The first term of the sequence is 12 and the common difference is -3.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
Given that a formula for the nth term. 5th term is 0; 45th term is -120. The common difference is calculated as,
a₁ + d(5-1) = 0
a₁ + d(45 - 1) = -120
Solve the above equation,
a₁ + 4d = 0
-a₁ - 44d= +120
___________
-40d = 120
d = -3
The value of the first term is,
a₁ + 4d = 0
a₁ + 4 x -3 = 0
a₁ = 12
Therefore, the first term of the sequence is 12 and the common difference is -3.
To know more about arithmetic progression follow
https://brainly.com/question/6561461
#SPJ1
(-42n+28p)(-1/4) simplify. Assume that no denominator equals zero
The value of (-42n+28p)(-1/4) is 249n/4
What are fractions?A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, three-fifths, three-quarters.
A fraction has a denominator and numerator. There are three types of fraction. Proper, improper and mixed fraction
Opening the parentheses of the equation
(-42n+ 28p)(-1/4).
= -42n× -1/4+ 28× -1/4
= (42n×-7)/4
= -294n/4
learn more about fractions from
https://brainly.com/question/78672
#SPJ1
A new gaming chair costs $309.99. You have already saved $131.49 and earn $25.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
25.5w − 131.49 = 309.99; w = 17
25.5 + 131.49w = 309.99; w = 7
25.5w − 309.99 = 131.49; w = 17
25.5w + 131.49 = 309.99; w = 7
The linear equation we need to solve is:
$25.50*w = $309.99 - $131.49
And the solution is w = 7.
How to write and solve the equation?We know that the cost of the gaming chair is $309.99.
To buy this, you already have saved $131.49, and save another $25.50 per week, then the amount you have after w weeks is:
f(w) = $131.49 + $25.50*w
So the linear equation we need to solve is:
$131.49 + $25.50*w = $309.99
To solve this we need to isolate w.
$131.49 + $25.50*w = $309.99
$25.50*w = $309.99 - $131.49
w = ($309.99 - $131.49)/$25.50 = 7
So they can buy the chair after 7 weeks.
Learn more about linear equations:
https://brainly.com/question/13763238
#SPJ1
5x + y = 8
2x + y = 5
Answer:
x=1 y=3
Step-by-step explanation:
By looking at the equations, you can use substitution
Set the equation equal to y
y=-5x+8
y=-2x+5
Then put equation together
-5x+8=-2x+5
Move numbers over
3x=3
x=1
Put x back into equation
5+y=8
2+y=5
y=3
A bus ticket used to cost $2.50
Today, 1 bus ticket costs $2.75
The increase in cost is?
The percent increase is?
What is the mode for test scores 84,76,95,66,87,91,79,88,81,87?
Answer: mode is 94
Step-by-step explanation:
Emma learned in science class that fruit fly populations can increase by about 30% each day. She found 7 fruit flies on a rotten banana today, and she is curious how many fruit flies could be on the banana in a few days. You can use a function to approximate the number of fruit flies on the banana after x days.
The exponential function that approximates the number of fruit flies on the banana after x days is y = 7 x 1.3ˣ.
What is an exponential function?An exponential function is a mathematical function form of y = aⁿ or y = abˣ, where b is a constant or the base of the function, a is a variable, and n is the variable exponent.
Exponential functions must always contain an exponent, which is an integer raised to some power.
When the exponent is positive, it implies the function is increasing in value and vice versa.
Percentage increase per day = 30%
The number of fruit flies found = 7
The number of days = x days
Let the number of flies after x days = y
y = 7 x 1.3ˣ
Thus, an exponential representation of the function which Emma can use to model the number of fruit flies after x days is y = 7 x 1.3ˣ.
Learn more about exponential functions at https://brainly.com/question/12940982
#SPJ1
convert 7 yards per minute to feet per second. (3 feet=1 yard)
please help fast!! my life is in risk!
Answer:
The answer you are looking for is 0.35 foot per second.
Step-by-step explanation:
Formula = divide the speed by 20
(Or in this case 7 divided by 20).
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Do the measurements 15,17,22 make up a right triangle? Yes or no explain??
answer me fast
The measurements 15, 17, 22 do not form a right triangle.
In this question, we have the measurements 15, 17, 22
We check whether the measurements 15, 17, 22 is Pythagorean triple.
22^2 = 484
15^2 = 225
17^2 = 289
15^ + 17^2 = 225 + 289
= 514
≠ 484
i.e., 15^ + 17^2 ≠ 22^2
This means, these measurements do not form a right triangle.
Therefore, the measurements 15, 17, 22 do not form a right triangle.
Learn more about Pythagorean triple here:
https://brainly.com/question/15190643
#SPJ9
33.21 divided by 9
What is the answer? And can you explain pls
Answer:
[tex]33.21 = \frac{3321}{100} \\ \\ \frac{33.21}{9} = \frac{3321}{100 \times 9} = \frac{3321}{900} = \frac{369}{100} = 3.69[/tex]Step-by-step explanation:
Thanks
A 5-pound package of
ground beef is $10.10. A
1/2 pound package is $1.05.
What is the difference in
the cost per pound between
the larger and smaller
packages of beef?
Answer: I would say a half of beef is cheaper the pounds are different maybe subtract a half from five
Step-by-step explanation:
Last year, Ivanna opened an investment account with $7500. At the end of the year, the amount in the account had decreased by 7.8%. How much is this
decrease in dollars? How much money was in her account at the end of last year?
0.065=x/5800
x=$377; that is the dollar value of the decrease
The account is now worth $5423.
The measurements of two sides of a triangle are 12cm and 17cm Which side length could be the measurement of the third side of the triangle
Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.
In the given question,
The measurements of two sides of a triangle are 12 cm and 17 cm.
We have to find which side length could be the measurement of the third side of the triangle.
We know that,
The sum of the length of any two sides is always greater than the third side.
The given sides of triangles are 12 cm and 17 cm.
Hence, the length of the third side should be shorter than the total of the other two sides,
12 + 17 = 29 cm.
Considering that the third side must be less than the difference between the first two sides,
17 – 12 = 5 cm
So, the length of the third side falls between 5 cm and 29 cm.
To learn more about triangle link is here
brainly.com/question/25813512
#SPJ1
The population of a city can be modeled using the formula P=100,000e^(0.05t), where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000?
Group of answer choices
t=3/(0.05e)
t=ln3/0.05
t=(ln200,000)/0.05
t=log3/0.05
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Given,
The population of a city can be modeled using the formula P=100,000e^(0.05t)
t is the number of years after 2012
P is the population of the city
We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.
Here,
Substitute 300000 in for P and solve for t
300000=100000e^0.05t
Divide both sides by 100000:
We get,
3 = e^0.05t
Multiply both sides by the natural log (ln)
Then,
ln(3) = 0.05t
Now, divide 0.05 on both sides to get t by its self
t = ln(3) / 0.05
Therefore,
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Learn more about population of a city here;
https://brainly.com/question/28390579
#SPJ1
Alex house is 15 blocks from school. Carlene lives 7 blocks from Alex's house. Which equation represents the location of Carlene's house in relation to the school?
|x+7|=15
|x-7|=15
|x+15|=7
|x-15|=7
Answer:
Answer is b
Step-by-step explanation:
Because
|x-7|=15--->x=15+7, x=22Translate the equation into a verbal sentence 8-x=2
Answer:
See below
Step-by-step explanation:
Eight minus unknown quantity 'x' equals two.
Convert 0.8 grams to grains
Answer:
12.3459 grains
Step-by-step explanation:
Answer:
12.346 grains
Step-by-step explanation:
for an approximate result, multiply the mass value by 15.432
( which is basically 0.8 times 15.432)
Use the number line to plot –3, 1, and 3.
Which statements are true
Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1
The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.
The correct statements regarding the number line are given as follows:
1 < 3.–3 < 1.How to plot an integer number on the number line?Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.
These numbers are plotted marking a symbol such as a X or a circle on the number line.
The number line is increasing, so the negative numbers appear before the positive numbers.
This means that if a number a is to the left another number b, the number a is less than b, hence:
1 < 3–3 < 1.As the order in which the numbers appear is given as follows:
-3, 1 and 3.
More can be learned about the number line at https://brainly.com/question/28761820
#SPJ1
f(x) = x + 2
g(x) = 3x² - 5
Find (f.g)(x).
OA. (f g)(x) = 3x³ - 10
OB. (f g)(x) = 3x³ + 6x² - 5x - 10
OC. (f. g)(x) = 3x³ + 10
OD. (f g)(x) = 3x³ + 6x² + 5x + 10
SUBMIT
Answer:
It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10
Step-by-step explanation:
In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.
• Take the products of both functions.
f(x)g(x) = 3x²+5 • x-2
• Next, expand the functions. We expand by combining like terms.
= 3x^3 - 6x^2 + 5x - 10
Since the function cannot be simplified further, this leads to option B being our answer.
Hope this helps!
Find the value of each variable. For the circle, the dot represents the center.
The values of each variable are ∠d=71°, ∠c=87°, arc a=121°, arc b=53°.
What is meant by circle?A circle is a shape formed by all points on a plane that are at a fixed distance from the center. It is the curve sketched out by a point moving in a plane such that its distance from a particular point remains constant. The radius is the distance between any point on a circle and the center. The radius must usually be a positive integer. Degenerate case is a circle with r=0. Except when otherwise specified, this article is about circles in Euclidean geometry, and specifically the Euclidean plane.
1) Measure of ∠d
∠d+109°=180°
∠d=71°
2) Measure of ∠c,
∠c+93°=180°
∠c=87°
3) Measure of arc a is,
109°=1/2[97°+arc a]
218°=97°+arc a
arc a=121°
4) Measure of arc b,
87°=1/2[121°+arc b]
174°=121°+arc b
arc b=53°
Therefore, the values of each variable are ∠d=71°, ∠c=87°, arc a=121°, arc b=53°.
To know more about circle, visit:
https://brainly.com/question/11833983
#SPJ1
Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
The exponential function that can model the county population, y, x decades after Tiana was born, is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 when y = 600000, hence:
[tex]y = 641000(0.99)^x[/tex]
[tex]600000 = 641000(0.99)^x[/tex]
[tex](0.99)^x = \frac{600000}{641000}[/tex]
[tex]\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}[/tex]
x = 6.6 decades.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2y - 3x = 6
Equation of the line is y = 3/2x + 3.
Define slope intercept form.Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The "slope-intercept" form is one of the most popular methods. It is so named because it makes the slope and y-intercept of the equations in the equation more clear. The number that is placed before the x is the slope.
Given,
Slope intercept form:
Formula:
y = mx + b
Where m = slope
2y - 3x = 6
2y = 6 + 3x
Equation:
y = 3 + 3/2x
y = 3/2x + 3
Equation of the line is y = 3/2x + 3.
To learn more about slope intercept form, visit:
https://brainly.com/question/9682526
#SPJ1
Am I correct? Did I do this right?
Answer:
Step-by-step explanation:
Yes, you did it right.
find the equation of a line parallel to 3x +2y=14 that passes through the point (8,8)
The equation of the parallel line is y = (-3/2)x + 20
What does the term Slope of a Straight Line means?
A line's slope is defined as the change in y coordinate with respect to the change in x coordinate. The net y coordinate change is y, while the net x coordinate change is x.
Solution:
Firstly we need to find the slope of the given line 3x+2y = 14
Since, the equation is in the form ax + by = c
Therefore, by comparing we can say a = 3 and b = 2
Slope = -(b/a) = -3/2
Since we need to find the equation of the parallel line
So, the slope of the parallel line will be -3/2
y = mx + b
we know that the line passes through the point (8,8)
putting x,y = 8 and m = -3/2
8 = (-3/2)*8 + b
8 = -12 + b
b = 20
So, the equation of the parallel line is y = (-3/2)x + 20
To learn more about Straight Line and its Slope from the given link
https://brainly.com/question/16949303
#SPJ9
The area of the rectangle shown is 44 m².
Work out the missing length x.
Answer:
x = 12 m
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × width
here A = 44 , then
x × 3 [tex]\frac{3}{4}[/tex] = 44 ( change mixed number to improper fraction )
x × [tex]\frac{11}{3}[/tex] = 44 ( multiply both sides by 3 to clear the fraction )
11x = 132 ( divide both sides by 11 )
x = 12 m
Mr. Harris is adding tiles to his patio area. On Monday, he tiled 1/3 of his patio, and on Tuesday, he tiled 1/2 of the patio area. How much would he have left to tile on Wednesday?
Responses
On Wednesday 1/6 of the patio area is left to tile
Let the patio area be x
On Monday, he tiled 1/3 of his patio = 1/3 x
on Tuesday, he tiled 1/2 of the patio area = 1/2 x
The area left to tile on Wednesday
= x - (1/3 x + 1/2 x)
x - 1/3 x - 1/2 x
(6x - 2x - 3x)/6
= 1/6 x
The area left to tile on Wednesday is 1/6 of the patio area
Therefore, 1/6 of the patio area is left to tile on Wednesday
To learn more about fractions refer here
https://brainly.com/question/78672
#SPJ9
which ones bigger -1.35 or -1 4/9 by the way 4/9 is a fraction
Answer:
[tex]-1.35[/tex] is bigger (larger)
Step-by-step explanation:
[tex]-1\frac{4}{9}=-1.\overline{44}[/tex]
Therefore, because [tex]-1.35[/tex] is less negative than [tex]-1.\overline{44}[/tex],
[tex]-1.35[/tex] is bigger (larger).
9.
A.O
B.
1 12
Genevieve's
Function
Gary and Genevieve both plot lines on a coordinate grid. Gary plots the function y=2x-5, and Genevieve plots the function y=-3x + 4. Which of these represents their lines as well as the solution of the system?
The coordinate plane that represents both lines as well as the solution of the system is shown in the diagram below.
What is the Solution of a System of Equations?The solution to a system of equations is the value of x and y that will make the equations of the system true if they are plugged in into either of the two equations in the system.
Thus, when the equations or functions are plotted as a line on a coordinate grid, the system intersect at a point The coordinates of this point is the solution of the system of equations.
The function for Gary, y = 2x - 5, would be a line that has a slope of 2 and cuts the y-axis at -5, while that of Genevieve y = -3x + 4 will have a slope of -3, and will intercepts the y-axis at 4.
The red line in the coordinate grid in the image below is Gary's function y = 2x - 5, while the blue line is that of Genevieve y = -3x + 4. They bot intersect at (1.8, -1.4).
The solution is: (1.8, -1.4).
Learn more about system of equations on:
https://brainly.com/question/25976025
#SPJ1
What is the y-intercept of a line that has a slope of 2 and ( - 2, 3 ) is a point on the line?
The y-intercept of the line will be equal to 7.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that a line that has a slope of 2 and ( - 2, 3 ). The y-intercept of the line will be calculated as,
y = mx + c
3 = (-2 x 2 ) +c
3 = -4 + c
c = 4 + 3
c = 7
Therefore, the y-intercept of the line will be equal to 7.
To know more about an equation of the line follow
brainly.com/question/18831322
#SPJ1
Ned help pretty please someone
The missing value is 22
Direct Proportionality:Direct proportion is the relation between two quantities or values where the ratio of the two will always equal a constant value. The symbol used for proportion is the symbol '∝'.
When two quantities are in direct proportion, if we increase one value, then the other will also increase, and if we decrease one value then the other value will also decrease.
Here we have
x - 1 2 3 4 5
y - -2 4 10 16 ?
As we see the value of x is directly proportional to y
For every 1 unit value of x, the y value is increasing 6 units
For more Understand observe the following
at x = 1 => y = -2
at x = 2 => y = -2 + 6 = 4
at x = 3 => y = -2 + 2(6) = 10
Therefore,
The relation between x and y can derive as given below
=> y = - 2 + (x-1)6
=> y = - 2 + 6x -6
=> y = 6x - 8
at x = 5 => y = 30 - 8 =22
Therefore,
The missing value is 22
Learn more about Proportionality
https://brainly.com/question/28445193
#SPJ1
