Answer:
8 (sorry if i got it wrong)
How do you solve AAS triangles?
Triangles are said to be congruent if their two angles and corresponding non-included sides are congruent with each other according to the AAS (Angle-Angle-Side) formula. thus proven.
Consider two triangles from figures ABC and DEF, where,
[Corresponding Angles] B = E The corresponding angles are C = F. And
AC = DF [Side by side]
Triangle's property of angle sum allows us to know this;
∠A + ∠B + ∠C = 180 ………(1)
∠D + ∠E + ∠F = 180 ……….(2)
Equations 1 and 2 allow us to state;
∠A + ∠B + ∠C = ∠D + ∠E + ∠F
∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D
thus in the triangle formed by ABC and DEF,
∠A = ∠D
AC = DF
∠C = ∠F
As a result, according to ASA,
Δ ABC ≅ Δ DEF
The proof of the AAS (Angle-Angle-Side) congruence rule follows.
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Triangles are said to be congruent if their two angles and corresponding non-included sides are congruent with each other according to the AAS (Angle-Angle-Side) formula. thus proven.
Consider two triangles from figures ABC and DEF, where,
[Corresponding Angles] B = E The corresponding angles are C = F. And
AC = DF [Side by side]
Triangle's property of angle sum allows us to know this;
∠A + ∠B + ∠C = 180 ………(1)
∠D + ∠E + ∠F = 180 ……….(2)
Equations 1 and 2 allow us to state;
∠A + ∠B + ∠C = ∠D + ∠E + ∠F
∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D
thus in the triangle formed by ABC and DEF,
∠A = ∠D
AC = DF
∠C = ∠F
As a result, according to ASA,
Δ ABC ≅ Δ DEF
The proof of the AAS (Angle-Angle-Side) congruence rule follows.
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Find the distance between (3, 11) and (4, 3). Provide an answer accurate to the nearest tenth.
The distance between coordinates is d = 7.1 units.
What are Cartesian plane?The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line. The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction. The point is to the right of the origin if the sign of x is positive; otherwise, it is to the left.
Given coordinates,
(3, 11) and (4, 3)
the distance between coordinates is
d=√((x₂ – x₁)² + (y₂ – y₁)²)
here x₁ = 3, x₂ = 4, y₁ = 11 and y₂ = 3
d=√((x₂ – x₁)² + (y₂ – y₁)²)
d=√((4 – 3)² + (4 – 11)²)
d = √(1 + 49)
d = √50
d = 7.0710 units
d = 7.1 units nearest tenth
Hence the distance is d = 7.1 units nearest tenth.
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Your teacher has 48 juice boxes and 64 candies for a halloween party. Each student will receive the same amount of juice boxes/candies, and all juice boxes/candies must be used. What is the greatest number of students that can attend the party?.
The greatest number of students that can attend the party is 16.
A factor defines a number that divides another number, leaving no remainder, which is equal to zero.
And if we multiply two whole numbers to give us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division.
Now, let us know factors 48 and 64
factors of 48 are 1,2,3,4,6,8,12,16,24,48.
factors of 64 are 1,2,4,8,16,32,64.
so the common factors of 48 and 64 are: 1,2,4,8, and 16
In the common factors of 48 and 64, 16 is the greatest number.
Therefore, the greatest number of students that can attend the party is 16.
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The numerical value of the standard deviation can never be:
i Zero
ii Negative
iii Larger than the variance
Which of the following statements is true:
a. (i) & (ii)
b. (ii) & (iii)
c. (i), (ii) & (iii)
d. None of the above
Non of the above Statement is true.
What is standard deviations?Standard deviation is a mathematical measure of how spread out a dataset is. It is a measure of the variation or dispersion of a set of values from the mean. It is calculated by taking the square root of the variance. Standard deviation can be used to measure the risk associated with an investment, to compare data sets, or to measure the accuracy of a data set.
The standard deviation is a measure of the dispersion of a set of data from its mean, and it is always a non-negative number. It can sometimes be zero, and it can also be larger than the variance.
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A turtle can walk 12 miles in 3 hours what is the average speed of the turtle
Answer:
0.13 to 0.30 mp
Step-by-step explanation:
A survey organization conducted telephone interviews in December 2008 in which 1,009 randomly selected adults in the United States responded to the following question: At the present time, do you think television commercials are an effective way to promote a new product? Of the 1,009 adults surveyed, 676 responded "yes." In December 2007, 622 of 1, 020 randomly selected adults in the United States has responded "yes" to the same question. Do the data provide convincing evidence that the proportion of adults in the United States who would respond "yes" to the question changed from December 2007 to December 2008?
The p-value is less than a chosen significance level (alpha), such as 0.05, we reject the null hypothesis and conclude that there is evidence that the proportion of adults who would respond "yes" to the question changed from December 2007 to December 2008. Otherwise, we fail to reject the null hypothesis.
It is important to note that the sample size and the significance level used to calculate the p-value can affect the result of the test. Additionally, it's important to consider other factors that may have affected the results, such as economic conditions or media coverage.
Hypothesis Test Proportion ChangeTo determine if the proportion of adults in the United States who would respond "yes" to the question changed from December 2007 to December 2008, we need to perform a hypothesis test. The null hypothesis is that the proportion of adults who would respond "yes" to the question did not change from December 2007 to December 2008, and the alternative hypothesis is that the proportion of adults who would respond "yes" to the question did change.
One way to perform the hypothesis test is by using a two-sample proportion test. The test statistic is calculated as:
(p1 - p2) = (676/1009 - 622/1020) = 0.0548
where p1 is the proportion of adults who responded "yes" in December 2008 and p2 is the proportion of adults who responded "yes" in December 2007.
Then, we need to find the p-value for the test statistic, which represents the probability of observing a test statistic as extreme or more extreme than the one calculated if the null hypothesis is true.
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3gh^2 x 4g^3 h^3 what is the answer
Answer: 12, g with exponent 4, h with exponent 5 . (12
g
4
h
5
Brainliest would be much apprechiated
Answer:
2+3+3=8
3×4=12
Step-by-step explanation:
What is the perimeter of a triangle with vertices (-1,1), (-3, -4), and (5,-2)?
The perimeter of the triangle is 21
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
The perimeter of the triangle is found by adding all the sides
The vertices of the triangle ABC are (-1,1), (-3, -4), and (5,-2). let A be (-1,1), B be (-3, -4) and C be (5,-2).
The distance between And B = √ (-3-(-1))²+( -4-1)²
Line AB = √ 2²+-5²
AB = √ 4+25
AB =√29 = 5.4
line AC = √5-(-1)² + (-2-1)²
AC = √ 6²+3²
AC = √ 36+9
AC = √ 45
AC = 6.7
The distance between B and C = √( -3-5)² + (-4-(-2)²
BC = √ 8²+4²
BC =✓64+16
BC = √80
BC = 8.9
Therefore the perimeter of the triangle is AB+ BC + AC = 5.4+6.7+8.9 = 21
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A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour. Find each temperature. Show your work.
If it continues to fall at this rate, what will the temperature be:
in 2 hours? _______ in 5 hours? _______ in half an hour? _______ 3 hours ago ______
If it continues to fall at the rate of 3°C per hour, the temperature will be:
In 2 hours ⇒ - 6 °C In 5 hours ⇒ -15 °C In half an hour ⇒ - 1.5 °C 3 hours ago ⇒ 9 °C How to find the temperature ?The temperature is currently 0°C and is falling at the constant rate of 3°C per hour which means that in 2 hours, the temperature would be:
= 0 - 3 - 3
= - 6 °C
In 5 hours the temperature would be :
= Current temperature + ( Change in temperature x number of hours )
= 0 + ( - 3 x 5 )
= - 15 °C
In half an hour:
= 0 - ( 3 x 0.5 )
= - 1. 5 °C
3 hours ago:
= Current temperature - ( Change in temperature x number of hours )
= 0 - ( - 3 x 3 )
= 0 + 9
= 9 °C
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PLEASE HELP MARKING BRAINLIEST!!!
A horizontal number line is given.
A number line that starts at negative four with tick marks every one half unit up to positive four. The values of negative three halves and positive three halves are labeled.
How do the two values plotted compare, and what is their relationship to zero?
The values are opposites of each other and have different distances to zero.
The values are opposites of each other, and their distance to zero is three halves units.
The values are the same, and their distance to zero is three halves units.
The values are the same, and their distance to zero is negative three halves unit
The two values on the number line are of opposite values, and have a distance of three halves units to zero. Thus option B.
Number Line.A number line is a system in which the position of a directed number is located. It extends from negative infinity to positive infinity, thus all numbers can be located on a number line.
A directed number is any type of number which has either a negative or positive sign i.e its direction.
Considering the values given in the question, it can be deduced that;
i. Both values are opposite of each other because of the negative and positive signs (i.e their directions)
ii. The two values are at a distance of one and a halve to the zero point. So that;
one and a halve = 1 1/2
= 3/2
Thus both values are at a distance of three halves to zero.
Therefore, the correct option is B. The values are opposites of each other, and their distance to zero is three halves units.
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Please help me answer this
The product requested is equal to -108.8. The result found is a rational number.
Classification numbersThe numbers can be classified as rational or irrational. A number is classified as a rational number when this number is represented by a ratio between two integers numbers ([tex]\frac{b}{c}[/tex]), where c ≠0. Besides, this ratio can be simplified in decimal form.
On the other hand, an irrational number represents a number that cannot be written in the form of a fraction, only in decimal form. In this case, the decimal never repeats.
Multiplication Sign RulesThe rules for the multiplication of numbers are:
+ + or - -The result presents a positive sign (+) because the signs are the same.
+ - or - +The result presents a negative sign (-) because the signs are different.
The question asks the product between [tex]\sqrt{1024}[/tex] and -3.4.
Initially, you have noted that from factoring 1024= [tex]2^{10}[/tex], consequently, your root is equal to [tex]2^5[/tex]. Here, you have that [tex]2^5=32[/tex]. After that, you should multiplicate 32 by -3.4.
Thus, you have 32 * (-3.4)= -108.8.
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let f(x) = 1 3x . compute lim h→0 f(5 + h) − f(5) h .
For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.
In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L
x→a⁻ x→a⁺
We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.
So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)
= 16+ 3h
Now, lim [ f(5 + h) − f(5)]/ h
h→0
= lim [(16 + 3h) − (16) ]/ h
h→0
= lim [ 16 + 3h - 16 ]/ h
h→0
= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]
h→0 h→0
= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]
h→0 h→0
= lim 3 (1) = 3 ( since, x⁰ = 1 )
h→0
Hence, the required limit value is 3.
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help me figure this out pls
Answer:
The rest would be 39, 48, 57
A triangle on a coordinate plane is translated according to the rule t–3, 5(x, y). which is another way to write this rule? (x, y) → (x – 3, y 5) (x, y) → (x – 3, y – 5) (x, y) → (x 3, y – 5) (x, y) → (x 3, y 5)
The way to write the rule is
(x, y) is (x – 3, y + 5).
A triangle which is on a coordinated plane is translated to the rule
Two lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line.
The original rule x and y coordinates
that are being moved to the left-hand side of the equation by
decreased by 3 units and rise up by 5 units.
Based on the information given,
we can come to the conclusion that other way to
write the given rule is
(x, y) is (x – 3, y + 5).
Hence, the other rule which are given are incorrect.
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(x, y) → (x – 3, y + 5)
The given rule is t–3, 5(x, y). This means that the triangle plane is translated 3 units to the left, and 5 units up. This can be written in another way as (x, y) → (x – 3, y + 5).
The given rule t–3, 5(x, y) states that the triangle is translated 3 units to the left, and 5 units up on the coordinate plane. This can be rewritten as (x, y) → (x – 3, y + 5). This means that for each point (x, y), the new point after the translation will be (x – 3, y + 5). In other words, the x-coordinate of the new point will be three units less than the original x-coordinate, and the y-coordinate of the new point will be five units more than the original y-coordinate. This translation of the triangle can also be visualized as moving the triangle three units to the left and five units up on the coordinate plane.
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What is the difference of 2x + 7 and 2x - 4?
Answer:
plus or minus 11
Step-by-step explanation:
2(1)+7
=9
2(1)-4
=-2
and the difference between the 9 and -2 is -11 but the difference between -2 and 9 is 11 so that why it positive or negative 11
evaluate the iterated integral by converting to polar coordinates. a 0 0 2x2y dx dy − a2 − y2
A. The result of the iterated integral by converting to polar coordinates is 0.
To evaluate this iterated integral, we will convert it to polar coordinates. First, we need to make the substitution x = rcos(θ) and y = rsin(θ). Then, we will need to find the limits of integration for r and θ. The region of integration is the area between the circles with radii a and 2 and between the x-axis and y-axis.
In polar coordinates, the integral becomes ∫∫r dr dθ from r = a to r = 2, and θ = 0 to θ = π/2.
We can now solve the integral by multiplying the integral of r by the integral of θ.
∫2^2 r dr dθ = ∫π/2^0 (-1/2)r^3 dθ = -1/2 * [(r^2)/2] from r = 2 to r = a = -1/2*(2^2 - a^2) = -1/2*(4-a^2) = -2+a^2/2
So the result of the integral is -2+a^2/2 = -2+4/2 = -2+2 = 0
Note that this is not a common way to solve iterated integrals, but rather a way to check the correctness of the solution. The common way is to find the limits of integration by solving the inequality and graphing the area of integration.
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What is the length of the third side?
Answer:
8
Step-by-step explanation:
This is a right triangle.
Since it's a right triangle with given side lengths,
we can use Pythagoras theorem, a² + b² = c² (a and b legs, c is hypotenuse)
to calculate the missing side.
Let x represent the missing side:
[tex]( {2 \sqrt{41} )}^{2} = {10}^{2} + {x}^{2} [/tex]
Calculate the square values[tex]164 = 100 + {x}^{2} [/tex]
Subtract 100 from both sides[tex]64 = {x}^{2} [/tex]
Find the root of the both sides[tex]8 = x[/tex]
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:
B. 2.3p – 10.1 = 6.49p – 4
C. 230p – 1010 = 650p – 400 – p
How to determine the required equations?From the information provided, we have the following equation:
2.3p – 10.1 = 6.5p – 4 – 0.01p
Next, we would simplify the given equation by collecting like terms as follows;
2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4
2.3p - 10.1 = 6.49p - 4
What is the multiplication property of equality?In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.
By multiplying both sides of the given equation by 100, we have the following;
100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)
230p - 1010 = 650p - 400 - p
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Here is a regular hexagon and a regular pentagon work out the size of the angle marked x.
The angle marked x in the regular hexagon is 120 degrees, and in the regular pentagon is 108 degrees.
The angle marked x in the regular hexagon is 120 degrees, because the sum of all the angles in a hexagon is 720 degrees (360 x 2). Each of the angles in a regular hexagon is 120 degrees, so the angle marked x must also be 120 degrees. The angle marked x in the regular pentagon is 108 degrees, because the sum of all the angles in a pentagon is 540 degrees (360 x 1.5). Each of the angles in a regular pentagon is 108 degrees, so the angle marked x must also be 108 degrees.
Regular Hexagon:
Sum of angles = 720 degrees
Number of angles = 6
Angle x = 720 ÷ 6 = 120 degrees
Regular Pentagon:
Sum of angles = 540 degrees
Number of angles = 5
Angle x = 540 ÷ 5 = 108 degrees
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helloooo i need heelpppp pleaseeeeee
Answer:
[tex]21[/tex]
Step-by-step explanation:
[tex]\textrm{If y varies directly with x we can write this relationship as}[/tex]
[tex]y = k \cdot x[/tex]
[tex]\textrm{k is referred to as the constant of proportionality.}[/tex]
[tex]\textrm{Substituting these values into the above equation we get}[/tex]
[tex]3 = k \cdot 2[/tex]
[tex]So\; k = \dfrac{3}{2}[/tex]
[tex]\mathrm{When }[/tex] [tex]x = 14,[/tex]
[tex]y = \dfrac{3}{2} \cdot 14[/tex]
[tex]y = 21[/tex]
is the faithful representation of reality in literature, and it presents life
as it actually is.
Romanticism
Naturalism
Realism
Regionalism
Realism is the faithful representation of reality in literature, and it presents life as it actually is. Option (c) is correct.
What do you mean by Reality?Reality is the state of things as they actually are, as opposed to how we would like them to be.
While "Naturalism is a manner and style of writing by which the author portrays 'life as it is' in accordance with the philosophic idea of determinism," "Realism is a manner and method of composition by which the author describes normal, average life, in an exact, truthful way."
Realism is a literary approach used by various schools of writing and is broadly referred to as "the faithful representation of reality" or "verisimilitude."
Therefore, Option (c) is correct. Realism is the faithful representation of reality in literature, and it presents life as it actually.
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A motorboat travels kilometers in hours going upstream and kilometers in hours going downstream. What is the rate of the boat in still water and what is the rate of the current
The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.
We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.
Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.
Use the distance , in speed/rate formula ,
Rate × Time = Distance
Upstream : (B-S)6 = 258
=> B - S = 43 --(1)
Downstream: (B+S)6 = 330
=> B + S = 55 --(2)
Solve the linear equations by elimination method. Add the two equations.
=> 2B = 98
=> B = 49 km/hr
Substitute this value of B in equation(2) and solve for S, B+S = 55
=> 49+S = 55
=> S = 6 km/hr
So, the rate of the current is 6 km/hr.
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Complete question:
A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.
Increase 68kg by 12%
Answer:
76.16kg
Step-by-step explanation:
68kg x (1+0.12)
the x (1+0.12) shows we are increasing by 12%
can also be written as
(68kg x 1) + (68kg x 0.12)
Find the height of the right trapezoid shown below and choose the appropriate result.
Answer:
answers is 78 because if 6x45 that 87
Which functions are symmetric about the y-axis? check all of the boxes that apply.
The functions that are symmetric about the y-axis are;
1) The function in the first option; f(θ) = cos(θ)
2) The function in the third option; f(x) = x²
Definition;
A function is symmetric about the y-axis is also known to be an even function such that the same value of the function is arrived at when x is replaced with -x
Analysis of the graphs;
First Function Graph; The graph represents the graph of cos (θ)
∴ The function is f(θ) = cos(θ)
The value of the function when x = π, f(π) = -1
Similarly, the value of the when x = -π, f(-π) = -1
f(π) = f(-π)
∴ f(x) = f(-x)
Therefore; the first function is an even function
Second Function Graph; The function of the graph is x = y²
∴ y = √(x)
The value of the function when x = 4, y = f(4) = 2
However, the when x = -4, f(-4) does not exist
f(4) ≠ f(-4)
∴ f(x) ≠ f(-x)
Therefore; the second function is not an even function (the function, x =
y², is however symmetric about the x-axis)
Third Function Graph; The function the graph represents is y = x²
The value of the function when x = 2, f(2) = 4
Similarly, the value of the when x = -2, f(-2) = 4
f(2) = f(-2)
∴ f(x) = f(-x)
Therefore; the third function is an even function
From the above, the functions which are symmetric about the y-axis, (even functions) are;
The first and the third functions
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Answer:
1 and 3.
Step-by-step explanation:
edg
x intercept for 5x - 9 = -8y - 3
The x intercept for 5x - 9 = -8y - 3 is calculated to be 6/5
What are intercepts?The term intercept refers to the location where a line or curve crosses a graph's axis.
The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.
At the x-intercept, the value of y is zero, because of this the equation
5x - 9 = -8y - 3 is solved as follows
5x - 9 = -8y - 3 at y = 0
5x - 9 = -8 * 0 - 3
5x - 9 = - 3
solving for x
5x = -3 + 9
5x = 6
dividing through by 5
5x/5 = 6/5
x = 6/5
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D) 3-2 (s-1) = 13+6s
Answer: -1
E) 2 (n+9) = -6 (2n-5) +8
Answer: 10/7
F) 5 (4k-3) -5k = 10+2 (3k+1)
Answer: 3
Explain how u got answer
The solutions to each equality are given as follows:
D) s = -1.
E) n = 10/7.
F) k = 3.
How to solve the equalities?The expressions are solved applying the distributive property when needed, then combining the like terms, and finally isolating the variable.
The solution for item d is given as follows:
3 - 2s + 2 = 13 + 6s -> Distributive property.
8s = 5 - 13 -> Combine the like terms.
8s = -8
s = -8/8
s = -1.
The solution for item e is given as follows:
2(n + 9) = -6(2n - 5) + 8
2n + 18 = -12n + 30 + 8 -> Distributive property.
14n = 20 -> Combine the like terms.
n = 20/14
n = 10/7.
The solution for item f is given as follows:
5(4k - 3) - 5k = 10 + 2(3k + 1)
20k - 15 - 5k = 10 + 6k + 2
15k - 15 = 12 + 6k
9k = 27
k = 27/9
k = 3.
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How many four digits numbers can be formed by using 1,2 3 4 5 6 7 which are greater than 3400?
There are 6 four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 that are greater than 3400.
To determine the number of four-digit numbers that can be formed using the digits 2, 5, and 3, we can use the formula nPr, where n is the number of digits we are working with (in this case, 3) and r is the number of digits we want in each combination (in this case, 4).
Therefore, the number of four-digit numbers that can be formed using the digits 2, 5, and 3 is 3P4 = 3! / (3 - 4)! = 3! / (3 - 4)! = 3! / -1! = 3! / 1 = 3 x 2 x 1 = 6.
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I really need help with this if you could also add an explanation that would be much appreciated.
From the rectangle, the value of x is 4.9 or -2.4
What is a rectangle?A rectangle is a four sided polygon whose opposite sides are equal and parallel, The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.)
The parameters given for the solution are
Area = 24m
Length = x+2
width = 2x-9
Area = l*w
This implies that (x+2)(2x-9)=24
Collecting like terms we have
2x2-5x-24=0
Solving the equation we have
(5±√25+192)/4
⇒(5±√217)/4
⇒(5+14.7)/4 or( 5-14.7)/4
x=4.9 or x = 2.4
Therefore the value of x in the figure is 4.9 and -2.4 respectively
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Find the length of the third side. Write is simplest radical form show work.
Answer:
4
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
9^2 + b^2 = (sqrt(97) )^2
81 + b^2 = 97
Subtract 81 from each side
b^2 = 97-81
b^2 = 16
Take the square root of each side
sqrt(b^2) = sqrt(16)
b = 4
[tex] \longmapsto \: 9^2+b^2 = (\sqrt(97))^2[/tex]
[tex]\longmapsto \: 81+b^2=97[/tex]
[tex] \longmapsto \: b^2 = 97-81[/tex]
[tex] \longmapsto \: b^2 = 16[/tex]
[tex] \longmapsto \: b = 4[/tex]