The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.
How to find the number of dime and quarter?Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:
let
x = number of quarter
y = number of dime
Therefore,
y = 2 + x
y - x = 2
0.1y + 0.25x = 3
Multiply equation(ii) by 10
y - x = 2
y + 2.5x = 30
subtract equation(i) from equation(ii)
3.5x = 28
x = 28 / 3.5
x = 8
Hence,
y = 2 + 8
y = 10
Therefore,
number of dime = 10
number of quarters = 8
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Find the largest area for a rectangle that is inscribed in a semicircle with radius 4 inches.
The area of the largest rectangle is 25 square units.
It is given that the radius of the semicircle is [tex]4[/tex].
It is required to inscribe a rectangle of maximum area.
Consider a rectangle of sides [tex]x[/tex], [tex]y[/tex] as shown in the given figure.
From the attached figure,[tex]AB=x[/tex], [tex]OB=r[/tex] and [tex]OB=\frac{y}{2}[/tex].
Now, in the triangle OAB, apply Pythagoras' theorem as,
[tex](OA)^{2}=(OB)^{2}+(AB)^2[/tex]
[tex]r^2=(\frac{y}{2} )^2+x^2\\\\[/tex]
[tex]16=\frac{y}{4}+x^2[/tex]
[tex]y^2=4(16-x^2)[/tex]
[tex]y=2\sqrt{16-x^2}[/tex]
So, the area of the rectangle will be,
Area,
[tex]A = 2x \times y[/tex]
= [tex]2x \times \sqrt{(16 - x^2)}[/tex]
Differentiate the area with respect to ,
[tex]A' = 2 \times \sqrt{(16 - x^2)} - 2x^2/(16 - x^2)[/tex]
Differentiate the area twice as,
When[tex]x = 0, y = 5[/tex] and when [tex]x = 5, y = 0[/tex], [tex]area = 0[/tex].
It implies that area is maximum when the value of x lies between 0 and 5.
This will occur where [tex]A'= 0[/tex].
⇒ [tex]2 \times \sqrt{(16 - x2) }- 2x^2/(16 - x^2) = 0[/tex]
⇒[tex]2 \times \sqrt{(16 - x^2)} = 2x^2/(16 - x^2)[/tex]
On simplification, we get,
⇒ [tex]2 \times (16 - x^2) = 2x^2[/tex]
⇒ [tex]16 - x^2 = x^2[/tex]
⇒ [tex]2x^2= 16[/tex]
⇒ [tex]x^2 = 16/2[/tex]
⇒ [tex]x = \sqrt{8}[/tex]
Now, [tex]y = \sqrt{(16 - x^2)}[/tex] becomes
⇒[tex]y = \sqrt{(16 - (\sqrt8)^2)}[/tex]
⇒ [tex]y = \sqrt{(16 - 8)}[/tex]
[tex]y =\sqrt{8}[/tex]
Maximum area = 2xy
[tex]=2(\sqrt{8)}(\sqrt{8})[/tex]
[tex]=16[/tex]
Therefore, the area of the largest rectangle is 16 square units.
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What is the perimeter of the composite figure?
(Round to the nearest tenth)
The perimeter of the composite figure would be = 21 (to the nearest tenth).
What is perimeter?Perimeter is defined as the quantity that is used to evaluate the total length of the sides of an object.
From the given diagram, the composite figure is made up of 6 sides. The addition of these sides is the figures perimeter.
The sides of the composite figure are:
a = 6; b = 12; c = 9; d = 9; e = -9; f = -6.
The perimeter = a + b + c + d + e + f.
= 6 + 12 + 9 +9+ (-9) + (-6)
= 27 - 6
= 21 ( to the nearest tenth)
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16 divided by the sum of 2 and 6
Answer:
Step-by-step explanation:
16/(2+6)
16/8=2
Which compound inequality does not belong with the other three? Explain your reasoning.
1) a>4 or a<-3
2) a< -2 or a>8
3) a>7 or a<-5
4) a < 6 or a>-9
PLEASE HELP!
The a < 6 or a>-9 compound inequality is different than the rest as it involves one interval instead of a reunion of two intervals.
What is compound inequality?A phrase having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both truths in the compound phrase. It is when the solution sets for the various assertions to cross over or intersect.
When the word and is used to connect two inequalities, the compound inequality is solved when both inequalities are true at the same time. It is the intersection or overlap of each inequality's solutions.
1)(−∞,−3)∪(4,∞)
2)(−∞,−2)∪(8,∞)
3)(−∞,−5)∪(7,∞)
4)(−∞,6)∪(−9,∞)=(−9,6)
The fourth compound inequality is different than the rest as it involves one interval instead of a reunion of two intervals.
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A triangle has sides with lengths of 26 inches, 36 inches, and 46 inches. Is it a right triangle?
yes or no
Answer:
no
Step-by-step explanation:
You want to know if side lengths 26 in, 36 in, 46 in form a right triangle.
Pythagorean tripleThe integer side lengths will form a right triangle if they are a Pythagorean triple, or a multiple of one.
We notice that these side lengths have a common difference of 10 in. That makes them an arithmetic sequence. The only Pythagorean triples that are an arithmetic sequence are {3, 4, 5} and its multiples. The shortest side is 3 times the common difference.
The lengths {26, 36, 46} cannot form a right triangle. The attachment shows the triangle is an obtuse triangle.
No, the triangle is not a right triangle.
__
Additional comment
The side lengths will form a right triangle if and only if they satisfy the relation a² +b² = c², where a, b are the two short sides.
26² +36² = 1972 ≠ 2116 = 46²
Students in a classroom have eaten 20% of jellybeans from a jar. There are now only 100 jellybeans left! How many jellybeans were in the jar to begin with?
Using percentages we calculate in the beginning there were 125 jellybeans in the jar.
Let the number of jellybeans in the jar was x.
Now student ate 20% of the jellybeans.
Number of jellybeans students ate = 20% of x = 0.2x
Number of jellybeans left = x - 0.2x = 0.8x
But the number of jellybeans is given as 100.
Therefore 0.8x = 100
or, x = 100 /0.8 = 125
Hence there were 125 jellybeans in the jar.
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.
In other words, that is a relationship where it is always assumed that the value of the whole is 100.
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Please someone help me. Number 7 and 8. Thank you.
7. The composite functions are given as follows:
a. f(g(x)) = [tex]\frac{3x}{-x^2 + 3x - 1}[/tex].
b. g(f(x)) = [tex]\frac{3x(x - 1)}{9x^2 + x - 1}[/tex]
c. (f(g(3)) = -9.
8. The inverse function is given as follows:
[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]
How to obtain the composite function?The composite functions are obtained using the inner function as the input to the outer function.
In this problem, the functions are defined as follows:
f(x) = x/(x - 1).g(x) = 3x/(x² + 1).The composite of f and g is:
[tex]f(g(x)) = f\left(\frac{3x}{x^2 + 1}\right) = \frac{\frac{3x}{x^2+1}}{\frac{3x}{x^2+1} - 1} = \frac{\frac{3x}{x^2+1}}{\frac{-x^2 + 3x - 1}{x^2 + 1}} = \frac{3x}{-x^2 + 3x - 1}[/tex]
At x = 3, the numeric value of the composite function is given as follows:
f(g(3)) = 9/(-9 + 9 - 1) = -9.
The composite function of g and f is given as follows:
[tex]g(f(x)) = g\left(\frac{x}{x - 1}\right) = \frac{\frac{3x}{x - 1}}{\left(\frac{3x}{x - 1}\right)^2 + 1} = \frac{3x}{x - 1} \times \frac{(x - 1)^2}{9x^2 + x - 1} = \frac{3x(x - 1)}{9x^2 + x - 1}[/tex]
Inverse functionThe function is given as follows:
y = (3x + 4)/(x - 1)
The find the inverse, the variables x and y are exchanged, and then y is isolated, as follows:
x = (3y + 4)(y - 1)
xy - x = 3y + 4
3y - xy = 4 + x
y(3 - x) = 4 + x
y = (4 + x)/(3 - x)
[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]
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Can someone help me on this question? I think it’s the 2nd answer but I’m not sure
From the properties of a right triangle is found that the missing length x= [tex]5\sqrt{3}[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The sum of the internal angles of a right triangle also is equal to 180°.
The question gives a figure which is compound for two right triangles.
For each triangle is informed two angles, then:
Triangle 1 - It is given the angle 45° and 90°, thus the third angle will be:45+90+ x = 180
135 + x =180
x=180-135
x=45°
Triangle 2 - It is given the angle 60° and 90°, thus the third angle will be:60+90+ y = 180
150+ y =180
y=180-150
y=30°
Thus, the angles for the given triangle are:
Triangle 1 - 45°, 45° and 90°Triangle 2 - 60°, 30° and 90°From the trigonometric ratio sinФ, you can find the hypotenuse the triangle 2. See below.
[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 45 =\frac{hypotenuse \ triangle 2 }{hypotenuse \ triangle 1} \\ \\ \frac{\sqrt{2} }{2}=\frac{hypotenuse \ triangle 2 }{10\sqrt{2} }\\ \\ 2*hypotenuse \ triangle 2 = 10*2\\ \\ hypotenuse \ triangle 2 = \frac{10*2}{2} \\ \\ hypotenuse \ triangle 2 =10[/tex]
If the hypotenuse of triangle 2 is 10, you can apply again the trigonometric ratio sinФ for finding x
[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 60=\frac{x }{hypotenuse \ triangle 2} \\ \\ \frac{\sqrt{3} }{2}=\frac{x }{10}\\ \\2x=10 \sqrt3\\ \\ x=5\sqrt3[/tex]
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Review the proof. Step 1 / cos(2x) =1-2sin2x
Which step contains an error?step 2/ step 4/ step 6/ step 8
Answer:
Step 6 is wrong
A balloon was originally filled to a volume of 4,400 cubic centimeters. air inside the balloon leaks out over time. write an inequality that describes v, the volume of the balloon in cubic centimeters as air leaks out.
Answer:
V<4400
Step-by-step explanation:
Answer:
the answer is V<4,400
if you are using khan academy, do not add the comma for 4,400, otherwise it will not work.
khan academy answer: V<4400
Step-by-step explanation:
if the air leaked out, which is V, that means V would be less than 4,400 because 4,400 is what we have started with.
Therefore, the inequality would be V<4,400 or for khan academy, V=4400
The shaded area below is 79 m².
Work out the area of the smaller rectangle.
If your answer is a decimal, give it to 2 d.p.
x+4 m
x + 3 m
x+2m
2x+5 m
Not drawn accurately
Answer:
[tex](x + 4)(2x + 5) - (x + 3)(x + 2) = 79 \\ 2x {}^{2} + 5x + 8x + 20 - {x}^{2} - 2x - 3x - 6 = 79 \\ {x}^{2} + 8x + 14 = 79 \\ {x}^{2} + 8x - 65 = 0 \\ {x}^{2} + 13x - 5x - 65 = 0 \\ x(x + 13) - 5( x + 13) = 0 \\ (x - 5)(x + 13) = 0[/tex]
x-5=0
x=5
the length of smaller rectangle= 8 m
and breadth of s. rectangle= 7 m
l x b = 8 x 7
[tex]56 {m}^{2} [/tex]
hopefully this will u
24 greater than or equal to 2X - 10 less than -6
The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper. What is the area of the circle on the paper? Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
The area of the circle on the paper is 4.5 cm when traced around the edge of the quarter on a sheet of paper.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper.
The area of the circle on the paper = πr²
Here r = (diameter of a quarter)/2 = 2.4/2 = 1.2 cm
The area of the circle on the paper = π(1.2)²
The area of the circle on the paper = π × 1.44
The area of the circle on the paper = 4.5238
Round the answer to the nearest tenth.
The area of the circle on the paper = 4.5 cm
Thus, the area of the circle on the paper is 4.5 cm
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Answer:its 4.5
Step-by-step explanation:
a) Work out the gradient of the line y=5x-3 (1)
Gradient = (Answer here)
b) Work out the gradient of the line 3y-12x+7=0 (1)
Gradient = (Answer here)
Answer:
5 and 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
(a)
y = 5x - 3 ← is in slope- intercept form
with gradient m = 5
(b)
3y - 12x + 7 = 0 ( add 12x to both sides )
3y + 7 = 12x ( subtract 7 from both sides )
3y = 12x - 7 ( divide through by 3 )
y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form
with gradient m = 4
Find the length of side AC. Give your answer to 1 decimal place.
The length of AC is 17.3 cm
What is rectangle?We also refer to a rectangle as an equiangular quadrilateral since all of its angles are equal.A closed 4-sided shape is called a quadrilateral.A rectangle can also be referred to as a right-angled parallelogram because its sides are parallel.A quadrilateral with equal and parallel opposite sides is referred to as a parallelogram.Paralleograms are a specific instance of rectangles.acc to our question,
AC is the perpendicularAB is the base and θ = 68°So,tan 68° = or, AC = tan 68°×AB 17.3 (approx)Hence,The length of AC is 17.3 cm
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Can someone help me with this please! I really need it done
increase the amount of the ingredients by 5 and by 20
Using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 350gIncreased by 20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 51.75gIncreased by 20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 7.5gIncreased by 20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 11.5gIncreased by 20 = 46g(G) Crushed red pepper: 1.15g
Increased by 5 = 5.75gIncreased by 20 = 23gWhat do we mean by mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.We can recall the PEMDAS steps in the following order: Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction (from left to right).So, we can calculate missing values as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 18×20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 70×5 = 350gIncreased by 20 = 70×20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 10.35×5 = 51.75gIncreased by 20 = 10.35×20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 1.5×5 = 7.5gIncreased by 20 = 1.5×20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 2.3×5 = 11.5gIncreased by 20 = 2.3×20 = 46g(G) Crushed red pepper: 1.15g
Increased by 5 = 1.15×5 = 5.75gIncreased by 20 = 1.15×20 = 23gTherefore, using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 350gIncreased by 20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 51.75gIncreased by 20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 7.5gIncreased by 20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 11.5gIncreased by 20 = 46g(G) Crushed red pepper: 1.15g
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Graph the line that passes through the points (9,2) and (3,4) and determine the equation of the line ( I need it with graph)
The equation of the line that passes through the points (9,2) and (3,4) is x + 3y = 15 and the graph is shown below .
In the question ,
it is given that
the required line passes through the points (9,2) and (3,4)
in order to find the equation of line we first need to find slope .
so , the slope(m) will be
m = (4-2)/(3-9)
m = 2/(-6)
m = -1/3
The equation of the line passing through the point (3,4) having slope -1/3 is
y - 4 = (-1/3)(x - 3)
3(y - 4) = -1(x - 3)
3y - 12 = -x + 3
x + 3y = 12 + 3
x + 3y = 15
the graph of the line is drawn below .
Therefore ,The equation of the line that passes through the points (9,2) and (3,4) is x + 3y = 15 .
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Fill in the missing values from the similar figures in the table
Step-by-step explanation:
9 × 1/2 = 4.5
8 × 1/2 = 4
hope it's helpful
Deshaun works as a busboy making $9 per hour and as a theater usher making $10 per hour. Let b be the number of hours he works as a busboy this
month, and let u be the number of hours he works as an usher.
His goal this month is to earn more than $1400 total
Answer:
[tex]9b + 10u > 1400[/tex]
3z + 6(z-5) = -48
What does this equal please help
Answer: z=-2
Step-by-step explanation:
3z+6z-30=-48
9z-30=-48
9z-30=-48+30
9z=-18
z=-2
a group of people were given a spelling test. the table shows their marks. work out the range of the marks. how many students are in the group. work out the mean mark of the group.
Answer: a) = 4
b) = 30
Step-by-step explanation:
a) They are asking for the range of the marks so you do 10-6 as 10 is the highest mark and 6 is the lowest
b) You find this out by adding the frequency up 10+4+7+4+5 = 30
Please help now !!!!!!
Answer:
The tablet costs more than the smartphone
Step-by-step explanation:
1 year tablet = $1.50
1 year smartphone = $0.02x12months = $0.24
kumiko decides to buy the same number of apps and games, and she decides to spend as much of the $50 as possible. how many apps and games does she buy? how much money does she have left on her gift card?
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "."
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
What is Inequality?Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both.
The number of apps Kumiko buy is a and the number of games she can buy is g.
The gift card has 50$.
Total amount of apps = 1.25a
Total amount of games = 2.5g
So, the linear equality will be [tex]1.25a+2.5g\leq50[/tex].
She can can only games and apps for amount less than and equal to $50.
Therefore, The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
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The given question is Incomplete. Here is the complete question:
Kumiko has a $50 gift card for a Web site that sells apps and games. Games cost $2.50 each, and apps cost $1.25 each. Write an inequality that represents the number of apps a and the number of games g that Kumiko can buy and describe any constraints.
Factor the expression (72a9b3 − 18a7b5) completely.
The factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Given expression:
= 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex]
divide by 18 .
= 4[tex]a^{9} b^{3}[/tex] - [tex]a^{7} b^{5}[/tex]
divide by [tex]a^{7}[/tex]
= 4[tex]a^{2}b^{3}[/tex] - [tex]b^{5}[/tex]
divide by [tex]b^{3}[/tex]
= 4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]
= 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Therefore the factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
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Jane received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.39 per pound. After buying the coffee, she had $28.05 left on her card. How many pounds of coffee did she buy?
Answer:
85 ggoooofffffyyy
Step-by-step explanation:
Which value of y makes the two matrices inverses of each other?
[6 14]. [-1 -7/2]
[-2-4] [y. 3/2]
-1/2
-5/14
1/2
2
The value of y that makes the two matrices inverse of each other is 1/2
The inverse of a square matrix A, denoted by A⁻¹.
The formula is [tex]\frac{1}{|A|}.adj(A)[/tex]
The product of A and A⁻¹ should be the identity matrix. The identity matrix that results will be the same size as matrix A.
Inverse of given first matrix is
[tex]\left[\begin{array}{cc}6&14\\-2&-4\end{array}\right][/tex]
Determinant = |A| = 6(-4) - (14)(-2)
= -24 + 28
= 4
Adjoint of matrix = [tex]\left[\begin{array}{cc}-4&-14\\2&6\end{array}\right][/tex]
Inverse of matrix = [tex]\frac{1}{|A|}.adj(A)[/tex]
Therefore , Inverse = [tex]\frac{1}{4}.\left[\begin{array}{cc}-4&-14\\2&6\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}-4/4&-14/4\\2/4&6/4\end{array}\right][/tex]
A⁻¹ = [tex]\left[\begin{array}{cc}-1&-7/2\\1/2&3/2\end{array}\right][/tex]
Is required inverse
If we compare the inverse with second matrix
y = 1 / 2
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Answer:
third option: 1/2
Step-by-step explanation:
Find the nth term for 13 8 3 -2 -7 and the 100th term
Answer:
see explanation
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
8 - 13 = 3 - 8 = - 2 - 3 = - 7 - (- 2) = - 5
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 13 and d = - 5 , then
[tex]a_{n}[/tex] = 13 - 5(n - 1) = 13 - 5n + 5 = 18 - 5n
then
a₁₀₀ = 18 - 5(100) = 18 - 500 = - 482
36 is 40% of what number?
[tex]\fbox{90}[/tex]
In order to find 36 is 40% of what number, we will need to use the following formula:
[tex]number\times100/Percent[/tex]
[tex]\frac{36\times100}{40}[/tex]
[tex]36\times100=3,600[/tex]
[tex]3,600\div40[/tex]
[tex]=90[/tex]
The solution of the number in the expression ''40% of a number is 36'' is 90.
Given that,
To find the solution for 40% of that number is 36.
Used the concpet of percentage which stated that,
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.
Let us assume that the solution of the given condition is x.
So, it can be written as,
[tex]40\% \times x = 36[/tex]
[tex]\dfrac{40}{100} \times x = 36[/tex]
Multiply both sides by 100,
[tex]40x = 36 \times 100[/tex]
[tex]40x = 3600[/tex]
Divide both sides by 40,
[tex]x = \dfrac{3600}{40}[/tex]
[tex]x = 90[/tex]
So, the solution for the number is 90.
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The sequence below is arithmetic. Complete parts (a) through (d) below.
- 1, 2, 5, 8, ...
(a) Find the common difference.
The common difference is d= . (Type a whole number.)
(b) Find the eighth term.
The eighth term is ag =
(Type a whole number.)
(c) Find a recursive rule for the nth term.
(Type an equation.)
(d) Find an explicit rule for the nth term.
(Type an equation.)
Answer:
see explanation
Step-by-step explanation:
- 1, 2, 5, 8
(a)
the common difference
d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3
(b)
to find a term in the sequence add d = 3 to the previous term
a₅ = = 8 + 3 = 11
a₆ = 11 + 3 = 14
a₇ = 14 + 3 = 17
a₈ = 17 + 3 = 20
(c)
the recursive rule is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 : a₁ = - 1
(d)
the explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 1 and d = 3 , then
[tex]a_{n}[/tex] = - 1 + 3(n - 1) = - 1 + 3n - 3 = 3n - 4
Joe and Chris share a locker at school. if they each have 8 classes and each class has 2 books, how many books are in the locker. Please show the work! :)
Answer:
32 books
Step-by-step explanation:
Well if each have 8 classes and 2 books per class then to get the total of books you'd multiply 8x2 and you get 16 for one alone. Since its two people sharing a single locker than add 16 with another 16 and you get 32!
sorry I can't physically show the work but writing down a 8x2 on the side and then adding 16 to that answer should show it off! :]