The value of AB after solving the triangle is 10√3.
Since angle C is the right angle in triangle ABC, we know that angle A = 90 - m2C = 90 - 30 = 60. And since triangle ABC is a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse, AB.
The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So in this case,
AB^2 = AC^2 + BC^2 = 10^2 + BC^2 = 100 + BC^2.We know that angle A is 60, so we can use the trigonometric function sine to find the value of BC/AB. We know that
sin(A) = BC/AB. So BC/AB = sin(60) = √3/2.We can then square both sides of this equation to get
(BC/AB)^2 = (√3/2)^2 = 3/4.Since we know that BC/AB = 3/4, we can substitute this value into the equation
AB^2 = 100 + BC^2 to get
AB^2 = 100 + (BC^2) = 100 + (3/4)AB^2.
Solving this equation for AB, we get AB = 10√3
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The following federal tax table is for biweekly earnings of a
single person.
A single person earns a gross biweekly salary of $840. By
claiming 2 more withholding allowances, they would have
$30 more in their take home pay. How many withholding
allowances do they currently claim?
Therefore , the solution to the given problem of unitary method comes out to be he will have $870.
What is unitary method, exactly?The unit method is a method of problem-solving that entails calculating the variable of one unit, multiplying that value, and then calculating the required value. To describe it simply, the unit method is employed to obtain a single entity value from a specified multiple. One pen costs 400 rupees, thus 40 needles would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Logic of matrices or operators, algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.
Here,
To address the issue,
if the person gets a gross biweekly salary of $840 and claims 2 extra withholding allowances,
their take-home pay would increase by $30.
thus,
They will have 840 + 30 = $870
Therefore , the solution to the given problem of unitary method comes out to be he will have $870.
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Fill in the blank so that products unloaded and time are in a proportional relationship.
A conveyer belt unloads 48 products in 6 minutes. The same conveyor belt unloads
⬜ products in 1 minute.
Answer: 8 products in 1 minute
Step-by-step explanation:
6 min=48 products
48/6=8
1 min= 8 products
You have $12 to spend at a vending machine. A pack of Starbursts cost $1 and a pack of M&M chocolates cost $2. You want to buy at least three packs of Starbursts.
a. Write a system of linear inequalities that represents this situation.
b. How many packs of each type of candy can you possibly purchase?
Answer:yes
Step-by-step explanation:
yes
Answer:
Starbursts = 12 dollars
M&M = 2 dollars
1. Make Startbursts and M&Ms into "x"
(a) 1x + 2x = 12
2. 3*1= 3
4+2x=12
(b) 4 packs
Find the 6th term of the geometric sequence whose common ratio is 3/2 and whose first term is 4
6th terms of given geometric progression whose common ratio is 3/2 and first term is 4 is 243/8 using the farmula ar^(n-1).
What is a geometric sequence?
A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.
Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).
a = First term where
The common Ratio is r.
nth term = ar^(n-1)
6th terms ar^(6-1) = ar^5.
given is that r =3/2. a = 4.
6th term = 4 * (3/2)^5
= 4 * 3^5/2^5
=4*243/4*8
=243/8.
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Select the interval where the graph h is increasing.
Answer: B
Step-by-step explanation:
Based on the graph, we know that it is increasing if it is going up from left to right.
A: incorrect
Looking at choice A, it says the interval is from -5<x<-4. This means we have to find x=-5 and x=-4. On the graph, that interval is going down from left to right, so it is decreasing.
B: correct
Looking at choice B, it says the interval is from -2<x<2. This means we have to find x=-2 and x=2. On the graph, that interval is going up from left to right, so it is increasing.
C: incorrect
Looking at choice C, it says the interval is from 3<x<4. This means we have to find x=3 and x=4. On the graph, that interval is going down from left to right, so it is decreasing.
Therefore, B is the correct answer.
Select all ratios equivalent to 2:14. A3:21b.1.2.c
16:112
The ratios equivalent to 2:14 are 3:21 and 16:112. Option A &C
What is equivalent ratios?Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.
2:14 = 2/14
Reducing 2/14 to the lowest terms = 1/7
2:14 is equivalent to 1:7
3:21 = 3/21 = 1/7
Reducing 3/21 to the lowest terms = 1/7
3:21 is equivalent to 1:7
1:2 = 1/2
1:2 is not equivalent to 1:7
16:112 = 16/112 = 1/7
Reducing 16/112 to the lowest terms = 1/7
16:112 is equivalent to 1:7
Hence, 2:14, 3:21 and 16:112 are all equivalent ratios
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What 3 numbers make a right triangle?
Answer:
A right triangle equals to 90 degress, and has 2 equal angles.
Example: 20 degress, 20 degrees and 50 degress could make a right triangle.
I hope this helps you!
May someone please help me.
Answer: x=9
Step-by-step explanation:
Here the given angles are,
50,80,6x-4
The sum of the angles of a triangle is 180 degrees and hence
50+80+6x-4=180
130+6x-4=180
126+6x=180
6x=180-126
6x=54
x=54/6
x=9
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Could someone give me a hand here I’m rlly in a rush I needa get this over with
Answer:
c = √52
Step-by-step explanation:
applying pythagoras theorem: a² + b² = c²
where 'a' and 'b' are legs and 'c' the hypotenuse.
Substitute values:
6² + 4² = c²
c² = 36 + 16
c² = 52
c = √52
URGENT!!
Which of the following lists is in order from least to greatest?
Answer:
It's B, -2, v/5 4, and 3².
I need help on solving this
Answer:
Irrational
Step-by-step explanation:
it equals 6.7 which is not a perfect square
Please help me to find the slope
Answer:
Step-by-step explanation:
the formula for the slope is y2 - y1 / x2 - x1
so 1 - 0 / -3 --3/7
on the calculator
- 7 / 18
A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.Which of the following is the best interpretation of the probability 0.20 ?
"For all finance workers, 20% will have a tattoo" is the best interpretation of the probability 0.20.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
This can be calculated by taking the number of finance workers with tattoos and dividing it by the total number of finance workers, and then multiplying by 100 to express the result as a percentage.
(Number of finance workers with tattoos / Total number of finance workers) x 100 = 20%.
Here,
"20% of all finance workers will have a tattoo," is the best explanation of the probability 0.20.
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Complete question: A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.
Which of the following is the best interpretation of the probability 0.20 ?
A- For all workers in the United States, 20% will work in finance.
B- For all finance workers, 20% will have a tattoo.
C- For all people with tattoos, 20% will work in finance.
D- For a specific group of 5 finance workers, 1 will have a tattoo.
E- For a specific group of 5 people with a tattoo, 1 will work in finance.
is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by
The scale factor of segment AB was 1.94.
What is scale factor?Scale factor is a number by which a given set of measurements is multiplied in order to increase or decrease the size of the measurements. It can be used to enlarge or reduce the size of an object, image, or diagram. It is a useful tool in many areas of mathematics, including geometry, engineering, and computer graphics.
The scale factor for segment AB can be found by taking the ratio of the lengths of the two segments. To calculate this, use the distance formula to find the length of segment AB and A'B' and set them equal to each other.
The distance formula is: d = √[(x2-x1)^2 + (y2-y1)^2]
The coordinates of A and B are (0, 0) and (6, 9), respectively. The coordinates of A' and B' are (0, 6) and (6, 9), respectively.
For segment AB, the distance formula becomes: d = √[(6-0)^2 + (9-0)^2], which simplifies to d = √[36 + 81], which simplifies to d = √117.
For segment A'B', the distance formula becomes: d = √[(6-0)^2 + (9-6)^2], which simplifies to d = √[36 + 9], which simplifies to d = √45.
The scale factor is then found by taking the ratio of the two distances, √117/√45, which simplifies to √117/3, or approximately 1.94. Therefore, the scale factor of segment AB was 1.94.
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What is the solution to 3 4?
The solution of the fraction 3/4 is 0.75
The term fraction is defined as represent the parts of a whole or collection of objects
Here we have given the fraction 3/4.
Now, we have to do the following steps in order to find the decimal equivalent for the fraction.
First of all we just need to divide the numerator by the denominator.
Then we get the fraction is 3/4 which means we need to divide: 3 ÷ 4.
The division process is illustrated on the following image.
Then the decimal equivalent to the fraction written as 3/4 is expressed as 0.75 in the decimal form.
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please help with this shapes question
Given the surface area of the sphere, and the formula for the surface area, the value of the radius is 11 cm
How to find the radius ?The radius of the sphere allows for the surface area of the sphere to be calculated, with the formula 4 πr².
Given that the surface area of the sphere is 484 π cm then the radius can be found to be :
484 π = 4 πr²
r ² = 484 π / 4 π
r ² = 121
The value of the radius would then be:
r ² = 121
r = √ 121
r = 11 cm
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which postulate proves these two triangles are congruent
The given triangles are congruent by SAS criteria.
What are congruent triangles?Congruent triangles have both the same shape and the same size.
Given are two right angled triangles as shown in the image.
In the right angled triangles -
Two corresponding sides are equal.
They both have one right angle common.
We can conclude them as congruent by SAS Rule.
Therefore, the given triangles are congruent by SAS criteria.
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Write −0.39¯¯¯¯¯ as a fraction in simplest form.
Answer:
-0.3999... = -⅖
-0.393939... = -13/33
Step-by-step explanation:
Only ones I could think of.
Answer:
-39/100
Step-by-step explanation:
What are the 4 steps in solving simple problems in mathematics?
The 4 steps in solving simple problems in mathematics is explained below.
According to the author called Polya created his famous four-step process for problem solving that one is used all over to aid people in problem solving
The first and foremost Step is to understand the problem which includes identification of the unknowns and figure out what the problem tells you is important and then we have to identify any information that is irrelevant to the problem.
Then the nest step is to Devise a plan which means that Look for a pattern and then by using it we have to make a table, diagram or chart and then write an equation.
Then we have to move onto the next steps that is to carry out the plan which means the process of solving the question.
Then the final step is to Look back problem that is none other than check and interpret its reliability of the solution
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Find a polynomial which when added to the polynomial 3x^2+3x-1, is equaivelant to the following expressions: 1
The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:
P = 2 - 3x² -3x.P = -2 -x² -3xP = 6 -2x -3x².What is a Polynomial?This is referred to as algebraic expressions that consist of variables and coefficients.
For 1; it is calculated as:
3x²+3x-1 + P = 1.
P = 2 - 3x² -3x.
For 2x²-3, it is calculated as:
3x²+3x-1 + P = 2x²-3
P = -2 -x² -3x
For x +5; it is calculated as:
3x²+3x-1 + P = x +5
P = 6 -2x -3x².
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The full question is:
Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5
Is x2 4x 4 a perfect square trinomial?
x² + 4x + 4, this is a perfect square trinomial, which is expressed as
(x + 2)²
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 4x + 4
= (x)² + 2(2x) + 4
= (x)² + 2(x)(2) + 2²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 2)²
= (x + 2) (x + 2)
so, this is a perfect square trinomial.
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16 quarts of soil are used to completely fill 5 flower pots. If each pot holds the same amount of soil, how many quarts will each pot hold?
How many quarts of soil are used to fill 3 flower pots?
9.6 quarts
First, find the unit rate, which is that when you divide 16 and 5 and you will get 3.2, then you multiply it with 3 for the 3 flower pots, and that's how you end up with the answer
Albert has 225 strawberry plants that he wants to plant in a square formation in evenly spaced rows. How many strawberry plants should he plant in each row?
Answer:
15
Step-by-step explanation:
to determine the number of plants per row, take the square root of 225
sqrt(225) = 15
There should be 15 plants per row
Answer:
Step-by-step explanation:
Since the formation of the strawberry plants should represent a square, it implies that the dimensions of the formation (i.e length and breadth) must be equal.
To achieve this, we have to calculate its square root as the formula for the area of any square is given as (side)^2.
Now, [tex]\sqrt{225}[/tex] = 15
implies that each as well as each column will contain 15 strawberry plants
help for 100 points please please
Answer:
Step-by-step explanation:
Take the percentages for both 1992 and 2000 and make the average. that is your answer
Solve the inequality. Graph the solution. -3y<-14
Answer:
y > 14/3
Step-by-step explanation:
-3y<-14
Divided both sides by -3. Because divided by a negative number, the < will switch to the >
y > 14/3
Which point represents the value of –(–2) on the number line?
A number line has points A, negative 3, B, blank, 0, blank, C, 3, D.
Point A
Point B
Point C
Point D
The point that is -2 on the number line is point B. Option B
What is the number line?We know that the number line can be taken as a representation of the numbers. We ought to know that the numbers that we find on the number line are the numbers that are increasing to the right as shown.
In the question that we have, the task that is before us is that we should be able to locate the point on the number line that has been labelled as -2 on this the point B non the line. This is the point that is read off as -2.
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Which is a correct expansion of (4x + 1)(2x7 - 2)?
Answer:
So the correct expansion of (4x + 1)(2x7 - 2) is 8x^27 - 8x2 + 2x7 - 2
Step-by-step explanation:
When expanding an algebraic expression like (4x + 1)(2x7 - 2), you can use the distributive property to find the product of each term in the first set of parentheses with each term in the second set of parentheses, and then add them together. The distributive property is the process of multiplying one term in the parentheses by each of the terms outside the parentheses.
Here is the correct expansion of (4x + 1)(2x7 - 2):
(4x + 1)(2x7 - 2) = 4x(2x7) + 4x(-2) + 1(2x7) + 1(-2)
= 8x^27 + -8x2 + 2x71 + -21
= 8x^27 + -8x2 + 2x7 + -2
= 8x^27 - 8x2 + 2x7 - 2
So the correct expansion of (4x + 1)(2x7 - 2) is 8x^27 - 8x2 + 2x7 - 2
It's important to note that you can also use FOIL method which is the acronym for the steps of the distributive property, First, Outside, Inside, Last.
An isosceles trapezoid has a perimeter of 38 ft and a leg measuring 8 ft. A similar trapezoid has a leg measuring 3ft. Find its perimeter.
The perimeter of a trapezoid is 28ft.
An isosceles trapezoid is a trapezoid whose non-parallel sides (the legs) are equal in length.
The perimeter of an isosceles trapezoid (P) = a + b+ 2c
where a is the top, b is the bottom, and c is the leg of the trapezoid
According to the question,
perimeter = 38ft
leg of an isosceles trapezoid = 8ft
38 = a +b +2 × 8
⇒ 38 = a+b +16
⇒a +b = 38 -16
⇒a +b = 22
Another similar trapezoid has a leg measuring 3ft.
Perimeter of this trapezoid is =( 22 + 2× 3) ft
= (22 +6)ft
= 28 ft
So, the perimeter of a trapezoid is 28ft.
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Are 2 sides of an isosceles triangle?
Yes, the lengths of the two sides of an isosceles triangle are equal.
An isosceles triangle is a type of triangle that has two sides that are equal in length. The other side of the triangle can be either longer or shorter than the two equal sides. The two equal sides are called the legs, and the other side is called the base. The angles opposite the two equal sides are also equal in measure. Because of this, the two equal sides create an angle bisector that divides the base into two equal parts. This angle bisector forms two angles of equal measure as well. Thus, the two equal sides of an isosceles triangle are a defining feature of the shape.
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On a negatively skewed curve, which is true?
a.The median is lower than the mode which is lower than the mean. b.The mean, median, and mode are the same. c.The mean is lower than the median which is lower than the mode. d.The mode is lower than the mean which is lower than the median. e.The mean is lower than the mode which is lower than the median.
The mean of negatively skewed data is smaller than the median. If the data are displayed symmetrically, the distribution is not skewed regardless of tail length or thickness. So, option d. is correct.
What do you mean by skewed curve?A skew curve is a type of statistical distribution in which the data are unevenly distributed. This is often called an asymmetric distribution, meaning that the two halves of the curve look different. A skewed curve can be either positively or negatively skewed, depending on the direction in which the data points are shifted. Positively skewed curves tend to have long tails to the right, while negatively skewed curves tend to have long tails to the left. This type of distribution is common in real-world data such as income and wealth distributions.
A negatively skewed curve is indicated by the negative tail of the chart. This means that the data points are likely to be below average. Therefore, the mean is lower than the mode, which is lower than the median. The mean is the arithmetic mean of all data points, the mode is the most common value, and the median is the midpoint of the data points.
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