Answer: an=3n-1 a₅=14 a₁₀₀=299
Step-by-step explanation:
a=2 d=3
[tex]\boxed {a_n=a_1+d(n-1)}\\\\a_n=2+3(n-1)\\\\a_n=2+3n-3\\\\a_n=3n-1\\\\a_{100}=3(100)-1\\\\a_{100}=300-1\\\\a_{100}=299\\\\a_5=3(5)-1\\\\a_5=15-1\\\\a_5=14[/tex]
Two positive integers that differ by 9 are in the ratio of 8 to 11. What is the value of the smaller of the two numbers?
The numbers are 24 and 33 so the smaller one is 24
Answer:
24 and 33 are the numbers among which 24 is the smallest.
Step-by-step explanation:
Let one positive integer be x, then another will be x - 9
Solve:
[tex]\sf \dfrac{x-9 }{x} = \dfrac{8}{11}[/tex]
cross multiply
[tex]\sf 11x-99= 8x[/tex]
collect like terms
[tex]\sf 11x-8x = 99[/tex]
simplify
[tex]\sf 3x = 99[/tex]
divide both sides by 3
[tex]\sf x = 33[/tex]
As the integer is positive, x = 33, then another will be 33 - 9 = 24.
convert the radio to a percent
Answer:
62.5%
Step-by-step explanation:
We only have the measurement of 2 corresponding sides AE and A'E'. We are going from the large to the small.
Let x = the scale factor
4x = 2.5 Divide both sides by 4
x = .625 to change that to a decimal multiply by 100
.625 x 100 = 62.5%
Choose the estimate closest to the length of a pen: 30cm, 160mm, or 16mm.
The estimate closest to the length of a pen is 160mm
How to estimate the closest length of a pen?Estimation is when we use approximate values in a calculation to give an approximate, predicted answer rather than an exact answer.
We can estimate some lengths and distances using approximate values for measurements.
For example, 16 cm is approximately the length of a pen.
Therefore, the estimate of a pen is 16 cm.
Since the length in cm is not in the option, we have to convert.
Hence,
1 centimetres = 10 millimetres
16 centimetres = ?
cross multiply
estimated length of a pen = 160 millimetres.
Therefore, the estimate closest to the length of a pen is 160mm
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One way to simplify an expression containing trigonometric functions is to first write the expression in terms of
---Select---
and
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only.
One way to simplify an expression containing trigonometric functions is to first write the expression in terms of sines and cosines only.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
The law of cosine.In order to determine the missing side length of a geometric figure with the adjacent and hypotenuse side lengths given, you should apply the law of cosine:
C² = A² + B² - 2(A)(B)cosθ
Similarly, the law of sine can be used to determine the missing side length of a geometric figure with the opposite and hypotenuse side lengths are given:
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
In this context, we can reasonably infer and logically deduce that an expression containing trigonometric functions can be simplified by first writing the expression in terms of sines and cosines only.
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14. A certain real estate agent uses what he calls a step- strategy to sell houses. He puts a house on the market at a higher-than - expected selling price and if it hasn't sold in two weeks, he drops the price by 5%. If it still hasn't sold in another 2 weeks , he drops the price by another 5 %. After that , he continues to drop the price by 3% every two weeks until it reach es a cut -off amount assigned by the home owner , or the house sells , whichever comes first . If a house is originally listed at $200,000 and the homeowner sets a cut -off amount of $166,000 , what is the final selling price given that the house sells after being on the market for 9 weeks ? A ) $162,901.25 B) $164,737.48 $166,000.00 D ) $169,832.45
Answer:
vvvyaz
Step-by-step explanation:
szahvzlvzlz
Kim drew a map of Mississippi Rive. The scale was 5 centimeters represents 120 mikes. Th as tusk length is 2320 miles. What is actual length in centimeters of the Mississippi River?
The actual length of the river on centimetres is 97 centimetres
How to find the length of the Mississippi River using the scale?The scale was 5 centimetres represents 120 miles.
Therefore, on the scale
5 centimetres = 120 miles
Now, let's find the length in centimetres if the river is measured as 2320 miles.
120 miles = 5 centimetres
2320 miles = ?
cross multiply
actual length of the river in centimetres = 2320 × 5 / 120
actual length of the river in centimetres = 11600 / 120
actual length of the river in centimetres = 96.6666666667
actual length of the river in centimetres = 97 centimetres.
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Given n(J) = 255, n(K) = 186 and n(J ∪ K) = 429, find n(J ∩ K).
Answer:
12
Step-by-step explanation:
[tex]n(J \cap K)=n(J)+n(K)-n(J \cup K) \\ \\ =255+186-429 \\ \\ =12[/tex]
What are the scale factors
Answer:
10 if going from the smallest to the largest or 1/10 if going from the smallest to the largest.
Step-by-step explanation:
Let s = scale factor
10s = 100 Divide both sides by 10
s = 10
The price of 3 citrons and 4 fragrant wood apples is 51 units. The price of 4 citrons and 3 fragrant wood apples is 54 units. Find the price of a citron and the price of a wood apple.
Answer:9 citronella and 6 fragrant wood apples
Step-by-step explanation:
Please help me
Find the slope of the line on the graph
Answer:
slope = 6/10
Step-by-step explanation:
Point 1: (0,2)
Point 2: (10,8)
m= Slope= Rise/run = (y2-y1)/(x2-x1) = (8-2)/(10-0) = 6/10
The function f is given in three equivalent forms.
Which form most quickly reveals the y-intercept?
Choose 1 answer:
Answer:
c
Step-by-step explanation:
C is straight forward that the value of the y intercept is 8, unlike the A and B where you must first simply by removing the brackets
1) determine the result when 2x^2+4x+2 is subtracted from 4x^2-8x+3
Answer:
[tex]2x^2 - 12x + 1[/tex]
Step-by-step explanation:
Hello!
Given the expression: [tex]4x^2 - 8x + 3 - (2x^2 + 4x + 2)[/tex]
Simplify by combining like terms.
Like terms are terms with the same variable and raised to the same power.
Simplify[tex]4x^2 - 8x + 3 - (2x^2 + 4x + 2)[/tex][tex]4x^2 - 8x + 3 - 2x^2 - 4x - 2[/tex][tex]4x^2 - 2x^2 - 8x - 4x +3 - 2[/tex][tex]2x^2 - 12x + 1[/tex]The simplified form is [tex]2x^2 - 12x + 1[/tex].
Evaluate the following expression: (3x+2)+5
Answer:
3x + 7
Step-by-step explanation:
Hope this helps you :)
In the given figure AB = AC, BAD = 50 and AD = AE. find the value of x
Answer:
[tex]x=25^o[/tex]
Step-by-step explanation:
Angle sum of a triangle: [tex]< A + < B+ < C=180^o\\[/tex]
Types of Triangles: Isosceles, Equilateral, Scalene
Given AB = AC are two sides of the big triangle, then ΔABC is Isosceles.
Isosceles triangles are defined to have two equal sides and two equal angles (opposite the congruent(equal) sides).
Also, since ABC is defined as a triangle, BC is a straight line, a.k.a., it is a [tex]180^o[/tex] angle. As the image shows, the line, AD creates a right angle on one side, therefore it creates a right angle([tex]90^o[/tex]) on the other side.
Back to Isosceles Triangles, AD = AE means ΔADE is isosceles and <ADE = <AED
Using the Angle sum formula of a triangle, you can fill in <A, <B, and <C with the following:
<A=[tex]50^o[/tex]
<B=<C=y [This is because <ADE = <AED]
[tex]50^o+2y=180^o\\2y=130^o\\y=65^o[/tex]
Now, this means that <ADE=[tex]65^o[/tex] and <ADC =[tex]90^o[/tex]
<x is better seen as <EDC
<EDC+<ADE=<ADC
Since we know <ADE is 65 and <ADC is 90, we can plug in these to the formula above.
[tex]x+65^o=90^o\\x=25^o[/tex]
how to write 673465 in standerd form
6 hundred and 73 thousand and 65..
Write each number in standard form.
2. eight and fifty-nine hundredths
3. seven and three thousandths
1
4.3 +2× +4×
1,000
The values given in standard form are 8.59 and 7.003
Writing in standard formThe standard form of a number is a way of writing the number in a form that follows certain rules. Any number that has exponents and decimals is said to be a standard notation.
Given the following statements
eight and fifty-nine hundredths
8 + 59/100
8 + 0.59
8.59
For the expression seven and three thousandths
7 + 3/1000
7 + 0.003
7.003
Hence the values given in standard form are 8.59 and 7.003
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Can someone please help me does anyone know the rest of the problem I can’t sloved please help
The equation of the given function will be h=-0.096x+30.6. The mass will be 63.5 grams.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
1.) The slope of the given function will be,
Slope = (25.8 - 30.6) / (50 - 0) = -4.8/50 = -0.096
Now, substitute the values in the general linear equation,
h = -0.096x + c
30.6 = -0.096(0) + c
c = 30.6
Therefore, the equation of the given function will be h=-0.096x+30.6.
2.) Mass when the height is given as 24.5 cm, will be,
h = -0.096x + 30.6
24.5 = -0.096x + 30.6
24.5 - 30.6 = -0.096x
-6.1 = -0.096x
x = -6.1/-0.096
x = 63.5
Hence, the mass will be 63.5 grams.
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Can someone help me pls
Answer:
See below
Step-by-step explanation:
2) a number v divided by 12
how many real solutions does 3x² +24x = -48 have
Answer:
1
Step-by-step explanation:
3x² +24x = -48
3x² +24x + 48 = 0
x² +8x + 16 = 0
By using cross multiplication,
(x-4)² = 0
Therefore,
x-4 = 0
x = 4 (repeated)
Answer:
Only one real solution
Step-by-step explanation:
[tex]{ \tt{ {3x}^{2} + 24x = - 48}} \\ { \tt{ {3x}^{2} + 24x + 48 = 0 }} \\ { \tt{ {x}^{2} + 8x + 16 = 0}} \\ { \tt{(x + 4) = 0}}
Answer this question please
The solution to the inequality is w ≥ 470 or w ≤ 530
How to determine the solution to the inequality?The given parameters are:
Number of words = 500
Absolute deviation = 30
Acceptable number of words = w
The absolute value inequality is represented as
|w - Number of words| ≥ Absolute deviation
So, we have
|w - 500| ≥ 30
Remove the absolute bracket
So, we have
w - 500 ≥ -30 or w - 500 ≤ 30
Add 500 to both sides of the inequality
So, we have
w ≥ 470 or w ≤ 530
Hence, the solution to the inequality is w ≥ 470 or w ≤ 530
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Which of the following numbers is irrational? -4.8237, pi/2, the square root of 4 to the third power, or 4 + the square root of 25
Answer:
Did you already get the answer?
Step-by-step explanation:
Which number sentence is not true?
A) -4.51 4.5
B) |0| < |-45|
C) |45|> 0
D) 14.5| |-45|
Question
If the point (1, 4) is on the graph of an equation, which statement must be
true?
о A. The values x= 1 and y = 4 are the only values that make the
equation true.
O B. The values x = 1 and y = 4 make the equation true.
C. There are solutions to the equation for the values x= 1 and x = 4.
OD. The values x = 4 and y = 1 make the equation true.
SUBMIT
(23)n=(1111)2 what is the value of n
Answer:
Hello,
n=6
Step-by-step explanation:
1111 in binary is 15 in décimal
(23) base n=15 ==>
2*n+3=15
2n=12
n=6
one seventh times the absolute value of the quantity x minus 3 end quantity minus 2 equals 9
The solutions of "one seventh times the absolute values of the quantity x minus 3 minus 2 equals 9" is 80 and -74
The absolute value of the quantity x minus 3 = |x-3|
The one seventh time the absolute value of the quantity x minus 3 minus 2 equal to 9
Then the equation will become
(1/7)×|x-3|-2=9
Solve the equation
(1/7)×|x-3|-2= 9
(1/7)×|x-3|= 11
|x-3| = 11×7
|x-3|= 77
The absolute value equation will become
x-3= 77
x-3 = -77
Solve both equation
x-3=77
x= 80
x-3 = -77
x= -74
Hence, the solutions of "one seventh times the absolute values of the quantity x minus 3 minus 2 equals 9" is 80 and -74
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aaron, brandon, and clara sit in class so that they are at the vertices of a triangle. it is 15 feet from aaron to brandon, and it is 8 feet from brandon to clara. give the range of possible distance from aaron to clara
The range of distance between Aaron and Clara is 7<d<23.
What is the triangle?Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The sum of the triangle's three angles equals 180 degrees. Every triangle has three sides and three angles, which may or may not be the same. In the case of a right triangle, the sides are given special names, with the side opposite the right angle being known as the hypotenuse and the other two sides being known as the legs.The range of possible distance from Aaron to Clara:
15+d > 8 ⇒ d > -78+d > 15 ⇒ d>715+8 > d ⇒ d < 23So, the range is: 7<d<23
Therefore, the range of possible distance from Aaron to Clara is 7<d<23.
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To convert kilograms to pounds, Abby halves the number of kilograms, n, then subtracts 10% from the result of that calculation, whereas Renato subtracts 10% first and then halves the
result. (a) Write an algebraic expression for each method.
Abby's expression:
Renato's expression:
(b) Do the methods give the same answer?
Abby's method and Renato's method of converting kilograms to pounds gives the same answer.
Algebraic expressionNumber of kilograms = nAbby:
1/2n - 10%
= 1/2n - 0.1
Renato:
-10% + 1/2n
= -0.1 + 1/2n
Therefore, Abby's method and Renato's method of converting kilograms to pounds gives the same answer.
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Translate the point (5, -3) 3 units left and 1 unit up.
The image point is located at ____.
Answer:
(2,-2)
Step-by-step explanation:
help me please I need a good grade
Answer: x=32
Step-by-step explanation:
x-7+2x+1=90
x+2x-7+1=90
3x-6=90
3x=96
x=32