Two rational numbers between −7/2 and 4/3 are -20/6 and 7/6.
The two given rational numbers are −7/2 and 4/3.
What are rational numbers?A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0.
Now, two rational numbers between −7/2 and 4/3 can be found as follows:
Make denominators the same by taking the LCM of denominators.
LCM of 2 and 3 is 6.
Change denominators of both the rational numbers to 6 by multiplying the same number by numerator and denominator.
So, the rational numbers become −21/6 and 8/6.
Now, two rational numbers between −21/6 and 8/6 are -20/6 and 7/6.
Therefore, two rational numbers between −7/2 and 4/3 are -20/6 and 7/6.
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Which temperature is hottest?
-32°C
-34°C
33°C
31°C
Answer:
Step-by-step explanation:
33
The prices of two different brands of hot
chocolate are shown below.
What is the difference in price between the two
brands when buying 800 g of hot chocolate?
Give your answer in pounds (£).
Brand A
HOT
CHOCOLATE
£2.85
160 g
Brand B
HOT
CHOCOLATE
£3.40
200 g
The difference in price between the two brands when buying 800 g of hot chocolate is 0.
What is arithmetic operation?
A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.
For brand A
For 160g of hot chocolate is $2.85
For 1g of hot chocolate is 2.85/160
For 800g of hot chocolate is [tex]\frac{2.85}{160} \times 800[/tex]
= 2.85 [tex]\times[/tex] 5
= $14
For brand B
For 200g of hot chocolate is $3.40
For 1g of hot chocolate is 3.40/200
For 800g of hot chocolate is [tex]\frac{3.40}{200} \times 800[/tex]
= 3.40 [tex]\times[/tex] 4
= $14
Difference of brand A and brand B of hot chocolate of 800g is $14 - $14 = 0.
Therefore, the difference in price between the two brands when buying 800 g of hot chocolate is 0.
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A diver jumps from a cliff that is 48 ½ feet above the surface of the water. She stops descending
12 ½ feet under the water. What was the total distance of her jump?
Answer:
61
Step-by-step explanation:
are the expressions (5x + 3) + 3x2 - 2 and (5x + 1) + 3x2 equivalent
Answer:
Yes they are equivalent.
In fact any value of x will make both equations equivalent.
Step-by-step explanation:
Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
y=2 x⁺⁴
y-4x⁻¹=0
The solved logarithmic functions are log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: y = 2x⁺⁴, y - 4x⁻¹ = 0
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take expression y = 2x⁺⁴
Applying log on both sides, we get,
log y = log (2x⁺⁴)
log y = log 2 + log x⁺⁴
log y = log 2 + 4 log x
To Check Results,
Taking exponential,
y = e^[log 2 + 4 log x]
y = e^(log 2) × e^[4 log (x)]
y = 2 × e^(log x⁴)
y = 2x⁴
Thus, the answer is verified.
Take expression y - 4x⁻¹ = 0
Applying log on both sides, we get,
log y = log (4x⁻¹)
log y = log 4 + log x⁻¹
log y = 2 log 2 - log x
To Check Results,
Taking exponential,
y = e^[2 log 2 - log x]
y = e^(2 log 2) × e^[-log (x)]
y = e^(log 4) × e^(log x⁻¹)
y = 4x⁻¹
y - 4 x⁻¹ = 0
Thus, the answer is verified.
Hence, the solved expression is log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.
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What is the quotient ∛8 x⁶ y¹² / √4 x⁴ y⁸ ?
The given quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) is x² y⁴.
This question can be easily solved by using the concept of roots. The two root terms mentioned in the question are ∛8 ( cubic root of 8 ) and √4 (square root of 4 ). This question can be solved in 4 easy steps
Determining the power of the root and find the LCM of those numbers..
In this case, the powers of root for ∛8 and √4 are 3 and 2, respectively. Take LCM of 3 and 2.
LCM = 3 x 2 = 6
=> We get the LCM of 3 and 2 as 6.
Writing the given numbers as fractional powers.
∛8 = 8¹ˡ³ => The power of 8 = 1/3
√4 = 4¹ˡ² => The power of 4 = 1/2
Step 3 : Multiply and divide the powers of the base number ( in this case 8 and 4 ) with a number such that you get the denominator as the LCM's ( in this case 6 )
1/3 can be multiplied and divided by 2 to get the denominator as 6
=> 1 * 2 / 3 * 2 = 2/6
1/2 can be multiplied and divided by 3 to get the denominator as 6
=> 1 * 3 / 2 * 3 = 3/6
Step 4 : Divide the two terms
6√8² x 6√4³ = 6√( 4 x 2 x 4 x 2 / 4 x 4 ) = 6√1 = 1
Also, x⁶ y¹² / x⁴ y⁸ = x² y⁴
Therefore, using the concept of roots and fractions, we get The quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) as x² y⁴.
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what is 5 - x = 12?
Answer:
x = -7
Step-by-step explanation:
to solve this first subtract 5 to both sides
5 - x - 5 = 12 - 5
- x = 7
now multiply -1 to both sides
-x(-1) = 7(-1)
x = -7
that is your answeer
A student has taken three math tests so far this semester. His scores for the first three tests were 75,79 , and 83.
a. Suppose his test scores continue to improve at the same rate. What will be his grade on the sixth (and final) test?
Answer:
75
Step-by-step explanation:
there is a pattern in which you can get your answer 75 to 79 you are counting in three 75,76,77,78,79 if you look closely you will see the pattern and you continue to his sixth test and that is how you will get your answer
Put the reasons in the correct order that will justify the statements given
The statements that completes the two column proof table, obtained through the use of complementary, and angle addition postulates, arranged using the numbering on the given table are as follows;
Given ‹PQR is a right angleDefinition of Right AnglesAngle addition postulateSubstitutionDefinition of Complementary AnglesGiven ‹TQP and <SQR are complementary angles [tex] \angle PQS \cong \angle TQP[/tex]What are complementary angles?Two angles are said to be complementary angles if they sum up to 90°A right angle is an angle that measures 90°.The angle addition postulate states that the measure of an angle formed by two smaller angles is equal to the sum of the two anglesThe reasons that completes the two column proof table are as follows;
1. ‹PQR is a right angle; Given ‹PQR is a right angle
2. m‹PQR = 90°; Definition of Right Angles
3. m‹PQS + m‹SQR = m<PQR; Angle addition postulate
4. m‹PQS + m‹SQR = 90°; Substitution
5. ‹PQS and ‹SQR are complementary angles; Definition of Complementary Angles
6. ‹TQP and <SQR are complementary angles; Given ‹TQP and <SQR are complementary angles
7 [tex] \angle PQS \cong \angle TQP[/tex]
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find the perimeter of rectangle BCEF. (0,3) (4,-1) (2,-3) (-2,1)
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ 4- 0~~)^2 + (~~ -1- 3~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 4 )^2 + ( -4)^2}\implies \boxed{BC=\sqrt{32}}[/tex]
[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) ~\hfill CE=\sqrt{(~~ 2- 4~~)^2 + (~~ -3- (-1) ~~)^2} \\\\\\ ~\hfill CE=\sqrt{( -2)^2 + ( -2)^2}\implies \boxed{CE=\sqrt{8}} \\\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad F(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ -2- 2~~)^2 + (~~ 1- (-3)~~)^2} \\\\\\ ~\hfill EF=\sqrt{( -4)^2 + ( 4)^2}\implies \boxed{EF=\sqrt{32}}[/tex]
[tex]F(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill FB=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill FB=\sqrt{( 2)^2 + ( 2)^2}\implies \boxed{FB=\sqrt{8}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter} }{\sqrt{32}+\sqrt{8}+\sqrt{32}+\sqrt{8} ~~ \approx ~~ \text{\LARGE 16.97}}[/tex]
Use long division to convert 11/20 to a decimal.
It should be noted that converting 11/20 to a decimal through division will gives 0.55.
How to illustrate the information?This can be illustrated as follows. It should be noted that the quotient is the value obtained by dividing one value by another. The quotient is 11.
The divisor is the value that divides. It should be noted that in this case, this is illustrated as 20.
It should be noted that 11 is the numerator and 20 is the denominator.
Therefore, it should be noted that converting 11/20 to a decimal through division will gives 0.55.
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Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=0.0015(10) x
The function y=0.0015(10)ˣ showcases exponential growth.
What do we mean by exponential function?An exponential function is a mathematical function with the formula f (x) = ax.Where an is the function's base constant and x is a variable.The most common exponential-function base is the transcendental number e, or approximately 2.71828.So,
Given function: y=0.0015(10)ˣ
If we put x = 1 as follows:
y = 0.0015×10y = 0.015Then, if we put x = 2 as follows:
>>y = 0.0015×(10)²>>y = 0.0015×100>>y = 0.15Hence, we see that 0.15 > 0.15.
So, when x increases, y also increases.Therefore, the function y=0.0015(10)ˣ showcases exponential growth.
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How do you find all real and complex zeros of a polynomial function?
Real and complex zeros of a polynomial function can be find as:
First convert the polynomial to factored form. set factor equal to zero to solve for the real zerosWhat is Polynomial function?A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, 2x+5 is a polynomial that has exponent equal to 1.
Given:
We have to find all real and complex zeros of a polynomial function.
first convert the polynomial to factored form. Once all factors are found, set each individual factor equal to zero to solve for the real zeros
So, according to fundamental theorem of Algebra
It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.
A complex zero is a complex number that is a zero of a polynomial. For example, i (the square root of negative one) is a complex zero of the polynomial x² + 1, since i² + 1 = 0.
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Which one of the following points lies on the line 3y=2x-1?
The graph given below y = -x + 2 have a negative slope and a positive y intercept. The point (2, 1) lies on the line 3y = 2x - 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The graph given below have a negative slope and a positive y intercept. The graph is given by y = -x + 2
Given the equation
3y = 2x - 1
When x = 2:
3y = 2(2) - 1
y = 1
Therefore, The point (2, 1) lies on the given line 3y = 2x - 1
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Choose the correct term to complete the following sentence.
An asymptote of the ____ occurs at θ=π/2 , and repeats every π units.
An asymptote of the tangent occurs at θ=π/2 , and repeats every π units.
Asymptote of the tangent
Due to the fact that tan(x)=sin(x)cos(x), the tangent function is undefined for cos(x)=0. In light of this, whenever cos(x)=0 the tangent function exhibits a vertical asymptote. Similar to the sine function, the tangent function has zeros for integer multiples of because tan(x)=0 when sin(x)=0.
Typically, dashed lines are used to separate asymptotes from the function itself. The vertical lines that frequently appear on the tangent function's graph are spaced 180 degrees apart from one another.
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Solve each equation. Check for extraneous solutions. √3 x+3 -1=x
The extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.
We are given an equation:
√3 x + 3 - 1 = x
√3 x + 2 = x
Subtract 2 from both the sides, we get that:
√3 x = x - 2
Raise both sides to the power 2, we get that:
3 x² = x² + 4 - 4 x
2 x² = 4 - 4 x
x² = 2 - 2 x
x² + 2 x - 2 = 0
x = - 1 ± √ 3
Therefore, we get that, the extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.
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9 - 3x + x - 15 combining like terms
Hey there!
9 - 3x + x - 15
= 9 - 3x + 1x - 15
COMBINE the LIKE TERMS
= (9 - 15) + (-3x + 1x)
= (-3x + 1x) + (9 - 15)
= (-3x + x) + (9 - 15)
= -3x - x + 9 - 15
= -2x - 6
Therefore, your answer should be:
-2x - 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A scientist captures a sample of fish from 100 different locations along the
Yellowstone river and measures the proportion of fish affected by copper toxicity for
each sample. Describe how the scientist could use the data to estimate the
proportion of fish affected by copper toxicity in the entire population along this
portion of the river.
It should be noted that the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river by dividing the number of fishes affected by the fishes collected
How to illustrate the information?Let the number of fish collected in sample be represented as N.
Let the number of fish affected in it be represented by X.
Therefore, the proportion will be;
= X/N
Therefore, this can be used by the scientist to estimate the proportion of fish affected by copper toxicity in the entire population.
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I need help with question 1
800/____ =200. Mathematical questions.
Answer:
X = 4
Step-by-step explanation:
If I have the numbers 2,5,9,7,4,11 what is the smallest fraction I can make?
Answer:
2/5+9+7+4+11 or 2/11
Step-by-step explanation:
2 is the smallest then we just add everything on the bottom together
Or just 2/11 since 2 is the smallest and 11 is the biggest
If you have a question ask
Which statement about the ordered pairs (-9, 3) and (2, -4) is true for the equation 6x=14? 2
Both ordered pairs are solutions.
(-9, 3) is a solution to the equation.
Neither ordered pair is a solution.
(2, 4) is a solution to the equation.
Answer:
neither ordered pair is a solution
Step-by-step explanation:
to determine if the pairs are a solution, substitute the x- coordinate into the left side of the equation and if equal to the right side then they are a solution.
(- 9, 3 ) with x = - 9
6(- 9) = - 54 ≠ 14 ← not a solution
(2, - 4 ) with x = 2
6(2) = 12 ≠ 14 ← not a solution
PLEASE HELP IMMEDIATELY
Answer: 55 degrees
Step-by-step explanation: If the Whole is 180 and you subtract 125 degrees you are left with 55.
What two functions could represent length and width for given values of x based on the combined function? f(x) = x + 7 and g(x) = x + 3 f(x) = x – 7 and g(x) = x – 1 f(x) = x2 + 7 and g(x) = x3 + 3 f(x) = x – 7 and g(x) = x – 3
The length is greater then width with degree one so f(x) = x + 7 and g(x) = x + 3 represents length and width respectively so option (A) will be correct.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Perimeter of rectangle = 2( length + width).
A rectangle has two dimensions of size one is greater called length and another is small known as width.
The length and width both are on units of length only such that meter, cm.
In the given option
x + 7 > x + 3 so f(x) will be length and g(x) will be width.
In the option (B) x - 7 < x - 3 so it will not.
Option (C) x² + 7 can not be a unit of length.
Option (D) x - 7 < x - 3 so it will not.
Hence "The length is greater then width with degree one so f(x) = x + 7 and g(x) = x + 3 represents length and width respectively".
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Answer: is A
Step-by-step explanation:
I did that
Pls help this assignment is due today! I will give brainliest!
Answer:
Step-by-step explanation:
The slope is defined as the ratio of the “rise” divided by the “run” between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.
The inclination of a straight line is the angle that the line makes with the positive direction of the x-axis. The tangent of the angle that a line makes with the positive direction of the x-axis is called the slope or gradient of the line. The slope of a line is generally denoted by m.
Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is y = (y2 – y1)/(x2 – x1)
The slope-intercept form of a line is given by y = mx + b gives the slope of line m and the y-intercept of line b. The inclination of the line with the horizontal axis is called the slope of the line. The point at which the curve cuts or crosses the y – axis is called the y-intercept.
Simplify each expression. √8x⁵-√18x⁵
The simplified expression is [tex]-\sqrt{2} x^{2} \sqrt{x}[/tex].
English expressions, also commonly known as expressions, are words, or groups of words that when used in a certain way convey a certain meaning. Expressions come in many forms, for instance, some of them are collocations, others are common phrases, while others are idioms or even phrasal verbs.
The written expression refers to a highly complex, cognitive, self-directed process. Higher-order components include planning, translating (drafting), reviewing, and revising.
Emotional expression is simply the acknowledgment of these emotions we are built to feel. Healthy expression allows us to understand emotions, truly feel them, and move on.
[tex]\sqrt{8x^{5} } =2\sqrt{2} x^{2} \sqrt{x}\\\sqrt{18x^{5} }=\sqrt{2} 3x^{2} \sqrt{x}\\=2\sqrt{2} x^{2} \sqrt{x}-\sqrt{2} 3x^{2} \sqrt{x}\\=-\sqrt{2} x^{2} \sqrt{x}[/tex]
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In the last academic year, miss taylor supported 23 students. this year she only has 14 students to support. written as a percentage to one decimal place, how much has miss taylor cohort fallen by?
Answer:
39.13%
Step-by-step explanation:
14/23=60.87%
Since the question asks how much has miss Taylor cohort fallen by we do this:
100%-60.87%=39.13%
Answer = 39.13%
Hope this helps :)
Use a table to solve each equation. Round to the nearest hundredth.
5²x=56
[tex]5^{2x}[/tex] = 56 => x = 1.252, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Given: [tex]5^{2x}[/tex] = 56
Taking logarithm on both sides:
=>log([tex]5^{2x}[/tex]) = log (56)
As [tex]log_b(a)^m = m (log_b(a))[/tex],
=> 2x ( log 5) = log (56)
=> 2x = [tex]\frac{log56}{log5}[/tex]
=> 2x = [tex]\frac{1.748}{0.698}[/tex]
=> 2x = 2.504
=> x= 1.252
Hence, [tex]5^{2x}[/tex] = 56 => x = 1.252, by properties of logarithm.
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Gordon rolls a fair dice 162 times.
How many times would Gordon expect to roll a number greater than 3?
Answer:
81 times.
Step-by-step explanation:
A dice has 6 sides.
The dice is fair, so each side has a 1/6 chance of being rolled.
The are 3 numbers greater than 3 - 4, 5 and 6.
Each of those numbers have a 1/6 chance of being rolled.
Together, their chance of being rolled is:
1/6 + 1/6 + 1/6 = 3/6 = 1/2
The dice is rolled 162 times.
162 x 1/2 = 81
Gordon should roll a number greater than 3 81 times.
What is the volume of this triangular prism?
576 ft ^3
288 ft ^3
34 ft ^3
29 ft 63
The volume of the triangular prism that is 16 ft long is calculated as: 288 ft³
What is the Volume of a Right Triangular PrismA triangular prism has two triangular bases. The volume of the triangular prism can be found by using the formula below:
Volume of triangular prism = 0.5 * b * h * L, where:
the length of the the base of the triangular face = bthe height of the triangular face = h, and,the length is triangular prism = LGiven the parameters below:
Length of the the base of the triangular face (b) = 4 ft
Height of the triangular face (h) = 9 ft
the length is triangular prism (L) = 16 ft
Volume of the triangular prism = 0.5 * 4 * 9 * 16
Volume of the triangular prism = 288 ft³
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