Answer:
find the three postive consecutive integers such that the product of the smallest and the largest is 17 more than 3 times the median intger
Answer: 5, 6, 7
Step-by-step explanation:
Let three positive consecutive integers equal to x, x+1, x+2
Hence,
[tex]\displaystyle\\x(x+2)-3(x+1)=17\\x^2+2x-3x-3=17\\x^2-x-3-17=17-17\\x^2-x-20=0\\x^2-5x+4x-20=0\\x(x-5)+4(x-5)=0\\(x-5)(x+4)=0\\x-5=0\\x-5+5=0+5\\x=5\in\ (x > 0)\\x+4=0\\x+4-4=0-4\\x=-4\notin\ (x > 0)\\5+1=6\\5+2=7[/tex]
Given f(x) = 2(3 - x) - 2x, what is the value of f(x) = -10?
The value of x for f(x) = 2 (3-x) -2x at f(x) = -10 is 4.
To find the value of f(x) when f(x) equals -10, we substitute -10 into the equation and solve for x.
Given:
f(x) = 2(3 - x) - 2x, we have:
-10 = 2(3 - x) - 2x
Let's simplify the equation step by step:
-10 = 6 - 2x - 2x
-10 = 6 - 4x
-10 - 6 = -4x
-16 = -4x
To solve for x, divide both sides by -4:
x = (-16) / (-4)
x = 4
Therefore, when f(x) = -10, the value of x is 4.
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What number is equal to √9?
Answer:
3
Step-by-step explanation:
x =√9
x= 9½
Multiply both sides by the power of 2
x²=9½*²
x²= 9
x²=3²
x=3
If the length of a certain rectangle is increased by 1, then the area of the rectangle is increased by 12. If instead, the width is increased by 2, then the area of the rectangle is increased by 42. What is the area of the original rectangle?
Answer: Let the length and breadth of a rectangle are x and y units , its area is x.y units^2
Step-by-step explanation: sorry no explanation
Subtract (5.3 x 108) − (8.2 x 106).
2.9 x 102
5.218 x 102
2.9 x 108
5.218 x 108
Answer: 5.218*10^8 ==> Option 4
Step-by-step explanation:
(5.3 x 10^8) − (8.2 x 10^6)=
(5.3*10^2 x 10^6) − (8.2 x 10^6)=
(5.3*100*10^6)-(8.2*10^6)=
(530*10^6)-(8.2*10^6)=
(530-8.2)*10^6=
(530.0-8.2)*10^6=
521.8*10^6=5.218*10^8 ==> Option 4
Which segment (s) are perpendicular to AB?
Answer:
B) Segment CD onlyStep-by-step explanation:
In the plane, there is exactly one perpendicular line to a line from a particular point.
We can see CD is marked as perpendicular segment and there are no more such possible segments.
Correct choice is B.
Answer:
b) Segment CD only
Step-by-step explanation:
Now we have to,
→ find the segment perpendicular to AB.
The segment will be,
→ CD (only)
* As it is 90° from the segment AB, we can say that it is perpendicular to AB.
Hence, option (b) is correct answer.
An airplane that can travel 450 mph in still air, encounters a 30-mph headwind. How long will it take the plane to travel 1050 miles into the wind?
The time plane will take to travel 1050 miles into the wind is 2.5 hours.
What is speed?Speed is defined as the rate of change of position in unit time.
Mathematically,
Speed = Distance/Time
Now given that,
Speed of airplane in still air = 450 mph
Speed of wind = 30 mph
Distance to travel = 1050 miles
So, Actual speed of wind = 450 mph - 30 mph
⇒ Actual speed of wind = 420 mph
So, since Speed = Distance/Time
⇒ Time = Distance/Speed
⇒ Time = 1050/420
⇒ Time = 2.5 hours
Thus, the time plane will take to travel 1050 miles into the wind is 2.5 hours.
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finding the rise and the run on the graph
Answer:
rise = 4, run = 5. The slope would be 4/5
Step-by-step explanation:
You go up by four then right by 5
Use the distributive property to solve the equation. 5x/2-x=x/6-8/3.
Answer:
Step-by-step explanation:
i know
coin $a$ is flipped three times and coin $b$ is flipped four times. what is the probability that the number of heads obtained from flipping the two fair coins is the same?
The probability that the number of heads obtained from flipping the two fair coins is the same is 35/128.
Probability:
Probability means the fraction of favorable outcome and the total number of outcomes.
So it can be written as,
Probability = Favorable outcomes / Total outcomes
Given,
The coin a is flipped three times and coin b is flipped four times.
Here we need to find the probability that the number of heads obtained from flipping the two fair coins is the same.
We know that,
There are 4 ways that the same number of heads will be obtained;
0, 1, 2, or 3 heads.
The probability of both getting 0 heads is
[tex]$\left(\frac12\right)^3{3\choose0}\left(\frac12\right)^4{4\choose0}=\frac1{128}$[/tex]
Probability of getting 1 head,
[tex]$\left(\frac12\right)^3{3\choose1}\left(\frac12\right)^4{4\choose1}=\frac{12}{128}$[/tex]
Probability of getting 2 heads is,
[tex]$\left(\frac12\right)^3{3\choose2}\left(\frac12\right)^4{4\choose2}=\frac{18}{128}$[/tex]
And the probability of getting 3 heads is,
[tex]$\left(\frac12\right)^3{3\choose3}\left(\frac12\right)^4{4\choose3}=\frac{4}{128}$[/tex]
Therefore, the probability that the number of heads obtained from flipping the two fair coins is the same is,
=> (1/128) + (12/128) + (18/128) + (4/128)
=> 35/128.
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PLEASE HELP!!!! IMPORTANT!!!!
a market woman bought n eggs at the rate of 12 eggs at €60. 8 of the eggs were broken so she sold the remaining at the rate of 4 eggs at €24 and made a profit of €12. how many eggs did she buy.
Answer:26 eggs
Step-by-step explanation: yes
The market woman bought 60 eggs.
The market woman bought n eggs at the rate of 12 eggs for €60.
So, the cost price of each egg is given by:
Cost price per egg = €60 / 12 = €5
The total cost of n eggs is the cost price per egg multiplied by the number of eggs (n):
Total cost = €5 * n = 5n
After buying n eggs, 8 of them were broken.
So, the market woman had (n - 8) eggs left to sell.
She sold the remaining eggs at the rate of 4 eggs for €24.
The selling price of each egg is given by:
Selling price per egg = €24 / 4 = €6
The total selling price of the remaining (n - 8) eggs is the selling price per egg multiplied by the number of remaining eggs (n - 8):
Total selling price = €6 * (n - 8) = 6n - 48
The profit is the difference between the total selling price and the total cost:
Profit = Total selling price - Total cost
Since the problem states that the market woman made a profit of €12, we can set up the equation:
6n - 48 - 5n = 12
Solve for n.
Combine like terms:
n - 48 = 12
Add 48 to both sides:
n = 60
So, the market woman bought 60 eggs.
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for #13-14 determine if the lines are parallel, perpendicular or neither 10x +5y=-5 and y=-2x+6
Answer:
48
because. Of the time
√21 √9/√63 indadicate opretion and simplifying
Sorry in my keyboard there is no symbol for squareroot
Alisa has $2.00 in change. If she has 7 quarters, what is the maximum number of dimes she can have?
a) 3² x 3* = 37
Find the value of x.
b) 78 + 7 = 76
Find the value of y.
c) (q¹)² = q¹²
12
Find the value of z.
Marks
z = 3 or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex] is the value of z in linear equation.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.a ) Simplify using exponent rule with same base = a[tex]a^{n} . a^{m} = a^{n + m}[/tex]
Based on the given conditions, corresponding exponents are equal = [tex]3^{2 + x} = 3^{7}[/tex]
Rearrange unknown terms to the left side of the equation = 2 + x = 7
Calculate the sum or difference x = 5
b) Calculate the power 5764801 + [tex]7^{y}[/tex] = 117649
Rearrange unknown terms to the left side of the equation
7^{y} = 117649 - 5764801
The equation is not defined.
c) the equations z = 3 or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]
answer z = 3 or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]
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Which of the following is equivalent to (7y + 5x) + 8x?
35xy + 8y
7y + 13x
8x(7y + 5x)
7y + 40x
Answer:
7y + 13x
Step-by-step explanation:
Let's simplify step-by-step.
7y+5x+8x
Combine Like Terms:
=7y+5x+8x
=(5x+8x)+(7y)
=13x+7y
The expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x which is correct answer would be option (B).
What is algebra?Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.
What is the algebraic expression?
Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.
⇒ (7y + 5x) + 8x
Open parenthesis and combine like terms to get the solution,
⇒ 7y + 5x + 8x
⇒ (5x + 8x) + (7y)
⇒ 13x + 7y or
⇒ 7y + 13x
Therefore, the expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x.
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966500 in scientific notation
9.665 x 10^5
966500.0
Move the dot to the right 5 times
Fine the least common denominator for these fractions. Enter your answer in the space provided. 1/2 and 5/6
Answer: The LCD is 2
Step-by-step explanation: I think that because 2, 4, 6 but I'm not sure. (please don't get mad if I'm wrong)
Answer:
6.
Step-by-step explanation:
Factorise 2 and 6:
2 = 2
6 = 2*3
In calculating the LCM we only use the 2 once, as it is duplicated in the 2 lists of factors.
The LCM = 2 * 3 = 6.
(Note LCM = LCD.)
7. Vernon filled his gas tank with 16 gallons of
gas. The table shows the linear relationship
between the amount of gas remaining in his
tank and the miles driven. What is the rate of
change of gallons of gas per mile driven?
Miles Driven
Gas (gal)
0,16
84,12
105,11
336,0
* coordinates is a chart x representing miles driven y representing gas(gal)
Vernon put 16 liters of gas in his tank. 21 miles per gallons of gas are consumed each mile that is driven.
Given that,
Vernon put 16 liters of gas in his tank.
The table depicts the linear relationship between the mileage driven and the amount of gas in his tank.
We have to find how many gallons of gas are consumed each mile that is driven.
From the table we can say
The total Distance is 336
The total gallons of gas is 16
Rate= Total distance/Total gallons
Rate=336/16
Rate=21 miles per gallons
Therefore, 21 miles per gallons of gas are consumed each mile that is driven.
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Please help due tonight.
Answer: Choice C
This is the result of subtracting 3x from both sides. The inequality sign does not flip. It only flips if we multiply or divide both sides by a negative number.
The list of ingredients for chocolate
brownies given at right will make 16
brownies.
Use the list to decide how much of
each ingredient is needed to make 6
brownies.
2
3
5 ounces unsweetened chocolate
1/2 cups sugar
cup butter
2 teaspoons vanilla
2 eggs
1 cup flour
www
cup(s) of butter is needed.
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)
ounce(s) of chocolate are needed
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)
The following ingredients are needed to make 6 brownies:
Cups of butter needed is 1/4 cups
Ounces of chocolate needed is 1 7/8
Cups of sugar needed is 9/16
Ounces of vanilla needed is 3/4
How much ingredients are needed?
Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero. An example of an integer is -1.
A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator.
Cups of butter needed = (2/3 x 6) / 16
4 / 16 = 1/4 cups
Ounces of chocolate needed = (5 x 6) / 16
= 30 / 16 = 1 14/16 = 1 7/8
Cups of sugar needed = ( 1 1/2 x 6) / 16
(3/2 x 6) / 16 = 9/16
Ounces of vanilla needed = ( 2 x 6) / 16
= 12 / 16 = 3/4
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4x-18=x-3 will give ten points for answer asap
Answer: x=5
Good luck :)
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
The quotient of 4 and the difference of 7 and a number.
Answer:
4/x+x-7
Step-by-step explanation:
1. 4/x
2. x-7
3. adding the two steps
The plan for a concrete birdbath is shown
below. The bowl is a cylinder with a depth
of 10 cm. If the bowl has a diameter of
30 cm, what is the exposed surface area
of the birdbath, including the pillar and
pedestal?
Answer:
Step-by-step explanation
10 cm
Answer: unknwon
Step-by-step explanation:
because height of pillar not given
Ken and Hamid run around a track.
It takes ken 80 seconds to complete one lap
It takes Hamid 60 Seconds to complete one lap
Ken and Hamid start running at the same time from the start line
How may laps will they each run when they next meet on the start line?
It is found that Ken will have run 3 laps and Hamid will have run 4 around a track.
What is prime factorization?Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities. Prime factorization is when all those factors are prime numbers.Thus, prime factorization expresses an integer in terms of multiples of prime numbers.
Prime factorization is unique for each integer.
To determine the number of seconds that will have passed when they meet again. We will use the LCM, or least common multiple, for this.
Thus the prime factorization of each number:
80 = 10(8)
10 = 5(2)
8 = 2(4)
4 = 2(2)
80 = 2(2)(2)(5)(2)
60 = 10(6)
10 = 5(2)
6 = 2(3)
60 = 2(2)(3)(5)
For the LCM,
2(2)(5)(2)(2)(3) = 240
This means every 240 sec; they will both be at the start line.
Since Ken completes a lap in 80 seconds, then he will completes
240/80 = 3 laps in 240 seconds.
Since Hamid completes a lap in 60 seconds, then he will completes 240/60 = 4 laps in 240 seconds.
Hence, It is found that Ken will have run 3 laps and Hamid will have run 4.
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There are 55 stickers in each box how many stickers are in seven boxes
Answer: 385 stickers
Step-by-step explanation:
7 boxes * 55 stickers/1 box=
7 * 55/1=
7*55=385 stickers
Amys weight this year is 50 pounds lessthan twice her weight from last year. if she weighs 120 pounds this year, what equation can be used to find her weight from last year?
Answer:
190
Step-by-step explanation:
(120*2) - 10 = 190
hope this helped !!
Tallie wants to buy a new iPhone. The iPhone costs
$850. She has saved $325 to put down as an initial
payment and will pay another $75 each month until
the phone is paid off. How many months will it take
for Tallie to pay for her new iPhone?
Answer:
7 months to pay it off.
Step-by-step explanation:
see attached for details.
a gas station sells regular gas for $2.10 per gallon and premium gas for $2.90 a gallon. at the end of a business day 280 gallons of gas had been sold, and receipts totaled $652. how many gallons of each type of gas had been sold?
200 gallons of regular gas and 80 gallons of premium gas were sold.
Let the amount of regular gas sold be x gallons. So, the amount of premium gas sold will be (280 - x).
Now, forming the equation using the given information, to find the amount of each type of gallon.
Equation -
2.10x + 2.90(280 - x) = 652
Performing multiplication with values inside bracket in Left Hand Side
2.10x + 812 - 2.90x = 652
Rewriting the equation -
812 - 652 = 2.90x - 2.10x
Performing subtraction
160 = 0.8x
Rewriting the equation according to x
x = 160÷0.8
Performing division to find the value of x
x = 200
So, 200 gallons of regular gas was sold.
Amount of premium gas sold = 280 - 200
Performing subtraction
Amount of premium gas sold = 80 gallons
Hence, 200 gallons of regular gas and 80 gallons of premium gas was sold.
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Calculate the electric potential energy in a capacitor that stores 1.0 x 10^-10 C
of charge at 100.0 V. Use PE = 1/2QAV.
OA. 1.0 x 10-8 J
OB. 1.0 x 102 J
O C. 5.0 × 10¹ J
OD. 5.0 × 10-9 J
The electric potential energy is 5.0 × 10^(-9) J
How to calculate the electric potential energy?
The formula to calculate the electric potential energy in a capacitor is;
E = 1/2 * C * V²
Where;
E = electric potential energy
C = capacitance = charge
V = voltage applied
We are given;
Voltage applied; V = 100 V
Capacitance (Charge) = 1 × 10⁻¹⁰ C
Plugging in the relevant values gives
E = 1/2 * 1 × 10⁻¹⁰ * 100
E = 1/2 * 1 × 10⁻⁸
E = 0.5 × 0⁻⁸ volts
E = 5.0 × 10^(-9) J
Thus, we conclude that the electric potential energy is 5.0 × 10^(-9) J
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