Answer:
7900 is the round off to the nearest hundred
let f(x)=7x-4
what is f(6)?
Answer:
38
Step-by-step explanation:
To find the value of f(6), we substitute the value 6 where x is into the function. You would get:
7(6) - 4
42 - 4
f(6) = 38
Answer:
See my writting here have answer
Here are the first five terms of a sequence. 4, 11, 22, 37, 56 Find an expression, in terms of , for the th term of this sequence.
Answer:
[tex] a_n = 2n^2 + n + 1 [/tex]
Step-by-step explanation:
4, 11, 22, 37, 56
11 - 4 = 7
22 - 11 = 11
37 - 22 = 15
56 - 37 = 19
After the first difference, 11 - 4 = 7, each difference is 4 more than the previous difference.
Difference of differences:
11 - 7 = 4
15 - 11 = 4
19 - 15 = 4
Since we need the difference of differences to find a constant, this must be a second degree function.
[tex] a_1 = 4 = 2^2 + 1(0)[/tex]
[tex] a_2 = 11 = 3^2 + 2 = 3^2 + 2(1) [/tex]
[tex] a_3 = 22 = 4^2 + 6 = 4^2 + 3(2) [/tex]
[tex] a_4 = 37 = 5^2 + 12 = 5^2 + 4(3) [/tex]
[tex]a_5 = 56 = 6^2 + 20 = 6^2 + 5(4)[/tex]
[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]
[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]
[tex] a_n = n^2 + 2n + 1 + n^2 - n [/tex]
[tex] a_n = 2n^2 + n + 1 [/tex]
find missing side of triangle. help
Answer:
x² + 2² =(√15)²
x²+ 4. =15
x² =15-4
x² =11
x. =√11 mi
so the answer is 4th option
685 gym members were asked if they use the elliptical machine or treadmill as their primary cardiovascular exercise. 257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.
a.) Organize this using a venn diagram (2 marks)
b.) A gym member is chosen from this group. What is the probability that this member uses the treadmill only? (1 mark)
Given:
Total number of gym members = 685
257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.
To find:
a. The venn diagram.
b. The probability that a member uses the treadmill only?
Solution:
(a)
We have,
Total number of gym members = 685
Treadmill user = 257
Elliptical user = 157
Who use both = 85
Only treadmill user is:
[tex]257-85=172[/tex]
Only Elliptical used
[tex]157-85=72[/tex]
Therefore, the venn diagram for the given situation is shown below.
(b)
The member who use treadmill only = 172
Total user = 685
The probability that a member uses the treadmill only is:
[tex]P(\text{Only treadmill})=\dfrac{\text{Only treadmill users}}{\text{Total users}}[/tex]
[tex]P(\text{Only treadmill})=\dfrac{172}{685}[/tex]
Therefore, the probability that a member uses the treadmill only is [tex]\dfrac{172}{685}[/tex].
Sales of a certain product are declining at a rate proportional to the amount of sales. If at the end of the first year the sales have declined by 22%, then how many years will have passed (since the beginning of the first year) when sales become only 31% of their original value? Express your answer as a decimal, correct to within 0.001 years.
Answer:
The answer is "6.093 years".
Step-by-step explanation:
The rate of decline in sales in [tex]22\%[/tex] per year.
The starting sales is 100 units:
Using compounding formula:
[tex]\to 100 \times (1-\frac{22}{100})^t=22\% \ of \ 100\\\\\to 100 \times (\frac{100-22}{100})^t=\frac{22}{100} \times \ 100\\\\\to (\frac{78}{100})^t=\frac{22}{100}\\\\\to 0.78^t=0.22\\\\\text{taking \log on both the sides}\\\\[/tex]
taking log on both sides
[tex]\to \log_e \ 0.78^t= \log_e\ 0.22\\\\\to t \log_e \ 0.78= \log_e\ 0.22\\\\\to t = \frac{\log_e 0.22}{\log_e 0.78}\\\\[/tex]
[tex]= \frac{-0.6575}{-0.1079}\\\\= \frac{0.6575}{0.1079}\\\\=6.093[/tex]
Using interval notation, identify the domain for the function:
Answer:
d)
Step-by-step explanation:
>The domain are all the values of x , so you can graph on the calculator that on the x-axis the graph starts at 9 and keeps going to the right so the domain is x≥9 or [9,∞)
or
>Solve for x in the given equation when f(x) =y = 0 to find the roots
√(x-9) = 0 , square both sides
x-9 = 0 , add 9 to both sides
x= 9
from this root the graph moves to the right to ∞
the domain is [9, ∞)
What is the solution for this inequality? -10x ≤ 40 A. x ≤ -4 B. x ≤ 4 C. x ≥ -4 D. x ≥ 4
Answer:
C. x ≥ -4
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-10x ≤ 40
Step 2: Solve for x
[Division Property of Equality] Divide -10 on both sides: x ≥ -4Answer:
C. x ≥ -4
Step-by-step explanation:
To solve this inequality isolate the variable. Do this by using the properties of equality, specifically the division property. So, divide both sides by -10. This equals, x ≤ -4. However, whenever an inequality is divided or multiplied by a negative number the sign must be flipped. Therefore, the final answer is x ≥ -4.
I need help. Someone please figure it out
Answer:
[tex]\frac{1}{2^{n} }[/tex]
Step-by-step explanation:
The rules of exponents state that
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] and [tex]a^{0}[/tex] = 1
Thus
[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]
[tex]2^{-4}[/tex] = [tex]\frac{1}{2^{4} }[/tex] = [tex]\frac{1}{16}[/tex]
[tex]2^{-3}[/tex] = [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]
and so on , to
[tex]2^{0}[/tex] = 1
Find the missing side of the triangle using the Pythagorean Theorem.
Answer: a^2 + b^2 = c^2
c^2 - a^2 = b^2 \/---
b^2
Step-by-step explanation: once completed you have ur answer
Answer:
[tex]\boxed {\boxed {\sf 18 \ yards}}[/tex]
Step-by-step explanation:
This triangle is a right triangle. We know this because of the small square in the corner representing a 90 degree angle. Therefore, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
In this formula a and b are the legs of the triangle and c is the hypotenuse.
In this triangle, the legs are 24 and a, because these sides form the right angle. 30 is the hypotenuse because it is opposite the right angle.
a=a b= 24 c= 30Substitute the values into the formula.
[tex]a^2+(24)^2=(30)^2[/tex]
Solve the exponents.
(24)²= 24*24=576 (30)^2= 30*30=900[tex]a^2+ 576=900[/tex]
We are solving for a, the missing side of the triangle. We must isolate the variable. 576 is being added. The inverse of addition is subtraction, Subtract 576 from both sides of the equation.
[tex]a^2+576-576=900-576\\a^2=900-576\\a^2=324[/tex]
a is being squared. The inverse of a square is a square root. Take the square root of both sides.
[tex]\sqrt{a^2}=\sqrt{324}\\a=\sqrt{324}\\a=18[/tex]
The missing side of the triangle is 18 yards.
If a > b and b > a, then ?
That's impossible. There are no solutions.
2
Solve the equation log, (3t+9) - log, 21 =1
Answer:
67
Step-by-step explanation:
log(3t+9)-log21 = 1
Applying, the law of logarithm,
log(3t+9)/21 = 1
converting the log into index
(3t+9)/21 = 10
solving for t
3t+9 = 21×10
3t+9 = 210
3t = 210-9
3t = 201
t = 201/3
t = 67
Determine the x-intercepts of the function. Check all that apply.
(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)
Answer:
-2,-1,0,1,2
Step-by-step explanation:
Answer:
-2.0
0,0
Step-by-step explanation:
i just did the test
If f(x) = 7x - 3 and g(x) = x^2, what is (g° 0(1)?
( f ∘ g ) ( x ) is equivalent to f ( g ( x ) ) . We solve this problem just as we solve f ( x ) . But since it asks us to find out f ( g ( x ) ) , in f ( x ) , each time we encounter x, we replace it with g ( x ) . In the above problem, f ( x ) = x + 3 . Therefore, f ( g ( x ) ) = g ( x ) + 3 . ⇒ ( f ∘ g ) ( x ) = 2 x − 7 + 3 ⇒ ( f ∘ g ) ( x ) = 2 x − 4 Basically, write the g ( x ) equation where you see the x in the f ( x ) equation. f ∘ g ( x ) = ( g ( x ) ) + 3 Replace g ( x ) with the equation f ∘ g ( x ) = ( 2 x − 7 ) + 3 f ∘ g ( x ) = 2 x − 7 + 3 we just took away the parentheses f ∘ g ( x ) = 2 x − 4 Because the − 7 + 3 = 4 This is it g ∘ f ( x ) would be the other way around g ∘ f ( x ) = 2 ( x + 3 ) − 7 now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them. g ∘ f ( x ) = 2 x + 6 − 7 Next, + 6 − 7 = − 1 g ∘ f ( x ) = 2 x − 1
Hello,
[tex]f(x)=7x-3\\g(x)=x^2\\\\(fog)(x)=g(f(x))=g(7x-3)=(7x-3)^2=49x^2-42x+9\\\\(gof)(x)=f(g(x))=f(x^2)=7x^2-3\\\\(fog)(0)=g(f(0))=49*0^2-42*0+9=9\\\\(gof)(0)=f(g(0))=7*0^2-3=-3\\[/tex]
Since i don't know what is (g°O(1) and you haven't correct your question ,
i has put the 2 possibles answsers.
please help ,,
supply the missing reason in statement 4 of the proof of the isosceles triangle theorem.
Answer:
h
Step-by-step explanation:
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
The batting order for nine players on a team with 11 people.
Given:
The batting order for nine players on a team with 11 people.
To find:
The number of possibilities for the given scenario.
Solution:
First, we need to select 9 players from 11 people, it involves combination, i.e. [tex]^{11}C_9[/tex].
Second, we need to arrange the order of 9 selected players, it involves permutation, i.e., [tex]^9P_9[/tex].
The number of possibilities for the given scenario is:
[tex]\text{Possibilities}=^{11}C_9\times ^9P_9[/tex]
[tex]\text{Possibilities}=\dfrac{11!}{(11-9)!9!}\times \dfrac{9!}{(9-9)!}[/tex]
[tex]\text{Possibilities}=\dfrac{11\times 10\times 9!}{2!9!}\times \dfrac{9!}{0!}[/tex]
[tex]\text{Possibilities}=\dfrac{110}{2\times 1}\times \dfrac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{1}[/tex]
[tex]\text{Possibilities}=55\times 362880[/tex]
[tex]\text{Possibilities}=19958400[/tex]
Therefore, the following scenario involves both permutation and combination, and the number of possibilities is 19958400.
Which of the following is a composite number?
A. 1
B. 63
C.O
D. 19
B. 63
some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite
Translate the sentence into an equation.
Nine times the sum of a number and 4 is 3.
In the graph increasing, decreasing, or constant?
Answer:
Step-by-step explanation:
slope>0 so graph is increasing.
Solve the equation and enter the value of x below. 3(x + 4) = 123
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]3(x + 4) = 123 \\ 3x + 12 = 123 \\ 3x = 123 - 12 \\ 3x = 111 \\ x = \frac{111}{3} \\ x = 37[/tex]
=> The answer is 37.
Answer:
X=37
Step-by-step explanation:
3(x+4)=123
3x+12=123
3x=123-12
3x=111
3x/3 =111/3
x=37
Find an equation for the perpendicular bisector of the line segment
whose endpoints are (9, -3) and (-5, –7).
Step-by-step explanation:
So here is my attempt. And i guess its correct
3/x + 4/5 = 11/10
For what value of x is the equation above true?
A) 3
B) 5
C) 7
D) 10
Answer:
The answer is
[tex] \frac{3}{x} = \frac{11}{10} - \frac{4}{5} \\ \frac{3}{x} = \frac{55 - 40}{50} \\ \frac{3}{x} = \frac{15}{50} \\ \frac{3}{x} = \frac{3}{10} \\ x = 10[/tex]
In the equation 17x2 = 12x, the value of c is:
O 0
O 12
O 17
The value of c is 0.
By question,
17x² = 12x
or,(17x-12):x=0
or,17x - 12 = 0#
For some tips,
In the equation 17x2 = 12x,Rewrite in factored formMove terms to the left sideCreate separate equationsHENCE PROVED ##
Sophia worked for 6 hours and got paid $85. How much money did Sophia will earn if she works for 18
hours?
Answer: $255
Step-by-step explanation:
Use proportions:
[tex]\frac{6hr}{85} =\frac{18hr}{x}[/tex]
Cross-multiply & solve:
[tex]6x=18 * 85\\6x=1530\\x=255[/tex]
which of the following give the highest future value is 6000000 is invested at 6% for 3 years
Answer:
$5084745.76271
Step-by-step explanation:
Given data
Final amount= $6000000
Rate=6%
Time= 3 years
Now let us find the initial amount which is the principal
using the simple interest formula we have
6000000 = P(1+0.06*3)
6000000 =P(1+0.18)
6000000 =P*1.18
P= 6000000 /1.18
P=$5084745.76271
Hence the initial deposite is $5084745.76271
ℎ = 6 + 11 − 22
calculation path
Answer:
[tex]h = 6 + 11 - 22 \\ h = 17 - 22 \\ h = - 5[/tex]
Answer:
-5
Step-by-step explanation:
6+11 = 17↓
17-22 = -5
or
11-22 = -11↓
-11+6 = -5
Solve this equation : 12p-5=25
write step by step.
Answer:
P=2.5
Step-by-step explanation:
12p = 25+5
12p = 30
P =30/12
Simplification:
P= 15/6
= 5/2 = 2.5
A marketing researcher interviews a large number of respondents and asks them a set of questions that are listed in a questionnaire. The respondents are required to select a response from a given set of options. In this case, the researcher is _____.
Answer: conducting quantitative research
Step-by-step explanation:
Quantitative research refers to the collection and the analysis of numerical data. Quantitative research can be used in making predictions, and testing casual relationships.
Quantitative research methods emphasize the numerical analysis of data which can be collected through questionnaires, polls, surveys etc.
Could someone please help me with this question? Thanks.
Answer:
Step-by-step explanation:
MM oute le iloa
William used 15 cm of tape to wrap 3 presents. Find the length of tape to wrap for 1 present?
Answer:
The length of tape to wrap = 5 cm
Step-by-step explanation:
Let the length of tape used to wrap 1 present be = x
Tape length Number of presents
15 cm 3
x 1
[tex]\frac{15}{x} = \frac{3}{1} \\\\x \times 3 = 1 \times 15\\\\x = \frac{15}{3} = 5 \ cm[/tex]
Зу = х - 9
y = -x + 1
Using the graphing method, which of the following choices is the solution of the system?
A=(-3 ,-2)
B=(3 ,-2)
C= Infinite solutions
D= No solutions
Answer:
did i got it correct if yes follow plz
used a graphing tool to, well, graph it
see the solution in the screenshot, it's the point where the two lines intersect