^5
What is the length and width of the rectangle?
Width= ?
Length=?
Answer:
The length of the rectangle is[tex](4+7y^3)[/tex] and its width is[tex]3y^2[/tex]
Step-by-step explanation:
Given:
The Area of the rectangle =[tex]12y^2+21y^5[/tex].
Width is the greatest common factor of [tex]12y^2[/tex] and[tex]21y^5[/tex]
To Find:
The length and width of the rectangle = ?
Solution:
Step 1: Finding the greatest common factor of [tex]12y^2[/tex]and[tex]21y^5[/tex]
[tex]12 y^2[/tex]= 2 x 3 x 3 x y x y
[tex]21y^5[/tex] = 3 x 7 x y x y x y x y x y
Thus the greatest common factor is [tex]3y^2[/tex] which is the width
Step 2: Finding the length and width
The area of the rectangle = length x breath
width x length= [tex]12y^2+21y^5.[/tex]
Taking[tex]3y^2[/tex] commonly from each term, we get
width x length= [tex](3y^2)(4 + 7y^3)[/tex]
if anyone can answers these i will give them a brainlist.
1. A tree casts a shadow 21 m long. The angle of
elevation of the sun is 51°. What is the height of the
tree?
2.a helicopter is hovering over a landing pad 100m from where you are standing. the helicopter’s angle of elevation off the ground is 12 degrees. what is the altitude of the helicopter?
Answer:
1. X= 25.9 meters
2.X= 21.3 meters
Step-by-step explanation:
1. Tan 50°= X/21
2. Tan 12°= X/100
(-8,-4)&(2,-9) fint the distance between each pair of points
Answer:
[tex]5 \sqrt{5} [/tex]
Step-by-step explanation:
We want to find the distance between (-8,-4) and (2,-9).
We use the distance formula:
[tex]d = \sqrt{ {(x_2-x_1)^2} +(y_2-y_1)^2 } [/tex]
We substitute the coordinates to get:
[tex]d = \sqrt{ {(2- - 8)^2} +( - 9 - - 4)^2 } [/tex]
We simplify to obtain:
[tex]d = \sqrt{ {(2 + 8)^2}+( - 9 + 4)^2 } [/tex]
Add the numbers within the parenthesis to get:
[tex]d = \sqrt{ {(10)^2}+( -5)^2 } [/tex]
Find the squares of the numbers under the radical
[tex]d = \sqrt{ {100}+25} [/tex]
[tex]d = \sqrt{125} = 5 \sqrt{5} [/tex]
How to solve 7(x+2y)=
Answer:
7x + 14y
Step-by-step explanation:
7(x + 2y)
Multiply 7 by the values inside the parenthesis (x + 2y)
7x + 14y
Hope this helps :)
Distributive property of 1/2 • -2 2/5
Answer:
-6/5
Step-by-step explanation:
-2 2/5=-12/5
1/2*-12/5=-12/10=-6/5
Select all the functions whose graphs include the point (16,4). Pick 2 answers. A. y=2x B. y=x2 C. y=x+12 D. y=x−12 E. y=1/4x
Option "D. y=x−12" and "E. y=1/4x" are the functions whose graphs include the point (16,4)
Step-by-step explanation:
In order to find the functions whose graph includes the point we will put the point in the functions one by one
So,
A. y=2x
Putting x = 16 and y = 4
[tex]4 = 2(16)\\4\neq 32[/tex]
B. y=x^2
Putting x= 16 and y=4
[tex]4 = (16)^2\\4 \neq 256[/tex]
C. y=x+12
Putting x= 16 and y=4
[tex]4 = 16+12\\4 \neq 28[/tex]
D. y=x−12
Putting x= 16 and y=4
[tex]4 = 16-12\\4 = 4[/tex]
E. y=1/4x
Putting x= 16 and y=4
[tex]4 = \frac{1}{4} * 16\\4 = 4[/tex]
Hence,
Option "D. y=x−12" and "E. y=1/4x" are the functions whose graphs include the point (16,4)
Keywords: Functions, graphing
Learn more about functions at:
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Answer:
Step-by-step explanation:
The answers are D and E
A triangle has vertices at A(-7, 6), B(4,9), C(-2, -3). What are the coordinates of each vertex if the triangle is translated 4 units right and 6 units down?
Answer:
[tex]A'(-3,0),B'(8,3),C'(2,-9)[/tex]
Step-by-step explanation:
we know that
the triangle is translated 4 units right and 6 units down
so
The rule for the translation is
[tex](x,y) -----> (x+4,y-6)[/tex]
Applying the rule for the translation find the image of each vertex
1) [tex]A(-7,6) -----> A'(-7+4,6-6)[/tex]
[tex]A(-7,6) -----> A'(-3,0)[/tex]
2) [tex]B(4,9) -----> B'(4+4,9-6)[/tex]
[tex]B(4,9) -----> B'(8,3)[/tex]
3) [tex]C(-2,-3) -----> C'(-2+4,-3-6)[/tex]
[tex]C(-2,-3) -----> C'(2,-9)[/tex]
An 8-oz tub of yogurt causes two dollars and a 32 ounce tube cost is six dollars what fraction of the cost of the large tube is the small tub?
The required fraction is [tex]\bold{\frac{1}{3}}[/tex]
Solution:
Given:
Cost of 32 ounces tub = $6
Cost of 8 ounces tub = $2
To find:
what fraction of the cost of the large tube is the small tub.
From the given, here we can understand that the large tub is the 32 ounces tub and the smaller one is the 8 ounces tub.
Let k be the required fraction.
Therefore, [tex]\bold{k\times6=2}[/tex]
On solving we get,
[tex]\bold{\Rightarrow k=\frac{2}{6}\rightarrow k=\frac{1}{3}}[/tex]
The coordinates of the midpoints of GH are M (4,3) and the coordinates of one endpoints are G (5,-6) the coordinates of the other endpoints are
Answer:
The co - ordinates of another end point is
(x,y) = (3, 12)
Step-by-step explanation:
step :-
mid point formula:-
Let [tex](x_{1} ,y_{1} ) and (x_{2} ,y_{2} )[/tex] be any two end points
Mid point of two given points are
[tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]
let (x,y ) be the another end point
given one end point is (5,-6)
now by using mid-point formula , we get
[tex](\frac{x+5}{2} , \frac{y-6}{2} )[/tex] this is equating to given mid-point is M(4,3)
now [tex](\frac{x+5}{2} , \frac{y-6}{2} )=(4,3)[/tex]
simplify , we get
[tex]\frac{x+5}{2} =4 and \frac{y-6}{2} =3[/tex]
cross multiplication and simplify
[tex]x+5 = 8 and y-6=6[/tex]
x = 3 and y = 12
The another point is (x,y) = (3,12)
Find the next two terms of this sequence
112, 28, 7, ...........
Answer:
1.75, 0.4375
Step-by-step explanation:
Note there is a common ratio between consecutive terms, that is
r = 28 ÷ 112 = 7 ÷ 28 = 0.25
Thus the sequence is geometric.
To obtain a term in the sequence multiply the previous term by 0.25
7 × 0.25 = 1.75
1.75 × 0.25 = 0.4375
The next 2 terms in the sequence are 1.75, 0.4375
What is the perimeter of this red polygon?
Answer:
Answer: The perimeter of the red polygon is 26 cm.
Step-by-step explanation:
Answer:
Tangents from an external point are equal. This can be used to find the perimeter
Perimeter = 22+22+22+22+27+27+98+98
= 338 in.
Hope this helps!
A math teacher wants to buy 25 new scientific calculators for the classroom. Acme and Zenith makes two different type of calculators. Acme calculators cost $15 each. Zenith calculators cost $12 each. The math teacher has $330 to spend. How many of each calculators can she buy?
Answer: 10 Acme and 15 Zenith.
She can buy 10 Acme and 15 Zenith calculators.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
A math teacher wants to buy 25 new scientific calculators for the classroom.
Acme and Zenith makes two different type of calculators.
Acme calculators cost $15 each.
Zenith calculators cost $12 each.
The math teacher has $330 to spend.
Let x represents the number Acme calculators and y represents Zenith.
Now, we have the system of equations,
x + y = 25
So, y = 25 - x
And 15x + 12y = 330
Substituting the value of y,
15x + 300 - 12x = 330
3x = 330 - 300
3x = 30
x = 10
So, y = 15
Therefore, 10 Acme and 15 Zenith calculators.
To learn more about the system of equation;
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PLS I NEED ASAP WILL GIVE BRAINLIEST
Which equation is linear?
y=2x+2
2
y=2x^+2
3
y=2x^+2
4
y=2x^+2
For this case we have that by definition, a linear equation is of the form:
[tex]ax + b = 0[/tex]
The variable (s) involved in the equation always have exponent 1.
Some examples of linear equations are:
[tex]x + 5 = 3y\\y + 6 = 3x\\y = 2x + 2[/tex]
Answer:
In a linear equation the variables have exponent 1.
[tex]y = 2x + 2[/tex]
A gym instructor has a total of 60 hand weight in her studio. Some of the hand weights are 3 pound weights and the rest are 5 pound weights. If there are 10 more 5-lb weights than 3-lb weights, then how many of each kind does she have?
Answer:
35 5-lb weights25 3-lb weightsStep-by-step explanation:
Let t and f represent the numbers of three- and five-pound weights. The problem statement tells us ...
f + t = 60
f - t = 10
Adding these two equations, we get ...
(f +t) +(f -t) = (60) +(10)
2f = 70 . . . . . eliminate parentheses
f = 35 . . . . . . divide by 2
She has 35 5-lb weights, and 25 3-lb weights.
A man and his wife go shopping. They begin with $200 total. First, they stop for lunch, spending $15.00. Then, they buy three items at $20.00 each. Later, the wife spends twice what her husband spends. They return home with $20.00 cash. How much did the wife spend?
Amount spent by the wife is $70
Step-by-step explanation:
Given:
the total amount = $200
Amount spent on Lunch = $15.00
They buy three items at $20.00 each
The wife spends twice what her husband spends
They return home with $20.00 cash.
To Find:
Amount spent by the wife = ?
Solution:
Initially after spending $15.00 on lunch they balance cash with them will be
200 - 15.00 = $185
Then they are buy 3 items each of which costs $20.00
So the balance after buying the 3 items will be
= 200 - 3(20)
= 185- 60.00
= $125
Now the wife is spending twice what her husband spends
so let the amount spent be the husband be x then the amount spent by the wife will be 2x.
Now after spending 2x+x amount they are left with $20.00
that is
125 -2x+x = 20
125 -3x = 20
125 -20 = 3x
105 = 3x
[tex]x = \frac{105}{3}[/tex]
x = 35
So the wife will be spending 2(35) = $70
a supermarket sells 2 kg and 4 kg of sugar a shipment of 1100 bags of sugar has a total mass of 2900 kg. How many 2 kg bags and 4 kg bags are in the shipment
To find the number of 2 kg and 4 kg sugar bags in the shipment, we use a system of equations. By setting x as the number of 2 kg bags and y as the number of 4 kg bags, we determine that there are 750 bags of 2 kg sugar and 350 bags of 4 kg sugar.
Explanation:To solve the problem of determining how many 2 kg bags and 4 kg bags of sugar are in the shipment of 1100 bags with a total mass of 2900 kg, we need to set up a system of equations and solve for the variables representing the quantities of each type of bag. Let's denote x as the number of 2 kg bags and y as the number of 4 kg bags.
The first equation represents the total number of bags:
x + y = 1100.
The second equation represents the total weight of the bags:
2x + 4y = 2900.
We can solve these equations using substitution or elimination methods. For simplicity, let's multiply the first equation by 2 and subtract it from the second equation:
2(x + y) = 2(1100) --> 2x + 2y = 2200(2x + 4y) - (2x + 2y) = 2900 - 22002y = 700y = 350Now that we know y, we can substitute it back into the first equation to find x:
x + 350 = 1100x = 750Therefore, there are 750 bags of 2 kg sugar and 350 bags of 4 kg sugar in the shipment.
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You take a pan of brownies out of the oven and set them on the counter in a room that is 70 degrees F, If the brownies start at 400 degrees F, approximately how long will it be before they are cool enough to eat at 160 degrees F? Use Newton's Law of Cooling with k = 0.035.
Answer:
i would say wait abought 50 mins
Step-by-step explanation:
i dont know whow to explain i might be wrong but its some whaere around 50 mins irl
Using Newton's Law of Cooling with a cooling constant of 0.035, it will take approximately 42.53 minutes for the brownies to cool from 400 degrees F to 160 degrees F.
To estimate the time it would take for brownies to cool from 400 degrees F to 160 degrees F using Newton's Law of Cooling, we can use the equation [tex]T(t) = T_s + (T_0 - T_s)e^{(-kt)[/tex], where T(t) is the temperature of the object at time t, T_s is the surrounding temperature, T_0 is the initial temperature of the object, and k is the cooling constant (0.035 in this case).
First, set T(t) = 160 degrees F (the desired temperature), T_s = 70 degrees F (room temperature), and T_0 = 400 degrees F (initial temperature of brownies). Plug in the values into the equation: 160 = 70 + (400 - 70)e^(-0.035t).
Simplify and solve for t. Subtract 70 from both sides: 90 = 330e^(-0.035t). Divide both sides by 330: 90/330 = e^(-0.035t), which simplifies to 0.2727 ≈ e^(-0.035t).
Take the natural logarithm of both sides to solve for t: ln(0.2727) = -0.035t. Solving for t gives t ≈ -ln(0.2727)/0.035, which calculates to approximately t ≈ 42.53 minutes.
Hence, the brownies should cool to 160 degrees F in about 42.53 minutes.
A gardener uses a wheelbarrow to move soil from a truck to his garden. On the first trip from the truck to the garden, the wheelbarrow
is half-full of soil and the gardener applies a certain force to cause it to accelerate. On the second trip, the wheelbarrow is full of soil.
Although the gardener applies the same amount of force to the wheelbarrow, he cannot move it with the same rate of acceleration.
What should the gardener do to move the wheelbarrow at the same rate of acceleration for the second trip?
A. reduce the amount of soil by one-half and apply the same amount of force
B. keep the amount of soil the same and apply less force
C. reduce the amount of soil by one-quarter and apply the same amount of force
D. double the amount of soil, and apply less force
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Answer:
Step-by-step explanation:
it seems to me that if he wants the same rate of acceleration as the first trip, then he would need the same amount of soil as the first trip.
Therefore, he should reduce the amount of soil by one half and apply the same force. <====
Because the first time it was half full.....and since the second trip was all the way full, if he reduced it by one half, it would contain the same amount as the first trip....so he can then get the same rate of acceleration.
Answer:
A.
Step-by-step explanation:
According to Newton's second law of motion, an object with a larger mass requires more force to accelerate it at a certain rate than an object with less mass. This means that an object with a larger mass requires more force to accelerate.
To move the wheelbarrow at the same rate of acceleration for the second trip, the amount of soil must be the same as in the first trip. Since the gardener first filled only one-half of the wheelbarrow with soil, the gardener must reduce the amount of soil by one-half and apply the same amount of force.
Consider the transformation shown
Use the drop-down menus to complete the sentence.
The transformation is
because the
preserved
Image
Pre-image
Answer:
Nonrigid
Segment lents are not
Step-by-step explanation:
Answer:
answer in picture
Step-by-step explanation:
Teresa, Charlie, and Justin served a total of 153 orders Monday at the school cafeteria. Justin served 4 times as many orders as Charlie. Teresa served 9 more orders than Charlie. How many orders did they each serve?
Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders
Solution:
Let "a" be the orders served by Teresa
Let "b" be the orders served by Charlie
Let "c" be the orders served by Justin
Teresa, Charlie, and Justin served a total of 153 orders
Therefore,
a + b + c = 153 -------- eqn 1
Justin served 4 times as many orders as Charlie
Orders served by Justin = 4( orders served by Charlie )
c = 4b ---------- eqn 2
Teresa served 9 more orders than Charlie
orders served by Teresa = 9 + orders served by Charlie
a = 9 + b ----------- eqn 3
Let us solve eqn 1 and eqn 2 and eqn 3
Substitute eqn 2 and eqn 3 in eqn 1
9 + b + b + 4b = 153
9 + 6b = 153
6b = 153 - 9
6b = 144
b = 24
Substitute b = 24 in eqn 3
a = 9 + 24
a = 33
Substitute b = 24 in eqn 2
c = 4(24)
c = 96
Thus Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders
BICYCLING The bicycle path at the
park is a loop that covers a distance
of m miles. Dot biked 2 loops each on
Monday and Wednesday and 3 loops
on Friday. On Sunday, Dot biked
10 miles. Write an expression in
simplest form that represents the
total distance that Dot biked this
week.
Dot bikes 7m+10 miles this week.
Step-by-step explanation:
Distance of one loop = m miles
Distance of 2 loops = 2m
Distance of 3 loops = 3m
Distance covered on Sunday = 10 miles
Total distance = Monday + Wednesday + Friday + Sunday
Total distance = 2 loops + 2 loops + 3 loops + 10 miles
Total distance = 2m + 2m + 3m + 10
Total distance = (7m+10) miles
Dot bikes 7m+10 miles this week.
Keywords: addition, distance
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3x = x+6 show the steps please
Answer:
x = 3
Step-by-step explanation:
Given
3x = x + 6 ( subtract x from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Answer:
Step-by-step explanation:
3x = x + 6.....subtract x from both sides
3x - x = x - x + 6
2x = 6 ...divide both sides by 2
(2/2)x = 6/2
1x = 6/2
x = 3 <=====
rearrange the equation so b is the independent variable a-7=3(b+2)
Answer:
Step-by-step explanation:
a - 7 = 3(b + 2)
a - 7 = 3b + 6
a - 7 - 6 = 3b
a - 13 = 3b
(a - 13) / 3 = b <====
Answer:
-13-1/4 b
Step-by-step explanation:
b is on the outside of the fraction not with the four.
-13-\frac{1}{4b}
Complete the equation of the line through (-6,-5) and (−4,−4)
Use exact numbers.
y=
Please help me!!!!
Answer:
y=1/2x -2. Hope this helps!
Find the value of the polynomial 3xy+7x^2−3x^2y+3y^2x−2x^2−2xy+4x^2y−2y^2x, when x=1 and y=−2
Answer:
[tex]5[/tex]
First Method:
Substitute the given values in for [tex]x[/tex] and [tex]y[/tex].Solve.This isn't the only method, but it seems the least likely to result in an incorrect answer.
If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:
[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]
Substitute [tex]1[/tex] for [tex]x[/tex] and [tex]-2[/tex] for [tex]y[/tex].[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)(-2)+7(1)^2-3(1)^2(-2)+3(-2)^2(1)-2(1)^2-2(1)(-2)+4(1)^2(-2)-2(-2)^2(1)[/tex]
Wow. That's a lot. Let's try simplifying things. I'd start by multiplying all our [tex]1[/tex]'s because any number multiplied by [tex]1[/tex] is that very same number, so we can easily reduce the length of our equation without much worry for messing up our math in the process.[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]
It still looks like torture trying to figure out this equation, but let's take it in chunks instead of all at once.[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]
First, I'm going to deal with all the exponents, and turn them into integers.[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)[/tex]
Notice that things are starting to look less complicated. We are taking our math in chunks. This will make it less likely for us to mess up, although it is more time consuming.Now, let's do multiplication. Any number within a parentheses is going to be multiplied by the number next to it. Remember that this only applies when there is no sign between them. I'm going to go one at a time.[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2+4+4(-2)-2(4)\\-6+7+6+12-2+4-8-2(4)\\-6+7+6+12-2+4-8-8\\[/tex]
This is a lot of steps, but hopefully it doesn't looks as bad after seeing that I just did multiplication over and over. I'll go over another method after this that may make things less complicated.Now, we add these together. It doesn't matter what order you do this in.[tex]-6+7+6+12-2+4-8-8\\7+4+6+12-6-2-8-8\\11+18-8-16\\29-24\\5[/tex]
Our final answer is [tex]5[/tex].
Here's another method:
If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:
[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]
Because we know that any number multiplied by [tex]1[/tex] will be that same number, let's just substitute in [tex]x[/tex] for now.[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\[/tex]
Now, just like before, we can multiply [tex]1[/tex] without doing complicated math. Just basically get rid of it even when it's squared because [tex]1^2=1*1=1[/tex].[tex]3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\3y+7-3y+3y^2-2-2y+4y-2y^2\\3y^2-2y^2+3y-3y-2y+4y+5\\y^2+2y+5[/tex]
Looks a LOT less complicated. Substitute [tex]-2[/tex] in for [tex]y[/tex] and get your final answer.[tex]y^2+2y+5\\(-2)^2+2(-2)+5\\4-4+5\\5[/tex]
I need help -6(2x+6)=-132
Answer:
x=8
Step-by-step explanation:
First you want to distribute -6 to (2x+6) which you will then get -12x-36=-132. Now you want to get x by itself by getting rid of -36, so add 36 on both sides of the equation to get -12x=-96. Isolate x by dividing by -12 on both sides of the equation which will leave you with the equation x=8
Is 1.4949949994.. a rational number
Alegbra, K12 Question. Answer needed ASAP --- Brainliest to the correct answer!
Good evening ,
Answer:
-1Step-by-step explanation:
From the table :
f(x) = g(x) only when x = -1 then -1 is the only solution
f(-1) = 9 = g(-1)
note : the equation could have some other solutions not shown in the table
:)
Eight less than 1/3 a number n is -13?
Graph the system of linear inequalities. y≥2/3 x-3 y<-4x+7
Answer:
The answer is given in the graph attached.
Step-by-step explanation:
i) The answer is given in the graph attached.