Answer:
\(8^{-3}\)
Step-by-step explanation:
\(8^{3}/8^6\) = \(8^{3-6}\) = \(8^{-3\)
How can I describe a ordered pair
Answer:
Ordered Pair An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.
Step-by-step explanation:
i hope this helped! :)
Answer:
An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. To graph a point, you draw a dot at the coordinates that corresponds to the ordered pair.
Step-by-step explanation:
2. To evaluate the effect of a treatment, a sample was obtained from a population with a mean of 9: Sample scores: 10,7,9,6, 10, 12, (a) Compute a 95% confidence interval for the population mean for the treatment group. (b) Compute Cohen's d to estimate the size of the described effect. (e) Perform a hypothesis test to decide whether the population ment of the treatment group is significantly different from the mean of the general population (dy Compute und interpret a Baves factor for the model (either Hoor Hi) with the best predictive adequacy. Key Compute und interpret the posterior model probability for the winning model chosen in part (a),
(a) The 95% confidence interval for the population mean of the treatment group is [7.02, 10.98].
(b) To calculate Cohen's d, we need the standard deviation of the sample. Using the given sample scores, the standard deviation is approximately 2.68. Cohen's d is then (9 - 8.31) / 2.68 = 0.26, indicating a small effect size.
(c) To perform a hypothesis test, we compare the sample mean of 8.31 (obtained from the given sample scores) with the population mean of 9. Using a t-test, assuming a significance level of 0.05 and a two-tailed test, we calculate the t-value as (8.31 - 9) / (2.68 / sqrt(6)) = -0.57. The critical t-value for a 95% confidence level with degrees of freedom of 5 (n-1) is 2.571. Since |-0.57| < 2.571, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference between the population mean of the treatment group and the mean of the general population.
(d) Bayesian factor (BF) represents the strength of evidence for one hypothesis over another. Without specific information about the alternative hypothesis, we cannot compute a Bayesian factor in this case.
(a) To compute a 95% confidence interval for the population mean of the treatment group, we can use the formula:
Confidence Interval = sample mean ± (t-value * standard error)
From the given sample scores, the sample mean is (10 + 7 + 9 + 6 + 10 + 12) / 6 = 8.31. The t-value for a 95% confidence level with degrees of freedom 5 (n-1) is 2.571. The standard error can be calculated as the sample standard deviation divided by the square root of the sample size.
Using the sample scores, the sample standard deviation is approximately 2.68. The standard error is then 2.68 / sqrt(6) ≈ 1.09.
Plugging in the values, the 95% confidence interval is 8.31 ± (2.571 * 1.09), which gives us [7.02, 10.98].
(b) Cohen's d is a measure of effect size, which indicates the standardized difference between the sample mean and the population mean. It is calculated by subtracting the population mean from the sample mean and dividing it by the standard deviation of the sample.
In this case, the population mean is given as 9. From the sample scores, we can calculate the sample mean and standard deviation. The sample mean is 8.31, and the standard deviation is approximately 2.68.
Using the formula, Cohen's d = (sample mean - population mean) / sample standard deviation, we get (8.31 - 9) / 2.68 ≈ 0.26. This suggests a small effect size.
(c) To perform a hypothesis test, we can compare the sample mean of the treatment group (8.31) with the mean of the general population (9) using a t-test. The null hypothesis assumes that the population mean of the treatment group is equal to the mean of the general population.
Using the sample scores, the standard deviation is approximately 2.68, and the sample size is 6. The t-value is calculated as (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).
Plugging in the values, the t-value is (8.31 - 9) / (2.68 / sqrt(6)) ≈ -0.57. The critical t-value for a 95% confidence level with 5 degrees of freedom (n-1) is 2.571.
Since |-0.57| < 2.571, we fail to reject the null hypothesis. This means there is not enough evidence to suggest a significant difference between the population mean of the treatment group and the mean of the general population.
(d) Bayesian factor (BF) represents the strength of evidence for one hypothesis over another based on prior beliefs and data. However, to compute a Bayesian factor, we need specific information about the alternative hypothesis, which is not provided in the given question. Therefore, we cannot calculate a Bayesian factor in this case.
(a) The 95% confidence interval for the population mean of the treatment group is [7.02, 10.98].
(b) Cohen's d suggests a small effect size, with a value of approximately 0.26.
(c) The hypothesis test does not provide enough evidence to suggest a significant difference between the population mean of the treatment group and the mean of the general population.
(d) A Bayesian factor cannot be computed without information about the alternative hypothesis.
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what is the assertiveness
Answer:
Confident or forceful behaviour
Step-by-step explanation: I have a dictionary
HELP PLEASE WOULD REALLY APPRECIATE IT ?? :))
Answer:
1
-1
-3
3
Step-by-step explanation:
f(1) = 2(1) -1
f(1) = 1
f(0) = 2(0) -1
f(0) = -1
f(-1) = 2(-1) -1
f(-1) = -3
f(2) = 2(2) -1
f(2) = 3
Answers in order from top to bottom:
1-1-33===========================================
Explanation:
To get each answer shown above, we replace each x value with a single specific value.
In the top row, we have x = 1. So we'll replace every x with 1 to get...
f(x) = 2x-1
f(1) = 2(1)-1
f(1) = 2-1
f(1) = 1
So that's why 1 goes in the first box.
--------------------
We repeat the same structure of steps for x = 0
f(x) = 2x-1
f(0) = 2(0)-1
f(0) = 0-1
f(0) = -1
Meaning that -1 goes in the second box.
----------------------
Repeat for x = -1
f(x) = 2x-1
f(-1) = 2(-1)-1
f(-1) = -2-1
f(-1) = -3
When we subtract a positive from a negative, we're really adding the two positive versions of the number, and then making the final result negative.
So -3 goes in the third box.
-----------------------
Repeat for x = 2
f(x) = 2x-1
f(2) = 2(2)-1
f(2) = 4-1
f(2) = 3
We have 3 go in the fourth box.
-----------------------
Side note: This is a linear function in slope intercept form y = mx+b. We have m = 2 as the slope and b = -1 as the y intercept.
Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement Number of Measurement Estimated Digit Significant Figures 14.8 m 3 ✓ Choo *4.8 Txa 14. $10.25 Choose... 0.05 L Choose 1.000 g/ml Choose.. 6200 cm Choose... 403 kg Choose Figures 14.8 m 3 Choose... $10.25 ✓ Choose... 10.35 10,2% 1x.25 NO.25 0.05L Choose. 1.000 g/ml Choose 6200 cm Choose. Choose.. 403 kg place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m 3 Choose... $10.25 Choose... II 0.05 L ✓ Choose.. 0.x5 x.05 0.0x 1.000 g/mL Choose... 6200 cm Choose... 403 kg Choose... Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m Choose... 3 $10.25 Choose... 0.05 L Choose... 1.000 g/mL Choose 1.00 1.0x0 X.000 1.200 Choose... 6200 cm Choose.. 403 kg Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m Choose... 3 $10.25 Choose... Choose... 0.05 L Choose... 1.000 g/ml 6200 cm ✓ COD Bx00 x200 620x 6220 Choose 403 kg Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement Number of Measurement Estimated Digit Significant Figures Choose... 14.8 m 3 $10.25 Choose... Choose... 0.05 L 1.000 g/mL Choose.. Choose... 6200 cm 403 kg ✓ Choose XO3 40% 4x3
The table shows the estimated digit and significant figures of each measurement and their representation with x.
Number of Measurement Estimated Digit Significant Figures
14.8 m 3 ✓
$10.25 - ✓
0.05 L - ✓
1.000 g/mL - ✓
1.200 - ✓
6200 cm - ✓
403 kg - ✓
For each measurement, the estimated digit is replaced with an x to represent the number with the correct number of significant figures. The correct representations for each measurement are:
14.8 m: 15.0 m$10.25: $10.30.05 L: 0.050 L1.000 g/mL: 1.00 g/mL1.200: 1.206200 cm: 6200 cm403 kg: 400 kgNote that in some cases, the representation requires adding zeros to the right of the decimal point to indicate the number of significant figures. In other cases, the representation requires rounding up or down to the correct number of significant figures.
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the number of cars that go through the drive-in window at a local bank each hour is an example of a continuous random variable.
The first statement is false and the second statement is true.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. There are two types of random variables.
Discrete random variablesContinuous random variablesA random variable that takes a finite number of possible values can be defined as a Discrete random variable. A random variable that takes an infinite number of possible values can be defined as a Continuous random variable. A continuous random variable consists of only continuous values.
Continuous random variables are defined at intervals of values. Continuous random variables are represented by the area under a curve.
⇒ The number of cars that go through the drive-in window at a local bank each hour.
The number of cars can be counted and can be an integer like 10, 20,100 etc.
∵ The number of cars is countable it is not an example of a continuous random variable
⇒ The high daily temperature in Anchorage.
High daily temperature can be an integer or function like 60°, 120° etc
∵ The high daily temperature is an example of a continuous random variable.
Therefore, The number of cars that go through the drive-in window at a local bank each hour is not an example of a continuous random variable and The high daily temperature in Anchorage is an example of a continuous random variable.
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The complete question is
Simplify the expression by combining any like terms. 3x−6x+x−4+4x
2(x - 2)
Explanation:The given expression is:
3x−6x+x−4+4x
Collect like terms
3x - 6x + x + 4x - 4
Simplify the resulting expression
2x - 4
Factor out the common term (2) from the expression
2(x - 2)
Answer:
2(x−2)
Step-by-step explanation:
Solution Steps
3x−6x+x−4+4x
Combine 3x and −6x to get −3x.
−3x+x−4+4x
Combine −3x and x to get −2x.
−2x−4+4x
Combine −2x and 4x to get 2x.
2x−4
evaluate the integral. 1 (u + 2)(u − 3) du 0
Evaluating the integral- \(\int_0^1 (u+2)(u-3) du\) we get the simplified answer = -37/6.
Let's evaluate the integral as follows -
\(\int_0^1 (u+2)(u-3) du\)
now lets multiply the expression and we will get,
\(= \int_0^1 u^2-u-6 d u\)
Distributing the integrals to each expression.
\(= \int_0^1 u^2 d u+\int_0^1-u d u+\int_0^1-6 d u\)
By the Power Rule, the integral of \($u^2$\) with respect to u is \($\frac{1}{3} u^3$\).
\(= \left.\frac{1}{3} u^3\right]_0^1+\int_0^1-u d u+\int_0^1-6 d u\)
Since -1 is constant w.r.t u, move -1 out of the integral of the second term.
\(= \left.\frac{1}{3} u^3\right]_0^1 -\int_0^1u d u+\int_0^1-6 d u\)
By using the power rule, the integral of \($u^2$\) w.r.t to u is \($\frac{1}{2} u^2$\)
\(= \left.\left.\frac{1}{3} u^3\right]_0^1-\left(\frac{1}{2} u^2\right]_0^1\right)+\int_0^1-6 d u\)
Let's Combine \($\frac{1}{2}$\) and \($u^2$\).
\(= $$\left.\left.\frac{1}{3} u^3\right]_0^1-\left(\frac{u^2}{2}\right]_0^1\right)+\int_0^1-6 d u$$\)
Now, apply the constant rule,
\(= $$\left.\left.\left.\frac{1}{3} u^3\right]_0^1-\left(\frac{u^2}{2}\right]_0^1\right)+-6 u\right]_0^1$$\)
Substituting the limits and simplifying we get,
= -37/6
Hence, the simplified answer for the given integral \(\int_0^1 (u+2)(u-3) du\) is -37/6.
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The complete question is-
Evaluate the integral- \(\int_0^1 (u+2)(u-3) du\).
For f(t)=t−5 and g(t)=t−3, find: а) ( f/g)(t)= ___ and (f/g)(-4) = ___
The value of solutions are,
(f/g) (t) = (t - 5) / (t - 3)
And, (f/g) (- 4) = 9/7
We have to given that,
Functions are,
f (t) = t - 5
And, g (t) = t - 3
Hence, Simplify the function as,
(f/g) (t) = f (t) / g (t)
(f/g) (t) = (t - 5) / (t - 3)
At t = - 4;
(f/g) (t) = (t - 5) / (t - 3)
(f/g) (- 4) = (- 4 - 5) / (- 4 - 3)
(f/g) (- 4) = - 9/- 7
(f/g) (- 4) = 9/7
Thus, We get;
(f/g) (t) = (t - 5) / (t - 3)
And, (f/g) (- 4) = 9/7
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-1/6 + 4/5 Write your answer in simplest form
Answer:19/30
Step-by-step explanation:
1. multiply and divide(left to right)-1/6
=-1/6+4/5
2.multiply and divide(left to right)4/5
=-1/6+4/5
3. add and subtract(left to right)-1/6+4/5=19/30
=19/30
Find the 75th term: 88, 81, 74, 67, 60
Answer:
a₇₅ = - 430
Step-by-step explanation:
There is a common difference between consecutive terms, that is
d = 81 - 88 = 74 - 81 = 67 - 74 = 60 - 67 = - 7
This indicates the sequence is arithmetic with nth term
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 88 and d = - 7 , then
a₇₅ = 88 + ( 74 × - 7) = 88 - 518 = - 430
The 75th term of the arithmetic progression is -430
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is
Tn = a + (n - 1) d, where Tₙ = nth term and a = first term.
Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP : Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the Arithmetic progression be = 88 , 81 , 74 , 67 , 60 ...
The first term of the AP is a ₁= 88
Now , the common difference of the AP d = second term - first term
= 81 - 88
= -7
Now , the nth term of the arithmetic progression is given by ,
Tn = a + (n - 1) d
Substituting the values in the equation , we get
T₇₅ = 88 + ( 75 - 1 ) ( -7 )
= 88 + 74 ( -7 )
= 88 - 518
= -430
Therefore , the value of T₇₅ is -430
Hence , The 75th term of the arithmetic progression is -430
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WILL MARK BRAINLIEST!!
I. Write 2-7i in polar coordinates on the complex plane.
II. Find (1+i)^8 using DeMoivre's theorem.
(r,θ) = (7.28,254.05°) are 2-7i in polar coordinates on the complex plane.
What are polar coordinates?The polar coordinates system is a two-dimensional coordinate system in which each point is determined by distance from the point and an angle from the reference direction.
I. Polar form = (r,θ) = (7.28,254.05°)
z = 2 - i7
r= \(\sqrt{ 2^2+-7^2}\)
= √53
= 7.28
θ = tan^-1 (-7/-2)
=3.5
= 74.05
Point lies in the third quadrant
Hence θ = 180+74.05
= 254.05°
Polar form = (r,θ) = (7.28,254.05°)
II. Z=16
De Moivre's theorem states if
z= r(cos(θ) + i sin (θ)) , then
\(z^2=r^2(cos(n\theta)+ i sin (n\theta))\)
\(r= \sqrt{1^2+1^2}\)
= √2
θ= arc tan (1/1)
= π / 4
z= √2 (cos (π / 4)+i sin (π / 4))
z^8 = (√2 (cos (π / 4)+i sin (π / 4)))^8
= (√2 (cos (8π / 4)+i sin (8π / 4)))^8
=16 (cos(2π) + i sin (2π)
=16
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g/4 -5 = 1
i need help
Answer:
g=24
Step-by-step explanation:
g/4 -5 = 1
g/4 = 6
g = 24
Answer:
\(g=24\)
Step-by-step explanation:
When given the following equation,
\(\frac{g}{4}-5 = 1\)
Solve for the variable (g) using inverse operations,
\(\frac{g}{4}-5=1\)
Add (5) to both sides
\(\frac{g}{4}=6\)
Multiply both sides by (4)
\(g=24\)
suppose you are interested in testing whether there is a significant association between covid-19 and life expectancy. among 15 states in the u.s. you conduct a simple linear regression model. the slope is 32.55 and the standard error is 10.5. what is the p-value obtained when assessing the null hypothesis that the slope
The p-value for the test is 0.006, which is less than the commonly used significance level of 0.05. This suggests that there is a significant association between COVID-19 and life expectancy in the 15 states tested.
To obtain the p-value for the null hypothesis that the slope is zero (i.e., no significant association between COVID-19 and life expectancy), we need to use the t-distribution.
The formula for calculating the t-statistic is:
t = (b - 0) / SE
where b is the estimated slope coefficient, 0 is the hypothesized value of the slope coefficient under the null hypothesis, and SE is the standard error of the slope coefficient.
In this case, b = 32.55, 0 = 0, and SE = 10.5. Therefore, the t-statistic is:
t = (32.55 - 0) / 10.5 = 3.1 (rounded to one decimal place)
To find the p-value, we need to look up the t-distribution table with n-2 degrees of freedom (where n is the sample size, which is 15 in this case) and find the probability of getting a t-value greater than or equal to 3.1 or less than or equal to -3.1 (since we are conducting a two-tailed test).
Using a t-distribution table or calculator, we find that the probability of getting a t-value of 3.1 or greater (or less than -3.1) with 13 degrees of freedom is approximately 0.006.
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Verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem
Since y_1(0) = 1, it satisfies the initial condition. However, y_2(0) = 0 does not satisfy the initial condition, as it should be y(0) = 1. Therefore, only y_1(t) is a solution of the initial value problem.
To verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem, we first need to understand what the problem is. An initial value problem is a differential equation that includes an initial condition. In this case, we can assume that the initial condition is y(0) = 1.
Now, let's substitute both y_1(t) and y_2(t) into the differential equation and see if they satisfy the initial condition. The differential equation is not provided, but assuming it is y'(t) = -t/2, we have:
y_1'(t) = -1
y_2'(t) = -t/2
Substituting y_1(t) and y_2(t) into the differential equation gives:
y_1'(t) = -1
= -t/2 (when t = 2)
y_2'(t) = -t/2
= -t/2 (for all t)
Thus, both y_1(t) and y_2(t) satisfy the differential equation. Now, let's check if they satisfy the initial condition.
y_1(0) = 1 - 0
= 1
y_2(0) = -0^2/4
= 0
In conclusion, y_1(t) = 1 - t is the only solution that satisfies the differential equation and initial condition, while y_2(t) = -t^2/4 is not a solution since it does not satisfy the initial condition.
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What does it mean when a number And a variable are place right next to each other In an equation
Answer:
d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
What percentage of the shape is green?
Answer:
51%
Step-by-step explanation:
51 of the 100 cubes are green so 51/100 is equal to 51%
At the Sunnyvale Playhouse, the price for an adult ticket is $12 and the price of a child's ticket is $6. For Saturday night's play, 125 tickets were sold, totaling $1,140.
Which system of equations correctly represents this situation where a represents the number of adult tickets sold for Saturday night's play and c represents the number of child tickets sold?
A) 12a + 6c = 125
a + c = 1140
B) 6a + 12c = 125
a + c = 1140
C) a + c = 125
12a + 6c = 1140
D) a + c = 125
6a + 12c = 1140
Answer: the answer is 1.499495
cristian solved a problem 3x^2 24x 9=0 by completing the square.
Cristian found the solutions to the equation \(3x^2 + 24x + 9 = 0\)to be \(x = -4 \pm \sqrt(13)\), by completing the square.
How to find the solution by completing the square?Cristian completed the square for the equation \(3x^2 + 24x + 9 = 0\) by following the given below steps:
First, divide both sides of the equation by 3 to simplify it:\(x^2 + 8x + 3 = 0\)
Move the constant term to the right-hand side of the equation:\(x^2 + 8x = -3\)
Take half of the coefficient of x (which is 8), square it, and add it to both sides of the equation:\(x^2 + 8x + 16 = -3 + 16\)
The left-hand side is now a perfect square trinomial: \((x + 4)^2.\)Simplifying the right-hand side gives:\(x^2 + 8x + 16 = 13\)
Take the square root of both sides of the equation:\(x + 4 = \pm \sqrt(13)\)
Solve for x by subtracting 4 from both sides:\(x = -4 \pm \sqrt(13)\)
Therefore, Cristian found the solutions to the equation \(3x^2 + 24x + 9 = 0\)to be \(x = -4 \pm \sqrt(13)\), by completing the square.
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If Z1 and Z4 are adjacent and
supplementary, what reason would
support this statement?
Statement
Reason
21 + 24 = 180° [? ]
A. Addition property of equality
B. Linear pair postulate
C. Adjacency theorem
Explanation:
As the name implies, "linear pair" means the two angles combine to form a straight line of 180 degrees. Think of gluing the angles together.
As an example, let's say angle 1 was 50 degrees and angle 4 is 130 degrees. They combine to 50+130 = 180 which is a straight angle. I recommend using a protractor to help draw these angles.
The blue points follow a pattern. Drag the black point to show your prediction for what come next then explain your thinking
The new point will be located at the coordinate (7,8)
What are patterns?Patterns are simply the procedures and the rules that are followed to create a sequence.
Determining the pattern on the graphFrom the graph, we have the following highlights
A point is translated 2 units upThe same point is then translated 3 units right, to form the next pointThe position of the new pointUsing the above pattern, the new point will be located at the coordinate (7,8)
See attachment for the next position
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At what x-values does the graph of f (x) = (x+3) ² - 7 intersect the x-axis?
Pls, help I need this before tomorrow.
explanation and answer pls
Step-by-step explanation:
1) Total rectangle area = W x H = 12 x 8 = 96 cm^2
area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2
Nonshaded portion = 96 - 28 cm^2 = 68 cm^2
ratio shaded:nonshaded is then 28 : 68 = 7:17
2) Look at the two middle triangles : Height of each = 8 cm
then reading across the diagram height + base + height = 21 cm
so base = 5 cm
area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2
total area for FOUR of them = 80 cm^2
498,147,846,267
+ 32,870,714,538
Answer:
531018560805
Step-by-step explanation:
What makes a triangle congruent by HL?.
The HL postulate states that two triangles are congruent if the hypotenuse and leg of one right triangle are congruent with the hypotenuse and leg of another right triangle.
Hypotenuse Leg Theorem
hypotenuse theorem proof shows how a given set of right triangles is congruent when the corresponding hypotenuses and one leg are of equal length.
Statement:
Two triangles are congruent by the hypotenuse leg theorem if the hypotenuse and one leg of a right triangle are congruent with the hypotenuse and leg of another right triangle.
given: where ABC is an isosceles triangle, AB = AC, and AD is perpendicular to BC.
Proof : AD as altitude is perpendicular to BC and forms ADB and ADC as right triangles. AB and AC are the respective hypotenuses of these triangles and we know they are equal. Because AD = AD is common for both triangles.
That is, AB = AC and AD is common.
Therefore, the hypotenuse and pair of legs of the two right-angled triangles satisfy the definition of the HL theorem.
We know that angles B and C are equal (property of isosceles triangle).
We also know that the angles BAD and CAD are equal (AD bisects BC and BD equals CD).
Therefore, △ADB ≅ △ADC
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1.) DaNae paid $15.45 for a t-shirt that was on sale at H&M. The sale price DaNae paid was 75% of the original price. What was the original price of the t-shirt?
2.) After a “25% Off Sale”, DaNae paid $15.45 for a t-shirt at H&M. What was the price of the t-shirt before the discount?
1) The original price of the t-shirt is $20.6.
2) Price of the t-shirt before the discount is $20.6.
What is discount?
Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.
Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.
1) Here the Cost price of the t-shirt = $15.45
She bought t-shirt which is cost of 75% of the original price. Then
=> 75% =15.45
Original price = 15.45×\(\frac{100}{75}\)
=> original price = $20.6
Hence the original price of the t-shirt is $20.6.
2) The cost price of the t-shirt = $15.45
Then cost price = (100%-25%) of original price
=> 15.45 = 75% of original price
=> original price = \(\frac{15.45*100}{75}\) = $20.6.
Hence price of the t-shirt before the discount is $20.6.
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How many solution S does the system X 2y 3 3x 6y 9 have?
To find the number of solutions that the system x + 2y = 3 and 3x + 6y = 9 has, we can solve the system using various methods, such as graphing, substitution, or elimination.
What does the term "system of equations" mean?
A system of equations is a collection of two or more equations that are solved simultaneously. A solution to a system of equations is a set of values for the variables that makes all of the equations in the system true simultaneously.
One way to solve this system is to use the substitution method. We can solve the first equation for y and substitute the result into the second equation to obtain an equation in one variable.
x + 2y = 3
y = (3 - x) / 2
Substituting this expression for y into the second equation, we get:
3x + 6((3 - x) / 2) = 9
Simplifying the right-hand side, we get:
3x + 3 - 3x = 9
Combining like terms, we get:
0 = 9
This equation is not true for any value of x, so the system does not have a solution. As a result, the system is incoherent.
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Evaluate expressions- if r=45 and t=9 what is the value of the following expression?
A.36
B.75
C.80
D.66
Answer:
\(d. \: \: 66\)
Step-by-step explanation:
\(r + 63 \div t \times 3\)
\(45+63÷9 \times 3\)
\(45+7 \times 3\)
\(45 + 21\)
\(66\)
Hope it is helpful...Solve the system using substitution (1 point)
x + y = 8
y = 3x
(A). (4, 12)
(B). (2, 6)
(C). (1/2, 3/2)
(D). (-4, -12)
The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.
To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.
Given the system:
x + y = 8
y = 3x
Substituting the value of y from the second equation into the first equation, we have:
x + (3x) = 8
4x = 8
x = 2
Now, substitute the value of x into the second equation to solve for y:
y = 3(2)
y = 6
Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.
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If you sleep 7 hours every night how many hours are you AWAKE in a year?