Answer:
no it is not 1/3
Step-by-step explanation:
(x-2) / (x-6)
This does not simplify
Rewriting x-2 as (x-6 +4)
(x-6 +4)/ ( x-6)
Replacing x-6 as m
( m+4) /m
Simplifying
m/m + 4/m
1 + 4/m
Replacing m with x-6
1 + 4/ ( x-6)
This is not 1/3
Nine less than the quotient of
twice a number and four.
Answer:
-1
Step-by-step explanation:
Twice a number of 4 equals 8
4×2=8
less than 9 of the quotient (answer) of twice a number of 4, is -1
8-9= -1
The required expression for Nine less than the quotient of twice a number and four gives the equation, y =2x/4 - 9.
An expression Nine less than the quotient of twice a number and four. is to be determined.
The process in mathematics to operate and interpret the function to make the function simple or more understandableis called simplify and the process is called simplification.
The quotient is the result when one value gets divided by some other value.
Using simple arithmetic,
Let the number be x,
A number y is equal to nine less than the quotient of twice of x and four. So,
y = quotient of 2x and four - 9
y = 2x/4 - 9
Thus, the required expression for Nine less than the quotient of twice a number and four gives the equation, y =2x/4 - 9.
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Matrices and determinants What is 4c?
Answer:
Answer is D.
Step-by-step explanation:
do 4 times every value in the ( )
Answer:
[tex]\boxed{\sf D}[/tex]
Step-by-step explanation:
Which of the following is the correct factorization of 64x³ + 8? (2x + 4)(4x² - 8x + 16) (4x + 2)(16x² - 8x + 4) (4x - 2)(16x² + 8x + 4) (2x - 4)(4x² + 8x + 16)
Answer:
work is pictured and shown
Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your work and include units. If he had a jet pack, would you use distance or displacement? Why?
Answer:
if he needs to walk, we can see that between the street and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.
Now he has a jet-pack, he can ignore the buildings and just travel in the shorter path, so we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.
One of the cathetus is the vertical distance, in this case, is 1km, and the other one is the horizontal distance, also 1km.
So the actual distance is given by the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse, then:
H^2 = 1km^2 + 1km^2
H = (√2)km = 1.41km.
Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, so in this case the distance and the displacement would be the same.
Distance: "how much ground an object has covered"
Displacement: "Difference between the final position and the initial position"
When he walks, the distance is 2km, but the displacement is 1.41km
When he uses the jet-pack, both the distance and the displacement are 1.41km
Answer and Step-by-step explanation:
The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km. The result of this is a total of 4¨*0.5 km = 2 km. The second thing is that he must walk 2 kilometers. On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings. This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home. As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km. The result is that these catheti have a length of 2*0.5 km = 1 km. The other is the distance of the horizontal line, which is 1 km. The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2. Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2. As well, H = (√2)km = 1.41 km. Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow. For this specific situation, the displacement, and the distance would be the exact same. The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered. Also, when he walks, the distance is 2 km and the displacement is 1.41 km. Also, when he utilizes the jet pack, the distance is equal to the displacement. Both of these are 1.41 km.
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.
Answer:
[tex]V_2=305.14\ \text{inch}^3[/tex]
Step-by-step explanation:
The volume of a gas in a container varies inversely as the pressure on the gas.
[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]
If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?
So, using the above relation.
So,
[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]
So, the new volume is [tex]305.14\ \text{inch}^3[/tex].
The graph of g(x) is the result of translating the graph of f(x) = (one-half) Superscript x three units to the left. What is the equation of g(x)?
Answer:
[tex]g(x) = 0.5^{(x+3)}[/tex]
Step-by-step explanation:
Assuming f(x) = [tex]0.5^{x}[/tex] is a correct interpretation of f(x),
the way to translate three units to the left is to change x to x+3. This gives our answer: [tex]g(x) = 0.5^{(x+3)}[/tex]
Answer:
B. g(x) = (1/2)⁽ˣ⁺³⁾
Hope this helps!
Step-by-step explanation:
A computer store sells new computers for $500 and refurbished computers for
$200. In March, the store sold 20 computers for $6,400, meaning they sold ?
refurbished computers.
Answer:
no of new computers sold : 8
no. of refurbished computer sold : 12
Step-by-step explanation:
Let the no. of new computers sold be x
let the no. of refurbished computers sold be y
Given
In March, the store sold 20 computers
x + y = 20
y = 20-x ----- equation 2
selling price of new computer = $500
selling price of x new computer = 500*x = 500x
selling price of refurbished computer = $200
selling price of y refurbished computer = 200*y = 200y
Total selling price of x new computer and y refurbished computers = 500x+200y
given that
total prioce of computer is $6400
thus
500x+200y = 6400
using y = 20-x from equation 2
500x+200(20-x) = 6400
=> 500x+ 4000 - 200x = 6400
=> 300x = 6400 - 4000 = 2400
=> x = 2400/300 = 8
Thus,
no of new computers sold = 8
no. of refurbished computer sold = 20 -8 = 12
Find the area of the surface generated by revolving x=t + sqrt 2, y= (t^2)/2 + sqrt 2t+1, -sqrt 2 <= t <= sqrt about the y axis
The area is given by the integral
[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]
where C is the curve and [tex]dS[/tex] is the line element,
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
We have
[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]
[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]
[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]
So the area is
[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]
Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:
[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]
a department store regularly sells a pair of pants for $49.95. they are having a sale where clothing 30% off.
after including an 8% sales tax, how much do the pants cost on sale?
A. $30.97
B. $38.96
C. $37.76
D. $32.17
Answer:
C. $37.76
Step-by-step explanation:
30% of $49.95
=30/100×49.95
=$14.99
selling price = 49.95 -14.99
= $34.96
8% sales tax included
=8/100×34.96
=$2.80
new price= 34.96+2.80
=$37.76
Whats 18x^3 divided by 7x?????
Consider the given function and the given interval.
f(x) = 8 sin x - 4 sin 2x, [0,pi]
(a) Find the average value f ave of f on the given interval.
(b) Find c such that f ave = f(c).
(a) The average value of f(x) on the closed interval [0, π] is
[tex]\displaystyle\frac1{\pi-0}\int_0^\pi f(x)\,\mathrm dx = \frac1\pi\int_0^\pi(8\sin(x)-4\sin(2x))\,\mathrm dx = \boxed{\frac{16}\pi}[/tex]
(b) By the mean value theorem, there is some c in the open interval (0, π) such that f(c) = 16/π. Solve for c :
8 sin(c) - 4 sin(2c) = 16/π
8 sin(c) - 8 sin(c) cos(c) = 16/π
sin(c) - sin(c) cos(c) = 2/π
Use a calculator to solve this. You should get two solutions, c ≈ 1.2382 and c ≈ 2.8081.
Find the value of x.
Answer:
5
Step-by-step explanation:
This shape is formed by two right triangles.
Let's start by the little one.
Let y be the third side.
Using the Pythagorian theorem we get:
y^2 = 6^2 + 3^2
y^2 = 36 + 9
y^2 = 45
y = 3√(5)
●●●●●●●●●●●●●●●●●●●●●●●●
Now let's focus on the second triangle. Let z be the third side.
The Pythagorian theorem:
6^2 + x^2 = z^2
Using the Pythagorian theorem on the big triangle :
[3√(5)]^2 + z^2 = (3+x)^2
45 + z^2 = 3x^2 + 6x + 9
36 +z^2 = 3x^2 +6x
So we have a system of equations.
36+ x^2 = z^2
36 +z^2 = 3x^2 +6x
We want to khow the value of x so we will eliminate z .
Add (36+x^2 -z^2 =0) to the second one.
36 + x^2-z^2+36+z^2 = 3x^2+6x
72 + x^2 = 3x^2 +6x
72 - 2x^2 -6x = 0
Multipy it by -1 to reduce the number of - signs
2x^2 + 6x -72 = 0
This is a quadratic equation
Let A be the discriminant
● a = 2
● b = 6
● c = -72
A = b^2-4ac
A = 36 -4*2*(-72) = 36 + 8*72 =612
So this equation has two solutions
The root square of 612 is approximatively 25.
● (-6-25)/4 = -31/4 = -7.75
● (-6+25)/4 = 19/4 = 4.75 wich is approximatively 5
A distance cannot be negative so x = 5
how to find the roots of a quadratic equation -10x^2 + 0x +250
Answer:
Step-by-step explanation:
The first thing you want to do is to factor in any quadratic equation.
So, -10(x^2-25)
Now, we see this is a special case, whenever we see a equation in this case, x^2 - b^2, we factor it to this (x+b)(x-b)
So, -10(x+5)(x-5)
x = -5 and x = 5
Find the function h(x) = f(x) - g(x) if f(x) = 3^x and g(x) = 3^2x - 3^x. A.h( x) = 0 B.h( x)=-3^2x C.h( x) = 3^x (2 - 3^x) D.h( x) = 2(3^2x)
Answer:
3^x( 2-3^x)
Step-by-step explanation:
f(x) = 3^x and g(x) = 3^2x - 3^x
h(x) = f(x) - g(x)
3^x - ( 3^2x - 3^x)
Distribute the minus sign
3^x - 3^2x + 3^x
2 * 3^x - 3 ^ 2x
Rewriting
We know that 3^2x = 3^x * 3^x
2 * 3^x - 3^x* 3^x
Factoring out 3^x
3^x( 2-3^x)
help help help help help help
Answer:
75 yards long and 90 yards wide.
Step-by-step explanation:
Let's first find the perimeter of the main rectangle:
100x2 + 65x2 =
330
_________________________________________
Next we need to find two numbers that match:
75 and 90
75x2 + 90x2 =
330
_________________________________________
75x90 is 6750 (More Area)
100x60 is 6500 (Less Area)
ASAP!!!!!!!asap!!!!!!!!!!!! asap asap asap
Answer:
7). x = 3.2, AC = 42.8
8). a = 6, YZ = 38
Step-by-step explanation:
It is given in the question that a point B is between A and C of the line segment AC.
⇒ AB + BC = AC
By substituting the values of segments,
5x + (9x - 2) = (11x + 7.6)
14x - 2 = 11x + 7.6
14x - 11x = 7.6 + 2
3x = 9.6
x = 3.2
Therefore, AC = 11x + 7.6
= 11(3.2) + 7.6
= 35.2 + 7.6
= 42.8
Question (8).
If Y is a point between X and Z,
⇒ XY + YZ = XZ
By substituting the measures of these segments given in the question,
(3a - 4) + (6a + 2) = (5a + 22)
9a - 2 = 5a + 22
9a - 5a = 22 + 2
4a = 24
a = 6
Since, length of segment YZ = 6a + 2
= 6(6) + 2
= 38
perform the indicated operation (8-15i)(-3 + 2i)
Answer:
[tex] - 24 + 16i + 45i + 15 = 9 + 61i[/tex]
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
What is the slope of the line shown below?
A. -13/6
B. 6/13
C. 13/6
D. -6/13
-
Answer:
13/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (6 - -7)/(1 - -5)
= ( 6+7)/ (1+ 5)
= 13/6
A box is 30 inches wide, 16 inches long, and 14 inches high. To the nearest cubic inch, what is the volume of the box?
Answer:
6720 in ^3
Step-by-step explanation:
Volume = length * width * height
= 30*16*14
=6720 in ^3
Allowance bank received a deposit of 28,000 and is free to lend out 25,480 what is the reserve rate?
Answer:
Reserve rate = 9%
Step-by-step explanation:
Reserve ratio/rate is the percentage of deposits which commercial banks are required to keep as cash, as directed by the central banks.
first, let us calculate the reserve amount as follows:
Reserve = Deposit - (free amount to lend out)
Reserve = 28,000 - 25,480 = $2,520
[tex]Reserve\ rate = \frac{Reserves}{Deposits} \times100\\Reserve\ rate = \frac{2520}{28000} \times100\\=\frac{252000}{28000} =9\%[/tex]
Therefore the reserve rate = 9%
Help please, I don't understand :(
Answer:
38 = JKL
Step-by-step explanation:
JKM = JKL + LKN + NKM
Substituting what we know
104 = JKL + LKN +33
KN bisects LKM so NKM = LKN
33 = LKN
104 = JKL + 33 +33
104 = JKL + 33 +33
Combine like terms
104 = JKL +66
104 - 66 = JKL
38 = JKL
Answer: ∡JKL=38°
Step-by-step explanation:
KN bidects ∡LKM => ∠KLN=∡NKM=33°
=> ∡LKM=∠KLN+∡NKM=33°+33°=66°
=>∡JKL= ∡JKM-∡LKM= 104°-66°=38°
∡JKL=38°
GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
A 16-inch piece of string is 40.64 centimeters long. To the nearest 0.01 centimeter, how long will a 42-inch price of string be?
A. 56.64 cm
B. 82.64 cm
C. 106.68 cm
D. 1,706.88 cm
Please show ALL work! <3
Answer:
106.68 centimeters
Step-by-step explanation:
40.64 cm/16 in = x cm/42 in
Cross multiplying, we get:
16x = 40.64(42)
16x = 1706.88
x = 106.68 centimeters
Answer two questions about Equations A and B: A.5x=20 \ B.x=4 1) How can we get Equation B from Equation A? Choose 1 answer: (Choice A) Multiply/divide both sides by the same non-zero constant (Choice B,) Multiply/divide both sides by the same variable expression (Choice C) Add/subtract the same quantity to/from both sides (Choice D) Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
Given the equations :
5x = 20 ___ (A)x = 4 _____ (B)To obtain the value ; x = 4 from A
We multiply (A) by the same non-zero constantHere, the constant value which can be used is 5 in other to isolate 'x'
5x/5 = 20/5
x = 4
Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"
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If the length of the legs of a right triangle are 13 and 13,what is the length of the hypotenuse? Round your answer to the nearest tenth,if necessary.
Answer:
a² + b² = c²
13² + 13² = c²
169 + 169 = c²
338 = c²
c = √338 or 18.385 or 13√2
Answer:
18.4
Step-by-step explanation:
13² + 13² = x²
169 + 169 = x²
338 = x²
x = 18.38477....
Which option is correct and how would one solve for it?
Answer:
2+4+6+8
Step-by-step explanation:
We have the sum of 2n where n runs from 1 to 4
n=1 2(1) = 2
n=2 2(2) = 4
n=3 2(3) = 6
n=4 2(4) = 8
The sum is add
2+4+6+8
Which relationships have the same constant of proportionality between y and x as the equation 3y=2x? SELECT 3 ANSWERS
*Correct Question:
Which relationships have the same constant of proportionality between y and x as the equation 3y=27x?
Answer:
A, B, C
Step-by-step explanation:
Given that [tex] 3y = 27x [/tex] , we can simplify to get a proportionality statement that exists between X and y. Thus
[tex] 3y = 27x [/tex]
Divide both sides by 3
[tex] \frac{3y}{3} = \frac{27x}{3} [/tex]
[tex] y = 9x [/tex]
Thus, we can say, y would always be 9 times the quantity of x.
From the options given, examine which options have this proportionality statement as well.
Option A, y = 9x is same as the statement.
Option B, 2y = 18x, conforms to the same statement. If we simply further, we would have y = 9x
Option C, the graph shows that when x = 1, y = 9. This also confirms to the same constant of proportionality in the given equation.
Option D and E do not have same constant of proportionality.
The right options are A, B, and C.
Find x.
A. 21(route)2
B. 7
C.21(route)3/2
D. 21(route)2/2
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the right ΔABD,
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{BD}}{\text{AB}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}[/tex]
BD = [tex]7\sqrt{3}\times \frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{21}{2}[/tex]
Now by applying Cosine rule in the right ΔBDC,
Cos(45)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}[/tex]
x = [tex]\frac{21}{2}\times \sqrt{2}[/tex]
x = [tex]\frac{21\sqrt{2}}{2}[/tex]
Therefore, Option (D) is the correct option.
(Small sample confidence intervals for a population mean) suppose you are taking a sampling of 15 measurements. you find that x=75 and s =5. assuming normality, the 99% confidence interval for the population mean is:__________
Answer:
The 99% confidence interval is [tex]71.67 < \mu < 78.33[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 15[/tex]
The sample mean is [tex]\= x = 75[/tex]
The standard deviation is [tex]s = 5[/tex]
Given that confidence is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical values of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]
Generally the margin for error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{ s}{ \sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{ 5}{ \sqrt{15} }[/tex]
=> [tex]E = 3.3307[/tex]
The 99% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]75 - 3.3307 < \mu <75 + 3.3307[/tex]
=> [tex]71.67 < \mu < 78.33[/tex]
What is f ( 1/3)? When the function is f(x) =-3x+7
Answer:
f(1/3) = 6
Step-by-step explanation:
f(x) =-3x+7
Let x = 1/3
f(1/3) =-3*1/3+7
= -1 +7
= 6
Answer:
f(1/3) = 6
Step-by-step explanation:
The function is:
● f(x) = -3x+7
Replace x by 1/3 to khow the value of f(1/3)
● f(1/3) = -3×(1/3) +7 = -1 +7 = 6
