Answers
The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).
What are Similar Triangles?Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
The right triangle is given in the question, as shown.
AD = 4 cm and BD = 5
In ΔACD and ΔABC
∠ACD = ∠ABC
∠ACD = ∠BAC = 90°
∠CAD = ∠ACD (remaining)
So ΔACD and ΔABC are similar
Hence
AD / AC = AC/ BC
Apply the cross-multiplication operation, and we get
AC² = AD × BC
AC² = 4 × 9
AC² = 36
AC = 6 cm
So, the side length of AC is 6 units.
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Related Questions
Look at the following speeds.
4mph 8mph 16mph 32mph 64mph 128mph
By what factor did the speeds change for each consecutive speed from the first speed to the sixth speed.
A. 8
B. 32
C. 4
D. 2
Answers
The factor by which ths speed increases is 2, then the correct option is D.
By what factor did the speeds change for each consecutive speed?Here we have the sequence of numbers:
4, 8, 16, 32, 64, 128
Where these have units of miles per hour, but can be ignored, as we only care for the numbers. To get the factor by which the speed change for each consecutive speeds, we just need to take the pairs of consecutive numbers and take their quotients.
We will get:
8/4 = 2
16/8 = 2
32/16 = 2
etc.
Then the factor is 2, the correct option is D.
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A chemist has a 25% and a 50% acid solution. How much of each solution should be
used to form 200 ml of a 35% acid solution?
P.S: no decimal is used in this solving. For example 0.25, 0.50, and 0.35 is converted to 25%, 50% and 35%.
Answers
The required amount each type of solution to make mixture are 120 ml of 25% acid and 80 ml of 50% acid.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Explain Acid solution.A liquid mixture known as an acidic solution is created when water and hydrogen ions react. The Brnsted-Lowry theory states that whereas bases "receive" hydrogen protons, acids "give" hydrogen protons. Different solutions have different levels of acidity.
According to question:Let there be (200 - x) ml of 50% acid and x ml of 25% acid.
200*0.35 = 0.25x+0.5(200-x)
0.25x +100 -0.5x = 70
30 = 0.25x
x=120
200 - x = 200 - 120 = 80, resulting in 120 ml of 25% acid and 80 ml of 50% acid.
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For the mixture, 120 ml of 25% acid and 80 ml of 50% acid are needed for each type of solution.
What is a percentage?A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. Therefore, the percentage refers to a component per 100. The word percent simply means "per 100." Its symbol is the letter "%."Describe Acid solution.Water and hydrogen ions react to form an aqueous mixture known as an acidic solution. According to the Brnsted-Lowry theory, while bases "get" hydrogen protons, acids "give" them. Acidity levels vary among various solutions.Let's say there are (200 - x) ml of 50% acid and x ml of 25% acid.200*0.35 = 0.25x+0.5(200-x) (200-x)0.25x +100 -0.5x = 7030 = 0.25xx=120200 minus x equals 200 minus 120 equals 80, yielding 120 ml of 25% acid and 80 ml of 50% acid.To learn more about percentage refer:
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D Study the Example showing how to write the equation of a line in slope-intercept form from a graph. Then solve problems 1-5. Example An oceanographer is studying the growth of giant kelp. She selects one giant kelp plant and records its height each day. Then she draws this graph. What is the equation of the line in slope-intercept form? Define your variables. (0, 10) and (2, 60) are two points on the line. 60 - 10 2-0 = 50, or 25 m= Height (cm) 120 100 80 y 60 40 20 0 The slope is 25. The line intersects the y-axis at (0, 10). The y-intercept is 10. The equation y = 25x + 10 shows the height, y, of the giant kelp plant after x days. 0 1 3 4 2 Time (days) What do the slope and y-intercept in the Example represent in this situation?
Answers
The slope of the line in the example is 25 and the y-intercept is 10. These values can be used to write the equation of the line in slope-intercept form, y = 25x + 10.
The slope, m, represents the rate of change of the height of the giant kelp plant. In this case, the slope is 25, meaning that for every day that passes, the height of the giant kelp plant increases by 25 centimeters.
The y-intercept, b, represents the height of the giant kelp plant at time = 0. In this case, the y-intercept is 10, meaning that the giant kelp plant is 10 centimeters tall at time = 0.
So in this situation the slope represents how much the height of the kelp plant changes with respect to time and the y-intercept represents the initial height of the kelp plant at time = 0.
What is the solution to the system?.
8x - 8y =-8
X=-3y=13
Answers
x=-8
y=-7
F(-7, 12) and G(3, -8)
Answers
The coordinates of the midpoint M of the segment FG is (-2,2).
This question is incomplete, the complete question is;
What is the midpoint M of a line having two endpoints F(-7, 12) and G(3, -8),
What is the coordinates of the midpoint M of the segment FG?The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point F (-7, 12)
x₁ = -7y₁ = 12Point G (3,-8)
x₂ = 3y₂ = -8To determine the midpoint, plug the given points into the formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( (-7 + 3 )/2, ( 12 + (-8) )/2 )
M = ( ( -4 )/2, ( 12 - 8 )/2 )
M = ( ( -4 )/2, ( 4 )/2 )
M = ( -2, 2 )
Therefore, the midpoint M of the segment is (-2,2)
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Answer choices
AA
SAS
SSS
GIVEN
alternative interior angles are congruent
Vertices angles are congruent
Answers
The first statement is given, the second statement is true because they are vertically opposite angles and the third statement is true by SAS congruency of triangles.
What is congruence of triangles?
Two triangles that are congruent will have precisely the same three sides and three angles.
The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.
The first statement is true because this is already given in the question.
The second statement is true because ∠KLJ and ∠MLN are vertically opposite angles and we know that vertically opposite angles are always equal. Therefore, the second statement is true.
The third statement is true because of the SAS congruency of triangles.
As we are given ratio of two sides equal to ratio of corresponding sides and the angle between the sides to be equal.
Hence, the two triangles are congruent.
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You brake your car from a speed of 55 mph. The table shows data that represent your car's speed versus the amount of time elapsed from the moment that you began to brake.
Elapsed Time (sec)
Speed (mph)
1
45
2
35
3
25
4
15
5
15
6
15
Evaluate the following graph based on the data in the table.
A graph has elapsed time (seconds) on the x-axis, and speed (miles per hour) on the y-axis. A line goes through points (1, 45), (2, 35), (3, 25), (4, 15), (5, 15), (6, 15).
What is the slope of the line segment that represents the period of time during which the speed decreases?
a.
The slope is 0.
c.
The slope is 10.
b.
The slope is -10.
d.
The slope is -11.
Answers
The slope of the line segment that represents the period of time during which the speed decreases is: C: The slope is -10.
How to find the Slope?The parameters given are:
Starting speed of the car = 55 km/hr
Let us suppose when t=0 , the speed of car was 55 km/hr.
Then car broke down.
The following Data are given regarding car's speed versus the amount of time elapsed from the moment that it began to brake.
Elapsed Time (sec) Speed (mph) → 1 :45 ,2 :35, 3 :25, 4 :15, 5 :15 ,6 :15
Slope of line passing through two points (a, b) and (p, q) is given by the formula:
Slope = (q - b)/(p - a)
Thus, Slope of line passing through two points (1,45) and (2,35) is:
Slope = (35 - 45)/(2 - 1)
Slope = -10
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if 3/4 of a certain number is equal to 4 1/2 find the number
Answers
Answer:
6
Step-by-step explanation:
4 1/2= 4.5
3/4=0.75
4.5/0.75= 6
just to check, 3/4 x 6 =4.5
Write about a real-world situation that can
be represented by the equation y = 7x. Be sure to explain what the variables
represent in the situation.
Answers
Answer:
the equation could represent your paycheck at the end of a shift. y is equal to the total amount of money you made, 7 is equal to your hourly wage, and x is equal to the number of hours worked. For example if you worked two hours one day, the equation would be y=7(2), which could be simplified to y=14, so after a two hour shift you would make a total of $14
Step-by-step explanation:
A shipping container will be used to transport several 80-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 27000
kilograms. Other shipments weighing 13600 kilograms have already been loaded into
the container. Which inequality can be used to determine x, the greatest number of
80-kilogram crates that can be loaded onto the shipping container?
80(13600+ x) ≤ 27000
27000 13600 - 80x
27000 13600 + 80x
80(13600+ x) ≥ 27000
Submit Answer
Answers
The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.
In mathematics, Inequality is an expression that is used for unequal comparison of two numerical expressions or algebraic expressions.
Instead of an equal sign here, we use signs like Less than (<), Greater than (>), Less than or equal (≤), Greater than or equal (≥), and Not equal (≠), etc.
Like Linear equations here we use variables like x, y, z .. etc. to represent the unknown quantities or numbers
Here we have
A shipping container will be used to transport several 80-kilogram crates across the country by rail.
The greatest weight that can be loaded in container is 27000 kilograms.
Other shipments weight = 13600 kilograms
Let 'x' be the number of crates that can be transported
Weight of 'x' number of crates = 80kg × (x) = 80x kg
As we know the greatest weight that can be loaded is 27000 kilograms. So here is the total weight of 'x' crates and the other shipment's weight must be less than 27000 kilograms but not more.
=> 80x + 13600 ≤ 27000
Therefore,
The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.
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Solve for a.
a+ (−4) = −13
Answers
Answer: a= -9
Step-by-step explanation:
a+ (−4) = −13
a - 4 = -13 (the 4 becomes -4 as when it comes to + or - it is always -)
a = -13 +4 (when you switch the side -4 becomes +4)
a= -9
A survey was given to a random sample of 45 voters in the United States to ask about
their preference for a presidential candidate. Of those surveyed, 80% of the people
said they preferred Candidate A. Determine a 95% confidence interval for the
percentage of people who prefer Candidate A, rounding values to the nearest tenth.
Answers
Answer: A confidence interval is a range of values that is likely to contain the true population value with a certain level of confidence. To determine a 95% confidence interval for the percentage of people who prefer Candidate A, we can use the following formula:
(Sample proportion) +/- (Margin of error)
The margin of error can be calculated using the formula:
Margin of error = (Critical value) * (Standard deviation)
The critical value is a factor used to compute the margin of error. The critical value for a 95% confidence interval is approximately 1.96. The standard deviation is calculated as:
Standard deviation = √((Sample proportion) * (1 - Sample proportion) / (Sample size))
Plugging in the given values:
Sample proportion = 80% = 0.8
Sample size = 45
Margin of error = (1.96) * √((0.8) * (1 - 0.8) / (45))
Step-by-step explanation:
A number is picked at random from the set of consecutive integers from 29! – 2992 to 29! + 2992 inclusive. What is the probability that it is divisible by 1995?
Answers
When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.
what is probability ?A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A chance is a number between zero and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or chance that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed in percentages ranging from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.
given
99-20+1 = 80 potential outcomes.
Now, a number that may be divided by 12 must include the digits 2*2*3.
The realisation that c(c21)(21) = c(c1)c(c+1) is the same as c3c3 is perhaps the trickiest.
The latter statement indicates that you indeed have a group of three consecutive integers that are divisible by 12. Every three consecutive integers must be divisible by three, according to a rule.
The main question is how many of the numbers you choose are divisible by 22=4 22=4.
In this scenario, c can either be 21, 23, 25, 95, 97, 99, so 99212 9921/2 + 1 = 40 OR 20, 24, 26, 92, 96, so 96204 9620/4 + 1 = 20.
Thus, 40+2080 = 60/80 and 40+20/80 = 40/80
60/80 = 3/4
When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.
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a mechanical system comprises three subsystems in series with reliabilities of 0.98, 0.96, and 0.94. what is the overall reliability of the system?
Answers
The system's total dependability is 0.8813.
The reliability of the individual components determines the overall reliability of multi-component systems.
R = (0.98) (0.96) (0.94)
= 0.8813
The likelihood that a system operates well for a given period of time is known as reliability. When performing this right action:
No maintenance or repairs are necessary. The system correctly complies with the established performance requirements.
The dependability decreases when more time is taken into account for reliability calculations since it obeys the exponential failure rule.
In other words, a system's reliability will initially be high and steadily decline to its lowest level over time.
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The value of the overall reliability of the system is 0.8813.
The possibility that a system will work successfully over a certain time period is referred to as reliability. No repair is necessary or done during this right procedure. The system adheres to the performance standards as specified.
The overall reliability of multi-component systems is determined by the reliability of the individual components.
R = (0.98) (0.96) (0.94)= 0.8813
The possibility that a system will perform well over a particular length of time is referred to as dependability. There is no need for maintenance or repairs while doing this appropriate step. The system satisfies the defined performance criteria.
Because it follows the exponential failure rule, dependability falls as more time is factored into reliability assessments.
In other words, the reliability of a system will begin high and gradually drop to its lowest level over time.
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Tell whether each figure creates the conditions to form a unique triangle, more than one triangle, or no triangle.
_________3 in.
________6 in. ___
________10 in. _____________
Answers
From the figure we see that by the conditions , the figure does not form any Triangle .
A Triangle is defined as the three sided closed figure made up of line segments .
In the figure , the two lines forms a right angle at the base , that means both the line segments are perpendicular ,
and if the two line are perpendicular to the same base then the two line will be called as parallel lines and we know that parallel lines do not intersect .
Therefore , The triangle will form No Triangle as the lines do not meet .
The given question is incomplete , the complete question is
Tell whether the figure given below creates the conditions to form a unique triangle, more than one triangle, or no triangle.
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the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 4.2. the probability there are 8 occurrences in 10 minutes is
Answers
The likelihood of 8 occurrences in a period of 10 minutes is around 0.091 or 9.1%.
According to the Question
A Poisson distribution issue exists here. The Poisson distribution is a discrete probability distribution that quantifies the likelihood of a certain number of events occurring at a certain average rate, regardless of the interval between occurrences, in a given amount of time or space.
The following formula determines the likelihood that x will occur in a Poisson distribution with parameter λ :
P(x; λ) is equal to x / (λx * e(-λ))!
where
λ = the average number of occurrences within the specified time period.
λ in this situation is 4.2. (the mean number of occurrences in 10 minutes).
In order to determine the likelihood of 8 occurring in 10 minutes:
P(8; 4.2) = (4.2^8 * e^(-4.2)) / 8!
⇒ P(8; 4.2) = 0.091 or 9.1%.
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5. On Monday, Mandy made 25 cupcakes for her bakery On Thursday, she made twice the amount of cupcakes from Monday minus eight cupcakes. Write an expression to show how many total cupcakes Mandy made on Monday and Thursday.
Answers
Answer:y=25 x 2 -8
Step-by-step explanation:
25 x 2-8
Gina Wilson All Things Algebra Unit 5: Congruent Triangles homework 1 PLEASE HELP
Answers
As per the angle sum property, the value of x is 14°
In math the term called angle sum property states that the sum of interior angles of a triangle is 180°.
Here we have the following diagram and we need to find the value of x.
While we looking into the diagram, we have identified the value of the angles are listed as follows:
=> (10x - 11)°
=> (3x - 2)°
=> (3x + 1)°
Now we have to solve this by using the angle sum property then we get,
=> (10x - 11)° + (3x - 2)° + (3x + 1)° = 180°
When we simplify this one then we get,
=> 16x - 12 = 180°
=> 16x = 168°
=> x = 14°
Complete Question
Find the value of x one the following diagram.
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The citizens of Herrington County have an existing dog
park for dogs to play, but have decided to build another
one so that one park will be for small dogs and the other
will be for large dogs. The plan is to build a rectangular
fenced in area adjacent to the existing dog park, as
shown in the sketch. The county has enough money in
the budget to buy 1000 feet of fencing.
What should the dimensions of the dog park be to maximize the area?What is the maximum area of the park?
Answers
To maximise the area it should be build as a square having side=250 feet each and having area=62500 feet.
what are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
Given
total fencing available=1000feet
perimeter=1000
4*s=1000
s=250 feet
Therefore,
Area=250^2
=62500 feet^2
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Randall purchased a flat screen TV for $1090. The tax rate was 8.5%. What was the total cost of his purchase?
Answers
Answer:
$1182.65
Step-by-step explanation:
(8.5/100)×$1090
(85/1000)×1090
$1853/20
=$92.65
thus, $1090+$92.65
=$1182.65
What is the median of this data set? {13, 13, 13, 15, 15, 16, 16, 17, 177
I NEED HELP ASAP PLEASE
Answers
Answer:15
Step-by-step explanation:
its the middle number
Answer: i think it's 15!!
hope this helps lol
Solve this system of equations by graphing. First graph the equations, and then type the solution.
3x-y=-6
y=x+4
The solution is (_,_)
Answers
The solution to the system of equations in this problem is given as follows:
(5,9).
How to obtain the solution to the system of equations?The system of equations for this problem is defined as follows:
3x - y = 6.y = x + 4.We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
From the image given at the end of the answer, the solution to the system of equations is given as follows:
(5,9).
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the grade 6 cla 40 pupil .if thre are 18 girl in a cla what i the ratio of girl to the boy?
Answers
The ratio of girls to boys in the 6th grade class of 40 pupils is 18:22.
This can be calculated by first finding the total number of boys in the class. 40-18=22. We then use the formula for ratio, which is the ratio of two or more numbers. In this case, it is the ratio of girls to boys. 18:22. This ratio can also be expressed as 18/22 or 0.818181818181818181818181818181818181818181818182 (to three decimal places). A ratio is a comparison of two numbers and can be used to compare different parts of a whole. It can also be used to compare different groups or classes of people. In this case, it is used to compare the number of girls to boys in a 6th grade class.
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find cot theta, cos theta, sec theta,
Answers
we would here like to find out the values of given trigonometric ratios . A right angled triangle is given to us with perpendicular= 3 and hypotenuse= 8
Firstly by Pythagoras theorem, we have ,
[tex]\longrightarrow h^2 = p^2 + b^2\\ [/tex]
[tex]\longrightarrow 8^2 = 3^2 + b^2 \\[/tex]
[tex]\longrightarrow 64 = 9 + b^2\\ [/tex]
[tex]\longrightarrow b^2 = 64 -9 = 55\\ [/tex]
[tex]\longrightarrow b =\sqrt{55}\approx 7.41 [/tex]
now as we know that,
[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{7.41}{8}\\ [/tex]
[tex]\longrightarrow \underline{\underline{ \cos\theta = 0.92 \approx 1}} [/tex]
And ,
[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{7.41}{3}\\[/tex]
[tex]\longrightarrow \underline{\underline{\cot\theta = 2.47 \approx 2 }} [/tex]
Finally,
[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{8}{7.41}\\[/tex]
[tex]\longrightarrow \underline{\underline{\sec\theta = 1.07 \approx 1 }} [/tex]
and we are done!
Work out the value of x. Show your working clearly.
Answers
Given the triangle below, what is the value of x?
Answers
Given, you have 55 degree and 70 degree.
180 degree - 55 degree = 125 degree
125 degree - 70 degree = 55 degree remaining.
Now we know the remaining angle equals 55 degree
55 degree = 9x + 10
55 - 10 = 9x
45 = 9x
x = 45/9
x = 5
The cost C (in dollars) of producing x cell phone cases is C=2.2x+10.6. The revenue R (in dollars) for selling x cell phone cases R = 6.91x.
To calculate profit, subtract the cost from the revenue.
(a) Write and simplify an equation for the profit P in terms of x.
P = ?
Answers
Answer:
P =4.71x-10.6
Step-by-step explanation:
R = 6.91x
C=2.2x+10.6.
P = R - C = 6.91x-2.2x -10.6 =4.71x-10.6
Consider the equation. X + 5 7 = 31 7 If you use the addition property of equality, what number would you add to both sides of the equal sign to isolate the variable? What is the solution?
Answers
Regarding the addition property of equality, the number would add to both sides of the equal sign to isolate the variable x = 26/7.
What amount would you add to both sides of the equal sign if you were to isolate the variable using the addition property of equality?
The official term for the equality-related characteristic that enables one to multiply both sides of an equation by the same amount. One of the most frequently applied properties for solving equations is this one.
To solve the problem, you would take away 5/7 from both sides.
What is the remedy?
x = 3 and 5/7 or 26/7.
x + 5/7 = 31/7
Subtract 5/7 from both sides of the equation:
x + 5/7 - 5/7 = 31/7 - 5/7
x = 26/7
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Answer:
1: -5/7
2: 26/7
Step-by-step explanation:
What is the factored form of 4x+16
Answers
Answer:
The factored form of 4x+16 is (4x + 8)(2). This can be found by using the distributive property, or by using the prime factorization method.
How many teaspoons are there in 6 milliliters?
Answers
The number of teaspoons that are there in 6 milliliters is 1.21731 US teaspoons.
How can the conversion be done?The concept that will be used here is conversion of units. Unit conversion is the process of changing measurements of the same quantity between different units by multiplying or dividing them. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.
1 tsp = 4.93 mL
Then Xtsp = 6ml
The cross multiply, Xtsp= (1 tsp *6ml)/4.93 mL
Then 6 milliliters= 1.21731 US teaspoons
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