5√2 is the solution of surd .
What does a math surd mean?
When a square root, cube root, or other root symbol is used in an expression, it is known as a surd. Irrational numbers cannot be stated accurately in decimal form because their decimals do not finish or recur. Surds are used to write irrational numbers precisely.In mathematics, an index is an exponent or power applied to a number or a variable. For instance, the index of 2 in the number 24 is 4.= √25+√45-√20
= √70 - √20
= √50
= 5√2
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given < 1 and 3 prove < 6 and <4
It is given that ∠1 ≅ ∠3 and ∠1 = ∠4 and ∠3 = ∠6 as of vertically opposite angles, therefore ∠6 ≅ ∠4 too.
What is vertically opposite angles?Vertical angles, also known as vertically opposite angles, are formed when two lines cross each other at an angle that is opposite to it. Angles that are vertically opposite to one another are always equal to one another.
A vertical angle and the angle to which it is adjacent are also supplementary angles; that is, they add up to 180 degrees. As an illustration, if two lines intersect to form an angle, say X=45°, then the opposite angle is also 45°. And angle X's neighbor will have a measure of 180 minus 45, or 135 degrees.
Two lines are said to intersect when they come together at a single point in a plane. They are referred to as parallel lines when they do not intersect anywhere in a plane.
We have given that ∠1 ≅ ∠3
We can see that ∠1 = ∠4 as they are vertically opposite angles.
Also ∠3 = ∠6 as they are vertically opposite angles.
Thus, It is given that ∠1 ≅ ∠3 and ∠1 = ∠4 and ∠3 = ∠6 as of vertically opposite angles, therefore ∠6 ≅ ∠4 too.
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If the ratio of A to B is 3 : 4, and the ratio of B to C is 2 : 3, what is the value of A when C is 5?
If the ratio of A to B is [tex]3 : 4[/tex], and the ratio of B to C is [tex]2 : 3[/tex], then the value of A when C is [tex]5[/tex] is [tex]2.5[/tex].
In the given question,
The ratio of A to B is [tex]3 : 4[/tex].
The ratio of B to C is [tex]2:3[/tex].
We have to find the value of A.
It is given that the value of C is [tex]5[/tex].
The given ratios are,
A : B [tex]=3 : 4[/tex]
B : C [tex]=2:3[/tex]
As we can see that the ratio of B is not same in both ratio so we first equal the ratio of B.
We can equal the ratio of B by multiplying [tex]2[/tex] on both side in the ratio of
B : C.
B : C [tex]=2\times2:3\times2[/tex]
After multiplying we get
B : C [tex]=4:6[/tex]
As given in the question that C [tex]=5[/tex].
They given in the ratio which means there have any number in the multiple of ratio. That which we can get real value from the ratio.
So we used [tex]x[/tex] as a multiple of ratio.
And the ratio of C is [tex]6x[/tex].
So we get that
[tex]6x=5[/tex]
Hence the value of [tex]x=\frac{5}{6}[/tex].
Now finding the value of A.
The ratio of A is [tex]3x[/tex].
And the value of [tex]x=\frac{5}{6}[/tex].
Now putting the value
A [tex]=3\times\frac{5}{6}[/tex]
A [tex]=\frac{5}{2}[/tex]
A =[tex]2.5[/tex].
The value of A is [tex]2.5[/tex].
Hence, if the ratio of A to B is [tex]3 : 4[/tex], and the ratio of B to C is [tex]2 : 3[/tex], then the value of A when C is [tex]5[/tex] is [tex]2.5[/tex].
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How do you write 3.2 x 10° in standard form? i cant seem to figure this out could somebody pls help me out?
Answer:
3.2
Step-by-step explanation:
Any number raised to the zero power is one. 3.2 x 1 = 3.2
4 x + 2 + x = blank x – 19
The result of the equation 4 x + 2 + x = x – 19 is - 5.25.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables.
Given equation -
4 x + 2 + x = x – 19
Simplify the equation
5x + 2 = x - 19
5x - x = -19 - 2
4x = -21
x = -21 / 4
x = -5.25
Hence, -5.25 is the answer to the equation 4 x + 2 + x = x - 19.
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y = 2x+1 how do I solve this?
Solving an inequality, it is found that the interval over which the function y = 2x + 1 is positive is given by:
(-1/2, ∞).
When a function is positive and when it is negative?To verify if the function is positive or negative, we have to look at the graph of the function relative to the x-axis, as follows:
A function is positive when it is above the x-axis, that is, if y > 0, as the x-axis represents y = 0.A function is negative when it is below the x-axis, that is, if if y < 0.In the context of this problem, the function is given by:
y = 2x + 1.
We want to find when the function is positive, hence we have to solve this following inequality:
y > 0
2x + 1 > 0
2x > -1
x > -1/2.
Hence the interval is:
(-1/2, ∞).
What is the missing information?The problem asks for the interval in which the function is positive.
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i need to submit this by tonight, please insert answer in blank area thxx <#
Answer:
1) 4
2) 12
3)AB
Step-by-step explanation:
1) AC is 8, and since it bisects it is cut in 2
2) With the Pythagorean theorem, we know that side a² x side b² = side c²
so 4² x 9² = c² aka 16x9 = 144
square root bla bla, 12
3) as explained in 1) , it got cut into two, so AB = BC
A revenue function is an equation that shows how much revenue a factory will generate at a given price. Suppose a manufacturer of calculators has determined that, for a particular model of calculator, the revenue function is R = -150p2 +21000p where p is the retail price (in dollars) of the calculator and R = f(p) is the revenue generated from the calculator sales (in dollars). Please graph this equation and tell what is the lowest price at which $600,000 could be earned?
Answer: heem
Step-by-step explanation:
Answer:
$40/unit
Step-by-step explanation:
See attached graph.
Rewrite each expression as a single fraction.
A. 3/8 - 1/6
B. 4/5 + 3/5
C. 5/9 - 1/5
In fraction form^
Answer:
A. 5/24
B. 7/5
C. 16/45
Step-by-step explanation:
hope this helps
A rental car company charges $46.75 per day to rent a car and $0.13 for every mile driven. ximena wants to rent a car, knowing that: she plans to drive 100 miles. she has at most $200 to spend. write and solve an inequality which can be used to determine dd, the number of days ximena can afford to rent while staying within her budget.
The number of days Ximena can afford to rent while staying within her budget is 4 days.
Given that, a rental car company charges $46.75 per day to rent a car and $0.13 for every mile driven.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
We know that it costs $0.13 for every mile driven and we plan to drive 100 miles, that means we can set the inequality as:
46.75x + 0.13(100) ≤ 200
46.75x + 13 ≤ 200
Rearranging the inequality so we have the variable alone on one side, we get:
46.75x ≤ 187
Divide both sides by 46.75 to get x alone
x ≤ 4
Hence, the number of days Ximena can afford to rent while staying within her budget is 4 days.
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The ratio of Fatima's income to her savings is 4:1. The percentage of money saved by her is:
ファティマの収入と貯蓄の比率は 4:1 です。彼女が節約したお金のパーセンテージは次のとおりです。
the 1st question can someone help a bro out
Answer:
3/19
Step-by-step explanation:
No. of people who ordered the small lemon yogurt divided by total no. of people
= 9/57
= 3/19
a new community wellness complex is being built in hadleyville. the perimeter of the rectangular playing field is 290 yards. the length of the field is 5 yards less than double the width. what are the dimensions of the playing field
The rectangular playing field's perimeter is 290 yards. The field's length is 5 yards less than its width. The playing field's measurements length and width will be 70 and 75.
Given that,
In Hadleyville, a brand-new community wellness complex is being constructed. The rectangular playing field's perimeter is 290 yards. The field's length is 5 yards less than its width.
We have to find what are the playing field's measurements.
Take the width as x.
Length is x-5.
Perimeter of the rectangle is 2l+2w
290=2l+2w
290=2(x-5)+2x
290=2x-10+2x
290=4x-10
4x=290+10
4x=300
x=300/4
x=75
The length will be x-5=75-5=70
The width will be x=75
Therefore, the playing field's measurements length and width will be 70 and 75.
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Find the least common denominator. Then express each fraction using the least common denominator.
3/10 and 2/15
The least common denominator (LCD) of the fractions 3/10 and 2/15 is 30.
Given fractions:
3/10 and 2/15
First the least common multiple for denominators (10,15) is 30.
Calculations to rewrite the original inputs to equivalent fractions with LCD:
3/10 = 3/10 * 3/3 = 9/30
2/15 = 2/15 * 2/2 = 4/30
Therefore the least common denominator (LCD) of the fractions 3/10 and 2/15 is 30.
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Select all the expressions which have 3 as the greatest common factor of the terms.
A. b + 3 + 6c
B. 27n + 66p
C. 38 – 9j + 6k
D. 12x + 75y + 21
E. –32 – 24z
There are A to E equations. The equation B and D area the equations have 3 as the greatest common factor.
Given that,
There are A to E equations.
We have to find that which equation is having 3 as the greatest common factor.
To check the the greatest common factor we have to multiply by 3.
A. b+3+6c
Divide by 3.
b/3+3/3+6c/3
b/3+1+2c
The equation does not have 3 as the greatest common factor.
B. 27n+66p
Divide by 3
27n/3+66p/3
9n+22p
The equation have 3 as the greatest common factor.
C.38-9j+6k
Divide by 3
38/3-9j/3+6k/3
38/3-3j+2k
The equation does not have 3 as the greatest common factor.
D.12x+75y+21
Divide by 3
12x/3+75y/3+21/3
4x+25y+7
The equation have 3 as the greatest common factor.
E. -32-24z
Divide by 3
-32/3-24z/3
-32/3-8z
The equation does not have 3 as the greatest common factor.
Therefore, The equation B and D area the equations have 3 as the greatest common factor.
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If c is a number with no exponent, what is the value of c in the equation below?[tex]\frac{ {4}^{7} }{ {4}^{3} } = {a}^{b} = c[/tex]
Answer:
c = 256
Explanation:
Given the equation:
[tex]\frac{ {4}^{7} }{ {4}^{3} }={a}^b=c[/tex]We apply the division law of indices to obtain:
[tex]\frac{ {4}^{7} }{ {4}^{3} }={4^{7-3}=4^4=256}[/tex]The value of c is 256.
Shannon read that the latest model of a car made in Europe travels to speeds up to 120 kilometers per hour. Approximately how many per miles is 120 kilometers per hour? Show your work.
74.5645 miles is 120 kilometers per hour.
Both kilometers and miles represent units used to measure distance, and their magnitudes are comparable. The only distinction left is in the length units because both speed units have a time dimension that is measured in hours. A kilometer is a unit first from the metric system, whereas the mile is a part of something like the imperial unit system, which is used in many nations like the United States as well as the United Kingdom.Although it is a more recent measurement, the mile does have a lengthy history, going at least as far back as the Romans.The Roman mile was approximately 5,000 feet long, as well as additional miles with differing lengths in various locales and eras, such as the English, Irish, and Italian miles.Divide the speed of the vehicle by 1.609 to get an approximation.
Therefore, 120 kilometers per hour = 120/1.609
=74.5645 miles per hour
74.5645 miles is 120 kilometers per hour.
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carlos tiene 120 dolares, roxana tiene 200 dolares, claudina 180 dolares ; para viajar a ambato el pasaje cuesta 18 dolares ¿cuántos viaje de vueltas hay para viajar en el mundo? ayudenme plis unu es para mañana
The number of trips that can be taken based on the money than they have is 27 trips.
How to calculate the value?The amount that each person has is illustrated below:
Carlos = $120
Roxana = $200
Claudia = $180..
In order to travel around Ambato, $18 is needed. Therefore, the trips that can be taken will be:
= Total amount / Value for each trip
= ($120 + $200 + $180) / 18
= 500 / 18
= 27
There'll be 27 trips.
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Help pls asap thx alot lol
The expression that is equivalent to [tex]\frac{5^{-10}}{5^{4}5^{0}}[/tex] is 1/5¹⁴
Expression:
An expression is a mathematical statement that does not contain an equal sign. It cannot be solved for unless the value of the variable is given.
Given,
Here we have the expression [tex]\frac{5^{-10}}{5^{4}5^{0}}[/tex]
Now we need to find the equivalent expression for this one.
In order to find the equivalent expression first we have to simplify the given expression.
For that we have to use the exponent rule,
1) Product of powers rule
When we multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.
2) Quotient of powers rule
When we dividing two bases with same value, keep the base the same, and then subtract the exponent values.
3) Negative exponent rule.
While we have the negative exponent then we have to convert them into fraction.
Based on the rule 1, we have simplify the denominator as,
[tex]\frac{5^{-10}}{5^{4}5^{0}}=\frac{5^{-10}}{5^{4+0}}\\\\= > \frac{5^{-10}}{5^{4}}[/tex]
Now we have to apply the rule (2), then we get,
=> 5⁻¹⁰⁻⁴
=> 5⁻¹⁴
Finally, we have to apply the thirds rule,
=> 1/5¹⁴
Therefore, the equivalent expression is 1/5¹⁴.
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camille finds a pieace of wood that is 15.65 centimeters long and thier freind finds one that is 16.24 centimeter what is the total lenght if camille attched them together
The total length of the wood attached together is 31.89 centimetres
Size of the wood found by Camille = 15.65 centimetres
Size of the wood found by her friend = 16.24 centimetres
The act of determining an object's length in some standard or non-standard units is known as a length measurement. In our daily lives, the ability to measure length is crucial.
Let's say Mathew is shopping with a friend when he notices a lovely picture frame that can be displayed in his parent's bedroom. But how would he go about telling them how long the frame was? If he knows the length of a particular unit, such as 3 feet, he can do that.
The total length of the wood = 15.65 + 16.24 = 31.89 centimeter
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find the sime interest owed for the loan $5,100 at 10% for 1 year
Step 1: write out the formula
The simple interest on the loan can be calculated using the formula:
[tex]\text{simple int}erest\text{ =}\frac{p\text{ x r x t}}{100}[/tex]where p is the principal, in our case, it is the loan = $51000
r is the rate = 10%
t is the time = 1 year
Step2: substitute the values into the equation.
Our next step is to put the values of p, r, and t into the equation so that
[tex]\text{simple interest =}\frac{51000\text{ x 10 x 1}}{100}=5100\text{ }[/tex]Therefore, the simple interest on the loan is $5, 100
A student claims that 3.8¯ is an irrational number because it is a non-terminating decimal. Is the student correct? Justify your answer. If the student is incorrect, write 3.8¯ as a fraction. If the student is correct, use mathematics to explain how you know you cannot write the number as a fraction. Enter your answer and your work or explanation in the space provided.
If a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal, then, he/she is incorrect as 3.8¯ can be represented as a fraction which is (35/9).
As per the question statement, a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal.
We are required to determine if the claim is correct or incorrect, and if the claim is correct, then we will have to justify our answer, while if it is incorrect, we will have to determine the fraction that is equal to 3.8¯.
To solve this question, let us first try to convert our concerned decimal 3.8¯ into its equivalent fraction.
Now, 3.8¯ = 3.888...
Let us assume a random variable "x" such that, 3.8¯ = x = 3.888...
Then, 10x = (10 * 3.888...) = 38.888...
Now, [(10x - x) = {(38.888...) - (3.888...)}]
Or, (9x = 35)
Or, x = (35/9)
That is, the non-terminating decimal 3.8¯ can be converted to a fraction which is equal to (35/9).
Hence, the student's claim that that 3.8¯ is an irrational number because it is a non-terminating decimal is incorrect.
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what is 7.13X6=????????????????????
7.13 x 6 = 42.78
7 x 6 = 42
0.1 x 6 = 0.6
0.03 x 6 = 0.18
12 + 0.6 + 0.18 = 42.78
Elijah bought earrings to give to his mother for her birthday. The earrings are in a case shaped like a rectangular prism that is 2 inches long, 1 1/2 inches wide, and 1 1/2 inches tall. He doesn't want his mother to guess what the gift is, so he put the case in a larger, cube-shaped gift box. The gift box is 4 inches along each edge.
What is the volume of the extra space left in the gift box?
Mr. Apple noticed that an error had been made on his account. The "loss of $800" should have been a "gain of $800." Locate and label both points that represent "a loss of $800" and "a gain of $800" on the number line below. Describe the relationship of these two numbers when zero represents no change (gain or loss). HHHHHHHHH O
A loss is represented as a negative number (a number less than 0) and a gain is represented by a possitive number (a number grather than 0)
For the given data you get the next graph:
The relationship as 0 is not change is: The loss is a change of $800 being a decrease of the amount in the account. The gain is a change of $800 being a increase of the amount in the account.
Both are changes of $800 but represent different types of changes (increase and decrease)
what is the fraction in decimal form ?19/25choose : 0.76, 1.31, 2.06, 7.6
We want to write in decimals the following fraction
[tex]\frac{19}{25}[/tex]To write this as a decimal number, first we need to convert the denominator to a power of 10. We can do that by multiplying both the numerator and denominator by 4.
[tex]\frac{19}{25}=\frac{19}{25}\cdot\frac{4}{4}=\frac{19\cdot4}{25\cdot4}=\frac{76}{100}[/tex]Now, we just effectuate the division
[tex]\frac{76}{100}=0.76[/tex]0.76 is our answer.
What is 32% of 495. I have to type more because its not in the 20 charter lenth.
Answer:
158.4
Step-by-step explanation:
32% multiple 495
=158.4
simply (4x-6)-(5x+1)
Through the given equation the simplification of (4x-6)-(5x+1) is = -x -7.
What is an example of distributive property?An illustration of distributive property:
When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you wish to multiply 5 by the product of 10 plus 3. When two terms are similar, we often sum the two amounts before multiplying by 5. However, the property states that you should first multiply each addend by 5.
The expression provided is:
(4x-6)-(5x+1)
Using the distributive property, expand the brackets to get:
4x-6- 5x-1
Organize the terms to get,
4x- 5x -1 -6
combine similar phrases to simplify to obtain;
-x -7
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Jasmine ran for 98.4 minutes. Throughout her run, she ran at a pace of 8.2 minutes per mile.How many miles did Jasmine run? Jasmine ran___ miles.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
time = 98.4 minutes
rate = 8.2 minutes per mile = 8.2 minutes / mile
distance = ?
Step 02:
[tex]\begin{gathered} \text{distance = time / rate } \\ \text{distance = }\frac{98.4\text{ minutes}}{8.2\text{ minutes /mile}} \end{gathered}[/tex]distance = 12 miles
The answer is:
Jasmine ran 12 miles.
help asap! this is due in 30 minutes!
Answer:
0.5Step-by-step explanation:
By determining the value of y when x=1, we'll find the constant of proportionality.
[tex]\sf y=0.5[/tex]
when, x = 1
The constant of proportionality:-
[tex]\sf \cfrac{y}{x},\:is\:\cfrac{0.5}{1}\: or \: 0.5[/tex]
Therefore, your answer is 0.5 .
________________________
Hope this helps!
Have a great day!
If the speed limit is 80kilometers per hour and Elena’s mom was driving 75 miles per hour was she speeding by how m,uch
Elena's mom was speeding up by 25.29 miles/h.
What is unit conversion?
Conversion of units is the conversion between different units of measurement for the same quantity.
Given is the speed limit of 80 kilometers per hour.
To convert from kilometers per hour to miles per hour, divide the measurement in km/h by 1.609344.
Therefore, in miles per hour we can write -
80 Km/h = (80/1.609344) = 49.71 miles
75 - 49.71 = 25.29 miles/h
Therefore, Elena's mom was speeding up by 25.29 miles/h.
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