If a ≤ b, then it is not true for all real numbers that a²≤ b² .
Consider a ≤ b.
Then squaring on both sides,
⇒ a²≤ b² .
But this is true only when both a and b are non-negative numbers.
For example, if we take a = 2 and b = 5, then clearly,
2² = 4 ≤ 5² = 25
Now we need to prove that this result is not true for all real numbers. So we find two real numbers a and b which does not follow this result.
Let a = -7 and b = 3
So here, a < b
Now a² = (-7)² = 49
and b² = 3² = 9
So here, a² > b².
Thus a = -7 and b = 3 is the required counter example to show that the given result is not true for all real numbers.
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PLEASE HELP! INEQUALITY PROBLEM!
Please help, I struggle with word problems. Thank you.
There are 200 marbles in a box. All the marbles are either red or blue. If there are 40 more red marbles than blue, how many red marbles are in the box?
If your SF = 6/5, what type of dilation is it?
Answer:
enlargement
Step-by-step explanation:
if scale factor > 1 then enlargement
if scale factor 0 < SF < 1 then reduction
here SF = [tex]\frac{6}{5}[/tex] = 1.2 > 1 so enlargement
Answer:
Enlargement
Step-by-step explanation:
Due to the scale factor properties stating that a SF value must be more than one to become an enlargement factor, we know that 6/5 is more than one whole. Thus, the SF is enlargement.
6m=-12n-10 I was wondering if anyone could help me
Answer:
Check options down below!
Step-by-step explanation:
If solving for n:
n = -m/2 - 5/6
If solving for m:
m = -2n - 5/3
A point on the edge of a symmetrical canyon is 4500 feet above a river that cuts through the canyon floor. The angle of depression from each side of the canyon to the canyon floor is 60o.
a) Find the length of the canyon wall (from the edge to the river).
feet
b) Find the distance across the canyon.
feet
c) Is it more or less than a mile across the canyon? (5280 feet = 1 mile) more or less
The length and distance across the canyon is 5196.15 feet and it is more than 1 mile.
a) To find the length of canyon, we will sine function. As per the sine theta = length of opposite side ÷ hypotenuse. Keep the values in formula to find the hypotenuse, which is the length of the canyon wall.
sin 60 = 4500 ÷ hypotenuse
Hypotenuse = 4500 ÷ (✓3/2)
Hypotenuse = 4500 × 2 ÷ ✓3
Hypotenuse = 9000 ÷ ✓3
Hypotenuse = 5196.15 feet
The length of the canyon wall is 5196.15 feet.
b) To find the distance across the canyon, we will use cosine function. As per the cos theta = base ÷ hypotenuse. Keep the values in formula to find the base, which is half the length of the distance across the canyon.
cos 60 = base ÷ 5196.15
cos 60 × 5196.15 = base
Base = (1/2) × 5196.15
Base = 2958.075 feet
Total distance across the canyon = 2958.075 + 2958.075
Tota distance across the canyon = 5196.15 feet
c) Using the relation, 5280 feet = 1 mile
5196.15 feet = 5196.15 ÷ 5280 mile
5196.15 feet = 1.12 miles
So, distance across the canyon is more than 1 mile.
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Which values, when substituted for x in the expression _/x , will result in an irrational number? Select all that apply.
The values, which when substituted for x in the expression √x , would result in an irrational number are:
x = 168x = 2x = 8x = 21x = πThe types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbersWhole numbersRational numbersIrrational numbersReal numbersIntegersWhat is an irrational number?An irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 168, 2, 8, 21, π, 11.
In conclusion, when a perfect square or 4 is substituted for x in the expression √x, the result is not an irrational number because it is neither a terminating nor a repeating decimal.
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Complete Question:
Which values, when substituted for x in the expression √x, will result in an irrational number? Select all that apply.
x = 168
x = 2
x = 8
x = 21
x = π
x = 4
when x is a perfect square.
solve the equation for y. 2/5x+y=7
If there are 30 dogs and 36 cats at a pet daycare, fill out all of the possible ratios of
dogs to cats that could be made.
There are 30 dogs for every 36 cats (30:36 ratio)
There are
dogs for every cats try
Type in an equivalent ratio of dogs and cats.
8
(14)
19 (20)
(25) (26)
13
15
6
10 11 (12)
(16
(18)
23 (24)
28 (29) (30
17
(18)
(19) (20) (21) (22) (23) (24
(25)
(31)
(22)
(30)
(35) (36)
Answer:
1:2
Step-by-step explanation:
Use a table to solve each equation. Round to the nearest hundredth.
3x⁻¹=72
3[tex]x^{-1}[/tex] = 72 => x = 0.4167, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.Given: 3[tex]x^{-1}[/tex] = 72
=> [tex]x^{-1}[/tex] = [tex]\frac{72}{3} =[/tex] 24
=> [tex]\frac{1}{x}=24[/tex]
=> x = 0.4167
Hence, 3[tex]x^{-1}[/tex] = 72 => x = 0.4167, by basic algebra.
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If f(x)=x+1 and g(x)=x²-3 x-4 , what is (f ⁰ g)(x) ?
(F) x²-3 x-3 (G) x²-x-6 (H) x²-x (I) x²-x-3
The value of the composite function f o g (x) is x² - 3 x - 3.
We have the functions:
f (x) = x + 1 and g (x) = x² - 3 x - 4
We need to find the composite function:
f o g (x)
= f ( g (x) )
Substituting the values, we get that:
= ( x² - 3 x - 4 ) + 1
= x² - 3 x - 4 + 1
= x² - 3 x - 3
Therefore, the value of the composite function f o g (x) is x² - 3 x - 3.
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Which statement is true of the numbers 39/7 and-0.3287 A Only 39/7 is rational. B Only -0.328 is rational. C Both numbers are rational. D Both numbers are not rational.
Both numbers are rational numbers, so the correct answer is (C).
What are rational numbers?An irrational number cannot be expressed using fractions, whereas a rational number can be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers are non-terminating and non-recurring, whereas rational numbers have terminating decimals. It is now possible for 12 rational numbers between -1 and 2 to be: 0, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, -0.1, -0.2, and -0.3. It's important to remember that there are other solutions besides the 12 rational numbers listed above.So,
39/7 is already a rational number as it is already in a fraction with a denominator not equal to zero.
And -0.3287 can also be expressed in fractions where the denominator will not be equal to 0. (Refer to the image below for work)So, we can say that both numbers are ratio numbers.Therefore, both numbers are rational numbers, so the correct answer is (C).
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According to the given solving we can say that both numbers are rational.
The correct option is C.
Why are rational number?The ratio or fraction among two numbers, p/q, where both p and q are the numerator and denominator, respectively, can be expressed as a rational number. For example, 3/7 and any integer represent rational numbers..
Why are numbers irrational and rational?Rational numbers can really be expressed as ratios (such P/Q and Q0), while irrational numbers can indeed be expressed as a fraction. Both of these numbers, nevertheless, are real and can be displayed on a number line.
According to the given data:39/7 and-0.3287
The decimal number as a fraction:
0.3287 = 0.3287/1
this can be written as:
[tex]\frac{0.3287}{1}[/tex] x [tex]\frac{1000}{1000}[/tex] = [tex]\frac{3287}{1000}[/tex]
So we can say that:
-0.3287 = [tex]\frac{-0.3287}{1000}[/tex]
According to the given solving we can say that both numbers are rational number.
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If the Social Security tax is 6% of a person's wages, what would the Social Security tax on wages of $80 be?
Answer: $4.8
Step-by-step explanation:
80*0.06=4.8
Question 10 of 10
Which of the following is most likely the next step in the series?
Answer:
A
Step-by-step explanation:
each step has added one extra side you might have trouble thinking it’s d but the pattern is x color (I’m colorblind) blue x blue so your answer is a
Please help me this is timed giving brainiest if right and 14 points (sorry it's all I have) :)
The given expressions and their verbal descriptions (meaning) are as follows;
2•(x - 3) → Twice the difference between x and 3[tex]x + \frac{3}{4} [/tex] → Three fourths more than x. '5 + x' → The sum of five and the number, x[tex] \frac{3}{4} \cdot x[/tex] → Three fourths part of x.5 - x → five less xx - 5 → Five less than x2•x - 3 → Twice x minus three[tex] \frac{5}{x} [/tex] → The quotient of 5 and xHow can the expressions be described verbally?The given mathematical expressions and their correct verbal expressions or meaning are as follows;
2•(x - 3) can be described as two times or twice the difference between x and 3
[tex]x + \frac{3}{4} [/tex]
The above mathematical expression can be described as three fourths added to x, which is the same as; three fourths more than x.
'5 + x' can be described as the sum of five and x, which is the same as the sum of five and the number, x.
[tex] \frac{3}{4} \cdot x[/tex], The expression means the product of three fourths and x, which is the same as three fourths part of x.
5 - x can be written as the difference between five and x, which is the same as five less x
x - 5 can be written as the difference between x and 5, which means a number that is 5 less than x
2•x - 3 can be written as two times x minus three, which can be described as twice x minus three
[tex] \frac{5}{x} [/tex] can be written as fI've divided by x. which can be written as the quotient of 5 and x
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which of the following expressions is equivalent to 2^4x-5
The height of the house is 26 ft. What is the height of each r story
The height of each story based on the information is 10 feet.
How to calculate the value?It should be noted that from the information given, the storey building as a roof of 6 feet and the height of the house is 26 ft.
Therefore, the height of each story will be:
= (26 - 6) / 2
= 20 / 2
= 10 feet
Therefore, the height of each story based on the information is 10 feet.
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A 2 storey building as a roof of 6 feet.. The height of the house is 26 ft. What is the height of each story
Justin borrowed money from a credit union for 2 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $840. How much money did he borrow?
Justin borrow $6,000 from a credit union for 2 years.
What is Principal amount?
The amount of money initially borrowed from the lender, and as the loan is repaid, it can also refer to the amount of money still owed, is called Principal amount.
Given that;
Simple interest = $840
Time = 2 years
Annual rate = 7%
Now, The formula for calculate the principal amount is,
Simple interest = Principal amount × Rate × time / 100
Principal amount = Simple interest × 100 / Rate × time
Hence,
Principal amount = 840 × 100 / 7 × 2
Principal amount = 84,000 / 14
Principal amount = $6000
So, Justin borrow $6,000 from a credit union for 2 years.
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I which of the numbers
are solutions to the
equation x² = 100? Select all that apply.
-10,000
-50
-10
0
10
50
10,000
The numbers that fits into the equation X² = 100 are -10 and 10.
How to illustrate the information?It should be noted that squares simply means multiplying a number by itself.
In this case, X² = 100.
Therefore, the numbers that fits X will be:
X² = 100
Square root both sides
X = ✓100
X = 10
Also, it should be noted that (-10)² = 100
Therefore, the numbers that fits into the equation X² = 100 are -10 and 10.
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simplify the expression (-3m^-4)(-5m^7). Explain your process and justify each step by naming the appropriate property
help
By the use of algebra properties, the expression (- 3 · m⁻⁴) · (- 5 · m⁷) is equivalent to 15 · m³.
How to simplify an algebraic expression
In this question we find a product of two monomials, each monomial has a constant, a variable and a grade and the entire expression must be simplified by means of algebra properties. The complete procedure of simplification is now presented:
(- 3 · m⁻⁴) · (- 5 · m⁷) Given[(- 3) · (- 5)] · [(m⁻⁴) · m⁷] Commutative and associative properties15 · m³ Multiplication of two negative numbers / Multiplication of powers with the same base / ResultTo learn more on algebraic expressions: https://brainly.com/question/21443100
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Im wasting 10 points on a post that will get taken down so please enjoy it,
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Answer:
AWSOME IMAGE!
Step-by-step explanation:
You make it??!!!
Answer: AIght thx for the points
Step-by-step explanation:
Find 6y + 10z - 2yz, use y=2 and z=3
Answer:
30
Step-by-step explanation:
6(2) + 10(3) - 2(2)(3)
12 + 30 - 2(6)
42 - 12
30
The value of the expression 6y + 10z - 2yz when y = 2 and z = 3 is 30.
What is the value of the expression when y=2 and z=3?Given the expression in the question:
6y + 10z - 2yz
y = 2
z = 3
To determine the value of the expression 6y + 10z - 2yz, we simply substitute y = 2 and z = 3 into the expression and then simplify.
6y + 10z - 2yz
Plug in y = 2:
6( 2 ) + 10z - 2(2)z
Plug in z = 3:
6( 2 ) + 10( 3 ) - 2(2)(3)
Simplifying, we get:
12 + 30 - 12
Add 12 and 30:
42 - 12
Subtract 12 from 42:
30
Therefore, the value of the expression is 30.
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Si por el consumo de 80m de agua se pagan $57 ¿cuánto se pagaron por 50m de agua?
What is the length of HN?
Answer:
Given the length of all 3 segments is 38, we are counting two-thirds of 38. You would find this by multiplication.
Step-by-step explanation:
Conversion to improper fractions/Simplification
[tex]\frac{38}{1} \times \frac{2}{3} = \frac{76}{3}\\\\\frac{76}{3} = 76 \div 3 = 25\frac{1}{3}[/tex]
Therefore, HN = [tex]\sf 25\frac{1}{3}[/tex]
Simplify each expression.
10¹/₂ . 10¹/₂
The result of simplifying each number 10¹/₂ . 10¹/₂ using the exponent rules is 10
To solve this exercise we have to resolve algebraic operations following the exponent rules.
10¹/₂ . 10¹/₂
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
10(¹/₂⁺¹/₂)
10(²/₂)
10¹
10
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Question 1 of 10
The equation y =
[25x
OA. $950
B. $30
OC. $38
OD. $25
0≤x≤38
represents Michelle's regular
30(x-38)+950 x > 38
hourly and overtime wage. Based on this equation, what is Michelle's
overtime hourly pay?
Michelle’s overtime hourly payment is 35.22
Given that ,
Equation represents Michelle’s regular hourly and overtime wage
= 130 (x – 38) + 950% > 38
We have to find Michelle’s overtime hourly payment.
Let’s solve the above given equation:
130 (x – 38) + 950% x 38 = 0
130x – 4940 + (950/100) x 38 = 0
130x – 4940 + 9.5 x 38 = 0
130x – 4940 + 361 = 0
130x – 4579 = 0
130x = 4579
X = 4579 / 130
X = 35.22
That is, Michelle’s overtime hourly payment is 35.22.
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unit 3 parallel and perpendicular lines, homework 1
Answer:
Not enough info.
Step-by-step explanation:
During this basketball season trey took 250 shots and made 72 baskets what was his shooting percentage
The relationships in the table below are functions. Write a function rule.
Answer: y = 25x + b
Step-by-step explanation:
how do i rate an answer
Answer:
press the stars.
Step-by-step explanation:
Find the inverse of each function.
y=log₂4 x
The inverse function of the function y = log₂ 4x is f ⁻¹(x) = 2ˣ/4.
Given the function is :
y = log₂4x
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now interchange the positions of x and y in the function.
x = log₂4y
the next step is to isolate the dependent variables.
f ⁻¹(x) = 2ˣ/4
hence, we get the inverse of the given function as f ⁻¹(x) = 2ˣ/4
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