[tex]\text{First term,}~ a = x+1\\\\\text{Common ratio,}~ r = \dfrac{x-3}{x+1}= \dfrac{x-1}{x-3}\\\\\text{Now,}\\\\~~~~~~\dfrac{x-3}{x+1} = \dfrac{x-1}{x-3}\\\\\\\implies (x-3)(x-3) = (x-1)(x+1)\\\\\\\implies (x-3)^2 = x^2 -1\\\\\\\implies x^2 -2\cdot 3x +3^2 =x^2 -1\\\\\\\implies -6x+9=-1\\\\\\\implies -6x = -1 -9\\\\\\\implies -6x = -10\\\\\\\implies x =\dfrac{-10}{-6}\\ \\\\\implies x = \dfrac 53[/tex]
I have a question please help
Answer:
[tex]\sf 2\sqrt{2}[/tex]
Step-by-step explanation:
First find h(10)
h(x) = 2x - 8
h(10) = 2*10 - 8
= 20 - 8
= 12
[tex]\sf g(x)=\sqrt{x-4}\\\\ g(h(10) = g(12) = \sqrt{12-4}\\[/tex]
[tex]\sf = \sqrt{8}\\\\ = \sqrt{2*2*2}\\\\ = 2\sqrt{2}[/tex]
Lisa played soccer for 234 hours on Saturday and for 135 hours on Sunday. How many hours did she play soccer during the weekend?
Answer:
Lisa played 4.35 hours over the weekend :)
Step-by-step explanation:
What negative impact can interdependence have on a country?
A. Threat to industrialization
B. Increased progress and industrialization
C. Threat to security
D. Threat to political interference
Step-by-step explanation:
In an interdependent world, nations tend to cooperate more with each other. Some even argue that big wars are less likely to happen because countries need each other. The downside is that nations tend to have less autonomy when it comes to making major decisions.
What is the value of the following expression if x 22: "five times a number
decreased by 2"?
Answer:
108
Step-by-step explanation:
five times a number x decreased by 2 can be expressed as by 5x- 2
What's the difference between numerical and algebraic expressions? How is the order of operations used to evaluate these expressions?
a numerical expression is a mathematical statement involving only numbers and one or more operation symbols. and a algebraic expession is an expressions that includes at least one variable and at least one operation. Order of operation goes (), exponent, divison, multiplication, addtion and subratcion
Part B Write an expression to find how many rolls of wallpaper Jackie needs to buy. Show the steps you used to evaluate the expression.
A. The rolls of groovy wallpaper is needed to cover the apartment bedroom. 9 rolls
B.The cost to re-wallpaper the apartment room $143.10
What is the cost?Based on the question, we have to assume there are no windows and no doors in that bedroom... to calculate how much less wallpaper we really need, and we cover completely from the floor to the ceiling.
A. If one rolls covers 50 sq ft, how many rolls do we need?
First, let's calculate the perimeter of that room, which is 16'x10'.
P = 16 + 10 + 16 + 10 = 52 feet of perimeter.
Now, the walls are 8 feet high... so, let's see just how big is the area to cover.
A = 52 feet * 8 feet = 416 sq feet to cover all walls.
Since we know each roll covers 50 sq ft, we will need:
416 / 50 = 8.32 rolls.
When talking about quantity you need to buy or to fill something, you always have to round up to the next unit. Because you usually can't buy a portion of a unit and if you round it down, you'll miss material to cover your walls.
So, we will need 9 rolls.
B. Total cost, based on $15.90 per roll.
We already know we need 9 rolls... so how much will it cost us?
C = 9 * $15.90 = $143.10
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:34a
Step-by-step explanation:
because 6a-4=2a
4a+28=32a
2a+32a=34a
Josh has been saving $24 every 3 weeks. If he continues to save at this rate, how much money will he have in 12 weeks?
Answer:
96
Step-by-step explanation:
12 ÷ 3 = 4 (therefore he is saving $24 four times in 12 weeks)
24 × 4 = 96
In circle EE, the length of \overset{\LARGE\frown}{FG} = 4\pi
FG
⌢
=4π and m\angle FEG=80^\circ∠FEG=80
∘
. Find the area shaded below. Express your answer as a fraction times \piπ.
PLEASE HELP IM STUCK
Find the inverse of {(-2, 4), (-3, -1), (2, 2), (3, 4)}. State whether the inverse is a function.
Answer:
(-4, 2), (-1, -3), (2,0), (4,3).
Theresa pays $9.56 for 4 pounds of tomatoes. What is the cost of 1 pound of tomatoes?
Answer:
$2.39
Step-by-step explanation:
to find the cost of 1 pound , divide the cost of 4 pounds by 4
$9.56 ÷ 4 = $2.39
Which of the following are square roots of the number below? Check that all apply. 36 A. 18 I B. 8 C. 6 D. -6 O E. 361/2 OF F. -361/2
Answer: C and D
Step-by-step explanation:
√36 = ±6
The value of a company’s stock is represented by the expression x2 – 2y and the company’s purchases are modeled by 2x + 5y. The company’s goal is to maintain a stock value of at least $6,000, while keeping the purchases below $2,000. Which system of inequalities represents this scenario?
A.) x2 – 2y ≥ 6000
2x + 5y < 2000
b.) x2 – 2y > 6000
2x + 5y < 2000
C.) x2 – 2y > 6000
2x + 5y ≤ 2000
D.) x2 – 2y ≤ 6000
2x + 5y ≤ 2000
Answer:
the answer is A
Step-by-step explanation:
Given x2-2y= stock value
and
2x+5y= purchases
stock value must stay at or more than 6000
while purchases must stay under 2000
Mugdo paid $250 for a sneaker and there is a 61% advertised discount. How much is the discount?
Answer:
152.5
Step-by-step explanation:
Someone Help Me Solve This
Answer: Choice C
f(x) = x+5
===========================================
Explanation:
The input x = -3 has 5 added to it to get x+5 = -3+5 = 2
The diagram shows the "-3" in the input oval pointing to "2" in the output oval.
Through similar steps, we have the input -2 map to the output 3. Also, the input 0 points to the output 5.
The input -5 should map to 0, but 0 isn't in the output list. So we ignore -5 in the input oval.
The top of a rectangular table has an area of 11 square feet. It has a length that is 3.5 feet more than the width. Find the dimensions of the table top.
The length of the table is ____ feet and the width of the table is ____ feet.
Step-by-step explanation:
If we let the width be w, then the length is w+3.5.
This means that w(w+3.5)=11
w^2 + 3.5w - 11 = 0
2w^2 + 7w - 22 = 0 (multiply both sides by 2)
(2w+11)(w-2)=0
w = -11/2 or w = 2 (disregard w = -11/2 as distance is positive)
This means that w=2, and thus the length is 2+3.5=5.5
Consider the series 4 + 12 + 36 ... Find the sum of the first 9 terms.
Answer:
39364
Step-by-step explanation:
You can simplify the equation to make 4(1+3+9...) The nth term is therefore [tex]3^{n-1}[/tex] so u can substitute that into the equation so 4([tex]3^{n-1}+ 3^{n} + 3^{n+1}[/tex]..). This would simplify to 4([tex]3^0 +3+3^2[/tex]+[tex]3^3+3^4+3^5+3^6+3^7+3^8[/tex]). By simplifying this, you can make it so 4([tex]2^2+6^2+18^2+42^2+81^2[/tex]) = 4(4+36+324+2916+6561) =39364
hi! how do you do this?
Answer:
a +7d = 11
Step-by-step explanation:
The sum of an arithmetic series is given by the formula ...
Sn = (n/2)(2·a1 +d(n -1))
where n is the number of terms, a1 is the first term, and d is the common difference.
__
Here, you are given n=15, S = 165, a1=a, and asked to find a relation for 'a' and 'd'. Substituting the known values, we have ...
165 = (15/2)(2a +d(14))
11 = a +7d . . . . . . . . simplify and divide by 15
We have found the relation to be ...
a +7d = 11 . . . . . as required
Two functions are shown below.
f(x) = 1/2*2x
g(x) = 5x+2
What is the largest value of x for which f(x) = g(x)?
Answer:
x = 6
Step-by-step explanation:
As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.
For small values of x, we have that f(x) < g(x). For example:
f(1) = 1/2 * 2 = 1
g(1) = 5*1 + 2 = 7
f(2) = 1/2 * 4 = 2
g(2) = 5*2 + 4 = 14
So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.
For x = 5, we have:
f(5) = 1/2 * 32 = 16
g(5) = 5*5 + 4 = 29
For x = 6, we have:
f(6) = 1/2 * 64 = 32
g(6) = 5*6 + 4 = 34
For x = 7, we have:
f(7) = 1/2 * 128 = 64
g(7) = 5*7 + 4 = 39
So the largest integer value of x for f(x) ≤ g(x) is x = 6.
Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).
Answer:
x = 6
Step-by-step explanation:
We assume your functions are ...
f(x) = (1/2)(2^x)g(x) = 5x+2In general, mixed polynomial and exponential functions have no algebraic solution. That means we need to solve f(x) = g(x) using a table of values, or by graphing.
__
Attached is a graphical solution. It shows the largest value of x for which f(x) = g(x) is x=6.
Check: f(6) = 1/2(2^6) = 32 = g(6) = 5(6) +2
__
Additional comment
We can start with f(x) = g(x) and subtract g(x) from both sides of the equation. This gives ...
f(x) -g(x) = 0
Many graphing calculators readily identify the zeros of a function or expression. We have used that fact to find the two values of x where these functions are equal: ≈0.32 and 6.
For x>6, the exponential function increases without bound, so the graphs never cross again. Likewise, for x < -0.32, the linear function decreases without bound, so the graphs never cross again.
The lower value of x where the graphs cross is an irrational number near −0.319886722135.
A sail shaped like a right triangle is shown. PART A : Find the unknown side length. Enter the correct answer in the box. PART B : Do these lengths form a Pythagorean triple? YES or NO PLEASE HELP ME ASAP!!
Answer:
Step-by-step explanation:
unknown length=√(13²-12²)=√(169-144)=√25=5
B
yes
Which of the following is the maximum value of the equation y = −x2 − x + 6?
Step-by-step explanation:
f(x) = y= -x²-x+6
When y is max, f'(x) = 0
f'(x) = -2x-1
Equating to 0,
-2x-1= 0
x= -1/2
Put the value of x in f(x)
y = -(-1/2)² -(-1/2) +6
= -1/4+1/2+6
= 6+1/2
y= 13/2
100 points plus brainilest
What decimal is equivalent to the fraction 5/8? Enter your answer in the box.
Answer:
0.625
Step-by-step explanation:
5/8th simplified is just 5 divided by 8
5/8 = 0.625
hope this helps!
Turn to decimals
5/85×125/8×125625/10000.625Done!
A right triangle has acute angles C and D. If tanC=15/8 and cosD=15/17, what are cotD and sinC?
The values of CotD and SinC from the information given in the task content are; 15/8 and 15/17 respectively.
What is the value of cotD and sinC?It follows from the task content that the right triangle has tanC = 15/8 and cosD=15/17.
On this note, it follows from Pythagoras theorem that the other value are as follows;
sinC = 15/17, cosC = 8/17sinD = 8/17 and tanD = 8/15Hence, it follows that the values of cotD and sinC are; 15/8 and 15/17 respectively.
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f(x)= -4(x-2)^2+100 answer all questions below show work if there is any.
a) find the y-intercept(s) (write your answer(s) as ordered pairs)
b) Find the vertex
c) Find the x-intercept(s) (write your answer(s) as ordered pairs)
e) what is the domain of the function? (use interval notation)
f) what is the range of the function? ( use interval notation)
The vertex of the given function [tex]f(x)= -4(x-2)^2+100[/tex] is (2, -25). the y-intercept is (0,-21). the x-intercept are (-3,0) and (7,0).
What is x-intercept of a function?The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.
The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis,
where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
We have the function,
[tex]f(x)= -4(x-2)^2+100[/tex]
On simplifying, we get,
[tex]f(x)= x^2 - 4x -21\\\\f(x) = (x+3)(x-7)[/tex]
Now, the factors of the given functions are (x+3) and (x - 7).
We have,an intercept form of the function is .
[tex]f(x) = (x+3)(x-7)[/tex]
Now, we know that,
Value of x-coordinate of the vertex is -b/2a
= 4 / 2
= 2
x = 2
Then,
[tex]f(2)= 2^2 - 4(2) -21\\\\f(2)= -25[/tex]
So, the vertex of the function is (2, -25).
Further, we know that 'the y-intercept of a function is the point where the function crosses the y-axis'.
So, when x=0, we have, i.e. f(0) = -21
Thus, the y-intercept is (0,-21)
Also, 'the x-intercept of a function is the point where the function crosses x-axis'.
Then, for f(x)=0, we have i.e. i.e. x= -3 and x= 7
Thus, the x-intercept are (-3,0) and (7,0).
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Using the graphing function on your calculator, what is the solution to the system of equations show below? y + 2x = 14 2y - x = 3
A. X= 5, y = 4
B. x = 4, y = 5
C. More than 1 solution
D. No solution
Answer:
A. x= 5, y = 4
Step-by-step explanation:
The attachment shows a graphing calculator solution to this system of equations.
(x, y) = (5, 4) . . . . . one solution
If a phone cost $224 what would it cost if there was a 7% sales tax.
Answer:
$239.68
Step-by-step explanation:
Given
Cost = $224Sales Tax = 7%Solving
Cost w/ Tax = Cost (1 + Tax)Cost w/ Tax = 224 (1 + 0.07)Cost w/ Tax = 224 * 1.07Cost w/ Tax = $239.68Which of the following is an arithmetic sequence with a common difference of +3?
Question 6 options:
A)
4, 7, 10, 13, ...
B)
1, 3, 9, 12, ...
C)
17, 14, 11, 8, ...
D)
12, 15, 19, 24, ...
Answer:
A
Step-by-step explanation:
10-7= 7-4= 3
That's it!
Easy math questions giving brainlest
Answer:
97 degrees
Step-by-step explanation:
supplementary angles are 2 angles that add up to 180 degrees
so
180- 83 = 97
[tex]\boxed{\sf 97~degrees}\boxed{explanation~below}[/tex]
[tex]\sf Given~\angle F = 83deg.[/tex][tex]\sf Supplementary~angles~add~up~to~180deg.~so~subtract~\angle F~by~180[/tex][tex]\sf 180 - 83 = 97deg.[/tex]
I need this answer kinda fast lol
Answer:
2
Step-by-step explanation:
The point being shown is 4,2 so the constant of proportinality is just a simple multiplication problem 2x2=4 so 2 is the answer.
Solve by factoring
x^2 - 8x - 84 = 0
Show all work
Answer:
X= -6 & x= 14
Step-by-step explanation:
The factors are -14 and 6, these numbers are multiplied to get -84 and added to get -8.
Therefore the new equation is:
x^2 -14x +6x -84 = 0
factorize: x (x -14) 6 (x - 14)
So: (x+6) (x-14) = 0
x = -6 and 14