For n = 8, the sum of squares from 1 to 8 would be:
Σ i² = 8(8 + 1)(2(8) + 1) / 6 = 204.
What is the significance of summation?The act of adding anything up is called summarizing. To produce an action potential in the nervous system, numerous stimuli that are each individually subthreshold must be combined to reach a suprathreshold level (a response). Usually, a sum of numerous terms is indicated by the symbol "sigma." To include all terms that must be taken into account when computing the sum, this symbol is typically followed by an index that varies.
The summation notation "Σ" is used to represent the sum of a sequence of numbers. The expression "Σ i²" means the sum of the squares of the numbers from i=1 to i=8.
The formula to find the sum of the squares from 1 to n is given by:
Σ i² = n(n + 1)(2n + 1) / 6
So, for n = 8, the sum of squares from 1 to 8 would be:
Σ i² = 8(8 + 1)(2(8) + 1) / 6 = 204.
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What is the answer for these expressions
Answer:
a.7a-ab+b
=7×3-3×5+5
=21-15+5
=11
b.10a÷(2b)
=10×3÷(2×5)
=30÷10
=3
C.4ab-6b+5a
=4×3×5-6×5+5×3
=60-30+15
=45
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URGENT!!!
Consider the graph of the polynomial function y=f(x) given below. The graph continues forever at both ends. Determine the following features (make sure you write all intervals in interval notation and all intercepts as points):
(A) State the domain and range.
(B) State the x-intercepts.
(C) State the y-intercept.
(D) State the interval(s) for which the function is increasing.
(E) State the interval(s) for which the function is decreasing.
(F) State the interval(s) for which the function is constant.
(G) State any symmetry about any axis and/or the origin.
(H) Determine whether the function is even, odd, or neither.
The features of the given polynomial graph are;
A) Domain: (-∞, ∞)
Range: (-∞, 16)
B) The x-intercepts are; (-2√2, 0), (0, 0), (2√2, 0)
C) The y-intercept is; (0, 0)
D) The interval(s) for which the function is increasing is; (-∞, -2) and (0, 2)
E) The interval(s) for which the function is decreasing. is; (-2, 0) and (2, ∞)
F) The graph has no constant interval.
G) It is symmetrical about the y-axis
H) Even function
How to find the domain and range of a polynomial graph?The domain of a function is defined as the set of all possible input values for which the function holds. The range of a function is defined as the set of all possible output values for all possible input values.
A) The x-values intervals we reckon will be positive and negative infinity as the graph extends till infinity. However, the maximum value of the y-values will be 16 while the minimum is negative infinity.
B) The x-intercepts are the points where the graph crosses the x-axis and they are; (-2√2, 0), (0, 0), (2√2, 0)
C) The y-intercepts are the points where the graph crosses the y-axis and it has the coordinate; (0, 0)
D) Looking at the given graph, it is increasing when the curve rises and in this case it is; (-∞, -2) and (0, 2)
E) Looking at the given graph, it is decreasing when the curve descends and in this case it is; (-2, 0) and (2, ∞)
F) The graph has no constant interval.
G) It is symmetrical about the y-axis
H) The function is an even function
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9. Hachi uses 2 tablespoons of peanut butter on each slice of toast she prepares. Let s represent the number of slices of toast, and let t represent the number of tablespoons of peanut butter she needs. Write an equation to represent this relationship, and use it to determine how many tablespoons of peanut butter she would need for 5 slices of toast.
The following vitamins, minerals, and nutrients are particularly notable in each 2-tablespoon (tbsp) portion of smooth peanut butter: Protein. Protein content per 2-tbsp portion of peanut butter is 7.02 grammes (g).
How much protein is in 2 spoons of peanut butter?Although peanut butter is high in protein, vitamins, and minerals, it may also be quite calorie-dense, salty, and high in unsaturated fat. Given that many commercial brands include sugar and oil additives, low-sugar homemade peanut butter can be a decent alternative.Nutrients included in peanuts and peanut butter could help people with their blood sugar levels and heart health.Depending on how peanut butter is incorporated into a person's diet, it may aid in weight loss or weight gain during bodybuilding or weightlifting.The high calorie and fat content of peanut butter, however, means that it should only be consumed in moderation.In this piece, we examine the advantages of consuming peanut butter and outline its hazards.The Complete Question.
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factorise the following:
4p + 10
Answer:
2(2p+5)
Step-by-step explanation:
4p + 10
taking common values
2(2p+5)
The expression 4p + 10 can be factored by grouping the like terms together.
4p + 10 can be factored as:
2(2p + 5)
This is the prime factorization of the given expression. Here we have factored out the common factor 2 from 4p and 10. This is the most simplified form of the expression.
During _____________, the cell uses information from messenger RNA to produce proteins. Responses A respirationrespiration B transcriptiontranscription C amino acid sequencingamino acid sequencing D translationtranslation
Answer:
D) During translation, the cell uses information from messenger RNA to produce proteins.
Step-by-step explanation:
Hope it helps! =D
show that the medians of the triangle with (non-colinear) vertices (a1, a2, a3) intersect at a1 a2 a3 3
The medians of a triangle connect the midpoints of each side and intersect at the centroid of the triangle.
Medians of a triangle are lines that connect the midpoints of each side of the triangle to the opposite vertex. This means that they divide the triangle into two halves, each with an area that is equal to half of the area of the entire triangle. The medians of a triangle with vertices (a1, a2, a3) intersect at a point known as the centroid of the triangle, which is located at the intersection of the three medians. The centroid can be found by taking the average of the three vertices, or by finding the intersection of the three medians. The centroid is the point at which the three medians of the triangle intersect and is the center of gravity for the triangle. In other words, it is the point that all three medians will intersect at.
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Solar panel position
For locations between 20° and 60° north latitude a solar collector panel should be mounted so that its angle with the horizontal is 20°
greater than the local latitude. Consequently, the solar panel mounted on a roof forms a 54° angle with the horizontal. The bottom edge of the 12-ft long panel is resting on the roof and the high edge is 5 feet above the roof. What is the total area of the rectangular solar collector panel?
The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
A=12h
sin54°= h/5
ℎ= 5 / sin54°
h= sin54° / 5
Therefore: A=12 * sin54° / 5
74.164 feet2
The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
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An artist wants to paint a canvas based on a photograph that measures 4 inches by 5 inches. based on the canvas prices listed in the table, the artist could use canvases at which prices to make a painting that is proportional to the photograph? click on the canvas prices you want to select. $6.43, $11.65,$18.47, $22.80.
The artist wants to paint a canvas that is proportional to the photograph, which measures 4 inches by 5 inches.
To calculate the proportionality, we will use the formula for converting inches to centimeters. 1 inch is equal to 2.54 centimeters. Therefore, 4 inches is equal to 10.16 centimeters and 5 inches is equal to 12.7 centimeters. Therefore, the artist should purchase canvases that are 10.16 centimeters by 12.7 centimeters in size. This will correspond to the following canvas prices: $6.43, $11.65, $18.47, and $22.80. By purchasing these canvases, the artist will ensure that the painting is proportional to the photograph.
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PLEASE HELP
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Use the equation -10 + 6( h - 8 ) = -4( 2h + 3 ) to answer Parts A, B, and C below.
Part A: What property can be used to eliminate the parentheses in the equation?
Part B: Solve the equation. Show all work.
Part C: Verify the solution. Show all work.
The distributive property is used eliminate the parentheses in the equation and the solution of the equation is not correct.
What property can be used in the equation?Part A: The distributive property can be used to eliminate the parentheses in the equation.
Part B: Using the distributive property, we get:
-10 + 6h - 48 = -8h - 12
6h + 8h = 48 + 10 -12
14h = 70
Now we divide both sides by 14:
h = 70/14
h = 5
Part C: To verify the solution, we can substitute 5 back into the original equation and see if both sides are equal.
-10 + 6(5 - 8) = -4(2(5) + 3)
-10 + 6(-3) = -4(10 + 3)
-10 - 18 = -4(13)
-28 = -52
Thus, the solution is not correct.
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Answer:
Part A: The distributive property can be used to eliminate the parentheses in the equation.
Part B: Using the distributive property, we get:
-10 + 6h - 48 = -8h - 12
6h + 8h = 48 + 10 -12
14h = 70
Now we divide both sides by 14:
h = 70/14
h = 5
Part C: To verify the solution, we can substitute 5 back into the original equation and see if both sides are equal.
-10 + 6(5 - 8) = -4(2(5) + 3)
-10 + 6(-3) = -4(10 + 3)
-10 - 18 = -4(13)
-28 = -52
Thus, the solution is not correct.
Step-by-step explanation:
what is the radius,diameter, ad circumference of the area of a circle that is 2289.1ft squared long
For the given Circumference, the radius of the circle is 364.50 feet, and diameter is 729 feet.
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
How do you figure out a circle's radius and area?A circle's circumference is equal to two times its radius or diameter, where r is the radius and d is the diameter. Where r is the circle's radius, the area of a circle is equal to πr2
The Circumference of the circle is 2289.1 sq. feet,
Circumference = 2πr
2289.1 = 2 π r
⇒ 2289.1 = 2 × 3.14 × r
⇒ r = 2289.1 / 6.28
⇒ r = 364.50
We know, Diameter = 2 × Radius
⇒ Diameter = 2 × 364.50 = 729
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Let V be the set of functions f : R 5 R. For any two functions f , g in V , define the sum f + g to be the function given by (f + g)(x) = f(x) + g(x) for all real numbers x. For any real number c and any function f in V , define scalar multiplication c f by (cf)x) = cf(x) for all real numbers x. Answer the following questions as partial verification that V is a vector space. (Addition is commutative:) Let f and g be any vectors in V . Then f(x) + g(x) = for all real numbers x since adding the real numbers f(x) and g(x) is a commutative operation. zero vector exists:) The zero vector in V is the function f given by f(x) = for all x_ (Additive inverses exist:) The additive inverse of the function f in V is a function g that satisfies f(x) + g(x) for all real numbers X. The additive inverse of f is the function g(x) for all x. (Scalar multiplication distributes over vector addition:) If c is any real number and and g are two vectors in V , then c(f + g)(x) = c(f(x) + g(x)) =
V is a set of functions that map from [tex]R^5[/tex] to R. It is a vector space because it has a commutative addition operation, a zero vector, additive inverses, scalar multiplication that distributes over vector addition, associativity of vector addition, a multiplicative identity for scalars, and a multiplicative inverse for non-zero scalars.
cf(x) + cg(x) for all real numbers x.
Associativity of vector addition: Let f, g, and h be any vectors in V. Then (f + g) + h = f + (g + h) for all real numbers x.
Existence of a multiplicative identity for scalars: The multiplicative identity for scalars in V is 1, such that for any vector f in V, 1f(x) = f(x) for all real numbers x.
Existence of a multiplicative inverse for nonzero scalars: For any nonzero real number c, there exists a multiplicative inverse 1/c such that c(1/c)f(x) = f(x) for all real numbers x and for any vector f in V.
All these properties are the standard conditions for a vector space, therefore V is a vector space.
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Help with homework please!
The exponential depreciation rate to the nearest tenth of a percent is -0.2%.
How to calculate the exponential depreciation rate?we need to use the exponential decay formula to find exponential rate.
A = A0 * e^(-rt)
where:
A0 = initial value of car (52,000)
A = final price of the car (45,000)
t = elapsed time (32 months)
r = exponential depreciation rate
Rearrange the formula to solve for the exponential depreciation rate "r".
r = -ln(A/A0) / t
Insert value:
r= -ln(45,000 / 52,000) / 32
r = -0.067115074/32
r = -0.002097288
The exponential depreciation rate, expressed as a percentage to the nearest tenth of a percent, is obtained by multiplying by 100.
r = -0.002097288 * 100
r = -0.21D
44 Therefore, the exponential depreciation rate to the nearest tenth of a percent is -0.2%.
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Find the recursive formula for the geometric sequence. Then find a5,
2, 14, 98, 686, ...
A) an = an - 1 . 7; 33,614
B) an = an - 1 . 7; 693
C) an = an - 1 . 7; 4,802
D) an = an - 1 . 7; 98
an = an - 1 . 7; 4,802 is the recursive formula for the geometric sequence.
What exactly is a geometric series?
A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.
2, 4, 8, 16, 32, 64,..., which has a common ratio of 2, is an illustration of a geometric sequence.
2, 14, 98, 686, ...
as shown in total
2 * 7 = 14 14 * 7 = 98 98 * 7 = 686
So aₙ = aₙ₋¹
a₅ = a₄ . 7
= 686 . 7 = 4802
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the present age of neha is 4 times the age of her 4 year old son.if her son is presently 14years old, find neha's present age.
Answer: 40
Step-by-step explanation:
A grocery supplier believes that the mean number of broken eggs per dozen is 0.6, with a standard deviation of 0.5. Olaf buys 3 dozen eggs without checking them.
a. How many broken eggs does Olaf expect to get?
b. What's the standard deviation?
c. Is it necessary to assume the cartons of eggs are independent? Why?
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
a. Olaf expects to get 1.8 broken eggs.
b. The standard deviation is 0.5.
c. Yes, it is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs, and if they are not independent, the probability of one carton containing broken eggs will influence the other cartons.
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
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Suppose that a sample of size 100 is selected from a population with unknown variance. If this information is used to construct a confidence interval for the population mean, which of the following statements is true?O The sample standard deviation cannot be used to estimate the population standard deviation because the sample size is too small, O The 2-score must be used in computing the limits for the confidence interval O The sample must be normally distributed O The population is assumed to be normally distributed
In the given case, the population is assumed to have a normal distribution.
When creating a confidence interval for the population mean with a sample size of 100, the population is taken to have a normal distribution. This is due to the Central Limit Theorem, which asserts that regardless of the population distribution's form, the distribution of the sample means approaches a normal distribution as the sample size increases.
Therefore, it is safe to infer that the population mean is normally distributed when the sample size is large enough, for instance, n>30. Additionally, it is also ideal to conclude that the population mean has a normal distribution since a sample size of 100 is greater than 30.
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Determine a definite integral that represents the area. region in the first quadrant within the limacon r = 5 + sin(o)
The area of the region in the first quadrant within the limacon r = 5 + sin(o) is 25π/2 + 5π - 2.
The definite integral that represents the area of the region in the first quadrant within the limacon r = 5 + sin(o) is given by:
∫0π/2 (5 + sin(o))2 do
This integral can be evaluated by using the formula for the area of a circle, A = πr2, and converting it to polar coordinates. Since the radius of the limacon is given by r = 5 + sin(o), the area of the region within the limacon is calculated by:
A = ∫0π/2 (5 + sin(o))2 do
= ∫0π/2 (25 + 10 sin(o) + sin2(o)) do
= 25π/2 + 5π - (cos(π/2) - cos(0))
= 25π/2 + 5π - 2
Therefore, the area of the region in the first quadrant within the limacon r = 5 + sin(o) is 25π/2 + 5π - 2.
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There were seven serving lines at the
annual pancake breakfast. The total
number of people served at each of
the seven lines were 126, 118, 127, 134,
98, 132, and 121. What was the median
number of people served?
Answer: 126
Step-by-step explanation: Given that the median is the middle number in a sorted, ascending, or descending list of numbers and can be more descriptive of that data set than the average. We know that we need to put the numbers in order from greatest to least or least to greatest first.
Step 1: Ordering the numbers (from least to greatest)
98,118,121,126,127,132,134
Step 2: Finding the value in the middle
98,118,121, 126 ,127,132,134
We now know that 126 is the median number of people served.
Answer: 126 is the median number of people served.
Step-by-step explanation:
The median is found by arranging the data points in a set from lowest to greatest. Once this is done, if there are an odd number of data points, simply find the number in the middle. If there is an even number, find the average of the two middle numbers. Here, you would arrange the numbers as such, 98,118,121,126,127,132,134. Once this is done, since there are seven lines (an odd number of data points, therefore), figure out which number is in the middle, and here it is 126. Hence, the median is 126 (people)
For a system to be closed under an operation, and when any two elements in the system are combined using the operation, the result must still be an element of that system. For instance, when any two natural numbers (1, 2, 3, . . .), are added together, the result will always be a natural number. When answering the following questions, consider the system of all polynomial equations and the system of all rational equations.
Part A
Which systems are closed under addition? If either system is not closed under addition, provide a counterexample
Part B
Which systems are closed under subtraction? If either system is not closed under subtraction, provide a counterexample.
Part C
Which systems are closed under multiplication? If either system is not closed under multiplication, provide a counterexample.
Part D
Which systems are closed under division? If either system is not closed under division, provide a counterexample.
Part E
Based on which operations the system of polynomial equations is closed under, which system of numbers is most similar to the system of polynomial equations? Explain your answer, and provide any needed counterexamples.
Part F
Based on which operations the system of rational equations is closed under, which system of numbers is most similar to the system of rational equations? Explain your answer, and provide any needed counterexample
The answers to all parts is shown below.
What are Numbers?An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labelling. Thus, mathematics is built on numbers.
1. Real numbers are "closed" under addition Integers are "not closed" under division. Irrational numbers are "not closed" under multiplication. Rational numbers are "closed" under subtraction.
2. Rational numbers are "closed" under subtraction. If an operation is closed under a set of numbers that means that the result of the operation will always be within that same set of numbers.
3. The closure property of multiplication holds for natural numbers, whole numbers, integers and rational numbers.
4. Rational numbers are closed under division as long as the division is not by zero. Irrational numbers are not closed under addition, subtraction, multiplication or division.
5. The whole number system and the polynomial system are nearly identical. Actually, there are not many differences between polynomial functions and our whole number system. We employ a base-10 (decimal) approach for counting. The above-mentioned polynomial is an example of a "base x" system.
6. The system of polynomials is almost the same with the system of whole numbers.
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consider the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1). the fourth vertex lies above the point (0,0) at height 1. see the picture below a tetrahedron as described in the problem setup an integral the represents the volume of the tetrahedron then evaluate it.
The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
The integral that represents the volume of the tetrahedron is given by:
$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$$
Evaluating the integral, we get:
$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx = \int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx = \int_0^1 \frac{1}{2} (1-x)^2\,dx = \frac{1}{6}$$
Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
We first set up the integral that represents the volume of the tetrahedron. The integral is a triple integral, so it can be written as $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$. This integral is the volume of a 3-dimensional region enclosed by the limits $x \in [0,1]$, $y \in [0,1-x]$, and $z \in [0,1-x-y]$. This region is exactly the same as the volume of the tetrahedron because it is the same 3-dimensional region.
Next, we evaluate the integral. First, we integrate with respect to $z$, which gives us $\int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx$. Then, we integrate with respect to $y$, which gives us $\int_0^1 \frac{1}{2} (1-x)^2\,dx$. Finally, we integrate with respect to $x$, which gives us $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.
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HELPPPP I NEED HELP!!!!
Answer:
مرتم باشگاه ورزشی خیلی علاقه داشتم خیلی قشنگ بی که خیلی تخفیف فایل که خیلی خوعه بچه آخر بی
Answer:
After four bites, Alice would be 256 inches tall.
An exponential function that models this growth would be f (x) = 64.22 where x is the number of bites she takes.
If Alice doesn't take any bites (zero bites), her height would be 64 inches.
are true statements.
If Alice takes two bites, she will be 256 inches tall. is false and After three bites, Alice would be 192 inches tall is also false.
Answer all 3 as soon as any can
The domain of the expression is all real numbers except where the expression is undefined.
How do you find the domain and range?In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).
Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money.
Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range. A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavour will be provided.
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Factor this:
(will mark the brainliest
Answer: [tex]a^{n}(n^{2}+n+1)[/tex]
Step-by-step explanation:
Since the equation a^n+a^n+1+a^n+2
= a^n+n*a^n+n^2*a^n
= a^n*(n^2+n+1)
Answer:
[tex] {a}^{n} ( {a}^{2} + a + 1)[/tex]
Step-by-step explanation:
Remember exponent product rule: [tex]a^{n+m}=a^n*a^m[/tex]
Rewritten: [tex]{a}^{n} + ( {a}^{n}* {a}^{1}) + ({a}^{n} * {a}^{2})[/tex]
factor the common factor [tex] {a}^{n} [/tex] to get
[tex] {a}^{n} (1 + a + {a}^{2} )[/tex]
reorder from highest exponent to get answer.
Vita wants to center a towel bar on her door that is 27 inches wide.
end of the door is 9 inches. Write and solve an equation to find the length
She determines that the distance from each end of the towel bar to the
of the towel bar.
The length of the towel bar is 9.5 inches.
How to solve the equation?Length is used to measure distance, In the International System of Quantities, a quantity with the distance dimension is referred to as length. The majority of measurement systems select a base unit for length from which all other units are derived. The metre serves as the International System of Units' fundamental unit of length.
Suppose, the length of the towel bar is x inches
The distance from each end of the towel bar to the end of the door is 9
inches. So, the total width of the door will be:[(x+(9*2)]=(x+18) inches
Given that, the width of the door is 27 inches 27.5 So, the equation will be.
x+18=27.5
x=27.5-18=9.5
Thus, the length of the towel bar will be 9.5 inches.
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The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept.
Shawn should use the point-slope formula ⇒ y - y₁ = m(x - x₁) and the y-intercept is -12.
We already know that the point-slope formula goes as such -
⇒ y - y₁ = m(x - x₁)
We have also been told that the slope of the line is 4 and the line passes through the point (1,-8). So, point (1,-8) = (x₁ , y₁) and the slope, m = 4.
Using the given values and the formula of point-slope, we get -
⇒ y - (-8) = 4(x - 1)
⇒ y + 8 = 4x - 4
⇒ 4x - y = -12
⇒ y = 4x - 12
This is the equation of the line.
From this, we get the y-intercept = -12
The complete question that you might be looking for is given below -
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept, and what is the y-intercept of the line?
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what is the value of -6 ^ 3
Answer:
-216
Step-by-step explanation:
[tex]-6^3\\-6*-6*-6 = -216[/tex]
Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
y = 3z2 − 3x2
(Write an equation for the cross section at z = −1
using x and y.)
(Write an equation for the cross section at z = 0
using x and y.)
(Write an equation for the cross section at z = 1
using x and y.)
(Write an equation for the cross section at y = −1
using x and z.)
(Write an equation for the cross section at y = 0
using x and z.)
(Write an equation for the cross section at y = 1
using x and z.)
(Write an equation for the cross section at x = −1
using y and z.)
(Write an equation for the cross section at x = 0
using y and z.)
(Write an equation for the cross section at x = 1
using y and z.)
Answer:
Cross section at z = -1: y = 3(-1)^2 - 3x^2 = -3x^2
Cross section at z = 0: y = 3(0)^2 - 3x^2 = -3x^2
Cross section at z = 1: y = 3(1)^2 - 3x^2 = -3x^2
Cross section at y = -1: x^2 = (3z^2+1)/3; x = sqrt((3z^2+1)/3) or x = -sqrt((3z^2+1)/3)
Cross section at y = 0: x = 0;
Cross section at y = 1: x^2 = (3z^2-1)/3; x = sqrt((3z^2-1)/3) or x = -sqrt((3z^2-1)/3)
Cross section at x = -1: z^2 = (3y+1)/3; z = sqrt((3y+1)/3) or z = -sqrt((3y+1)/3)
Cross section at x = 0: z = 0;
Cross section at x = 1: z^2 = (3y-1)/3; z = sqrt((3y-1)/3) or z = -sqrt((3y-1)/3)
Step-by-step explanation:
Which of the following tables represents a proportional relationship between x and y?
The numbers in table are in proportion. Therefore, option B is the correct answer.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
Here,
From the table A:
1/5 = 3/15 = 5/20 = 7/28
1/5 = 1/5 ≠ 1/4 = 1/4
Here, numbers are not in proportion.
From the table B:
3/9 = 5/15 = 7/21 = 8/24
1/3 = 1/3 = 1/3 = 1/3
The numbers are in proportion.
From the table C:
4/12 = 6/18 = 7/28 = 9/36
1/3 = 1/3 ≠ 1/4 ≠ 1/4
The numbers are not in proportion.
From the table D:
2/8 = 3/12 = 4/16 = 5/30
1/4 = 1/4 = 1/4 ≠ 1/6
The numbers are not in proportion.
Therefore, option B is the correct answer.
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Plsssss help number one and two!!!!!!!
According to the Pythagorean Theorem 1. b = 122. a = 1/4 for more detail scroll down.
What is the Pythagorean Theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as an equation: c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
1. To use the Pythagorean theorem to find the length of side b, you can use the equation: c^2 = a^2 + b^2. In this case, c = 15 and a = 9, so you can substitute those values into the equation and solve for b:
15^2 = 9^2 + b^2
225 = 81 + b^2
b^2 = 225 - 81
b^2 = 144
b = sqrt(144)
b = 12
2. In the second case a is unknown and the other two sides are in fraction form, so we can use Pythagorean theorem to find the value of a.
The equation is c^2 = a^2 + b^2
(5/12)^2 = a^2 + (4/12)^2
25/144 = a^2 + 16/144
a^2 = 9/144
a = sqrt(9/144)
a = sqrt(1/16)
a = 1/4
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melissa is younger than natalie and is older and shorter than jason. natalie is taller and younger than ken, but ken is taller than jason. list the ages of the four people in order, starting with the oldest. list the heights of the four people in order, starting with the tallest.
Ages in order starting with the oldest : ken , natalie , melissa , jason.
Heights in order starting with the tallest : natalie, ken , jason , melissa.
by descending order.
From the information given in the question :
natalie (N) is older than melissa (M)
melissa (M) is older than jason (J)
ken (K) is older than natalie (N)
So , similarly ken is the oldest among those 4. and then order follows as natalie older than melissa older than jason.
K>N>M>J
jason (J) is taller than melissa (M)
natali (N) is taller than ken (K)
ken (K) is taller than jason (J)
So, similarly natali is the tallest among all 4, and then order follows as
ken taller than jason taller than melissa.
N>K>J>M
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