The area of a rectangle is 14 yd2 , and the length of the rectangle is 3 yd less than twice the width. find the dimensions of the rectangle.
The dimensions of the rectangle are 4 yd by 7/2 yd
How to determine the dimensions of the rectangle?The area is given as:
Area = 14 yd^2
Let the width be x. So, the length is:
Length = 2x - 3
The area is then calculated as:
Area = (2x - 3) * x
Expand
Area = 2x^2 - 3x
Substitute 14 for Area
2x^2 - 3x = 14
Rewrite as:
2x^2 - 3x - 14 = 0
Factorize
(2x- 7)(x+2)=0
Solve for x
x=7/2 or x=-2
Width cannot be negative.
So, we have:
x = 7/2
Substitute x = 7/2 in Length = 2x - 3
Length = 2 * 7/2 - 3
Evaluate
Length = 4
Hence, the dimensions of the rectangle are 4 yd by 7/2 yd
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8(10−k)=2k
solve for k
The value of k is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
8 (10 - k) = 2k
Multiplication over subtraction.
8 x 10 - 8k = 2k
80 - 8k = 2k
Combine like terms.
80 = 2k + 8k
80 = 10k
Divide both sides with 10
k = 8
Thus,
The value of k is 8.
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I AM SO CONFUSED ????
4. The following function defines a recursive sequence.
f(0) = -4
f(1) = 12
f(n) = -3•f(n -1) - 2•f(n - 2); for n > 1
Which of the following sequences is defined by this recursive function? (4 points)
a) -4, 12, -28, 60,
b) -4, -12, -28, -60,
c) -4, 12, -18, 54,
d) -4, 12, -18, -54,
Samantha invests $11,000 at 5% simple interest for 1 year. How much is in the account at the end of the 1 year period?
9.6 - (3.1)²
Please explain the steps you used and how you worked it out . Thank you and advance
An open box can hold 80 cm3. It is made from a square piece of tinplate with 3 cm squares cut from each of its 4 corners. Find the dimensions of the original piece of tinplate.
Volume of Open box which is made from square piece of tinplate=80 cm³
⇒Squares of side 3 cm is cut from 4 of it's corner.It means the square boxes are cubical.
Volume of cube=Side × Side × Side
=(Side)³
Volume of 4 cubical box having each side 3 cm
=4×3×3×3
=108 cm³
Total Volume of box=108 cm³ +80 cm³=188 cm³
Since the box is open .
Let the dimension of box be
Length= x cm
Breadth= x cm
Height = x cm
Volume of Original box=188 cm³
[tex]\rightarrow x^3=188\\\\\rightarrow x=(188)^{\frac{1}{3}}\\\\x=5.728\text{approx}[/tex]
So, Original dimension of cubical Square Box=5.73 cm(Approx)
How many times larger is 9 x 10-4 than 3 x 10-10? A) 3 x 10^5 B) 3 x 10^6 C) 6 x 10^5 D) 6 x 10^6
Answer:
The correct option is B.
Step-by-step explanation:
We need to find how many times larger is [tex]9\times 10^{-4}[/tex] than [tex]3\times 10^{-10}[/tex].
Let [tex]9\times 10^{-4}[/tex] is x times larger than [tex]3\times 10^{-10}[/tex].
[tex]x\times 3\times 10^{-10}=9\times 10^{-4}[/tex]
Divide [tex]3\times 10^{-10}[/tex] on both sides.
[tex]x=\frac{9\times 10^{-4}}{3\times 10^{-10}}[/tex]
It can be written as
[tex]x=\frac{9}{3}\times \frac{10^{-4}}{10^{-10}}[/tex]
[tex]x=3\times \frac{10^{-4}}{10^{-10}}[/tex]
Using quotient property of exponent, we get
[tex]x=3\times 10^{-4-(-10)}[/tex] [tex][\because \frac{a^m}{a^n}=a^{m-n}][/tex]
[tex]x=3\times 10^{-4+10}[/tex]
[tex]x=3\times 10^{6}[/tex]
[tex]9\times 10^{-4}[/tex] is [tex]3\times 10^{6}[/tex] times larger than [tex]3\times 10^{-10}[/tex].
Therefore the correct option is B.
Which rigid transformation would map ΔAQR to ΔAKP?
Answer:
A. Rotation around point a
Step-by-step explanation:
I hope this helps.
Simplify , You may leave the numerator and denominator of your answer in factored form ?
find the value of x
Naomi invested $3,425 in an account that pays 3% simple annual interest. What was the total balance in the account after 15 years?
Account Balance = $___________
Answer: 4966.25
Step-by-step explanation:
Magnesium combines with oxygen to form magnesium oxide. A 100-gram sample of magnesium combines with 65.8 grams of oxygen. A 10-gram sample of magnesium combines with 6.58 grams of oxygen. Which point of Dalton’s atomic theory is supported by these findings? All atoms of the same element have the same mass, and atoms of different elements have different masses. All elements are composed of atoms. In a particular compound, atoms of different elements always combine in the same way.
Answer: The correct answer is in a particular compound, atoms of different elements always combine in the same way.
Explanation:
Postulates of Dalton's theory were:
Matter is made up of indivisible particle which are known as atoms.The properties of all the atoms of an element are same including its mass. It can also be said that the mass of all the atoms of an element is same while the mass of all atoms of different elements are different.Atoms of different elements combine in fixed ratio by their mass to form compounds. Atoms are neither created nor destroyed. It can also be said that in a chemical reaction, atoms can neither be created nor be destroyed.We are given a reaction of magnesium with oxygen to produce magnesium oxide.
Case 1:Mass of magnesium = 100 grams
Mass of oxygen = 65.8 grams
Mass ratio of magnesium and oxygen = [tex]100:65.8=1.51:1[/tex]
Case 2:Mass of magnesium = 10 grams
Mass of oxygen = 6.58 grams
Mass ratio of magnesium and oxygen = [tex]10:6.58=1.51:1[/tex]
From both the cases, it is visible that magnesium and oxygen are combining in a fixed ratio by their masses to form magnesium oxide.
Hence, the correct answer is in a particular compound, atoms of different elements always combine in the same way.
Answer:
In a particular compound, atoms of different elements always combine in the same way.
Step-by-step explanation:
Dalton's atomic theory postulate:
1.All matter consist of indivisible particles called atoms.
2.Atoms of same element are identical in shape and mass. Atoms of different element are different in shape and mass.
3.Atoms cannot be created or destroyed.
4.Atoms of different elements may combine with each other in a fixed , simple, whole number ratios to form compounds.
5.Atoms is the smallest unit of matter that can take part in a chemical reaction.
Mass of magnesium in a sample=100 g
Mass of oxygen in a sample=65.8 g
Ratio of Mg to O=100:65.8=1.52:1
Mass of magnesium in other sample=10 g
Mass of oxygen in other sample=6.58 g
Ratio of Mg to O=10:6.58=1.52:1
Hence, the ratio of Magnesium to oxygen in each sample=1.52:1
Therefore, the point supported by given information is
In a particular compound, atoms of different elements always combine in the same way.
Answer:In a particular compound, atoms of different elements always combine in the same way.
PLEASE HELP DON'T ANSWER UNTIL I POST THE SCREENSHOT
Alice and her friend want to meet for lunch at a point halfway between their homes. Alice's home can be represented by the point (-1, 2) and her friend's home by the point (3, 4). What are the coordinates of the point that represents the location where they should meet?
to find midpoint add the 2 x numbers and divide by 2
and add the 2 y numbers and divide by 2
X = -1 + 3 = 2, 2/2 =1
Y = 2 +4 = 6, 6/2 = 3
coordinate is (1,3)
The coordinates of the point that represents the location where they should meet is (1,3).
Given that,
Alice's home can be represented by the point (-1, 2).And, her friend's home by the point (3, 4).Based on the above information, the calculation is as follows:
X = -1 + 3 = 2,[tex]2\div2 =1[/tex]
Y = 2 +4 = 6, [tex]6\div2 = 3[/tex]
Therefore we can conclude that the coordinates of the point that represents the location where they should meet is (1,3).
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what type of equation is this
What is the intersection of planes GDH and GHF?
A) Line FA
B) Line HC
C) Line GH
D) Line DC
Roger is buying a new pair of shoes for 25% off. if the original price of the shoes was $70.00, how much money is roger saving on the shoes?
Answer:
17.5
Step-by-step explanation:
△XLW≅△XDG.
What is length of line GX?
we know that
The CPCTC states that corresponding parts of congruent triangles are congruent
so
△XLW≅△XDG.
that means
[tex]XL=XD\\LW=DG\\XW=XG[/tex]
we have
[tex]XL=6.2\ units\\LW=4.5\ units\\XW=5.7\ units[/tex]
therefore
[tex]GX=5.7\ units[/tex]
the answer is
the length of GX is [tex]5.7\ units[/tex]
Increase 140g by 12.5%
157.5 g is when 140g is increase by 12.5%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Initial amount = 140 g
Final amount.
= 140 + (12.5% x 140)
12.5% = 12.5/100 = 125/1000 = 0.125
= 140 + (0.125 x 140)
= 140 + 17.5
= 157.5 g
Thus,
The final quantity is 157.5 g.
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Segment ab had endpoints a(-1,3) and b(0,7) what is the length of ab
A. Square root 5
B.square root 10
C.square root 17
D.square root 101
A square garden has an area of 182 square feet about how many feet of fencing do u need
Which type of sandwich consists of two slices of bread or two halves of a roll, a spread and a filling?
A snail travels at a rate of 2.44 feet per minute. • Write a rule to describe the function. • How far will the snail travel in 7 minutes?
Which two points are on the graph of y = x - 3?
(1, -2), (-1, 3)
(1, 2), (0, 3)
(0, -3), (4, 1)
(3, 0), (0, 3)
Answer:
(0, -3), (4, 1)
Step-by-step explanation:
Given: Graph of y = x - 3
We need to find which points are on the graph of y = x - 3 .
A point [tex]\left ( x_1,y_1 \right )[/tex] is said to lie on the graph of y = f(x) if it satisfies the equation. i.e if [tex]y_1=f(x_1)[/tex]
Here, we will first check if points (0, - 3), (4, 1) lie on the graph:
For (0, - 3):
L.H.S = y = - 3
R.H.S = x - 3 = 0 - 3 = - 3
L.H.S = R.H.S
So, (0, - 3) satisfies the given equation.
For (4, 1):
L.H.S = y = 1
R.H.S = x - 3 = 4 - 3 = 1
L.H.S = R.H.S
So, (4, 1) satisfies the given equation.
Therefore, two points (0, - 3), (4, 1) satisfy the equation y = x - 3
△ABC is mapped to △A′B′C′ using each of the given rules.
Which rules would result in △ABC being congruent to or not congruent to △A′B′C′ ?
Drag and drop each rule into the boxes to classify it as Congruent or Not Congruent.
Answer:
Congruent: (x, y)→(x+3, y-4); (x, y)→(-x, -y)
Not Congruent: (x, y)→(3x, 3y); (x, y)→(0.4x, 0.4y); (x, y)→(x/3, y/3)
Step-by-step explanation:
Transformations that result in congruent figures are translations, rotations and reflections. Translations that result in figures that are not congruent are dilations.
The first transformation, (x, y)→(x+3, y-4) is a translation 3 units to the right and 4 units down. This will result in congruent figures, since it only slides the figure.
The second transformation, (x, y)→(3x, 3y) is a dilation by a factor of 3. A dilation is a stretch or a shrink; a dilation factor of 3 will stretch the figure. Since it is stretched, it is not the same size and therefore not congruent.
The third transformation, (x, y)→(0.4x, 0.4y) is a dilation by a factor of 0.4. This dilation will shrink the figure. Since it is shrunk, it is not the same size and therefore not congruent.
The fourth transformation, (x, y)→(x/3, y/3) is a dilation by a factor of 1/3. This dilation will shrink the figure. Since it is shrunk, it is not the same size and therefore not congruent.
The fifth transformation, (x, y)→(-x, -y) is a reflection. This does not change the size of the figure, just the placement and orientation of it. Since the size is not changed, the figure is congruent.
Answer:- Congruent = (x, y)→(x+3, y-4)
(x, y)→(-x, -y)
Not Congruent= (x, y)→(3x, 3y)
(x, y)→(0.4x, 0.4y)
(x, y)→(x/3, y/3)
Explanation:
1.The transformation (x, y)→(x+3, y-4) is a translation ,where the x coordinates of points of ΔABC translate 3 units toward right and the y coordinate translate 4 units downwards .Translation is rigid transformation which does not change the size of the figure, it just translate every point of a figure by a fixed distance to create its image. Thus this would result in △ABC being congruent to △A′B′C′.
2.The transformation (x, y)→(3x, 3y) is a dilation by a factor of 3.Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.
3.The transformation (x, y)→(0.4x, 0.4y) is a dilation by a factor of 0.4.Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.
4.The transformation (x, y)→(x/3, y/3) is a dilation by a factor of 1/3. Since after dilation the size of image becomes different, thus this would result in △ABC being not congruent to △A′B′C′.
5.The transformation (x, y)→(-x, -y) is a reflection. Reflection is a rigid transformation which does not change the size of the figure, it create exactly same sized image of the original figure, Thus this would result in △ABC being congruent to △A′B′C′.
3/5 of a Conductors Club went on the last camping trip.If 39 people went on the trip, how many are in the club?
Bob is hiking down a 60-mile country trail. He could hike at 10 mph for the first two hours and then go the rest of the way at 30 mph or he could just go the whole way at 20 mph. How long would each of these options take? Which option is the faster?
SOMEONE PLEASE HELP ME!!!!!!!!!!!! 100 points and brainliest answer to whoever answers all 3 correctly first!!!!!!!!!!!
1. (picture 1, 2nd answer is not correct, question & answers in picture)
2. (picture 2, 1st answer is not correct, question & answers in picture)
3. (picture 3 and text below, 2nd answer is not correct. The answers to this question is in picture 3)
The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees who have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees who have been with the company for at least three years, but fewer than six years can expect an increase of $1.00. Employees who have been with the company for at six years, but fewer than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but fewer than twelve years receive an increase of $2.00.
Which of the following tables accurately represents the hourly wage increase for some of the employees?
1st picture ix X <4 then y = -X+8
when x = 2 y = -2+8 = 6
Last table works.
2nd picture :
0.50 <3
1.00 at least 3 less than 6
1.50 at least 6 but less than 9
2.00 at least 9 less than 12
2nd function works and 2nd table works
One of two complementary angles is 8 degrees less than the other.
Which of the following systems of equations represents the word problem?
x + y = 90 and x - y = 8
x + y = 90 and 90 - x = 8
x + y = 90 and y = 8x
Answer:
( x+y = 90 ) and ( x - y = 8 )
Step-by-step explanation:
In this question we will form the equation as per statements given.
"One of two complementary angle is 8 degrees less than the other."
Let the two angles are 'x' and 'y'
By the statement ( y = x - 8 )
y - x = (-8)
or x - y = 8 -----------(1)
"Both the angles are complementary."
x + y = 90° -----------(2)
Therefore, system of equations will be
( x+y = 90 ) and ( x - y = 8 )
Option A. is the correct answer.
Aaron can run 2 kilometers in 14 1/2 minutes. Find his rate of speed in kilometers per minute
The rate of speed in kilometers per minute is 0.14 km/minute.
What is speed?The speed of a thing is how quickly it progresses throughout time. There are many ways to determine speed, including in terms of kilometers per hour (km/h) as well as meters per second (m/s). the speed at which an object's location changes in any orientation. The total distance divided by the time it took to travel that distance is how fast something is moving.
The rate of speed that is determined is at Aaron has a 2-kilometer time of 14 and a half minutes.
A time of 14 and a half minutes can also be written at 14.5
distance = rate * time
2 = r * 14.5
r = 2 / 14.5
r = 0.14 km/minute
The rate will be 0.14 km/minute
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