Answer:
6
Step-by-step explanation:
Assuming C lies on segment BD, we know that by the segment addition postulate,
[tex]BC+CD=BD \\ \\ 2+2x-6=x+2 \\ \\ 2x-4=x+2 \\ \\ x=6[/tex]
The values of BC = 2, CD = 2x - 6 and BD = x + 2 then the value of x = 6.
How to find the value of x?The algebraic expression should be any one of the conditions such as addition, subtraction, multiplication, and division.
In mathematics, an algebraic expression exists as an expression built up from integer constants, variables, and algebraic operations. For example, 3x² − 2xy + c exists as an algebraic expression.
To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Given: BC = 2, CD = 2x - 6 and BD = x + 2 then
BC+CD= BD
2+2x-6=x+2
Simplifying,
2x-4=x+2
Thus,
x=6
Therefore, the value of x = 6.
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a=-2x^2 + 36x
solve for x
Answer:
x= 18,0
Step-by-step explanation:
Find an equation of the tangent to the curve at the given point
x=cos(t)+cos(2t)
y=sin(t)+sin(2t)
(-1,1)
y=?
Equation of the tangent to the curve at point (-1,1) is: y=2x+3
Given,
x=cos(t)+cos(2t)
y=sin(t)+sin(2t)
P(-1,1)
For the point(-1,1), the value of t satisfy the equations x=cos(t)+cos(2t) and y=sin(t)+sin(2t) is pi/2.
To find an equation of the tangent to the curve at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2, we need to first find the slope of the tangent line at this point. To do this, we need to take the derivative of the x and y functions with respect to t:
dx/dt = -sin(t) + 2sin(2t)
dy/dt = cos(t) - 2cos(2t)
Now we can use this information to find the slope of the tangent line at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2:
slope = dy/dx = (cos(t) - 2cos(2t)) / (-sin(t) + 2sin(2t)) evaluated at t = pi/2
slope = (cos(pi/2) - 2cos(2pi/2))/(-sin(pi/2) + 2sin(2pi/2)) = 0 - (-2)/0 + 0 = 2
Now, we can use this slope to find the equation of tangent using:
(y-y1)= m(x-x1)
=> y-1=2(x+1)
=>y=2x+3
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3. Mariana has a fish tank that is 30 in x 12 in x 16 in. What unit of measurement should she use for volume?
square inches
cubic feet
cubic inches
pounds
Answer: cubic inches
Step-by-step explanation: volume is cubed since it is 3 dimensions and it is in inches which are the units given
Find the slope of the line. 4y-2x= -30
Answer:
The slope is 1/2
Step-by-step explanation:
To find the slope of the line, put the equation in slope intercept form.
y= mx+b where m is the slope and b is the y intercept
4y -2x = -30
Add 2x to each side
4y -2x+2x = 2x-30
4y = 2x-30
Divide by 4
4y/4 = 2x/4 -30/4
y = 1/2x -15/2
The slope is 1/2
Answer:
0.5
Step-by-step explanation:
To find the slope of the line you have write this in slope intercept form.
That is,
y = mx + c.Here,
m - Slope
c - y intercept
Now, to write this expression in slope intercept form, you have to make y the subject of this expression.
[tex] 4y - 2x = - 30[/tex]
Add 2x to both sides.
4y = 2x - 30
Now divide both sides by 4.
y = 2/4x - 30/4
Accordingly,
[tex]y = 0.5x - 7.5[/tex]
Slope of the line (m) = 0.5
3(0.4h+5) > 4(0.2h+7)
Whenever you want to add clarification, explanation, or a side remark to a statement, you should use parentheses ().
How to find the calculation?3(0.4h+5)=4(0.2h+7)
When adding extraneous information or an aside to a sentence, parentheses, a pair of punctuation marks, are most frequently utilized.
Two curving vertical lines can be seen in parentheses: ( ). Parenthesis refers to a single instance of this punctuation.
To the left, we reposition every term:
3(0.4h+5)-(4(0.2h+7))=0
Parentheses are increased.
0h-(4(0.2h+7))+15=0
-(4(0.2h+7)), which we calculate as follows:
4(0.2h+7)
Parentheses are increased.
0h+28
In addition, we add up all the numbers and variables.
h+28
Resuming the equation
-(h+28)
In addition, we add up all the numbers and variables.
h-(h+28)+15=0
Parentheses are removed.
h-h-28+15=0
In addition, we add up all the numbers and variables.
-13!=0
For this equation, there is no answer.
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Triangle Theorems.
What is the Value of X?
Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.
How to find the value of x in a triangle? Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown".The triangle in question is an equilateral triangle.The unknown is called a variable. In order to solve for a variable (like x), you need to isolate the variable. You can isolate the variable by using inverse operations to manipulate the equation. Addition is the inverse of subtraction, and multiplication is the inverse of division.If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle.Alternatively, multiply the hypotenuse by cos(θ) to get the side adjacent to the angle.Thus, all angles are equivalent to 60 degrees.
So, for a triangle, we know that Interior angle + neighbouring outside angle = 180°, 60° + x = 180°, and x = 180° - 60° = 120°.
Thus, a triangle's x value is 120°.
The side x of the right triangle can be found using trigonometric ratios.Therefore,sin 30° = opposite / hypotenusesin 30 = x / 81 / 2 = x /8cross multiply8 = 2xdivide both sides by 28 / 2 = 2x / 2x = 4To learn more about Triangle refer to:
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Pls help! Will appreciate so much. Evaluate 4+ (m - n)^4 when m = 7 and n =5.
Answer:
20
Step-by-step explanation:
P= 2(l+w)
solve for l?
Answer:
[tex]l = \frac{P}{2} - w[/tex]
Step-by-step explanation:
[tex]P= 2(l+w)[/tex]
[tex]\frac{P}{2} = l +w[/tex]
[tex]l = \frac{P}{2} - w[/tex]
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed. Division Line
2 3/5 divided by 1 1/4
The quotient is [tex]2\frac{2}{25}[/tex]. The quotient is a mixed number.
What is a fraction bar?
With mathematics, a fraction bar is a visual representation of fractions that aids in fraction comparison and fraction operations. A part-to-whole representational model is fraction bars or fraction strips. Each fraction bar segment represents one unit of a larger whole.
Given that [tex]2\frac{3}{5}[/tex] divide by [tex]1\frac{1}{4}[/tex].
The mathematical representation is
[tex]2\frac{3}{5}[/tex] ÷ [tex]1\frac{1}{4}[/tex]
Convert the mixed fraction to improper fraction:
= (2×5 + 3)/5 ÷ (1×4+1)/4
=(13/5) ÷ (5/4)
To convert the division sign into a multiplication sign, take the reciprocal of 5/4.
= (13/5) × (4/5) [Reciprocal of 5/4 is 4/5]
= 52/25
If 52 is divided by 25, the quotient is 2 and the remainder is 2.
Convert 52/25 into a mixed fraction:
52/25 =[tex]2\frac{2}{25}[/tex].
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Solve for u.
U/4 = 3
U = ?
there are 2 sections to this question: a group of teenagers are asked about their favourite hobbies. 9 males and 7 females like sports, a total of 16 people; 2 males and 3 females like video games, a total of 5 people; 3 males and 8 females like watching films, a total of 11 people, a total of 14 males and 18 females participated. question 1 - in fractions what is the probability that a teenager selected at random is female and their favourite hobby is watching films? you can simplify this fraction if you wish. question 2 - the teenager from the question above rejoins the group and another teenager is picked at random what is the probability that the teenager picked at random is male and their favourite hobby is playing video games? you can simplify this fraction if you wish
a) In fractions the probability that a teenager selected at random is female and their favorite hobby is watching films is given as: 1/4, while
b) if the teenager from the question above rejoins the group and another teenager is picked at random, the probability that the teenager picked at random is male and their favorite hobby is playing video games is 1/6.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
With regard to problem (a),
There is a total of 32 teenagers.
Of those, 8 are female with a favorite hobby of watching films.
Thus,
Related Probability = 8/32; divide both numerator and denominator by 8 to get;
= 1/4
With regard to problem (b), the probability that the teenager picked at random is male and their favorite hobby is playing video games is:
P = (14/32) x (2/14)
P = 2/32; thus
P = 1/16.
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Full Question:
A group of teenagers are asked about their favourite hobbies. The results are shown in the following table: Sports Playing video games Watching films Total
Male 9 2 3 14
Female 7 3 8 18
Total 16 5 11 32
Q6a. In fractions, what is the probability that a teenager selected at random is female and their favorite hobby is watching films? You can simplify this fraction if you wish.
Q6b. the teenager from the question above rejoins the group and another teenager is picked at random what is the probability that the teenager picked at random is male and their favourite hobby is playing video games? you can simplify this fraction if you wish
Without graphing the equations, decide whether the system has one solution, no solution, or infinitely many solutions. 5y =x-6 4x-10y=12
Answer:
One solution:
[tex]\boxed{x = 0,\;y = -\dfrac{6}{5}}[/tex]
Step-by-step explanation:
The solution strategy is to isolate one of the variables by eliminating the other. There are several ways to do this. This is my preferred way
The equations are
[tex]5y = x-6 \cdots[1]\\\\4x - 10y = 12 \cdots[2]\\\\[/tex]
Transform equation [1] into the same form as [2] with x and y variables on the left and the constant on the right:
Subtract x from both sides of equation [1]:
[tex]-x + 5y = -6\cdots[3][/tex]
Multiply equation [3] by 2 to get the coefficients of y the same
[3] x 2 gives
[tex]-2x + 10 y = -12\cdots[4][/tex]
In equations [2] and [4], the coefficients of y are the same but of opposite sign
Add equations [2] and [4] to get
[tex]4x - 10y + (-2x + 10y) = 12 + (-12)\\\\4x - 10y -2x - 10y = 12 -12\\\\4x - 2x -10y + 10y = 0\\\\2x = 0\\\\x = 0\\\\[/tex]
Substitute for x = 0 in any of the equations [1] or [2] and solve for y
Let's pick equation 1
Substitute for x = 0 in [tex]5y = x - 6\\[/tex]
[tex]5y = 0 - 6\\\\5y = -6\\\\y = -\dfrac{6}{5}\\\\[/tex]
So this is a system of equations with one solution:
[tex]\boxed{x = 0,\;y = -\dfrac{6}{5}}[/tex]
In a retail store with 36 employees, 29 work with customers, 11 work in the
warehouse, and 4 do neither. How many employees both work with customers and
work in the warehouse?
Answer: 8 employees doing both jobs.
Step-by-step explanation:
If 4 do neither, we can subtract this from the total number of employees. This will give us the employees that work with customers, the warehouse, or both.
36 - 4 = 32 employees
Next, we need to find how many do both. We can add 29 and 11 together to find the total number of jobs worked in these sections (this will include employees doing both jobs).
29 + 11 = 40 employees
Lastly, we will subtract the total number of employees working in these sections from the number above to find how many are doing both jobs.
40 - 32 = 8 employees doing both jobs.
Solve.
4 Laqueta has n red apples and m green apples in a basket.
She puts 3 more red apples into the basket. Write an
expression for the total number of apples Laqueta has
in the basket.
Therefore, the expression for the total number of apples Laqueta has in the basket is (n+3) + m.
Define expression.An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Define symbols.A figure or a group of figures used to represent a mathematical item, an action on a mathematical object, a relationship between mathematical objects, or to organize other symbols that appear in a formula are known as mathematical symbols.
The total number of apples Laqueta has in the basket = n+m
When she puts 3 more red apples into the basket, the total number of red apples becomes n+3.
So, the total number of apples Laqueta has in the basket is (n+3) + m.
This can be simplified as n+m+3.
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What is the equation of the line that passes through the point (5, 5) and has a slope of -1?
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options.
Answer:
follow me if this helped you
Step-by-step explanation:
The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Xin uses 20 yards of fencing to build the walls of square chicken coop. which equation and solution represent x, the length, in yards, of each wall of square coop
The equation of the square coop is 4x = 20 and the length is 5yd .
What is equation ?
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.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
20yd of fencing to build the walls of a square coop.
Therefore, the perimeter of the square coop is 20 yd .
Then the equation of the perimeter of the square coop is 4x = 20.
Solving the equation,
4x = 20
We get,
x = 5yd
The equation of the square coop is 4x = 20 and the length is 5yd .
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x is a whole number such that -4 < x < 2
Answer:
x = [-3, 1]
Step-by-step explanation:
I wrote it in interval notation but if x can be any whole number between those two it can literally be -3, -2, 1, 0 or 1. Unless there are further restrictions or some sort of equation, there is no one number answer. Pick your poison, write it like x = {-3, -2, 1, 0, 1} if you'd like or the way I wrote it.
2. Which number below is an odd number? (1
O533
0422
1,022
0874
Answer:
533
Step-by-step explanation:
Ends in an odd number
Answer:
the first one: 0533
Step-by-step explanation:
1,3,5,7,9 are basic odd numbers
2,4,6,8 are basic prime numbers
see what the last digit is aka the ones place
see if it ends in an odd or even
the only one that has the last digit as an odd number is the first one 0533, therefore it is the answer.
A dog runs along a railroad track. A train that is 270 meters long passes her in 18 seconds. The speed of the train is 20 meters per second. What is the dog's speed?
The dog moves quickly through 250-meter passes
What is unitary method?This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
According to our question-
dog run =11 metres per second
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Solve the system by the addition method.
-5x - 9y = 28
-4x + 5y = -2
The solution of the given system of equations is (-2, -2).
What is addition method?
Using the Addition Method to Solve Systems of Equations in Two Variables. The addition method, also known as the elimination method, is a third strategy for resolving linear equation systems. With this approach, we add two terms that share the same variable but have opposing coefficients, resulting in a sum of zero.
Consider, the given system of equations
-5x - 9y = 28 ..(1)
-4x + 5y = -2 ..(2)
Multiply equation (1) by 5 and multiply equation (2) by 9.
-25x - 45y = 140 ..(3)
-36x + 45y = -18 ..(4)
Adding equation (3) and (4), we get
-25x - 45y = 140
+ -36x + 45y = -18
______________________
-61x + 0 = 122
-61x = 122
x = -2
Plug x = 2 in equation (1)
-5(-2) - 9y = 28
10 - 9y = 28
9y = -18
y = -2
Hence, the solution of the given system of equations is (-2, -2).
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please help with steps
Answer:
Okay so, if he is getting a console for $17.50, then you first want to do is subtract that from the total amount that he has which is $49.
49 - 17.50 = $31.50
Now each game costs $5.25
You can either just keep adding 5.25 by itself until you get to 31.50, or you can just divide 31.50 by 5.25, but I am going to just multiply then by certain numbers until I get the result.
5.25 * 5 = 26.25 so we know he can buy more than 5.
5.25 * 6 = 31.50
He can buy 6 games!
Step-by-step explanation:
Hope it helps! =D
According to the CDC, 6% of people who contract measles also develop pneumonia. If there were 1,296 cases of the measles in the United States in 2019, how many people developed pneumonia? Round to the nearest whole person.
By approximately what percentage (relative change) did measles decline between 2014-2015? Round your answer to two decimal places.
The people that developed pneumonia will be 78 people.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
According to the CDC, 6% of people who contract measles also develop pneumonia. If there were 1,296 cases of the measles in the United States in 2019, the people that developed pneumonia will be:
= 6% × 1296
= 78 people.
The second question can't be solved as the information isn't given.
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Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use.
what is the probability that the first unbelted driver is in the 6th car stopped?
Answer:
20%
Step-by-step explanation:
The probability that the first unbelted driver is in the 6th car stopped is
(1 - 0.20)^5 * 0.20,
where 0.20 is the probability that a driver does not wear their seatbelt (20%),
and (1 - 0.20)^5 is the probability that the first 5 cars stopped all have drivers who wear their seatbelts.
This simplifies to (0.8)^5 * 0.2 = 0.32768 * 0.2 = 0.065536.
You and some friends have $30. You want to order large pizzas (p) that are $10 each and drinks (d) that cost $1 each. Make a table of possible choices(including intercepts) and graph an inequality that shows how many pizzas and drinks you can order.
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]
See attachment for the graph of the inequality.
Step-by-step explanation:
Given information:
Maximum amount of money available = $30Cost of one large pizza (p) = $10Cost of one drink (d) = $1The inequality to represent the given information is:
10p + d ≤ 30To complete the given table, input p from 0 through 3 into the inequality and solve for d.
[tex]\begin{aligned}p=0 \implies 10(0) + d & \leq 30\\d & \leq 30\end{aligned}[/tex]
[tex]\begin{aligned}p=1 \implies 10(1) + d & \leq 30\\10+d & \leq 30\\d & \leq 20\end{aligned}[/tex]
[tex]\begin{aligned}p=2 \implies 10(2) + d & \leq 30\\20+d & \leq 30\\d & \leq 10\end{aligned}[/tex]
[tex]\begin{aligned}p=3 \implies 10(3) + d & \leq 30\\30+d & \leq 30\\d & \leq 0\end{aligned}[/tex]
Completed table:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]
To graph the inequality:
Let the x-axis represent the number of pizzas (p).Let the y-axis represent the number of drinks (d).Plot two points from the table: (0, 30) and (3, 0).Draw a solid line through the points.Shade under the line.list two ways you can tell if a pair of numbers is a solution to an equation
Answer:
Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.
Step-by-step explanation:
What is the area of a hexagon 10m by 5m
The area of the hexagon is approximate, Area = (150 √3) m².
What is a formula of a hexagon?
A Regular hexagon has six sides and angles that are congruent and is made up of six equilateral triangles. The formula to find out the area of a regular hexagon is as given:
Area = (3√3 s²)/ 2
where 's' represents the length of a side of the regular hexagon.
A hexagon is a six-sided polygon. The area of a hexagon can be calculated using the formula:
Area = (3 * √3 * (side length)^2) / 2
In this case, the hexagon is 10m by 5m, so the side length of the hexagon is 10m. Plugging this into the formula, we get:
Area = (3 * √3 * (10m)^2) / 2
Area = (3 * √3 * 100m^2) / 2
Hence, the area of the hexagon is approximate:
Area = (150 √3) m².
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35% of 40 is what value? 5 12 14 23
Answer:
14
Step-by-step explanation:
35% of 40
= [tex]\frac{35}{100}[/tex] × 40
= 0.35 × 40
= 14
(3x² + 3) + (3x2+x+4)
O A. 9x²+x+12
OB. 6x²+x+7
OC. 6x² + x + 12
OD. 9x²+x+7
I need helpppp asap!!
Answer:
The answer is 6x²+x+7
Step-by-step explanation:
(3x²+3) + (3x²+x+4)
3x²+3 + 3x²+x+4
COLLECT LIKE TERMS
3x²+3x²+x+3+4
ADD UP LIKE TERMS
6x²+x+7
Camila is a seamstress and is creating wedding dresses. She has 192 yards of silk fabric. For each dress, the skirt requires 6 yards of silk and the bodice requires 2yards of silk. How many dresses can she make with the amount of silk she has?
With the amount of silk she has, she can create 48 garments.
What is unitary method?
This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
According to our question-
She possesses 144 yards of silk cloth.
Each dress needs 3 yards of silk for the skirt and 1 yard for the bodice.
According to the data given, the calculation is as follows:
144/3
48
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