Step-by-step explanation:
f(x) = 2x
g(x) = -8x + 2
h(x) = x² + x + 3
= f(g(6))
= 2x
= 2.(-8x + 2)
= 2.(-8.6 + 2)
= 2.(-48 + 2)
= 2.(-46)
= -92
= g(h(-4))
= -8x + 2
= -8.(x² + x + 3) + 2
= -8.((-4)² + (-4) + 3) + 2
= -8.(16 - 1) + 2
= -8.15 + 2
= -120 + 2
= -118
= g(f(x))
= -8x + 2
= -8.(2x) + 2
= -16x + 2
2) Let a =i+2j-7k and b=5i-2j+4K Find
a) a.b
b) axb
C) The direction cosine of axb
D) The Unit Vector Perpendicular to both a&b
a) Dot product: recall that
i • i = j • j = k • k = 1
i • j = i • k = j • k = 0
Then
a • b = (i + 2j - 7k) • (5i - 2j + 4k)
a • b = 5 (i • i) - 4 (j • j) - 28 (k • k)
a • b = 5 - 4 - 28
a • b = -27
b) Cross product: recall that
i × i = j × j = k × k = 0
i × j = -(j × i) = k
j × k = -(k × j) = i
k × i = -(i × k) = j
Then
a × b = (i + 2j - 7k) × (5i - 2j + 4k)
a × b = -2 (i × j) + 4 (i × k) + 10 (j × i) + 8 (j × k) - 35 (k × i) + 14 (k × j)
a × b = -12 (i × j) - 6 (j × k) - 39 (k × i)
a × b = -6i - 39j - 12k
c) Recall the dot product identity
x • y = ||x|| ||y|| cos(θ)
We have
||a × b|| = √((-6)² + (-39)² + (-12)²) = 9√21
Then the direction cosines α, β, γ of a × b are
(a × b) • i = ||a × b|| ||i|| cos(α)
⇒ cos(α) = -6/(9√21) = -2/(3√21)
(a × b) • j = ||a × b|| ||j|| cos(β)
⇒ cos(β) = -39/(9√21)
(a × b) • k = ||a × b|| ||k|| cos(γ)
⇒ cos(γ) = -12/(9√21) = -4/(3√21)
d) a × b is perpendicular to both a and b, so we can get a unit vector by scaling this down by its magnitude. This is the same as the vector of direction cosines:
(a × b)/||a × b|| = (-6i - 39j - 12k)/(9√21)
(a × b)/||a × b|| = -2/(3√21) i - 39/(9√21) k - 4/(3√21) k
How many platelets are in 3 milliliters of blood write your answer in standard form
Round 0.007492 to the nearest hundredth
Answer:
0.01
Step-by-step explanation:
Nearest hundredth is the second digit after the decimal point.
If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit.
given f(x) = 4x+1
evaluate f(2)
f(2) = ?
evaluate f(-3)
f(-3)= ?
The value of the functions are:
f(2) = 9
f(2) = -11
Use the concept of fucntion defined as:
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
The given function is,
f(x) = 4x+1
Put x = 2 in the given fucntion,
f(2) = 4(2) + 1
f(2) = 9
Put x = -3 in the given fucntion,
f(2) = 4(-3) + 1
f(2) = -11
Hence, The functions,
f(2) = 9
f(2) = -11
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7. AB=x+9, BC = 3x-4. Find AC.
B
с
хто + 3x
-3x
3х
2
A
2х
-2x=
The value of AC = 4x + 5.
How to do addition of the variables?A variable is defined as any property, number, or amount that can be counted or measured.
Even despite their different operations, adding and subtracting variables follow the same rule: once adding or subtracting terms with the identical variables, you either add and otherwise subtract the coefficients and leave the result with the variable.
Addition. So because variables are the same in this equation, you can add every one of the coefficients (2, 5, and 4). (a).2a + 5a + 4a = 11a
Subtraction. Since the variables are equal in this equation, you could indeed subtract each of the coefficients (11, 5, and 4). (a).11a – 5a – 4a = 2a
Similarly with the question;
AB = x+9, BC = 3x-4
AC = AB + BC
AC = x + 9 + 3x - 4
Add the variable and constant part separately.
AC = 4x + 5
Thus, the value of AC is found as 4x + 5.
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Need help with this please
Answer:
7)B
8)B
9)A
10)C
Step-by-step explanation:
LET ME KNOW IF THIS HELPS.
HURRYYY: How many times smaller is 5 x 10−7 than 8.5 x 10−4?
A: 59
B: 170
C: 1,700
D: 5,882
Answer:
1,700
Step-by-step explanation:
5x10^-7 is 0.0000005, while 8.5x10^-4 is 0.00085
0.00085/0.0000005=1700
Thus5 x [tex]10^{-7}[/tex] is 1700 times smaller than 8.5 x [tex]10^{-4}[/tex].
Option C is the correct answer.
Given,
5 x [tex]10^{-7}[/tex] and 8.5 x [tex]10^{-4}[/tex]
We need to find how many times smaller is 5 x [tex]10^{-7}[/tex] than 8.5 x [tex]10^{-4}[/tex].
What are exponents?Exponents are the power of a given number.
Example: a²
a - base
2 - exponent
Compare 5 x [tex]10^{-7}[/tex] and 8.5 x [tex]10^{-4}[/tex].
5 x [tex]10^{-7}[/tex] can be written as 5 / 10000000
8.5 x [tex]10^{-4}[/tex] can be written as 8.5 / 10000
Now,
5 / 10000000 = 0.0000005
8.5 / 10000 = 85 / 100000 = 0.00085
We see that,
0.0000005 is less than 0.00085
Now,
0.0000005 x 1700 = 0.00085
5 x [tex]10^{-7}[/tex] is 1700 times smaller than 8.5 x [tex]10^{-4}[/tex].
We can also write as:
5 x [tex]10^{-7}[/tex] x 17 x 10 ²
= 5 x 17 x [tex]10^{-7}[/tex] x 10²
= 85 x [tex]10^{-7 + 2}[/tex]
= 85 x [tex]10^{-5}[/tex]
= 85/10 x 10 x [tex]10^{-5}[/tex]
= 8.5 x [tex]10^{-5 + 1}[/tex]
= 8.5 x [tex]10^{-4}[/tex]
Thus 5 x [tex]10^{-7}[/tex] is 1700 times smaller than 8.5 x [tex]10^{-4}[/tex].
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A study was performed with a random sample of 5 people from a certain city. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
High sample size is typically crucial in order to be able to draw generalizations from a sample, aside from avoiding bias. Since the sample size is modest, it will thus be possible to draw general conclusions about the study utilizing a larger sample, in my opinion.
The size of the sample has a significant impact on whether an experiment is legitimate. The central limit theorem states that as sample size rises, the sample mean approaches the population means value.
Because of this, generalizing from just five samples regarding a population of city dwellers won't produce a result that can be generalized.
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5. Explain how to determine which operation to complete first when simplifying the expression (15 ÷ 5+4²) − [4³ − |(13² + 2) ÷ (4 − 1)]. Be specific.
Answer: Parentheses
Step-by-step explanation: Parentheses always go first because if you look at the work PEMDAS, P= parentheses, E= exponents, M= Multiplication, D= division, A= addition, and S= subtraction.
This is the question
Answer:
x<0: 0<x<1; x>1
Step-by-step explanation:
The denominator cannot be 0 (since division by 0 is undefined), meaning x cannot be 0 or 1.
So, the domain is x<0: 0<x<1; x>1.
❌❌PLEASE HELPILL MARK BRAINLIEST❌❌❌Does coordinate m or coordinate n represent a greater number in the following parallelogram?
(0,1)
Choose 1 answer:
B
(3,5)
m
n
(m, n)
(10,5)
Answer:
The answer would be m.
Step-by-step explanation:
The point would be (7,1) If you look at the top two points, (3,5) and (10,5) You can see that the y coordinates are the same. They are both 5. So on the bottom left (0,1) we know that are n will be 1 . Now we have to figure out m. If we look on the top (3,5) (10,5) We can see from the x's 10 and 3, that they are a distance of 7 apart. Since our bottom left hand corner is (0,1) If we add 7 to 0 we get 7. That makes m equal 7
Jim began a 145mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 7 hours. If Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour, find the amount of time he spent on the bicycle.
The amount of time he spent on bicycle is 4.5 hours.
Given Jim began a 145 mile bicycle trip.
The whole trip took 7 hours.
Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour.
speed = distance / time
time = distance / speed
ride:
d = distance ridden
t = d/30 (given from the problem)
walk:
t = (145 - d)/4 (given from problem)
total trip time:
7 = d/30 + (145 - d)/4.
7 = 4d/120 + 30(145 - d)/120
7×120 = 4d + 30(145 - d)
840= 4d +4350-30d
840 ₋ 4350 = ₋30d ₊ 4d
₋3510 = ₋26d
d = 3510/26
d = 135
d=135 then from here using the formula t = d / s we can solve
t=135/30 = 4.5 hours
hence the amount of time Jim spent on the bicycle is 4.5 hours.
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Un centro recreacional cuenta con dos piscinas
temperadas, una para adultos que tiene una
capacidad de 240 000 litros de agua y una para
niños cuya capacidad es 2/3 de la de adultos. Cada
una de estas piscinas cuentan con un desagüe que
permite desalojar 2 500 litros de agua cada 5 min.
Si se requiere vaciar el agua de ambas piscinas y los
desagües se abren a las 8:10 am.
1. ¿A qué hora se terminará de vaciar cada piscina?
2. ¿cuánto más tardará en vaciarse una piscina que la otra que la otra?
1) La piscina grande tardó 8 horas en ser vaciado, culminando a las 4: 10 PM, y la piscina pequeña tardó 5 horas y 20 minutos en ser vaciado, culminando a las 1: 30 PM.
2) La piscina grande tardará 2 horas y 40 minutos más en vaciarse que la piscina pequeña.
¿Cómo determinar y estimar tiempos de vaciado de una piscina?
En este problema tenemos el caso de dos piscinas de diferente capacidad, la primera piscina tiene una capacidad de 240 000 litros de agua y la segunda piscina tiene una capacidad de 160 000 litros de agua. Ambas cuenta con un desagüe que desaloja a una tasa de 500 litros de agua por cada minuto de operación.
El tiempo total de vaciado es igual a volumen de la piscina dividido por la tasa de vaciado, entonces:
Piscina grande (V = 240 000 L, Q = 500 L / min)
t = V / Q
t = (240 000 L) / (500 L / min)
t = 480 min
Piscina pequeño (V = 160 000 L, Q = 500 L / min)
t = V / Q
t = (160 000 L) / (500 L / min)
t = 320 min
1) La piscina grande tardó 8 horas en ser vaciado, culminando a las 4: 10 PM, y la piscina pequeña tardó 5 horas y 20 minutos en ser vaciado, culminando a las 1: 30 PM.
2) La piscina grande tardará 2 horas y 40 minutos más en vaciarse que la piscina pequeña.
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Which number is a rational number?
13
16
9
|୯
2
V34
√49
Answer:
49
Step-by-step explanation:
Express in kg the mass of 0.3 tonne
0.3 tonnne=300 kilograms
In the given question mass is given in tonne and we have to convert it into tonne.
Among the SI base units, the kilogram (kg) is the only one whose name and symbol, for historical reasons, include a prefix. "Kilo" the SI prefix for 1000 or 103. Names and symbols for decimal multiples and submultiples of the unit of mass are formed by attaching prefix names to the unit name "gram," and prefix symbols to the unit symbol "g."
To calculate a tonne value to the corresponding value in kg, just multiply the quantity in tonne by 1000 (the conversion factor). Here is the formula:
Value in kg = value in tonne × 1000
Suppose you want to convert 0.3 tonne into kg. Using the conversion formula above, you will get:
Value in kg = 0.3 × 1000 = 300 kg
final answer is 0.3 tonne=300 kilograms.
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Solve for c.
2c 12c + 13c = 12
The value of c is 4.
Here, we are given an equation
2c - 12c + 13c = 12
Since, all the terms on the left hand side have a c in them, we can take it common outside the bracket as follows-
c (2 - 12 + 13) = 12
or c (2 + 13 - 12) = 12
Firstly, we add the positive terms in the bracket which will give us
c (15 -12) = 12
Now, we subtract 12 from 15 to get
c (3) = 12
or 3c = 12
Dividing by 3 on both sides we get
c = 12/3
c = 4
Thus, the value of c is 4.
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Your question was incomplete. Find the full content below-
Solve for c.
2c-12c+13c=12
In a bag of mixed nuts, 46% were peanuts, 0.16 were cashews, and 56 out of the 150 nuts were almonds. Select the statements that are true, based
on the information above. Select all that apply.
A. 16 of the nuts cashews
B. 1/6 of the nuts were cashews
C.69 of the nuts were peanuts
D.25 of nuts were cashews
Steve has $5. Nancy has 250% as much money as Steve. How much money does Nancy have?
The amount of money Nancy has is $12.5.
Given that, Steve has $5. Nancy has 250% as much money as Steve.
We need to find out how much money Nancy has.
What is the percentage?A specific portion or amount in every hundred is what is meant by the term percentage. It is a fraction with the denominator 100, and the symbol for it is "%."
Let the amount of money Nancy has to be x.
Now, x=250% of 5
=250/100 × 5
=2.5 × 5
=12.5
Therefore, the amount of money Nancy has is $12.5.
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A number is chosen at random from 1 to 10. Find the probability of selecting number 4 or smaller numbers
The probability of selecting number 4 or smaller numbers 2 / 5 .
Probability could be a live of the chance of an occasion to occur. several events can not be expected with total certainty. we are able to predict solely the possibility of an occasion to occur i.e. however doubtless they're to happen, using it. likelihood will direct from zero to one, wherever zero suggests that the event to be Associate in Nursing not possible one and one indicates a definite event.The likelihood formula is outlined because the chance of an occasion to happen is adequate the quantitative relation of variety|the amount|the quantity} of favourable outcomes and also the total number of outcomes.Probability of event to happen P(E) = variety of favourable outcomes/Total variety of outcomes
We have given number from 1 to 10.
The number which are smaller than four and equal to 4 = 4
Total number of outcomes = 10
Probability = 4 /10
= 2 / 5
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Give the domain and the range for the relation.
{(3,1), (6,4), (9,9)}
Answer:
domain: {3,6,9}
range: {1,4,9}
Step-by-step explanation: take the x values in increasing order for domain and the y values in increasing order for range. Do not repeat values.
Q2. The diagram shows the position of town A.
Scale: 1 cm represents 10 km
Town B is 64 km from town A on a bearing of 070°.
Mark the position of town B, with a cross (*).
Use a scale of 1 cm represents 10 km.
The position of town B in cartesian plane is 6.4 cm in 1st quadrant at an angle of 70°.
As per the question statement, we are given that a diagram which shows the position of town A and the scale of 1 cm representing 10 km.
Town B is 64 km from town A on a bearing of 070°. We are supposed to tell the position of town B.
Let's assume that town A lies at origin in cartesian plane and as 1 cm represents 10 km therefore,
[tex]1cm = 10 km\\1 km = 0.1 cm\\64 km = 64*0.1=6.4 cm[/tex]
The town B is 6.4 cm from the origin and as the angle is given as 70° so the position of town B is in 1st quadrant.
Therefore the position of town B is 6.4 cm in 1st quadrant at an angle of 70° when town A lies at origin in the cartesian plane.
Cartesian Plane: The cartesian coordinate system includes a two-dimensional plane known as the Cartesian Plane. Numerical coordinates can be used to describe any point on a cartesian plane.To know more about cartesian plane, click on the link given below:
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1: Find the slope:
Y
-9
X
-1
0
1
2
-3
39 what’s the slope
Answer:
Step-by-step explanation:
83.9
Slopes vs. gradients vs. % grades
Slope
Angle (degrees) Gradient Grade (%)
40 1 83.9
41 1 86.9
42 1 90.0
Lucy’s chocolate bar is 46% cocoa. If the weight of the chocolate bar is 62 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answer: 28,5 grams of cocoa
Step-by-step explanation:
[tex]\frac{62*46}{100}[/tex]
Solve the formula for the specified variable.
I = Prt
t
Find the average rate of change of the function from x₁ to X₂.
x-Values
X1 = 1, X₂ = 6
Function
f(x) = x² - 2x + 6
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm
The possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm
How to determine the possible rectangle's length and width?The given parameters are
Area = 15 square cm
The area is given as
Area = 15 square cm
The formula of area is
Area = Length x Width
Using the above formula, we have:
A) 1 cm and 15 cm ⇒ 15 square cm
B) 2 cm and 7 cm ⇒ 14 square cm
C) 3 cm and 5 cm ⇒ 15 square cm
D) 4 cm and 4 cm ⇒ 16 square cm
Hence, the possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm
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Possible question
The area of a rectangle is 15 square cm
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm
evaluate the function f(x) = square root of x at given value
Answer:
2/11
Step-by-step explanation:
since the square root of 4 is 2 and that of 121 is 11
The perimeter of the triangle below is 54 units. Find the value of y.
Answer:
y = 7
Step-by-step explanation:
3y + (y+1) + (4y-3) = 54
3y + y + 4y + 1 - 3 = 54
8y - 2 = 54
8y = 54 + 2
8y = 56
y = 56/8
y = 7
Check:
3*7 + (7+1) + ((4*7)-3) = 54
21 + 8 + 28-3 = 54
29 + 25 = 54
Someone help with this too pls
The answer is 18 months as per the asked question and visible graph
Step-by-step explanation:
Find $900 and follow the horizontal line until it touches the red tilted line
As soon as it touches the red line, go down vertically and find where the line leads you and voila, it leads you to 18 months!
A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month the peanuts had not sold well, so, in order to sell 90 pounds of peanuts, the manager decided to mix the 90 pounds of peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue?
The number of pounds of cashews should be mixed with the peanuts to ensure no change in the revenue is; 360 pounds
How to Solve Algebra Word Problems?Let the number of pounds of cashews be x.
Now, we are told that A nut store normally sells cashews for $4.00 per pound. Thus;
Cost of x pounds of cashews = $4x
He wants to mix the above with 90 pounds of peanuts and sell the mixture for $3.5 per pound. Thus, the equation here is;
((90 * 1.5) + (4x))/(x + 90) = 3.5
135 + 4x = 3.5(x + 90)
135 + 4x = 3.5x + 315
4x - 3.5x = 315 - 135
0.5x = 180
x = 180/0.5
x = 360 pounds of peanuts
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