Answer:
f(g(1)) = - 2
Step-by-step explanation:
Find g(1) then use the value obtained to find f(x)
g(1) = 1 ← value of y when x = 1 (1, 1 ) , then
f(1) = - 2 ← value of y when x = 1 (1, - 2 )
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 15/ms2. If the same force acts upon another object whose mass is
10kg, what is this object's acceleration?
Answer:
[tex]a = 6m/s^2[/tex]
Step-by-step explanation:
Given
When mass = 4kg; Acceleration = 15m/s²
Required
Determine the acceleration when mass = 10kg, provided force is constant;
Represent mass with m and acceleration with a
The question says there's an inverse variation between acceleration and mass; This is represented as thus;
[tex]a\ \alpha\ \frac{1}{m}[/tex]
Convert variation to equality
[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)
Make F the subject of formula;
[tex]F = ma[/tex]
When mass = 4kg; Acceleration = 15m/s²
[tex]F = 4 * 15[/tex]
[tex]F = 60N[/tex]
When mass = 10kg; Substitute 60 for Force
[tex]F = ma[/tex]
[tex]60 = 10 * a[/tex]
[tex]60 = 10a[/tex]
Divide both sides by 10
[tex]\frac{60}{10} = \frac{10a}{10}[/tex]
[tex]a = 6m/s^2[/tex]
Hence, the acceleration is [tex]a = 6m/s^2[/tex]
The length and width of a rectangle are measured as 58 cm and 45 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
Error in calculated area = [tex]\pm 10.3 cm^2[/tex]
Step-by-step explanation:
x = 58 cm
y = 45 cm
A = x*y
delta A
= delta (x*y)
= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)
= 45(0.1) + 58(0.1)
= 103(0.1)
= 10.3 cm^2
How many solutions does the system have? x+2y=2 2x+4y=−8
Answer:
Step-by-step explanation:
x + 2y = 2
2x + 4y = -8
-2x - 4y = -4
2x + 4y = -8
0 not equal to -12
no solution
6. Sam is buying tickets to a movie
online. The price of one ticket is $8.50.
An equation showing the total cost is
C = 8.50t +3.50 where t is the
number of tickets and $3.50 is a
convenience fee. What is the total cost
if he buys 4 tickets?
power sharing helps the ruling party to retain power for a long time. tick or wrong
The highest mountain in earth is 29,028 ft. The lowest under sea trench is -35,840ft. Which has the highest absolute value
Answer:
undersea trench
Step-by-step explanation:
Absolute value is the distance from zero
The highest mountain trench is |29028| or 29028 ft from zero
The lowest under sea trench is | -35840| of 35840 ft from zero
The highest absolute value is the undersea trench
Height always be positive .
Highest mountain in earth=29028ftAbsolute value:-
[tex]\\ \sf\longmapsto |29028|=29028ft[/tex]
Lowest undersea trench=-35840ftAbsolute value:-
[tex]\\ \sf\longmapsto |-35840|=35840ft[/tex]
The equation| x + 4| = x has solution a. X = -2 b. X = 2 c. X = -4 d. X = 4
Answer:
B) 2
/////////////////
Use Lagrange multipliers to minimize the function subject to the following two constraints. Assume that x, y, and z are nonnegative. Question 18 options: a) 192 b) 384 c) 576 d) 128 e) 64
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option C is the correct option
Step-by-step explanation:
From the question we are told that
The equation is [tex]f (x, y , z ) = x^2 +y^2 + z^2[/tex]
The constraint is [tex]P(x, y , z) = x + y + z - 24 = 0[/tex]
Now using Lagrange multipliers we have that
[tex]\lambda = \frac{ \delta f }{ \delta x } = 2 x[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta y } = y[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta z } = 2 z[/tex]
=> [tex]x = \frac{ \lambda }{2}[/tex]
[tex]y = \frac{ \lambda }{2}[/tex]
[tex]z = \frac{ \lambda }{2}[/tex]
From the constraint we have
[tex]\frac{\lambda }{2} + \frac{\lambda }{2} + \frac{\lambda }{2} = 24[/tex]
=> [tex]\frac{3 \lambda }{2} = 24[/tex]
=> [tex]\lambda = 16[/tex]
substituting for x, y, z
=> x = 8
=> y = 8
=> z = 8
Hence
[tex]f (8, 8 , 8 ) = 8^2 +8^2 + 8^2[/tex]
[tex]f (8, 8 , 8 ) = 192[/tex]
A chemical company makes two brands of antifreeze. The first brand is
55%
pure antifreeze, and the second brand is
80%
pure antifreeze. In order to obtain
130
gallons of a mixture that contains
70%
pure antifreeze, how many gallons of each brand of antifreeze must be used?
9514 1404 393
Answer:
52 gallons of 55%78 gallons of 80%Step-by-step explanation:
Let x represent the quantity of 80% solution. Then the quantity of 55% solution is (130-x) and the total amount of antifreeze in the mix is ...
0.55(130 -x) +0.80(x) = 0.70(130)
0.25x +71.5 = 91 . . . simplify
0.25x = 19.5 . . . . . . subtract 71.5
x = 78 . . . . . . . . . . . divide by 0.25; amount of 80%
130-78 = 52 . . . . amount of 55%
52 gallons of the 55% brand, and 78 gallons of the 80% brand must be used.
List the sides of ΔRST in ascending order (shortest to longest). m∠R=2x+11°, m∠S=3x+23°, and m∠T=x+42°
Answer:
ST, RS, RT
Step-by-step explanation:
Angles of a triangle add up to 180°.
2x + 11° + 3x + 23° + x + 42° = 180°
6x + 76° = 180°
x = 17⅓
m∠R = 2x+11° = 45⅔°
m∠S = 3x+23° = 75°
m∠T = x+42° = 59⅓°
The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.
ST, RS, RT
You catch an expected number of 1.51.5 fish per hour. You can catch a fish at any instant of time. Which distribution best characterizes the number of fish you catch in one hour of fishing
Answer:
The distribution is Poisson distribution
Step-by-step explanation:
From the question we are told that
An expected number of fish was caught per hour is 1.5
The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution
This because generally the Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time
What is the equation of a circle with center (-4,7) and a radius 6
Answer:
( x +4)^2 + ( y-7)^2 = 36
Step-by-step explanation:
We can write the equation of a circle as
( x-h)^2 + ( y-k)^2 = r^2
where ( h,k) is the center and r is the radius
( x- -4)^2 + ( y-7)^2 = 6^2
( x +4)^2 + ( y-7)^2 = 36
Answer:
(x+4)[superscript]2 + (y-7)[superscript]2 = 36
Jamal and Sean plan to make T-shirts to sell at a fair. Jamal plans to make 6 T-shirts
each day and Sean plans to make 4 T-shirts each day. On which day will Jamal have
made 12 more T-shirts than Sean?
Answer:
Jamal will have made 12 more T-shirts than Sean on the 6th day.
Step-by-step explanation:
1 day for Jamal - 6 T-shirts. 1 day for Sean - 4 T-shirts. 2 day for Jamal - 12 T-shirts. 2 day for Sean - 8 T-shirts. 3 day for Jamal - 18 T-shirts. 3 day for Sean - 12 T-shirts. 4 day for Jamal - 24 T-shirts. 4 day for Sean - 16 T-shirts. 5 day for Jamal - 30 T-shirts. 5 day for Sean - 20 T-shirts. 6 day for Jamal - 36 T-shirts. 6 day for Sean - 24 T-shirts. Number between 24 and 36 = 12.
What is the x-value of point A?
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 5
▹ Step-by-Step Explanation
The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
The x value is 5
Step-by-step explanation:
The x value is the value going across
Starting where the two axis meet, we go 5 units to the right
That is the x value
Can you please me with the word problem thank you so much
Answer:
4. 53
5. 66
6. 89
7. 31
Step-by-step explanation:
4. 14 + 18 + 21
^ ^
33 + 21
53
5. 86 - 20
66
6. 34 + 55
89
7. 14 + 11 + 6
^ ^
25 + 6
31
please solve it fastand give the correct answer pleaseeeeee
Answer:
a. False b. True c. True d. False e. False
Step-by-step explanation:
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find area of an older 35-inch television whose screen has an aspect ratio of 4:3
Greetings from Brasil...
The TV format is 4:3.
4 ÷ 3 = 1.33...
Let's assign the smallest side of the TV screen as X. Since the ratio between the sides is 4:3 = 1.33, then the other side (the largest) will be 1.33 times larger than the smaller side X, that is
smaller side = X
bigger side = 1.33X
The diagonal expression of the rectangle is:
D = √(base² + height²)
35" = √[(1.33X)² + X²]
35" = √(1.7689X² + X²) squaring both members
(35")² = 1.7689X² + X²
1225" = 2.7689X²
X² = 1225/2.7689
X² = 442.414
X = √442.414
X ≅ 21"
Tthe bigger side:
1.33X
1.33 · 21 ≅ 28"
Rectangle Area = base × height
Rectangle Area = 28 × 21
Rectangle Area = 588Fill in the following blanks to prove that n 2^1 n < 2^n n+1 < 2^(n+1) is Box 3 Options: True | False Next, assume that Box 4 Options: 1 < 2^1 k + 1 < 2^(k+1) k < 2^k as we attempt to prove Box 5 Options: k < 2^k k + 1 < 2^(k+1) 2 < 2^1 Therefore, we can conclude that Box 6 Options: k < 2^k k + 1 < 2^(k+1) 2^1 < 2^k k + 2 < 2^(k+2)
Answer:
see below
Step-by-step explanation:
n < 2^n
First let n=1
1 < 2^1
1 <2 This is true
Next, assume that
(k) < 2^(k)
as we attempt to prove that
(k+1) < 2^(k+1)
.
.
.
Therefore we can conclude that
k+1 < 2^(k+1)
Answer:
Step-by-step explanation:
Hello, please consider the following.
First, assume that n equals [tex]\boxed{1}[/tex]. Therefore, [tex]\boxed{1<2^1}[/tex] is [tex]\boxed{\text{True}}[/tex]
Next, assume that [tex]\boxed{k<2^k}[/tex], as we attempt to prove [tex]\boxed{k+1<2^{k+1}}[/tex]
Since .... Therefore, we can conclude that [tex]\boxed{k+1<2^{k+1}}[/tex]
The choice for the last box is confusing. Based on your feedback, we can assume that we are still in the step 2 though.
And the last step which is not included in your question is the conclusion where we can say that we prove that for any integer [tex]n\geq 1[/tex], we have [tex]n<2^n[/tex].
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the values of x which satisfy the following inequation:
x3 – x² <12x
Answer:
x< -3 and 0 < x < 4
Step-by-step explanation:
x^3 – x² <12x
Subtract 12x from each side
x^3 -x^2 - 12x< 0
Factor
x( x^2 -x-12) <0
Factor
x( x-4) ( x+3) < 0
Using the zero product property
x=0 x=4 x=-3
We have to check the signs regions
x < -3
-( -) (-) < 0 True
-3 to 0
-( -) (+) < 0 False
0 to 4
+( -) (+) < 0 True
x>4
+( +) (+) < 0 False
The regions this is valid is
x< -3 and 0 < x < 4
I need help with this I will appreciate if I get an answer for this problem
Answer:
what's the problem!?......
angle CDT is the opposite angle of ADN
and the segment DF=FN, so AD= AN
and thats why angle FAN= angle FAD
here, Angle FAN =60,
therefore, FAD=60, and AFD = 90 so angle ADN must be 30 degree
and the opposite of ADN is CDT, and the opposite angles are equal.
Hope u got it.
Which term best describes a figure formed by three segments connecting three non Collin ear points
Answer:
Triangle
Step-by-step explanation:
Venn diagrams: unions, intersections, and complements
Attached is the photo reference
Answer:
a) 0
b) 2,3,4,5,6,7
c)3,4,6,7
Step-by-step explanation:
Answer the question you hopeless heathens
Monico recently hired a roofer to do some necessary work. On the final bill, Monico was charged a total of $605. The amount listed for parts was $285 and the rest of the bill was for labor. If the hourly rate for labor was $64, how many hours of labor was needed to complete the job?
(A) First write an equation you can use to answer this question. Use x as your variable. The equation is ___________________
(B) Solve your equation in part (A) to find the number of labor hours needed to do the job. Answer: The number of labor hours was ________________
Answer:
A) 64x + 285 = 605
B) 5 hours
Step-by-step explanation:
64x + 285 = 605
64x + 285-285 = 605 - 285
64x = 320
64x/64 = 320/64
x = 5
Double check
($605 Total - $285 parts) / $64 Hourly rate = Labor per hour
$320 Labor / $64 Hour = 5 hours
or 64x
32 to 34 Directions: Given the following set of
numbers find the mean, median, and mode.
12, 13, 15, 15, 16, 19, 19, 19, 20, 21, 25
39.
32. Mean =
a. 17.64
b. 19
c. 15
40. 1
33. Median
a. 17.64
b. 19
c. 15
Answer:
32. A
33. B
Step-by-step explanation:
32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is
33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end
Select the graph of the solution. Click until the correct graph appears.
Answer:
convert the 27 degree into grades
A children's rectangular pool holds 480 cubic feet of water. What is the depth of the pool of its length is 30 feet and it's width is 16 feet
Answer:
1 ft
Step-by-step explanation:
1, 480/30=16
2, 16/16=1
3, 1 ft
What is the measure of m?
Answer:
√245
Step-by-step explanation:
altitude on hypotenuse theorem:
m^2=7*35
m^2=245
m=√245
7 (w+8) = 2w+10
What is the value of w makes the equation true? Enter the answer in the box.
Test.mapnwea.org.
Answer:
w = -46/5
Step-by-step explanation:
Answer:
w=-9.2
Step-by-step explanation:
7(w+8)=2w+10
7w+56=2w+10
7w-2w=10-56
5w=-46
w=-9.2
PLS HELP! VERY URGENT PICTURE INCLUDED!!
Answer:
y = 6x ^2 - 6x + 9
Step-by-step explanation:
hopefully it's visible
:)