What does it mean to determine the two positive integers that each value is between??? I'm confused
Answers
Answer:
11. {7, 8}
12. {8, 9}
13. {8, 9}
14. {4, 5}
Step-by-step explanation:
You want consecutive integers that bracket each of the given irrational roots.
Square rootsA square root of an integer will be rational only if the integer is a perfect square. The first few perfect squares are ...
1² = 12² = 43² = 94² = 165² = 256² = 367² = 498² = 649² = 81You know these because you know your multiplication tables.
The square root of a number between these perfect squares will lie between the roots of the squares.
11. √5050 lies between the squares 49 = 7² and 64 = 8². That means √50 lies between 7 and 8.
Your calculator tells you that √50 ≈ 7.0710678, which is a number that lies between the integers 7 and 8.
12. √7272 lies between the squares 64 = 8² and 81 = 9². That means √72 lies between 8 and 9.
13. √6565 lies between the squares 64 = 8² and 91 = 9². That means √65 lies between 8 and 9.
14. √2323 lies between the squares 16 = 4² and 25 = 5². That means √23 lies between 4 and 5.
__
Additional comment
The purpose of questions like this appears to be to have you make use of your knowledge of integer perfect squares to guess an approximation of a square root.
A calculator can answer these questions immediately. Of course the two consecutive integers are the integer part of the root, and the next higher integer.
The question is not well-posed. The answer to "integers each value is between" could be 1 < √50 < 50. For integers greater than 1, the square root is always smaller than the integer being rooted. We've seen questions like this enough times that we can guess the intention is for you to identify consecutive integers.
Extra credit
Knowing the integer part of the root and the difference between the number and its next lower perfect square, you can approximate the root as follows:
For integer n = a² +b, the root √n lies between a +b/(2a+1) and a +b/(2a).
For example, 65 = 8²+1, so √65 lies between 8 1/17 and 8 1/16.
Related Questions
During a game of one-on-one, Rodney and Justin scored 39 points altogether. If Justin lost the game by 1 point, how many points did each player score? Use a system of linear equations in two variables to solve the problem
Answers
The points scored by Rodney is 20 points.
The points scored by Justin is 19 points.
How many points did each player score?x + y = 39 equation 1
x - y = 1 equation 2
Where:
x = points scored by Rodney
y = points scored by Justin
In order to determine the points scored by Justin, take the following steps:
Subtract equation 2 from equation 1 :
2y = 38
Divide both sides of the equation by 2
y = 38/2
y = 19 points
To determine the value of x, substitute for y in equation 2
x - 19 = 1
Combine similar terms: x = 19 + 1
Add similar terms together: x = 20
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Solve the linear equation 7x+4^2=12x-8
Answers
Answer:
x = 24/5
Step-by-step explanation:
Solve, 3|x−4|−6≤9.
Graph the solution on the number line.
Answers
Answer:
Step-by-step explanation:
Tom got 72 marks in 8 tests. How much did he get in each test on average?
Answers
Given
Tom got 72 marks in 8 tests.
Answer
[tex] \frac{72}{8} = 9[/tex]
he get 9 mark on average
2x + 5 < -3 or 6x - 5 > 7
Answers
Answer: 2x-5/3=7
Tiger shows you, step by step, how to Isolate x (Or y or z) in a formula
9. The average amount of soda consumed per person in the US from 1990 to 2010 can be modeled by the following equation, where x is the number of years since 1990. f(x) 5.852x^4-0.002x³ + 0.006x² + 0.029x + 47.855 Find the average rate of change for each time interval. a. 1990 to 1996 b. 1990 to 2000 c. 2005-2010
Answers
Using it's concept, the average rates of change are given as follows:
a. 1264.03 soda per person per year.
b. 5851.89 soda per person per year.
c. 128010.89 soda per person per year.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For this problem, the function is given as follows:
f(x) = 5.852x^4 - 0.002x³ + 0.006x² + 0.029x + 47.855.
From 1990 to 1996, we have t = 0 to t = 6, hence:
f(0) = 47.855.f(6) = 5.852(6)^4 - 0.002(6)³ + 0.006(6)² + 0.029(6) + 47.855 = 7632.01.Hence the rate is:
(7632.01- 47.855)/6 = 1264.03.
1264.03 soda per person per year.
From 1990 to 2000, we have t = 0 to t = 10, hence:
f(0) = 47.855.f(10) = 5.852(10)^4 - 0.002(10)³ + 0.006(10)² + 0.029(10) + 47.855 = 58566.75.Hence the rate is:
(58566.75 - 47.855)/10 = 5851.89.
5851.89 soda per person per year.
From 2005 to 2010, we have t = 15 to t = 20, hence:
f(15) = 5.852(15)^4 - 0.002(15)³ + 0.006(15)² + 0.029(15) + 47.855 = 296300.39.f(20) = 5.852(20)^4 - 0.002(20)³ + 0.006(20)² + 0.029(20) + 47.855 = 936354.84.Hence the rate is:
(936354.84 - 296300.39)/5 = 128010.89.
128010.89 soda per person per year.
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I’ll give points + brainalist
Answers
The line which is perpendicular to the given line y = -x/8 + 3 is y - 8x =-2, there slopes are negative reciprocals of each other
How to fine the line that is perpendicular to the given lineGiven data
line y = -x/8 + 3
The equation of a line is represented as y = mx + c where m represents the slope. The unique feature of perpendicular line is that the slopes are negative reciprocals of each other.
Hence we find the line that has same value of m which is the slope
using the second option: y - 8x = -2
y - 8x = 2
y = 8x - 2
y = 8x - 2
the slope here is m = 8 which is equal to the negative reciprocals of the slope in the given equation and hence the correct option
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Is 7 a solution of 5x - 3 = 12 ? Justify your answer
Answers
Answer:
Step-by-step explanation:
NO x=3
Question
Shonda jogs 5 miles per hour.
Graph the relationship between the number of hours Shonda jogs and the total number of miles jogged.
Answers
here hope this helps u
help help help.........
Answers
Answer:
The answer is A
Domain means look at the x-axis. So you’re looking at it from left to right and finding the smallest number to the highest number on the x-axis. In this case, the smallest number the graph falls on is -2 and it stops at 4.
Remember: a filled in circle means “greater than or equal to”
how do you solve this problem
chan is filling a box with 1 inch cubes. he filled the bottom layer with 5x1 inch cubes long, and 4x1 inch cubes wide. The box is 6 inches tall.
Answers
Answer:
120 cubes will fill the box
Step-by-step explanation:
You want to know the number of 1-inch cubes it takes to fill a box that is 5 cubes long, 4 cubes wide, and 6 inches tall.
LayerTo cover the bottom of the box, Chan needs to make an array of cubes that has 4 rows with 5 cubes in each row. That layer will have ...
4 × 5 = 20 . . . . cubes per layer
VolumeEach layer occupies 1 inch of height, and the box is 6 inches high. The volume of the box will be filled with six of these layers. That will take this many cubes:
(6 layers) × (20 cubes/layer) = 6 × 20 cubes = 120 cubes
Chan will need 120 cubes to fill the box.
Find the average rate of change of f (x)=x-2√x on the interval [1, 9].
Answers
The average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
We have,
f(x) = x - 2√x
On the interval [1,9].
[1, 9] = [a, b]
The average rate of change:
= f(b) - f(a) / b - a
= f(9) - f(1) / 9 - 1
= [(9 - 2√9) - (1 - 2√1)] / 8
= [ (9 - 6) - (1 - 2) ] / 8
= (3 + 1) / 8
= 4 / 8
= 1/2
Thus the average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
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Wayne recorded the eye colors of the people who have already signed up for a lecture on genetics.
green 2
blue 30
brown 38
What is the experimental probability that the next person to sign up will have blue eyes?
Write your answer as a fraction or whole number.
P(blue)=
Answers
The experimental probability of next person to have Blue eyes is 3/7.
Probability :Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
It is based on the possible chances of something to happen.
Probability (P) = Number of a Favourable outcome {n (E)} / Total number of outcomes {n (S)}
Simply, P = n (E) / n (S)
Given, Eye colors of the people
Green = 2
Blue = 30
Brown = 38
To find the probability of next person to have blue eyes, first we will add the given eye colors
Total number of Eye Colors = 2 + 30 + 38 = 70
Number of Blue Eyes = 30
Then, Probability to have blue eyes P(blue) = Number of Blue Eyes / Total number of Eye Colors
= 30/70
= 3/7
So, there is 3/7 chances to next person to have blue eyes.
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Answer:
3/7
Step-by-step explanation:
The zookeeper mentioned that the scale used to weigh some of the larger animals can be off by 12 pounds. The scale read 438.2 lbs. for one of the larger animals. If the animal’s actual weight is x pounds, write an expression to represent the number of pounds the weight on the scale is from the actual weight of the animal. Then explain the range of values in which the actual weight might be.
Answers
The actual weight of the animal is between 450.2 and 426.2 pounds
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequality can be used to show that two variables or numbers are not equal to each other.
The weight of the larger animals can be off by 12 pounds. Let x represent the actual weight of the animal. If the scale reads 438.2 lbs, hence:
|x - 438.2| = 12
x - 438.2 = 12; or -(x - 438.2) = 12
x = 450.2; or x = 426.2
The actual weight of the animal is between 450.2 and 426.2 pounds
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A helicopter takes off from the roof of a building that is 225 feet above the ground. The altitude of the helicopter increases by 125
Answers
Answer: i think you want y=125x+225
Step-by-step explanation:
the linear equation is created by sticking these two numbers into y=mx+b
so we start at 225 feet, which means that goes where b is, and the helicopter goes up 125 per whatever, which means we put 125 where m is
Positive multiples of 4
Answers
Answer:
4, 8, 12, 16, 20, 24, 28, 32, 36, and 40 are some multiples of 4 that are positive.
the difference between nine times a number and one more than five times the number
Answers
The required expression for the given statement is 4x + 1.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
The given statement is,
the difference between nine times a number and one more than five times the number
Let x be the number.
Thus, we have
nine times a number = 9x
one more than five times the number = 1 - 5x
Thus, the numerical expression we get is
9x + (1 - 5x)
Expanding we get
9x + 1 - 5x
Solving we get
4x + 1
this is the required expression
Thus, the required expression for the given statement is 4x + 1.
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does anyone know how to do this
Answers
Answer:
Step-by-step explanation:
add 99 and 36 together to get 135 degrees
Answer:
135°
Step-by-step explanation:
You add the two angles together.
Tracey paid $145 for an item that was originally priced at $360. What percent of the original price did Tracey pay?
Round your percentage answer to two decimal places.
Do NOT include a
%
symbol with your answer.
Answers
Answer:
Tracy paid 40.28 percent of the total price.
What is the slope of the line represented by the equation y = x - 3?
O-3
--3--
45
O3
Answers
Answer:
Slope is 1
Step-by-step explanation:
From the general linear equation:
[tex]{ \rm{y = mx + c}}[/tex]
m is the slope
Comparing with the equation given:
[tex]{ \rm{y = { \green{1}}x - 3}}[/tex]
[tex]f(x)=x^{2} +2x-24[/tex]
Answers
(X+6)(x-4)
Hope this helps
1. Rhonda is competing on a game show. First she randomly decides on a target of 1 or 2 and chooses card A or B. Then she spins the spinner on the other side
of the card.
a) What is P(1) if Rhonda chooses spinner A? P(1|A) = __
b) What is P(1) if Rhonda chooses spinner A? P(1|B) = __
c) Choose the correct symbol to make the statement true
Answers
Using probability we get (a) P(1|A) = 1/2 and (b)P(1|B) =3/4 , hence P(1|A) ≠ P(1|B).
Probability is the study of chance . The part of mathematics known as probability deals with fractional representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, 0 denotes the event's impossibility and 1 denotes certainty.
Probability is calculated by the fraction possible outcomes ÷ total outcomes
a) The first spinner has the total 4 sections. so there are 4 total outcomes.
Favorable outcome = 1
Total number of favorable outcome=2
Probability P(1|A) = favorable outcome ÷ total outcome
∴ P(1|A) =2/4 or P(1|A) =1/2
b) The first spinner has the total 4 sections. so there are 4 total outcomes.
Favorable outcome = 1
Total number of favorable outcome=3
Probability P(1|B) = favorable outcome ÷ total outcome
∴ P(1|B) =3/4 or P(1|B) =3/4
c)Therefore P(1|A)≠P(1|B) so the events A and B are dependent.
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Use the segment addition postulate to solve for the length of BC, if AC = 16, BC = x + 11, and AB = 3x-7.
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4-5 what are the answers!! please give correct answers ill give brainlist!!!!
Answers
Answer:
4a.) 0.0005 = 5 x 10 to the exponent -4
4b.) 0.0025 = 2.5 x 10 to the exponent -3
5a.) 2 x 10 to the exponent -2 = 0.02
5b.) 16 x 10 to the exponent -4 = 0.0016
Tip:
The number being multiplied has to be less than or equal to 10. Count the places the decimal point moves from the end of the number to the number in the original equation.
Example: 0.05 = 5 x 10 to the exponent -2
0.05 has 2 spaces for the decimal point to move up to 5 going right. We use a negative decimal because 0.05 is less than 5. Here is an example where the exponent is positive:
5000 = 5 x 10 to the exponent 3
5000 has 3 spaces for the decimal point to move down to 5 going left.
Debra bought 4 hammers and 6 tape measures for $94. Heather bought 5 hammers and 3 tape measures for $77 . Letting x represent the price of each hammer and y represent the price of each tape measurewrite a cost equation for both Debra and Heather
Answers
The cost equation for Debra is given by 4x + 6y = 94 and for Heather is 5x + 3y = 77.
What are Linear equations in two variables?Linear equations in two variable have one, none, or infinitely many solutions, with the highest exponent order of 1 in each of the two variables. The standard form of a two-variable linear equation is ax + by + c = 0, where x and y are variables. Solutions can also be written in pairs, for example (x, y). A two-variable linear equation system is represented graphically by two straight lines that can intersect, parallelize, or coincide.
According to the given condition, we have 2 equations:
4x + 6y = 94
5x + 3y = 77
Now, multiply by 2 on both sides of the equation 5x + 3y = 77 to obtain:
10x + 6y = 154
Now, subtracting the equation 10x + 6y = 154 and 4x + 6y = 94.
[10x + 6y = 154] - [ 4x + 6y = 94]
6x + 0y = 60
x = 10
Putting the value of x = 10 in equation 4x + 6y = 94, we get
y = 9
So, the cost of 1 hammer is 10$ and tape is 9$.
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wats the answer help mee
Answers
Need an explanation?
Answer:
6
Step-by-step explanation:
The diameter is half of the given radius, therefore, split the radius in half.
[tex]\frac{12\:in^2}{2} = 6\:in^2[/tex]
A girl owns 1 pairs of pants, 3 shirts, 4 ties, and 3 jackets. How many different outfits can the girl wear to school if each outfit must consist of one of each item?
Answers
Answer: She can wear 3 outfits to school because
Step-by-step explanation: She is able to wear the pants multiple times so she can have 1 pants 1 shirt 1 tie and 1 jacket for three days
Solve the equation 5k^2−20k=15 . Present exact values of the solutions. If there are more than one solutions, separate them by a comma.
Answers
The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.
What are the roots of the equation?Let the equation be ax² + bx + c = 0.
Then the roots of the equation will be
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\\[/tex]
The quadratic equation is given below.
5k² - 20k = 15
Simplify the equation, then we have
k² - 4k = 3
k² - 4k - 3 = 0
Then the roots of the equation will be
[tex]\rm k = \dfrac{ -(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times (-3) }}{2 \times 1}\\\\k = \dfrac{4 \pm \sqrt {28}}{2}[/tex]
Simplify the equation, then we have
k = (4 ± 5.30) / 2
k = (4 + 5.30) / 2, (4 - 5.30) / 2
k = 4.65, -0.65
The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.
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Is 7x+y+3=y a linear equation
Answers
Answer:
7x+y=3 is not a linear equation.
SOME HELP ME PLS, I ONLY NEED CORRECT ANSWERS SO DON’T PUT A RANDOM ANSWER
Answers
Answer:
≈67.81
Step-by-step explanation: