Answer:
x = -8 and x = 4
Step-by-step explanation:
given
f(x) = (x+8) (x - 4)
recall that at any point on the x-axis, y = 0 [i.e f(x) = 0]
hence to find where the graph crosses the x-axis, we simply substitue f(x) = 0 into the equation and solve for x
f(x) = (x+8) (x - 4)
0 = (x+8) (x - 4)
Hence
either,
(x+8) = 0 ----> x = -8 (first crossing point)
or
(x-4) = 0 ------> x = 4 (second crossing point)
Hence the graph crosses the x-axis at x = -8 and x = 4
Answer:
A (-8, 0) and (4, 0)
Bryan invests $500 in an account earning 3.5% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:
After 10 years?
After 15 years?
After 20 years?
Answer:
$705.30, $837.67, $994.89 Respectively
Step-by-step explanation:
Given
P= $500
r= 3.5%= 3.5/100= 0.035
Applying the compound interest formula we have
[tex]A= P(1+r)^t[/tex]
where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
1. for t= 10 years[tex]A= 500(1+0.035)^1^0\\\ A= 500(1.035)^1^0\\\\ A= 500*1.410598\\\ A=705.299[/tex]
A= $705.30
2. for t= 15 years[tex]A= 500(1+0.035)^1^5\\\ A= 500(1.035)^15\\\\ A= 500*1.67534\\\ A=837.67[/tex]
A= $837.67
3. for t= 20 years[tex]A= 500(1+0.035)^2^0\\\ A= 500(1.035)^2^0\\\\ A= 500*1.98978\\\ A=994.89[/tex]A= $994.89
find the value of a, b, c, and d,
type exact answers and use radicals as needed
Step-by-step explanation:
Using trigonometrical functions we can obtain the required side lengths.
[tex] \sin 45\degree = \frac{a}{16\sqrt 2}\\\\
\therefore \frac{1}{\sqrt 2}= \frac{a}{16\sqrt 2}\\\\
\therefore a = \frac{16\sqrt 2}{\sqrt 2}\\\\
\huge\red {\boxed {\therefore a = 16}} \\\\
\cos 45\degree = \frac{c}{16\sqrt 2}\\\\
\therefore \frac{1}{\sqrt 2}= \frac{c}{16\sqrt 2}\\\\
\therefore c = \frac{16\sqrt 2}{\sqrt 2}\\\\
\huge\purple {\boxed {\therefore c = 16}} \\\\
\sin 30\degree = \frac{a}{b}\\\\
\therefore \frac{1}{2}= \frac{16}{b}\\\\
\therefore b = {16\times2}\\\\
\huge\orange{\boxed {\therefore b = 32}} \\\\
\tan 30\degree = \frac{a}{d}\\\\
\therefore \frac{1}{\sqrt 3}= \frac{16}{d}\\\\
\therefore d = {16\times\sqrt 3}\\\\
\huge\pink {\boxed {\therefore d = 16\sqrt 3}} \\\\
[/tex]
The original price of a 2018 Honda Shadow to the dealer is $17,715, but the dealer will pay only $16,985 after rebate. If the dealer pays Honda within 15 days, there is a 2% cash discount.
Answer:
The final price to be paid after the 2% discount has been made will be $ 16,645.30.
Step-by-step explanation:
Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:
16,985 x 2/100 = X
33,970 / 100 = X
339.70 = X
Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.
f(x) = x + 2
g(x) = x - 4
(fg)(x) =
Answer:
Step-by-step explanation:pleased to help u....
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = (n − 2)! n!
Answer: Diverging
Step-by-step explanation:
Find explanations in the attached file
A sample of radioactive material disintegrates from 6 to 4 grams in 100 days. After how many days will just 3 grams remain?
Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
Learn more about radioactive materials here:
https://brainly.com/question/24339152?referrer=searchResults
A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 3.5%. What will the area be after 5 years
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
[tex]\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.
At the beginning the area is 2100
After one year the area will be
2100*(1-3.5%)=2100*0.965
After n years the area will be
[tex]2100\cdot0.965^n[/tex]
So after 5 years the area will be
[tex]2100\cdot0.965^5=1757.34027...[/tex]
So rounded to the nearest square kilometer is 1757
Hope this helps
Answer: 1757 km²
Step-by-step explanation:
Because 3.5% = 0.035, first do 1-.035 to get .965. Then do 2100*.965*.965*.965*.965*.965 to get 1757.34027.
Find the value of x.
Answer:
[tex]\huge\boxed{y=\sqrt{55}}[/tex]
Step-by-step explanation:
ΔADC and ΔDBC are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AC}{CD}=\dfrac{CD}{BC}[/tex]
Substitute:
[tex]AC=6+5=11\\BC=5\\CD=y[/tex]
[tex]\dfrac{11}{y}=\dfrac{y}{5}[/tex] cross multiply
[tex](11)(5)=(y)(y)\\\\55=y^2\to y=\sqrt{55}[/tex]
Solve the given simultaneous equations : 2x + 3y = 17 ; 3x - 2y = 6
Answer:
x= 4, y=3
Step-by-step explanation:
2x + 3y = 17
3x - 2y = 6
----------
If we double the first and triple the second equation, and add up, we can get rid of y:
4x+6y= 34+9x - 6y= 18-----------------13x= 52x= 4Then it is easy to find the value of y:
2*4+3y= 173y= 9y= 3Answer is: x= 4, y=3
Here is a sample distribution of hourly earnings in Paul's Cookie Factory:
Hourly Earning $6 up to $9 $9 up to $12 $12 up to $15
Frequency 16 42 10
The limits of the class with the smallest frequency are:_________
A) $6.00 and $9.00.
B) $12.00 and up to $14.00.
C) $11.75 and $14.25.
D) $12.00 and up to $15.00.
Answer:
The correct answer is:
$12.00 and up to $15.00 (D)
Step-by-step explanation:
Let us arrange the data properly in a tabular format.
Hourly Earnings($) 6 - 9 9 - 12 12 - 15
Frequency 16 42 10
The frequency of a distribution is the number of times that distribution occurs in a particular group of data or intervals.
From the frequency table above the following observations can be made:
Highest frequency = 42 (hourly earnings of $9 - $12)
smallest frequency = 10 ( hourly earnings of $12 - $15)
This means that among a total of 68 workers (16 + 42 + 10), the people earning $12 - $15 form the smallest group (only 10 people), while 42 workers earn $9 - $12, forming the largest majority
6th grade math help me, please :)
Answer:
B. 168 students
Step-by-step explanation:
Given that there are a total of 600 students.
28% of the students pack their lunch.
To find:
Total number of students who pack their lunch = ?
Solution:
Percentage of a given number is calculated using the following method.
[tex]y\%[/tex] of a number [tex]x[/tex] is given by:
[tex]x \times \dfrac{y}{100}[/tex]
i.e. multiply the number by percentage to be found and divide by 100.
So, we have to find 28% of 600 here, to find the answer to the question.
[tex]\therefore[/tex] Number of students who pack their lunch is given as: (Multiply the given number 600 with 28 and divide by 100.)
[tex]600 \times \dfrac{28}{100}\\\Rightarrow 6 \times 28\\\Rightarrow \bold{168}[/tex]
So, the correct answer is:
B. 168
Which statement is true about figures ABC D & ABCD
Answer:
it's option b that is the right answer
Which value of x makes the equation 0.75( x + 20) = 2 + 0.5(x - 2) true?
Answer:
0.75x+15=2+0.5x-1
0.25x=1-15
0.25x=-14
x=-56
Step-by-step explanation:
Can you help me with this.
Answer:
You would basically expand all the equations!
1. 7(4z+8b) is equal to 28z+56b.
2. 8(2x+3^2) is equal to 16x+72
3. 4(r+r+r+r) is equal to 4r+4r+4r+4r
4. 9(3+8x) is equal to 27+72x
5. 4^2(3+6f) is equal to 48+96t
6. (t+t+t)/4 is equal to t/4+t/4+t/4
7. 2(4s^3+2) is equal to 8s^3+4
8. 30(3x+4) is equal to 90x+120
9. 6(5a+9b) is equal to 30a+54b
10. 9(3x+5^4) is equal to 27x+5625
11. 7(c+c+c) is equal to 7c+7c+7c
12. 9(2+7f) is equal to 18+63f
13. 7^5(4g-8d) is equal to 67228g-134456d
Step-by-step explanation:
Evaluate the expression. 1/2 x (4+8)
Answer:
Hey there!
1/2 x (4+8)
1/2 x (12)
6
Hope this helps :)
Answer: 6x
Step-by-step explanation:
.5x*(4+8)
.5x*(12)
6x
Hope it helps <3
Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by compounding continuously? Round to the nearest cent.
Answer:
$7200
Step-by-step explanation:
The interest rate on $5,000 accumulated by Edgar is 20%.
He does not make any payment for 2 years and the interests are compounded continuously.
The amount of money he owes after 2 years is the original $5000 and the interest that would have accumulated after 2 years.
The formula for compound amount is:
[tex]A = P(1 + R)^T[/tex]
where P = amount borrowed = $5000
R = interest rate = 20%
T = amount of time = 2 years
Therefore, the amount he will owe on his debt is:
[tex]A = 5000 (1 + 20/100)^2\\\\A = 5000(1 + 0.2)^2\\\\A = 5000(1.2)^2\\[/tex]
A = $7200
After 2 years, he will owe $7200
Answer:7,434.57
Explanation: A= 5000(1+0.2/12)^12•2
Which of the following inequalities is not true?
A) -2/2 < 3
B) |-1| ≥ 0
C) |-9| ≠ |9|
D) -7 ≤ -5
Answer:
C) |-9| != |9|
Step-by-step explanation:
The definition of absolute value is simply the non-negative value of the argument without regards to the sign. With this in mind, let's walk through these options.
A) -2/2 < 3 ==> -1 < 3 which is True
B) |-1| >= 0 ==> 1 >= 0 which is True since 1 is > 0
C) |-9| != |9| ==> 9 != 9 which is False since 9 == 9
D) -7 <= -5 which is True since -7 is < -5
Cheers
pls help me help me
Answer:
A
Step-by-step explanation:
For an inequality to have a shaded area above the graph, the variable has to be on the left side of a greater than sign, or a greater than or equal to sign.
A is the only option with one of these signs, so it is the correct answer.
help me pls pls pls
Answer:
i think it is E
Step-by-step explanation:
if ade has 23hand bag and he sells one for 409$ and he sells 22 for toby what will be the amount
Step-by-step explanation:
Hello there!
Its simple,
Given that, Ade had 23 hand bags.
selling price of each bag=$409
total sold bags= 22.
now, total amount he got was = no.of sold bag×sp of each bag.
so, total amount = 22×$409
=$8998.
Therefore, he has $ 8998 now.
Hope it helps...
If sinθ = 12/13 and θ is an acute angle, find cotθ.
Answer:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \sin \theta = \frac{12}{13}[/tex]
Where θ is an acute angle, and we want to find cot(θ).
Recall that sine is the ratio of the opposite side over the hypotenuse. In other words, our opposite side is measures 12 units and our hypotenuse measures 13 units.
Find the adjacent side:
[tex]\displaystyle \begin{aligned} a^2 + b^2 & = c^2 \\ \\ (12)^2 + b^2 & = (13)^2 \\ \\ b & = 5\end{aligned}[/tex]
Hence, our adjacent side is 5, our opposite side is 12, and our hypotenuse is 13.
Recall that cotangent is the ratio of the adjacent side to the opposite side. Therefore:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
In conclusion:
[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]
Answer:
-5/12
Step-by-step explanation:
I just completed Quiz 2: Evaluation of Functions. Of which, this was one of the questions.
Help Please! Solve this problem without the law of cosines.
Answer:A
Step-by-step explanation:
Which system type is a linear system with infinitely many solutions?
Answer:
down b3low
Step-by-step explanation:
The point where the two lines intersect is the only solution. An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect. A dependent system has infinitely many solutions.
3
Easton mixed
kg of flour with
kg of sugar.
6
Determine a reasonable estimate for the amount of flour and sugar combined.
Choose 1 answer:
1
Less than
2
kg
B
More than
1
kg but less than 1 kg
2
More than 1 kg
A cryptarithm is a math puzzle in which the digits in a simple equation are replaced with letters. Each digit is represented by only one letter, and each letter represents a different digit. So, for example, we might represent 51+50 = 101 as AB + AC = BCB. In the cryptarithm SEND + MORE = MONEY, what digit does the letter Y represent?
Answer:
[tex]\large \boxed{\sf \begin{aligned}9567&\\+1085&\\----&-\\10652&\\\end{aligned}}[/tex]
Step-by-step explanation:
Hello, let's do it step by step and see what we can find.
[tex]\begin{aligned}\text{ SEND}&\\+\text{ MORE}&\\-----&-\\\text{ MONEY}&\\\end{aligned}[/tex]
We assume that M is different from 0, otherwise we could find several different solutions I would think.
It means that S + M is greater than 10, otherwise the number of digit of the result would have been 4 and not 5.
The only possible number for M is then 1. M = 1
[tex]\begin{aligned}\text{ SEND}&\\+\text{ \boxed{1}ORE}&\\-----&-\\\text{ \boxed{1}ONEY}&\\\end{aligned}[/tex]
But then, S can only by 9, otherwise S + 1 < 10. S = 9
S + 1 = 10 + O if there is no carry over, so S = 9 + O
1 + S + 1 = 10 + O if there is a carry, so S = 8 + O
So O = 0 or O = 1. Wait !? M is already equal to 1 so O must be 0
E cannot be equal to N so 1 + E = N, meaning that there must be a carry over from column second from the right.
and E < 9 as we know that there is no carry over from column 3 from the right.
N + R = 10 + E => 1 + E + R = 10 + E => R = 9, impossible, as S=9
or 1 + N + R = 10 + E => 1 + 1 + E + R = 10 + E => R = 8
And there is a carry over from the column 1 from the right, so:
Y cannot be 0 or 1, as already used so D + E > 11
8 and 9 are already taken so we could have 7 + 5 = 12, 7 + 6 = 13 and that's it.
It means that E is 7 or D is 7.
If E is 7 then E+1=9=N, impossible, so D = 7
Then, E is 5 or 6
if E = 6 E + 1 = N = 7, impossible, so E = 5 and N = 6.
And 7 + 5 = 12 so Y = 2.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Function f is shown on the graph below where two points are marked. If function f is horizontally compressed by a factor of 2, plot the two corresponding points that would lie on the transformed function.
Answer:
If you have
[tex]f(x) = x^2[/tex]
The point (2,4) would be transformed to (1,1)
Step-by-step explanation:
If your compression is horizontal then the transformation you are making is the following
[tex]g(x) = f(x/2)[/tex]
Therefore, if you have
[tex]f(x) = x^2[/tex]
The point (2,4) would be transformed to (1,1)
Select the correct answer from each drop-down menu. The graph represents the piecewise function.
Answer:
1). f(x) = x² if ∞ < x < 2
2). f(x) = 5 if 2 ≤ x < 4
Step-by-step explanation:
The graph attached shows the function in two pieces.
1). Parabola
2). A straight line parallel to the x-axis.
Standard equation of a parabola is,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the given parabola is (0, 0).
Equation of the parabola will be,
y = a(x - 0)² + 0
Therefore, the function will be,
f(x) = ax²
Given parabola is passing through (-1, 1) also,
1 = a(-1)²
a = 1
Therefore, parabolic function will be represented by,
f(x) = x² if ∞ < x < 2
2). Straight line parallel to the x-axis,
y = 5 if 2 ≤ x < 4
Function representing the straight line will be,
f(x) = 5 if 2 ≤ x < 4
Answer:
Please mark me as Brainliest :)
Step-by-step explanation:
Simplify 3 (2x + 1) - 2 (x + 1)
Let's simplify step-by-step.
3(2x+1)−2(x+1)
Distribute:
=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)
=6x+3+−2x+−2
Combine Like Terms:
=6x+3+−2x+−2
=(6x+−2x)+(3+−2)
=4x+1
4x+1 is the answer to the question
cual es la derivada de ()=√x sin
Answer:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
Step-by-step explanation:
We assume that the function of interest is:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
Find the value of EB
Answer:
31Step-by-step explanation:
Given,
AD = 38
EB = 7x - 4
FC = 6x - 6
Now, we have to find the value of X
[tex]eb \: = \frac{1}{2} (ad \: + fc \: )[/tex] ( Mid segment Theorem )
Plug the values
[tex]7x - 4 = \frac{1}{2} (38 + 6x - 6)[/tex]
Calculate the difference
[tex]7x - 4 = \frac{1}{2} (32 + 6x)[/tex]
Remove the parentheses
[tex]7x - 4 = \frac{32}{2} + \frac{6x}{2} [/tex]
[tex]7x - 4 = 16 + 3x[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex]7x - 3x = 16 + 4[/tex]
Collect like terms
[tex]4x = 16 + 4[/tex]
Calculate the sum
[tex]4x = 20[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{20}{4} [/tex]
Calculate
[tex]x = 5[/tex]
The value of X is 5
Now, let's find the value of EB
EB = 7x - 4
Plug the value of X
[tex] = 7 \times 5 - 4[/tex]
Calculate the product
[tex] = 35 - 4[/tex]
Calculate the difference
[tex] = 31[/tex]
The value of EB is 31
Hope this helps..
Best regards!!