The three positive integers are 34, 35, 36
Three positive integers are given as (x-1),x and (x+1)
Sum of these three integers are 105,
As we know the total sum of the three positive integers, we can get the value by adding the three integers to the sum value.
Thus,
(x-1) + x + (x+1) = 105
x - 1 + x + x + 1 = 105
3x + 0 = 105
3x = 105
x = 105/3
x = 35
Then, the integers are (35 - 1) , 35 , (35 + 1)
Therefore, the three positive integers are 34, 35, 36
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Confused on how to solve this
The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.
What is the limit?The value that approaches the output for the given input value. Limits are a very important tool in calculus.
The graph of the function is shown below.
The function is a piecewise function. The function is continuous between o to a, a to b, and b to till ∞.
The value of the function at b will be 1 which can be shown as,
[tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex]
The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.
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a jet plane traveling at 480 mph overtakes a propeller plane traveling at 200 mph that had a 3 hour head start. how far from the starting point are the planes?
The distance of both the planes from the starting point will be 1029 miles.
This is a question of time, speed and distance.
Given that:-
Speed of jet plane = 480 mph
Speed of propeller plane = 200 mph
Also, the propeller plane has a 3 hour head start.
We have to find the distance of both the planes from the starting point.
When the jet plane overtakes the propeller plane both of them would have covered the same distance.
Let the time taken by the jet plane to overtake the propeller plane be t hours.
Hence, the propeller plane would have travelled for (t+3) hours.
Hence, we can write,
480*t = 200*(t+3)
480t = 200t + 600
280t = 600
t = 600/280 = 15/7 hours.
Hence, distance from both the planes from the starting point = (15/7)*480 = 1028.57 miles = 1029 miles.
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f(x)= 2x-7/3x-4
Vertical and horizontal asymptotes.
We need to know about asymptotes to answer this question. The vertical asymptote is x=4/3 and the horizontal asymptote is y=2/3
When the graph of a function lies very close to the axis and extends to infinity it is called an asymptote. Vertical asymptote is a vertical line that directs but does not form a part of the graph of a function. Horizontal asymptote is a horizontal line that shows how the function behaves at extreme edges. Horizontal asymptote exists for functions whose numerator and denominator have same degree or degree of numerator is less than numerator of denominator.
f(x)=2x-7/3x-4
The horizontal asymptote of the function can be given by dividing the leading coefficients.
HA=2/3
The vertical asymptote can be found by equating the denominator to zero.
3x-4=0
x=4/3
Therefore the horizontal asymptote is y=2/3 and the vertical asymptote is x=4/3.
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At a constant temperature, the atmospheric pressure p in pascals is given by the formula p=101.3 e⁻⁰.⁰⁰¹h , where h is the altitude in meters. What is p at an altitude of 500 m ?
At an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.
The exponential constant, denoted by the symbol e, is an essential mathematical constant. Its value is approximately equal to 2.718. This value occurs very frequently in mathematics when it is used to model physical and economic phenomena.
Here, we are given an exponential function- p = 101.3[tex]e^{-0.001h}[/tex]
where p = atmospheric pressure in pascals
h = altitude in meters.
If the altitude is 500m
h = 500
Then,
p = 101.3 [tex]e^{-0.001 * 500}[/tex]p
= 101.3 [tex]e^{-0.5}[/tex]p
= 101.3/ [tex]e^{-0.5}[/tex]p
= 101.3/ 1.648p
= 61.46
Thus, at an altitude of 500 meters, the atmospheric pressure (p) will be 61.46 pascals.
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Model with mathematics. Graph the fraction -1 2/5 on the number line.
The fraction -1 2/5 is modeled on the number line by: graph A.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
In this scenario, we can reasonably infer and logically deduce that the fraction -1 2/5 is modeled on the number line by graph A because each interval increases by 2/5 or 0.4.
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Write an equation for the parabola in vertex form whose vertex is at (2, 3) and passes through (0, 2).
The equation of the parabola in discuss such that the parabola has a vertex at (2, 3) and passes through (0, 2) is; y = (-1/4) (x - 2)² + 3.
What is the equation of.the parabola in discuss whose vertex is at (2, 3) and passes through (0, 2)?It follows from the task content that the equation of the parabola whose vertex is at (2, 3) and passes through (0, 2) is to be determined.
Since, the vertex form equation of a parabola is;
y = a (x-h)² + k
where the vertex is; (h, k) which is (2, 3) in this scenario.
Therefore, we have;
y = a (x - 2)² + 3
Ultimately, to find the value of a; substitute; x = 0 and y = 2 from the point (0,2) into the equation;
2 = a (0-2)² +3
-1 = 4a
a = -1/4.
Ultimately, the equation of the parabola as required in the task content is;
y = (-1/4) (x - 2)² + 3
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Please help me please help me please please
Answer:
Step-by-step explanation:
180-degree rotation
I explained previously, but I will explain again.
A 180-degree rotation is just a switch of signs on the numbers
Explanation:
Replica U=(2, 1) Original U=(-2, -1)PLEASE HELP!!! PLEASE HELP RIGHT NOW ASAP!!!!!
Kevin has a pitcher that holds 2.75 quarts of juice. How many 1.4 quart cups can he fill up with one pitcher of juice?
Find any points of discontinuity for each rational function. y=x+5 / x²+9 x+20
points of discontinuity for each rational function. y=x+5 / x²+9 x+20 is x = -4
Given,
y=x+5 / x²+9 x+20
It can be expressed in the form of -
⇒ y = (x+5) / (x+5) (x+4)
⇒ y = 1 / (x+4)
The function will be undefined if the denominator will be 0
⇒ x+4 = 0
⇒ x = -4
So, we can conclude that the given function will be having points of discontinuity as x = -4
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What are some reasons you should be intentional about saving money? in other words,
Answer:
Step-by-step explanation:
The reason why you should save money because if you spend all of your money you won't able to take care of yourself, your house, or have nothing to do
3. Between which two numbers is √74?
(A) 5 and 6
B) 6 and 7
7 and 8
C
D
8 and 9
Martha spent of her pocket money on
magazines.
She then spent
of what she had left on a
present.
After that, she had £3 left.
How much pocket money did she have to start
with?
Give your answer in pounds (£).
Answer:
Step-by-step explanation:
Martha spent 1/6 of her pocket money on magazines.
Albert invested money into the stock market, and the table represents his earnings. What type of function could be used to model his bank account as a function of time? Justify your answer.
Week Balance ($)
1 1,400.00
2 1,470.00
3 1,543.50
4 1,620.68
This is a linear function because there is a common difference in the balance between the weeks.
This is a linear function because there is a common ratio in the balance between the weeks.
This is an exponential function because there is a common difference in the balance between the weeks.
This is an exponential function because there is a common ratio in the balance between the weeks.
The correct option regarding the bank amount as a function of time is:
This is an exponential function because there is a common ratio in the balance between the weeks.
When a linear function should be used and when an exponential function should be used?A linear function should be used when there is a common difference between the amounts.An exponential function should be used when there is a common ratio between the amounts.For this problem, the differences are given as follows:
1620.68 - 1543.5 = $77.18.1543.5 - 1470 = $73.5.1470 - 1400 = $70.The ratios are given as follows:
1620.68/1543.5 = 1.05.1543.5/1470 = 1.05.1470/1400 = 1.05.Due to the same ratios, an exponential function should be used, and the correct option is given by:
This is an exponential function because there is a common ratio in the balance between the weeks.
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Answer:c
Step-by-step explanation:
What is the difference in the approximate number of wins between the first place team and the last place team?
A. 50
B. 45
C. 40
D. 35
Answer:
65-72
Step-by-step explanation:
The length and width of a rectangle are consecutive odd integers. The perimeter of
the rectangle is 80 centimeters. Find the length and width of the rectangle.
The length of the rectangle = 21 cm
and the width of the rectangle = 19 cm
In this question, the length and width of a rectangle are consecutive odd integers.
Let n, n + 2 be the width and the length of a rectangle.
The perimeter of the rectangle is 80 centimeters.
Using the formula of the perimeter of the rectangle ,
P = 2 × [n + (n + 2)]
80 = 2(2n + 2)
40 = 2(n + 1)
20 = n + 1
n = 19
This means, the width of the rectangle is 19 centimeters.
And the length = n + 2
= 19 + 2
= 21 cm
Therefore, the length of the rectangle = 21 cm
and the width of the rectangle = 19 cm
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What is the solution to x 4 + 4x 3 ≤ 12x 2?
Answer:
16<24
Step-by-step explanation:
4+(4×3)<(12×2)
4+12<24
=16<24
Nathan is planning to ride his bike for 24 minutes if he rides at a rate of 5 miles per hour how far will he travel
The distance that Nathan can ride his bike is 2 miles.
What is the distance Nathan can ride?The rate is the total distance per time. Rate is determined by dividing the total distance travelled by the total time travelled.
Rate = total distance / total time.
Distance = rate x time
The rate is in miles per hour while the time given is in minutes. Thus, minutes has to be changed to hour. To do this, divide 24 minutes by 60.
60 minutes = 1 hour
24/ 60 = 2/5
Distance = 2/5 x 5= 2 miles
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Find the value of x and A C if B is between points A and C. (Lesson 1-2)
A B=12, B C=8 x-2, A C=10 x
If B is collinear and between points A and C, then the value of x is 5 and the value of AC is 50.
Collinear points refers to the points that lies on the same straight line.
If B is collinear with points A and C, and lies between them, then the sum of the distance from A to B and the distance from B to C is equal to the distance from A to C.
AB + BC = AC
Given:
AB = 12
BC = 8x - 2
AC = 10x
Substitute the expressions given to the equation and solve for x.
AB + BC = AC
12 + 8x - 2 = 10x
8x - 10x = 2 - 12
-2x = -10
x = 5
Substitute the value of x in the expression for AC.
AC = 10x
AC = 10(5)
AC = 50
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I need help with algebra
Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
To solve an algebraic word problem:
Define a variable.
Write an equation using the variable.
Solve the equation.
If the variable is not the answer to the word problem, use the variable to calculate the answer.
To know about algebra you have to know about your Arithmetic.
Remember PEMDAS.
Get Positively Comfortable with Negative Numbers.
Show Your Work.
Don't Let the Letters Scare You.
Formulas Are Your Friends.
Be Sure to Answer the Right Question.
Work Practice Problems.
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Write each equation in logarithmic form.
10⁴=10,000
The equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.
Given that
10^4 = 10000 - - - - - -( 1 )
We have [tex]a^{y}[/tex] = x - - - - - ( 2 )
Comparing ( 1 ) and ( 2 ) we get
a = 10, y = 4, x = 10000
The logarithmic form is written as logₐ (x) = y .It is rearrangement of the exponential form [tex]a^{y}[/tex] = x.
By logarithmic definition
y = logₐ (x)
so we got 4 = log₁₀ (10000)
Therefore, the equation of 10⁴=10,000 in logarithm form will be log₁₀ (10000) = 4.
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The average temperature in the mountains is 65° in April. The average temperature in that same spot is −5° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
Answer:
65 + |-5| = 70, 65 is the farthest away from 0
Step-by-step explanation:
Tom Harris is twenty-four years old. He wishes to purchase $7,000 of a ten-year term insurance. What will be his annual premium?
The annual premium of Tom Harris is $29.05
What is annual premium?Annual premium is the amount of money that policyholder has to pay in a policy year.
Annual formula = (face value of policy per $1000)* (rate of insurance)
Given that Tom Harris is twenty four years old man want to purchase a $7000 for a ten year term insurance.
From the given table we can say that the rate of insurance for a 24 year old man per $1000 for a 10 year terms is 4.15
Face value of insurance = $7000
Face value of insurance per $1000 = 7000/1000 =$7
Then the annual premium = $7 * 4.15 =$ 29.05
Therefore, the annul premium paid by Tom Harris is $29.05
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If 3(x-2)= 2x+6 then x equals?
Answer:
x = 12
Step-by-step explanation:
First, distribute the 3 into the parentheses:
3(x-2) = 2x+6 ----> 3x-6 = 2x+6
Next, combine like terms by adding 6 to both sides of the equation:
3x-6 = 2x+6 ----> 3x = 2x+12
Then, subtract 2x from both sides:
3x = 2x+12 ----> 1x = 12
Finally, divide both sides by 1 to get x by itself:
x = 12
suppose you want to line pennies up, diameter to diameter, until the total length is 1 kilometer. assume the width of 1 penny is 2 cm. how many pennies will you need? how accurate is this estimation?
Answer: 50,000 pennies
Step-by-step explanation: there are 100,000 centimeters in a kilometer, since a penny is 2 centimeters in length, divide 100,000 by 2 t get 50,000
The point k lies on the segment JL. Find the coordinates of k so that jk is 1/4 of JL L(19,10) J(-1,-2)
(4,5) i'm pretty sure I can't explain why but just go with it
Find the difference.
(9ab+7a-7) (4ab-5)
The difference is 5ab + 7a + 13
What is Arithmetic Operation?An arithmetic operation is specified by combining operands with one arithmetic operator. Arithmetic operations can also be specified by the ADD, SUBTRACT, DIVIDE, and MULTIPLY
given:
(9ab+7a-7) (4ab-5)
So, the difference is
(9ab+7a-7) - (4ab-5)
=9ab + 7a - 7 -4ab + 20
=9ab - 4ab +7a -7 +20
=5ab + 7a + 13
Hence, the difference is 5ab + 7a + 13.
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421 Students go on a field trip. There are 19 vehicles, some vans and some buses. 7 students can fit in a van, and 25 students can fit in a bus.
There were ___ buses.
There were ___ vans.
The number of vans and buses conveying the students to the field trip is 3 and 19 respectively
How to solve number of buses and Vans simultaneouslylet
number of van = xNumber of bus = yx + y = 19
7x + 25y = 421
From (1)
x = 19 - y
Substitute x = 19 - y into (2)
7x + 25y = 421
7(19 - y) + 25y = 421
133 - 7y + 25y = 421
- 7y + 25y = 421 - 133
18y = 288
y = 288/18
y = 16
Substitute y = 16 into (1)
x + y = 19
x + 16 = 19
x = 19 - 16
x = 3
Therefore, there are 3 vans and 16 buses conveying the be students to the field trip.
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A bean plant grew 15 feet in eight days after 16 days the plant was 30 feet tall is the ratio of feet to days equivalent
Based on the height that the bean plant grew after a certain number of days, the ratio of feet to days is equivalent.
How to find equivalent ratios?The bean plant was able to grow 15 feet in 8 days and then doubled to 30 feet when the number of days doubled to 16 days.
The ratio of feet to days can be found as:
(Number of feet after 16 days / Number of feet after 8 days) : 16 days / 8 days
Solving for the ratio of feet to days gives:
30 / 15 : 16 / 8
2 : 2
The ratio of feet to days is the same which means that it is equivalent.
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Luisa sells stuffed animals. She sells a stuffed elephant for $34.90, and the sales tax is 9% of the sale price. About how much is the sales tax on the elephant?
$4.90
$0.32
$4.95
$3.15
Answer: $3.15
Step-by-step explanation: 9% of 34.90 is 3.15
Please help
Which of the following lines is perpendicular to y = 1/4x -3. Select all that apply.
A. Y=4x+9
B. 8x-2y=3
C. 4x-y=-2
D. Y=-4x+6
E. Y=4x
The slope of a line is y=mx+c, where m is the slope. The lines is perpendicular to y = 1/4x -3 is Y=-4x+6.
What is slope intercept form?
The slope of a line is y=mx+c, where m is the slope.
The given line is y = 1/4x -3.
slope m1=1/4.
slope of second line=-(1/m)
=-(1/1/4)
=-4
point slope intercept form is y-y1=m(x-x1)
Equation of the perpendicular line passing through point (0,6) is
y-6=-4(x)
y=-4x+6
Therefore the line perpendicular to y = 1/4x -3 is Y=-4x+6.
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