Answer:
given
f(x).4x+5
fog(x).8x+13
now
fog(x):8x+13
4x+5(g(x)):: 8x+13
g(x):: 8x+13/4x+5
Answer:
g(x) = 2x + 2
Step-by-step explanation:
One is given the following information:
f(x) = 4x + 5f o g (x) = 8x + 13One is asked to find the following:
g(x)Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:
f(g(x)) = 8x + 13
Substitute the given infromation into the equation:
4(g(x)) + 5 = 8x + 13
Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:
4(g(x)) + 5 = 8x + 13
Inverse operations,
4(g(x)) + 5 = 8x + 13
4(g(x)) = 8x + 8
g(x) = (8x + 8) ÷ 4
g(x) = 2x + 2
Find the area of the parallelogram with vertices A(−1,2,3), B(0,4,6), C(1,1,2), and D(2,3,5).
Answer:
5*sqrt3
Step-by-step explanation:
The vector AB= (0-(-1), 4-2,6-3) AB= (1,2,3)
The modul of AB is sqrt(1^2+2^2+3^2)= sqrt14
The vector AC is (1-(-1), 1-2, 2-3)= (2,-1,-1)
The modul of B is sqrt (2^2+(-1)^2+(-1)^2)= sqrt6
AB*AC= modul AB*modul AC*cosA
cosA=( 1*2+2*(-1)+3*(-1))/ sqrt14*sqrt6= -3/sqrt84=
sinB= sqrt (1- (-3/sqrt84)^2)= sqrt75/84= sqrt 25/28= 5/sqrt28
s= modul AB*modul AC*sinA= sqrt14*sqrt6* 5/ sqrt28= 5*sqrt3
The owner of a small hardware store employs three men and three women. He will select three employees at random to work on Christmas Eve. Find the probability that exactly two men (and one woman) will be selected to
work (2DP)
Answer:
Step-by-step explanation:
This is a hypergeometric distribution
[tex]\frac{{3\choose2}*{3\choose1}}{{6\choose3}}[/tex]=.45
Which equation represents the slope-intercept form of the line below?
y-intercept = (0, 2)
slope 3/7.
Answer:
A
Step-by-step explanation:
y=mx+c, plugging in slope and y intercept, we have, y=(-3/7) + 2.
Jack is 4 times as old as Lacy. 3 years from now the sum of their ages will be 71 . How old are they now?
Answer:
Lacy is 13 and Jack is 52
Step-by-step explanation:
In 3 years their ages will add up to 71 so you have to subtract 6 as there are two of them to get 65. Lacy's age is represented by x and since Jack is 4 times older his age is represented by 4x. So added together their age is 5x. So 5x=65. Then 65/5=13. So 13=x. So Lacy is 13 and Jack is 52 as 13x4 is 52.
A tortoise is walking in the desert. It walks 7.5 meters in 3 minutes. What is its speed?
Answer:
Step-by-step explanation:
speed is calculated using formula v=d/t
m= 7.5m
t= 3 min
v=?
v= 7.5m/3min
v= 2.5m/min
Individual claim sizes may be modeled by a uniform distribution function on the interval [$1000, $5000]. Eighty claims are examined. Assume claims are independent.
What is the approximate probability that total claims will be between $250,000 and $300,000?
a) 17%
b) 34%
c) 50%
d) 84%
e) 97%
An angle measures 36° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
Since they are supplementary, they add up to 180 degrees. Since one is 38 degrees more than the other, you can use the equation x + (x+36) = 180 to find both angles
Step-by-step explanation:
In the accompanying diagram, ΔA′B′C′ is the image of ΔABC. Which type of transformation is shown in the illustration?
A. rotation
B. translation
C. reflection
D. dilation
Answer:
Reflection
Step-by-step explanation:
It is the opposite of the first,...
Hi can I have help pls thanks :)
Answer:
Hello,
Step-by-step explanation:
The result i a rotation of 360°
The image is the same as the preimage.
Options : A,B,D are true
C and E are false
Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookies. if she wants each container to have the least number of cookies possible,how many plastic containers does she need?Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookies. if she wants each container to have the least number of cookies possible,how many plastic containers does she need?
Answer:
6
Step-by-step explanation:
If she's looking for the least number per box she wants the greatest common factor of both numbers.
The GCF of 30 and 48 is 6.
Give the measure of angle C.
B
A
D
С
110°
E
G
F
Answer:
Step-by-step explanation:
U just add all the angles together and the divide but the number of the numbers
Estimate the line of best fit using two points on the line.
.
10
9
8
7
6
5
(6,8)
(9,6)
N
1 2 3 4 5 6
8 9 10
O A. y-2x+12
O B. y--{x+12
O C. y=
O D. y=-3x+12
Answer:
B. y = -2/3x + 12
Step-by-step explanation:
Formula to find the slope when given two points on a line:
y2 - y1
x2 - x1
Substitute the two given points (6, 8) (9, 6):
6 - 8
9 - 6
Slope = -2/3x
We found the slope! And the answer choices already gave us one y-intercept, which is 12. The last thing we do is we form an equation with the information we solved and that was given to us.
y = slope (x) + y-intercept
y = -2/3x + 12
The answer choice that matches this equation is B.
In conclusion, the equation that best estimates the line of best fit shown above is answer choice B.
An equation of a line with given coordinates is y= -2/3 x+12. Therefore, option B is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given graph, the coordinate points are (6, 8) and (9, 6).
We know that, the formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
Here, slope = (6-8)/(9-6)
= -2/3
Substitute m=-2/3 and (x, y)=(6, 8) in y=mx+c, we get
8=-2/3 (6)+c
8=-4+c
c=12
So, equation of a line is y= -2/3 x+12
Therefore, option B is the correct answer.
To learn more about the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ7
Workbook
WB-21
38. What is the circumference of a circle that has a diameter of 12 inches? (Use
3.14 for 1.)
a. 15.14 inches
b. 37.68 inches
c. 376.8 inches
d. 9.42 inches
HUN
39. A ski resort reported 53.9 inches of snow in November, 73.75 inches of
snow in December and 95.8 inches of snow in January. What is the average
amount of snow that fell for the three months?
a. 80 inches
b. 223.15 inches
c. 74 inches
d. 74.48 inches
40. Dan is building a deck. He has a board 5 1/2 feet long and another
board 7 feet long. How many 1 1/2-foot boards can he cut from the
7-foot board?
a.
5
b. 3
c. 5 1/2
d. 1
Answer:
1=circum=37.7inc&diam=7 inc
0.003 is 1/10 of
Please help I need this for homework !!!!!!!!!!!!
Answer:
0.03
Step-by-step explanation:
If I get paid $100 a week but my car cost $4, 990 how long will I have to save to officially buy my car?
Answer:
50 weeks.
Step-by-step explanation:
Did the math like u should've
Rules for multiplying exponents
Answer and Step-by-step explanation:
When multiplying exponents:
- Product of Powers: When the base of the exponents are the same, and the bases are being multiplied to each other, the exponents are added together.
Example: [tex]a^x + a^y = a^{x+y}[/tex]
- Different bases Same Exponents: When the bases of the exponents are different, but the exponents are the same, the bases multiply together (within a parenthesis) with the exponent on the parenthesis.
Example: [tex]a^x*b^x = (a*b)^x[/tex]
- Quotient of Powers: When the base of the exponents are the same, and they are being divided by each other, the exponents will subtract from each other.
Example: [tex]\frac{a^x}{a^y}= a^{x-y}[/tex]
- Power of a Power: When a base has an exponent, and that entire term has and exponent, the exponents multiply together.
Example: [tex](a^x)^y = a^{x*y}[/tex]
- Power of a Product: The opposite of Different bases Same Exponents. Distribute the exponent onto the different bases.
Example: [tex](ab)^x = a^x*b^x[/tex]
- Power of a Quotient: The opposite of Quotient of Powers. Distribute the exponent to the dividing bases.
Example: [tex](\frac{a}{b} )^x = \frac{a^x}{b^x}[/tex]
- Zero Power: Any number raised to the 0 power equals 1.
Example: [tex]a^0 = 1\\999999^0=1[/tex]
- Negative Exponent: Any number raised by a negative number goes to the denominator of a fraction (if not already in the denominator), and vise versa (goes to the numerator if not already in the numerator).
Example: [tex]a^-2 = \frac{1}{a^2} \\\\\frac{1}{b^-3} = b^3[/tex]
- Power of One: Any number raised to the power of 1 is the same number.
Example: [tex]a^1 = a\\\\999^1 = 999[/tex]
I hope this helps!
#teamtrees #PAW (Plant And Water)
If θ is an angle in standard position and its terminal side passes through the point (7,-4), find the exact value of
sec
θ
secθ in simplest radical form.
9514 1404 393
Answer:
(√65)/7
Step-by-step explanation:
We can use the relation between the secant and the tangent:
sec(θ)² = tan(θ)² +1
sec(θ) = √(1 + (-4/7)²) = √(65/49)
sec(θ) = (√65)/7 . . . . . . secant is positive in the 4th quadrant
For the right angle, find the missing quantity indicated below the figure.
Answer:
The Answer is 28.........
If I toss a fair coin five times and the outcomes are TTTTT, then the probability that tails appears on the next toss is
1) 0.5
2) greater than 0.5
3) 1
4) less than 0.5
5) 0
Answer:
1. 0.5
Step-by-step explanation:
The probability of flipping a coin and landing on heads or tails is 100%. So 3)1 would be incorrect. In probability, we learned that just because something was picked more than once, it does not lower the chances of the thing being picked again. So 5)0 would be incorrect. The chances of getting tails are 50% also 0.5 and the chances of getting heads are 50% also 0.5. So 1 is correct.
There is a 0.5 percent chance that the following coin will land on its side.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
The sample space, which is typically represented using set notation, contains a list of all the potential ordered outcomes as elements. A sample space with all possible outcomes exists for a series of five fair coin tosses. The example of a fair coin toss is 2*2*2H,T.
{HHHHH,HHHHT,HHHTH,HHTHH,HTHHH........TTTTT} The likelihood that the next coin will land on its side is always equal to It doesn't matter if previous results were TTTTT, HHHHH, or TTHT. The probability that the next number will be a tails is therefore still 0.5 in each of these cases as well as all others.
To learn more about Probability refer to:
https://brainly.com/question/24756209
#SPJ2
What is A11 for the geometric sequence 3,072, −1,536, -768, −384...?
Answer:
3
Step-by-step explanation:
The general formula of the series is 3072/(-2)^(n-1). A11=3072/(-2)^10=3
Please help it’s due today
Answer:
67 degrees
Step-by-step explanation:
23 + 90 = 113
180 - 113 = 67
The point p=(2/5,y) lies on the unit circle below what is the value of y in simplest form
Step-by-step explanation:
distance of (1,0) from the origin is,
√{(1-0)²+(0-0)²}
= √1
= 1
So the radius of the circle is 1,
now for the point (2/5,y) distance from origin should be the same since it's the radius
so,
√{(2/5-0)²+(y-0)²} = 1
or, √(4/25+y²)=1
or, 4/25+y²=1
or, y² = 1-4/25
or, y²=21/25
or, y=√(21/25)
or, y=√21/5
so, the simplest form of y is,
[tex] \frac{ \sqrt{21} }{5} [/tex]
If a= -5 and b= -2,then what is the value of [a-b]2
Step-by-step explanation:
Substitute the values of a and b into [a-b]2
= [-5-(-2)]2
= [-5+2]2
= [-3]2
= -6
ABCD is a rectangle enclosed in a circle with centre at O
and radius of 7cm. AOC is a diameter of the circle. the area of the rectangle is
56 2
. find the height of triangle ADC if the base is AC.
9514 1404 393
Answer:
4 cm
Step-by-step explanation:
The area of the triangle is half the area of the rectangle. The base of the triangle is the diameter of the circle, 14 cm. So the height is found from ...
A = 1/2bh
(56 cm²)/2 = 1/2(14 cm)h
h = (28 cm²)/(7 cm) = 4 cm
The height of triangle ADC is 4 cm.
PLS HELP QUICK IM BEGGINGGGG!!!!! PLEASE HELP ME!!
The following box plot represents the heights of the students in Mr. Taylor's fourth grade math class.
In a complete sentence, answer the following question:
One of the values in this data set is 138. In this box plot, what does this value mean?
Answer:
The value 138 means that this height (138cm) is less than the average height of a 4th grader.
Answer: No credit wanted
Step-by-step explanation:
The other guy is completely right.
Bank B pays 5.9% annual percentage rate compound semiannually what is the effective annual yield round to the nearest hundredth
9514 1404 393
Answer:
5.99%
Step-by-step explanation:
The relationship between the effective annual yield (e) and the nominal annual interest rate (r) compounded n times per year is ...
e = (1 +r/n)^n -1
For r = 5.9% and n = 2, the effective rate is ...
e = (1 +0.059/2)^2 -1 = 0.059870 ≈ 5.99%
PLS HELP IM CONFUSED
Given the graph of a radical function, which statement is correct?
Radical function going from the point negative 3 comma negative 2 up to the right through the point comma 0
A. R colon open bracket y is an element of all real number close bracket
B. R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
C. R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 2 close bracket
D. R colon open bracket y is an element of all real numbers such that y is greater than or equal to 1 close bracket
Answer:
The answer to your question will be the choice "D."
find the measure of y
Answer:
Step-by-step explanation:
x = 90°-47° = 43°
y = x = 43°
Solve (2x – 1)2 = 9. Question 11 options: A) x = 2, –1 B) x = 2, 1 C) x = –2, –1 D) x = –2, 1
Answer:
(2x – 1)2 = 9
4x-2=9
4x=9+2
4x=11
x=11/4
x=2.75
Which graph represents the function h(x) = |x – 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
Answer:
option 3
Step-by-step explanation:
i know because i got it right.
