Answer: A) -4, 3, 10, 17, 24, 31
Step-by-step explanation: To solve the given problem we need to calculate the first six terms of the sequence (starting with a1):
a1=-4
a2=a1+7
a2=-4+7
a2=3
a3=a2+7
a3=3+7
a3=10
a4=a3+7
a4=10+7
a4=17
a5=a4+7
a5=17+7
a5=24
a6=a5+7
a6=24+7
a6=31.
Reggie currently has a square rug in his living room. He is moving soon and has determined that for his new living room, he will need a rug that has a width that is two feet shorter than his current rug and a length that is five feet longer than his current rug. Let x represents the side measure of Reggie's current rug, in feet. Determine the equation that represents the area, y, in square feet, of the rug needed for his new living room.
y = x2 + 3x - 10
y = x2 - 7x + 10
y = x2 - 3x - 10
y = x2 + 7x + 10
Answer:
C. y = x² + 3x - 10
Step-by-step explanation:
Reggie's current rug has a square shape.
This means that:
length of rug = x ft
width of rug = x ft
For the new rug:
1- the length is 5 ft longer than the current rug. This means that:
new length = x + 5 ft
2- the width is 2 ft shorter than the current rug. This means that:
new width = x - 2 ft
The area of the new rug can be calculated as follows:
area of new rug = new length * new width
area of new rug = (x + 5)(x - 2)
area of new rug = x(x) - 2(x) + 5(x) - 5(2)
area of new rug = x² - 2x + 5x - 10
area of new rug = x² + 3x - 10 ft²
Just took the test <3.Michelle is having a poster printed from a picture that is 4 inches wide by 6 inches tall. The enlarged poster is 20 inches wide and 30 inches tall. Which proportion can be used to represent the picture sizes
Answer with Step-by-step explanation:
Michelle is having a poster printed from a picture that is 4 inches wide by 6 inches tall.
The enlarged poster is 20 inches wide and 30 inches tall.
20=4×5
i.e. width of enlarged picture=5×width of actual picture
30=6×5
i.e. height of enlarged picture=5×height of actual picture
Hence, proportion that can be used to represent the picture sizes is:
picture:enlarged picture = 1:5
The rain caused the river to rise a total of 6 and 2/3 inches. The river was rising at an average of 2/3 of an inch each hour. How many hours did it rain? (must be a whole number)
(there is a ratio) (2/3 divided by 1) and (6 and 2/3 divided by what?)
1.) Keeping in mind that a function's rate of change is a measure of how fast the function is increasing or decreasing, what does the slope of a linear function indicate?
Sue's Sushi placed two orders with its fish supplier. One order was for 15 pounds of salmon and 8 pounds of tuna; the order totaled $259. The other order was for 12 pounds of salmon and 6 pounds of tuna; this order totaled $204. What is the cost for one pound of salmon and one pound of tuna?
According to these three facts, which statements are true?
Circle W has center (−3, 0) and radius 8.
Circle V is a translation of circle W, 2 units down.
Circle V is a dilation of circle W with a scale factor of 2.
Select each correct answer.
The radius of circle V is 16.
The center of circle V is (−5, 0).
Circle V and circle W are similar.
Circle V and circle W have the same center.
Answer:
I am in K12 the answer is below
The radius of circle V is 16.
Circle V and circle W are similar.
Step-by-step explanation:
In the standard equation for a circle centered at any point, a change in the value of the number that is part of the x-term results in a vertical movement ? True or false?
Answer:
It is False as Changing value of x coordinate results in horizontal movement not in vertical moment.
Step-by-step explanation:
Standard form of circle is given by,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, ( h, k ) = Coordinates of circle and r is radius of circle.
here h is part of x- term.
So, if change value of h to p keeping k and r constant. The coordinate of center shifted in horizontal line whose equation is y = k.
Therefor, It is False as Changing value of x coordinate results in horizontal movement not in vertical moment.
Suppose that x=6 and y=8. If y is inversely related to x, what is y when x=3?
A)4
B)5
C)16
D)18
The value of y when x=3 is 16.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
we have x=6 and y= 8.
If y is inversely related to x
y α 1/x
y= k/x
where is constant of proportionality
k = yx
k = 8(6)
k =48
So, y= k/x
y = 48/ 3
y= 16
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What are the solutions to the equation? n2−8n+16=25 Enter your answers in the boxes.
n1=
n2=
What is the value of 0.36 repeating times 11/2?
The value of 0.36 repeating times 11/2 is 2.
What is Fraction?A fraction represents a part of a whole.
To find the value of 0.36 repeating (which we can write as 0.36363636...) times 11/2.
Convert the repeating decimal to a fraction.
Let x = 0.36363636...
Then 100x = 36.36363636...
Subtracting x from 100x, we get:
99x = 36
x = 36/99 = 4/11
Now Multiply the fraction by 11/2.
(4/11) x (11/2) = 2
Therefore, the value of 0.36 repeating times 11/2 is 2.
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PLEASE SOMEONE HELP ME ON THIS!!
ILL GIVE BRAINLIEST TO YOU IF YOUR ANSWER IS CORRECT
please someone help me!
What is the next number in the sequence? 55, 34, 21, 13, 8…?
a cylinder has a circumgerence of 12pi cm and a height that is half the radius. what is the total surface
EXPERTS/ACE/TRUSTED HELPERS
Suppose that F(x) = x^3 and G(x) = (4x)^3 − 5. Which statement best compares the graphs of F(x) and G(x)?
A.The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.
B.The graph of G(x) is the graph of F(x) stretched horizontally and shifted 5 units down.
C.The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down.
D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.
The graph of G(x) is the graph of F(x) stretched horizontally by a factor of 4 and shifted 5 units down.
Explanation:Comparing the functions [tex]F(x) = x^3[/tex] and [tex]G(x) = (4x)^3 - 5[/tex]reveals the relationship between their graphs. G(x) is a horizontal stretch of F(x) by a factor of 4 due to the presence of "4x." Additionally, the constant term "-5" shifts the graph downward by 5 units. Consequently, G(x) can be accurately characterized as a horizontal stretching of F(x) and a vertical shift downward by 5 units, altering the shape and position of the original cubic function F(x).
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Give 4 equations that uses at least 2 different operations. (PEMDAS) The answer has to be
- 23
- 25
- 27
and
- 28
REMEMBER: 4 equations, one for each answer
Please help
Please help me, will give thanks, lots of points, friend request, and brainliest. Alongside that, I will help you with any questions in science, english, or history that you may have.
Assume a and b are nonzero rational numbers and c and d are irrational numbers. For each of the following expressions, determine whether the result is irrational, rational, or both. Justify your answers.
Part A: b(a + d)
Part B: left parenthesis b square root of five end square root right parenthesis cubed
Part C: a + (cb)
One of the factors of 6x3 − 864x is
A. 4
B. X^2
C. X + 12
D. X - 8
Consider the expression [tex]6x^3-864x.[/tex] This expression consists of two terms: [tex]6x^3[/tex] and [tex]-864x.[/tex]
These two terms have common factors 6 and x, because:
[tex]6x^3=6x\cdot x^2;[/tex][tex]-864x=6x\cdot (-144).[/tex]Then
[tex]6x^3-864x=6x(x^2-144).[/tex]
You know that [tex]144=12^2.[/tex] Use the formula for the difference of squares:
[tex]x^2-144=x^2-12^2=(x-12)(x+12).[/tex]
Therefore,
[tex]6x^3-864=6x(x-12)(x+12).[/tex]
Answer: correct choice is C.
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A company that sells prefabricated homes ships the frames for each home in large shipping containers. Each shipping container is in the shape of a rectangular prism and its volume can be represented by the polynomial expression 5x3 + 7.5x2, where x is the width of the shipping container.
If the length of the shipping container is five times the width, write the expression that represents the height of the shipping container in terms of its width, x.
Answer:
h = x + 1.5
Step-by-step explanation:
Start with the width. The width = x
The length is 5 times the width = 5*x or 5x
The volume of this is
Two things V = 5x^3 + 7.5x^2V = l * w * h Substitute the length and width into the raw formula5x^3 + 7.5x^2 = 5x * x * h
5x^3 + 7.5x^2 = 5x^2 * h Divide both sides by 5x^2
5x^3 / 5x^2 + 7.5x^2 / 5x^2 = 5x^2*h/ 5x^2
x + 1.5 = h <<<< Answer
A study found that 3939% of the assisted reproductive technology (art) cycles resulted in pregnancies. twenty-fourfour percent of the art pregnancies resulted in multiple births. (a) find the probability that a random selected art cycle resulted in a pregnancy and produced a multiple birth. (b) find the probability that a randomly selected art cycle that resulted in a pregnancy did not produce a multiple birth. (c) would it be unusual for a randomly selected art cycle to result in a pregnancy and produce a multiple birth? explain
Hays builds model sailboats as a hobby. The dimensions of the sailboats are given. What is the height, x, of the smaller sailboat's sail? Enter your answer, as a decimal, in the box. x = in. Two sailboats with sails that are right triangles. The top angle on the sails are marked congruent to each other. The smaller sail has a height of x and a base of 7 inches. The larger sail has a height of 12 inches and a base of 8 inches.
The smaller sail has a height of 10.5 inches.
Given to usTwo sailboats with sails that are right triangles.The top angle on the sails is marked congruent to each other.The smaller sail has a height of x and a base of 7 inches.The larger sail has a height of 12 inches and a base of 8 inches.Similarity of trianglesWe know that for the two sails of the sailboat,
the right angle will be equal,
the angles at the top of the sail are congruent, {given}
therefore, the third angle will be equal for both the triangles.
thus, both the triangles will be similar to each other.
For similar triangles,The sides will be in ratio.
[tex]\dfrac{12}{8}=\dfrac{x}{7}[/tex]
[tex]\dfrac{12\times 7}{8}=x\\x = 10.5[/tex]
Hence, the smaller sail has a height of 10.5 inches.
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Find the area of the parallelogram with vertices a(1,2,3), b(1,3,6), c(3,8,6), and d(3,7,3,)
Your Turn: Using the figure, a
c
= d
a
.
What steps need to be taken to change this to a² = cd?
Example: Multiply by 2; divide by a, etc
If a chicken farm sold 3000 dozen eggs last week how many individual eggs were sold
Choose the graph of y > x2 − 9.
Answer with explanation:
The given inequality which represents parabola:
y> x²-9
Checking whether, (0,0) origin satisfies this inequality or not
0 > 0²-9
0> -9
Inequality is true.
So, origin will come under the shaded region.
Points on the boundary are not included.
Using the graph below, what is the 10th term of the arithmetic sequence?
A.a10 = 26
B.a10 = 31
C.a10 = 30
D.a10 = 436
The 10th term of an arithmetic sequence can be found using the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Without the graph or additional information, we cannot compute the 10th term for the given sequence.
Explanation:The question asks us to determine the 10th term of an arithmetic sequence using a provided graph. Unfortunately, the actual graph is not provided in the question. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. To find the 10th term of an arithmetic sequence, we would use the formula:
an = a1 + (n - 1)d
where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is the common difference. However, without the graph or additional information such as the first term or the common difference, we cannot accurately determine the 10th term, and any answer from the provided options would be purely a guess.
To find the 10th term of an arithmetic sequence, we need to use the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, the common difference is -3. Substituting the values into the formula, the 10th term is -24.
Explanation:To find the 10th term of an arithmetic sequence, we need to identify the common difference and use the formula:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In this case, the given sequence is 3; 14; 11; 5; 16; 17; 28; 41; 31; 18. By comparing the terms, we can see that the common difference is -3.
Substituting the values into the formula:
a10 = 3 + (10-1)(-3) = 3 - 27 = -24
The 10th term of the arithmetic sequence is -24.
what is the surface area?
1. Write using exponents. (–4)(–4)