2 consecutive integers with the product of 702 are 27 • 26, or since the question doesn’t specify whether it should be positive or negative, it could also be (-27) • (-26)
Final answer:
The two consecutive integers whose product is 702 are found by solving the quadratic equation n² + n - 702 = 0. Factoring the equation leads to the integers 26 and 27.
Explanation:
To find two consecutive integers whose product is 702, we can denote the first integer as 'n' and the second as 'n+1'. Then the equation to represent their product is n(n+1) = 702. To find the value of 'n', we solve the quadratic equation
n² + n - 702 = 0.
Factoring the quadratic equation, we look for two numbers that multiply to -702 and add up to 1. We find that 26 and -27 meet these criteria. So the equation factors to (n + 27)(n - 26) = 0. The two possible values for 'n' are -27 and 26.
The two consecutive integers are 26 and 27 because -27 gives negative integers which do not result in a positive product of 702. Therefore, the two consecutive integers whose product is 702 are 26 and 27.
your friend says the sum of two linear expressions is always a linear expression. is your friend correct? explain.
Final answer:
The statement that the sum of two linear expressions is always a linear expression is correct, due to properties such as additivity and commutativity. Adding like terms and constants of two linear expressions together will yield another linear expression. This principle applies to linear equations and functions as well.
Explanation:
Your friend's assertion that the sum of two linear expressions is always a linear expression is correct. A linear expression is generally of the form αx + β, where α and β are constants and x is the variable. When adding two linear expressions, say αx + β and γx + δ, the result is (α+γ)x + (β+δ), which is also a linear expression. This is due to the additive property, which states that like terms can be added and constants can be added separately. Also, considering the commutative property of addition, which implies A+B = B+A, we can see that the order of addition does not affect the linearity of the expression.
Examples or specific cases also illustrate this concept. For instance, if one linear expression is 3x + 2 and the other is 5x + 4, adding them together yields (3+5)x + (2+4), which simplifies to 8x + 6, clearly a linear expression. The linear nature of the sum is further illuminated by considering functions or equations that involve only constants. If one function equals a constant and another equals a constant, their sum is also constant, preserving linearity.
In the context of linear differential equations, the principle that linear combinations of solutions are also solutions applies. This means that if we have two functions that are solutions to a linear differential equation, their sum (a linear combination) will also be a solution to the same linear differential equation. This indicates that linearity is preserved when combining linear items, whether they are expressions, functions, or equations.
Luis rides his bicycle 34 mile in 5 minutes, or 112 hour, along the bike trail. Assuming he rides at a constant rate, what is his speed, in miles per hour?
Answer:
[tex]408\frac{miles}{hour}[/tex]
Step-by-step explanation:
we know that
To find the speed divide the total distance by the time
so
[tex]\frac{34}{(1/12)}=34*12=408\frac{miles}{hour}[/tex]
Answer question please
given 4y = 2x - 10 and y = 6, then
2x - 10 = 24 ( add 10 to both sides )
2x = 34 ( divide both sides by 2 )
x = [tex]\frac{34}{2}[/tex] = 17
what is the product of −1/8*(1/8)
−1/8*(1/8) =
-(1/8)² =
-1/64
A function is defined as {(0, 1), (2, 3), (5, 8), (7, 2)}. Isaac is asked to create one more ordered pair for the function. Which ordered pair can he add to the set to keep it a function? please help.
1) (0, 2)
2) (1, 3)
3) (5, 3)
4) (7, 0)
Correct answer is option(2).
Isaac can add the ordered pair (1, 3) to the set to keep it a function.
A function is a relation where each input (or domain element) is associated with exactly one output (or range element).
This means that in the set of ordered pairs representing a function, no two pairs can have the same first element (input) but different second elements (outputs).
Given the function defined as : {(0,1),(2,3),(5,8),(7,2)},
we need to add one more ordered pair without violating the property that each input maps to exactly one output.
Let's examine each option:
1.) (0, 2) : This pair has the same first element as (0, 1). Adding (0, 2) would imply that the input 0 maps to both 1 and 2, which is not allowed in a function because each input must map to exactly one output.
2.) (1, 3) : This pair has a first element of 1, which is not present in the original set of ordered pairs. Therefore, adding (1, 3) does not create any conflicts. The input 1 is not repeated, so each input still maps to exactly one output. This maintains the function property.
3.) (5, 3) : This pair has the same first element as (5, 8). Adding (5, 3) would imply that the input 5 maps to both 8 and 3, which violates the definition of a function.
4.) (7, 0) : This pair has the same first element as (7, 2). Adding (7, 0) would imply that the input 7 maps to both 2 and 0, which also violates the definition of a function.
Therfore , Only the pair (1,3) can be added to the set without violating the function property. This pair introduces a new input that does not conflict with the existing inputs in the set.
what is the area of a square
The answer would be 108 because you multiply the 9 and the 12 together and get 108. I hope this helps.
Draw a figure that contains at least three angles and requires three letters to name each angle PLEASE HELP
You can draw a triangle or a quadrilateral since they have at least three angles. For the second part, any angle can be named with three letters. After naming each corner/angle of the figure, name an angle so that the actual angle letter is the middle letter, surrounded by the letters of the corners that is just next to it.
There are Infinite number of figure , that contains at least three angles and requires three letters to name each angle
1.Any of the Triangle, either Acute, Obtuse, Right, Scalene, Isosceles, or Equilateral.
2. Any of the Quadrilateral, Parallelogram,Rectangle, Square, Trapezoid, and Kite.
→Or In General
Any of the Polygon whether it is Regular or Irregular.
→Because, A polygon is defined as ,a simple closed figure made up of three or more line segment.
A student works no more than 25 hours each week at a part-time job. Write an inequality that represents how many hours the student can work each day. (how do you solve this)
Given that a student works no more than 25 hours per week, and that work is performed every day of a 7-day week, the maximum number of hours they can work per day is approximately 3.57, making it fair to say they can work up to 3 hours each day. This scenario can be represented by the inequality h ≤ 3.
Explanation:To answer your question, we need to find an inequality that represents how many hours the student can work each day given they work no more than 25 hours every week.
If we assume a typical week encompasses 7 days, and the student works every day of the week, then we should distribute the maximum hours worked per week over these seven days.
This results in 25 hours ÷ 7 days ≈ 3.57 hours/day. However, since you can't work a fraction of an hour, the student can work up to 3 hours a day.
The inequality representing this scenario would be h ≤ 3, where 'h' represents the number of hours the student can work each day.
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20 POINTS
Select equivalent or not equivalent to indicate weather the expression above is equivalent or not equivalent to the values or expressions in the last column
The correct expressions are as follows:
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]
[tex]\texttt{ }[/tex]
Further explanationLet's recall following formula about Exponents and Surds:
[tex]\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }[/tex]
[tex]\boxed { (a ^ b) ^ c = a ^ { b . c } } [/tex]
[tex]\boxed {a ^ b \div a ^ c = a ^ { b - c } }[/tex]
[tex]\boxed {\log a + \log b = \log (a \times b) }[/tex]
[tex]\boxed {\log a - \log b = \log (a \div b) }[/tex]
Let us tackle the problem!
[tex]\texttt{ }[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7^2)^{\frac{7}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7)^{2\times \frac{7}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5} + \frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{15}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{3}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{343}[/tex]
[tex]\texttt{ }[/tex]
From the results above, it can be concluded that the correct statements are:
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]
[tex]\texttt{ }[/tex]
Learn moreCoefficient of A Square Root : https://brainly.com/question/11337634The Order of Operations : https://brainly.com/question/10821615Write 100,000 Using Exponents : https://brainly.com/question/2032116Answer detailsGrade: High School
Subject: Mathematics
Chapter: Exponents and Surds
Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.
Answer:
equivalent
not equivalent
equivalent
not equivalent
-step explanation:
39,189 rounded to nearest thousand
To round 39,189 to the nearest thousand, we need to look at the digit in the hundreds place. If the digit in the hundreds place is 5 or greater, we round up, if it is less than 5, we round down. In this case, 1 is less than 5, so we round 39,189 down to 39,000.
Explanation:To round 39,189 to the nearest thousand, we need to look at the digit in the hundreds place. In this case, it is 1. If the digit in the hundreds place is 5 or greater, we round up to the next thousand. If it is less than 5, we round down to the current thousand. Since 1 is less than 5, we round 39,189 down to 39,000.
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BRAINLIEST ANSWER!! The product of 3, and a number increased by seven, is -36. Translate the equation, then solve.
Product is multiplication.
Let the number = x
3 *( X+7) = -36
Use distributive property:
3x +21 = -36
Subtract 21 from each side:
3x = -57
Divide both sides by 3:
x = -57 /3
x = -19
Check: 3 * (-19 +7) = 3 * -12 = -36
The number is -19
What is 4 divided by 28 in long division
This is fast and easy, hope this helps :)
The quotient of 4 divided by 28 is 0.142857.
To perform long division for 4 divided by 28, follow these steps:
1. Write 4 as the dividend and 28 as the divisor.
___
28 | 4
2. Determine how many times 28 can be divided into 4 without exceeding it. In this case, 28 cannot be divided into 4, so we write 0 above the division line.
0
___
28 | 4
3. Multiply the divisor (28) by the quotient (0), and write the product below the dividend.
0
___
28 | 4
0
4. Subtract the product from the dividend. In this case, 4 minus 0 is 4.
0
___
28 | 4
0
----
4
5. Bring down the next digit from the dividend, which is 0.
0
___
28 | 4
0
----
40
6. In this case, 28 can be divided into 40 once, so we write 1 above the division line.
01
___
28 | 4
0
----
40
7. Multiply the divisor (28) by the quotient (1), and write the product below the 40.
01
___
28 | 4
0
----
40
28
8. Subtract the product (28) from the 40.
01
___
28 | 4
0
----
40
28
----
12
9. The final quotient is 0.142857.
Therefore, 4 divided by 28 equals 0.142857.
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Marrisa bought 12.8 pounds of potatoes at $1.35 per pound. How much did Marissa spend for the potato’s
12.8 * 1.35 =17.28
Therefore Marissa spent $17.28 on potatoes.
Hope you have a good day!!! Cant wait until friday lol
She spent 17.28$, all you have to do is 12.8 x 1.35 = 17.28, hope this helps :D
Which of the following is NOT true about unit rates?
A.
A unit rate relates a quantity to 1.
B.
Unit rates can be used to compare two rates.
C.
Any rate is equivalent to its unit rate.
D.
A unit rate always relates quantities with the same units.
Answer:
The answer is 4) A unit rate always relates quantities with the same units.
Step-by-step explanation:
It cannot be 1 because a unit rate relates a quantity to 1. Hence the word unit which means single or undivided whole.
It cannot be 2 because you can indeed use unit rates to compare two rates. In fact we do all the time in math! Just like comparing fractions.
It cannot be 3 because the rate has to be equivalent to its unit rate or else its wrong.
Thus making it four!
Hope this helped! If it did please consider marking this as brainliest! :)
Option D is not true about unit rates.
Unit rate is simply a rate that has the denominator as 1. For example, if we want to write the rate at which water is poured per sec. If the speed is 7 m/s, then we can say the rate is 7m per 1 second. Option A; This statement is true because as seen in the speed rate earlier explained, unit rate relates a quantity to one because it only has its denominator as one. Option B: Statement is true because unit rates of similar units are often compared with each other. For example if we want to know which person has a higher speed every second while running a race. Option C: This statement is correct because like said in option B explanation above, unit rates must have same units otherwise, it is no longer a unit rate as different units could lead to different unit rates.Option D: This statement is not correct because unit rates does not always relate quantities with same units.Read more at; brainly.com/question/8406966
Steve packed 350 containers of mealworms for the fishing store. Of those containers, 237 hold 6 mealworms each. The rest of the containes hold 8 mealworms each. How many mealworms did he pack in all.
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x represent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can Sharla afford the down payment with the money she earns selling her necklaces? Explain your answer
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x represent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can Sharla afford the down payment with the money she earns selling her necklaces? Explain your answer
this is the wrong subject
A) 25x+15y=650
25x+15(40)=650
Or it could be 25x=650 and 15y=650
B) No because she makes $15 for every necklace which she only has 40 necklaces 15x40=600
6. Given the following equation , write a real-life problem about a gym that could be modeled by this equation. Remember to identify your variables.
No equation is given .
1.8499x10^9 move the decimal right 9 places
1.8499 × 10^9 = 1,849,900,000
To convert 1.8499 × 10^9 by moving the decimal nine places to the right, you get 1,849,900,000. This is achieved by shifting the decimal point and adding zeros as needed.
To move the decimal nine places to the right for the number 1.8499 × 10^9, you follow these steps:
Start with the number 1.8499Move the decimal point nine places to the right: 1,849,900,000.If there aren’t enough digits, add zeros as necessary.Thus, 1.8499 × 10^9 in standard notation becomes 1,849,900,000.
lin measured the diameter of a circle in two different directions. Measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm. Explain sone possible reasons why these measurements differ.
Answer:
Diameter of circle while measuring vertically=3.5 cm
Diameter of circle while measuring Horizontally=3.6 cm
As you have not written by which instrument from geometry box you have measured the length of diameter.
1. By Scale i.e ruler 2. By Divider Or 3. By mere Observation i.e by comparing length
1.If you have done measurement by simply observation there are maximum possibility of having error.
2. Then if you have measured these lengths by scale or ruler there is very less chances of getting error in measurement of length because sometimes divison in scale varies i.e if a point lies between 4.5 to 4.6 we can't say exactly whether it is 4.5 or 4.6.
3. So it is better to compare line segments by Divider.There is no chances of getting error.
Most probably you have measured Diameter by ruler, Due to that you have faced the problem.
Answer:
The possible reasons are shown below:
The shape is not a perfect circle as it is difficult to draw a perfect circle.Measurements could be rounded, not exact.It may be possible that the thickness of the circle affected the measurement.The length of vertical measurement is small, so may be she did't measure across the widest part when she is measuring vertically.Step-by-step explanation:
Consider the provided information.
lin measured the diameter of a circle in two different directions. Measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm.
The diameters of a circle should have the same length, If the length are not same then the reasons can be:
The shape is not a perfect circle as it is difficult to draw a perfect circle.Measurements could be rounded, not exact.It may be possible that the thickness of the circle affected the measurement.The length of vertical measurement is small, so may be she did't measure across the widest part when she is measuring vertically.Write an inequality for each description.
1) Thirty subtracted from four times a number is greater than the opposite of ten.
And the 2nd one in the picture
1: Thirty subtracted from four times a number is greater than the opposite of ten.
Let the number be x, so equation becomes : [tex]30-4x>-10[/tex]
2: Given equation is [tex]27-2b\leq-6[/tex] this states that the result of 27-2b is less than equal to opposite of six.
|x-2|-5 <-2 help!!!!!!!!!!!
[tex]|x-2|-5 <-2 \\\\|x-2|<3\\\\x-2<3 \wedge x-2>-3\\\\x<5 \wedge x>-1\\\\x\in(-1,5)[/tex]
Each jar contains 55 buttons. There are 16 jars on the shelf. How many buttons are there altogether
how could you estimate the sale price of items that are 1/4 off
Multiply the original price by .25, then subtract that answer from the original price.
Hope I could help! :)
there are 6 cans in the box . there are 4 boxes how many cans in total
24 cans in total is your answer
6 times 4
6 · 4 = 24
24 cans in total
Help Immediately! 98 points!!!!!!!
Which of the following would eliminate the variable on the left side of the given equation?
36 - 19w = -6w + 41
add -19w
add 6w
add 19w
add -36
the answer is a add -19w and dont forget to do it on each side
You should put brainliest to the other person that answered this question.
szybko pomocy wykonaj mnożenie i zredukuj wyrazy podobne (x-4) (x-3) + (2-x) (x-1).
(x - 4)(x - 3) + (2 - x)(x - 1)
= x² - 3x - 4x + 12 + 2x - 2 - x² + x
= x² - x² -3x - 4x + 2x + x +12 - 2
= 0 -4x +10
Answer: -4x + 10
One of the fastest recorded speeds of the elephant is 6.9 m/s. Approximately, what is this speed in kilometers per hour? [1 kilometer = 1,000 meters] [1 hour = 60 minutes = 3,600 seconds]
To answer this question, we know that 1km equals 1000m
and 1 hour is equal to 60 minutes. In the same way 1 minute equals 60 sec onds
So we have to change the units of elephant speed to km per hour.
For this we do the following procedure:
1) we multiply 6.9 m / s by the conversion factor from meters to kilometers (1 km / 1000m)
[tex]6.9 \frac{m}{s} *\frac{1 km}{1000 m}=0.0069\frac{km}{s} \\[/tex]
2) The result obtained is multiplied by the conversion factor from seconds to minutes (60s / 1min)
[tex]0.0069 \frac{km}{s} *\frac{60 s}{1 min}=0.414 \frac{km}{min}\\[/tex]
3) The result obtained is multiplied by the conversion factor from minutes to hours (60min / 1hr)
[tex]0.414\frac{km}{min}*\frac{60 min}{1 h}= 24.84\frac{km}{h} \\[/tex]
The answer is 24.84 km / h
You can skip step 2) multiplying 0.0069 km / s by the conversion factor from seconds to hours (3600 s / 1h)
helpppp
x + 9 = 18 + -2x
x+9=18+-2x
divide 2x from both sides
which makes it 3x+9=18
subtract 9 from the 18
which is 3x=9
divide 3 from both sides
which gives you x=3
x+9=18+(-2x) add the 2x to the x and you should get 3x+9=18. Then you would subtract the 9 from the 18 and should get 3x=9. Then just divide the 9 by the 3 and get x=3 which is your answer. Hope this helps!
Please help I really need to give this in tomorrow I will give you a thanks please
(a) Lily: 5 * 2 - 12 + 3 = 1 pt
(b) Rose: -3 * 2 -1 + 6 + 7 = 6 pts
(c) Rose
A diver went down 25.75 feet below the surface of the ocean, and then 17.5 feet further down, he then rose 12.75 feet. Enter and solve an expression to find the diver's new depth.
The answer would be -30.75 hope this helps !!