The required function of h i.e f(h) is expressed as
[tex]f(h) = \dfrac{1}{h^2-3}[/tex]
Substitution of a function means replacing a variable with another variable without changing the structure of such function. According to the function given, we can see that we are simply meant to replace x with h as shown below:
Given the expression
[tex]f(x) = \frac{1}{x^2-3}[/tex]
To get f(h), we will substitute f in place of x that is x -> h as shown
[tex]f(h) = \frac{1}{h^2-3}[/tex]
Hence the required function of h i.e f(h) is expressed as
[tex]f(h) = \dfrac{1}{h^2-3}[/tex]
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is the value of these expressions the same? explain.
Answer:
No.
Step-by-step explanation:
Using the order of operations:
4 · 6 - 4 = 20 (Multiplication is done first.)
4 · (6 - 4) = 8 (Parentheses is done first.)
In a class, students can complete extra-credit
assignments for either 7 points or 12 points. Each student can complete at most four of the 7-point assignments and
at most four of the 12-point assignments. If Barbara
completes six extra-credit assignments, what is a
possible number of points she can earn?
Answer:
31 PTS
Step-by-step explanation:
Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 5 inches. The heights of 9 randomly selected students are 66, 71, 63, 74, 69, 64, 66, 68 and 67.
Answer:
The mean is about 68 (67.5555)
Step-by-step explanation:
(63+64+66+66+67+68+69+71+74) / 9 ≈ 68
a road rises 16 feet for every 50 feet of horizontal distance covered. in percent what is the grade of the road?
Answer:
32%
Step-by-step explanation:
The slope of the road is measured as
slope = [tex]\frac{rise}{run}[/tex] = [tex]\frac{16}{50}[/tex]
To express as a percentage multiply the fraction y 100% , that is
slope = [tex]\frac{16}{50}[/tex] × 100% = 16 × 2 = 32%
Write the quadratic equation whose roots are 2 and -4 and whose leading coefficient is 2
Answer:
2x^2+4x-16
Step-by-step explanation:
The quadratic can be written as
f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots
f(x) = a (x-2)(x- -4)
a is the leading coefficient
f(x) = 2(x-2)(x+4)
= 2(x^2 -2x+4x-8)
= 2(x^2 +2x-8)
= 2x^2 +4x-16
PRECAL QUESTION - please help thanks
Answer:
203/169 -183i/169
"A"
Step-by-step explanation:
[tex]\frac{9-19i}{12-5i}[/tex]
[tex]\frac{9-19i}{12-5i}[/tex] * [tex]\frac{12+5i}{12+5i}[/tex]
12^2 - (5i)^2 = 144 + 25 = 169
FOIL: 108 +45i - 228i + 95
203 -183
what is differnciation
Answer:
Differentiation is concerned with things like speeds and accelerations, slopes and curves ect. These are Rates of Change, they are things that are defined locally. The Fundamental Theorem of Calculus is that Integration and Differentiation are the inverse of each other.
find the measure of the angle
Answer: 86
Step-by-step explanation:
This is a cyclic quadilateral in which opposite angles adds upto 180.
Let the unknown angle be x
ATQ
x + 94 = 180
x = 180 - 94
x = 86
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An athletic club charges a monthly membership
fee of $65. Members can also take classes for an
additional $15 per class. For this month only, the
club has a special that includes two free classes for
all new members. Which of the following functions
expresses the cost for the month for new members
who take x classes this month, where x > 2?
(A) C(x) = 2x + 65
(B) C(x) = 15x + 65
(C) C(x) = 2(x - 15) + 65
(D) C(x) = 15(x - 2) + 65
Jim took a loan of R30 000.00 for 18 months at a simple interest rate of 12.5% per year. Determine the amount that Jim
will pay in 18 months.
Answer:
R35625
Step-by-step explanation:
(R30,000×.125×18/12)+R30000
=R35625
Y= 3x-1
2x+6=y substitution method
Answer: (7, 20)
Concept:
There are three general ways to solve systems of equations:
EliminationSubstitutionGraphingSince the question has specific requirements, we are going to use substitution to solve the equations.
Solve:
Given equations
y = 3x - 1
2x + 6 = y
Substitute the y value since both equations has isolated [y]
2x + 6 = 3x - 1
Add 1 on both sides
2x + 6 + 1 = 3x - 1 + 1
2x + 7 = 3x
Subtract 2x on both sides
2x + 7 - 2x = 3x - 2x
[tex]\boxed{x=7}[/tex]
Find the value of y
y = 3x - 1
y = 3(7) - 1
y = 21 - 1
[tex]\boxed{y=20}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Turn 43 1/23 into an improper fraction
Answer:
990/23
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
23 × 43 = 989
Step 2
Add the answer from Step 1 to the numerator
989 + 1 = 990
Step 3
Write answer from Step 2 over the denominator
990/23
I hope this answer helps you out! Brainliest would be appreciated.
12
Detroit, Michigan covers an area of 142.9 square miles. There are approximately
672,800 people living in Detroit. Grand Rapids, Michigan has an area of 45.3 square
miles and has a population of approximately 195,100 people. How many more
people, per square mile, live in Detroit verses Grand Rapids? Round to the nearest
person per square mile.
Answer:
401 more people per square mile
Step-by-step explanation:
Find how many people there are per square mile in both cities by dividing the number of people by the number of square miles:
672,800/142.9
= 4708 people per square mile (Detroit)
195,100/45.3
= 4307 (Grand Rapids)
Find how many more people per square mile live in Detroit by finding the difference between these two numbers:
4708 - 4307
= 401
So, there are 401 more people per square mile living in Detroit versus Grand Rapids.
Mia walks her dog twice a day. Her evening walk is two and a half times as far as her morning walk. At the end of the week she says she walked her dog 30 miles. How long is her morning walk?
9514 1404 393
Answer:
1 11/49 ≈ 1.224 miles
Step-by-step explanation:
Let m represent the length of the morning walk. Then the length of the evening walk is 2.5m, and the total each day is m+2.5m = 3.5m.
The total for 7 days is ...
7(3.5m) = 30
m = 30/24.5 = 60/49 ≈ 1.224 . . . . miles
Mia's morning walks are 1 11/49 miles, about 1.224 miles.
Suppose that one state’s license plates consist of 1 digit followed by 4 letters followed by 2 digits. How many such plates can the state issue?
Answer:
The state can issue 456,976,000 license plates.
Step-by-step explanation:
For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.
For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.
For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:
[tex]\frac{10}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{10}[/tex] [tex]\frac{10}[/tex]
= 10*26*26*26*26*10*10
=456,976,000.
Therefore, the state can issue 456,976,000 license plates.
The sum of 5 consecutive odd integers is 425. Find the integers.
Answer:
Hello,
Step-by-step explanation:
This a method knowing nothing.
1+3+5+7+9=25
425-25=400
400/5=80
Numbers are 80+1,80+,80+5,80+7,80+9 whose sum is 425.
HELP! I really need the answer quick!!!!!!!
Answer:
139°
Step-by-step explanation:
8x+51+6x-25=180
14x+26=180
14x=180-26
14x=154
x=154/14
x=11
<AOB= 8x+51 = 8(11)+51 = 88+51 = 139
Add.
3+ (-6) =
-6 + (-3) =
An article is marked to sell at a gain of 10%. If it be sold for Rs. 7.50 less there would be loss of 5%, find the cost price.
Answer:
750,. is answer
I hope it helps
Hello can someone answer please
Answer:
hello thereeeee
ans is 23.5
Step-by-step explanation:
so lets start
first of all remove decimal of divisor 1.1/25.85 multiplying by 10
11/258.5
now first multiply by 2
now we get 22 and subtract with 25 => 25-22 = 3
so left is
38
now 11*3 = 33
so now by 3
38-33= 5
bringing another 5 down
we get 55
now quotient is 23. something ( as we bought .5 down)
and now 11*5 = 55
so
23.5 is answer
When Asia was young, her father marked her height on the door frame every month. He noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches, and multiplying the result by one-third.
Create an equation linking her predicted height, h, with her age in months, m, and solve to find when her height will be 30 inches.
Answer:
15 months old.
Step-by-step explanation:
Let m = months and h = height:
h = 1/3(m + 75) ⇔ h = 1/3m + 25
Let h = 30:
[tex]30=\frac{1}{3}m+25\\5=\frac{1}{3}m\\15=m[/tex]
Therefore, when Asia is 30 inches tall, she will be 15 months old.
For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).
Answer:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystlye F(x) = x^2 - 2x + 4[/tex]
And we want to find F(b + 3).
We can substitute:
[tex]\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4[/tex]
Expand:
[tex]\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4[/tex]
Rearrange:
[tex]\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)[/tex]
Combine like terms. Hence:
[tex]\displaystyle = b^2 +4b + 7[/tex]
In conclusion:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
URGENT!!!PLEASE HELP! PLEASE PLEASE!
Choose the number below that fits into the following number sets:
Natural Number
Whole Number
Integer
A. -½
B. 4.9
C. π
D. 6
Answer:
d) 6
Step-by-step explanation:
natural number = +ve numbers, so -1/2 is out
4.9 and π arent whole numbers nor intergers
What is the complete factorization of the polynomial below?
x3 + 4x2 + 16x + 64
Answer: (x+4) ( x-4i)(x+4i)
Discussion:
Factor the polynomial:
x^3+4x^2+16x+64 = (x +4 ) ( x^2 + 16) (*)
Factor x^2 +1 6 over the complex numbers:
x^2 + 16 = (x -4i)(x+4i) (**)
Combing (*) and (**) gives the full factorization
(x+4) ( x-4i)(x+4i)
Write the equation of the sinusoidal function shown.
A) y = 2 sin(2x)
B) y = 2 sin x + 2
C) y = 2 cos x + 2
D) y = 2 cos(2x)
Answer:
2 sin(2x)
Step-by-step explanation:
sin x stretched vertically by a factor 2 and compressed horizontally by a factor 2.
The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.
so, we get,
However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.
Hence, The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.
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what is the absolute value of -5/9
Answer:
5/9
Step-by-step explanation:
In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:
Negative -> Positive
Positive -> Positive
Since we are working with a negative value, it will turn positive.
Best of Luck!
F(x)=x^2 what is g(x)
Answer:
stop spamming
Step-by-step explanation:
Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?
After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
What is a quadratic equation?"It is a polynomial equation with degree two."
What is completing the square method?"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "
For given example,
We have been given a quadratic equation.
[tex]3x^{2} -12x-15=0[/tex]
First we divide above quadratic equation by 3,
[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex] ................(i)
Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]
[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]
Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),
[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]
Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
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1) A 22-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.)
2)How high does the ladder reach on the building? (Round your answer to the nearest whole number.)
Answer:
21.9 ft
Step-by-step explanation:
Answer:
Part A)
About 74.2°.
Part B)
About 21 feet.
Step-by-step explanation:
A 22 feet ladder is leaning against a building, where the base of the ladder is six feet from the base of the building.
This is shown in the diagram below (not to scale).
Part A)
We want to determine the angle of elevation of the ladder. That is, we want to find the value of θ.
Since we know the values adjacent to θ and the hypotenuse, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent is 6 and the hypotenuse is 22. Thus:
[tex]\displaystyle \cos \theta = \frac{6}{22} = \frac{3}{11}[/tex]
Take the inverse cosine of both sides:
[tex]\displaystyle \theta = \cos^{-1}\frac{3}{11}[/tex]
Use a calculator. Hence:
[tex]\displaystyle \theta = 74.1733...\approx 74.2^\circ[/tex]
The angle of elevation is approximately 74.2°
Part B)
We want to find how high up the ladder reaches on the building. In other words, we want to find x.
Since x is opposite to θ and we know the adjacent side, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
The opposite side is x and the adjacent side is 6. The angle θ is cos⁻¹(3/11) (we use the exact form to prevent rounding errors). Thus:
[tex]\displaystyle \tan \left(\cos^{-1}\frac{3}{11}\right) = \frac{x}{6}[/tex]
Solve for x:
[tex]\displaystyle x = 6 \tan \left(\cos^{-1}\frac{3}{11}\right)[/tex]
Use a calculator. Hence:
[tex]x = 21.1660... \approx 21\text{ feet}[/tex]
The ladder reaches about 21 feet up the building.
Length of tangent line - geometry please help
Answer:
12
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
PC * PA = PB^2
(PA+AC) * PA = PB^2
(4+32) * 4 = PB^2
36*4 = PB^2
144 = PB^2
Taking the square root of each side
sqrt(144) = sqrt(PB^2)
12= PB
Answer:
a
Step-by-step explanation:
Given a tangent and a secant to a circle from an external point, then
The square of the tangent is equal to the product of the external part and the whole of the secant , that is
PB² = PA × PC = 4(4 + 32) = 4 × 36 = 144 ( take square root of both sides )
PB = [tex]\sqrt{144}[/tex] = 12 → a
