Answers
The length of x is 4.1.
Given:
Base = 9 + 4.5 = 13.5
From figure:
= [tex]\sqrt{9^{2}+5^{2} }[/tex]
= [tex]\sqrt{81+25}[/tex]
= [tex]\sqrt{96}[/tex]
= 9.797
4.5 opposite is equal to 4.5.
5 opposite equal to 5 and remaining to x - 5.
According to pythagorean theorem:
= [tex]\sqrt{4.5^{2}+(x-5)^{2} }[/tex]
[tex]13.5^{2} +x^{2} =(\sqrt{96}+\sqrt{4.5^{2} +(x-5)^{2} })^{2}[/tex]
[tex]\sqrt{13.5^{2} +x^{2} }[/tex] - [tex]\sqrt{96} = \sqrt{20.25+x^{2} +25 -10x}[/tex]
squaring on both sides
182.25 + [tex]x^{2}[/tex] - 96 = [tex]x^{2}[/tex] - 10x + 45.25
10x = 45.25 + 96 - 182.25
10x = 41
x = 4.1.
Therefore the value of x is 4.1.
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Related Questions
which graph represents y=-2x
Answers
A graph which represents the linear function y = -2x is: graph B.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Generally speaking, the graph of any proportional relationship is characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) either increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.
In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in the graph of y = -2x is proportional as it passes through the origin (0, 0).
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Part 2 - Find the error(s) and solve the problem correctly.
Answers
The error made in the calculation was improper use of quotient rule of logarithm
How to solve the logarithm equation correctlyThe problem will be solved by using the rules of logarithm as done below
logₐ 2x + 2 ( logₐ x - logₐ y )
expanding the parenthesis
logₐ 2x + 2logₐ x - 2logₐ y
applying exponential rule of logarithm
logₐ 2x + logₐ x² - logₐ y²
applying product rule of logarithm
logₐ (2x * x²) - logₐ y²
logₐ (2x³) - logₐ y²
applying quotient rule of logarithm
logₐ (2x³/ y²)
The error was that the quotient rule of logarithm was not properly applied
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table student is in 3nf. student studentid ssn name class d111 111-11-1111 connor freshman d222 222-22-2222 trevor freshman d333 333-33-3333 connor sophomore d444 444-44-4444 parker sophomore d555 555-55-5555 connor sophomore group of answer choices true false
Answers
Functional dependency SSN --> Name exists in the table STUDENT is TRUE, The correct option is (A)
due to the fact that a student ID is a primary key in a table and that (StudentID, SSN) can also combine to form a composite key that can be used to identify a record in a table in a unique way. The augmented functional dependency between the StudentID and SSN enables you to locate additional data in the table. However, using only StudentID will also assist you in finding data in the table.
Since it could be a candidate key, this is true because it can be used in part of augmented functional dependency.
Thus, the SSN matches the name in the STUDENT table.
So, SSN ----> Name holds in STUDENT table.
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(complete question)
Observe the table STUDENT:
STUDENT
StudentID SSN Name Class
D111 111-11-1111 Connor Freshman
D222 222-22-2222 Trevor Freshman
D333 333-33-3333 Connor Sophomore
D444 444-44-4444 Parker Sophomore
D555 555-55-5555 Connor Sophomore
Functional dependency SSN --> Name exists in the table STUDENT.
True
False
What is the equation of this line in standard form?
A - 9x−8y=23
B - 8x−9y=−23
C - 8x−9y=23
D
8x−7y=−25
Answers
Answer:
The correct answer is B
Step-by-step explanation:
I went a weird way to get this. I wrot the line in the slope intercept form and then converted it to the standare form.
For the slope intercept form I need a slope and a y interctp. I used the two points given to find the slope. The slope is the change in y over the change in x. From the points the y values are 3 and -1. The x values are 1.2 and -4
[tex]\frac{3 - -1}{\frac{1}{2}- - 4 }[/tex] = [tex]\frac{3+1}{\frac{1}{4}+4 }[/tex] = [tex]\frac{4}{\frac{9}{2} }[/tex]
4 ÷[tex]\frac{9}{2}[/tex] = [tex]\frac{4}{1}[/tex] x [tex]\frac{2}{9}[/tex] = [tex]\frac{8}{9}[/tex]
[tex]\frac{8}{9}[/tex] is the slope
Now to find the y intercept
I will use
slope [tex]\frac{8}{9}[/tex] (m)
y = -1 from the point (-4,-1) given
x = -4 from the point (-4,-1) given
y=mx + b
-1 = [tex]\frac{8}{9}[/tex](-4) + b
-1 = [tex]\frac{-32}{9}[/tex]x + b Add [tex]\frac{32}{9}[/tex] to both sides
[tex]\frac{23}{9}[/tex] = b
y = [tex]\frac{8}{9}[/tex]x + [tex]\frac{23}{9}[/tex] Multiply all the way thorugh by 9
9y = 8x + 23 Subtract 9y from both sides
0 = 8x -9y + 23 Subtract 23 from both sides
-23 = 8x -9y
or
8x -9y = -23
A base-10 three digit number $n$ is selected at random. Which of the following is closest to the probability that the base-9 representation and the base-11 representation of $n$ are both three-digit numerals?
A. 0.3 B. 0.4 C. 0.5 D. 0.6 E. 0.7
Answers
The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.
Given,
We require the following inputs to determine the probability that both the base-9 representation and the base-11 representation are three-digit numbers:
The lowest base 10-based 3-digit base-11 numberThe largest three-digit base 9 in base 10 number.The total amount of 3-digit base-10 numbersThe base-11's lowest 3-digit number is 100.
The comparable number is 121 when expressed in base 10.
888 is the biggest 3-digit base-9 number.
The corresponding number is 728 when expressed in base 10.
As a result, there are the following possibilities:
Possibilities = 728 - 121 + 1
Possibilities = 608
The total number of 3-digit base-10 numbers is
Count = 999 - 100 + 1
Count = 900
The necessary probability is:
P = 608/900
Evaluate
P = 0.6753 ≈ 0.7
Therefore,
The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.
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a) How many times does the line y = -6 intersect with the circle x² + y² = 36 ?
b) Hence, use a single word to describe what the line is to the circle.
Answers
Answer:
a) Once,b) Tangent.Step-by-step explanation:
Part AGeneral equation of circle:
(x - h)² + (y - k)² = r², where (h, k) is center and r- radiusComparing with the general equation we see that the circle x² + y² = 36 has:
Center at the origin,Radius of 6 units.The circle radius of 6 units, so y = - 6 has only one common point.
Part BSince there is only one common point of the circle and line, the line is tangent to the circle.
Determine which integers in the set S:{-24, -6, 12, 24) will make the inequality (m-3) s(m-12) false. OS:{-24, 24} OS:{-24, -6} OS:{-6, 12} OS:{12, 24}
Answers
The integers in the set S:{-24, -6, 12, 24) that will make the inequality 1/3(m - 3) ≤ 1/6(m - 12) false are: S:{12, 24}.
How to determine the integers?In order to determine which integers are true and false with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;
For integers (-24, 24), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(-24 - 3) ≤ 1/6(-24 - 12)
1/3(-27) ≤ 1/6(-36)
-9 ≤ -6 (True).
For integers (-24, 24), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(24 - 3) ≤ 1/6(24 - 12)
1/3(27) ≤ 1/6(36)
9 ≤ 6 (False).
For integers (-24, -6), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(-6 - 3) ≤ 1/6(-6 - 12)
1/3(-9) ≤ 1/6(-18)
-3 ≤ -3 (True).
For integers (-6, 12), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(12 - 3) ≤ 1/6(12 - 12)
1/3(9) ≤ 1/6(0)
3 ≤ 0 (False).
For integers (12, 24), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(12 - 3) ≤ 1/6(12 - 12)
1/3(9) ≤ 1/6(0)
3 ≤ 0 (False).
1/3(m - 3) ≤ 1/6(m - 12)
1/3(24 - 3) ≤ 1/6(24 - 12)
1/3(27) ≤ 1/6(36)
9 ≤ 6 (False).
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Solve the equation. 3 + |t + 4| = 10
Question 9 options:
[-3, 11]
[-11, 3]
[3, 11]
[-3, -11]
Answers
Answer:
b) [-11, 3]
Step-by-step explanation:
Given equation,
→ 3 + |t + 4| = 10
Now the value of t will be,
→ 3 + |t + 4| = 10
→ 3 + t + 4 = 10 || → 3 -(t + 4) = 10
→ t + 7 = 10 || → -t - 1 = 10
→ t = 10 - 7 || → -t = 10 + 1
→ [ t = 3 ] || → [ t = -11 ]
Hence, value of t is 3 (or) -11.
Find the exact value of the expression. Do not use a calculator.
sin 79°-cos 11°
I got 0. I'm not sure if that's right.
Answers
Answer:
sin(79°) - cos(11°) = 0
Step-by-step explanation:
Based on the rule sin(90-x) = cos(x), we can transform the expression. See the attached for more details
-3(x + 4) + 5x simplify
Answers
Answer:
Answer: 2x-12
Step-by-step explanation:
First, you distribute and then combine like terms. :)
Answer:
Step-by-step explanation:
Step 1 : Distribute
The distributive property is a rule in mathematics that is used to help simplify equations by using brackets
-3(x+4) + 5x
-3x - 12 + 5x
Step 2 : combine similar tribes
Similar terms are terms in algebra that have the same variables or constants in algebra. Similar terms of the algebraic form above are. Similar terms are terms in algebra that have the same variables or constants in algebra.
-3x - 12 + 5x
2x - 12
Step 3 : common factor
Common factor is the same factor of two or more numbers. For example, the factors of the numbers 18 and 12 can be determined in the following way. So, the common factors of these two numbers are 2, 3, and 6.
2x - 12
2 (x-6)
Completion
2(x-6)
One dimension of a rectangle is 3 more than twice the other dimension. Let x be the
shortest dimension. Write an equation for the area of the rectangle.
A= x + 2x + 3
A = x(2x + 3)
A= 3x +2
A= 2x +3
Answers
The area of the rectangle with one dimension sizes three more than twice the other dimension is A= x(2x+3)
We assume that there is rectangle ABCD with lines AB and CD are parallel with each other. Meanwhile lines BC and DA are parallel with each other. We could ssume that lines BC and DA are the shortest lines.
Please take a look at the picture below.
Based on the formula of rectangle, the area of rectangle could be calculated using the multiple between the longest line and the shortest line.
It could be written based on the rectangle we have into such formula:
A = AB × BC
A = CD × DA
A = AB × DA
A = CD × BC
If we input the rules from the question, then we could find the relationship between the shortest and the longest lines. Hence:
AB = CD = 2(BC) + 3
AB = CD = 2(DA) +3
if we assume that the shortest line is x, then we will get the formula:
BC = DA = x ...(1)
AB = CD = 2x+3 ...(2)
If we input equation (1) and (2) into the rectangle area formula, we will get the result:
A = AB × BC
A = (2x+3)
A = x(2x+3)
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The federal unemployment tax act (futa) is a payroll tax paid by employers on employee wages. The tax is 6. 0% on the first $7,000 an employee earns each year. If walmart has 1. 5 million employees in the u. S. , about how much does it pay in futa taxes annually?.
Answers
The amount of tax that Walmart pay annually in FUTA is $630 million .
In the question ,
it is given that ,
the amount that an employee earns in 1 year(E) = $7000
the tax rate (r) = 6%
number of employees in Walmart = 1.5 million = 1.5 × 10⁶
So , the amount of tax paid by Walmart in Federal Unemployment Tax Act(FUTA) can be calculated using the formula
Amount = r × n × E
Substituting the values of r , n , E in the amount formula ,
we get ,
Amount = 0.06 × 1.5 × 10⁶ × 7000
= 630,000,000
= 630 million .
Therefore , The amount of tax that Walmart pay annually in FUTA is $630 million .
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The edges of a rectangular solid have these measures: 1. 5 feet by 1½ feet by 3 inches. What is its volume in cubic inches?.
Answers
Volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.
As given in the question,
Given measures of edges of the rectangular solid is equal to :
1. 5 feet by 1½ feet by 3 inches
Length = 1.5 feet
Conversion 1 feet = 12 inches
1.5 feet = 1.5 × 12
= 18 inches
Width = 1½ feet
= 3/2 feet
= ( 3/2 ) × 12
= 18 inches
height = 3 inches
Volume of the rectangular solid = length × width × height
= 18 × 18 × 3
= 972 cubic inches
Therefore, volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.
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Hot dogs are sold in packages of 10. Hot dog buns are
sold in packages of 8. What is the least number of
packages of each that need to be purchased so every
hot dog you buy for a picnic will have a bun?
Answers
Answer:
4 Hot dogs packages and 5 hot dog buns packages.
Step-by-step explanation:
This question seems to be regarding the LCM or the least common multiple. Least common multiple is found by figuring out the first time when both numbers, in this case 10 and 8 have the multiple. You can do this by setting up a table with the multiples of each number.
8 | 16 | 24 | 32 | 40
10 | 20| 30 | 40
We can see that the LCM is 40 so we can see that we need 4 Hot Dog packets and 5 buns packets.
If h(x) = -2x + 10, what is the value of x when h(x) = 2
Answers
Answer:
-6
Step-by-step explanation:
to solve you need to substitute the value of x in the equation which is given as 2so if you rewrite the equation it will be
-2(2)+10
=(-2*2)+10
=-4+10
=6
Two Tofurkys will serve six people. How many people will fourteen Tofurkys serve?
Answers
Answer:
7
Step-by-step explanation:
Solve the equation
2x²+ 8x - 1 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Answers
Answer:
x = 0.08
Step-by-step explanation:
2x²+ 8x - 1 = 0
4x + 8x - 1 = 0
12x - 1 = 0
Add 1 to the -1 and to the 0 too
12x = 1
Divide both side
x = 0.08
a
b
c
d
which is the right answer
Answers
The function is odd because f(-x) = -f(x)
What is a Function?
A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
Solution:
For a function to be even it must satisfy the condition that,
f(-x) = f(x)
else,
if f(-x) = -f(x), then the function is odd
we are given with the function f(x) = [tex]4x^{3}[/tex]
replacing x by (-x)
f(-x) = 4(-x)^3
f(-x) = -4x^3
this implies that, f(-x) = -f(x)
Therefore, the function is an odd function
So, option D is correct
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A wholesale food supplier charges x dollars for each bag of flour and y dollars for each bag of sugar. Bakery A purchases seven bags of flour and five bags of sugar for a total cost of $260.45. Bakery B purchases five bags of flour and three bags of sugar for a total cost of $171.35. What is the cost of each bag of flour? Each bag of sugar?
Answers
The cost of each bag of flour is $ 18.85 and the cost of each bag of $ 25.7 which a wholesale food supplier charges for each bag of flour and for each bag of sugar.
Given that:
The cost of each bag of flour = x dollars
The cost of each bag of sugar = y dollars
Bakery A purchases seven bags of flour and five bags of sugar for a total cost of $260.45.
Bakery B purchases five bags of flour and three bags of sugar for a total cost of $171.35.
Making equation from both the above statements. We get,
7x + 5y = 260.45 ...... (1)
5x + 3 y = 171.35 ....... (2)
Multiplying equation (1) by 5 and equation (2) by 7. We get the value,
35x + 25y = 1302.25 ....... (3)
35x + 21y = 1199.45 ........ (4)
Subtracting equation (4) from (3). We get,
4y = 102.80
=> y = $ 25.70
Putting the value of y in equation (1). We get,
7x + 25.70 x 5 = 260.45
7x = 260.45 - 128.5
7x = 131.95/7
=> x = $ 18.85
Hence, we can say that a wholesale food supplier charges 18.85 dollars for each bag of flour and 25.7 dollars for each bag of sugar.
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Patrick has a rectangular backyard at his new house. After he built a square brick patio, he planted grass in the rest of the yard, as shown below. The grass area is 656 square feet. Two measurements of the grass region are shown in the diagram below. What is the side length of the square patio? Note: The figure is not drawn to scale.
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.Find the y-intercept of (2,4) and (4, 8) and
2.What is the slope of the points that go through (2,4) and (4, 8)
3.Upload a picture of the slope intercept form of the points (2,4) and (4, 8)
Answers
Answer:
1. Y = 2x
2. 2
3.
Step-by-step explanation:
2. Slope = (y2- y1)/(x2-x1)
(8-4)/(4-2)
4/2
2
3.
2x4+6+5x8=_______________
will mark brainiest
Answers
The simplification of the given expression will be 54.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
Given that the expression is 2 x 4 + 6 + 5 thex 8
To solve the given expression we have to first solve the multiplication operation.
2 x 4 + 6 + 5 x 8
8 + 6 + 40
Now add the terms;
8 + 6 + 40
= 54
Hence, the simplification of the given expression will be 54.
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The purchase price of an iPad is $610. If the sales tax rate is 6.5%, what is the amount of sales tax?
Answers
Answer:
Step-by-step explanation:
$603.5
Answer:39.65
Step-by-step explanation:
turn 6.5% to 0.065
610 x 0.065=39.65
The regular price of swimming lessons is $20 per hour. The sale price for new students is 75% of the regula
price. What is the sales price?
Answers
If the half life of a radioactive
substance is 5.3 years and there are
8.4 grams present initially, when will
there be 1 gram remaining?
[?] years
Use the function f(t) = Pert and round
your answer to the nearest year.
Enter
Answers
So in this equation you would get 8.4 *(0.5)^ t/5.3
So if you have access to a graphing calculator you could graph it and get approximately 16.25 years or you could go by half life’s and say after one cycle it will be 4.2
After two cycles it will be 2.1 after 3 cycles it will be 1.05 which rounds to one. Now take your cycles and multiple by 5.3 per cycle to get approximately 16
PLEASE HELP. I need both the x and y and the length of DF
Answers
The value of x is 17, y is 2 and length of DF is 20.
Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
For x
DG = GE ( Given )
DG + GE = DE
DE = 2(DG)
DG/DE = 1/2
hence GH/EF = 1/2
By Basic Proportionality Theorem ( BPT )
(x – 3) / 28 = 1/2
after cross multiplication
2(x – 3) = 28
2x – 6 = 28
2x = 34
x = 17
For y
By Basic Proportionality Theorem (BPT) to side DF
DF = 2(DH)
DH/DF = 1/2
(y + 8) / (y + 8 + x – 7) = 1/2
after cross multiplication
2(y + 8) = y + 8 + x – 7
put x = 17
2(y + 8) = y + 8 + 17 – 7
2(y + 8) = y + 18
2y + 16 = y + 18
2y = y + 2
2y – y = 2
y = 2
DF = 2(2+8)
= 2(10)
= 20
Hence, x is 17, y is 2 and DF is 20.
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wich is the smallest angle in MNO?
Answers
For the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.
As given in the question,
In the given triangle MNO,
Measure of the sides of the triangle are as follow:
MN = 18 yd
NO = 17 yd
MO = 19 yd
Arrange them in ascending order we have,
17 < 18 < 19
NO < MN < MO
From the given measurement of the sides of the triangle , smallest side is NO.
Angle opposite to side MN = ∠O
Angle opposite to side NO = ∠M
Angle opposite to side MO = ∠N
Angle opposite to the smallest side is the smallest angle.
∠M is the smallest angle.
Therefore, for the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.
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Can someone help me with this
Answers
Can you guys help me please bc I tried this and I got it wrong .
Answers
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
you multiply the denominator with the denominator and the numerator with the numerator
[tex]\frac{5}{6}x\frac{2}{5}[/tex]
[tex]\frac{5x2}{6x5}[/tex]
[tex]\frac{10}{30}[/tex]
[tex]\frac{1}{3}[/tex]
Hopes this helps please mark brainliest
Question 12
<
>
Cost of Bottled water. A water bottling company charges $8 per month for their water dispenser and
$4 for each gallon of water delivered. If you have g gallons of water delivered in a month, then the
expression 8 + 4g gives the amount of your bill for that month. Find the monthly bill for 20 gallons.
Answers
The monthly bill for 20 gallons of water is $88.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A water bottling company charges $8 per month for their water dispenser and $4 for each gallon of water delivered.
If you have g gallons of water delivered in a month.
Then, the equation to represent the amount of your bill for that month.
8+ 4g
Now, for g=20 the amount of bill would be
= 8 +4(20)
= 8+ 80
= $88
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