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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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.
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,
How much simple interest is earned on 6,000 at an interest rate of 2.25% in 4 1/2
Which rigid transformation would map ΔAQR to ΔAKP?
Answer:
A. Rotation around point a
Step-by-step explanation:
I hope this helps.
Approximately how many kcal are contained in 3 ounces of 80-proof rum?
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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A gardener has an area 320 sq ft. its width is 4 feet less than its length. what are the dimensions of the garden?
Answer: C
Step-by-step explanation:
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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Which statement is needed to complete this syllogism?
If two angles are vertical, then the angles are congruent.
If two angles are congruent, then the angles have equal measure.
Therefore, if ________________________, then the angles have equal measure.
two angles are vertical
two angles have equal measure
two angles are congruent
There is not enough information to say.
Answer:
Step-by-step explanation:
It IS "two angles are vertical".
I answered wrong on my quiz and got corrected to this answer.
Which type of sandwich consists of two slices of bread or two halves of a roll, a spread and a filling?
Adam wrote a check for $38 to pay his monthly gas bill, but when balancing his checkbook, he accidently recorded it as a credit rather than his debit. How will his check register compare to his monthly bank statement when he receives it?
Answer:
76 dollars more
Step-by-step explanation:
Given that Adam wrote a check for $38 to pay his monthly gas bill.
Normally cheques issued would be debited to the account maintained by the customer thus making the balance less than the previous one.
If the customer had x as balance after cheque issued the balance would be x-38
This is a debit entry
But since Adam by mistake entered as credit, he would have recorded in his books balance as x+38
Thus as a result of this
Adam check register shows x+38-(x-38)
= 76 dollars more than monthly bank statement
You can represent the measures of an angle and its complement as x° and (90 − x)°. Similarly, you can represent the measures of an angle and its supplement as x° and (180 − x)°. Use these expressions to find the measures of the angles described. The measure of an angle is equal to four times the measure of its supplement. The measure of the angle is ° and the measure of its supplement is °.
To determine the size of an angle and its supplement when the angle is four times the size of its supplement, we use the equation x = 4(180 - x) and solve for x to find that the angle measures 144 degrees and its supplement measures 36 degrees.
To find the measures of an angle and its supplement when the angle is four times its supplement, we use the expressions x and 180 - x. We can set up the equation x = 4(180 - x). Then we can solve for x to find the measures of the angle and its supplement.
By expanding and rearranging the equation, we get:
x = 720 - 4x5x = 720x = 144Thus, the angle measures 144 degrees and its supplement measures 36 degrees (since 180 - 144 = 36).
find the value of x
Calculate the slope of the line that goes through the points (-15,70) and (5,10)
The slope of the line that goes through the point (-15,70) and (5,10) is - 3.
What is slope?The slope is the measure of the angle a line has with respect to the positive x-axis.
We know when two points of a line is given slope can be obtained by rise over run where the rise is the difference between the points of the y-axis and run is the difference of the points of the x-axis.
Given points are (-15,70) and (5,10) through which a line passes.
∴ Slope(m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Slope(m) = (10 - 70)/(5 + 15).
Slope(m) = -60/20.
Slope(m) = -3.
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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
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?
What percent of 10 is 6?
To determine what percent of 10 is 6, you multiply 6/10 by 100, which equals 60%, thus 6 is 60% of 10.
Explanation:To find what percent of 10 is 6, we can use the formula for percentage which is (Part / Whole) * 100.
In this case, the 'part' is 6 and the 'whole' is 10.
So the equation to find the percentage is (6 / 10) * 100.
Calculating that out, we get 0.6 * 100, which equals to 60%.
Therefore, 6 is 60% of 10.
This is a basic concept in mathematics where you are trying to find out how one number compares to another in terms of percentage.
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The sum of two consecutive odd integers is 72 write an algebraic equation to determine the two integers
A football team gained 6 yards on a first down, lost 15 yards on the second down, and gained 12 yards on the third down. how many yards do they need to gain on the fourth down to have a 10 yard gain from their starting position?
Answer:
They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position
Step-by-step explanation:
To gain a new set of downs, a football team has four downs(tries) to gain 10 net yards, in total.
Gained 6 yards on first down
Net of 6 yards gained
Needs 10-6 = 4 yards
Lost 15 yards on second down
6 - 15 = -9
In all, they have lost 9 yards, so they need
4 + 15 = 19 yards
Gained 12 yards on third down
-9 + 12 = 3 net yards(need 10)
19 - 12 = 7
They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position
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?
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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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)
The formula that describes an object's motion is given by S=ut+1/2at^2 , where S is the distance traveled, u is the initial velocity, a is the acceleration , and t is the time.
Which equation represents a in terms of the other variables?
A. a= 2S-2u/t
B. a=2S+2u/t
C. a=2S-2ut/t^2
D. a=2S+2ut/t^2
△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]
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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Which type of function best models the data in the table below?
A. inverse variation
B. linear
C. logarithmic
D. quadratic
Answer: Option A inverse variation
Explanation:
when we compare the values from the given table x is increasing and y is decreasing hence we can see it is an inverse variation.
In option B difference among all consecutive values of x is 2 but in y it is not same among all consecutive terms. In linear function change in y over change in x must be same.
In option C x is increasing but y is decreasing which is violating the property of logarithmic function. In logarithmic function if x increases then y should increase.
In option D first value of x is 2 following quadratic property meaning giving square of itself in y which is 4. But not all values of y are square of x except first value. In quadratic function value of y should be square of x.
The type of function that best models the table given is: A. inverse variation.
What is Inverse Variation?Inverse variation can be described as a relationship between two variables, whereby, the product of the two variables will give a constant. It is expressed as, k = xy.
In an inverse variation, if one variable increases, the other variable decreases.
The table shows an inverse variation because as x increases, y decreases, and can be expressed as k = xy.
Therefore, the type of function that best models the table given is: A. inverse variation.
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What is 4527 written in scientific notation?
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.