If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
What is congruent triangle?The SSS congruence theorem tells us that the triangles are congruent because there are three pairs of congruent sides. The corresponding triangle sides are also in proportion, so they are similar according to the SSS similarity theorem.The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.The measurement of side DF is 4cm.If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.Here in the figure attached below,
Given two triangles ΔABC and ΔDEF
Also given that,
ΔABC and ΔDEF are congruent to each other.
Given AC = 4cm
Since both triangles are congruent ,
Side AC is congruent to DF
Therefore DF = 4cm (based on SSS theorem).
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Is 3/8 the same as 1 1/2 of a 4th
(Please give an explanation)
Answer: Yes.
Step-by-step explanation: 3/8 and 1 1/2 of a fourth are equivalent amounts. To see why, you can use a common denominator to compare the two fractions. If we convert both fractions to eighths, then 3/8 becomes 3/8 and 1 1/2 of a fourth becomes 6/8. Since 3/8 and 6/8 are both equal to 3/4, it follows that 3/8 and 1 1/2 of a fourth are also equal.
Use power series operations to find the Taylor series at x = 0 for the following function. xsin(Злх/2). The Taylor series for sin x is a commonly known series. What is the Taylor series at x = 0 for sin x? Use power series operations and the Taylor series at x = 0 for sin x to find the Taylor series at x = 0 for the given function.
The taylor series as per the power series operation is sin(x) = 0 + 1x + 0x + −1/3!+3 + 0x
given,
f(x) = sinx
c = 3pi/4
the required series will be .
f(x) = f(c) + f' (c)( x-c ) + f''(c)/2! + .... f x n(c)/n! (x-c)^n
f(c) = sin(c)
= sin(3pi/4)
= 1/2
on solving the equation becomes,
sin(x) = 0 + 1x + 0x + −1/3!+3 + 0x
Assume that f(x) is a real or composite function and that it is a differentiable function of a real or composite neighbourhood number. The following power series is then described by the Taylor series.
The Taylor series can be expressed using sigma notation, where f(n)(a) = nth derivative of f n! = factorial of n.
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7x - y = 6
-7x + y = -6
Answer:
X= 6+y/7
Step-by-step explanation:
Which fraction is equivalent to a whole number?
Select all that apply.
Answer:
The answers are A B and C
they could be whole numbers
Step-by-step explanation:
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Micha is getting a fountain drink. He can pick from four cup sizes, eight different drink flavors and two different straw colors. How many drink outcomes are possible?
Micha can choose her drink is 64 different ways.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, She can pick from four cup sizes, eight different drink flavors, and two different straw colors.
∴ The no. of ways in which she can choose from is [tex]^4C_1 \times ^8C_1 \times ^2C_1[/tex] ways.
= 4!/(4-1)!1! + 8!/(8-1)!1! + 2!/(2-1)!1!.
= 4!/3! × 8!/7! × 2!/1!.
= 4 × 8 × 2.
= 64 ways.
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Solve x 2 =-6x-5 by completing the square
[tex]\fbox{x=$\dfrac{-7}{6}$ }[/tex]
Flip the equation:
[tex]-6x-5=2[/tex]
Add 5 to both sides:
[tex]-6x-5+5=2+5[/tex]
[tex]-6x=7[/tex]
Divide both sides by -6:
[tex]\dfrac{-6x}{-6} =\dfrac{7}{-6}[/tex]
[tex]x=\dfrac{7}{-6}[/tex]
Rewrite the fraction in the sentence below as a percentage. The 20 overseas investors own 1/10 of the business
The value of the equation A = 1/10 is 10 %
So , the 20 overseas investors owns 10 % of the business
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the percentage of business owned by the overseas investors be = A
Now , the equation will be
The number of overseas investors = 20
The fraction of business the overseas investors own = 1/10
Now , the percentage is always expressed in terms of 100
So ,
The percentage of business owned by the overseas investors = fraction of business the overseas investors own x 100
Substituting the values in the equation , we get
Percentage of business owned by the overseas investors = ( 1/10 ) x 100
Percentage of business owned by the overseas investors = 10 %
Therefore , the value of A is 10 %
Hence , the 20 overseas investors owns 10 % of the business
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Like has blue and red balls.
Every day he win 2 blue balls and lose 3 red.. after 5 days he won the same amount of blue balls as red. After 9 days he had twice as many blue balls as red. How many red balls he have at the beginning
Like has 47 red balls in the beginning.
What is probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The likelihood of choosing a blue and then a red ball at random when two balls are pulled is 5/18.
since, he loses everyday 3 red balls; after 1 day (y-3) red balls
Case1:
x + 10 = y -15
x - y = -25 equation 1
Case2:
(x + 18) = 2(y - 27)
x + 18 = 2y - 54
x - 2y = -54 - 18
x - 2y = -72 equation 2
Now subtract both eq1 and eq2
x - y = -25
x - 2y = -72
y = 47
Like has 47 red balls in the beginning.
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Mariam runs 7.5 miles in one hour How much distance will she cover in 3 hours
please help due now please very easy
Dontrell bought 5 1/2 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.
____________________
Answer: y= 0.64x
Step-by-step explanation:
Take 3.52 divided by 5.5 = $0.64 per pound of potato
y is the total cost, x is the number of pound
y= 0.64x
State all integer values of a in the interval -2 ≤ x ≤ 4 that satisfy the following
inequality:
-5x+5 ≥7
Explanation
Solve for x:
[tex]-5\text{x}+5 \ge 7\\\\-5\text{x} \ge 7-5\\\\-5\text{x} \ge 2\\\\\text{x} \le 2/(-5)\\\\\text{x} \le -0.4\\\\[/tex]
Note the inequality sign flips when we divide both sides by a negative number.
If x is an integer, then the largest x can be is x = -1, which means x can be any of these values: {..., -4, -3, -2, -1} where the three dots means the pattern continues on to the left forever. If it might help, then you can think of it like this: {-1, -2, -3, -4, ...} but it's of course not the standard way to sort negative numbers.
Now we're told that -2 ≤ x ≤ 4 which when combined with the set above, gets us the answer {-2, -1}
If we replaced x with -2, then,
-5x+5 ≥7
-5(-2)+5 ≥7
10+5 ≥7
15 ≥7
which is true and confirms x = -2 works. I'll let you try out x = -1.
9 less than the quotient of 2 and x.
the answer is 2/x-9
Answer:
[tex] \dfrac{2}{x} - 9[/tex]
Step-by-step explanation:
the quotient of 2 and x:
[tex] \dfrac{2}{x} [/tex]
9 less than the quotient of 2 and x:
[tex] \dfrac{2}{x} - 9[/tex]
COLLEGE PREP Which point lies on the perpendicular bisector of the segment with endpoints M(7,5) and N(-1,5) ?
(2,0)
(3,9)
(4,1)
(1,3)
The point on the perpendicular bisector of the segment MN, M(7, 5), N(-1, 5), is (3, 9)
What is the perpendicular bisector of a line?The perpendicular bisector of a segment, divides the segment into two segments that have the same length, and which forms an angle of 90° with the line.
The specified endpoints on the segment MN = M(7, 5), and N(-1, 5)
The y-coordinates of the points M and N are the same, therefore, the segment is an horizontal segment.
The midpoint of the line is therefore;
(7 + (-1 - 7)/2, 5 + (5 - 5)/2) = (3, 5)
The slope of the segment, MN, m = (5 - 5)/(-1 - 7) = 0
The slope of the perpendicular line is therefore;
-1/0 = ∞
The segment MN is parallel to the x-axis, therefore, the perpendicular bisector is parallel to the y-axis, and the x-values of points on the perpendicular bisector have the save value s the x-value of the midpoint of the segment MN, (3, 5), which is x = 3
The point that lies on the perpendicular bisector of the segment MN from the options is therefore; (3, 9)
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Classify the following triangle. Check all that apply.
A. Equilateral
. B. Obtuse
. C. Scalene
D. Right
N E. Acute
F. Isosceles
The given triangle is Equilateral triangle.
What is triangle ?Triangle is a two dimensional shape having three side and sum of all angles is equals to 360 degree .
A right angled triangle is a triangle having one of its angle with measure of 90° The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.
We have, triangle with an angle equal to each other and three equal sides.
So, We know that,
When a triangle have angle equals to each other then it is Equilateral triangle.
Now, When a triangle have equal sides then it is Equilateral triangle.
So,
From the above mentioned statements we can say that triangle is Equilateral triangle.
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help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 50 miles far the eye.
What is Barometric Air Pressure?The measurement of air pressure in a certain location is called barometric pressure, which is the force of air pressing down on the surface of the globe, the oceans, and the land. .
p(x) =0.48ln (x + 1) + 27
Lets take P(50)
P(50)= barometric pressure at 50 miles from the eye of the hurricane P(50) as x
P(50) = 0.48 ln (50 + 1) + 27
P(50) = 0.48 ln (51) + 27
P(50) = 0.48 x 3.9318 + 27
where,
ln(51) = 3.9318
P(50) = 28.89
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Jordan got a loan from her mom for school at $11,000 at 4% interest, compounded monthly. If she pays off $200 per month, how long will it take to pay off the loan? ________ months, or about _______ years. ?
Answer:
61 months, about 5.07 years
Step-by-step explanation:
You want the time it takes to pay off a loan of $11,000 at 4% compounded monthly when the payment is $200 per month.
Number of paymentsThe number of payments required can be found by solving the amortization formula, or using any spreadsheet, financial calculator, or suitable app.
The attachment shows the number of months required is about 60.9.
It will take 61 months, or about 5.07 years to pay off the loan.
__
Additional comment
The formula for the number of monthly payments on a loan amount of P at interest rate r with monthly payments of A is ...
[tex]N = -\dfrac{\log{\left(1-\dfrac{Pr}{12A}\right)}}{\log{\left(1+\dfrac{\vphantom{R}r}{12}\right)}}[/tex]
You wish to test the following claim H^Ц at a significance level of а=0.10. For the context of this problem. Ц₄=Ц₂-Ц₁ where the first data set represents a pre-test and the second data set represents a post-test.
Hₐ² Ц =0
Ha² Ц ≠0
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-4est simples for n=25 subjects. The average difference (post - pre) is d=-34.3 with a standard deviation of the differences of sd=42.9.
What is the critical value for this test? (Report answer accurate to three decimal places.) critical value . ± ____
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
fest statistic = ____
We have a two-tailed test, as we are testing if the mean is different of a value.
The t-distribution is used, as we have the standard deviation for the sample, and the parameters are given as follows:
25 - 1 = 24 degrees of freedom.Significance level of 0.10.Using a t-distribution calculator, the critical value is of:
t = ± 1.7109.
How to obtain the test statistic?The equation for the test statistic is defined as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are of:
[tex]\overline{x} = -34.3, \mu = 0, s = 42.9, n = 25[/tex]
Hence the value of the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{-34.3 - 0}{\frac{42.9}{\sqrt{25}}}[/tex]
t = -4.
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Select each equation which is equivalent to 60% of 25.
0.6 • 25 = x
x • 1.6 = 25
610=x25
60100=25x
x25=60100
6.0 • 25 = x
The equation which is equivalent to 60% of 25 is x = 0.6 * 25
What is a linear equation with an example?
Ax+By=C represents a two-variable linear equation in its standard form.
A standard form linear equation is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).
A linear equation with one variable has the conventional form Ax + B = 0. x is a variable, A is a coefficient, and B is constant in this situation.
An equation is used to show the relationship between variables, and numbers.
Let x represent the value of 60% of 25. Hence:
x = 60% of 25
x = 0.6 * 25
Hence, the equation which is equivalent to 60% of 25 is x = 0.6 * 25
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parallelogram ABCD with DE=3y+7 and DB=10y-6
Hence, the diagonals of parallelogram is not perpendicular to each other. They are equal in length and they bisect each other but diagonals are not perpendicular so it would be rectangle.
What is the parallelogram?
A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.
Here given that,
[tex]DE=3y+7 \\DB=10y-6[/tex]
As we know the slope of a line is
[tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope.
So,
[tex]DE=3y+7\\\\m_1=3\\\\\\DB=10y-6\\\\m_2=10[/tex]
Then,
[tex](m_1)(m_2)=(3)(10)\\\\(m_1)(m_2)\neq 30[/tex]
Draw the graph of given equations
Hence, the diagonals of parallelogram is not perpendicular to each other. They are equal in length and they bisect each other but diagonals are not perpendicular so it would be rectangle.
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shift the market price facing a competitive firm to a level where the firm makes an economic profit in the short run.
The price should be higher than the AVC and ATC in order to make a profit in the short term. Therefore, in order to achieve the requisite profit, the MR curve must rise above cost = 7.
When businesses in a cutthroat sector start making money, it opens the door for more businesses to enter the market, which leads to a shift to the right in the supply curve, a drop in price, and the return of all businesses to a state of no economic profit.
If the market price is lower than the average total cost, a company will experience positive economic profit in the short term.
In the short run, a monopolistically competitive firm optimises profits or avoids losses by producing the amount where marginal revenue equals marginal cost. If the average total cost is less than the market price, the company will make a profit.
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Every day after school, Patrick and his sister Nicole play their favorite video game, Wizarding Legends. The goal of the game is to earn power points by defeating goblins. There is a proportional relationship between the number of goblins defeated, x, and the number of power points earned, y.
The constant of proportionality is 5.
What is the constant of proportionality?
When two variables move in the same direction, this is known as direct variation. The other variable also rises when one rises. The points rise along with the number of goblins defeated. This is an exact alteration.
The equation used to represent direct variation is: y = kx
Where k is the constant of proportionality
5 = k
Please find attached the complete question.
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poly has 7 different books. She is going to arrange 3 of them on the shelf above her desk. In how many different ways can she arrange three books?
A sample of 200 g of an isotope decays to another isotope according to the function
How much money does Dana Jones have after 7 years if she invests $ 1100 at 5% interest compounded continuously?
Dana Jones has $__-after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
By using the concept of growth and depreciation, it can be calculated that
1a) Amount of sample left after 15 years = 123.76 g
b) Time taken by the substance to reduce to half is 21.66 years
2) Amount is $1560.97
3) It took 11.94 years for $900 to get doubled
What is growth and depreciation?
Growth is the increase in the value of an asset or cost or population at a certain rate over a certain period of time
Depreciation is the decrease in the value of an asset or cost or population at a certain rate over a certain period of time
1) Original weight of the isotope = 200g
Function = [tex]200e^{-0.032t}[/tex]
a) Time = 15 years
Amount of sample left after 15 years = [tex]200e^{-0.032 \times 15}[/tex] = 123.76 g
b) Amount left = 100g
100 = [tex]200e^{-0.032t}[/tex]
[tex]e^{-0.032t} = \frac{100}{200}[/tex]
[tex]e^{-0.032t} = \frac{1}{2}[/tex]
[tex]-0.032t = ln(\frac{1}{2})\\-0.032t = -0.693\\t = \frac{0.693}{0.032}\\[/tex]
t = 21.66 years
2) Principal = $1100
Rate = 5%
Time = 7 years
Amount = [tex]1100e^{\frac{5}{100} \times 7}\\[/tex]
= [tex]1100e^{0.35}[/tex]
= $1560.97
3) Principal = $900
Amount = $900 [tex]\times[/tex] 2 = $1800
1800 = [tex]900(1 + \frac{6}{1200})^{12n}[/tex]
[tex]\frac{1800}{900} = (\frac{201}{200})^{12n}[/tex]
[tex](\frac{201}{200})^{12n} = 2[/tex]
[tex]12n \times log(1.005) = log 2\\12n \times 0.0021 = 0.3010\\n = \frac{0.3010}{12 \times 0.0021}\\[/tex]
n = 11.94 years
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What are the coordinates of the image of vertex R after
a reflection across the y-axis?
(-4, 3)
(4, -3)
(-3, -4)
(3, 4)
Answer:
(3, 4 )
Step-by-step explanation:
under a reflection in the y-axis
a point (x, y ) → (- x, y ) , then
R (- 3, 4 ) → R' (3, 4 )
Find the requested measurement. Use 3.14 and round your answer to the nearest hundredth
Answer:
C) 20.72 (Question 1: Solve for Circumference)
Step-by-step explanation:
Question 1:
Using the formula:
[tex]C=2\pi r[/tex]
- C = circumference- π = the constant pi- r = radius of the circleGiven radius:⇒ r = 3.3
[tex]C=2\pi r[/tex]
[tex]2\times\pi\times3.3[/tex]
≈ [tex]20.73451[/tex]
Rounding, 20.72.
Thanks.
T/F?
Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference.
Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference. The given statement is False.
An array is a collection of items of same data type stored at contiguous memory locations. This makes it easier to calculate the position of each element by simply adding an offset to a base value, i.e., the memory location of the first element of the array.
In Pass by value, function is called by directly passing the value of the variable as an argument. So any changes made inside the function does not affect the original value.
In Pass by Reference, Function is called by directly passing the reference/address of the variable as an argument. So changing the value inside the function also change the original value. In JavaScript array and Object follows pass by reference property. Parameters passed as an arguments does not create its own copy, it refers to the original value so changes made inside function affect the original value.
Thus, the statement that Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference is False.
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(x - 4)^2 + 4 = 49
looking for the answer
Answer:
B
Step-by-step explanation:
Given the picture on the right, what could be the possible value of a?
Answer: 20.98
Step-by-step explanation: Pythagorean theorem to find a is the square root of c^2 - b^2 C is 27 and b is 17 so square root of 27^2 17^2 is 20.98
A person invested $8, 400 in an account growing at a rate allowing the money to double every 11 years. How much money would be in the account after 12 years, to the nearest dollar?
Answer: $16,800
Step-by-step explanation:
Given that f (x) = 2x + 1 and g(x) = 6 - x, find the following. If necessary, use a 0 in the denominator!
a. ( f + g) (2) = ____________
b. ( f - g) (-5) = ___________
c. ( g - f) (4) = ____________
d. ( f ⋅ g) ( 1/2) = ___________
e. ( f/g) (-1) = _____________
The results of operations between the two functions f(x) = 2 · x + 1 and g(x) = 6 - x are listed below:
(f + g)(2) = 9 (f - g)(- 5) = - 20 (g - f)(4) = - 7 (f · g)(1 / 2) = 11 (f / g)(- 1) = - 1 / 7How to derive and evaluate a composite function
In this problem we have the definitions of two functions, linear equations on both cases. The procedure consists in using the definitions of operations between two functions and evaluate the resulting expression at a given value of x:
Addition
(f + g)(x) = f(x) + g(x)
Subtraction
(f - g)(x) = f(x) - g(x)
Multiplication
(f · g)(x) = f(x) · g(x)
Division
(f / g)(x) = f(x) / g(x)
Now we proceed to derive each expression and evaluate the resulting expression:
(f + g)(x) = (2 · x + 1) + (6 - x)
(f + g)(x) = x + 7
(f + g)(2) = 2 + 7
(f + g)(2) = 9
(f - g)(x) = (2 · x + 1) - (6 - x)
(f - g)(x) = 3 · x - 5
(f - g)(- 5) = 3 · (- 5) - 5
(f - g)(- 5) = - 20
(g - f)(x) = (6 - x) - (2 · x + 1)
(g - f)(x) = - 3 · x + 5
(g - f)(4) = - 3 · 4 + 5
(g - f)(4) = - 7
(f · g) (x) = (2 · x + 1) · (6 - x)
(f · g) (x) = 2 · x · (6 - x) + 6 - x
(f · g) (x) = 12 · x - 2 · x² + 6 - x
(f · g) (x) = - 2 · x² + 11 · x + 6
(f · g)(1 / 2) = - 2 · (1 / 2)² + 11 · (1 / 2) + 6
(f · g)(1 / 2) = 11
(f / g) (x) = (2 · x + 1) / (6 - x)
(f / g)(- 1) = [2 · (- 1) + 1] / [6 - (- 1)]
(f / g)(- 1) = - 1 / 7
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