Answer:
1. -6, -24, -96, -384, -1,536
2. 3, 12, 21, 30, 39
Step-by-step explanation:
1. Given
[tex]a_1=-6\\ \\a_n=4a_{n-1}[/tex]
Find [tex]a_2, \ a_3,\ a_4,\ a_5:[/tex]
[tex]a_2=4a_{2-1}=4a_1=4\cdot (-6)=-24\\ \\a_3=4a_{3-1}=4a_2=4\cdot (-24)=-96\\ \\a_4=4a_{4-1}=4a_3=4\cdot (-96)=-384\\ \\a_5=4a_{5-1}=4a_4=4\cdot (-384)=-1,536[/tex]
2. Given
[tex]a_1=3\\ \\a_n=a_{n-1}+9[/tex]
Find [tex]a_2, \ a_3,\ a_4,\ a_5:[/tex]
[tex]a_2=a_{2-1}+9=a_1+9=3+9=12\\ \\a_3=a_{3-1}+9=a_2+9=12+9=21\\ \\a_4=a_{4-1}+9=a_3+9=21+9=30\\ \\a_5=a_{5-1}+9=a_4+9=30+9=39[/tex]
Angle Cis an inscribed angle of circle P. Angle C measures (3x+5)^arc AB measures (16x)^arc. Find X.
Answer:
x=1
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises
so
In this problem
m∠C=(1/2)arc AB
we have
m∠C=(3x+5)°
arc AB=(16x)°
substitute the values
[tex](3x+5)\°=(1/2)(16x)\°[/tex]
solve for x
[tex]3x+5=8x\\8x-3x=5\\5x=5\\x=1[/tex]
How many cubes with side lengths of 1/2 cm does it take to fill the prism? Height: 3/2 cm Width:1 cm length: 2 cm
Answer:
24
Step-by-step explanation:
If we want to cover the base of the prism having dimensions 2 cm × 1 cm with [tex]\frac{1}{2}[/tex] cm length of cube, then there will be (4 × 2) = 8 cubes that can occupy the base.
Width is 1 cm, so there can fit 2 cubes of length [tex]\frac{1}{2}[/tex] cm and length is 2 cm, where 4 cubes of length [tex]\frac{1}{2}[/tex] cm can fit. So, in total (4 × 2) = 8 cubes of [tex]\frac{1}{2}[/tex] cm length.
Now, height of the prism is [tex]\frac{3}{2}[/tex] cm where 3 cubes of length [tex]\frac{1}{2}[/tex] cm can fit.
Therefore, in total there can be (8 × 3) = 24 cubes of [tex]\frac{1}{2}[/tex] cm length. (Answer)
Answer:
24 cubes
Step-by-step explanation:
Please see the pictures below:
(I hope this helped! :) )
Question # 4
1) Brett is 18 years younger than Mark Carl is 10 years younger
than Mark. The sum of the ages of Brett, Mark, and Carl is 212
How old are each of the 3 men? explain in your own words of how u get the answer
Ages of Mark, Brett and Carl are 80 years, 60 years and 70 years respectively.
Solution:
Given that
Brett is 18 years younger than Mark.
Carl is 10 years younger than Mark.
The sum of the ages of Brett, Mark, and Carl is 212
Need to determine age of Brett, Mark, and Carl.
Let assume age of mark in years be represented by variable x
As it is given that Brett is 18 years younger than Mark , so if we subtract 18 from the age of Mark we will get age of Brett ,
=> Age of Brett = x – 18
Also given that Carl is 10 years younger than Mark , so if we subtract 10 from the age of Mark we will get age of Carl ,
=> Age of Carl = x – 10
Given sum of ages of Brett, Mark, and Carl is 212
=> Age of Mark + Age of Brett + Age of Carl = 212
=> x + ( x – 18 ) + ( x – 10) = 212
=> 3x – 28 = 212
=> 3x = 212 + 28
Age of Mark = x = 80 years
Age of Brett = x – 18 = 80 – 18 = 62 years
Age of Carl = x – 10 = 80 – 10 = 70 years
Hence Ages of Mark , Brett and Carl are 80 years, 60 years and 70 years respectively.
Find the distance between the points given. (-3, -4) and (0, 0) -5 √(22) 5
Distance between the points (-3, -4) is 5
Step-by-step explanation:
Given
points =(-3,-4) and (0,0)
To Find:
The Distance between the two given points =?
Solution:
[tex]Distance =\sqrt{(x2-x1)^2+(y2-y1)^2 }[/tex]
where
[tex](x_1, y_1)[/tex] = coordinates of the first point
[tex](x_2, y_2)[/tex] = coordinates of the second point
So here, we have
[tex]x_1[/tex] = -3
[tex]y_1[/tex] = -4
[tex]x_2[/tex] = 0
[tex]y_2[/tex] = 0
So, after putting the values of [tex]x_1[/tex] , [tex]y_1[/tex] , [tex]x_2[/tex] [tex]y_2[/tex] in the above equation, we have
[tex]Distance=\sqrt{(0+3)^2+(0+4)^2 }[/tex]
[tex]Distance=\sqrt{(3)^2+(4)^2 }[/tex]
[tex]Distance=\sqrt{(9)+(16) }[/tex]
[tex]Distance=\sqrt{(25)}[/tex]
Distance = 5
There are 5 bacteria in a petri dish at the start of an experiment. This type of bacteria doubles every 20 minutes.
Find the number of bacteria after 4 hours.
40
10,240
20,480
40,960
Answer:
The next answer is 3 hours
Step-by-step explanation:
I just did it on edge 2021 :)
Answer:
the first answer is c
Step-by-step explanation:
John has $8 in his bank account when he gets a job. He begins making $80 a day. A student found that
the equation that represents this situation is y = 8x + 80.
What is wrong with the student's equation? Complete the explanation and correct the student's error.
Answer:
y = 8 + 80x
Step-by-step explanation:
Given,
The equation is, y = 8x + 80
It is the wrong equation. Because John has $8 in his bank when he gets a job. It means it is fixed. On the other hand, since he begins earning $80 per day. It becomes variable earnings for him. We know that variables (x, y, z) are multiplied by the variable number (If there is no value for variables). Therefore, the equation will be =
As $8 is fixed and $80 is a variable earnings,
y = 8 + 80x
Here, x represents the number of days John will work. If he works for 20 days, the value will be changed for the number of days he earns. The fixed amount will never be changed.
An element with mass 820 grams decays by 26.8% per minute. How much of the element is remaining after 18 minutes, to the nearest 10th of a gram?
Answer:
3.0 grams of the element are left after 18 minutes
Step-by-step explanation:
Recall that an exponential decay that can be studied with the following formula for the amount of material (A) as a function of time (t):
[tex]A(t)=A_0(1-r)^t[/tex]
where:
[tex]A_0[/tex] is the starting amount of the substance (in our case 820 grams)
r is the rate of decay (which in our case given as 26.8% can be written in decimal form as 0.268
and t is the time in minutes (in our case t = 18 minutes)
Then we have:
[tex]A(t)=A_0(1-r)^t\\A(18)=820*(1-0.268)^18\\A(18)=820*(0.732)^18\\\\A(18)=2.985\,grams[/tex]
which can be rounded to 3.0 grams
Answer: 3.0
Step-by-step explanation:
a=820
r= rate= 26.8%=0.268
b=1-r=1-0.268=0.732
y=820(0.732)^18
y=2.985474
y=3
a buyer spend $164 for two loads of mulch at $22.50 per load $35 worth of flowers and 42 landscaping blocks. fine the cost per block
Answer:
The cost per block was about 45$
Step-by-step explanation:
I think so, but dont believe it... I may be wrong. Please mark me brainliest
The buyer spent $2 per landscaping block.
Explanation:Firstly, we need to find out how much money was spent on the landscaping blocks. Given that the buyer spent $164 for two loads of mulch at $22.50 per load and $35 worth of flowers, subtract the total cost of the mulch and flowers from the total amount spent. This gives us:
($22.50 x 2) + $35 =$80 spent on mulch and flowers. Therefore, $164 - $80 = $84 spent on landscaping blocks.
Finally, find the cost per block, by dividing the total amount spent on blocks by the number of blocks. So, $84 / 42 blocks = $2 per block.
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The graph shows g(x), which is a translation of f(x) = x^2. Write the function rule for g(x). Show step by step.
Points on nonlinear graph are (9,10) (5,10) (7,6).
Using the given points, solve for a, h, k in g(x) = [tex]a(x - h)^2[/tex] + k . The function rule is g(x) = [tex]a(x - h)^2[/tex] + k .
To find the function rule for g(x), which is a translation of the quadratic function[tex]\( f(x) = x^2 \)[/tex], we need to determine the horizontal and vertical shifts based on the given points on the graph. The general form for a translated quadratic function is [tex]\( g(x) = a(x - h)^2 + k \)[/tex], where (h, k) represents the vertex of the parabola.
Let's use the given points (9,10), (5,10), and (7,6) to find the translation values.
1. Vertex Form of Quadratic Function:
The vertex form of a quadratic function is [tex]\( f(x) = a(x - h)^2 + k \)[/tex], where (h, k) is the vertex. Let's find the vertex using the given points.
For (9,10):
[tex]\[ 10 = a(9 - h)^2 + k \][/tex]
For (5,10):
[tex]\[ 10 = a(5 - h)^2 + k \][/tex]
For (7,6):
[tex]\[ 6 = a(7 - h)^2 + k \][/tex]
2. Solve the System of Equations:
Solve the system of equations to find the values of a , h , and k .
3. Substitute into Vertex Form:
Once you find the values of a , h , and k , substitute them into the vertex form g(x) = [tex]a(x - h)^2[/tex] + k.
By following these steps, you'll obtain the function rule for g(x), which is a translation of [tex]f(x) = x^2[/tex] based on the given points on the graph.
What are the lengths of KN and KL.?
I think the answer is 90 degrees because both triangles are 90, but you're only finding KN and KL which is on ONE triangle not both. SO there's a 90 degree angle on the top triangle. So I'd go with 90, but I could be wrong.
ABCD is a trapezoid with mid-segment (E f). If Ad=5x-11, E f=3x+7, Bc=2x+7, how many units in length is (E f) i need equation, algebra procedures, value of x, and length of (E f)
Answer:
x = 18
Step-by-step explanation:
The length of the midsection is the sum of the two bases divided by 2. Remember that the bases of a trapezoid are the two parallel sides. So that means:
((5x - 11) + (2x + 7)) /2 = 3x + 7
Simplify ((5x - 11) + (2x + 7)) /2:
(5x - 11) + (2x + 7) /2 = (5x + 2x - 11 + 7) /2 = (7x - 4) /2
Therefore:
(7x - 4) /2 = 3x + 7
Now solve this simultaneous equation:
7x - 4 = 6x + 14
7x = 6x + 18
x = 18
In Dale's cooler there are 9 bottles of soda and 6 bottles of water.
Dale is going to choose 8 bottles at random from the cooler to give to his friends.
What is the probability that he will choose 5 sodas and 3 waters? Round your answer to three decimal places.
Answer:
5/18??? might be wrong
Step-by-step explanation:
The probability that Dale will choose 5 sodas and 3 water is 0.391 and this can be determined by using the concept of probability.
Given :
In Dale's cooler, there are 9 bottles of soda and 6 bottles of water. Dale is going to choose 8 bottles at random from the cooler to give to his friends.The following steps can be used in order to determine the probability that he will choose 5 sodas and 3 water:
Step 1 - The concept of probability is used in order to determine the probability that he will choose 5 sodas and 3 water.
Step 2 - First, determine the total number of bottles.
Total Bottles = 9 + 6
= 15
Step 3 - So, the probability that he will choose 5 sodas and 3 water is:
[tex]\rm P = \dfrac{\;^9C_5 \times ^6C_3}{\;^{15}C_8}[/tex]
Step 4 - Simplify the above expression.
[tex]\rm P = \dfrac{126 \times 20}{6435}[/tex]
P = 0.391
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what is the square root of 25/64
The value of square root of 25/64 will be;
⇒ 5/8
What is square root of a number?A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The number is,
⇒ square root of 25/64
⇒ √(25 / 64)
Now,
Since, The number is,
⇒ √25/64
⇒ √ (5×5 / 8×8)
⇒ 5 / 8
Thus, The value of √ 25/64 = 5/8
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PLZZZ HELP ME.I WOULD RLLY APPRECIATE IT
this is alegbra 1 so if your rlly good at that please help me, the problem is about systems of linear equations
question: Jack and Julio each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store.
Jack spent $22 on 1 daylily and 5 geraniums. Julio spent $30 on 13 daylilies and 1 geranium. Find the cost of one daylily.
Answer:
$2
Step-by-step explanation:
x = daylily
y = geranium
1x + 5y = 22
13x + 1y = 30
Multiply second equation by 5 and subtract the two equations.
1x + 5y = 22
- (65x + 5y = 150)
-64x = -128
x = 2
So one daylily costs 2 dollars
Evaluate the given algebraic expression for x = 7 and y = 3. 2x + 2y 10 20 23 15
Answer: 20
Step-by-step explanation:
x = 7
y = 3
2x + 2y = 2(x + y)
2(7+3) = 2 • 10 = 20
Answer:
20
Step-by-step explanation:
2(7) + 2(3)
14 + 6
20
2/5(10x+15)=26 solve for x
Answer:
x=5
Step-by-step explanation:
2/5(10x+15)=26
10x+15=26/(2/5)
10x+15=(26/1)(5/2)
10x+15=130/2
10x+15=65
10x=65-15
10x=50
x=50/10
x=5
Answer:
x=5
Step-by-step explanation:
what is the relationship between angle 1 and angle 5
Answer:
○ b Corresponding Angles
Step-by-step explanation:
These two angles are a mirror, so they correspond.
I am joyous to assist you anytime.
Angle 1 and angle 5 are alternate interior angles with the same measure.
Explanation:Angle 1 and angle 5 are alternate interior angles formed by a transversal line intersecting two parallel lines. Alternate interior angles are equal in measure, which means that angle 1 and angle 5 have the same measure. This relationship holds true regardless of the specific measurements of angle 1 and angle 5.
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Please help me and please use substitution
4x - y = 18
-8x – 2y = 4
If a truck holds 200 cubic feet of asphalt, how many truckloads do you need for covering a road that is 500 feet long by 20 feet wide, with a 6-inch-thick layer of asphalt?
Answer:
1
Step-by-step explanation:
2.5 \dfrac{\text{g}}{\text{cm}^3}2.5 cm 3 g 2, point, 5, start fraction, start text, g, end text, divided by, start text, c, m, end text, cubed, end fraction.
Answer:
bojdsvj
Step-by-step explanation:dvsDV
I sorry lol i need points :/
1. What are transition metals?
Answer:
Any of the set of metallic elements occupying a central block (Groups IVB–VIII, IB, and IIB, or 4–12) in the periodic table, e.g., iron, manganese, chromium, and copper. Chemically they show variable valence and a strong tendency to form coordination compounds, and many of their compounds are colored.
Step-by-step explanation:
For 3 and 4 find the slope of the line that passes through the given points
PLEASE HELP! I NEED TO GET THIS DONE SOON!
Given: Circle O, diameter, marked perpendicular, Chord BC= 10,
find x
Answer:6
Step-by-step explanation:
In a circle, a radius perpendicular to a chord bisects the chord. So BC = CA BC = 6 (given) x (or AC) = 6 Answer = 6. Tell me if I was right. Thanks.
Answer:
it's 6
Step-by-step explanation:
Which ordered pair is a solution of the equation? X+7y=17
Answer:
Both (10,1) and (-4,3)
Step-by-step explanation:
No need but hope it helps:D
Answer:
C
Step-by-step explanation:
if it is on khan this answer is right
for two weeks the highest temperature each day was recorded in four different cities lines l,m,n, and p are graphs of the temperature over time in Lubbock, Memphis, New Orleans, and phoenix which statement is true
As per the graphical diagram, the largest temperature for each day was recorded in four different cities shows n in lines 1 and m
The temperature in four different cities such as Lubbock, New Orleans, Phoenix, and Memphis is shown where Memphis is the only city that has the highest temperature. As the initial temperature of Lubbock is lower than Memphis the initial temperature is the on Y-axis. The line of Memphis slopes downward which shows a decrease in temperature while the line of other cities is loping upwards.Hence the option B is correct.
Learn more about the weeks the highest temperature recorded in four different cities lines l,m,n p.
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A metalworker has a metal alloy that is 20% copper and another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 60 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 20% copper and (blank) kilograms of the metal alloy that is 70% copper.
X+Y=60kg
X=60-Y
X*0.2+Y*0.7=60*0.5
(60-Y)*0.2+Y*0.7=30
12-0.2*Y+0.7*Y=30
0.5*Y=18
Y=36 kg
X=60-36
X=24 kg
The metal worker should use 24 kilograms of the metal alloy that is 20% copper and 36 kilograms of the metal alloy that is 70% copper.
Answer:
36kg 24kg
Step-by-step explanation:
PPPPPPPPPPLLLLLLLLLLLLZZZZZZZZ HHHHEEELLLPPP 3(9 - 7)² + 5 × 2
Answer:
22
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
Ed stein paid $40.00 interes tonaloan
OF $2,000 for 3 months
what's the rate of interest hepaid?
Answer:
The rate of interest paid on the principal amount is 8%.
Step-by-step explanation:
Here, Principal Amount = $2,000
Time = 3 months = (3/ 12 ) Years = 0.25 years
Rate = R
Interest Amount = $40
Now, as we know :
Simple Interest = [tex]\frac{P \times R \times T}{100}[/tex]
⇒[tex]40 = \frac{2,000 \times R \times 0.25}{100}\\\implies R = \frac{40 \times 100}{2000 \times 0.25} =8[/tex]
or, R = 8%
Hence, the rate of interest paid is 8%.
a. Which mix would make the most “appley” juice? Explain your
reasoning
Final answer:
To make the most 'appley' juice, use a mixture with a high percentage of pure apple juice and minimal amounts of other ingredients.
Explanation:
To make the most "appley" juice, you would want to use a mixture that has a high concentration of apple juice. In this case, the best choice would be a mixture with a high percentage of pure apple juice and minimal amounts of other ingredients. This would ensure that the flavor of the juice is predominantly apple.
For example, a mixture with 90% apple juice and 10% other fruit juices would have a strong apple flavor. On the other hand, a mixture with 50% apple juice and 50% other fruit juices would have a less pronounced apple taste.
By experimenting with different ratios of apple juice to other ingredients, you can find the mixture that results in the most "appley" juice.
Write the equation in function form
6y - 4x = 24
Answer:
f(x) = (2/3)x + 4
Step-by-step explanation:
An equation in function is found by isolating y, and changing "y" to "f(x)".
Isolate y by moving everything else to the other side
What is done to one side must be done to the other
6y - 4x = 24
6y - 4x + 4x = 24 + 4x (add 4x to both sides. -4x +4x cancels out)
6y = 24 + 4x
6y/6 = 24/6 + 4x/6 (divide both sides by 6)
y = 4 + (2/3)x (simplify)
y = (2/3)x + 4 (rearrange to a familiar format "y=mx+b")
f(x) = (2/3)x + 4 (replace y with f(x))