Answers
Answer: a
Step-by-step explanation:
Answer:
the answer is d. it is written in scientific notation.
Step-by-step explanation:
have a nice day!
Related Questions
Evaluate: Question(2): Z+8-6(z-2a)+5z
Answers
Answer:
Z+12a−z+8+12−+8
Step-by-step explanation:
Z+8−6(z−2a)+5z
+8−6(−2)+5
Z+8−6(−2a+z)+5z
+8−6(−2+)+5
Z+8−6(−2a+z)+5z
+8−6(−2+)+5
Z+8+12a−z+8+12−
Answer:
Z + 8 + 12a − z
12a + 8
Step-by-step explanation:
Question 4. Let p1 and p2 be the proportions of black renters in Section A and Section B, respectively. What is the value of the test statistic for the 2-sided hypothesis test using the two-proportion z procedure
Answers
The p-value can then be determined by comparing the calculated z value to a standard normal distribution with a mean of 0 and a standard deviation of 1.
Let p1 and p2 be the proportions of black renters in Section A and Section B, respectively. If we want to compare the proportions of two independent populations, we can use the two-proportion z procedure to calculate a test statistic and p-value for a hypothesis test.
For a two-sided hypothesis test, the test statistic is given by:
z = (p1 - p2) / SE
Here, SE is the standard error, which is calculated as:
SE = sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
In the above formula, n1 and n2 represent the sample sizes for Section A and Section B, respectively.
The null hypothesis for the test is that the two population proportions are equal (p1 = p2), while the alternative hypothesis is that they are not equal (p1 ≠ p2).
To calculate the test statistic, we need to know the values of p1, p2, n1, and n2. Once we have these values, we can calculate SE and use it to compute the value of z. The p-value can then be determined by comparing the calculated z value to a standard normal distribution with a mean of 0 and a standard deviation of 1.
In summary, the two-proportion z procedure allows us to compare the proportions of two independent populations by calculating a test statistic (z) and a corresponding p-value. The test helps us assess whether there is a significant difference between the proportions and provides statistical evidence to support or reject the null hypothesis.
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Fill in the blank question.
In △ABC, b=5, c=7,
and m∠A=20º.
What is the value of a?
Round the answer to the nearest tenth.
Answers
your answer is: A=2.9
Good luck :)
if the area of the shaded region shown below is 120 square units, and the height of the line segment above the horizontal axis is 4 units, what is point a?
Answers
Point A is located at (4, 4) in the coordinate plane.With these dimensions, we can determine that Point A is located at (4, 4) in the coordinate plane.
To find the coordinates of point A, we need to consider the properties of the shaded region. The shaded region consists of a rectangle and a triangle. We know that the area of the shaded region is 120 square units, and the height of the line segment above the horizontal axis is 4 units.
The rectangle's area is given by its length multiplied by its width. Since the height of the rectangle is 4 units, we can deduce that the length of the rectangle is also 4 units. Therefore, the width of the rectangle can be found by dividing the total area of the shaded region by the length of the rectangle.
Subtracting the width of the rectangle from the total width of the shaded region will give us the base of the triangle. Since the triangle is isosceles, the base length is equal to the height of the rectangle.
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1. Ben wrote a report on trains.
Author's Reason:
Explain:
Answers
Answer:
Step-by-step explanation:
the answer is 2 because if you subtract and add you will get your and and good luck on the state test 5th 6th and 7th and younger kids.
Do u love school? I while give u brainliest and alot of points to the people who answer first
Answers
Answer:
yes
Step-by-step explanation:
School is an educational building where you learn math and reading and it doesnt help you but it benifits you in jobs.
Answer:
well yes but no at the same time
Step-by-step explanation:
have a nice week. please mark as brainllest
[o]-[o]
\___/
In the figure below, m||n. Match the angle pairs with the
correct label for the pairs.
Answers
On solving the provided question, by properties of parallel lines we got to know that - 1 - A 2 - C 3 - B 4 - D
what is alternate exterior angles?When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.
Matches are -
1 - A
2 - C
3 - B
4 - D
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The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations? (a) n 15 t 1.66 a 0.05 o Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
Answers
The null hypothesis must be rejected as there is enough evidence that the diameter differs from 0.5 inches.
Given values are
The population mean is 0.5 inches
The Null hypothesis is : H₀ : μ = 0.5 inches
The Alternative hypothesis is given by Hₐ : μ ≠ 0.5 inches
Now let us consider the parameter given:
sample size is n = 15
test statistics is t = 1.66
The level of significance : α = 0.05
The degree of freedom: df = n-1 = 15 -1 =14
Calculating the critical value : \(t_\frac{\alpha}{2} ,df\) = 2.145
We are using the critical value of \(t_\frac{\alpha}{2}\) as the test is one-tailed .
Comparing the value of t and \(t_\frac{\alpha}{2}\) we can see that : \(t < t_\frac{\alpha}{2}\)
Hence the null hypothesis can be rejected.
Given that the value of t does not fall within the range covered by (i.e., the range from -2.145 to the bottom of the normal distribution curve), we are unable to reject the null hypothesis.
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SOMEONE PLEASE HELP ANSWER CORRECTLY !!!!! WILL MARK BRIANLIEST !!! HELPPPPPP MEEEEEEE !!!!!
Answers
Answer:
(-2,-3)
Step-by-step explanation:
A=(8,-5)
M=(3,-4)
The difference between them is that m is 5 to the left and 1 up. We need to do the same thing to find B.
B=(-2,-3)
•Exercise #2. Suppose a market with two firms, 1 and 2, facing the inverse demand p()=10− p(Q)=10-Q where =1+2Q=q1+q2. The two firms incur a marginal cost of production c1=c2=2c1=c2=2, produce a homogeneous good, and are Cournot competitors.
•Q4) Draw the firms’ best-response functions with 1q1 on the vertical axis and 2q2 on the horizontal axis.
•Q5) Determine firm 2’s quantity at the Cournot equilibrium.
•Q6) Assume firm 1 adopts a raising rival’s cost strategy at the expense of firm 2. While firm 1’s marginal cost remains at c1=2c1=2, firm 2’s marginal cost increases to c2=4c2=4. On the same graph as the one used to answer Q4, show the effect of the raising rival’s cost strategy on the firms’ best-response functions.
•Q7) Determine firm 2’s quantity at the new Cournot equilibrium.
Q8) Determine the market price at the new Cournot equilibrium.
Answers
firm 2's quantity at the Cournot equilibrium is q2=5/3.the inverse demand function: p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4. firm 2's quantity at the new Cournot equilibrium is q2=4/5.
The best response of firm 1 is given by 1q1=5−0.5q21+q2, and the best response of firm 2 is given by 2q2=5−0.5q12+q1. These best response functions are illustrated in the following diagram:
At the Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect.
Therefore, solving the two best response functions simultaneously for q1 and q2 gives:
q1=q2=5/3
Therefore, firm 2's quantity at the Cournot equilibrium is q2=5/3.
The new best response function for firm 2 is given by 2q2=5−q1+2q22. This is obtained by replacing c2=2 with c2=4 in firm 2's profit function. The new best response function is illustrated below:
At the new Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect. Therefore, solving the two best response functions simultaneously for q1 and q2 gives:
q1=11/5
q2=4/5
Therefore, firm 2's quantity at the new Cournot equilibrium is q2=4/5.
To determine the market price at the new Cournot equilibrium, we substitute the new equilibrium quantities into the inverse demand function:
p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4
Therefore, the market price at the new Cournot equilibrium is p=4.
In this exercise, we consider a market with two firms, 1 and 2, facing the inverse demand p()=10− p(Q)=10-Q where =1+2Q=q1+q2.
The two firms incur a marginal cost of production c1=c2=2c1=c2=2, produce a homogeneous good, and are Cournot competitors. The best response of firm 1 is given by 1q1=5−0.5q21+q2, and the best response of firm 2 is given by 2q2=5−0.5q12+q1. These best response functions are illustrated in the diagram below:
At the Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect
. Therefore, solving the two best response functions simultaneously for q1 and q2 gives q1=q2=5/3. Therefore, firm 2's quantity at the Cournot equilibrium is q2=5/3.The new best response function for firm 2 is given by 2q2=5−q1+2q22. This is obtained by replacing c2=2 with c2=4 in firm 2's profit function.
The new best response function is illustrated in the following diagram:At the new Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect.
Therefore, solving the two best response functions simultaneously for q1 and q2 gives q1=11/5 and q2=4/5. Therefore, firm 2's quantity at the new Cournot equilibrium is q2=4/5
To determine the market price at the new Cournot equilibrium, we substitute the new equilibrium quantities into the inverse demand function: p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4. Therefore, the market price at the new Cournot equilibrium is p=4.
In conclusion, we have analyzed the effect of a raising rival's cost strategy on a Cournot duopoly. We have shown that the strategy reduces firm 2's quantity and increases the market price, but does not affect firm 1's quantity.
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Define Torsion, pure torsion and it's assumptions, torsion
equation and limitation of its formula?
Answers
Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.
Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.
To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.
However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.
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1) The height, h, in feet of a ball above the ground is given by h = -16t2 + 64t+ 80, where t is the time in seconds. How long does it take the ball to hit the ground? es A) 3 seconds B) 4 seconds 95 seconds D) 6 seconds
Answers
Answer:
C) 5 seconds
Step-by-step explanation:
\(h = - 16t {}^{2} + 64t + 80\)
When the ball hits the ground, the height is 0.
\(0 = - 16t {}^{2} + 64t + 80\)
Factor out the greatest common factor: 16
\(0 = - 16(t {}^{2} - 4t - 5)\)
Find numbers whose sum is -5 and product is - 4.
Those numbers are - 5 and 1: - 5 × 1 = - 5, - 5 + 1 = - 4
\(0 = - 16(t - 5)(t + 1)\)
\(t - 5 = 0\)
Or
\(t + 1 = 0\)
So,
\(t = 5\)
Or
\(t = - 1\)
Since time cannot be a negative value the correct answer is 5 seconds.
Which number property does this equation represent?
(x+6) + 2 = x + (6 + 2)
Answers
Answer:
Associative property
Step-by-step explanation:
FOR MORE INFORMATION
Commutative property :
A+B=B+A
A*B=B*A
. Associative property :
(A+B)+C=A+(B+C)
(A*B)*C=A*(B*C)
. Distributive property :
(A+B)*C=A*C+B*C
. Identity property :
A+0=A
A*1=A
Use a dot plot to display the data. The data represents the life spans (in days) at 30 houseflies. Which plot represents a dotplot of the data? What does the dotplot suggest about the distribution of the life spans of houseflies? A. The life spans range from 4 to 14 days, with most lifespans greater than 13 days. B. The life spans range from 4 to 14 days, with most lifespans in the range of 5 to 9 days. C. The life spans range from 4 to 14 days, with most lifespans less than 5 days. D. The life spans range from 4 to 14 days, with most lifespans in the range of 10 to 14 days.
Answers
The correct dot plot representation of the life spans of houseflies is option B, with the life spans ranging from 4 to 14 days and most life spans in the range of 5 to 9 days.
A dot plot is a simple and effective way of visualizing data, especially for small data sets. A dot plot represents each data point as a dot on a number line, with the position of the dot indicating the value of the data point.
Option B states that the life spans range from 4 to 14 days, with most life spans in the range of 5 to 9 days. This means that the dot plot will have a number line running from 4 to 14, with the majority of dots clustered in the 5 to 9 range. This is the correct representation of the dot plot of the life spans of houseflies.
The dot plot suggests that the distribution of the life spans of houseflies is not symmetrical and has a mode (the most frequent value) between 5 and 9 days. This indicates that most houseflies live between 5 and 9 days, with fewer houseflies living either shorter or longer lives.
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HELP DUE IN 10 MINS! Find the missing side measurement.
Your answer should be a simplified radical or a whole number. (no decimals allowed)
x =
Answers
Answer:
9^2 + x^2 = 12^2
x^2 = 144 - 81
x^2 = 63
x = √63 = 3√7 or 8
hope that answers your question
Answer:
9^2 + x^2 = 12^2
x^2 = 144 - 81
x^2 = 63
x = √63 = 3√7 or 8
hope that answers your question
Step-by-step explanation:
What is the solution to the equation below? 2x/ x - 2 - x + 3/ x - 4 = -4x/ x^2 - 6x + 8
A) x = 3
B) x = 2
C) x = 2,4
D) x = 2,3
Answers
Answer:
A) x = 3
Step-by-step explanation:
The solution to the equation is x = 3
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 equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
2x/ ( x - 2 ) - ( x + 3 ) / ( x - 4 ) = -4x / ( x² - 6x + 8 )
On simplifying , we get
Taking LCM on both sides , we get
2x ( x - 4 ) - ( x + 3 ) ( x - 2 ) = -4x
Now , on further simplification , we get
2x² - 8x - ( x² + x - 6 ) = -4x
x² - 9x + 6 = -4x
Adding 4x on both sides , we get
x² - 5x + 6 = 0
On factorizing , we get
( x - 3 ) ( x - 2 ) = 0
So , the values of x = 2 and x = 3
Now , the solution is undefined for x = 2
Hence , the solution is x = 3
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yolanda is planning a 778-mile trip to visit her daughter in maryland. she plans to average 50 miles per hour. at that speed, approximately how long will the trip take? express your answer to the nearest tenth of an hour.
Answers
778miles/ 50 miles per hour= 15.56 hours
Emma tried to write and equation of the linear table but made an error
Answers
Answer:
The correct answer is (-3,-1) (0,5) (3,11)
Step-by-step explanation:
Emma's mistake was flipping her y-values, 11 matches with 3, not -3. The most likely reason she did this was accidentally making the slope negative. The table she wrote fits the line y=-2x+5. If you plug in -3 into the correct equation you will get -1 and 3 will get you 11.
Answer:
The correct equation is y = -2x + 5
The correct numbers for the graph are (-3,-11), (0,5), and (3,-1)
Step-by-step explanation: Emma put 2x as positive, however, if you put the x values into the variable next to the 2, you will find that some of the answers are incorrect. For example, y = 2(-3)+5. For this one, the answer needs to come up as 11 as it's the y in this case right? Well when you solve the equation, 2(-3) = -6 and -6 plus 5 = -1. However, if you change the 2x into -2x the answer comes up correctly. y= -2(-3) +5 ~ -2(-3) = 6 and 6 plus 5 = 11. This works for all of the x numbers in the table. Hope this helps! ✨
What is the exact solution to the equation 4^5x=3^(x-2)
list the steps to get the answer
Answers
Answer: x = -0.377
Step-by-step explanation:
We have the equation:
4^(5*x) = 3^(x - 2)
Now we can use the fact that:
Ln(A^x) = x*Ln(A)
Then we can apply Ln(.) to both sides of the equation to get:
Ln(4^(5*x)) = Ln(3^(x - 2))
(5*x)*Ln(4) = (x - 2)*Ln(3)
(5*x)*Ln(4) - x*Ln(3) = -2*Ln(3)
x*(5*Ln(4) - Ln(3)) = -2*Ln(3)
x = -2*Ln(3)/(5*Ln(4) - Ln(3)) = -0.377
What Square root equals 11
Answers
I need help to understand before my test today
Answers
Answer:
75 degrees
Step-by-step explanation:
All the angles within a triangle added together equals 180 degrees, so:
x + 25 + 2x - 5 + x = 180
add like terms
4x + 20 = 180
subtract 20 from both sides
4x = 160
divide by 4
x = 40
Now input 4 into the equation for C
2(40) - 5 = 80 - 5 = 75
Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of M′ if the preimage is translated 4 units up.
M′(−4, −1)
M′(4, −1)
M′(0, −5)
M′(0, 3)
Answers
The correct option for image coordinate is M′ is the right response.
(0, 3).
How to calculate the image coordinates?It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. You may have observed the use of grids in mathematics. Which grids are these? We can plot any point using these grids and its coordinates. So, in mathematics, what are coordinates? Let's look at the mathematical definition of coordinates.
Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identify a specific point's precise location on a grid. This grid is referred to as a coordinate plane.
We must add 4 to the y-coordinate of point M in order to obtain the image coordinates of M′ after a translation of 4 units up.
M (0, 1) becomes M′ when translated four units up. (0, 3).
Therefore, M′ is the right response.(0, 3).
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Answer:
D) M′(0, 3)
Step-by-step explanation:
I took the quiz and got a 100 meaning that i got this question right :)
How many boxes of cereal can you buy with $9 if one box costs $3? in one step eqution
Answers
Answer:
3 Boxes
Step-by-step explanation:
$9/$3 = 3 Boxes
Hence, you can buy 3 Boxes
[RevyBreeze]
Someone please solve this today!!
Please show work !
Also don’t waste your time sending that link that hacks you :/
Answers
Answer:
D
Step-by-step explanation:
bx -b -ax +a
collect like terms
bx - ax. + a - b
x(b-a) + b +a
Exit Ticket An art project takes Misty 4 hours to complete. She works for 3 hour each day. How many days does it take Misty to complete the art project? 4
Answers
She works for 3 hours each day.
The art project takes Misty 4 hours to complete
Let's call x to the number of days she needs to complete the project
The next equation model the situation
3x = 4
Solving for x:
x = 4/3 days
In the given figure ABCD, prove that
angleBCD= angleBAD+ angle ABC+angle ADC.
[Hint: Join A and C then extended AC to the point E]
Answers
We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:
Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.
Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.
Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).
Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.
Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).
Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.
Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.
Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.
Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.
Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
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Given: Quadrilateral \(\displaystyle\sf ABCD\)
To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)
Proof:
1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).
2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).
3. In triangle \(\displaystyle\sf ACD\):
- \(\displaystyle\sf \angle ACD = \angle BAD + \angle ADC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).4. In triangle \(\displaystyle\sf BCE\):
- \(\displaystyle\sf \angle BCE = \angle BAD + \angle ABC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):
- \(\displaystyle\sf \angle BCE = \angle BCD\).6. Combining the equations from steps 3 and 4:
- \(\displaystyle\sf \angle BCD = \angle ACD = \angle BAD + \angle ADC\). - \(\displaystyle\sf \angle BCD = \angle BCE = \angle BAD + \angle ABC + \angle ADC\).Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Plz helllllpppppp meeeeee
Answers
Answer: x = 25 mi
Step-by-step explanation:
Sides QO and TR are corresponding.
Sides QP and TS are corresponding.
Sides OP and RS are corresponding.
Create the proportion to solve for x:
5/x = 6/30
Cross multiply:
6x = 150
Divide both sides by 6:
x = 25 mi
Hope this helps!
find two real numbers that have a sum of 14 and a product of 38
Answers
To find two real numbers that have a sum of 14 and a product of 38, we can set up a system of equations. Let's call the two numbers x and y.
From the problem statement, we have the following information:
Equation 1: x + y = 14 (sum of the two numbers is 14)
Equation 2: xy = 38 (product of the two numbers is 38)
To solve this system of equations, we can use substitution or elimination method. Let's solve it using substitution:
From Equation 1, we can express y in terms of x by subtracting x from both sides:
y = 14 - x
Now we substitute this value of y into Equation 2:
x(14 - x) = 38
Expanding the equation, we have:
14x - x^2 = 38
Rearranging the equation to bring it to quadratic form:
x^2 - 14x + 38 = 0
Now we can solve this quadratic equation. We can either factorize it or use the quadratic formula. However, upon examining the equation, we find that it doesn't factorize easily. Therefore, we'll use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For our quadratic equation, the coefficients are:
a = 1, b = -14, c = 38
Substituting these values into the quadratic formula, we have:
x = (-(-14) ± √((-14)^2 - 4(1)(38))) / (2(1))
x = (14 ± √(196 - 152)) / 2
x = (14 ± √44) / 2
x = (14 ± 2√11) / 2
Simplifying further, we have:
x = 7 ± √11
So we have two possible values for x: 7 + √11 and 7 - √11.
To find the corresponding values of y, we can substitute these values of x back into Equation 1:
For x = 7 + √11, y = 14 - (7 + √11) = 7 - √11
For x = 7 - √11, y = 14 - (7 - √11) = 7 + √11
Therefore, the two real numbers that have a sum of 14 and a product of 38 are (7 + √11) and (7 - √11).
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what is the slope of y=4.5
Answers
y
=
m
x
+
b
y
=
m
x
+
b
, where
m
m
is the slope and
b
b
is the y-intercept.
y
=
m
x
+
b
y
=
m
x
+
b
Find the values of
m
m
and
b
b
using the form
y
=
m
x
+
b
y
=
m
x
+
b
.
m
=
0
m
=
0
b
=
4.5
b
=
4.5
The slope of the line is the value of
m
m
, and the y-intercept is the value of
b
b
.
Slope:
0
0
y-intercept:
(
0
,
4.5
)
Answer:
0
Step-by-step explanation:
there is no x so it is 0
0 it is
Find the equation of clean pulsations for a
left-mounted beam (for x=0) and simple pressed on the right (for
x=l) Take into account that: (sinx)^2+(cosx)^2=1
(chx)^2-(shx)^2=1
Answers
We can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.
To find the equation of clean pulsations for a left-mounted beam with a simple support on the right, we can use the differential equation that describes the deflection of the beam. Assuming the beam is subject to a distributed load and has certain boundary conditions, the equation governing the deflection can be written as:
d^2y/dx^2 + (chx)^2 * y = 0
Where:
y(x) is the deflection of the beam at position x,
d^2y/dx^2 is the second derivative of y with respect to x,
ch(x) is the hyperbolic cosine function.
To solve this differential equation, we can assume a solution in the form of y(x) = A * cosh(kx) + B * sinh(kx), where A and B are constants, and k is a constant to be determined.
Substituting this assumed solution into the differential equation, we get:
k^2 * (A * cosh(kx) + B * sinh(kx)) + (chx)^2 * (A * cosh(kx) + B * sinh(kx)) = 0
Simplifying the equation and applying the given identity (chx)^2 - (shx)^2 = 1, we have:
(A + A * chx^2) * cosh(kx) + (B + B * chx^2) * sinh(kx) = 0
For this equation to hold for all values of x, the coefficients of cosh(kx) and sinh(kx) must be zero. Therefore, we get the following equations:
A + A * chx^2 = 0
B + B * chx^2 = 0
Simplifying these equations, we have:
A * (1 + chx^2) = 0
B * (1 + chx^2) = 0
Since we are looking for nontrivial solutions (A and B not equal to zero), the expressions in parentheses must be zero:
1 + chx^2 = 0
Using the identity (sinx)^2 + (cosx)^2 = 1, we can rewrite this equation as:
1 + (1 - (sinx)^2) = 0
Simplifying further, we get:
2 - (sinx)^2 = 0
Solving for (sinx)^2, we find:
(sin x)^2 = 2
Since the square of the sine function cannot be negative, there are no real solutions to this equation. Therefore, we can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.
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