Point $D$ is the centroid of $△ABC$ . Find $CD$ and $CE$ .
DE=15
A triangle A B C is drawn. A line segment drawn from vertex A intersect the side B C. A line segment C E drawn from vertex C intersect the side A B. A line segment drawn from vertex B intersect the side A C. All the three line segments intersect each other at the centroid D.
The measure of the segment CD is 12 and CE is 8.
What is centroid?In a triangle, the centroid is the point of intersection of the three medians, which are line segments joining each vertex to the midpoint of the opposite side.
The centroid divides each median into two segments, with the distance from the centroid to the vertex being twice the distance from the centroid to the midpoint of the opposite side.
Let M be the midpoint of side AB, N be the midpoint of side AC, and P be the midpoint of side BC. Then, we have:
CD = 2DP
CE = 2DN
We are also given that DE = 15. Since D is the centroid, we have:
AD = BD = CD/3
AE = CE/3
DC + DP = PC
CE + DN = NE
AD + AE = DE
Using these relationships, we can find CD and CE:
CD = 2DP = 2(PC - DC) = 2((AD + DP) - (AD/3)) = 2(2AD/3) = 4AD/3
CE = 2DN = 2(NE - CE) = 2((AE + DN) - (AE/3)) = 2(2AE/3) = 4AE/3
To find AD and AE, we can use the fact that AD + AE = DE and AD = BD:
AD + BD = DE
AD + (2AD/3) = 15
5AD/3 = 15
AD = 9
AE = DE - AD = 15 - 9 = 6
Substituting these values into the equations for CD and CE, we get:
CD = 4AD/3 = 4(9)/3 = 12
CE = 4AE/3 = 4(6)/3 = 8
Therefore, CD = 12 and CE = 8.
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Can somebody give me the answer?
Answer:
200
Step-by-step explanation:
1inch=50miles
Now the distance between two places are 4 inches:
1 *4 inches = 50*4 miles
4inches= 200miles
Graphing equations for algebra
The solution for the inequality -4x-3>-5x+8 is x>11.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
1) -11+x≥-3
Move all terms not containing x to the right side of the inequality.
x≥8
2) -x/4 <7
Move all terms not containing x to the right side of the inequality.
-x<28
x>-28
3) The highest waterfall in the world is Angel falls in Venezuela at 1000 meters.
So, the inequality represent the height of waterfall is h≤1000.
4) -4x-3>-5x+8
Add 5x on both the sides of an inequality, we get
x-3>8
Add 3 on both the sides of an inequality, we get
x>11
5) Given that, Area≤48
Here, 1/2 ×8×x≤48
4x≤48
x≤12
6) -2x-9<-x-4
Add x on both the sides of an inequality, we get
-x-9<-4
Add 9 on both the sides of an inequality, we get
-x<5
x>-5
7) 1/2 x-8>-3
Move all terms not containing x to the right side of the inequality.
Here x>10
Therefore, the solution for the inequality -4x-3>-5x+8 is x>11.
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A recipe requires 1 1/2, cups of milk for every 1/2 of a cup of flour. What is the ratio of
cups of milk to one cup of flour?
Answer:
So the ratio of cups of milk to one cup of flour is 3:1.
Step-by-step explanation:
We can start by multiplying the denominator by 2 to get a denominator of 1:
1/2 * 2 = 1
Now we need to multiply the numerator by 2 as well to keep the ratio the same:
1 1/2 * 2 = 3
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x 4 - 81) (x - 3).
The final polynomial equation after synthetic division is \(x^5-3x^4-81x+243\)
We need to solve;
Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.
The polynomial equation given is;
\(\left(x^4-81\right)\left(x-3\right)\)
By using synthetic division;
⇒ \(x^4x+x^4\left(-3\right)-81x-81\left(-3\right)\)
\(x^5-3x^4-81x+243\)
→ The required final equation in descending powers of x is \(x^5-3x^4-81x+243\) .
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20 points!Can someone please help me I will mark brainliest
A tortilla measures 8 inches in diameter, shown below. What is the tortilla's area?
The required area of tortilla is 16π square inches.
What is an area of a circle?
Area of a circle is defined as the region occupied by the circle in two-dimensional plane.
Mathematically,
A = π (d/2)²
where d is the diameter of circle
or, A = π r²
where r is the radius of circle.
Now, given diameter of tortilla is 8inches.
⇒ d = 8inches
Since,tortilla is a circle
So, area of tortilla A = π (d/2)²
⇒ A = π (8/2)²
⇒ A = π (4)²
⇒ A = 16π square inches
Hence, required tortilla's area is 16π square inches.
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find 2 numbers if their ratio is 9:11 and their difference is 6
Answer:
27:33
Step-by-step explanation:
turn the ratio into an equation by and add 6 to 9x to mae it equal to 11x and solve for x
find the sum. 2/5 + 1/2
Answer:
9/10 NINE OVER 10
Step-by-step explanation:
To add two fractions they must be over a common denominator, which for this problem is 10. To put each fraction over a common denominator we must multiply each fraction by the appropriate form of 1. 2/5 + 1/2 ( 2/2 X 2/5 ) + (5/5 X 1/2 ) --> 4/10 + 5/10
We can now add the numerators of the two fractions over the common denominator: 4/10 + 5/10 ---> 4+5/10 ---> 9/10.
Hope this helps! I know what does though, marking me brainliest.
An athlete jumps these four distances In the long jump competition which jump does not run to 4.7 m²
Answer:
3rd jump
Step-by-step explanation:
The distance jumped is given in the table attached. to get the jump that do not round up to 4.7 meters, we round each of the jump to one decimal place and then select the jump that does not round up to 4.7 meters.
Therefore rounding off gives:
1st jump: 4.746 meters = 4.7 meters to one decimal place
2nd jump: 4.680 meters = 4.7 meters to one decimal place
3rd jump: 4.647 meters = 4.6 meters to one decimal place (does not round to 4.7 meters)
4th jump = 4.733 meters = 4.7 meters to one decimal place
HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr2,
Answer:
r = √(A/π)
Step-by-step explanation:
HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr²,
inverse formula
r = √(A/π)
rewrite x^4y^2 - 2x^3y^3
Answer: B
Step-by-step explanation:
Use a number bond to break apart and solve. 54 ÷ 6?
We shall apply the method of break apart and distribute to solve the question as follows;
Break apart 54 into multiples of 6;
Divide each part by 6
\(\begin{gathered} (\frac{12}{6})+(\frac{12}{6})+(\frac{12}{6})+(\frac{18}{6}) \\ =2+2+2+3 \\ =9 \end{gathered}\)Note that you may break apart the number 54 into bigger multiples of 6 (e.g, 30 and 24 OR, 36 and 18)
Please help and explain quickly im so confused
In the figure below, k || l and m || n. Find the values of y and x.
Answer:
x = 30
y = 115
Step-by-step explanation:
Suppose line m is parallel to line n:
65+y = 180 because they are supplementary angles
subtract 65 from both sides
y = 115
angle represented by y and the angle represented by 3x + 25 are alternate angles and their measure is equal, so to find the value of x we can write the following equation:
3x + 25 = 115 subtract 25 from both sides
3x = 90 divide both sides by 3
x = 30
i need hlp with this question offer I 50 points
The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, what is the linear speed of the car in miles per hour? Round your answer to the nearest tenth.
Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:
Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep
4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3
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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.
To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:
Calculate the circumference of the wheel:
The circumference of a circle is given by the formula
C = 2πr
where r is the radius of the wheel.
In this case, the radius is 30 inches, so the circumference is
C = 2π(30)
= 60π inches.
Calculate the distance traveled in one revolution:
Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.
Calculate the distance traveled in one minute:
Multiply the distance traveled in one revolution by the number of revolutions per minute.
In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.
Convert the distance to miles per hour:
There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.
Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.
The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.
Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.
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Consider the following small open economy: с = 200+ 0.69Y I = 80 - 1,000r G = 20 NX = 850.09Ye e = 90 M = 115 YL = 0.5Y - 200r Y = 300 C is consumption spending, I is investment spending, r is the interest rate, G is govern- ment spending, NX is net exports, e is the nominal exchange rate, M is money supply, YL is demand for money, and Y is long-run output. In this economy, the interest rate does not deviate from the foreign interest rate. The price level is fixed and set to one. Note that, in this problem, a decrease in e is synonymous with a depreciation of the nominal exchange rate. 1. Assuming that the economy is in equilibrium, find the value of the interest rate. (6 points) 2. Going from the equilibrium found in Question (1), assuming fixed nominal exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the size of the nominal money supply in the new short run equilibrium? (6 points) 3. Going from the equilibrium found in Question (1), assuming flexible exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the value of the real exchange rate in the new equilibrium? (6 points)
The interest rate is 10.89%
1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..
The size of the nominal money supply in the new short-run equilibrium is 121.07.
2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.
Real exchange rate will remain unchanged.
3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.
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coefficient on independent variable becomes statistically significant after controlling for something
When the coefficient on an independent variable becomes statistically significant after controlling for something, it means that the variable's effect on the dependent variable is considered significant and reliable, even when accounting for the influence of the controlled variable.
Controlling for something typically involves adding additional independent variables to a statistical model to examine their individual effects on the dependent variable while holding other variables constant. By doing so, we can assess the unique contribution of each variable and determine if the coefficient on the initially non-significant variable becomes significant when accounting for other factors.
If the coefficient on an independent variable becomes statistically significant after controlling for another variable, it suggests that the initially non-significant variable has an impact on the dependent variable that was previously masked or confounded by the presence of the controlled variable. This highlights the importance of considering multiple factors simultaneously to obtain a more accurate understanding of the relationship between variables.
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What is negative 9 divided by 2?
Answer:
-\(\frac{9}{2}\) = -4.5
Step-by-step explanation:
-9 ÷ 2
Fraction \(\frac{-9}{2}\) can be written as \(-\frac{9}{2}\) by extracting the negative sign.
\(-\frac{9}{2}\)
Factor:
\(\frac{(-1)x3^{2} }{2}\) = -4.5
Please help me 10 points
an edge of a square can be expressed as $4x-15$ meters or as $20-3x$ meters. what is its area in square meters?
The area in a square meter is 5$. We can equate the two expressions for the length of the edge of the square and solve for x:
$4x - 15 = 20 - 3x$
$7x = 35$
$x = 5$
The length of one edge of the square is 5 meters, so the area of the square is $5^2 = 25$ square meters. Therefore 5$ is the solution for the $4x-15$ and 20 - 3x$ equation. 15 and 3 will exchange their places to form 7$ and 35$ and 5$ is the end result of the problem that is given.
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Each side of a square mirror is 2 feet long. What is the mirror's perimeter?PLSSS HELP IVE BEEN STUCK ON THIS QUESTION FOR HOURS!!!!!!!!!!!!!!!
Answer:
The square perimeter is 8 ft long
Step-by-step explanation:
Answer:
Perimeter of the square =4*all length
Step-by-step explanation:
Perimeter =4*2=8
The Perimeter of the mirror =8
Find the slope of the line that goes through the points (8,13) and (3,6).
Answer:
7/5
Step-by-step explanation:
The slope equation is y2 - y1/x2 - x1
Answer:
7/5
Step-by-step explanation:
Use slope formula:
m = (6 - 13)/(3 - 8) = -7/ -5 = 7/5
Hope this helps!
tell me the answer for each box its on classkick and i can see if its wrong
Answer:
$19.35
Step-by-step explanation:
it takes two answers to mark someone brainliest so mark him now
What value of x satisfies the equation below?
x +x=12
3 6
A. x=12
B. x=6
C. x=24
D. x=72
The expression 2w^2 + 10w represents the area of a rectangle with width of w inches. select the situation that could be represented by the expression 100-10w-2w^2
Answer:
Option C
Step-by-step explanation:
We know that the expression:
2*w^2 + 10*w
Represents the area of a rectangle with width w.
Now we want to find the situation that can be represented with the expression:
100 - 10*w - 2*w^2
Let's rewrite this as:
100 - (2*w^2 + 10*w)
Then we are subtracting the area of our rectangle to an area of measure 100.
Now, suppose that we have a square of 10in by 10 in.
The area of that square will be:
A = 10in*10in = 100 in^2
Now if we cut our rectangle (with an area = 2*w^2 + 10*w) from that square, the new area of the figure will be:
area = 100in^2 - (2*w^2 + 10*w)
Which is exactly the expression in the question, then the correct option is:
Option C
A mother divided her land of 141/4 acres among her 5 adopted adult children. samuel received 11 acres, sophia received 9 acres, anthony received 8 acres, jasmine received 5 acres, and juan received 4 1/4 acres.
which of the children received more land if the land was divided evenly among them compared to the way the mother divided it?
a)anthony
b)jasmine
c)juan
d)sofia
The child who received more land if the land was divided evenly among them compared to the way the mother divided it is Sofia. Option (d) is correct.
A mother divided her land of 141/4 acres among her 5 adopted adult children such that Samuel received 11 acres, Sophia received 9 acres, Anthony received 8 acres, Jasmine received 5 acres, and Juan received 4 1/4 acres.
Among the given children, the child who received more land if the land was divided evenly among them compared to the way the mother divided it is Sofia.
To determine the land received by each child if the land was divided evenly among them, divide the total area by the number of children.
Therefore, each child would receive 141/4 ÷ 5 acres.
141/4 ÷ 5 = 113/20 ≈ 5.65 acres.
(to two decimal places)
Approximately, each child would receive 5.65 acres of land.
Which is not how the mother divided her land among the children.
Now, let's compare the area of land that each child received with the 5.65 acres they would have received if the land was divided evenly among them.Samuel received 11 acres.
11 > 5.65
So, Samuel received more land than they would have received if the land was divided evenly among them.Sophia received 9 acres.
9 < 5.65
So, Sophia received less land than they would have received if the land was divided evenly among them.
Anthony received 8 acres.
8 < 5.65
So,
Anthony received less land than they would have received if the land was divided evenly among them.
Jasmine received 5 acres.
5 = 5.65
So, Jasmine received the same land as they would have received if the land was divided evenly among them.
Juan received 4 1/4 acres.
21/4 = 5.25 and
5.25 < 5.65
So, Juan received less land than they would have received if the land was divided evenly among them.
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Which expression is equivalent to the given expression? Assume the denominator does not equal zero. (4m^5n^2 / m^2n)^3
Answer:
Step-by-step explanation:
Hope this Helps ;)
Nisha and Lee Nguyen are purchasing a new home with monthly mortgage payments of $740.16. Their annual property taxes are estimated to be $3,047.16, and their homeowners insurance policy has an annual cost of $2,149.76. They must also purchase wind insurance with an annual cost of $850.72. If the Nguyen family chooses to have these costs included in an escrow account, calculate their total monthly house payments.
Answer:
6787.8
explanation:
740.16 + 3047.16 + 2149.76 + 850.72 = 6787.8
i dont actually know if this is it so sorry if not