When segments intersect inside a circle, what is the relationship between the angle of intersection and the intercepted arcs?
Answer:
Angle of intersection is one half of the sum of measurements of intercepted arcs.
Step-by-step explanation:
An inscribed angle is the angle formed by the intersection of two chords having a common endpoint in a circle.
Also, by the angles of Intersecting Chords Theorem,
When two chords intersect inside a circle, then the measure of the angle formed is one half of sum of the measure of the arcs intercepted by the angle and its vertical angle.
Which is the relationship between the angle of intersection and the intercepted arcs.
What is the length of the other diagonal DF?
5 cm
16 cm
21 cm
32 cm
Applying the Pythagorean theorem, the length of diagonal DF is: C. 21 cm.
What is the Pythagorean Theorem?The sum of the squares of the two shorter legs of a right triangle equals the square of the length of the longest leg.
Let the point of intersection of the diagonals be O.
Diagonal FD bisects diagonal EG into equal segments EO and OG. EO = OG = 24/2 = 12 cm
Find the lengths of FO and OD using the Pythagorean theorem:
FO = √(20² - 12²) = 16 cm
OD = √(13² - 12²) = 5 cm
Length of diagonal DF = FO + OD = 16 + 5 = 21 cm.
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how many times does 28 go into 126????????
Nam has a beginning balance of $815 in her checking account. She writes a check for $210 and has a debit transaction of $525. What is her new balance?
$125
$80
$1550
$120
Write the rule for the nth term of an arithmetic sequence in which a10=46 and d=3
Final answer:
The rule for the nth term of the arithmetic sequence is given by the formula a_n = 19 + (n - 1)×3, where a1 is the first term of the sequence and d is the common difference.
Explanation:
To write the rule for the nth term of an arithmetic sequence where the 10th term a10 is 46 and the common difference d is 3, we use the formula:
an = a1 + (n - 1)d
We have that:
a10 is the 10th term of the sequence which is 46.
The common difference d is 3.
Firstly, we need to find a1, the first term of the sequence. We can use the given a10 to find a1.
a10 = a1 + (10 - 1)×3
46 = a1 + 9×3
46 = a1 + 27
a1 = 46 - 27
a1 = 19
Now we can write the rule for the nth term:
an = 19 + (n - 1)×3
This formula allows us to calculate any term in the sequence by substituting the desired term number for n.
add any three numbers of the following and answer should be 60
2 , 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58
Classify the number 0. Check all that apply.
Real
Irrational
Rational
Integer
Whole
Natural
Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up to Mandy. He tracks his book reading with a table on his door. Using his table below, what month will Bill have read the same amount of books as Mandy?
Month Books
May 4
June 8
July 12
Which of the following expressions describes the solution set m ≥ -3?
All real numbers that are negative three or greater.
All real numbers that are greater than negative three.
All real numbers that are negative three or less.
All real numbers that are less than negative three.
The correct expression of the solution set will be;
''All real numbers that are greater than negative three.''
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The solution set is,
m ≥ - 3
Now,
Here, The solution set is,
m ≥ - 3
Clearly, a number 'm' is greater than or equal to - 3.
Thus, We can formulate;
The correct expression of the solution will be;
''All real numbers that are greater than negative three.''
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A surveyor standing 67 meters from the base of the building measures the angle to the top of the building and finds it to be 36 degrees. The surveyor then measures the angle to the top of the radio tower on the building and finds it is 46 degrees. How tall is the radio tower?
my choices are: a. 11.81m , b. 20.7 m, c. 7.66 m, d. 8.81 m
Any advice or assistance is appreciated. ...?
Answer:
Option B is the correct answer.
Step-by-step explanation:
Refer the the figure below of the question given.
The height of radio tower = CD
CD = AD - AC
We have
[tex]tan46=\frac{AD}{AB}\\\\AD=ABtan46=67tan46\\\\tan36=\frac{AC}{AB}\\\\AC=ABtan36=67tan36\\\\CD=67tan46-67tan36=20.70m[/tex]
Option B is the correct answer.
2x-3y=13 y=1/2x-7/2 as a substitution problem
olivia has $180 to buy presents for her 3 sisters and 2 nephews. she wants to spend $20 more on each sister then she spends on each nephew.
Answer:
she spends 44 dollars per sister, 24 dollars per nephew
Step-by-step explanation:
180=3(20+x)+2x
180=60+3x+2x
120=5x
x=24
x+20=44
1.) Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52> How old is Mousy?
2.)Mike is 5 years more than twice as old as Tom. The sum of their ages is 65. How old is Mike?
On the way home from school, ross wears his 20-pound backpack and carries his 7-ounce lunchbox. how many ounces does he carry in total?
Answer: [tex]327[/tex] [tex]\text{ounce}[/tex]
Step-by-step explanation:
Given: On the way home from school, ross wears his [tex]20[/tex] pound backpack and carries his [tex]7[/tex] ounce lunchbox.
To Find: how many ounces does he carry in total.
Solution:
Weight of Ross's backpack [tex]=20[/tex] [tex]\text{pound}[/tex]
Weight of Ross's lunchbox [tex]=7[/tex] [tex]\text{ounce}[/tex]
Now,
As unit of weight of backpack and lunchbox is different, we need to convert it.
[tex]1[/tex] [tex]\text{pound}[/tex] [tex]=16[/tex] [tex]\text{ounce}[/tex]
Now weight of backpack is[tex]=\text{weight in pound}\times16[/tex]
[tex]20\times16[/tex]
[tex]320[/tex] [tex]\text{ounce}[/tex]
Total ounces carried by Ross [tex]=\text{weight of backpack}+\text{weight of lunchbox}[/tex]
[tex]320+7[/tex] [tex]\text{ounce}[/tex]
Hence Total ounce carried by Ross is [tex]320+7[/tex] [tex]\text{ounce}[/tex]
what is the answer to n/5- 9= 1/5
Can fractions still be considered natural, whole, integers, rational, irrational, or real numbers?
a bag of oranges weighs 5 1/4 pounds. how much do (1 & 1/2) bags weigh
*WRITTEN ANSWER....PLZ HELP, AND TELL ME HOW YOU SOLVED IT! THANK YOU AND HAVE A FANTASTIC DAY!*
Answer:
7 7/8 pounds
Step-by-step explanation:
Given that a bag of oranges weighs 5 1/4 pounds and you want to know how much do 1 1/2 bags weigh, the next proportion must be satisfied:
(5 1/4 pounds)/(1 bag of oranges) = (x pounds)/(1 1/2 bag of oranges)
Isolating x:
x = (5 1/4)*(1 1/2)/1
x = 7 7/8 pounds
What is 75% of 90? 67.5 6750 675 6.75
To calculate 75% of 90, convert the percentage to a decimal (0.75) and multiply it with 90, resulting in 67.5.
To find 75% of 90, we can use the concept that 'percent' means 'per hundred'. The calculation involves turning the percentage into a decimal by dividing by 100 and then multiplying by the number in question. Thus, 75% can be written as 0.75 (since 75 divided by 100 equals 0.75).
Therefore, to find 75% of 90, we multiply 90 by 0.75:
0.75 × 90 = 67.5
The correct answer is 67.5, not 6750, 675, or 6.75.
A function takes in values of the ____________________ variable, called inputs, and gives back values of
the ____________________ variable, called outputs. A function takes in values of the ____________________ variable, called inputs, and gives back values of
the ____________________ variable, called outputs.
Describe a real world situation that would show a strong negative correlation explain your reasoning
a number of apples divided into 12 baskets
-7 over -10 simplified
If 20% of all manually filed returns contain errors, and 0.05% of all electronically filed returns contain errors, how much more likely is a manual filer to make an error than an electronic filer?
a.
40,000 times more likely
b.
4,000 times more likely
c.
400 times more likely
d.
40 times more likely
Answer:
c. 400 times more likely
Step-by-step explanation:
This coordinate plane shows the shape of a hang glider. The perimeter of the glider is to be trimmed with a special material. What is the minimum length of material needed?
X = 24 ft Of Materials
Y = 2 ft Of Distance
X = (12,7)
Y = (0,2)
Using The Pythagoras Theorem
[tex]D=\sqrt{12^{2}+5^{2}}=13[/tex]
Total lenght is:
[tex]\left[\begin{array}{ccc}3*13+24+4=26\\26+28=54\end{array}\right][/tex]
Use the Distributive Property to complete the following statement:
4(x−1)=4x−
1.
–4.
4.
–1.
An employee receives a weekly salary of $340 and a 6% commission on all sales.
Find the employee's earnings for a week with $660 total sales.
The employee earns a fixed salary of $340 plus a 6% commission on sales. In a week with $660 in sales, his total earnings would be $379.60.
Explanation:The employee's weekly income is a combination of a fixed salary and a percentage of sales. His fixed salary is $340. From his sales, he earns a 6% commission. So for a week with $660 in sales, the commission would be 6/100 * 660, which equals $39.60. Adding this commission to the fixed salary: $340 + $39.6 = $379.60. So, the employee's overall earnings for the week would be $379.60.
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What is the simplified form of x + 6/3 - x + 2/3
The simplified form of the given expression x + 6/3 - x + 2/3 is 8/3 after combining like terms and simplifying the constants.
The question involves simplifying a mathematical expression.
The expression given is:
x + 6/3 - x + 2/3.
To simplify this expression, combine like terms.
Since x is present in both the first and third terms, they cancel each other out.
Next, combine the constant terms 6/3 and 2/3. This results in:
6/3 + 2/3 = (6 + 2) / 3 = 8/3
The simplified form of the expression is therefore 8/3.
Write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
We need to write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
Therefore, 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
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find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ? find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ?
The non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
Explanation:An expression is undefined when its denominator is equal to zero. Therefore, we need to find the values of x that make the denominator, 2x-4, equal to zero.
Solve the equation for x: 2x - 4 = 0 2x = 4 x = 2
Therefore, x = 2 is a non-permissible replacement because it makes the denominator zero.
Additionally, the expression also includes x^2 in the numerator. Since any number multiplied by zero is still zero, dividing any non-zero number by zero results in undefined. Therefore, x = 0 is also a non-permissible replacement.
In conclusion, the non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
Three mathematicians are applying for a job. There are five hats, three white, two black. They’re lined up, and a hat is placed on each. The first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the hats of the two people in front of her. The first person to correctly figure out what color hat he has gets the job; you guess wrong and you are killed. Assume these are INTELLIGENT mathematicians, and that they will do the logically correct thing at each stage — if something can be deduced, they will figure it out.
After a long pause,the first person, who cannot see any hats, says he knows the color of his hat. What is the color, and how does he know?