Answers
Answer:
1.3 m
Step-by-step explanation:
Given dimensions of rectangle ABCD:
width = xlength = (x + 4)[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\\\implies \sf Area\:of\:ABCD& = x(x+4)\\& = x^2+4x \end{aligned}[/tex]
Given dimensions of isosceles triangle ADE:
Base = DE = xHeight = AD = x[tex]\begin{aligned}\textsf{Area of a triangle} & = \dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of $\triangle$ADE}& = \dfrac{1}{2} \cdot x \cdot x\\& = \dfrac{1}{2}x^2\end{aligned}[/tex]
As the area of the portion remaining when ADE is cut off from ABCE is 6 m²:
[tex]\begin{aligned}\sf ABCD-ADE & = 6\\\implies x^2+4x-\dfrac{1}{2}x^2 & = 6\\2x^2+8x-x^2 & = 12\\x^2+8x & = 12\\x^2+8x-12 & = 0\end{aligned}[/tex]
Solve the found quadratic equation by completing the square.
Move the constant to the right side of the equation:
[tex]\implies x^2+8x-12+12=0+12[/tex]
[tex]\implies x^2+8x=12[/tex]
Add the square of half the coefficient of x to both sides:
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=12+\left(\dfrac{8}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2+8x+4^2=12+4^2[/tex]
[tex]\implies x^2+8x+16=12+16[/tex]
[tex]\implies x^2+8x+16=28[/tex]
Factor the perfect square trinomial on the left side:
[tex]\implies (x+4)^2=28[/tex]
Square root both sides:
[tex]\implies \sqrt{(x+4)^2}=\sqrt{28}[/tex]
[tex]\implies x+4=\pm \sqrt{28}[/tex]
[tex]\implies x+4=\pm \sqrt{4 \cdot 7}[/tex]
[tex]\implies x+4=\pm \sqrt{4}\sqrt{7}[/tex]
[tex]\implies x+4=\pm 2\sqrt{7}[/tex]
Subtract 4 from both sides:
[tex]\implies x=-4\pm 2\sqrt{7}[/tex]
As length is positive:
[tex]\implies x=-4+ 2\sqrt{7}\:\:\sf only[/tex]
Taking the value of √7 = 2.65:
[tex]\implies x \approx -4+ 2(2.65)[/tex]
[tex]\implies x \approx -4+5.3[/tex]
[tex]\implies x \approx 1.3[/tex]
Therefore, the width of the sheet is 1.3 m.
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Related Questions
Of the following fractions which one is the largest 9/19 , 5/11 ,7/15
Answers
Answer: 9/19
Step-by-step explanation:
9/19=0.4737
5/11=0.4545
7/15=0.4666
9/19 has the largest decimal making it largest.
The diameter
of the Earth is 1.3 × 10 km.
The diameter of the Moon is 3.5 × 10 km.
The diameter of the Sun is 400 times greater
than the diameter of the Moon.
How many times smaller is the diameter of
the Earth than the diameter of the Sun
Answers
Earth's diameter is 0.0092 times less than the sun's diameter.
Ratio, in math, is a time period this is used to examine or greater numbers. It is used to indicate how large or small a sum is in comparison to another.In a ratio, portions are as compared the use of division. Here the dividend is referred to as the `antecedent' and the divisor is referred to as the 'consequent'. For example, in a collection of 30 people, 17 of them opt for to stroll within side the morning and thirteen of them favor to cycle. We use the ratio formulation whilst evaluating the connection among numbers or portions. The popular shape of representing a ratio of among portions say 'a' and 'b' is a: b, that's examine as 'a is to b'.The Diameter of Earth = 1.3 * 10⁴ km
The Diameter of Moon = 3.5 * 10³ km
Let the diameter of sun be x km
According to the question
The diameter of the sun is 400 times that of the moon.
x = 400 * 3.5 * 10³ km
= 14 * 10⁵ km
The Diameter of earth / diameter of sun
= 1.3 * 10⁴ / 14 * 10⁵
= 0.0092
Hence, The diameter of the Earth is 0.0092 times that of the Sun.
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If w = 18, what is the value of 3w − 11?
A: 307
B: 65
C:43
D: 10
Answers
Answer: 43 ==> C
Step-by-step explanation:
3w − 11=
3(18)-11=
54-11=43 ==> C
Answer:
c, 43
Step-by-step explanation:
3 times 18, minus 11
Can someone please help me I will mark u brilliant
Answers
(Blank space filler)
Answer:
M would be at (0,-2)
Step-by-step explanation:
The question asks you to rotate the image 180 degrees clockwise. Clockwise means towards the right, such as how a clock moves. Each axis is 90 degrees, so by moving it twice would land at (0,-2).
A horizontal line (such as the x-axis) is 180 degrees, so by mirroring the point, you would see the point is at (0,-2).
Round 782,317.772 to the nearest whole number.
Answers
Nearest whole number will be 782318.
Nearest ones whole number is the first digit before the decimal point of a number.
For example nearest ones of 9.6 is equal to 10.
If the tenth digit (first number before decimal point) of the number is greater than or equal to 5 we round up and add 1 to ones of number, If the tenth digit of the number is less than 5 we remove the decimal part. Example:
124.6
The first number of right of decimal point is 6
6 is greater than 5, so we add 1.
Result = 125
Now given number is 782317.772
since the first digit after decimal is 7 which is greater than 5 thus the nearest whole number will be 782318.
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To make five cups of lemonade you mix three cups of water with two cups of lemon
juice. If there are sixteen cups in a gallon, how many cups of lemon juice are needed to
make ten gallons of lemonade?
A: 16
B: 32
C: 40
D: 48
E: 64
(I know the answer is E but I don't know how to get it)
Answers
Step by step
You have 5 cup recipe that’s made of 2c lemon juice
You want to make 10 gallons, let’s change it to cups
10 gallons x 16 cups per gallon = 160 cups
160 cups divided by the 5 cup recipe = 32 recipe portions
32 recipe portions x 2 cups lemon juice = 64 cups lemon juice
Determine the end behavior of each function.
(a)
p(x) = a(x + b)5(x − c)3
, where a, b, and c are constants and
a < 0
.
p(x) → as x → −∞
p(x) → as x → ∞
(b)
f(x) =
9x2 − 11x + 2
8x2 − 6
f(x) → as x → −∞
f(x) → as x → ∞
(c)
g(x) = 9 + e−6x
g(x) → as x → −∞
g(x) → as x → ∞
Answers
Step-by-step explanation:
(a)
a, b, c are constants and play no role with their value when it goes relative to enormous numbers and to infinity.
but the sign is important.
a < 0, so, it will stay < 0 for all eternity/infinity.
(x + b)⁵ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (the exponent 5 is odd, so a negative value put to an odd power will create a negative result value).
(x - c)³ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (for the same reasons - 3 is an odd number).
x going to -infinity,
p(x) = -×-infinity×-infinity = -infinity
x going to infinity,
p(x) = -×infinity×infinity = -infinity
(b)
the x² terms drown out all other terms with lower x exponent (so, incl. -11x or any constants).
what remains for very, very large x is
9x²/8x² = 9/8 = 1.125
since we have x² terms, it does not matter, if x is positive or negative, the result is always positive.
so, x going to infinity or to -infinity, p(x) is the same again :
p(x) = 9/8 = 1.125
(c)
finally, we have a different result for x going to -infinity or to infinity.
x going to -infinity :
the exponent of e is then -6×-infinity = infinity. and e to the power of infinity is infinity.
p(x) = 9 + infinity = infinity
x going to infinity :
the exponent of e is then -6×infinity = -infinity. and e to the power of -infinity is 1/e to the power of infinity.
and that is 1/infinity. the limit for that is 0.
p(x) = 9 + 0 = 9
3 1/3 divided by 3/8
Enter your answer, as a mixed number in simplest form,in the boxes
Answers
6.48 x 10 5
-------------------------
(2.4 x 10 4) (1.8 x 10 -2)
Answers
Answer:
1.5×10³
Step-by-step explanation:
You want to know the value of the expression given with numbers in scientific notation.
EvaluationThe usual rules of arithmetic and exponents apply. Your calculator or spreadsheet can use and display the numbers in scientific notation for you.
[tex]\dfrac{6.48\times10^5}{(2.4\times10^4)(1.8\times10^{-2})}=\dfrac{6.48}{2.4\times1.8}\times10^{5-4-(-2)}=\boxed{1.5\times10^3}[/tex]
4/z >= 3; z = 2
Please solve
Answers
The inequality expression 4/z >= 3 is false, when z = 2 because 2 is not greater than or equal to 3
How to evaluate the expression?The inequality expression is given as
4/z >= 3
The value of z is given as
z = 2
Substitute 2 for z in the inequality expression given as
4/z >= 3
So, we have:
4/2 >= 3
Evaluate the quotient
2 >= 3
The above inequality expression is false.
This is so because 2 is not greater than or equal to 3
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Write two expressions
that represent the volume of the cube, one with
exponents and one without.
Answers
The two expressions for the volume of a cube with a side length of S are:
V = S^3
V = S*S*S
How to express the volume of the cube?A cube is a rectangular prism where the 3 dimensions have the same measure, which we will call the side-length of the cube.
So, if S is the sidelength of the cube, the volume will be given by the product between the product between the dimensions of the cube, and the 3 dimensions measure the same thing, which is S, then:
V = S*S*S
That is the expression without exponents, and the expression with an exponent is really trivial, we have S multiplied by itself 3 times, so we get:
V = S^3
These are the two expressions for the volume.
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The sum of first five prime numbers is
Answers
Hope this helps
Can someone help me with this and show work please All the questions
Answers
The evaluation of the given angles are as follows;
A = 107.5° and B = 72.5°‹F = 18°, ‹E = 72°128° and 52°‹Q = 32°, ‹R = 58°45° and 135°33 s‹ABD = 47°, ‹DBC = 43°a = 8, b = 54a = 20m‹ADB = 25° , m‹BDC = 65°What are complementary and supplementary angles?Complementary angles sum up to 90°
Supplementary angles sum up to 180°
1. Let A and B represent the two angles, we have;
A + B = 180°
A - B = 35°
Which gives;
A + B + (A - B) = 180° + 35° =215°
A + B + (A - B) = A + A = 2•A
Which gives;
2•A = 125°
A = 215°/2 = 107.5°
A + B = 180°
B = 180° - A
Therefore;
B = 180° - 107.5° = 72.5°
The two angles are; A = 107.5° and B = 72.5°
2. ‹E + ‹F = 90° Definition of complementary angles.
‹E = ‹F + 54°
Which gives;
2•‹F + 54° = 90°
Therefore;
‹F = 18°
‹E = 72°
3. Let A represent the angle, we have;
A + A - 76° = 180°
A = 256°/2 = 128°
The measure of the angle is 128°
The measure of its supplement is 52°
4. ‹Q + ‹Q + 26 = 90
‹Q = (90-26)/2 = 32
‹Q = 32°
‹R = 32° + 26°= 58°
5. Let A represent the angle, we have;
A + 3•A = 180°
4•A = 180°
A = 180°/4
A = 45°
The measure of the supplement = 3 × 45° = 135°
6. Angle left = 90° - 35° = 55°
Speed= 35°/(21 s) = 5/3°/s
Time remaining for the bridge= 55°/(5/3°/s) = 33 s
7. 3•r + 5 + 5•r - 27 = 90
8•r - 22 = 90
r = 112/8 = 14
‹ABD = 3•r + 5 = 47°
‹DBC = 5•r - 27 = 43°
8. 4•a + 58 = 2•b - 18 = 90
a = 8
b = 54
9. a + 15 + a + 35 = 90
a = 40/2 = 20
10. 3•a + 10 + 13•a = 90
16•a = 80
a = 80/16 = 5
m‹ADB = 3•a + 10 = 25°
m‹BDC = 13•a = 65°
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helpppppppppppppppppppp...................................
Answers
Answer: Its quadrant 3
Step-by-step explanation:
Hope this helps!
Answer:
Quadrant 3
Step-by-step explanation:
Lets have an example
Lets say we are plotting the point (-4,-4)
so, we would go left on the x-axis, to -4. So we will be in either Quadrant 2 or Quadrant 3
Now we go down 4, so we end up in Quadrant 3
Hence, The answer is Quadrant 3
Hope this helps!^^
Challenge: A scuba diver has 30 cubic feet of air in his tank and dives under the water at
3:15pm. When he resurfaced at 3:30pm, he had 12 cubic feet of air left. How many cubic
feet of air per minute did he use?
Answers
The cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
Unit rateQuantity of air in his tank = 30 cubic feetTime he dives in = 3:15pmTime he resurfaced = 3:30pmQuantity of air remaining in the tank = 12 cubic feetCubic feet of air used per minute = Difference in quantity of air in his tank / difference in time
= (30 - 12) / (3:30pm - 3:15pm)
= 18 / 15
= 1.2 cubic feet of air per minute
Therefore, the cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
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Mate m.1 is so hard help me pls someone
Answers
8•5•18= 720/2= 360^3
9•14•6= 756/2= 378^3
378-360= 18cm
The second prism has a larger volume of 378cm^3. It is 18cm larger than the first prism
(Hope this helps)
|x-2|=|4+x|
How can I find the value of X?
Answers
Answer:
x = -1
Step-by-step explanation:
You want to find the value(s) of x that satisfy the equation |x-2| = |4+x|.
DomainsThe behavior of each absolute value function changes at the point where its argument is zero. For this equation, that will be two points:
x -2 = 0 ⇒ x = 2
x +4 = 0 ⇒ x = -4
These two points on the number line divide the domain of the equation into three parts:
x < -4-4 ≤ x < 22 ≤ x.The behavior of the equation will be different in those three domains.
x < -4In this domain, both absolute value functions negate their arguments. That means the equation is equivalent to ...
-(x -2) = -(4 +x)
2 = -4 . . . . . . . . . . add x to both sides
This has no solutions: there are no values of x that will make this true.
-4 ≤ x < 2In this domain, the absolute value function on the left negates its argument, so the equation is equivalent to ...
-(x -2) = (4 +x)
-2 = 2x . . . . . . . . . add x-4 to both sides
-1 = x . . . . . . . . . divide by 2
This value of x is in the domain, so represents a solution to the equation.
x = -1
2 ≤ xIn this domain, neither absolute value function negates its argument, so the equation is equivalent to ...
x -2 = 4 +x
-2 = 4 . . . . . . . subtract x
This has no solutions: there are no values of x that will make this true.
The given equation has one solution: x = -1.
__
Additional comment
When solving an equation like this graphically, it is often useful to put it in the form f(x) = 0. We can obtain that form by defining ...
f(x) = |x -2| -|4 +x|
The graph of this is attached. The only solution is where f(x) = 0, at x = -1.
Note that the function is parallel to the x-axis outside of the middle domain, so will not have any x-intercepts in those regions.
Use the multiplier method to decrease £56 by 14%
You must show your working.
Answers
- 7.84 is actual difference of percentage by multiplier method to decrease.
What percentage means?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.56 - Percentage decrease =
56 - (14% × 56) =
56 - 14% × 56 =
(1 - 14%) × 56 =
(100% - 14%) × 56 =
86% × 56 =
86 ÷ 100 × 56 =
86 × 56 ÷ 100 =
4,816 ÷ 100 =
48.16
56 decreased by 14% = 48.16
Absolute change (actual difference):
48.16 - 56 = - 7.84
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Write the decimal as a fraction.
8.33 = 10F
- 0.83 = -F
[?]
=
Hint: Subtract the first equation from this new
equation to eliminate the repeating decimal.
Enter the decimal value
Answers
the fraction form of the number will be 5 / 18.
We are given the decimal number as:
0.83(bar on 3) = F ...(1)
Now, we need to convert this into fraction.
For this, we will first multiply both the sides by 10
Do, we get that:
8.33 ( bar on 3) = 10 F ...(2)
Now, we will Subract (1) from (2), we get that:
9 F = 8.33 (bar on 3) - 0.83 (bar on 3)
9 F = 7.5
F = 7.5 / 9
F = 2.5 / 9
F = 25 / 90
Reducing the fraction into simplest form:
F = 5 / 18.
Therefore, we get that the fraction form of the number will be 5 / 18.
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Which of the following facts, if true, is enough information for you to prove that lines l and m are parallel? Write yes or no for each.
m<2 + m<4 = 180 degrees ______
m<1 = m<7 _______
m<2 = m<6 _______
m<6 + m<3 = 180 degrees ______
m<1 = m<8 _______
(Click document to see image.)
Answers
Adding yes or no to the information that is enough to proof lines l and m are parallel
m<2 + m<4 = 180 degrees no
m<1 = m<7 no
m<2 = m<6 yes
m<6 + m<3 = 180 degrees no
m<1 = m<8 yes
What are parallel lines?This is a term used in geometry to refer to lines that will never intersect. The concept of parallel lines is used to find angles that are related or equal to each other by the following theorems:
Vertical angles theoremCorresponding angles theoremAlternate interior angles theoremAlternate exterior angles theoremUsing the mentioned theorems we apply to the statements as follows: The first statement is correct but not used to prove parallel lines. The second statement is not correct.
The third statement is correct, it represents transitive property of equality angles, where m<2 equals m<3 by Vertical angles theorem and m<3 is equal to m<6 as by Alternate interior angles theorem.
m<6 + m<3 = 180 degree: the two angles are equal as earlier explained but their sum is not 180 degrees
m<1 = m<8: The equality of these two angles is shown by transitive property of equality angles, and it is enough to prove that line l and m are parallel lines
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Use your knowledge of angle relationships to solve
for x in the diagram. Leave your answer as an exact
decimal.
Answers
The nearest decimal which is the approximate value of x is 18°..
The two slanting lines given in the diagram are parallel.
Furthermore, the horizontal line crosses both parallel lines given above.
Then the measure of the angles marked in the question is equal.
Therefore, we have 5x + 7° = 9x - 63°.
⇒ 63° + 7° = 9x - 5x
⇒ 70° = 4x
⇒ x = 70°÷ 4 = 17.5° ≈ 18°(approximate to the nearest decimal)
Therefore, x = 18°
Let us now compute the magnitude of each angle.
5x + 7 = 5 × 18 + 7 = 90 + 7 = 97
9x - 63 = 9 × 18 - 63 = 162 - 63 = 99
The measurement of these two angles differs by two degrees.. Because the value of x is not exact. We used the approximated value.
Let us recalculate the angle measurements using the exact value 17.5.
5x + 7 = 5 × 17.5 + 7 = 87.5 + 7 = 94.5
9x - 63 = 9 × 17.5 - 63 = 157.5 - 63 = 94.5
So, the exact value of x is 17.5°.
Hence, The nearly value of x to the nearest decimal is 18°.
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A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 17 minutes, and then flies directly back to the hive at feet per second. It is away from the hive for a total of 19 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
Answers
Answer: (a) The equation is so called "time equation"
D/12 + 16*60 + D/8 = 19*60 seconds
(b) To determine the distance D, solve the equation
D/12 + D/8 = 19*60 - 16*60 = 3*60
multiply both sides by 24
2D + 3D = 3*60*24
5D =4320
D =4320/5 = 864 ft
Step-by-step explanation:
What geométric symbol would be represented by a baseball bat
Answers
Answer: i think the overall shape of a baseball bat would be more rectangular
Step-by-step explanation:
reason for thinking so: because a baseball bat depending on size, would normally fit into a rectangular box
At end of the first half of a football game, Nathan had carried the ball for 50.5 yards. By the end of the game, he carried the ball for a total of 75 yards. Find the percent of increase in the number of yards he carried. Round to the nearest whole tenth if necessary
Answers
The percent increase in the number of yards is 32.7%
How to calculate the percent increase ?At the end of the football game, Nathan carried the ball for 50.5 yards
At the end of the game, the ball was carried for a total of 75 yards
The percent increase in the number of yards can be calculated dividing the percentage change by the original value and multiplying by 100
= 75 - 50.5/75 × 100
= 24.5/75 × 100
= 0.3266 × 100
= 32.66
= 32.7%
Hence the percent increase in the number of yards is 32.7%
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A contract was made to be completed in 40 days and 24 men were put to work. After 28 days, 11 more men were engaged and the work was completed just in time. if not extra men engaged, how many days would the work have taken.
Answers
If no extra men were engaged then the work would have been completed in 45.5 days.
What is work?In physics, work is a measure of energy transfer that occurs when an object is moved over a distance by an external force, at least a portion of which is applied in the direction of displacement.So,
= (24 × 28) + (24 + 11) × 12= 672 + 420= 1092The time required by 24 men to complete their work is:
= 1092/24= 45.5Therefore, if no extra men were engaged then the work would have been completed in 45.5 days.
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PLEASE PLEASE HELP!!!
Answers
Answer:
Step 1: 1605 - 75 = 1530
Step 2: 1530 / 255 = 6
Step-by-step explanation:
ayudaaaa c x 4=32 porfaaa :vvv
Answers
Answer:C=8
Step-by-step explanation:
32 divided by 4 = 8
x[tex]x^{2}+ 10x =11[/tex]
Answers
Answer:
For this problem, x has multiple values, so we will solve for both.
Step-by-step explanation:
[tex]x^2+10x-11=11-11\\x^2+10x-11=0\\[/tex]
Quadratic rule
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:} a=1,\:b=10,\:c=-11[/tex]
[tex]x_{1,\:2}=\frac{-10\pm \sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}}{2\cdot \:1}[/tex]
Dealing with radicals
[tex]\sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}\\=\sqrt{10^2+4\cdot \:1\cdot \:11}\\=\sqrt{10^2+44}\\=\sqrt{100+44}\\=\sqrt{144}\\=\sqrt{12^2}\\=12\\[/tex]
Multi-solution expression
[tex]x_1=\frac{-10+12}{2\cdot \:1},\:x_2=\frac{-10-12}{2\cdot \:1}[/tex]
Solve for x₁
[tex]\frac{-10+12}{2\cdot \:1}\\=\frac{2}{2\cdot \:1}\\=\frac{2}{2}\\=1[/tex]
Solve for x₂
[tex]\frac{-10-12}{2\cdot \:1}\\=\frac{-22}{2\cdot \:1}\\=\frac{-22}{2}\\= -\frac{22}{2}\\= -11[/tex]
Thus, x has 2 values for 2 different numbers:
x₁ = 1
x₂ = -11
➲ Hope this helps!
36x+9 equals what
big blak vjndjgd
Answers
We can conclude that the equation 36x + 9 equals -1/4.
What exactly is an equation?An equation, in its most basic form, is a mathematical statement demonstrating that two mathematical expressions are equal.3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.So,
36x + 936x + 9 = 036x = -9x = -9/36x = -1/4Therefore, we can conclude that the equation 36x + 9 equals -1/4.
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An architect charges $1800 for a first draft of a three-bedroom house. If the work takes longer than 8
hours, the architect charges $105 for each additional hour. What would be the total cost for a first draft
that took 14 hours to complete?
Answers
The total cost for a first draft that took 14 hours to complete is $2430.
How to illustrate the expression?It should be noted that when the work takes longer than 8 hours, the architect charges $105 for each additional hour. For 14 hours, the additional hours will be:
= 14 - 8
= 6 hours
Therefore, the total cost will be:
= 1800 + (105 × 6)
= 1800 + 630
= 2430
Therefore, the total cost for a first draft that took 14 hours to complete is $2430.
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