The diagonals of a square are equal to each other
Let ABCD be a square.
We need to prove that the diagonals are equal to each other
AC=BD and AC and BD bisect each other at right angles
(i) Considering the ΔABC and ΔBAD,
AB=AB ( common line)
BC=AD ( opppsite sides of a square)
∠ABC=∠BAD ( = 90° )
ΔABC≅ΔBAD( By SideAngleSide property)
AC=BD ( by CPCT).
(ii) Now in triangles ΔOAD and ΔOCB,
AD=CB ( opposite sides of a square)
∠OAD=∠OCB ( transversal AC )
∠ODA=∠OBC ( transversal BD )
ΔOAD≅ΔOCB (ASA property)
OA=OC ---------(i)
Similarly OB=OD ----------(ii)
From (i) and (ii) we can conclude that AC and BD bisect each other.
Now in a ΔOBA and ΔODA,
OB=OD ( from (ii) )
BA=DA
OA=OA ( common line )
ΔAOB=ΔAOD----(iii) ( by CPCT
∠AOB+∠AOD=180° (linear pair)
2∠AOB=180°
∠AOB=∠AOD=90°
Therefore, it is proved that AC and BD bisect each other at right angles.
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Write an equation for the nth term of the arithmetic sequence 4, 7, 10, 13,
The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1
How to find nth term of arithmetic sequence?Arithmetic sequence can be represented with the formula as follows:
aₙ = a + (n - 1)d
where
n = number of termsd = common differencea = first termTherefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..
a = 4
d = 7 - 4 = 3
Therefore,
aₙ = 4 + (n - 1)3
aₙ = 4 + 3n - 3
aₙ = 3n + 4 - 3
aₙ = 3n + 1
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how many license plate combinations are there with either three letters then three numbers or three numbers then three letters
The license plate combinations with either three letters then three numbers or three numbers then three letters are 35152000.
The license plate combinations to be made are either three number followed by three letter or three letter followed by three number. we are here assuming that the repetition of the number and letter are allowed.
The number can be any three from 0-9. So, the total choices of number are 10.
The letter can be from A-Z. So, the total choices for letter are 26.
The total choices of the numbers possible are,
ΟΟΟ ΟΟΟ
1 2 3 4 5 6
The first three are the choices of letter and the last three are the choice of number. Two combinations are also possible by interchanging the position of the set of numbers and letters.
So, the possible combinations are,
2 x [26x26x26x10x10x10]
Hence,
The possible combinations for the license plate number are 35152000.
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Whats the answer to question 10?
Answer:
[tex]y = |x - 3|+ 5[/tex]
y = |x| is the equation that forms the triangular shape. -3 and 5 reflect the shape to that position.
There is a number written on the board.
One student increased the number by 12.
Another student multiplied the number written
on the board by 3. The first student’s result is 2
greater than the second student's result. What
number is written on the board?
The number written on the board is 2 2/5
What are linear equations?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0. where, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. where, x and y are variables, A and B are coefficients and C is a constant.
represent the number on the board by x, the result of the second student by y , therefore the result of the first student is 2y
solving for the first student, 12+x= 2y
for the second student , 3x= y
substituting 3x for y in first equation
12+ x= 2(3x)
12+x= 6x
collecting like terms
5x= 12
divide both side by5
x= 12/5= 2 2/5.
Therefore the number on the board is 2 2/5
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calculate a 95% confidence interval for the effect of a one unit increase in exercise on resting heart rate for a non-smoker
A level of confidence of 95% was used in the case above. A table at the back of a statistics textbook can be used to get the value of z* for a certain confidence level. For a 95% confidence level, the value of z* is 1.96.
An error margin of 3.92 is discovered when the value of z*, the demographic standard error, and the sample size are entered into the equation.
Statistical Estimation's Justification
Where does the confidence interval calculation formula come from?
The population mean's true value is never known; it can only ever be estimated or approximated. The easiest way of doing this is to choose many identical-sized random samples from the population.
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a hamburger regularly cost $6.00 each additional topping cost $0.59. on Monday the cost of hamburger only is half off
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A burger consistently cost $6.00 each extra fixing cost $0.59.
Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,
c = 0.59t + 6
On Monday the expense of the burger just is half off. Then the equation is given as,
c = 0.50(0.59t + 6)
c = 0.295t + 3
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
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Solve the inequality 4x-7<5
Answer:
x<3
Step-by-step explanation:
4x<5+7
4x < 12
4/4 x < 12/4
x < 3
astudy showed that 33% of allfirms in couniry a are owned by women. you are phoning local businesses, assuming that the national percentage is true in your area. you call 3 fims. what is the probability that all three are owned by women?
There is a 0.33 percent chance that a woman is the owner of each of the firms identified. Therefore, there is a 0.036 percent chance that women own ALL three of the called businesses.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The probability that each of the firms called is owned by a woman is 0.33. Therefore, the probability that ALL three of the firms called are owned by women is:
percentage=0.33*0.33*0.33
percentage=0.035937
=0.036
There is a 0.33 percent chance that each of the businesses is run by a woman. As a result, there is a 0.036 percent chance that women own ALL three of the businesses mentioned.
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Capital social 2.000.000 banco caixa 20.000 imovel 1.000.000 50% a vista 50% a prazo moveis 90.000 a vista transferencia bancaria veiculo 150.000 a prazo mercadoria a prazo 200.000
Solve the inequality statement:
-5ω < 15
---
w >3
wς 3
w< -10
The simplified form of the given inequality is w > -3.
What is inequality?
When two values are compared, an inequality reveals whether one is bigger than, less than, or simply not equal to the other. The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to one another. The occurrence of an unfair distribution of opportunities and resources among individuals of a certain society is referred to as inequality. To different people and in various contexts, the term "inequality" may mean different things.
Here the given inequality is ,
=> -5w<15
=> -5 *w < 15
=> w>15/-5
=> w > -3.
Hence the correct simplified form of the inequality is w >-3.
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One leg of a right triangle is 8 units long, and its hypotenuse is 14 units long. What is the length of the other leg? Round to the nearest whole number.
The other leg has its length to be 11.49 units
How to determine the length of the other leg distance?To calculate the length of the other leg distance, we make use of the Pythagoras theorem
Mathematically, this theorem is represented by:
w² = y² + z²
Such that x = hypotenuse, y = leg and z = other leg
From the question, we have the following parameters
w = 14, y = 8 and z = the other leg
Substituting these values in w² = y² + z²
14² = 8² + y²
Evaluate the exponents
196 = 64 + y²
Evaluate the like terms
y² = 132
Take the square roots of both sides
y = 11.49
Hence, the length of the other leg is 11.49 units
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Answer: 11 units
Step-by-step explanation: i took the test and got it right
Hello, I am finding inverse functions and ran into this fraction. How would I simplify from here to find Y by itself?
The inverse function for the function f(x) = (1 -2x) / 3x is 1/3x+2.
Inverse function:
Inverse function means a function that serves to “undo” another function.
For example,
if f(x) produces y, then putting y into the inverse of f produces the output x.
Given,
Here we have the function f(x) = (1 -2x) / 3x.
Now, we need to find the inverse function f⁻¹.
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables by interchange the value of x by y and the value of y as x.
Then we get,
x = (1 - 2y)/3y
Now, solve the equation
x = (1 - 2y)/2y
for y, then we get,
y = 1/(3x + 2)
Therefore, the inverse function is 1/3x+2.
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Calculus Math Minimum and maximum
Answer:
[tex]y_{min}=-17[/tex]
[tex]y_{max}=15[/tex]
Step-by-step explanation:
Given function:
[tex]y=2x^2-12x+1[/tex]
The critical points are those values of x which make the derivative of the function zero.
Differentiate the function:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2 \cdot 2x^{2-1}-12x^{1-0}+0[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=4x-12[/tex]
Set the derivative to zero and solve for x:
[tex]\implies 4x-12=0[/tex]
[tex]\implies 4x=12[/tex]
[tex]\implies x=3[/tex]
To find the y-value of the critical point, substitute the found value of x into the function:
[tex]\implies 2(3)^2-12(3)+1[/tex]
[tex]\implies 2(9)-12(3)+1[/tex]
[tex]\implies 18-36+1[/tex]
[tex]\implies -18+1[/tex]
[tex]\implies -17[/tex]
Therefore, the critical point is (3, -17).
To find the endpoints of the function in the interval [0, 7], substitute x = 0 and x = 7 into the function:
[tex]\begin{aligned} x=0 \implies 2(0)^2-12(0)+1&=0-0+1\\&=1\end{aligned}[/tex]
[tex]\begin{aligned} x=7 \implies 2(7)^2-12(7)+1&=2(49)-12(7)+1\\&=98-84+1\\&=14+1\\&=15\end{aligned}[/tex]
Therefore:
Critical point: (3, -17)Endpoints: (0, 1) and (7, 15)Therefore the minimum y-value is -17 and the maximum y-value is 15 in the given interval [0, 7]
The minimum and maximum y value of the function is -17 and 15 respectively.
This is a basic problem in calculus.
Given function: [tex]y=2x^{2} -12x+1[/tex]
Step 1: First, let's find the derivative of the function
[tex]\frac{dy}{dx} = 2.2x^{2-1} -12x^{1-0} +0\\\frac{dy}{dx} = 4x-12[/tex]
Step 2: Equate the derivative with zero
4x-12=0
x=3
Therefore, x=3 is the critical value for x
Step 3: Find the critical value for y
[tex]y=2x^{2} -12x+1[/tex]
[tex]y=2\times3^{2} -12\times3+1\\y=-17[/tex]
Thus, the critical points for the function [tex]y=2x^{2} -12x+1[/tex] are (3,-17)
Step 4: Find endpoints using the given interval [0,7]
This can be done by substituting x1=0 and x2=7 simultaneously in the given function and finding y1 and y2.
For x1=0,
[tex]y1=2\times0^{2} -12\times0+1\\y1=0+0+1\\y1=1[/tex]
For x2=7,
[tex]y2=2\times7^{2} -12\times7+1\\y2=98-84+1\\y2=15[/tex]
Now, we have both critical points and endpoints.
Therefore, The minimum and maximum y value of the function is -17 and 15 respectively.
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if the 90% confidence limits for the population mean are 45 and 55, which of the following could be the 99% confidence limits a) [48, 55] b) [49, 53] c) [42, 58] d) [46, 51] e) [49, 51] f) none of the above
The 99% confidence limit will be option B which is (45, 55)
90% confidence limits for the population mean are (46,54)
mean = 46+54 / 2 = 50.
the margin of error E = 54-46/2 = 4
For 90% Confidence Z- Critical value is = 1.645
But the margin of error
E = ZS/√n
4=(1.645)S/√n
S/√n = 4 / 1.645
= 2.4316
For 95% confidence Z-critical value is 1.96
A 95% confidence interval is = mean ± E
(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316
= 50+ 4.7660
= 45.2340, 54.7660
= (45, 55)
Hence the correct option is B which is (45, 55) as the 99% confidence limit.
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what is 5 divided by 1 over 3
Answer: 15 !
Step-by-step explanation:
Change the division sign to a multiplication sign and reverse the fraction.
5 x 3/1 = 15
Which expression is equivalent to 5(4x+3)-2x
How is the work shown?
Answer:
Step-by-step explanation:
18x+15. Step-by-step explanation: 5(4x+3)-2x. Distribute the 5. 20x +15 - 2x. Combine like terms. 20x-2x +15.
TWO FRIENDS EARNED MORE THAN
$400 SELLING T-SHIRTS. THEY
PAID THEIR PARENTS $55 FOR
SUPPLIES AND DIVIDED THE REST
OF THE MONEY EQUALLY. WRITE AN
INEQUALITY TO FIND POSSIBLE
AMOUNTS EACH FRIEND EARNED.
Determine which set of side measurements could be used to form a right triangle.
square root of 19 comma square root of 35 comma 54
square root of 15 comma 6 comma square root of 51
5, 8, 30
5, 6, 7
Answer:
Square root 19 comma, 5,8,30
Answer:5,8,30
Step-by-step explanation: i took a test
PLEASEE HELPPP GIVING ALL MY POINTS
Answer: 2
Step-by-step explanation:
This is because it is a scaled copy which means that the smaller has to multiply either by a whole or a fraction and the bigger can be divided by a whole or a fraction in order to be the smaller triangle if that makes sense. so 5*2=10, 12*2=24 thus if you were to divide 10/2=5, 24/2=12.
Answer:
The answer is 2:1
Step-by-step explanation:
This is because it is a 2/1 ratio
Can anyone write the equation of the graph?
The equation of the absolute value graph is f(x) = |x - 3| + 5
How to determine the equation of the graph?The graph represents the given parameter
From the graph, we can see that the graph is an absolute value graph
An absolute value graph is represented as
f(x) = a|x - h| + k
Where h and k are the vertex of the graph
In this case, they are
h = 3 and k = 5
This is because the minimum point of the graph is (3, 5)
Substitute values for h and k in the form of the equation
So, we have the following representation
f(x) = a|x - 3| + 5
A point on the graph is (2, 6)
This gives
a|2 - 3| + 5 = 6
When the value of variable a is solved, we have
a = 1
So, the equation becomes
f(x) = 1 * |x - 3| + 5
Evaluate the products
f(x) = |x - 3| + 5
Hence, the equation of the graph is f(x) = |x - 3| + 5
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Can someone help me with this and a reason why the equation chosen?
2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given that, Ariana purchased two drill set from a sale, each of them costs $25 less than its original price,
If f is the original price, then she must have purchased it at (f-25) and for two sets it's 2(f-25)
She paid $86 for her purchase, so,
2(f-25) = $86
Hence, 2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.
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Which expression is equivalent to -51 - (-60)−51−(−60)minus, 51, minus, left parenthesis, minus, 60, right parenthesis?
The required expression which is equivalent to -51 -(-60) is -51 + 60.
Given that,
Which expression is equivalent to -51 - (-60) is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression = -51 - (-60)
Simplify by applying the property of distribution under the parenthesis,
= -51 + 60
Thus, The required expression which is equivalent to -51 -(-60) is -51 + 60.
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1. The distance between the points (5, 7) and (8,-5) is
a) √153
b) √154
c) √13
d) √53
The distance between the points (5, 7) and (8,-5) is √13.
Define distance between points.The length of the path joining two points determines their distance from one another. It's crucial to know how to calculate the distance between two points when working with graphs. This makes it possible for a learner to estimate how long the line is, which is useful in a variety of circumstances. Using the distance formula is the most typical method of determining the distance.
Points (5, 7) and (8,-5)
Formula:
AB² = (x₂ - x₁)² + (y₂ + y₁)²
AB² = (8 - 5)² + (-5+7)²
AB² = (3)² +(2)²
AB² = 9 + 4
AB² = 13
AB = √13
The distance between the points (5, 7) and (8,-5) is √13.
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Dennis spends 1.5 hours practicing guitar each
day. What is the total amount of time (in hours)
that Dennis spent practicing guitar after 8 days?
Dennis spent 12 hours practicing.
1.5 hours = 90 mins
90 mins x 8
720 mins = 12 hours
The table shows the numbers of snare drum backbeats and bass guitar
notes in a disco song. Are the two quantities proportional? Explain.
Snare Drum Backbeats:
3
90
120
Bass Guitar Notes:
2
60
80
Yes, the two quantities have a proportional relationship because the variables x and y all have the same constant of proportionality.
What is a proportional relationship?Mathematically, a proportional relationship can be represented or modeled with the following mathematical expression:
y = kx
Where:
y represents the numbers of bass guitar notes.x represents the numbers of snare drum backbeats.k represents the constant of proportionality.In order for the two quantities to have a proportional relationship, the variables x and y must remain in a constant ratio.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 2/3
When x = 90 and y = 60, we have:
Constant of proportionality (k) = 60/90
Constant of proportionality (k) = 2/3
When x = 120 and y = 80, we have:
Constant of proportionality (k) = 80/120
Constant of proportionality (k) = 2/3
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we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can i. change the z value to a smaller number. ii. take a larger sample. iii. take a smaller sample.
Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.
In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the system of experimentation.
Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.
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Hey, guys! How is your day? (°ω°)
Wilson paints 40% of a bookcase in 20 minutes.
Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase.
The time taken for Wilson to paint the bookcase is 50 minutes.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Wilson paints 40% of a bookcase in 20 minutes. It should be noted that 40% = 0.4
Therefore, the time taken to paint the whole bookcase will be:
= Number of minutes / Percentage painted
= 20 / 0.4
= 50
He'll use 50 minutes.
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What is the size of an angle called a revolution
Answer:
Step-by-step explanation:
The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!
what is 1/1/2 x 2/23
Answer:
1/23
Step-by-step explanation:
marital status: of women according to the statistical abstract of the united states, 70.3% of females ages 20 to 24 have never been married. choose 5 young women in this age category at random. find the probability that a. none has ever been married
0.1717 is Probability that none has ever been married from selected 5 young women in age category at random.
In the question we have,
the number of females age 20 to 24 has never been married = 70.3%
the number of young women in this age category (20 to 24) at random = 5
We shall find out the probability that none has been maaried from selected group of 5 females.
Probability of female age 20 to 24 has never been married = 0.703
So, the probability that none has been married from selected group of 5 females ( p)= 0.703×0.703×0.703×0.73×0.73
= 0.1717
Therefore, The probability that none has ever been married is 0.1717.
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