The ΔABC and ΔDEF are congruent by SSS congruent criteria
According to the question,
We have to prove ΔABC and ΔDEF are congruent
Coordinates of ΔABC are given as :
A(-2 , -2) , B(4 , -2) and C(4,6)
By using Distance formula ,
AB = √(-2-(-2))²+ (4 - (-2))²
=> √(-2 + 2)² + (4 +2)²
=> √ 6²
=> 6
AC = √(6-(-2))²+ (4 - (-2))²
=> √(6 + 2)² + (4 +2)²
=> √ 56 + 36
=> √92
BC = √(6-(-2))²+ (4 - 4)²
=> √(6+ 2)²
=> √ 8²
=> 8
Coordinates for ΔDEF,
D(5 , 7) , E(5,1) and F(13 , 1)
By using Distance formula ,
DE = √(1 - 7)²+ (5 -5)²
=> √(-6)²
=> √36
=> 6
DF = √(1-7)²+ (13 - 5)²
=> √(-6)² + (8)²
=> √ 56 + 36
=> √92
EF= √(1 - 1)²+ (13 - 5)²
=> √ 8²
=> 8
Now, two triangles are congruent if they are equal sides or equal angles
Therefore , In ΔABC and ΔDEF
AB = DE
AC = DF
BC =EF
By the SSS criteria , ΔABC and ΔDEF are congruent
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need help fast will mark brainlist
The rate of change of y with respect to x for a given line is 4/5.
What is the rate of change?
The rate of change is measured by a line's slope. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.
The rate of change of y with respect to x for a given linear function is simply the slope expressed as:
dy/dx = (y2 - y1)/(x2 - x1)
Let us take the first 2 coordinates from the graph which are:
(0, 3) and (5, 7)
Thus;
dy/dx = (7 - 3)/(5 - 0)
dy/dx = 4/5
Hence, the rate of change of y with respect to x for a given line is 4/5.
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which expotential function has a y-intercept of (0, -4)?
HELP WILL MARK BRAINLIEST
Answer:
[tex]y=2^x-5[/tex]
Step-by-step explanation:
The y-intercept occurs when x = 0.
Therefore, substitute x = 0 into each equation to find its y-intercept.
[tex]\begin{aligned}\implies y&=(-4)^0\\&=1\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=2^0-5\\&=1-5\\&=-4\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=3^0+4\\&=1+4\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=(0)^{-4}\\&=0\end{aligned}[/tex]
Therefore, the exponential function that has a y-intercept of (0, -4) is:
[tex]\large\boxed{y=2^x-5}[/tex]
what’s 3.78153 rounded?
CAN SOMEONE HELP WITH THIS QUESTION?✨
The coordinates of point B are (4, 0)
How to determine the coordinates of point B?From the question, we have the following parameters that can be used in our computation:
A = (6, 10)
Midpoint = (5, 5)
The midpoint of a line from its endpoints is calculated using the following equation
Midpoint = (x₂ + x₁)/2 + (y₂ + y₁)/2
Substitute the known values in the above equation, so, we have the following representation
(5, 5) = (6 + x₁)/2 + (10 + y₁)/2
Multiply by 2
(10, 10) = (6 + x₁) + (10 + y₁)
By comparison, we have
x + 6 = 10
y + 10 = 10
Evaluate
x = 4
y - 0
Hence, the point is (4, 0)
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if the sum of a set of ten different positive prime numbers is an even number, which of the following prime numbers cannot be in the set? A. 2
B. 3
C. 5
D. 7
E. 11
The prime number that cannot be in the set is A . 2.
Prime number:
In math, prime number is a natural number greater than 1 that is not a product of two smaller natural numbers
Given,
Here we need to find the prime number that is not in the set, if if the sum of a set of ten different positive prime numbers is an even number.
Here we know that, all prime numbers except the first prime number are odd except 2.
And here we assume that the two prime numbers are different,
So, if one of the prime number is 2 which is even, the other prime number would be odd and hence sum of the prime numbers would be odd as sum of an even and an odd number is always odd.
Where as if none of the prime numbers are odd, then both the prime numbers would be odd and hence sum of the prime numbers would be even as sum of two odd numbers is always even.
There the correct option is A. 2.
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Two mobile phone companies have different data rates. Company A has a rate of
$100 for unlimited data, and Company B has a flat fee of $20 plus $5 per gigabyte of data. The point of intersection between these two linear relations is (16, 100).
What does this point of intersection represent?
a) Both phone companies would charge $16 per gigabyte used with a bill of $100.
b) Both phone companies would charge $100 if the customer used 16 gigabytes of data.
c) Both companies would charge $100 with a flat fee of $16.
d) Both companies would charge $16 per gigabyte if the customer used 100 gigabytes.
Explanation:
x = number of gigabytes of data used
y = total price
Company A has the equation y = 100. The x variable is not involved since the cost is $100 no matter what.
Meanwhile, company B has the equation y = 5x+20
The slope of 5 indicates how much per gigabyte is charged. The 20 at the end is the flat fee, aka y intercept.
If we were to graph those equations, then we'd find they intersect at (16,100) as mentioned.
This means x = 16 and y = 100 pair up together.
It further tells us that both companies charge the same ($100) when x = 16 gigabytes of data are used.
This points us to choice B as the final answer.
What is the Fibonacci Sequence (aka Fibonacci Series)?
The Fibonacci sequence is 1, 1, 2, 3, 5,... , here each number of the sequence is the sum of the two preceding numbers in the sequence.
The Fibonacci sequence is the sequence that each number in the sequence is the sum of the preceding numbers
The first term = 1
The second term = 1
Third term will be the sum of the two preceding numbers
Third term = First term + second term
= 1 + 1
= 2
The fourth term = second term + third term
= 1 + 2
= 3
The fifth term = Fourth term + Third term
= 2 + 3
= 5
The sequence will be 1, 1, 2, 3, 5....
Therefore, the Fibonacci sequence is the sequence each number is the sum of the two preceding ones
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What is the absolute max on the closed interval [0,1]?
Check the picture below.
What are rational numbers but not natural numbers?; Which set of numbers are rational numbers but not integers whole numbers or natural numbers?; Does the set of rational numbers contain the set of natural numbers?; What is a rational number that is not a real number?
The distinction between them is that an integer is a negative number without a decimal point.
What is integers?All whole numbers and negative numbers are considered integers. This means if we include negative numbers together with whole numbers, we form a set of integers.
Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers. In this article, let's learn more about integers, their definition, and their characteristics.
According to our question-
The group of integers that are neither whole nor a natural number are:
As previously noted, the third set of integers lacks a decimal point;
However, the difference between them is that; a negative number without a decimal point is referred to as an integer
From the provided set: only fit into the description of an integer, because
It does not have a decimal point
And that is unfavorable.
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Shaina is 55 kg.what is Shaina's weight in grams?
Answer:
55000 grams
Step-by-step explanation:
1 kg = 1000 grams ==> kilo means 1000, so 1 kilogram = 1000 grams
Now multiply 55 kg with the grams-kilograms conversion factor to get the total number of grams Shaina weighs.
55 kg* 1000 grams / 1 kg =
55 * 1000 grams / 1 = ==> cancel out the kg
55 * 1000 = 55000 grams
Bones from the skeleton of a prehistoric creature have lost 65 percent of their carbon-14. Note that for carbon-14, the constant of proportionality is approximately k=0.000124. Estimate the age of the bones. Round to the nearest tenth of a year
The age of the bones from the skeleton of a prehistoric creature is 8460 years.
The formula to be used for the calculation of age is
ln (N/N₀) = -kt
where, N/N₀ represents represents remaining time
k is constant of proportionality
t is age or time period
The remaining time is 100 - 65 = 35
Remaining time = 35% or 0.35
Keeping the values in the above formula, we have
ln (0.35) = - 0.000124 t
-1.049 = -0.000124 t
t = 8459.67 ≈ 8460 years
Thus, the age of the prehistoric creature is 8460 years.
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Find the equation of the line through (−2,−5) which is perpendicular to the line y=x3+7.
The equation of the line perpendicular to the line y = 3x+7 is 3y = -x-17
What is slope?The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Given that, a line is perpendicular to line y = 3x+7 and passing through points (-2,-5)
The slope of perpendicular lines is negative reciprocal of each other.
Therefore, the slope of the asked line is -1/3
Finding c,
-5 = -1/3x(-2)+c
c = -17/3
Therefore, the equation of the line is y = -1/3x-17/3 or 3y = -x-17
Hence, The equation of the line perpendicular to the line y = 3x+7 is
3y = -x-17
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Do a full analysis (carrying out steps A-H in section 4.4 from the Stewart textbook) on the following functions in order to sketch them: (a) f(2)=et te (b) f(x) = tan-(+)
complete analysis (carrying out steps A-H in section 4.4 from the Stewart textbook)
results as The graph of f(2) = et te is a straight line with a y-intercept of 1.
A) f(2) = et te
Step A) Identify the domain and range of the function:
Domain: All real numbers
Range: All real numbers
Step B) Find any x-intercepts:
x-intercepts: None
Step C) Find any y-intercepts:
y-intercept: f(0) = e0te = 1
Step D) Find any vertical asymptotes:
Vertical asymptotes: None
Step E) Find any horizontal asymptotes:
Horizontal asymptote: None
Step F) Find any points of inflection:
Points of inflection: None
Step G) Find any symmetry:
Symmetry: None
Step H) Sketch the graph:
The graph of f(2) = et te is a straight line with a y-intercept of 1.
B) f(x) = tan-(+)
Step A) Identify the domain and range of the function:
Domain: All real numbers
Range: All real numbers except -π/2, π/
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An ice cream stand uses the expression 2 + 0.5x2+0.5x2, plus, 0, point, 5, x to determine the cost (in dollars) of an ice cream cone that has xxx scoops of ice cream.
How much does an ice cream cone with 555 scoops cost?
\$$dollar sign
Answer:
qwqe
Step-by-step explanation:wqeqwe
Harriett Weiss earned $77 in simple interest in 6 months at an annual interest rate of 7%. How much money did she invest? The answer is supposed to be $2200 but I don't know how to set up the equation and solve it. Please help.
The required invested money is given as $2200.
Harriett Weiss earned $77 in simple interest in 6 months at an annual interest rate of 7%.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
Here,
Applying the standard formula for the simple interest.
SI = principal × rate × time / 100
77 =[ p × 7 × 6/12 ]/ 100
p = 77 / 7 × 2 × 100
p = 11 × 200
p = 2200
Thus, the required investment amount is specified as $2200.
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The youth group is going on a trip to the state fair. The trip costs $63. Include in that price is $13 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation represents the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answer: 13 + 2x = 63 and the cost of one ticket is $25 (x=25)
Step-by-step explanation:
Build the equation from what it tells you.
The entire trip costs $63
The concert ticket that is included costs $13
Two passes cost the same amount, use x for what you don't know, 2x.
So, 13 + 2x = 63.
Find x = cost one pass.
13 + 2x = 63
-13. -13
2x= 50
2x/2= 50/2
x= 25
When practicing statistics in real life, it is not very important to check the necessary assumptions of a statistical procedure in order to effectively carry out and use the results. True False
The given statement is FALSE.
Given statement;
When practicing statistics in real life, it is not very important to check the necessary assumptions of a statistical procedure to effectively carry out and use the results.
The above-mentioned statement is FALSE.
→ We are aware that checking assumptions is crucial when applying statistics in daily life because failing to do so will prevent us from receiving fair answers to our statistical queries or drawing valid inferences. To use the good process and appropriate statistical distributions while utilizing statistics in daily life, it is crucial to examine assumptions.
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John, Sally and Jane form a partnership. They agree to distribute profits by paying Sally a $50,000 salary and distributing the balance using a 2:1:2 ratio respectively. Profits for the year are $70,000. John’s share of the profits is:
Multiple Choice
$4,000
$8,000
$14,000
$54,000
The required share of John in the profit is given as $8000. Option B is correct.
Given that,
John, Sally, and Jane form a partnership. They agree to distribute profits by paying Sally a $50,000 salary and distributing the balance using a 2:1:2 ratio respectively. Profits for the year are $70,000.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
here,
total profit = 70000
Sally is salary = 50000
remaining profit = 70000 - 50000 = $20000
Now,
total share as of the proportions is 2 + 1 + 2 = 5
Jhon proportion for the share of the profit = 2 / 5
Now,
John share = 2 / 5 [20000] = $8000
Thus, the required share of John in the profit is given as $8000. Option B is correct.
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3 (5+4)² - 4² =
OA. 227
OB. 15
OC. 46
OD. 345
Answer: 227
Step-by-step explanation: (5 + 4 ) = 9
= 3 x 9^2 - 4^2
9^2 = 81
= 3 x 81 - 4^2
4^2 = 16
= 3 x 81 - 16
3 x 81 = 243
= 243 - 16
243 - 16 = 227
= 227.
An exponential function in the form y = 5832(b)* contains the point (3, 1). What is the value of b?
The value of 'b' obtained for the given exponential function is 0.055.
Explain the term exponential function?A mathematical function with the formula f (x) = aˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.The stated exponential function is-
y = 5832(b)ˣ
This, function contains the point (3, 1).
Put the value in the r function;
1 = 5832(b)³
(b)³ = 1/5832
b = ∛1/5832
b = 0.055
Thus, the value of 'b' obtained for the given exponential function is 0.055.
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I need help as soon as possible
Find the distance from the point (5, 5, 2) to the line
x=0, y= 5+3t , z=2+t
The distance from the point to the parametric line is given as follows:
5 units.
How to obtain the distance between the point and the parametric line?The first step is obtaining the vector from the line L(0, 5 + 3t, 2 + t) to the point P(5,5,2), as follows:
P - L = (5, -3t, -t).
The direction vector of the line is given as follows:
(0, 3, 1).
The dot product of the vector with the direction of the line is of zero, hence:
(5, -3t, -t)(0, 3, 1) = 0
-9t - t = 0
-10t = 0
t = 0.
Thus the point on the line which we will use to obtain the distance is of:
(0, 5 + 3(0), 2 + 0) = (0,5,2).
The the distance is obtained applying the formula for the distance between two points as follows:
Distance = square root [(5 - 0)² + (5 - 5)² + (2-2)²] = 5 units.
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A fibonacci sequence begins 0,1,1,2,3,5
a) what is the 8th number in the sequence
b) what is the 11th number in the sequence
In the given Fibonacci sequence , 8th number is 13 mad 11th number is 55 .
What is a Fibonacci Sequence?
The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
The next number is found by adding up the two numbers before it:
the 2 is found by adding the two numbers before it (1+1),the 3 is found by adding the two numbers before it (1+2),the 5 is (2+3),and so on!In a Fibonacci sequence, the number is equal to the sum of the two preceding numbers.
so the seventh number is 3+5 = 8
8th number is 5+ 8 = 13
11th number is 21+34 = 55
now the sequence becomes 0,1,1,2,3,5,8,13,21,34,55
Hence , the 8th number is 13 mad 11th number is 55.
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What is the complete factorization of the polynomial below?
x³ + 3x2 +9x+27
OA. (x+3)(x+3)(x+3/)
B. (x+3)(x+3)(x-3/)
O C. (x-3)(x+3)(x+3/)
O D. (x-3)(x+3)(x-3i)
Answer:
(x - 3 i) (x + 3 i) (x + 3)
Step-by-step explanation:
which is the graph of fx x2 2x 3
In the picture we can see the graph represents of the function f(x)=x²-2x+3 that is curve graph.
Given that,
We have to find the graph represents the function f(x)=x²-2x+3.
We know that,
The quadratic function is f(x)=x²-2x+3.
This is a vertical parabola open downward
The vertex is a maximum
We know,
A vertical parabola's equation in vertex form is equal to
y= a(x-h)²+k
where
a is a coefficient
(h,k) is the vertex
Here
a=1
(h,k)=(0,3) is vertex
The y-intercept is the point (0,3) is value of y when the value of x is equal to zero (is the same point that the vertex)
The x-intercepts are the points is values of x when the value of y is equal to zero
Therefore, In the picture we can see the graph represents of the function f(x)=x²-2x+3.
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which of these steps will eliminate a variable in this system 6x - 3y = 8
23 + 6y = 16
The values of x and y after solving this system of equations will be 32/35 and -88/105 respectively.
What are system of equations?System of equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations.
What is the method of elimination?For a set of two equations, in elimination we make the coefficient of any one variable equal to the coefficient of the same variable in the other equation. This can be done by multiplying or dividing the whole equation accordingly. Then we subtract the equations from each other and solve for one variable.
6x - 3y = 8 (multiplying this equation by -2 to make the coefficient of y equal to that of in the equation 23x + 6y = 16)
Now are equations are
-12x + 6y = -16 and 23x + 6y = 16
subtracting eq 1 from eq 2 gives,
35x = 32 (Note that y has now been eliminated)
x = 32/35
Substituting this value of x in any one of the equations will then give the value of y to be -88/105
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Compare the square root of 18 and twenty three fifths using >, <, or =. twenty three fifths is less than the square root of 18 twenty three fifths is equal to the square root of 18 the square root of 18 is greater than twenty three fifths the square root of 18 is less than twenty three fifths
Comparing the square root of 18 and twenty three fifths using an inequality is ✓18 < 23/5.
How to illustrate the inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
The square root of 18 will be 4.25
23/5 will be 4.6
Therefore, we can see that 4.6 is greater than 4.25.
In this case, ✓18 is less than 23/5.
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Given the recursive formula below, what are the first four terms of the sequence?
Please Help as soon as possible
The first four terms of the sequence given the sequence definition are 17, 15, 13 and 11
How to determine the first four terms of the sequence?From the question, we have the definition of the function that can be used in our computation:
f(n) such that
f(1) = 17
f(n) = f(n - 1) - 2 if n > 1
The above definitions imply that we simply subtract 2 from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
f(2) = 17 - 2
f(2) = 15
Also, we have
f(3) = 15 - 2
f(3) = 13
Lastly, we have
f(4) = 13 - 2
f(4) = 11
Hence, the the first four terms are 17, 15, 13 and 11
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A company manufactures two products, A and B, and each of these products must be processed on two different machines. Product A requires 2 min of work time per unit on machine 1 and 4 min of work time per unit on machine 2. Product B requires 3 min of work time per unit on machine 1 and 1 min of work time per unit on machine 2. Each day 200 min are available on machine 1 and 300 min are available on machine2. To satisfy certain customers, the company must produce at least 8 units per day of product A and at least 10 units per day of product B. If the profit of each unit of product A is Php50 and the profit of each unit of product B is Php60, how many units of each product should be produced daily in order to maximize the company's profits?
The maximum profit is maximized 70 of product A and 20 of product B are produced.
How to calculate the units that maximize the profit?The objective function:
The profit is 50 for each product A and 60 for each product B:
P = 50A + 60B
The machine 1 constraint:
2 minutes for each product A and 3 minutes for each product B; 200 total minutes available:
2A+3B ≤ 200
The machine 2 constraint:
4 minutes for each product A and 1 minute for each product B; 300 total minutes available:
4A+B ≤ 300
The production constraints:
At least 8 of product A and at least 10 of product B:
A ≥ 8
B ≥ 10
2A+3B=200
4A+B=300
4A+6B=400
5B=100
Divide
B = 100 / 5
B=20
Also, A=70
The units are 70 and 20 respectively.
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Draw a quick picture to find the product of 3×800
Answer:
daymn
it's gonna be okay
