Answer:
2958843/5 5/1000775747373838388484737372737375823What is the maximum number of students among whom 135 pens, 180 pencils and 300 books can be equally divided.
Answer:
Step-by-step explanation: You can add all of these numbers with a calculator. but be sure what are the numbers telling you what to do. So always focus on the words that are going to mention about the numbers.
Samera placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
Which statements are true of the quadrilateral she constructed? Select three options.
It is a rectangle.
It is a trapezoid.
It has only one right angle.
It has two right angles.
It has two sides that are parallel.
The correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
What is a trapezoid?A quadrilateral with at least one pair of parallel sides is called a trapezoid.
Given that, Samara placed the congruent sides of these two triangles together to form a quadrilateral.
2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.
If we construct such quadrilateral, we will get a trapezoid with one angle a right angle.
Hence, the correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.
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Answers:
1. B its a trapezoid
2. D it has two right angles
3. E it has 2 sides that are parallel
Step-by-step explanation:
PLEASE HELP!!! WILL AWARD BRAINLIEST!!!
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Top data set labeled males, minimum at 1, Q1 at 3, median at 11, Q3 at 14, maximum at 21, and an outlier at 30.
Bottom data set labeled females, minimum at 0, Q1 at 15, Median at 18, Q3 at 21.
Part A: Estimate the IQR for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Part D: Provide a possible reason for the outlier in the data set. (2 points)
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions
The estimated IQR for the males dataset is 24 , the estimated difference between median value of each dataset is 14.
What is median ?
The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution in statistics and probability theory. It can be regarded as "the middle" value for a set of data.
When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.
In a collection of numbers, the median is the value in the middle. A series of numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest in order to find the median value.
A. IQR for male dataset
The IQR is calculated as follows:
IQR = Q3 - Q1
=
For the male's data:
IQR = Q3 - Q1
= 25 - 1
= 24
Hence, the IQR of the male dataset is 24.
B. Difference in median values
We have:
median = 20 ----- Male dataset
median = 6 ----- Female dataset
So, the difference (d) is:
d = 20 - 6
= 14
Hence, the difference in median of both dataset is 14.
C. Best measure of center
The female box plot has an outlier. This means that the measure of center to use for the female dataset is the median.
The male box plot has no outlier; this means that the mean can be used as a measure of center for the male box plot
D. Reason for outlier
There are several reasons that could cause an outlier in a dataset. One of the reasons is human error during data entry.
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Triangle DEF was dilated according to the rule DO,One-third(x,y)(one-third x, one-third y) to create similar triangle D'E'F'.
On a coordinate plane, (0, 0) is the center of dilation. Triangle F D E is dilated to create smaller triangle F prime D prime E prime. Triangle F D E has points (negative 9, 3), (negative 9, 9), (negative 6, 6). Triangle F prime D prime E prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2).
Which statements are true? Select three options.
∠F corresponds to ∠F'.
Segment EE' is parallel to segment FF'.
The distance from point D' to the origin is One-third the distance of point D to the origin.
The measure of ∠E' is One-third the measure of ∠E.
△DEF △D'E'F'
A. ∠F corresponds to ∠F' is True.
B. Segment EE' is parallel to segment FF' is False.
C. The distance from point D' to the origin is One-third the distance of point D to the origin is True.
D. The measure of ∠E' is One-third the measure of ∠E is False.
E. △DEF ~ △D'E'F' is True.
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given:
As triangle DEF was dilated according to the rule DO, One-third(x, y)(one-third x, one-third y) to create similar triangle D'E'F'.
and, The center of dilation = (0, 0)
Also, Triangle FDE has points: (- 9, 3), (- 9, 9), (- 6, 6).
Triangle F'D'E' has points : (- 3, 1), (- 3, 3), (- 2, 2)
A) ∠F corresponds to ∠F'. ( True)
B) Segment EE' is parallel to segment FF'. (False)
As they intersect each other at the origin.
C) The distance from point D' to the origin is One-third the distance of point D to the origin. ( True)
Now, the length of DE
D = √(-9-0)² + (-9-0)²
D = 9√2
and, length of D'E'
D = √(-3-0)² + (-3-0)²
D = 3√2
Thus, DE / D'E' = 3√2/ 9√2 = 1/3
D) The measure of ∠E' is One-third the measure of ∠E. ( False)
E) △DEF ~ △D'E'F'. ( True)
As they are similar triangles.
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Answer:
A. ∠F corresponds to ∠F'.
C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.
E. △DEF ~△D'E'F'
Step-by-step explanation:
got it right on edge 23
How many solutions does 5x 2 7x 4 0 have?
The given equation gives two solution. We can find solution by using quadratic formula or discriminant.
How do you find the number of solutions?A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R. So a and b ≠ 0. When we consider a system of linear equations we can find the number of solutions by comparing the coefficients of the variables of the equations.
How do you find how many solutions are in a quadratic equation?
if the discriminant is positive. Then the quadratic equation has two solutions.
if the discriminant is equal. Then the quadratic equation has one solution.
if the discriminant is negative. Then the quadratic equation has no solution.
Here we have
a=5 b=-7 c=4
Disc= [tex]b^2[/tex]-4ac
Disc= [tex](-7)^2[/tex]-4(5)(4)
Disc= 49+80
=129
Disc >0 it has two solutions.
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Complete question is: How many solutions are there for 5x^2+7x-4=0?
a) 0
b) 1
c) 2
d) 3
In AAEC, G is the centroid.
A
B.
If EG = 6, find GB.
O 2
03
06
09
B) The length of GB is 3 in the given triangle.
The centroid of a triangle is the point at which the three medians of the triangle intersect. A median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. The three medians divide the triangle into six smaller triangles, each with a vertex at the centroid.
The ratio in which the centroid divides a median of a triangle is 2:1. That is, the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.
So, if G is the centroid and B is the midpoint of the side opposite to point A, the ratio of EG: GB is 2:1.
so the length of GB = EG/2
so the length of GB = 3
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Complete question:
In ΔAEC, G is the centroid , as shown in the figure .
if EG = 6 ,find GB
A) 2
B) 3
C) 6
D) 9
Find three consecutive numbers such that the sum of twice the first, three times the second and four times the third togetherbmakes 191.
Answer:
find 3 consecutive numbers such that twice the first , 3 times the second and 4 times the third together make 191 ?
Let n-1,n and n+1 be three consecutive numbers.
Given
2(n-1)+3n+4(n+1)=191
2n-2+3n+4n+4=191
9n+2=191
9n = 189
n = 21
So, n-1=20 and n+1=22
So the answer is 20,21,22
[tex] \huge \bold{\color{red}{ANSWER}}[/tex]
[tex]\pmb { \orange{Given }:} \sf{ Three \: Consecutive \: numbers}[/tex]
[tex]\pmb{\orange{To find}: } \sf{Least \: of \: the \: numbers}[/tex]
[tex]\pmb{\orange{Solution}: }[/tex]
[tex]\sf{Let \: the \: three \: consecutive \: numbers \: be }[/tex]
[tex] \sf\red x, \red {x+1}, \red{x+2}[/tex]
[tex]\sf{Twice \: the \: number = 2\red x}[/tex]
[tex]\sf{3 \: times \: the \: Second \: number = 3(\red{ x+1})}[/tex]
[tex]\sf{4 \: times \: the \: third \: number= 4(\red {x+2})}[/tex]
☆ according to question
[tex] \pmb{2\red x + 3(\red{x+1})+4(\red{x+2})= 191}[/tex]
[tex] \pmb{2\red{x} + 3\red{x}+3+4\red{x}+8= 191}[/tex]
[tex] \pmb{9\red{x}=191-11 = 180}[/tex]
[tex] \pmb{\red{x}=20}[/tex]
[tex] \sf{∴the \: three \: Consecutive \: numbers \: are} [/tex]
[tex] \pmb{\pink{20}, \pink{21}, \pink{22}}[/tex]
_________________......
[tex] \purple{ \pmb{LearningLifeII}}[/tex]
Is 2x3 is a polynomial?
In 2x^3, 3 is the greatest degree of the exponent. 2x^3 is a cubic polynomial as a result.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An example of a polynomial of a single indeterminate x is x² − 4x + 7.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.
For instance, the polynomial 3x+2x-5.
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
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Use the quadratic formula to find both solutions to the quadratic equation
given below.
4x² + 5x+1=0
A. X=-
-3-√√-7
8
□ B. x=-3-√7
8
C. x=
E. x=
-3+√√-7
8
D. x=-¹
+3+√7
8
F. x= -1
Answer: x=-1/4 and x=-1
Step-by-step explanation:
The answer choices you give are extremely hard to figure out, so I hope my explanations and answers help.
The quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]. Once we figure out a, b, c, we can plug them into the formula and solve for x.
The standard form equation is ax²+bx+c=0. The equation given matches this so we know that:
a=4
b=5
c=1
Plug them into the formula. There is a [tex]\pm[/tex] symbol, which stands for "plus or minus". This means we solve the formula with addition and subtractions separately. We should have 2 solutions at the end. Let's do them separately to show work.
Solution 1: addition
[tex]x_1=\frac{-5+\sqrt{5^2-4(4)(1)} }{2(4)}[/tex] [exponents]
[tex]x_1=\frac{-5+\sqrt{25-4(4)(1)} }{2(4)}[/tex] [multiply]
[tex]x_1=\frac{-5+\sqrt{25-16} }{8}[/tex] [inside square root]
[tex]x_1=\frac{-5+\sqrt{9} }{8}[/tex] [square root]
[tex]x_1=\frac{-5+3}{8}[/tex] [add]
[tex]x_1=\frac{-2}{8}[/tex] [divide top and bottom by 2]
[tex]x_1=-\frac{1}{4}[/tex]
Solution 2: subtraction
[tex]x_2=\frac{-5-\sqrt{5^2-4(4)(1)} }{2(4)}[/tex] [exponents]
[tex]x_2=\frac{-5-\sqrt{25-4(4)(1)} }{2(4)}[/tex] [multiply]
[tex]x_2=\frac{-5-\sqrt{25-16} }{8}[/tex] [inside square root]
[tex]x_2=\frac{-5-\sqrt{9} }{8}[/tex] [square root]
[tex]x_2=\frac{-5-3}{8}[/tex] [subtract]
[tex]x_2=\frac{-8}{8}[/tex] [divide]
[tex]x_2=-1[/tex]
I am not able to find the answer choices, but we know that x=-1/4 and x=-1.
In the figure shown, EF is tangent to the circle at F, and EG is
tangent to the circle at G. Line segments HF, PG, HJ, and PJ
are also tangent segments.
When mEF = 10 units, what is the perimeter of triangle EHP?
Explain your reasoning.
Answer:
The perimeter is 20 units----------------------------------
According to the two-tangent theorem, two tangent segments drawn to one circle from the same external point are congruent.
That is:
EF = EG,HF = HJ,PJ = PG.We have EF = 10 units, it means EG is also 10 units.
The perimeter of triangle EHP is:
P = EH + HP + EPWe can substitute:
HP = HJ + PJ, segment addition,HJ = HF, stated above,PJ = PG, stated above.Then the perimeter is:
P = (EH + HF) + (EP + PJ) = EF + EG = 10 + 10 = 20 unitsThe rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRYYYYYYYYYYY
The area of the floor in the scale drawing is 60 inches²
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Actual rectangular floor.
Length = 24 feet
Width = 40 feet
Scale rectangular floor.
Length = 6 inches
Width = 40/4 = 10 inches
The area of the scale rectangular floor.
= Length x Width
= 6 x 10
= 60 icnhes²
Thus.,
The area of the floor is 60 inches².
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What is the value of f in a function?
A function is generally indicated by f.
What is function?A mathematical expression that indicates a relationship between an independent variable and a dependent variable.
In other word, a function shows a relation between a set of input values to a set of output values in where each input value is connected to only a particular output value.
What is the value of f in a function?A function is generally, expressed by letters such as f, g and h and so on.
It is said that f(x) is a function of x or g(x) and h(x) are a function of x when functions are denoted by g or h.
For an input value of an independent variable x, the output value is denoted by f(x) that is equal to a dependent variable such as y. We can write, y = f(x)
The set of x value are the domain of function, and the set of f(x) value are the ranges of a function.
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Complete question is: What is the value of f in a function?
10. Find the degree of the monomial. 7m^6n^5
11
6
7
5
Answer:
(a) 11
Step-by-step explanation:
You want the degree of the monomial 7m^6n^5.
DegreeThe degree of a monomial is the sum of the exponents of its variables.
m has an exponent of 6
n has an exponent of 5
The degree is 6+5 = 11.
Suppose y varies directly with x, and y = 6.5 when x = 1.3. What direct variation equation relates x and y ?
Select one:
a.
y = − 5x
b.
y = x / 5
c.
y = 5x
d.
y = 1.5x
Answer:
c
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 6.5 when x = 1.3
6.5 = 1.3k ( divide both sides by 1.3 )
5 = k
y = 5x ← equation of variation
Law of sines: Which measures are accurate regarding triangle JKL? Check all that apply. M∠K = 84° m∠K = 94° k ≈ 3. 7 units k ≈ 4. 6 units KL ≈ 2. 5 units KL ≈ 3. 2 units
The median's class interval is 20 hours and 30 minutes. And the average number of hours is thought to be 26.17.
Who defines median?The median is the exact middle value of a dataset after it has been sorted. A measure of central tendency is the distance between the bottom 50% of data and the top 50% of values. The methods for determining the median will vary depending on whether you have an odd or even number of data points.
the class interval that have median.
total is frequency is as -
∑f = 30
median class of corresponds to half of the value
∑th is the value
i.e. 15th value.
least cumulative frequency higher than or equal to 15 is obtained by accumulating frequencies starting at the top.
[tex]2+8+9=19[/tex]
So, corresponds to the class interval = [tex]20 < h\leq 30.[/tex]
Hence, median class is [tex]20 < h\leq 30.[/tex]
Since this is a grouped data we use the midpoint
The median:-
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How to read linear equations?
To read a linear equation, first, identify the constants and the variable, then determine the coefficient of the variable.
A linear equation is an equation that contains two variables and can be written in the form of ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable. This coefficient will indicate how the variable is related to the constants. Then, solve the equation by isolating the variable to determine its value.
To read a linear equation, start by identifying the constants and the variable. The constant is the numerical value that is not connected to the variable. For example, in the equation "2x + 4 = 0", the constants are '2' and '4'. The variable is the letter that represents the values that can change. In this equation, the variable is 'x'.
Next, determine the coefficient of the variable. The coefficient is the numerical value in front of the variable. It represents how the variable is related to the constants. In this example, the coefficient of 'x' is '2'. This means that the value of 'x' will be twice as much as the constants.
Once the constants, variables, and coefficients have been identified, the equation can be solved.
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Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection. How many total coins are in her collection?
The total number of coins Piper has in her collection is 100 coins.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection.
Let, The total number f coins in the box be 'x'.
Therefore, 2% of 'x' is 12 which can be numerically expressed as,
(2/100)×x = 12.
0.02x = 12.
x = 2/0.02.
x = 100.
So, She has 100 coins in her box.
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Which functions have an axis of symmetry of x = –2? Check all that apply.
f(x) = x2 + 4x + 3
f(x) = x2 – 4x – 5
f(x) = x2 + 6x + 2
f(x) = –2x2 – 8x + 1
f(x) = –2x2 + 8x – 2
The quadratic functions that have an axis of symmetry at x = -2 are given as follows:
f(x) = x² + 4x + 3.f(x) = -2x² - 8x + 1.How to obtain the axis of symmetry of a quadratic function?The standard definition of a quadratic function is given by the rule presented as follows:
y = ax² + bx + c, in which a is different of zero.
The axis of symmetry is given by the x-coordinate of the vertex, hence it's equation is defined as follows:
x = -b/2a.
Meaning that the correct options are given by the first and by the fourth options in this problem.
For the first function, we have that:
a = 1, b = 4.
Hence the axis of symmetry is obtained as follows:
x = -4/2 = -2.
For the fourth function, we have that:
a = -2, b = -8.
Hence:
x = -8/4 = -2.
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Why is the sine of an acute angle less than one?
The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.
It's important to note that this is only true for acute angles, angles smaller than 90 degrees.
For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.
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P=-3w+9 solve for w
Pls help
Isolating for a variable: rearranging an equation so that a variable is on its own. This is done by performing inverse operations until a variable is isolated.
[tex]P-9=-3w+9-9[/tex]
[tex]p-9=-3w[/tex]
[tex]\frac{p-9}{-3}=\frac{-3w}{-3}[/tex]
[tex]-\frac{P-9}{3} =w[/tex]
at a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P\left(\overline{x}>22\right)\approx0.05P(x>22)≈0.05?
The Normal probability for all sample of 5 that the sample mean will be greater than 22 pounds is approximately 0.05. In this Question The normal probability distribution and the central limit theorem were used.
What is Normal probability distribution?The most prevalent continuous probability distribution is the Normal (or Gaussian) distribution. As the curve becomes closer to zero on either side of the mean, the function calculates the likelihood that a given event will fall between any two real number limits. The area under the normal curve is always one.
Central limit theorem
The central limit theorem implies that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently enough random samples from the population with replacement.
Normal probability distribution, ; Problems of normally distributed samples are solved using the z-score formula.
Mean standard deviation , the z-score of a measure X is given by:
Z = x-μ/σ
Given ,
The distribution of backpack with mean deviation = 19.7 pounds
And the standard deviation = 3.1 pounds
The number of standard deviations is measured by the Z-score. The average is used as the measure.
We glance at the z-score table after determining the Z-score to determine the p-value connected to it.
The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value.
1 is subtracted from the p value.
We calculate the likelihood that the measure exceeds X.
P(ä > 22) is the probability of the sample means being above 22.
For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.
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WILL GIVE BRAINLIEST PLEASE HELP
The following triangular prism has a base that is a right triangle.
A. Draw or describe the net of this triangular prism. Make sure to include the dimensions of each part of the net.
B. Use your net to calculate the surface area of the prism.
A. The net of a triangular prism is a flattened version of the prism that shows all the faces of the prism.
The prism's base is a right triangle with a base of 3 units and a height of 4 units. The prism is six units tall. The net of the triangular prism would look like a rectangle with a length of 3 units and a width of 4 units. On top of this rectangle, there would be two smaller triangles, each with a base of 3 units and a height of 6 units.
B. To calculate the surface area of the prism, we need to add the area of all the faces.
The base of the prism is a right triangle with an area of (1/2) (3 units) (4 units) = 6 square units.
The two triangular faces have an area of (1/2) (3 units) (6 units) = 9 square units each.
The rectangular face has an area of (3 units) (6 units) = 18 square units.
So, the total surface area of the prism is:
6 square units (base) + 9 square units (triangular face) + 9 square units (triangular face) + 18 square units (rectangular face) = 42 square units.
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Why are 3 4 5 and 5 12 13 Pythagorean triples?
A Pythagorean triple is a set of three positive integers a, b, and c that satisfies the equation a2 + b2 = c2.
In this case, the triple is (3, 4, 5) and (5, 12, 13).
The equation for the first triple is 32 + 42 = 52.
3² = 9
4² = 16
9 + 16 = 25
25 = 25
The equation for the second triple is 52 + 122 = 132.
5² = 25
12² = 144
25 + 144 = 169
169 = 169
Therefore, both sets of numbers are Pythagorean triples because they both satisfy the equation a2 + b2 = c2.
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just need help with #7. A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
Surface Area : Volume = 6 : s
What is cube ?A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
Surface Area of a Cube = 6a² in a square units
Volume of cube = a³ cubic units
where a is the side length of the cube.
Given length of the cube = s
Surface Area of cube A = 6s²
Volume of cube V = s³
Ratio between Surface Area and volume:
Surface Area / Volume = 6s² / s³
Surface Area / Volume = 6 / s
Surface Area : Volume = 6 : s
Hence the ratio between Surface area and volume of cube is 6 : s.
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Solve the system of equations by the addition method.
4x-5y=22
3x +2y = - 18
Using the provided equations, Applying the addition method in the system of equations, The answer is x=-2 and y =-6.
What do you mean by equation?An equation is a statement of equality between two expressions, usually containing one or more variables. Equations can be used to express mathematical relationships and can be solved to find the value of the variables. Equations can take many forms, such as linear equations, quadratic equations, and differential equations. They can also be represented graphically.
What is the addition method to solve system of equations?The addition method to solve a system of equations is a way to solve a system of two linear equations by adding them together. The goal is to eliminate one variable by adding or subtracting the equations. We can eliminate one variable by adding the equations together. To do this, we'll add the left-hand side of the first equation to the left-hand side of the second equation and add the right-hand side of the first equation to the right-hand side of the second equation. It is important to note that the addition method works only when the coefficients of the variable you want to eliminate are opposite in sign.
4x-5y=22
3x+2y=-18
multiplying first equation with 3 and second equation with 4 and subtracting them , we eliminate x and solve for y,
y=-6
put y=-6 in first equation , we get x,
x=-2
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a smallercircle passes through the center of, and is tanget to a larger cirlc the area of the smaller circle is 9 square units. What is teh area of the larger circle in square units
36 square units make up the larger circle's surface area.
We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.
Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.
We know that the area of a circle is given by the formula A = πr^2.
We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:
A = πr^2 => r^2 = 9/π => r = sqrt(9/π)
Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:
A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36
So the area of the larger circle is 36 square units
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For Drew’s week 1 classes identify the domain and range is the relation a function? Explain
From the table for Drew's week 1 classes:
Domain = {English, Math, History, Biology, Biology Lab}
Range = {60. 90, 45, 0}
What is domain and range?A function's domain is the set of values that can be plugged into it. This set contains the x values in a function such as f. (x). A function's range is the set of values that it can take. This is the set of values that the function returns when we enter an x value. They are the y values.
A function can be thought of as a machine on an assembly line. On one end of the assembly line, there are a few screws and bolts, and on the other end, there is a car. The function is represented by the machine in the middle. The domain consists of the screws and bolts that we insert into the machine (our function).
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A line passes through 3,1 and 0,-3 whats the equation
Answer:
y=(this is a fraction) 4/3 times x-3
Step-by-step explanation:
How do you find the legs of a 45 45 90 triangle given the hypotenuse?
The value of the legs of the triangle would be hypotenuse/√2.
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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What does a 30 60 90 triangle look like?
The 30-60-90 triangle is shaped like half of an equilateral triangle.
A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.
The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.
30°-60°-90° Triangle Rule:
In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.
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