Answer:
The fifth term is -1/4.
Step-by-step explanation:
We know that the first three terms of the geometric sequence is x, x + 2, and x + 3.
So, our first term is x.
Then our second term will be our first term multiplied by the common ratio r. So:
[tex]x+2=xr[/tex]
And our third term will be our first term multiplied by the common ratio r twice. Therefore:
[tex]x+3=xr^2[/tex]
Solve for x. From the second term, we can divide both sides by x:
[tex]\displaystyle r=\frac{x+2}{x}[/tex]
Substitute this into the third equation:
[tex]\displaystyle x+3=x\Big(\frac{x+2}{x}\Big)^2[/tex]
Square:
[tex]\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)[/tex]
Simplify:
[tex]\displaystyle x+3=\frac{(x+2)^2}{x}[/tex]
We can multiply both sides by x:
[tex]x(x+3)=(x+2)^2[/tex]
Expand:
[tex]x^2+3x=x^2+4x+4[/tex]
Isolate the x:
[tex]-x=4[/tex]
Hence, our first term is:
[tex]x=-4[/tex]
Then our common ratio r is:
[tex]\displaystyle r=\frac{(-4)+2}{-4}=\frac{-2}{-4}=\frac{1}{2}[/tex]
So, our first term is -4 and our common ratio is 1/2.
Then our sequence will be -4, -2, -1, -1/2, -1/4.
You can verify that the first three terms indeed follow the pattern of x, x + 2, and x + 3.
So, our fifth term is -1/4.
A hair stylist offers haircuts and hair coloring to his customers. A haircut costs $18 and hair coloring costs $42. Yesterday, the hair stylist had 12 customers and earned a total of $288. How many of the hair stylists customers received hair coloring yesterday
Answer:
haircut =9 and hair color= 3
Step-by-step explanation:
Step one:
GIven data
let the haircut be x
and hair color be y in numbers.
so
18x+42y=288------------1
x+y=12---------------------2
from 1
x=12-y, put this in 2, we have
18(12-y)+42y=288
216-18y+42y=288
collect like terms
24y=288-216
24y=72
divide both sides by 24
y=72/24
y=3
put y= 3 in 2
x+3= 12
x= 12-3
x=9
Someone help me please and thank you!! ASAP :(
Work Shown:
[tex](f+g)(x) = f(x)+g(x)\\\\(f+g)(x) = \frac{x-23}{x^2+9x-36}+\frac{1}{x+12}\\\\(f+g)(x) = \frac{x-23}{(x+12)(x-3)}+\frac{1(x-3)}{(x+12)(x-3)}\\\\(f+g)(x) = \frac{x-23+1(x-3)}{(x+12)(x-3)}\\\\(f+g)(x) = \frac{x-23+x-3}{x^2+9x-36}\\\\(f+g)(x) = \frac{2x-26}{x^2+9x-36}\\\\[/tex]
We must require that [tex]x \ne -12[/tex] and [tex]x \ne 3[/tex] to avoid having 0 in the denominator. This is why choice D is the answer.
PLSSSSSSS HELP ME I DON'T KNOW WHAT TO DO
Answer:
8 bulbs
Step-by-step explanation:
In the model, each + represents a dollar
4 +s for the shipping cost, 20 +s for the total cost.
Therefore we have 2x (since each bulb is $2) + 4 = 20
2x = 16
x = 8
Step-by-step explanation:
x is the number of bulbs.
We have $2x + $4 = $20.
=> $2x = $16, x = 8.
Hence Sheila can order 8 flower bulbs.
A coordinate plane. Use the coordinate plane to plot the points (6, 0) and (0, 5). Which statement is true? (0, 5) is located on the x-axis. (0, 5) is located at the origin. (6, 0) is located on the x-axis. (6, 0) is located at the origin.
Answer:
The correct option is (6, 0) is located on the x-axis.
Step-by-step explanation:
Given that we plot (6, 0) and (0, 5) on the xy–plane. We know that in (6, 0) 6 is the x-coordinate and 0 is the y-coordinate while in (0, 5) 0 is the x-coordinate and 5 is the y-coordinate.
Therefore, (6, 0) can be found on the x–axis not on the origin because it has shifted from 0 to 6 and (0, 5) can be found on the y-axis not on the origin because it has shifted from 0 to 5.
Hence, the correct option is (6, 0) is located on the x-axis.
Answer:
x-axis
Step-by-step explanation:
what is the solution to this system? y= 2x + 2, y= x - 1
Answer:
(-3, -4)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x + 2
y = x - 1
Step 2: Solve for x
Substitution
Substitute in y: 2x + 2 = x - 1Isolate x terms: x + 2 = -1Isolate x: x = -3Step 3: Solve for y
Define equation: y = x - 1Substitute in x: y = -3 - 1Subtract: y = -4HELP PLEASE IM ALMOST DONE I WILL MARK BRAINLIEST
Answer:
y = 94
x = 86
Step-by-step explanation:
brainliest plz
Which is the correct algebraic expression for each phrase?
(Image)
Please answer ASAP!
Answer:
10. G. d - 15
11. D. d ÷ 2
12. F. 2.5p
Hope that helps.
study the function table. HELP PLEASE
Answer:
E. y=x+3
Step-by-step explanation:
just add 3 to the value of x and if you get the result as same as the value of y, it is the correct answer..
can someone help me please. thanks!
Answer:
if you turn it sideways it looks like an acute so i think it will be 60* or 61* i am not sure
Step-by-step explanation:
Answer:
58?
Step-by-step explanation:
. An amusement park bought some arcade games that cost $2,000 each and photo booths that cost $3,200 each. A total of 22 of both types of machines were bought, for $53,600. How many arcade game machines did the park buy ?
Answer:
maybe 900 arcade games..good luck
Identify the value of x. Give your answers in the simplest radical form.
Answer:
15
Step-by-step explanation:
5√2/2 is the value of x in the triangle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The hypotanenuse is 5 cm
The angle opposite to right angle is 45 degrees.
As it is a right angle one angle is 90 degrees.
This is a right angled isosceles triangle whose sides are in the ratio 1:1:√2.
In an isosceles right triangle, the equal sides make the right angle. They have the ratio of equality, 1 : 1.
So 5/√2.
Multiply numerator and denominator by √2
We get 5√2/2
Hence, 5√2/2 is the value of x in the triangle.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ2
Reasoning The product of two factors is 4,200. If one of the factors is 60, what is the other factor? Explain.
Answer:
70
Step-by-step explanation:
Let's say something multiplied by 60 = 4,200
We will represent something with Y
Then,
Y × 60 = 4,200
60Y = 4,200
Divide both sides by 60, then we'll have
60Y/60 = 4,200/60
Y = 4,200/60
Y = 70
Therefore, the other factor is 70
If 2x – 2.12 = 9.88, what is the value of x? I need step-by-steps
Answer:
x=6
Step-by-step explanation
2x-2.12=9.88
+2.12 +2.12
2x = 12
12 divided by 2 is 6
x=6
To check you can do 12-2.12=9.88
if perimeter and length of a rectanguar field are 154m and 42m respectively, find its breadth
Answer:
Assuming you mean width not breadth (What is that)
The width would be: 35m
Step-by-step explanation:
Now its pretty staight forward
We know that the length is 42m
And the permineter is 154m
We know that the perimeter is the 2 widths and 2 lengths all added up to each other (basically very side added up)
An eaution could be used like, 2w+2l=154
We know length is 42 so
2w+2*42=154
Now just solve for W
2*42=84
2w+84=154
154-84= 70
70=2w
70/2=35
w=35
How much of a radioactive kind of antimony will be left after 12 days if you start with 96 grams and the half-life is 4 days?
Item 31
POSSIBLE POINTS: 2.44
An investigation was performed to determine the ability of yeast to metabolize different carbohydrates. Four experimental tubes, A, B, C, and D, each containing 0.5 gram of yeast, were filled with water. Different carbohydrates were added to each tube . The tubes were then sealed. At the end of 45 minutes, the amount of gas produced by the yeast was measured. The results are shown in the table below.
The gas produced by the yeast was most likely
hydrogen
hydrogen
oxygen
oxygen
nitrogen
nitrogen
carbon dioxide
Explain the survival of the fittest.
Answer:
Survival of the Fittest
There has been gradual evolution of life forms with new forms arising at different periods of history. Any population has built-in variations in characteristics which adapt it better to environment.The characteristics which enable some population or individuals to survive better in natural conditions (climate, food, physical factors) would out-breed others (Survival of the fittest).Adaptability is inherited and fitness is the end result of ability to adapt and get selected by nature.2.5m to 150 cm
express these ratios in its simplest form.
Answer:
The ratios in the simplest form is 5:3
Step-by-step explanation:
Given that:
2.5m to 150cm
We have to express these ratios in simplest form but we will convert the quantities into same unit first.
Therefore,
Converting meters into centimeters
1 meter = 100 cm
2.5 m = 100*2.5 = 250 cm
Ratio form;
250 cm : 150 cm
As both the number are multiples of 50,
[tex]\frac{250}{50}:\frac{150}{50}\\5:3[/tex]
Hence,
The ratios in the simplest form is 5:3
5. What is the solution set for -4 x - 10 s 2?
Answer:
-4x - 20x
Step-by-step explanation:
Multiply 2 by -10
If a triangle has two angles that measure 25 degrees each, what must be the measure of the
third angle?
Answer:
Step-by-step explanation:
Add up the two known angle measurements. All you have to know is that all of the angles in a triangle always add up to 180°. This is true 100% of the time. So, if you know two of the three measurements of the triangle, then you're only missing one piece of the puzzle. The first thing you can do is add up the angle measurements you know. In this example, the two angle measurements you know ...
Subtract this number from 180°. The angles in a triangle add up to 180°. Therefore, the remaining an…
How would I find 86% of 950?
Answer:
86% of 950 is 817
Step-by-step explanation:
You convert the fraction into a decimal by moving the point two spaces to the left. You then multiply .87 by 950 to get 817
A shop has a 15% sale. Originally a computer cost £275. How much does the computer cost in the sale?
Answer:
41.25?
Step-by-step explanation:
5%=13.75
10%=27.5
15%=41.25
Given m
n, find the value of x and y.
m
yo
(8x+12)
(3x-8)
Answer:
x = 16, y = 140
Step-by-step explanation:
(8x + 12)° and (3x - 8) are adjacent angles and are supplementary, sum to 180°
8x + 12 + 3x - 8 = 180
11x + 4 = 180 ( subtract 4 from both sides )
11x = 176 ( divide both sides by 11 )
x = 16
Then
8x + 12 = 8(16) + 12 = 128 + 12 = 140
(8x + 12) and y are alternate angles and are congruent , so
y = 140
The track at the middle school is 200 meters. Rachel runs 1 ½ laps in 90 seconds. Find Rachel’s speed in meters/second
Answer:
3.33 meters per second
Step-by-step explanation:
1 1/2 laps = 200+100 = 300
use formula: distance = rate x time
t = time (in meter per second)
300 = 90t
t = 300/90 which reduces to 3.33/1
Which object covers less area?
Object A: a parallelogram with a base of 3 cm and a height of 9 cm.
Object B: a parallelogram with a base of 5 cm and a height of 6 cm.
Answer:
give him brain
Step-by-step explanation:
hi hi hi hi hi
help plz I am being timed will give brainliest
Answer:
-3/4
Step-by-step explanation:
2 1/2 = 5/2 = 10/4
1 3/4 = 7/4
when you subtract, you add and change the sign of the second term (add the opposite)
-10/4 + 7/4 = -3/4
Help meeeeee. Ksjsjsjs:(
Answer:
a rule to know: a median divides the side into equal parts.
we know:
PR = -2a + 34
SR = 2a + 26
- based on the rule, SR is half of PR. in other words, PR is two times greater than SR.
so,
2SR = PR (now simply pluggin the expressions we have)
2(2a + 26) = -2a + 34 (solve the equation like any other equation prob.)
4a + 52 = -2a + 34
6a + 52 = 34
6a = -18
a = -3
- inorder to check if this is correct, simply reverse what we did. so pluggin the value of a to see if its correct.
hey i need help whit this problem Karla has problems with her spine and the doctor
she recommended not to carry weights greater than 5.5 kg. The end
Karla went to the market and loaded the following
items: 1 2/5 kg of oranges, 580 grams of ham,
1/5 kg of cheese, 1.2 kg of chicken, 3⁄4 kg of meat,
a 425 gram can of slices, a toilet soap
125 grams and 1⁄2 kg of tortillas.
Answer:
What is the question?
Step-by-step explanation:
Michela’s skateboard ramp is at an incline of 40°. When she attempts a trick on the ramp, she finds that it is too steep. She adjusts the ramp to half of the original incline. What is the measurement of the incline now?
Answer:
22.7604763 degrees
Step-by-step explanation:
Note that the answer is NOT 20 degrees.
She adjusted the ramp to half the original incline
Therefore we have tan 40 = x = 0.839099631.
We want an incline of y degrees where tan y = x/2 = 0.839099631/2 = 0.419549815
Taking the arctan of both sides, we get
y = arctan(0.419549815) = 22.7604763 degrees
O A box contains 40 oranges, 12 of which are
unripe. I pick one at random.
What is the probability that it is
a ripe
b unripe?
Step-by-step explanation:
Nø of sample space, n(s) = 40
nø of unripe oranges, n (u) = 12
no of ripe oranges, n (r) = 40 - 12 = 28
Now
The probability that it is ripe is, P(E)
= n(r) / n(s)
= 28 / 40
= 7 / 10
Also the probability that it is unripe is, P(E)
= n(u) / n(s)
= 12 / 40
= 3 / 10
Hope it will help :)❤
WILL GIVE BRAINLIEST! Given: ∆ABC, AB = BC, BM = MC
AC = 40, m∠BAC=42º
Find: AM
Answer:
Sorry that this was incorrect, I didn't mean to post something wrong, but I can't delete an answer either, so this is the least that I could do. Sorry.
Step-by-step explanation: