Step-by-step explanation:
Hey there!
Given;
f ( x ) = x² + 2x - 1
g ( x ) = 3x - 2
To verify:
[tex]( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} [/tex]
LHS:
[tex] (\frac{f}{g} )(x) = \frac{ {x}^{2} + 2x - 1}{3x - 2} [/tex]
~ Insert "2" instead of "x".
[tex] (\frac{f}{g} )(2) = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} [/tex]
Simplify it;
[tex] \frac{f}{g} (2) = \frac{4 + 4 - 1}{6 - 2} [/tex]
Therefore; (f/g)(2) = 7/4.
RHS:
[tex] \frac{f(x)}{g(x)} = \frac{ {x}^{2} + 2x - 1}{3x - 2} [/tex]
~Insert "2" instead of"x".
[tex] \frac{f(2)}{g(2)} = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} [/tex]
Simplify it.
[tex] \frac{f(2)}{g(2)} = \frac{4 + 4 - 1}{6 - 2} [/tex]
Therefore, f(2)/g(2) = 7/4.
Since (f/g)(2) = f(2)/g(2) = 7/4.
Proved!
Hope it helps!
Step-by-step explanation:
f(x) = x² + 2x - 1 g(x) = 3x - 2Soo :
[tex] \tt( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} [/tex]
[tex] \tt( \frac{ {x}^{2} + 2x - 1 }{3x - 2} )(2) = \frac{ {2}^{2} + 2(2) - 1 }{3(2) - 2} [/tex]
[tex] \tt( \frac{ {2}^{2} + 2(2) - 1}{3(2) - 2} )= \frac{7}{4} [/tex]
[tex] \boxed{ \tt \frac{7}{4} = \frac{7}{4} }[/tex]
Soo true.
I need to verify this function is symmetric with respect to the y-axis. How would I go about doing that?
h(x)=x^4-5x^2+3
Answer:
Yes, the function is symmetric about y-axis.
Step-by-step explanation:
To check whether the function is symmetric with respect to y-axis, replace each x as -x and simplify.
If h(x) = h(-x) then it is symmetric about y-axis.
Let's find h(-x) now.
h(-x)= [tex](-x)^4} -5(-x)^{2} +3[/tex]
Let's simplify it
h(-x)=[tex]x^{4}-5x^{2} +3[/tex]
Here, h(x) = h(-x). The function is symmetric about y-axis.
When this open-ended cylinder is opened out, it forms a rectangle with a width of 25 cm. What is the area of the rectangle?.
Answer:
Just want the points
Step-by-step explanation:
A 4.0kg brick is sliding on a surface. The coefficient of kinetic friction between the surfaces is 0.25. What is the size of the force of friction?
a. ON b. 1 N
c. 10 N
d. 4 N
Answer:
Choice C. 10N
Step-by-step explanation:
[tex]F_{k} =U_{k} *F_{N}\\F_{k} =.25*[(4kg*10m/s2)] : [40N][/tex]
[tex]F_{k} =10N[/tex]
The amount of water dispensed by a water dispenser is normally distributed,
with a mean of 11.60 ounces and a standard deviation of 0.15 ounces. In
which range will the amount of water dispensed be found 68% of the time?
A. 11.30 ounces to 11.90 ounces
B. 11.15 ounces to 12.05 ounces
C. 11.45 ounces to 11.75 ounces
D. 11.00 ounces to 12.20 ounces
SUBMIT
Answer:
The correct answer is - C. 11.45 ounces to 11.75 ounces.
Step-by-step explanation:
According to the empirical rule of the distribution for 68% falls under the normal curve falls within 1 standard deviation of the mean.
That is:
μ±δ
From the given information, the mean is
μ = 11.60
and the standard deviation is
δ = 0.15
We substitute the given parameters to obtain;
11.60±0.15
11.75 and 11.45
This means the lower limit is
11.45
and the upper limit is
11.75
What is the length of the hypotenuse in the right triangle shown below?
45°
45
6
Answer:
option A
Step-by-step explanation:
let the hypotenuse be x
take 45 degree as reference angle and use cos rule
cos 45 = adjacent/hypotenuse
1/[tex]\sqrt{2[/tex] = 6/x
do cross multiplication
6*[tex]\sqrt{2[/tex] = x *1
6[tex]\sqrt{2}[/tex] = x
Answer:
Answer is a
Step-by-step explanation:
Thats what i got
Identify the segment parallel to the given segment .
Answer:
MN => CB
ON => CA
AB => MO
CB => MN
OM => BA
AC => NO
Please help ASAP!!!
What is YZ?
Answer:
18.4 In
Step-by-step explanation:
36.8/2
= 18.4 In
that is the procedure above
Plz help out real quick
Answer:
b=55°..Step-by-step explanation:
b+6°+41°+b+23°=180°{sum of angle of triangle}2b+70°=180°2b=180°-70°b=110/2b=55°hope it helps.stay safe healthy and happy......please help SO CONFUSED
Answer:
SOH-CAH-TOA
[tex]h = \sqrt{ 9^{2} +5^{2} }[/tex]
~~~~~~~~~~
H= [tex]\sqrt{106}[/tex]
O= 5
A= 9
~~~~~~~~~~~~~~~~
Sin = [tex]\frac{5}{\sqrt{106 } }[/tex]
Cos= [tex]\frac{9}{\sqrt{106 } }[/tex]
Tan = [tex]\frac{5}{9 }[/tex]
Step-by-step explanation:
Classify the following triangle. Check all that apply.
104
O A. Right
O B. Equilateral
O c. Scalene
O D. Isosceles
E. Acute
O F. Obtuse
SUBMIT
Answer:
isosceles
obtuse
Step-by-step explanation:
We know that one angle is 104 and angles greater than 90 and less than 180 are obtuse
We know that 2 sides are equal indicated by the lines on the sides. That means the triangle is isosceles
Help anyone can help me do 16 and 17 question,I will mark brainlest.The no 16 question is find the area of the shaded region
Answer:
Question 16 = 22
Question 17 = 20 cm²
Step-by-step explanation:
Concepts:
Area of Square = s²
s = sideArea of Triangle = bh/2
b = baseh = heightDiagonals of the square are congruent and bisect each other, which forms a right angle with 90°
Segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
Question # 16
Step One: Find the total area of two squares
Large square: 5 × 5 = 25
Small square: 2 × 2 = 4
25 + 4 = 29
Step Two: Find the area of the blank triangle
b = 5 + 2 = 7
h = 2
A = bh / 2
A = (7) (2) / 2
A = 14 / 2
A = 7
Step Three: Subtract the area of the blank triangle from the total area
Total area = 29
Area of Square = 7
29 - 7 = 22
-----------------------------------------------------------
Question # 17
Step One: Find the length of PT
Given:
PR = 4 cmRT = 6 cmPT = PR + RT [Segment addition postulate]
PT = (4) + (6)
PT = 10 cm
Step Two: Find the length of S to PT perpendicularly
According to the diagonal are perpendicular to each other and congruent. Therefore, the length of S to PT perpendicularly is half of the diagonal
Length of Diagonal = 4 cm
4 ÷ 2 = 2 cm
Step Three: Find the area of ΔPST
b = PT = 10 cm
h = S to PT = 2 cm
A = bh / 2
A = (10)(2) / 2
A = 20 / 2
A = 10 cm²
Step Four: Find the length of Q to PT perpendicularly
Similar to step two, Q is the endpoint of one diagonal, and by definition, diagonals are perpendicular and congruent with each other. Therefore, the length of Q to PT perpendicularly is half of the diagonal.
Length of Diagonal = 4 cm
4 ÷ 2 = 2 cm
Step Five: Find the area of ΔPQT
b = PT = 10 cm
h = Q to PT = 2 cm
A = bh / 2
A = (10)(2) / 2
A = 20 / 2
A = 10 cm²
Step Six: Combine area of two triangles to find the total area
Area of ΔPST = 10 cm²
Area of ΔPQT = 10 cm²
10 + 10 = 20 cm²
Hope this helps!! :)
Please let me know if you have any questions
The length of a constantan wire P is twice of the constantan wire Q and the ratio of the diameter of wire P to
wire Q is 1:3. Given that the resistance of the wire varies directly as the length and inversely as the square of the
diameter, find the resistance ratio of wire P to wire Q.
Answer:
Hello,
9/2
Step-by-step explanation:
Using "la loi de Pouillet", i don't know the name in USA
[tex]R=\rho*\dfrac{l}{S} \\\\\rho: resistivity\\\\l: length\\\\S:section\ of \ the\ wire\\\\R_1=\rho*\dfrac{l_1}{S_1} \\S_1=\pi*d_1^2*\dfrac{1}{4} \\\\\\l_2=2*l_1\\d_2=3*d_1\\\\S_2=\pi*d_2^2*\dfrac{1}{4} =\pi*(3*d_1)^2*\dfrac{1}{4}=9*S_1\\\\\\\dfrac{R_1}{R_2} =\dfrac{\rho*\dfrac{l_1}{S_1}}{\rho*\dfrac{l_2}{S_2}} \\\\=\dfrac{\rho*\dfrac{l_1}{S_1}}{\rho*\dfrac{2*l_1}{9*S_1}} \\\\\\\boxed{\dfrac{R_1}{R_2} =\dfrac{9}{2}}[/tex]
17
x
3
8
Find the unknown side length, x. Write your answer in simplest radical form.
A 15
B. 5/10
C2/70
D. 4 37
==========================================================
Explanation:
It helps to add point labels. Let's place point A at the very top point of the triangle. Then point B will be at the 90 degree angle. Point C is the far left point. Lastly, point D is on segment BC such that DC = 3.
Since BC = 8 and CA = 17, we can use the pythagorean theorem to get...
(AB)^2 + (BC)^2 = (AC)^2
(AB)^2 + (8)^2 = (17)^2
(AB)^2 + 64 = 289
(AB)^2 = 289-64
(AB)^2 = 225
AB = sqrt(225)
AB = 15
Now focus on triangle ABD and apply the pythagorean theorem again to find side AD
(AB)^2 + (BD)^2 = (AD)^2
AD = sqrt( (AB)^2 + (BD)^2 )
AD = sqrt( (AB)^2 + (BC-CD)^2 )
AD = sqrt( (15)^2 + (8-3)^2 )
AD = sqrt(250)
AD = sqrt(25*10)
AD = sqrt(25)*sqrt(10)
AD = 5*sqrt(10) .... answer is choice B
WILL MARK BRAINLIEST! Can someone please help! I don't understand some of these questions :(
Answer:
18
Step-by-step explanation:
The interior and exterior angle of a polygon is supplementary
let interior be I
let exterior be E
I + E = 180
Since the interior angle is 8 times that of an exterior angle,
8E + E = 180 [replacing I with 8E]
9E = 180
E = 20
The exterior angle is 20 degrees
I + E = 180
I + 20 = 180
I = 160
The interior angle is 160 degrees.
The equation to find the interior angle of a polygon with 'n' number of sides is:
I = ( (n − 2) × 180 ) ⁄ n
We know the interior angle, so plug it in and solve for n:
160 = ( (n − 2) × 180 ) ⁄ n
160n = (n − 2) × 180
160n = 180n − 360
-20n = -360
n = 18
A research historian is interested in finding sunken treasure in the Atlantic Ocean. She knows that her equipment is only good enough to recover items that are at a depth of 5 000 m or less. The speed of sound through the water is 1 530 m/s. While working, the sonar equipment detects a reflection that is of interest. The echo from the item takes 6.2 s to return to the sonar detector. Will she be able to retrieve this item?
Answer:
Yes, she will be able to retrieve the item
Step-by-step explanation:
The information with regards to the research historian interest in finding a sunken treasure are;
The depth from which the equipment can recover items = 5,000 m
The speed of sound through water, v = 1,530 m/s
The time it takes the echo from the item to return to the sonar detector, t = 6.2 s
Let d, represent the depth at which the item is located
Given that an echo travels from the sonar detector to the item and back to the sonar detector, the distance traveled by the sound wave which is received as an echo by the sonar detector = 2 × d
Velocity, v = Distance/time
∴ Distance = Velocity × Time
The distance traveled by the echo = 2 × d = v × t
2 × d = v × t
∴ 2 × d = 1,530 m/s × 6.2 s
d = (1,530 m/s × 6.2 s)/2 = 4,743 m
The depth at which the item is located, d = 4,743 m is less than the maximum depth the equipment can recover items, therefore, she will be able to retrieve the item.
Express the following numbers in the Standard form 5x10-⁵
Step-by-step explanation:
5 × 10[tex] {}^{-5} [/tex]
is in standard form or scientific notification. I have assumed that you meant what is 5 × 10[tex] {}^{-5} [/tex]
as a number
so here it is :-
[tex]5 \times {10}^{-5} = \frac{5}{100000} [/tex]
[tex] = 0.00005[/tex]
the Standard form 5x10-⁵ is 0.00005.
Answer:
[tex]\bold{5*10^{-5}=\frac{5}{100000}=0.00005}[/tex]
P(x) = 1 – 2x2 – 3x3 + 4x has what order?
Answer:
3
Step-by-step explanation:
assuming you forgot you ^ mark after x x^3 would be the highest x order here making it the order for the equation.
Solve each system by substitution
y=4
-3x+5y=2
Answer:
x = 6; y = 4
Step-by-step explanation:
y=4
-3x+5y=2
-3x + 5(4) = 2
-3x + 20 = 2
-3x = -18
x = 6
Answer: x = 6; y = 4
Answer:
(6,4)
Step-by-step explanation:
y=4
-3x+5y=2
Substitute y=4 into the second equation
-3x+5*4=2
-3x +20 = 2
Subtract 20 from each side
-3x +20-20 = 2-20
-3x = -18
Divide by -3
-3x/-3 = -18/-3
x=6
(6,4)
Find the measure of the indicated angle.
Answer:
86°
Step-by-step explanation:
180-(2*47)
= 180-94
= 86
Answered by GAUTHMATH
In the diagram, MZACB = 65. mzECD = А E B C С D
Answer:
m<ECB = 65°
Step-by-step explanation:
<ACB and <ACD are vertical angles. That means they are congruent and have equal measures.
m<ECB = 65°
On a tuesday a magician said i made my wife disappear 31 days ago what day of the week did he make her disappear
Answer:
Saturday.
Step-by-step explanation:
To answer the above question, we must recognise that Tuesday appears once every 7 days.
If today is Tuesday, 31 days ago will be obtained as follow:
31/7 = 4 remainder 3
Thus
31 = (7 × 4) + 3
31 = (28) + 3
Thus, the 28th day is Tuesday. If we count 3 days back from Tuesday, the day will be Saturday.
Therefore, the magician made his wife disappear on Saturday.
Please help me to solve this question pleaseee
Answer:
Step-by-step explanation:
1) ML // JK , MK is transversal,
∠LMK = ∠MKJ {Alternate interior angles are congruent}
∠LMK = 30°
In ΔMKO,
30 + 115 + ∠ JLM = 180 {Angle sum property of triangle}
145 +∠ JLM = 180
∠ JLM = 180 - 145
∠ JLM = 35°
2) AB // CD , AC is transversal
∠DCA = ∠BAC {Alternate interior angles are congruent}
∠DCA = 23
∠BCD = ∠DCA + ∠BCA
= 23 + 37
= 60
3) EF // HG ; FH is transversal
∠FHG = ∠HFE {Alternate interior angles are congruent}
∠FHG = 77
4) ZY // WX ; WY is transversal
∠ZYW = ∠XWY {Alternate interior angles are congruent}
= 65
ZY // WX ; WY is transversal
∠ZWY = ∠WYX {Alternate interior angles are congruent}
= 36
In ΔWZY
36 + 65 + ∠z = 180
101 +∠Z = 180
∠Z = 180 - 101
∠Z = 79
A squirrel in a 14 ft tall tree looks down at an angle of 74 degrees at an acorn on the ground? Solve for the distance from the base of the tree to the acorn. Explain how you arrived at
your answer.
The population of West Algebra can be modeled by the equation
P = 30. 1.04^T, where T is the number of years since 2000 and P is
the population in millions. How many million people will there be
in 2020?
(1) 63.7 (2) 64.7
(3) 65.7
(4) 66.7
Answer:
65.7
Step-by-step explanation:
Given the population of West Algebra can be modeled by the equation
P = 30. 1.04^T
If T is the number of years since 2000 and P is the population in millions, in 2020, T = 2020 - 2000 = 20
Substitute T = 20 into the expression and get T
P = 30. 1.04^20
P = 30(2.1911)
P = 65.73
Hence the amount of people that will be there in 2020 is 65.7million people
To use energy efficiently, a certain washing machine should wash at least 2 kilograms of clothes. To avoid overloading the machine, at most 6 kilograms should be washed.
What is the range of the loads for this washing machine ?
Step-by-step explanation:
the answer is in the image above
The range of loads for this washing machine is from 2 to 6 kilograms to ensure energy efficiency and avoid overloading.
Given that,
The washing machine should wash at least 2 kilograms of clothes to use energy efficiently.
To avoid overloading the machine, the maximum weight that should be washed is 6 kilograms.
To find the range of loads for this washing machine,
Determine the minimum and maximum weight that can be washed.
The minimum weight that can be washed is 2 kilograms, as mentioned. And the maximum weight is 6 kilograms, as overloading the machine should be avoided.
Therefore,
The range of loads for this washing machine is from 2 kilograms to 6 kilograms.
This means that any load within this range can be efficiently washed without overloading the machine.
To learn more about the measurement unit visit:
https://brainly.com/question/777464
#SPJ2
Write the equation of a line in slope-intercept form that has a slope of -0.5 and passes through the point (-5, 1.5)
Splash Island and Magic Park are amusement parks. If you visit splash Island, you pay $3 per ride plus a $14 entrance fee. If you visit Magic Park, you pay $5 per ride plus a $7 entrance fee. You have $32. At which park could you go on more rides?
Answer:
Splash Island.
Step-by-step explanation:
Magic Park = 32 - 7 = 25 you would have 25 dollars to spend on rides which would only get you 5 rides.
Splash Island = 32 - 14 = 18 this gives you 18 dollars to spend on rides, which would get you 6 rides.
Therefore you can go on more rides at Splash Island.
Hope this helps!
In the diagram below, lines AB and CD are...
Answer:
Perpendicular
Step-by-step explanation:
Perpendicular lines intersect and create 4 90 degree angles
Line AB and CD intersect and create 4 90 degree angles therefore line AB and CD are perpendicular
In using the "2 to the k rule" to determine the number of classes for a frequency distribution, what is the meaning of the variable k? Multiple choice question. k is the greatest number of classes such that 2k
Answer:
k is the smallest number such that 2(to the k)>n
Step-by-step explanation:
Frequency distribution is defined as the number of times the value occurs. It contains the class interval as well as the corresponding frequencies. A pivot table is used to represent the frequency distribution.
The "2 to the k" rule states that 2 to the power k should be less than equal n, where n is the number of the given data points. It should be the smallest number.
Thus the answer is : k is the smallest number such that 2(to the k)>n.
3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
Show that x = 3.
Answer:
3X +ky=8 eqn 1
X-2ky=5 eqn 2
but we want to eliminate ky to get our X.
So let's multiply eqn 1 by 2.
We will have 6x +2ky=16 now eqn 3
now we add eqn 1 and 2
We will have 7x=21
divide by 7
x=3
