Given: JLM is equilateral. Z is the midpoint of JM.
Prove: JZL is congruent to MZL.
Answers
There are multiple ways to prove congruence between two triangles:
SSS - three sides are congruentSAS - two sides and the angle in between are congruentASA - two angles and the side in between are congruentAAS - two angles and one side are congruentHL - (applies only to right triangles) the hypotenuse and one leg are congruent.Keep in mind that the order of the letters matters.
Solving the Question
Given triangle JLM, we know that
S - Z is the midpoint of JM, meaning JZ is congruent to MZ.S - Both triangles share side LZ.S - Because JLM is an equilateral triangle, LJ is congruent to LM.This is only one of the ways to prove congruence with these two triangles.
Related Questions
A set of equations is given below.
Equation C: y = 7x + 12
Equation D: y = 7x + 2
How many solutions are there to the given set of equations?
O One solution
OTwo solutions
O Infinitely many solutions
O No solution
Answers
Answer:
2
Step-by-step explanation:
lucky guess from my boi tony
The speed of light is a constant and approximately equal to 300,000,000 meters per second.
Green lasers emit light at a wavelength of 532 nm. However, the material that is used to make most green lasers does not emit light at 532 nm. Instead, it emits light at a different wavelength, and the laser then uses a “frequency doubler.” This doubles the frequency of the emitted light, and the resultant light is the green 532 nm that we observe.
1 meter is equal to 1,000,000,000 nanometers.
What is the output light frequency of the material used before doubling?
Answers
The output light frequency of the material used before doubling will be 0.056 Hz.
What is the frequency?Frequency is defined as the number of repetitions of a wave occurring waves in 1 second.
Frequency is given by the formula as,
[tex]\rm v = \lambda \times f \\\\\ \rm f = \frac{v}{\lambda} \\\\ \rm f = \frac{3 \times 10^8}{532 \times 10^-9} \\\\ \rm f = 3 \times 10^{12} \\\\ f= 0.056 \ Hz[/tex]
Hence the output light frequency of the material used before doubling will be 0.056 Hz.
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11. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n=12, x = 5, p = 0,25
A) 0.082
B) 0.091
C) 0.027
D) 0.103
Answers
Answer
D
Step-by-step explanation:
The probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.
The correct answer is A) 0.082.
The probability of x successes given the probability p of success on a single trial, with n trials, can be calculated using the binomial probability formula:
[tex]P(x) = (n_C_x) * p^x * (1-p)^{(n-x)[/tex]
In this case, n = 12, x = 5, and p = 0.25. Let's substitute these values into the formula:
[tex]P(5) = (12C5) * (0.25)^5 * (1-0.25)^{(12-5)[/tex]
Using the combination formula ([tex]n_C_r[/tex]) to calculate ([tex]{12}_C_5[/tex]):
[tex]P(5) = (12!)/(5!(12-5)!) * (0.25)^5 * (0.75)^7[/tex]
Simplifying the combination:
[tex]P(5) = (12!)/(5!7!) * (0.25)^5 * (0.75)^7[/tex]
Calculating the factorial terms:
[tex]P(5) = (12111098)/(54321) * (0.25)^5 * (0.75)^7[/tex]
[tex]P(5) = 792 * 0.0009765625 * 0.1334838867[/tex]
P(5) ≈ 0.082
Therefore, the probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.
The correct answer is A) 0.082.
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If m∠B = 46°, and m∠D = 67°, what is m∠BEA?
67°
46°
88°
134°
Answers
The graph shows the growth rate of a certain bacteria in a lab, where the number of bacteria depends on the number of hours since the start of the experiment.Based on the graph, what is the approximate number of bacteria after 16 hours? 6 bacteria 8 bacteria 60 bacteria 80 bacteria
Answers
The approximate number of bacteria after 16 hours is 60 bacteria ,Option C is the right answer.
What is a Function ?A function is a Mathematical statement which connects a dependent variable and an independent variable.
The graph shows the the growth rate of a certain bacteria in a lab
the number of bacteria is on the y axis and
the number of hours is on the x axis
The function is continuous ,
From the graph the approximate number of bacteria after 16 hours is
60 bacteria
Therefore Option C is the right answer.
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Jill has c comic books. Tonya has 4 more than twice Jill's comic books. What variable expressions represents the total number of comic books Jill & Tony have all together?
Answers
Answer:
3c + 4
Step-by-step explanation:
Forming an expression
Number of books with Jill = c
To find the number of books with Tonya, multiply 'c' by 2 and then add 4 to it.
Number of books with Tonya = 2*c + 4
= 2c + 4
Total books all together = c + 2c + 4 {Combine like terms}
= 3c + 4
The triangle inequality theorem states the sum of the lengths of any two sides of a triangle is _____ the length of the third side.
Answers
Answer:
see explanation
Step-by-step explanation:
the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
if the sides are a, b, c , then the following must be true
a + b > c
a + c < b
b + c > a
for the 3 sides to form a triangle
What is the median of the data?
Answers
Answer:
The median is 3.
Step-by-step explanation:
Since, most of the values presented are 0-8 and median is the middle of any data set. It has to be 3.
Have a nice day
Simplify the following expression 7a + 5b - 2a + b
Answers
Answer:
5a + 6bStep-by-step explanation:
Simplify the following expression:
Simplify the following expression:
7a + 5b - 2a + b =
5a + 6b
Using Newton-Raphson method to find the approximate root of the equation x log_{10}x=1.2
( Carry out three iterations ). [tex] \\ \\ [/tex]
Thank uh!
Answers
Answer:
[tex]x \approx 2.740646096[/tex]
Step-by-step explanation:
Given:
[tex]x\log_{10}x=1.2[/tex]
Rewrite so that it's equal to zero:
[tex]\implies x\log_{10}x-1.2=0[/tex]
Therefore:
[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]
Differentiate the function:
Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:
[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]
[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]
[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]
[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]
[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]
Newton-Rhapson iteration formula
[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]
Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Therefore, the iteration formula is:
[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Let [tex]x_0=3[/tex]
Substitute this into the formula and carry out 3 iterations:
[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]
[tex]\implies x_2=2.740648841[/tex]
[tex]\implies x_3= 2.740646096[/tex]
write equation of the log base of 3
Answers
Answer:
see below
Step-by-step explanation:
The graph is shifted to the RIGHT so it will be a ' x-1'
and it is shifted UP 3 units so:
Looks like log3 (x-1) + 3
at x = 4 the value of the graph is 4
log3 (4-1) + 3 = 4 CHECK !
simplify the mathematical expression to determine the appropriate india product or quotient in a scientific notation round round do the 1st fractor goes to the 10th place 3.3x10^3 7.8 3.7 2.1x10^-3
Answers
From the power rules, the matching of each expression with its result is:
[tex](8.6*10^7)(9.1*10^{-8})=7.8[/tex]
[tex](6.9*10^5)(4.8*10^{-3})=3.3*10^3[/tex]
[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =2.1*10^{-3}[/tex]
[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=3.7[/tex]
Power RulesThere are different power rules, see some them:
1. Multiplication with the same base: you should repeat the base and add the exponents.
2. Division with the same base: you should repeat the base and subctract the exponents.
3.Power. For this rule, you should repeat the base and multiply the exponents.
4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.
From this for your question, you have:
[tex](8.6*10^7)(9.1*10^{-8})[/tex] - From the distributive property of multiplication and power rules you can do:[tex](8.6*10^7)(9.1*10^{-8})=(8.6*9.1)*(10^7*10^{-8})=78.26*10^{-1}=7.8[/tex][tex](6.9*10^5)(4.8*10^{-3})[/tex] - From the distributive property of multiplication and power rules you can do:[tex](6.9*10^5)(4.8*10^{-3})=(6.9*4.8)*(10^5*10{-3})=33.12*10^2=3.3*10^3[/tex][tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})}[/tex] - From the distributive property of multiplication and power rules you can do:[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =\frac{(3.7*4.6)*(10^2*10^{-3})}{(1.4*5.7)*(10^{-6}*10^{8})} =\frac{17.02*10^{-1}}{7.98*10^2} =2.13*10^{-3}=2.1*10^{-3}[/tex]
[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}[/tex] - From the distributive property of multiplication and power rules you can do:[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=\frac{(3.1*5.3)*(10^{5}*10^{-9})}{(7.3*6.1)*(10^{2}*10^{-7})} =\frac{16.43*10^{-4}}{44.53*10^{-5}}=0.36896*10^1=3.7[/tex]
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Solve for r in the following equation:
5r - r - 9 = 15
what is the first step?
A. Use the subtraction property of equality
B. Use the addition property of equality
C. Combine like terms
What does the equation look like now?
(type your answer)
Use your answer and finish solving the equation for r.
R=____
Answers
An equation is formed of two equal expressions. The value of r in the given equation is 6.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for the value of r in the given equation will be,
5r - r - 9 = 15
5r - r - 9 + 9 = 15 + 9
4r = 24
r = 6
A.) The first step is to Use the addition property of equality. Thus, the correct option is B.
B.) The value of r in the given equation is 6.
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Vector u has initial point P at (0, 0) and terminal point Q at (5, -8). What are the component form and magnitude of u?
• u = (5, -8): ||u|| = -√89
• u = (5, 8): ||u|| = -√89
• u = (5, -8): ||u|| = √89
• u = (5, 8): ||u|| = √89
Answers
The correct option for the given vector is the third one:
u = (5, -8): ||u|| = √89What are the component form and magnitude of u?If the initial point is (0, 0), then the component form of the vector is just equal to the terminal point of the vector.
Then we have:
u = (5, -8)
For a vector w = (x, y) the magnitude is:
[tex]||w|| = \sqrt{x^2 + y^2}[/tex]
In this case, the magnitude will be:
[tex]||u|| = \sqrt{5^2 + (-8)^2} = \sqrt{89}[/tex]
Then the correct option is the third one.
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Solve for x in the equation x/5 -2=11
Answers
Answer:
x = 65Step-by-step explanation:
Solve for x in the equation
x/5 - 2 = 11
x/5 = 11 + 2
x/5 = 13
x = 5 * 13
x = 65
-----------------
check
65/5 - 2 = 11
13 - 2 = 11
11 = 11
the answer is good
Question 29 of 40
Find f(-2) for f(x) = 5.3*.
Answers
Answer:
A. [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
To find f(-2) in f(x)=5*3^x, plug in -2 into all the x values.
f(-2)=5*3^-2, you can use calculator to calculate 3^-2 which equals 0.1, forever 1's.
f(-2)=5*0.1=0.5 Forever 5's.
f(-2)=0.5 or [tex]\frac{5}{9}[/tex]
Hope this helps!
If not, I am sorry.
Please help me answer question 6/11
Answers
The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.
The complete question is attached below.
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrix is given below.
[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]
Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.
Then the correct option is B.
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which choice is equivalent to the the expression
square root of -64
Answers
The equivalent expression of square root of -64 is 8i
How to determine the equivalent expression?We have:
square root of -64
Rewrite as:
√-64
Expand
√64 * √-1
Take the square root of 64
8√-1
In complex numbers
√-1 = i
So, we have:
8i
Hence, the equivalent expression of square root of -64 is 8i
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please help
PLEASE
Answers
Answer:
Step-by-step explanation:
4567890987654345678
a) Copy a segment using the construction tool. Insert a screenshot of the construction here.
Alternatively, construct a segment and copy it by hand using a compass and straightedge. Leave
all circle and arc markings.
Answers
We need to understand circles and colinear points in order to use the building tool to create a circle.
What exactly is a circle?It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
Draw arcs such that they all bisect one another at a point, which will be the center of the circle, starting with three non-colinear points (points A, B, and C).
Additionally, the radius will match the distance between the arcs' centers and their correspondingly drawn arcs.
Hence we need to understand circles and colinear points in order to use the building tool to create a circle.
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The slope of the line containing the points (-5, 3) and (-2, 1) is
O-2/3
02/3
0-3/2
Answers
Answer:
Step-by-step explanation:
slope=(1-3)/(-2-(-5))
=-2/(-2+5)
=-2/3
Which value must be added to the expression x2 16x to make it a perfect-square trinomial?
Answers
Answer:
16
Step-by-step explanation:
x^2+16x+16
(x+4)(x+4)
x^2+ 4x+4x+16
Answer:
The answer is C.) 64 on edge.
Now write 40,630 in scientific notation
Answers
Answer:
40630=4.063× 10 power 4Determine the relationship between the two triangles and whether or not they
can be
proven to be congruent.
Answers
Answer: These ARE congruent to each other.
Step-by-step explanation: Do you see the ''tick marks?'' They both have 1 set of 2, and 1 set of 1. If that makes sense. They also have a "angle" in one of their acute angles.
Partially factored form: f(x) = (x − 3)(x 3)(x2− 4x 5) use the quadratic formula to identify the zeroes of x2 − 4x 5. x =
Answers
Answer:
2 ± i
Step-by-step explanation:
by 5, I assume you mean +5
x² - 4x + 5 = 0
x = (-b±(√(b²-4ac)) / 2a
x = (4 ± (√(16 - 20)) / 2
x = (4 ± (√(-4)) / 2
√-4 = √4√-1 which is 2i
x = (4 ± 2i) / 2
x = 2 ± i
Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Select three options.
1 ≥ 2x
6x ≥ 3 + 8x – 4
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.
Answers
1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).Option A,B and C are correct.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
The solution to the given inequality is;
6x≥3+4(2x-1)
6x≥3+8x-4
2x≤1
x≤(1/2)
The correct options are;
A)1 ≥ 2x
B)6x ≥ 3 + 8x – 4
C)A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).
Hence, options A, B, and C are correct.
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Answer:
A, B, C
Step-by-step explanation:
Which polynomial is factored completely? 4 (4 x superscript 4 baseline minus 1) 2 x (y cubed minus 4 y squared 5y) 3 x (9 x squared 1) 5 x squared minus 17 x 14
Answers
The answer choice which represents a polynomial which is factored completely is; (y³ - 4y² +5)
Which polynomial is factored completely?The polynomials as given in the task content are;
4(4x⁴ -1) + 2x
(y³ - 4y² +5)
3x (9x² -1)
5x² -17x +14
Hence it follows that the polynomial which cannot be further factorised is; (y³ - 4y² +5).
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Answer:3 x (9 x squared + 1)
it is c because i did the test and put b but got it wrong
Step-by-step explanation:
help with both please :)
Answers
Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:
Method of Elimination1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i) multiplied by 2
10x + 2y = 18 - - - - (i)
10x - 7y = - 18 - - - - (ii) {subtraction of eq. (ii) from eq. (i)}
0 + 9y = 36
y = 36/9
y = 4
From eq. (i),
5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
-> x = 5/5
-> x = 1
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (ii) multiplied by 3
- 4x + 9y = 9 - - - - (i)
3x - 9y = - 18 - - (ii) {addition of eq. (ii) and eq. (i)}
- x + 0 = - 9
x = 9
From eq. (ii),
x - 3y = - 6
-> 9 - 3y = - 6
-> - 3y = -6-9
-> y = -15/-3
-> y = 5
So, x = 9 and y = 5
Method of Substitution1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i)
5x + y = 9
-> y = 9 - 5x
Value of eq. (i) in eq. (ii)
10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x = 1
From eq. (i),
5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (i)
- 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4
Value of eq. (i) in eq. (ii)
x - 3y = - 6
-> (9 - 9y) / -4 -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y = 5
From eq. (ii)
x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9
So, x = 9 and y = 5
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
Round 969.991 to the nearest whole number
Answers
Answer:
Round of 969.991
970
Rules of round off
1) If the digit is odd no. the no. will increase to 1
2) if it is even the no. will be same.
please help me with my math
Answers
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for y and z ~
[tex]\qquad \sf \dashrightarrow \: z + 61 = 180[/tex]
[ Co- interior angle pair ]
[tex]\qquad \sf \dashrightarrow \: z = 180 - 61[/tex]
[tex]\qquad \sf \dashrightarrow \: z = 119 \degree[/tex]
now,
[tex]\qquad \sf \dashrightarrow \: 5y + 14 = 119[/tex]
[ by Alternate interior angle pair ]
[tex]\qquad \sf \dashrightarrow \: 5y = 119 - 14[/tex]
[tex]\qquad \sf \dashrightarrow \: 5y = 105[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 21 °[/tex]
