The equations 2 x minus y = negative 2, 3 x + 2 y = 5, 4 x minus y = 2, and 22 x + 10 y = 7 are shown on the graph below. Which system of equations has a solution of approximately (–0.3, 1.4)? 2 x minus y = negative 2 and 22 x + 10 y = 7 3 x + 2 y = 5 and 4 x minus y = 2 4 x minus y = 2 and 22 x + 10 y = 7 2 x minus y = negative 2 and 3 x + 2 y = 5
Answers
Answer:
The correct option is;
(2·x - y = -2 and 22·x + 10·y = 7)
2 x minus y = negative 2 and 22 x + 10 y = 7
Step-by-step explanation:
2x - y = -2.........(1)
3x + 2y = 5.......(2)
4x - y = 2..........(3)
22x + 10y = 7...(4)
Given that the solution of the system of equation is (-0.3, 1.4), we have;
The system of equations consist of those equations that pass through the point (-0.3, 1.4)
We check as follows;
Equation (1)
2×(-0.3) - 1.4 = -2
Therefore, equation (1) passes through the point (-0.3, 1.4) and is one of the equations
Equation (2)
3×(-0.3) + 2×1.4 = 1.9 ≠ 5
Equation (2) is not part of the system of equations
Equation (3)
4×(-0.3) - 1.4 = -2.6 ≠2
Equation (3) is not part of the system of equations
Equation (4)
22×(-0.3) + 10×1.4 = 7.4 ≈ 7
Therefore, equation (4) approximately passes through the point (-0.3, 1.4) and is one of the equations
The correct option is A. [tex]2x - y = -2\ and 22x + 10y = 7.[/tex]
Given equations,
[tex]2x - y = -2.........(1)[/tex]
[tex]3x + 2y = 5.......(2)[/tex]
[tex]4x - y = 2..........(3)[/tex]
[tex]22x + 10y = 7...(4)[/tex]
Since the solution of the system of equation is [tex](-0.3, 1.4),[/tex] Hence the system of equation satisfy the above point.
Now check all the equations,
Equation (1),
[tex]2\times(-0.3) - 1.4 = -2\\-0.6-1.4=-2\\-2.0=-2[/tex]
Hence, equation (1) passes through the point[tex](-0.3, 1.4)[/tex] and is one of the equations.
Similarly, Equation (2)
[tex]3\times (-0.3) + 2\times1.4 = 5\\-0.9+2.8=5\\1.9=5\\[/tex]
Hence the above equation does not satisfy the solution, so it is not the other system of equation.
Now, Equation (3)
[tex]4\times(-0.3) - 1.4 = -2.6 \neq 2[/tex]
Hence Equation (3) is not part of the system of equations.
Now, Equation (4)
[tex]22\times (-0.3) + 10\times1.4 = 7.4[/tex]
Hence the above equation approximately passes through the solution[tex].(-0.3, 1.4)[/tex] and is one of the equations.
Hence the required system of equation is [tex]2x - y = -2[/tex] and [tex]22x + 10y = 7[/tex].
Therefore the correct option is A.
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Related Questions
Given ADC ACB and BDC BCA prove a squared + b squared = c squared. Use the two Column proof.
Answers
Answer:
a² + b² = c · (e + d) = c × c = c²
a² + b² = c²
Please see attachment
Step-by-step explanation:
Statement, Reason
ΔADC ~ ΔACB, Given
AC/AD = BA/AC, The ratio of corresponding sides of similar triangles
b/e = c/b
b² = c·e
ΔBDC ~ ΔBCA, Given
BC/BA = BD/BC, The ratio of corresponding sides of similar triangles
a/c = d/a
a² = c·d
a² + b² = c·e + c·d
a² + b² = c · (e + d)
e + d = c, Addition of segment
a² + b² = c × c = c²
Therefore, a² + b² = c²
8. The world's tallest
totem pole is in Alert
Bay, B.C., home of the
Nimpkish First Nation.
Twenty feet from the
base of the totem pole,
the angle of elevation
of the top of the pole
is 83.4º. How tall is
the totem pole to the
nearest foot?
Answers
Answer:
The height of the totem tree is approximately 172.8ft
Step-by-step explanation:
Hello,
To find the height of the totem pole, we need to use our date to make a pictorial representation so that we can know if the pole and base makes a right angle triangle with the angle of elevation.
See attached document for better illustration.
Let T represent the height of the pole.
Using trigonometric ratio,
SOHCAHTOA, we can use tangent since we have our adjacent and we're to solve for the opposite.
Tanθ = opposite/ adjacent
Opposite = T
Adjacent = 20ft
θ = 83.4°
Tan83.4 = T / 20
T = 20Tan83.4
T = 20 × 8.64
T = 172.8ft
The height of the totem tree is approximately 172.8ft
Polygon CCC has an area of 404040 square units. K 2ennan drew a scaled version of Polygon CCC using a scale factor of \dfrac12 1 2 start fraction, 1, divided by, 2, end fraction and labeled it Polygon DDD. What is the area of Polygon DDD?
Answers
Answer:
Area of polygon D = 10 square units
Step-by-step explanation:
Given:
Polygon C has an area of 40 square units.
It is scaled with a scale factor of [tex]\frac{1}2[/tex] to form a new polygon D.
To find:
The area of polygon D = ?
Solution:
When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.
And the area becomes one-fourth of the original polygon.
Let us consider this by taking examples:
First of all, let us consider a right angled triangle with sides 6, 8 and 10 units.Area of a right angled triangle is given by:
[tex]A = \dfrac{1}{2} \times Base \times Height\\\Rightarrow A = \dfrac{1}{2} \times 6 \times 8 = 24\ sq\ units[/tex]
If scaled with a factor [tex]\frac{1}{2}[/tex], the sides will be 3, 4 and 5.
New area, A':
[tex]A' =\dfrac{1}{2} \times 3 \times 4 = 6\ sq\ units = \dfrac{1}4\times A[/tex]
i.e. Area becomes one fourth.
Let us consider a rectangle now.Sides be 8 and 10 units.
Area of a rectangle, A = [tex]Length \times Width[/tex] = 8 [tex]\times[/tex] 10 = 80 sq units.
Now after scaling, the sides will be 4 and 5 units.
New Area, A' = 4 [tex]\times[/tex] 5 =20 sq units
So, [tex]\bold{A' = \frac{1}4 \times A}[/tex]
Now, we can apply the same in the given question.
[tex]\therefore[/tex] Area of polygon D = [tex]\bold{\frac{1}{4}}[/tex][tex]\times[/tex] Area of polygon C
Area of polygon D = [tex]\bold{\frac{1}{4}}[/tex][tex]\times[/tex] 40 = 10 sq units
Answer:
Step-by-step explanation:
10
I SHALL NAME THEE BRAINLIEST!! (: Pls help me. (#1) 4A - 1 = 3A + 8 solve and check (#2) 1 + F + 3 + F = F + 5 solve and check (#3) Naomi had B bushels of grain. After Ruth brought her 5 more bushels of grain, she had 11 bushels in all. How much grain did Naomi have to start with? Write an equation and solve.
Answers
Answer:
1. a=9 2. f=1 3. b=6
Step-by-step explanation:
1.) 4a-1=3a+8
subtract 3a from both sides
a-1+8
add 1 to both sides
a=9
2.) 1+f+3+f=f+5
combine like terms that are on the same side
2f+4=f+5
subtract f from both sides
f+4=5
subtract 4 from both sides
f=1
3.) construct a equation
b+5=11
subtract 5 from both sides
b=6
what is the value of 24% of 800?
Question of mathematics
Answers
We simply multiply 800 and 24% (0.24)
800(0.24) = 192
Answer:
[tex] \huge \boxed{192}[/tex]Step-by-step explanation:
[tex]24\% \: of \: 800[/tex]
By definition of p% = p/100
[tex] = \frac{24}{100} \times 800[/tex]
Reduce the numbers with Greatest Common Factor 100
[tex] = 24 \times 8[/tex]
Multiply the numbers
[tex] = 192[/tex]
Hope I helped!
Best regards!!
PLEASEEEEE I don't understand this question.
Answers
Answer:
262°
Step-by-step explanation:
The relationship between the angle at B (82°) and the arcs of the circle, CGF and CDF, is that the angle is half the difference of those arcs. Of course the sum of those arcs is 360°, since together they make a full circle. So. we have ...
CGF +CDF = 360
(CGF -CDF)/2 = 82
We need to solve this system of equations to find CGF.
__
Multiplying the second equation by 2 and adding the first, we get ...
2((CGF -CDF)/2) +(CGF +CDF) = 2(82) +(360)
2CGF = 524 . . . . . simplify
CGF = 262 . . . . . . divide by 2
The measure of arc CGF is 262°.
_____
Alternate solution
Here's another way to get there. Arc CDF is the supplement to angle B, so is ...
CDF = 180° -∠CBF
Of course, arc CGF is 360° minus arc CDF, so ...
CGF = 360° -(180° -∠CBF)
CGF = 180° +∠CBF . . . . . simplify . . . please note this is a general solution
Then ...
arc CGF = 180° +82° = 262°.
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike? if possible, I would like a clear equation.
Answers
Answer:
He hiked 10 miles.
Step-by-step explanation:
rate x time = distance
The distance up and the distance down are equal
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
4) Solve the problem for the compound events.
A bank has a special vault for valuable items. It has 3 dials that operate the combination. The
first dial has the numbers from 1 to 100, the second and third each have the 26 letters of the al-
phabet. In order to open the vault, the bank manager must correctly set each dial. How many
possible combinations are there for this vault?
Answers
Answer:
i think its 67600
Step-by-step explanation:
100*26=2600
2600*26=67600
how to do this question plz
Answers
Answer:
Depth of the milk = 4 cm
Step-by-step explanation:
In the figure attached,
Milk carton is in the shape of a cuboid having length = 8 cm, Width = 5 cm and Height = 15 cm
Depth of the milk in the carton = 12 cm
Milk inside the carton will have the same shape of cuboid, having same length and width but a different height.
Volume of the milk = volume of the cuboid shape of the milk
= Length × width × height
= 8 × 5 × 12
= 480 cm³
Now the carton is turned with its base on the shaded region.
By changing the base, dimensions of the milk inside the carton will change but the volume of the milk will remain the same.
New dimensions of the milk inside the carton will be,
Length = 15 cm
Width = 8 cm
Height = d cm (unknown side)
By using the formula of volume again,
V = l × b × h
480 = 15 × 8 × d
480 = 120d
d = [tex]\frac{480}{120}[/tex]
d = 4 cm
Therefore, depth of the milk in the carton will be 4 cm.
Find the angle measures given the figure is a rhombus. m=
Answers
Answer:
74°
Step-by-step explanation:
A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.
According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.
The remaining angle of the rhombus will be calculated as thus;
= 360° - (32°+32°)
= 360° - 64°
= 296°
This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°
This means that each obtuse angles of the rhombus will be 148°.
To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.
m° = 148°/2
m° = 74°
Hence the angle measure if m(1) is 74°
8x + 5y=-22
-3x - 5y = 2
Answers
Answer:
(-4, 2).
Step-by-step explanation:
8x + 5y=-22
-3x - 5y = 2 Adding the 2 equations:
5x = -20
x = -4.
Substitute x = -4 in the first equation:
8(-4) + 5y = -22
5y = -22 + 32
5y = 10
y = 2.
Answer:
[tex]x=-4,\:\\y=2[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}8x+5y=-22\\ -3x-5y=2\end{bmatrix}\\\mathrm{Multiply\:}8x+5y=-22\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:24x+15y=-66\\\mathrm{Multiply\:}-3x-5y=2\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:-24x-40y=16\\\\\begin{bmatrix}24x+15y=-66\\ -24x-40y=16\end{bmatrix}\\\\-24x-40y=16\\+\\\underline{24x+15y=-66}\\-25y=-50\\\begin{bmatrix}24x+15y=-66\\ -25y=-50\end{bmatrix}\\-25y=-50\\\mathrm{Divide\:both\:sides\:by\:}-25\\\frac{-25y}{-25}=\frac{-50}{-25}\\y=2\\[/tex]
[tex]\mathrm{For\:}24x+15y=-66\mathrm{\:plug\:in\:}y=2\\24x+15\times\:2=-66\\24x+30=-66\\24x+30-30=-66-30\\24x=-96\\\frac{24x}{24}=\frac{-96}{24}\\x=-4\\\\\\x=-4,\:y=2[/tex]
Which phrase refers to the legal act of lowering an individual’s tax liability?Which phrase refers to the legal act of lowering an individual’s tax liability?
Answers
Answer:
Tax avoidance - legal
Tax evasion - illegal
Find the value of
x in the triangle shown below.
Answers
Answer:
69.7° (corrected to 3 significant figures)
Step-by-step explanation:
Use the cosine formula to solve for x.
[tex]cosA=\frac{(b^2+c^2-a^2)}{2bc} \\cos x =(3.5^2+ 3.5^2 -4^2)}/[2(3.5)(3.5)]cos x =0.346939\\x=69.7[/tex]
hellpp plzzzzz.......
Answers
Answer:
120Step-by-step explanation:
Given
u = 14 , a = 8 , t = 4
Now, let's find the value of s
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
plug the values
[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]
Reduce the numbers with G.C.F 2
[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]
Multiply the numbers
[tex] = 56 + 4 \times {4}^{2} [/tex]
Calculate the product
[tex] = 56 + {4}^{3} [/tex]
Evaluate the power
[tex] = 56 + 64[/tex]
Add the numbers
[tex] = 120[/tex]
Hope this helps..
best regards!!
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a
Answers
Answer:
Unknown side = 28tan B = 7/24Step-by-step explanation:
The question is incomplete. Here is the complete question.
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.
Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.
From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;
c² = a²+b²
100² = 96² +b²
b² = 100² - 96²
b² = 10,000 - 9216
b² = 784
b = √784
b = 28
Hence, the unknown length is 28.
To get tanB, we will use the SOH, CAH, TOA trigonometry identity
According to TOA, tan B = opposite/adjacent
tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)
Given b = 28 and a = 96
tan B = 28/96
tan B = 4*7/4*24
tan B = 7/24
The graph of f(x)=4x^3-13x+9x+2 is shown below. How many roots of f(x) are rational numbers? Quick Please!!!!
Answers
Answer:
All three are rational numbers.
Step-by-step explanation:
I used Desmos (a graphing calculator online) and the roots were all able to be written with fractions.
Which phrase matches the expression p+7? A. 7 minus p B. the difference of 7 and p C. the quotient of p and 7 D. the sum of p and 7
Answers
Answer:
the sum of p amd 7
hopefully this helped :3
Answer:
D
Step-by-step explanation:
Since addings answer is a sum
p+7
D
PLEASE HELP
A hire purchase agreement offers gym equipment, with a marked price
$897, for $87 deposit and $46.80 a month payable over 2 years.
Calculate :
a) the total hire-purchase price
b) the amount of
amount of interest charged
Answers
Answer: a) $1,210.20 b) $313.20
Step-by-step explanation:
a) $87 down + $46.80(24 months) = $1,210.20 total paid
b) $1,210.20 - $897.00 = $313.20 interest paid
WILL GIVE BRAINLEST ANSWER IF ANSWERED IN THE NEXT 24 HRS Express the complex number in trigonometric form. -5i
Answers
Answer:
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Step-by-step explanation:
If a complex number is z=a+ib, then the trigonometric form of complex number is
[tex]z=r(\cos \theta +i\sin \theta)[/tex]
where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].
The given complex number is -5i.
It can be rewritten as
[tex]z=0-5i[/tex]
Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.
[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]
[tex]\tan \theta=\dfrac{-5}{0}[/tex]
[tex]\tan \theta=\infty[/tex]
[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex] [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]
[tex]\theta=\dfrac{3\pi}{2}[/tex]
So, the trigonometric form is
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Answer:
in degrees the answer is 5 (cos 270 + i sin 270)
in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))
Step-by-step explanation:
Boris is selling pirate hats. If he sells the hats for $50 he will sell 135 hats.
For each increase in price of $2 he will sell 3 fewer hats.
Determine the possible prices he could charge to earn $6486 or more.
Answers
Answer:
Current price $50eax135hats= $6750
Step-by-step explanation:
If he sells the hats at $52 he sells 3 less hats so $52x132=$6864
if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc
$56 x 126=$7056
Which is the definition of a rhombus?
a. A quadrilateral with four right angles
b. A quadrilateral with four congruent sides
c. A quadrilateral with interior angles that sum to 360°
d. A quadrilateral with two pairs of opposite congruent sides
Answers
Answer:
a) A quadrilateral with 4 right angles
Answer:
I think the answer is b
I'm sorry if I'm not correct
Choose the equivalent system of linear equations that will produce the same solution as the one given below 4x-y=-11 2x+3y=5
Answers
Answer: x = -2 , y = 3
Step-by-step explanation:
4x-y=-11
2x+3y=5
Solve 4x-y=-11 for y
Add -4x to both sides
4x-y+-4x=-11+-4x
-y=-4x-11
Divide both sides by -1
-y/-1=-4x-11/-1
y=4x+11
Substitute 4x+11 for y in 2x +3y=5
2x+3y=5
2x+3(4x+11)=5
Simplify both sides of the equation
14x+33=5
Add -33 to both sides
14x+33+-33=5+-33
14x=-28
Divide both sides by 14
14x/14=-28/14
x=-2
Substitute -2 for x in y= 4x+11
y=4x+11
y=(4)(-2)+11
Simplify both sides of the equation
y=3
Can someone answer all of them or at least one please. Thank you :)
1. Solve the equation below for the variable (y):
2x + 5y = 20
A. y = 20 - 2x / 5
B. y = 18x / 5
C. y = 5 (20 - 2x)
d. y = 2x - 20 / 5
2. Substitute r = 3 and h = 5 into the formula V = πr^2h then evaluate
A. 235.5
B. 47.1
C. 141.3
3. In a formula, any operation we can do to a number can also be done to a variable.
True or False?
Answers
Answer:
1) A. y= (20 - 2x) /5
2) C. 141.3
3) True ( Your answers are here.)
Answer:
1. is A 2. is C 3. is I believe True
Step-by-step explanation:
1.
2x + 5y = 20
-2x -2x
5y = 20 - 2x
/5 /5
Answer: y = 20 - 2x /5
2.
V = πr^2h
π=3.14 r=3 h=5
3.14*3^2*5
1.413*10^2 which = 141.3
3.
I am not completely sure but I think it is True
Hope this helps
We have 9 balls, numbered 1 through 9, and 27 bins. How many different ways are there to distribute these 9 balls among the 27 bins? Assume the bins are distinguishable (e.g., numbered 1 through 27).
Answers
Answer:
7625597484987 ways
Step-by-step explanation:
Given the following :
Number of ball(k) = 9
Number of bins (n) = 27
How many different ways are there to distribute these 9 balls among the 27 bins.
Here, the balls have different labels (1 to 9)
The bins are also distinguishable, therefore each ball can go into any of the 27 distinct bins.
Therefore, the different ways are there to distribute these 9 balls among the 27 bins equals = n^k
27^9 = 7625597484987 ways.
How many Real Solutions
Answers
Answer:
D.0
Step-by-step explanation:
Our system of equations is
y= x²+1y=xthen we can conclude that
x²+1 = xx²+1-x = 0x²-x+1 = 0This is a quadratic equation so we will use the dicriminant method:
Let Δ be our dicriminant
a= 1b= -1c= 1Δ = (-1)²-4*1*1 = 1-4 = -3 < 0The dicriminant is negative so this equation has no real solutions
the the system has no real solutions
Nora bought a car last year so that she could drive to work after school. She spent $250 last year for gas. This year she spent $295. Disregarding other factors, what is the inflation rate? 18% 19% 20% 21%
Answers
Answer:
here,
money spent in 1st year =$250
money spent in 2nd year=$295
total inflated amount=$295- $250
=$45
Then,
inflation rate= ($45/ $250)×100%
=18%
18x + 18 = 17 What is the variable x and how do you get that answer?
Answers
Answer:
x = - 1/18
Step-by-step explanation:
Move all terms not containing x to the right side of the equation
Divide each term by 18 and simplify
The result can be shown in multiple forms
x = -1/18
Decimal form= -0.05
Answer: x=-1/18
Step-by-step explanation:
18x+18=17
you subtract 18 from both sides
18x=-1
then you divide by 18 on both sides
x=-1/18
Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister (i.e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answers
Answer:
The larger canister has 8 times the volume and 4 times the volume of the smaller one.
Step-by-step explanation:
The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.
The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.
The canisters are in the shape of a cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
The surface area of a cylinder is given as:
A = 2πr(r + h)
SMALLER CANISTER
Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres
Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres
LARGER CANISTER
Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres
Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres
By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.
Answer:
Yeah, what they said above.
Step-by-step explanation:
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 and is the least intense sound a human ear can hear. What is the approximate loudness of a dinner conversation with a sound intensity of 10–7?
Answers
Answer:
The loudness of the dinner conversation is 40 dB
Step-by-step explanation:
Loudness in dB = 10[tex]Log_{10}[/tex] [tex](\frac{I}{I_{o} })[/tex]
where [tex]I_{0}[/tex] is the least intense sound a human can hear = [tex]10^{-12}[/tex] W/m^2
For a dinner conversation with sound intensity of [tex]I[/tex] = [tex]10^{-7}[/tex] W/m^2
Loudness = 10[tex]Log_{10}[/tex] [tex](\frac{10^{-7} }{10^{-12} })[/tex] = 10[tex]Log_{10}[/tex] [tex]( 10^{4} )[/tex] = 40 dB
Answer:
50 Db
Step-by-step explanation:
When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. Results. What is the value of ?
Answers
Answer:
0Step-by-step explanation:
Given the expression after 4 has been subtracted from both sides as
1/2 x = - 1/2 x, the original expression will be gotten by adding back 4 to both sides of the resulting expression as shown;
1/2 x + 4 = - 1/2 x + 4
x/2 + 4 = -x/2 + 4
Find the LCM of both equation;
(x+8)/2 = (-x+8)/2
Multiplying both sides by 2 will give;
x+8 = -x+8
Collecting the like terms;
x+x = 8-8
2x = 0
x = 0/2
x = 0
Hence, the value of x is 0
Answer:
0
Step-by-step explanation: