The 3 : 7 ratio of the leg lengths and the 42 cm length of the hypotenuse side using Pythagorean theorem, gives the lengths of the sides (the legs of the right triangle) as follows;
[tex]147 \cdot \sqrt{ \frac{2}{29} } [/tex] and [tex] 63 \cdot \sqrt{ \frac{2}{29} }[/tex]
What is Pythagorean theorem?Pythagorean theorem states the square that has the hypotenuse of a right triangle as its side length is equal in area to the sum of the areas of the two squares formed by legs of the right triangle.
Given;
The possible given parameters are;
The ratio of the length of the sides (the legs) of the triangle is 3 : 7
The length of the hypotenuse side = 42 cm
Required: The lengths of the other two sides of the triangle
Solution;
The lengths of the two sides are found as follows;
Let a and b represent the lengths of the legs of the right triangle, according to Pythagorean theorem, we have;
a² + b² = 42²
The ratio of the leg lengths gives;
a/b = 3/7
Therefore;
a = (3/7)•b
Which gives;
((3/7)•b)² + b² = 42²
b²•((3/7)² + 1) = 42²
b = 42²/(((3/7)² + 1)) = 42²×(58/49)
[tex]b = 147 \cdot \sqrt{ \frac{2}{29} } [/tex]
Which gives;
[tex]a =\frac{3}{7} \times 147 \cdot \sqrt{ \frac{2}{29} }= 63 \cdot \sqrt{ \frac{2}{29} }[/tex]
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get it down give u more points for the rest of the questions
What is the sum of the first 11 prime numbers?
Considering the definition of prime numbers, the sum of the first 11 prime numbers is 129.
Definition of prime numbersPrime numbers are those that are only divisible (when divided by another gives an integer) between themselves and 1. That is, prime numbers are those numbers, greater than 1, that only admit themselves and the number as divisors. number 1.
Sum of the first 11 prime numbersThe first 11 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
So their sum is:
sum= 2 +3 +5 +7 +11 +13 +17 +19 +23 +29
sum= 129
Finally, their sum is 129.
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(3, 9), (1, 1) write in standard form
A line passes through the points (−6, −3) and (6, −3). Which of the following points is also on the line? A. (−3, 0) B. (6, 0) C. (0, −3) D. (−6, 0)
Answer:
C
Step-by-step explanation:
Since the y-coordinates of both points are -3, the equation is [tex]y=-3[/tex].
The only option with a y-coordinate of -3 is option C.
Sorry for all the questions i'm askin i'm a slow learner so thank you guys for ya help!
50 points will b giving
Answer:
D. [tex]\sqrt{27}[/tex]
Step-by-step explanation:
A, B, and C are all perfect squares being square rooted. This means that they will all result in whole numbers.
For example: A. [tex]\sqrt{9}=3[/tex]
However, D. [tex]\sqrt{27}=3\sqrt{3}[/tex], which is not rational because it contains an unsimplifiable square root (sqrt 3)
Answer:
√27
Step-by-step explanation:
√9 = 3
√81 = 9
√36 = 6
√27 = not whole number
5. Below is a model of the infield of a baseballstadium. How long is each side of the infield?oth a perfectquare rootnumbers?A= 81 in.?
We have that the area of the infield is 81 in2.
This area is a square, which means it has equal sides, and its area is:
[tex]\text{Area}=side^2[/tex]If the area of the square is 81 in2, we have that:
[tex]\begin{gathered} \text{side}^2=81 \\ \text{side}=\sqrt{81} \\ \text{side}=9\text{ in} \end{gathered}[/tex]So the side of the infield is 9 inches.
Latisha has $40 in her checking account. She makes a withdrawal of $20 and then writes a check for $40. Then she deposits $30. Use the number line and complete the equation to find her final balance.
The final balance that will be in the account of Latisha is $10.
What is a checking account?A checking account simply means the account that makes use of a check. It is usually used by business owners.
From the information, Latisha has $40 in her checking account, she makes a withdrawal of $20 and then writes a check for $40 and then she deposits $30.
The appropriate operations to find the balance will be:
= 40 - 20 - 40 + 30
= 10
She will have $10 left. Note that a withdrawal is subtraction.
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what is the area of a rectangle wxyz with vertces w(0,1), x(3,4), y(-1,8), z(-4,5)
Answer: I think 43
Step-by-step explanation:
Draw on a graph out the points and then add up the middle of your shape.
Your welcome!
If x+y =8 and x^2+y^2=36 find x-y
If the vertical component of velocity for a projectile is 7.3 meters/second, find its hang time. a. 1.5 seconds b. 2.5 seconds c. 5.6 seconds d. 6.7 seconds e. 7.1 seconds
The hang time is calculated to be a. 1.5 seconds if the vertical component of velocity for the projectile is 7.3 meters/second.
The formula for the height of the projectile can be used to calculate the hang time as follows;
h = ut - 0.5at²
here;
h is the height of the projectile
u is the velocity = 7.3 m/s
a is the acceleration due to gravity
The standard value of acceleration due to gravity is equal to 9.81 m/s²
The height will be zero both the times when t=0 and when the journey has been completed
Now adding these values to the formula;
h = ut - 0.5at²
0 = 7.3t - 0.5(9.81)t²
Solving for t;
4.905t² = 7.3t
4.905t² / t = 7.3
4.905t = 7.3
t = 7.3 / 4.905
t = 1.49 ≈ 1.5
Therefore; the hang time is calculated to be 1.5 seconds.
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If A intersects B, B intersects C, C is parallel to D, and D intersects E, which is not true?
Following the descriptions of the relationship existing between the lines the option that is not true is the last option which is b || d which is read as b is parallel to d
What are parallel lines?Some set of lines are said to be parallel if the lines are equally spaced apart. This ensures that such line will never meet . Parallel lines is very useful in the field of geometry as it the foundation of many postulates and theorem.
Also, when two lines are being connected by a line. Say line x and line y and the connecting line is z. If the lines x and y makes similar angle with line z then line x and line y is said to be parallel.
Considering the descriptions given in the question. line b is tether perpendicular to line d. Hence saying that line b is parallel to line d is not true and the correct answer to the question.
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A contractor purchases 3 dozen pairs of padded work gloves for $43.56 incorrectly calculates the unit price as $14.52 per pair for the expense report. What is the correct unit price?What is the error?
Answer: I think the answer is $1.21
Step-by-step explanation: Instead of 3 pairs it says 3 dozen. A dozen is 12.
3 x 12 = 36
Then you should do 43.56 / 36
For one pair of gloves it should be $1.21
The contractor got $14.52 because he did a dozen (12) divided by 43.56.
I hope that helps! ^^
which two values or x are roots of the polynomial below? x2 - 11x + 13
The two values or x of roots of the polynomial are
[tex]x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}[/tex]
This is further explained below.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Generally, the equation for polynomial the is mathematically given as
x^2 - 11x + 13
Therefore
We know that,
[tex]x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]
Here,
a=1
b=-11
c=13
Putting the values,
[tex]x=\frac{-(-11) \pm \sqrt{(-11)^2-4 \times 1 \times 13}}{2 \times 1} \\[/tex]
[tex]&=\frac{11 \pm \sqrt{121-52}}{2} \\\\&=\frac{11 \pm \sqrt{69}}{2} \\[/tex]
Therefore
[tex]x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}[/tex]
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select the correct answer from the drop -down menu . A=[-9,0,3,-1] b= [0,4,-6,2] the order of matrix A+B is ?
If A=[-9,0,3,-1] b=[0,4,-6,2] , so the order of matrix A+B is 4x1(4 rows and 1 column).
What is matrix ?Matrix, a set of number arranged in rows and column so as to form a rectangular array. The number are called the elements, or entries, of the matrix .
What does the matrix serve as?Both data and mathematical equations can be represented by the numbers in a matrix. Multiplying matrices can provide quick but accurate approximations of considerably more complex calculations in many time-sensitive engineering applications.
The elements of the matrix are nothing but the entries of the matrix.
So according, To the question we are adding matrix A which is 4 rows and 1 column to matrix B which is also of 4 rows and one column obtaining a third matrix that has also 4 rows and 1 column :
[-9,0,3,-1]+[0,4,-6,2]=[-9,4,-3,1]
The resultant A+B is also of 4 rows and 1 column
Hence the order of matrix A+B is 4x1 (4 rows and 1 column)
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When 12 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
When 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2
Consider the number as x
Square of the number = [tex]x^{2}[/tex]
12 subtracted from the square of a number = [tex]x^{2} -12[/tex]
4 times the number = 4x
Then the equation will be [tex]x^{2} -12=4x[/tex]
Rearrange the terms and it will become a quadratic equation
[tex]x^{2} -4x-12=0[/tex]
Split the middle term and solve the equation
[tex]x^{2} +2x-6x-12=0[/tex]
Take common terms
x(x+2)-6(x+2) = 0
Take common term outside
(x-6)(x+2) = 0
Therefore
x = 6, -2
The negative solution is -2
Hence, when 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2
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last month a manufacturing company shipped 452 boxes of ball bearings each box contains 48 ball bearings how many ball bearings sis the company ship last month
Answer:
answer is B
Step-by-step explanation:
Sorry if this is incorrect
I no longer need this to be answered
Answer:
oh ok hope you got the answer
Step-by-step explanation:
Write an inequality that represents the fact that while making your product you can’t exceed this spending limit.
I'm making figures for $100 and selling them for $150, my spending limit is $200
The inequality which correctly represents the fact that the spending limit cannot be exceeded as described in the task content is; 100x ≤ 200.
Which inequality represents the fact that the spending limit cannot be exceeded?It follows from the task content that the inequality which correctly represents the spending limit as described be determined.
Since the given spending limit is; $200.
Let, x = the number of figures made.
Therefore, the cost of making x number of figures can be written algebraically as; 100x.
Hence, since it costs $100 to make each figure, it follows that the required inequality is;
100x ≤ 200.
This follows from the fact that each figure costs $100 to make.
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brunette college offers 444 math classes, 222 science classes, 333 language classes, and 555 art classes. sylvia needs to sign up for exactly one class in each subject. how many different combinations of classes does sylvia have to choose from?
The total number of different combinations is 120.
What is combination and permutation?
Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.We are to find the number of different combinations of classes does Sylvia have to choose from.
We will be using the following formula for number of combinations of n elements taken r (r is less than or equal to n) at a time:
nCr = n!/r!( n - r )!
Since Sylvia needs to sign up for exactly one class in each subject, so the total number of different combinations from which she has to choose will be
⁴C₁ * ²C₁ * ³C₁ * ⁵C₁
= 4!/1!( 4 - 1 )! × 2!/1! ( 2 - 1 )! × 3!/1! ( 3 -1)! × 5!/1! ( 5 - 1 )!
= 4 × 2 × 3 × 5
= 120
Thus, the total number of different combinations is 120.
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Kali just started a new sales floor job to save for college. She earns $15.75 per hour plus a flat fee of $50 per week. She wants to earn between $200 and $400 per week. The following inequality represents her earning potential: 200 ≤ 15.75x + 50 ≤ 400 Solve the inequality.
The solution set of the given inequality is:
9.52 ≤ x ≤ 22.22
Or [9.52, 22.22] if we write this as an interval.
How to solve the inequality?Here we have the inequality:
200 ≤ 15.75x + 50 ≤ 400
Which represents Kali's earning potential.
To solve the inequality we need to isolate the variable in the middle, if we subtract 50 in the 3 sides we get:
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50
150 ≤ 15.75x ≤ 350
Now we need to divide both all by 15.75, so we get:
150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75
9.52 ≤ x ≤ 22.22
This is the solution of the inequality, the solution set written as an interval will be [9.52, 22.22]
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Each box holds 48 pencils. The chart below shows the number of pencils in 1 box and 5 boxes.
Help ASAP please
Answer: No, 6 boxes will give you 288 penicils.
Step-by-step explanation: 1 box is 48 penicils, so if use this to the other boxes (4x48) we get 192. Now with six boxes (6x48) we get 288.
find the length of the sides indicated round to nearest tenth
Factorización prima de 162
Given the equation k over 22.8 equals 6.9, determine the value of k.
3.30
15.9
29.7
157.32
The value of k in the equation, k over 22.8 equals 6.9, is 157.32.
What is the value of k?The given equation is:
k / 22.8 = 6.9
In order to determine the value of k, multiply both sides of the equation by 22.8.
Multiplication is one of the basic mathematical operation. It is the operation that is used to determine the product of two or more numbers by adding a number with another number repeatedly over a number of times. The sign that represents multiplication is ×.
(k / 22.8) x 22.8 = 6.9 x 22.8
k = 157.32.
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Translate this phrase into an algebraic expression.
Nine less than the product of 18 and Jose's age
Use the variable j to represent Jose's age.
Answer:
J(18)-9
Step-by-step explanation:
j times 18 minus 9
Multiply 3.2x and 4x.
12.8x2
7.2x2
12.8x
7.2x
Answer: 12.8x2
Step-by-step explanation:
Based on the given task content; the solution to the Multiplication of 3.2x and 4x is 12.8x².
The correct answer option is option a.
Multiplication of numbersThis is a process of computing the sum of a number with itself in a specified number of times. Multiplication is also called product and it is represented by the sigh ×. The product of a and b means ab.
For instance, from the task which is given above;
3.2x and 4x
= 3.2x × 4x
= 12.8x²
In this answer above,
12.8 is the coefficient and
x² is the variable.
In conclusion, 3.2x × 4x will give the result 12.8x².
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a forest trail is 607 feet long. a person biked from one end to the other and back again 6 times in the past 5 weeks. how far the person bike over the past 5 weeks
The distance that the person bike over the past 5 weeks is 7284 feet.
How to illustrate the expression?Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered. Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.
From the information, the forest trail is 607 feet long and a person biked from one end to the other and back again 6 times in the past 5 weeks.
Therefore, the distance that the person covered will be:
= 2 × 6 × 607
= 7284 feet.
The distance is 7284 feet.
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HELP PLEASE!!!!
Simplify −4r(−11r + 2r − 14).
−36r^2 + 56r
−36r^2 − 56r
36r^2 + 56
36r^2 + 56r
Answer:
[tex]36r^2+56r[/tex][tex]36r^2+56r[/tex]
Step-by-step explanation:
First simplify [tex]-4r(-11r+2r-14)[/tex] into [tex]-4r(-9r-14)[/tex] by adding the terms with common variable r together,
then expand into the answer
Answer:
-36r^2 - 56r
Step-by-step explanation:
Between 10 pm and 7:45 am the water level in a swimming pool decreased by 3/16 inches
The rate of change of the level of the swimming pool is -0.019 inches per hour.
How to get the rate of change in the level of the swimming pool?
The rate of change will be given by the quotient between the change in the level of the water (-3/16 inches) and the time in which that change happens.
We know that the change happens between 10 pm and 7:45pm, so the number of hours is:
2 hours + 7 hours + 45 min
Where:
1 hour = 60 min
45 min = 45/60 hours = 0.75 hour
Then the total time is:
2h + 7h + 0.75h = 9.75h
Then the rate of change is:
R = (-3/16 inches)/(9.75 h) = -0.019 inches per hour.
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Find 3 decimals x such that : 4.1 < x < 4.2
Answer:
There are many numbers, but here are three
4.11, 4.12, 4.13
Step-by-step explanation: