The observation I can make of the pattern is that the sequence always increase by 10.
How to solve an arithmetic pattern?The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.
7, 17, 27, 37, 47, 57..
Therefore,
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore,
a = 7
d = 17 - 7 = 10
Hence, the arithmetic formula is as follows:
aₙ = 7 + (n - 1)10
aₙ = 7 + 10n - 10
aₙ = 10n - 3
The sequence always increase by 10.
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NO LINKS! Please help me with this vertex problem
Show work please: step by step
Answer:
[tex]f(x)=6(x-2)^2+18[/tex]
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=6x^2-24x+42[/tex]
To complete the square, begin by grouping the x terms within parentheses:
[tex]\implies f(x)=(6x^2-24x)+42[/tex]
Factor out the coefficient of x²:
[tex]f(x)=6\left(x^2-4x\right)+42[/tex]
Add the square of half the coefficient of the term in x inside the parentheses, and subtract the distributed value outside the parentheses:
[tex]\implies f(x)=6\left(x^2-4x+\left(\dfrac{-4}{2}\right)^2\right)+42-6\left(\dfrac{-4}{2}\right)^2[/tex]
Simplify:
[tex]\implies f(x)=6\left(x^2-4x+\left(-2\right)^2\right)+42-6\left(-2\right)^2[/tex]
[tex]\implies f(x)=6\left(x^2-4x+4\right)+42-6\left(4)[/tex]
[tex]\implies f(x)=6\left(x^2-4x+4\right)+42-24[/tex]
[tex]\implies f(x)=6\left(x^2-4x+4\right)+18[/tex]
Factor the perfect square trinomial inside the parentheses:
[tex]\implies f(x)=6(x-2)^2+18[/tex]
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Comparing the derived equation with the vertex formula, the vertex of the derived equation is (2, 18). Hence the completion of the square is correct.
A camp counselor and four campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the fourth and a camper who has a tendency to engage in food fights must sit to the counselor's immediate ?
Answer: 6 ways
Step-by-step explanation:
The vertex of the function f(x) = 2x² + 12x + 19 is at the coordinate (x, y), where:
x =
y =
Answer:
x = -3
y = 1
Step-by-step explanation:
Desmos is free and it will graph for you. See picture.
54 3. Joey opened a new store that sells jars of jelly. Joey sold 3 jars of jelly in his first week of business and 10 jars in his second week. He sold 31 jars in week 3 and 94 jars in week 4. If the number of jars he sells continues to increase in this pattern, how many jars of jelly will Joey sell in the fifth and sixth weeks?
Answer:
7
Step-by-step explanation:
THe answer is 7 because 10-3=7 SOrry if wrong
At a sale this week, a desk is being sold for $108.80 This is a 66% discount from the original price.
What is the original price?
Answer:
[tex]\$320.29[/tex]
Step-by-step explanation:
Determine the formula:
[tex]x - (x \times 0.66) = 108.90[/tex]
Solve for x to get the original price:
[tex]x - (x \times 0.66) = 108.90\\x - 0.66x = 108.90\\x(1-0.66) = 108.90\\x = \frac{108.90}{1-0.66}\\x = \frac{108.90}{0.34}\\x \approx 320.29[/tex]
Graph the line by plotting any two ordered pairs that satisfy the equation.
y=43x−6
Consider the following y-intercept and slope:
(0,−3), m=12
Step 2 of 2 : Determine the graph of the line with the given y-intercept and slope.
The equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.
First, let us understand the slope intercept form of a line:
The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.
We are given:
(0, −3), m = 12.
We need to determine the graph of the line with the given y-intercept and slope.
To find the value of b;
substitute the given values in the equation of the line, we will get;
y = mx + b
-3 = 12 *0 + b
b = -3
So, the equation of the line will be:
y = 12x -3
Thus, the equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.
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A biologist is studying a particular species of flower. She writes the following equation to
show the length of the flower petal f(w), in cm, after w weeks:
f(w) = 3(1.03)
Part A (3pts): Complete
the table using the
function.
0
1
2
3
4
5
f(w)
Part B (1pt) Highlight the data
needed to solve this from the
table in Part A.
(2pts): What is an average
rate of change of the function
f(w) when w = 2 to
w = 5?
Rate of change formula =
y₂-y₁
x₂-x
3.03
Part C (2pts): What does the y-intercept of
the graph of the function f(w) represent?
(Circle the correct answer.)
a.) initial length of the petal
b.) length of the petal after w weeks
c.) time it took for the flower to stop growing
d.) percentage of growth each week
Part D (2pts): At the end of the study the
length of the petal was 3.48 cm. What is a
reasonable domain to plot the growth
function?
Sws
A. The lengths of the flower petals corresponding to the weeks 0, 1, 2, 3, 4, and 5 are 0, 3.09, 6.18, 9.27, 12.36, and 15.45, respectively.
B. The average rate of change of the function f(w) from week two to week five is 3.09.
C. The y-intercept of the function f(w) represents the initial length of the petal.
D. The reasonable domain to plot the growth function is week 0 to week 2.
The length of the flower petal and the weeks passed are denoted by f(w) and w. The equation of the function is given below.
f(w) = 3(1.03)w
The simplified function is f(w) = 3.09w.
The rate of change of the function from weeks 2 to 5 is calculated below.
R = [f(5) - f(2)]/(5 - 2)
R = [3.09*5 - 3.09*2]/3
R = 3.09*(5 - 2)/3
R = 3.09
The length of the flower petal at the end of the study was 3.48 cm. The length lies between the week 0 and the week 2.
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What is the value of N?
The value of n in the line segment is - 9 / 4.
How to find the length of a line segment?The length of a line segment can be found as follows:
Two point of the line segment are 2n + 9 / 2 and 9 / 2. The distance of the line segment is 9 / 2.
Therefore, let's find n as follows:
9 / 2 - (2n + 9 / 2) = 9 / 2
9 / 2 - 2n - 9 / 2 = 9 / 2
9 / 2 - 9 / 2 - 2n = 9 / 2
- 2n = 9 / 2
cross multiply
-2n × 2 = 9
- 4n = 9
divide both sides by -4
n = 9 / -4
n = - 9 / 4
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A list of numbers is given below. If x is a number
in this list, which inequality could represent x?
{-5,
-12,-2,-9}
A. x < -13
B. X<-1
C. x>-12
D. X<-2
Answer:
B
Step-by-step explanation:
Since -1 is greater the values given then x is less than -1
Circular area rugs are priced at $5 per foot based on the circumference of the carpet used. What is the cost of the largest circular area rug that will fit in Susie’s dining room? Round your answer to the nearest whole number. Do not include the dollar sign in your answer.
A rectangle has length 12 feet and width 7 feet.
Answer:
The area of the room is 34*21 = 714 ft^2
the cost of the carpet is $5 per square foot, so the cost to carpet the whole room will be
5*714 = $3570
Step-by-step explanation:
3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that, Circular area rugs are priced at $5 per foot based on the circumference of the carpet used.
We need to find the cost of the largest circular area rug that will fit in Susie’s dining room.
The area of the room is 34×21 = 714 ft²
The cost of the largest circular area rug that will fit in Susie’s dining room
$5 per foot based on the circumference of the carpet
Multiply 5 with 714
5×714
3570
Hence, 3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.
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3. Your original purchase price was $825.00 plus 7% sales tax. You enter into an agreement
where the interest (12.5% APR) is waived for the first 12 months provided you make the
required monthly payments; otherwise the interest is accrued from the date of purchase. You
miss the first payment due date. The late fee is $35.00. How much is the interest?
O$103.13
O $110.34
O $8.59
O $9.20
The original price of purchasing is $825 plus 7% sales tax, then the interest will be $9.20. Hence, option D is correct.
What is the Percentage?The Latin term "per centum," which signifies "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship here between a component and a whole, in which the value of the whole is always assumed to be 100.
As per the given data in the question,
The original purchase price = $825
The sales tax = 7% of $825 = 825 × 7/100 = $57.75
Total credit = $825 + $57.75 = $882.75
The monthly interest rate = 12.5%/12 = 1.0417%
Interest = $882.75 × 1.0417/100
Interest = $9.20
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Identify the length of the missing section of each line. Assume that the lines are divided into equal parts.
The identification of the length of the missing section of each line, assuming that the lines are equally divided, is as follows:
a) The missing section is 24 units.
b) The missing section is 18 units.
c) The missing section is 10 units.
How are the missing sections computed?The missing sections can be computed using the mathematical operations of division and multiplication.
The product (quotient) of a division operation involves applying the divisor on the dividend using a division operand (÷).
The product of a multiplication operation applies the multiplier on the multiplicand using the multiplication operand (×).
a) The total units = 36
Division parts = 3
The units of each division = 12 (36/3)
The missing section = 24 (12 x 2)
b) The total units = 36
Division parts = 4
The units of each division = 9 (36/4)
The missing section = 18 (9 x 2)
c) The total units = 16
Division parts = 8
The units of each division = 2 (16/8)
The missing section = 10 (2 x 5)
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Directions. Answer questions (a – f) based on the following graph.
A: When x = -1, what is the value of y?
B. When y = 7, what is the value of x?
C. What is the y-intercept of the graph?
D. What is the x-intercept of the graph?
E. What is the slope of the line?
F. What is the equation of the line?
A. When x = -1, the value of y is equal to 3.
B. When y = 7, the value of x is equal to 1.
C. The y-intercept of the graph is equal to -2.5.
D. The x-intercept of the graph is equal to 5.
E. The slope of the line is equal to -1.75
F. The equation of the line is equal to y = -1.75x - 2.5
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
How to calculate the slope and equation of this line?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope of a line.x and y are the points on a graph.c represents the y-intercept.Making slope (m) the subject of formula, we have the following:
Slope, m = (y - c)/x
Slope, m = (1 - (-2.5))/-2
Slope, m = (1 + 2.5)/-2
Slope, m = -3.5/2
Slope, m = -1.75.
For the equation of this line, we have:
y = mx + c
y = -1.75x - 2.5
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If the area of a rectangular sign is approximately 4218 sq ft, and the width is approximately 57 ft, what is the height of this sign?
(a - 2b)3 when a = 3 and b = -1/2
Answer:
64
Step-by-step explanation:
Substitute the values so (3-2(-1/2))3
Then distribute so (3-(-1))3
Add since it's a double negative to get (4)3
And 4 cubed is 64
Which point is not a solution of the equation below?
(0, -5)
(2, 1)
(5, 5)
(-2, -9)
(2,1) because if you graph it, the dot won’t be on the line.
HELP ME PLEASE!!!?!!!!!?!!!?!!!!0.0
Answer:
wean positive realtionship
The physical plant at the main campus of a large state university recieves daily requests to replace
florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean
of 36 and a standard deviation of 4. Using the 68-95-99.7 rule, what is the approximate percentage
of lightbulb replacement requests numbering between 32 and 36?
Do not enter the percent symbol.
%6
ans =
> Next Question
The percentage of lightbulb replacement requests numbering between 32 and 36 is 34
According to the question,
The distribution of the number of daily request is bell-shapes means Number of daily request follows Normal distribution
Mean of normal distribution : μ = 36
Standard deviation : σ = 4
Let the lightbulb replacement requests number be "x"
So, the probability of lightbulb replacement requests numbering between 32 and 36 = P(32 < x <36)
below 36 i.e. mean of normal
32 = 36 - 4 is probability between one standard deviation and below mean
Percentage between mean ± standard deviation is always 68%
so , percentage of lightbulb replacement requests numbering between 32 and 36 will be half of 68% as mean + standard deviation is excluded
= 68/2
= 34
Hence , 34 percentage of lightbulb replacement requests numbering between 32 and 36.
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I NEED HELP PLEASE HELP
Answer:
Step-by-step explanation:
what is the value of this expression when x=3 and y=8?
[tex] {3x}^{2} + {2y}^{2} [/tex]
A. 25
B. 155
C. 210
D. 337
Answer:
B
Step-by-step explanation:
3([tex]3^{2}[/tex]) + 2([tex]8^{2}[/tex])
3(9) + 2(64)
27 + 128
155
5. The corresponding sides of the similar shapes have same
- In the figure given below, what is the value of x? (RED)
2 cm
3 cm
3 cm
2 cm
4 cm
x cm
(GR
4 cm
Using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
What exactly are mathematical operations?An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.
The arity of the operation is influenced by the number of operands.
PEMDAS, parenthesis, exponents, multiplication, and division.
So, the value of x will be:
The given two rectangles have similar sides.
2cm is similar to 4cm.
3cm is similar to xcm.
Now, we can calculate x as follows:
2/4 = 3/x
2x = 4×3
2x = 12
x = 12/x
x = 6
Therefore, using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
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The sum of two numbers is 12. The difference of the two numbers is 6. What are the two numbers?
Answer:
3 and 9
Step-by-step explanation:
x+y=12
y-x=6
y-x=6
+x. +x
y=6+x
x+(6+x)=12
6+2x=12
-6. -6
2x=6
/2. /2
x=3
3+y=12
-3. -3
y=9
Hopes this helps please mark brainliest
Two data sets and their mean absolute deviations are shown.
Study the plots of each data set, and then use the drop-down menus to answer the questions below?
Answer: you should watch a quick video about it :)
Step-by-step explanation:
Identify the greatest common factor.
8y, -12x, 4xy
The greatest common factor, GCF, of 8y, -12x, and 4xy is 4
Determining the Greatest common factor (GCF) of expressionsFrom the question, we are to determine the greatest common factor of the given expressions.
The given expressions are 8y, -12x, and 4xy
To determine the greatest common factor, we will express each of the expressions as a product of their factors.
8y = 2 × 2 × 2 × y
-12x = 2 × 2 × 3 × -x
4xy = 2 × 2 × x × y
From above, we can observe that the greatest common factor is
2 × 2
= 4
Hence, the greatest common factor is 4
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a rocket is 1 mile above the earth One minute and 5 miles above earth in three minutes. what is the rocket rate of change in miles per minute
Answer:
1.6repeat miles per minute
Step-by-step explanation:
I'm not totally sure, but i just divided 5/3 and that's how I got the answer
URGENT PLS HELPPPP!!!!!
Write the point-slope form of the equation of the line with a slope of -2 and an x-intercept of -1.
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.
Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
The equation of the line that has a slope of -2 and x-intercept of -1 in point slope form is y = -2(x + 1).
How to write equation in point slope form?Linear equations can be represented in different form such as point slope form, slope intercept form, general form and standard form.
Therefore, let's represent the equation of the line in point slope form.
Using point slope form,
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the variables.Therefore, the equation of the line has a slope of -2 and an x-intercept of -1.
The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.
hence,
m = -2 and (-1, 0)
x₁ = -1
y₁ = 0
Therefore,
y - 0 = -2(x + 1)
y = -2(x + 1)
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write 804 billion in ordinary decimal notation and in scientific notation
Answer:804,000,000,000 & 8.0e+11
Step-by-step explanation:
logic
if an odd number is added to an even number the result must be
Answer:
an odd number
Step-by-step explanation:
it always will be an odd number when you add an even and an odd number
HELP NOW
Which variables would the scatter plot at the right be most likely to represent?
A.The number of people at a concert and the total concession sales
B.The number of guests at a hotel and the total water consumption
C.The number of siblings a person has and the person's GPA
D.The total number of miles driven and the total gallons of gas used