[tex]f(x) = ab^x~\hfill \begin{array}{llll}\textit{we know that}~f(0)=-4\begin{cases}x=0\\f(x)=-4\end{cases}\\\\-4=ab^0\implies -4=a(1)\implies -4=a\end{array}\\\\\\\stackrel{therefore}{f(x)=-4b^x}~\hfill \textit{we also know that}~f(-2)=-64\begin{cases}x=-2\\f(x)=-64\end{cases}[/tex]
[tex]-64=-4b^{-2}\implies \cfrac{-64}{-4}=b^{-2}\implies 16=b^{-2}\implies 16=\cfrac{1}{b^2} \\\\\\ b^2=\cfrac{1}{16}\implies b=\sqrt{\cfrac{1}{16}}\implies b = \cfrac{\sqrt{1}}{\sqrt{16}}\implies b = \cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill f(x)=-4\left( \frac{1}{4} \right)^x~\hfill[/tex]
It is your birthday and you are going to get a new cellphone. The day you buy the phone, you will have to pay the $49 interest fee and a $200 down payment. The remaining balance of the phone will be paid off in 24 equal payments. The total bill is $980, including the interest fee and down payment. Write an equation to solve for p, the required monthly payments
Answer:
$30.46
Step-by-step explanation:
Total payment = down payment + interest fee + 24 equal payments
980 = 200 + 49 + 24 equal payments
24 equal payments = 24 * p, as we add p 24 times
980 = 249 + 24p
subtract 249 from both sides to isolate p and its coefficient
731 = 24p
divide both sides by 24 to isolate p
p = 30.46
find the value of p-8 when p=14
Answer:
6
Step-by-step explanation:
If p = 14
rewrite the equation
so replace the variable with 14.
now do basic subtraction.
14 - 8
= 6
Write the inequality
The inequalities which the number lines represent are as follows;
x > 3x <= 2.While writing inequalities represented on a number line;
We must observe the direction of the line; and also observe the shading on the starting point of the line.
In case 1:
The set of x values are represented as greater than 3; Therefore, the inequality is; x > 3In case 2:
The set of value are represented as less or equal to 2;Therefore, the inequality is; x <= 2The number line to represent the street sign is as in the attached image;
Read more on number line and inequalities:
https://brainly.com/question/1478009
Prove the identity.
sin(x+y) / cosxcosy = tanx+tany
[tex]\dfrac{\sin(x+y)}{\cos x \cos y}\\\\\\=\dfrac{\sin x \cos y + \sin y \cos x}{\cos x \cos y}\\\\\\=\dfrac{\tfrac{\sin x \cos y}{\cos x \cos y} + \tfrac{\sin y \cos x}{\cos x \cos y}}{\tfrac{\cos x \cos y}{\cos x \cos y}}\\\\\\=\dfrac{\tan x + \tan y}1\\\\\\= \tan x + \tan y[/tex]
Determine the probability of the event.
A survey found that about 90% of the junior class is right handed. If 2 juniors are chosen at random out of
100 juniors, what is the probability that at least one of them is not right handed?
Give an exact answer as a decimal.
Answer:
The probability is 1/100
Step-by-step explanation:
This is because there are only ten left-handed juniors (on average). Therefore there isn't a great chance that you would end up with one.
If the diameter of a circle is [tex]\sqrt{144}[/tex] then what is the radius?
Hey there!
√144
= 12^2
= 12 * 12
= 144
Therefore, your answer should be: 12
Side note: There’s many ways to find the result of the square root but I just made it “easier” to solve and tackle future problems like this on your own.
Anyways
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Right triangles 1, 2, and 3 are given with all their angle measures and approximate side lengths. Use one of the triangles to approximate the ratio (KL)/(JL).
- 0.64
- 0.77
- 0.83
- 1.2
Answer:
[tex]\frac{KL}{JL}[/tex] = [tex]\frac{6.4}{7.7}[/tex] = 0.83
Step-by-step explanation:
The key understanding here is that ΔJKL is similar to triangle 3 based on the AA criterion (they both have a right angle and a 40° angle).
We can find [tex]\frac{KL}{JL}[/tex] by setting up a proportion statement that includes KL, JL, and the lengths of their corresponding sides in triangle 3.
We can use this proportion:
[tex]\frac{KL}{6.4}[/tex] = [tex]\frac{JL}{7.7}[/tex]
[tex]\frac{KL}{6.4}[/tex] ⇒ opposite to 40° angle
KL, JL ⇒ ΔJKL
[tex]\frac{JL}{7.7}[/tex] ⇒ adjacent to 40° angle
6.4, 7.7 ⇒ triangle 3
[Now see the attachment]
Now we can rewrite the equation to show the ratios of the side lengths within each triangle.
[tex]\frac{KL}{JL}[/tex] = [tex]\frac{6.4}{7.7}[/tex]
[tex]\frac{KL}{JL}[/tex] ⇒ ΔJKL
KL, 6.4 ⇒ adjacent to 40° angle
[tex]\frac{6.4}{7.7}[/tex] ⇒ triangle 3
JL, 7.7 ⇒ adjacent to 40° angle
Answer: it’s 0.82
Step-by-step explanation:
3=2x
Solve this equation.
Then verify IT.
[tex] \huge \bf \: Question : [/tex]
[tex]3 = 2x[/tex]
This is an equation. We need to find the value of X and verify it.
[tex] \huge \bf \: Solution : [/tex]
Let's find out the value of X :-
[tex] \sf \implies \: 3 = 2x[/tex]
Firstly, over turn the equation :-
[tex]\sf \implies2x = 3[/tex]
Then, Divide both sides of this equation by 2 :-
[tex]\sf \implies \: \dfrac{2x}{2} = \dfrac{3}{2} [/tex]
Cancel 2/2 on this equation and Leave x :-
3/2 can't be cancelled.
[tex]\sf \implies \: \dfrac{ \cancel2x}{ \cancel2} = \dfrac{3}{2} [/tex]
[tex]\sf \implies \: x = \dfrac{3}{2} [/tex]
Hence the value of x is 3/2.
________________________________
[tex] \bf \huge \: Verification : [/tex]
Put the value of x on this equation :-
[tex]\sf \implies \: 3 = 2x[/tex]
On Putting 3/2 instead of x :-
As we know that x is multiplied with 2 so,
[tex]\sf \implies \: 3 = 2 \times \dfrac{3}{2} [/tex]
Simplify this equation(Cancel 2 and 2) :-
[tex]\sf \implies \: 3 = \cancel2 \times \dfrac{3}{ \cancel2} [/tex]
[tex]\sf \implies \: 3 = 3[/tex]
[tex]\sf \implies \bf \: L HS = RHS[/tex]
[tex] \boxed {\bf\huge Hence, verified.}[/tex]
______________________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
−10sin(x)=−4csc(x)+3
-10 sin(x) = -4 csc(x) + 3
Recall that csc(x) = 1/sin(x) :
-10 sin(x) = -4/sin(x) + 3
Multiply both sides by sin(x) :
-10 sin²(x) = -4 + 3 sin(x)
Move everything to one side:
10 sin²(x) + 3 sin(x) - 4 = 0
Factorize the left side:
(2 sin(x) - 1) (5 sin(x) + 4) = 0
Then we have two cases,
2 sin(x) - 1 = 0 or 5 sin(x) + 4 = 0
Solve for sin(x) :
sin(x) = 1/2 or sin(x) = -4/5
Solve for x :
• if sin(x) = 1/2, then
x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ
x = π/6 + 2nπ or x = 5π/6 + 2nπ
• if sin(x) = -4/5, then
x = arcsin(-4/5) + 2nπ or x = π - arcsin(-4/5) + 2nπ
x = -arcsin(4/5) + 2nπ or x = π + arcsin(4/5) + 2nπ
(where n is any integer)
Can someone please help me.
Answer:
make that 30 percent int a fraction and u should know what to do
Step-by-step explanation:
A
Hilda has a bank account balance of $1550. Each week, her balance changes by −$82.50. She wants to keep the balance above $395.
How many weeks will Hilda's balance remain above $395?
Select from the drop-down menu to correctly complete the statement.
Hilda's bank balance will remain above $395
Choose...
weeks.
Step-by-step explanation:
1550 - 395 = 1155
1155 / 82.5 = 14
Answer should therefore be 14 weeks.
Not my usual way of doing this sort of question but I'm interested to see if it's right. Alternatively you can subtract $82.50 from $1550 until/before you reach $395. Do not go below $395 though.
Answer:
K12 Answer
Step-by-step explanation:
7/10 of guest were over 25 what is the percentage
A restaurant is serving a special dinner combo meal that includes a drink, a main dish, and a dessert. Cus
4 drinks, 5 main dishes, and 3 desserts.
How many different combo meals are possible?
Select from the drop-down menu to correctly complete the statement.
Customers can create Choose... w different dinner combo meals.
1
2
3
4
Choose...
12
45
60
75
5
6
7
Answer:
Your Answer Is 60
Step-by-step explanation:
I Took The Test Just Now
The number of different combo meals are possible in a restaurant which is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 60.
What is arrangement?Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
The number of possible ways to arrange is the n!. Here, n is the number of objects.
A restaurant is serving a special dinner combo meal that includes a drink, a main dish, and a dessert.
Dinner includes 4 drinks,5 main types of dishes.3 types of desserts.The number of different combo meals are possible can be find out by simply multiplying all the meals. Thus,
[tex]n=4\times5\times3\\n=60[/tex]
Thus, the number of different combo meals are possible in a restaurant which is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 60.
Learn more about the arrangement here;
https://brainly.com/question/6032811
#SPJ2
Please help me with this i am ver confused
Answer:
1) 2/x³ the secound option
2)1/x²⁴ the secound option
I think
Find the 87th term of the arithmetic sequence 1,14,27,….
Answer:
[tex]a_{87}=1119[/tex]
Step-by-step explanation:
Arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
where d is the common difference between terms and n is the index of any given term.
Find the difference between the terms in the given sequence here:
[tex]14-1=13\\27-14=13[/tex]
Each term has a common difference of 13. Using that, you can write the equation for this sequence:
[tex]a_n=1+(n-1)13[/tex]
Finally, you can use this equation to find the 87th term by plugging in 87 for n:
[tex]a_{87}=1+(87-1)13\\a_{87}=1+(86)13\\a_{87}=1+1118\\a_{87}=1119[/tex]
50 mm = how many cm?
Answer:
5cm
Step-by-step explanation:
50mm ÷ 10 = 5cm
will mark brainliest Select the correct answer.
Which relation is a function?
ОА
ху
14 -2
5 -3
6 -2
7-3
ОВ.
ху
310
220
3 30
440
ОС
Х У
-52
-53
-104
-105
OD.
ху
1015
2025
8 30
2035
Simplify 4 to the seventh power over 5 squared all raised to the third power . (4 points)
a
4 to the tenth power over 5 to the fifth power
b
4 to the fourth power over 5
c
4 to the twenty-first power over 5 to the sixth power
d
12 to the seventh power over 15 squared
Answer: The answer is C, 4 to the 21st over 5 to the 6th power.
Select the correct answer. Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27
Answer:
(-5,-7)
Step-by-step explanation:
Set functions equal to each other.
2x+3= -4x-27
2x+4x = -3-27
6x=-30
x= -5
f(-5) = 2(-5) +3
f(-5) =-10+3 y= - 7
g(-5) = -4(-5) -27
g(-5) =20-27 y= -7
x=-5 y=-7
(-5,-7)
Answer:
(-5,-7)
Step-by-step explanation:
I need help asap very struggle with math
Answer:
16feet
part B is 18 feed for a good at a better than the price but the one
Find the area of the equilateral triangle.
Answer:
try 6.93 for answer on equilqteral triangle
When a number is subtracted from 24 and the difference is divided by that number, the result is 3. What is the value of the number?
a) 2
b) 4
c) 6
d) 12
e) 24
A 7-pound bag of lollipops costs $12.18. What is the unit price?
Answer:
The unit price is 1.74$
Step-by-step explanation:
12.18 / 7
is 1.74
Help help help math math math
81°
Step-by-step explanation:
The sum.of the interior angles of a triangle is equal to 180°. Hence, in our triangle, we can see that
[tex]41° + 58° + \angle{3} = 180° \Rightarrow 99°+\angle{3} = 180°[/tex]
We then see that
[tex]\angle{3} = 180° - 99° = 81°[/tex]
Answer: 81 i believe
Step-by-step explanation:
the perimeter of a regular Pentagon is 100m how long is each side
Answer:
20 cm is the answer.
20
Step-by-step explanation:
the parameter of any shape is the sum of all sides and since the pentagon has 5 sides we just have to divide the parameter by 5
100÷5=20
Sophia was measuring the height of her Christmas tree. The
first part she measured was 36 inches tall. The second part
was 2 feet tall. How tall was her Christmas tree?
Answer:
60 inches or 5 feet
Step-by-step explanation:
36 inches + 2 feet (24 inches) = 60 inches, also 5 feet
In the month of January, a certain restaurant claimed it sold 9,000 burgers and expects sales to grow at a rate of
4.8% per month over the next year. Which formula will determine the number of burgers the restaurant expects to sell
this year?
Answer:
11∑N=1 9000 (1.048)^n
Step-by-step explanation:
First month = a = 9,000burgers
Common ratio = r = 1 + 0.48 = 1.048
Total number of months = n = 11; from February to December.
Formula to determine the number of burgers the restaurant expects to sell this year:
= 11∑N=1 9000 (1.048^n)
Answer:
a
Step-by-step explanation:
The counting number ABAB is a multiple of 36. If different letters represent different digits, what is the greatest value ABAB can have? PLS HELP ONLY 10 minutes
The greatest value ABAB can have is 7272.
The given parameters:
Counting number ABAB = multiple of 36The counting number can be expanded as follows;
ABAB = 100 x AB + AB
= AB00 + AB
= AB(100 + 1)
= AB(101)
101 is a prime factor of AB and has only two factors.
The prime factor of 101 = 1 x 2
Since 101 is prime, the counting number AB must 2-digits multiples of 36.
The greatest value ABAB can have is calculated as follows;
ABAB = (36 x 2)(36 x 2)
ABAB = 7272
Thus, the greatest value ABAB can have is 7272.
Learn more about prime factors here: https://brainly.com/question/24612438
can some1 please help:(
A) -2/5hope it helps ....❤
Simplify \frac{10a^3}{55a^2} when a=3.
Answer:
(27000)(27225)
Step-by-step explanation:
Answer:
6/11
Step-by-step explanation: