Triangle EFG is formed by connecting the midpoints of the side of triangle BCD. The lengths of the sides of triangle EFG are shown. What is the length of CD? Figures not necessarily drawn to scale.
Answers
Applying the triangle midsegment theorem, the length of CD is: 8 units.
What is the Midsegment of a Triangle?If the midpoints of two sides of a triangle are joined together by a line segment, that line segment is called the midsegment of the triangle. Every triangle has three of these.
What is the Triangle Midsegment Theorem?According to the triangle midsegment theorem, the third side of a triangle is parallel to its midsegment, and also has a length that is twice of the length of the midsegment.
Given the image above, where points G, E, and F are the midpoints of the sides of the given triangle, thus:
EG is a midsegment that is parallel to a third side CD.
Therefore:
Length of CD = 2(EG)
Substitute
CD = 2(4)
CD = 8 units.
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Related Questions
find the solution for variables x, y, and z
Answers
The solution for variables x, y, and z are -
x = 100y = 3z = -3What is defined as the elimination method?The elimination method is the procedure of eliminating one of the variables in a system of linear equations by using addition or subtraction methodologies in conjunction with variable coefficient multiplication or division. Because it allows us to eliminate or remove one of the variables, allowing us to solve a much more simplified equation.The given linear equation are-
x - 6y - 2z = -8 .......equation 1.
-x + 5y + 3z = 2 ......equation 2.
3x - 3y - 4z = 15 .......equation 3.
Add equation 1 and 2; gives
-y + z = -6 .....equation 4
multiply equation 2 and subtract it with equation 3;
12y + 5z = 21 ......equation 5
multiply equation 4 with 5 and subtract it from equation 5.
17 y = 51
y = 3.
Put y = 3 in equation 4 and find z.
z = -6 + 3
z = -3
Put the value of y and z in equation 1 and find x.
x = -8 + 18 + 6
x = 100
Therefore, the solution for variables x, y, and z are -
x = 100y = 3z = -3To know more about the elimination method, here
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A company gives each worker a cash bonus on every Friday randomly giving a co-worker and amount with these probabilities $10.75 $50.25 over many weeks what is the expected workers weekly bonus
Answers
graph each equation by using a table -3=5x-y
Answers
The graph of the equation is shown below
Graph of linear equations
From the question, we are to graph the given equation
The given equation is
-3 = 5x - y
To graph the equation,
First we will determine the x-intercept and y-intercept
x-intercept
Put y = 0 in the equation
-3 = 5x - 0
-3 = 5x
x = -3/5
y-intercept
Put x = 0 in the equation
-3 = 5(0) - y
-3 = 0 - y
-3 = -y
y = 3
Using the x-intercepts and y-intercepts, we can plot the graph of the equation.
The graph of the equation is shown below
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What angles are adjacent to angle 4
Answers
Answer:
2,3
Step-by-step explanation:
They are the closest angles to 4.
Sarah finished reading 35 pages in her book. There were 250 pages in all. What percent of the book has Sarah left to read?
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Answer:
86% is the percent of the book has Sarah left to read?
The inverse of a conditional statement is if a number is negative then it has to be a cube root. What is the contra positive of the original statement
Answers
please help me solve
Answers
The equation for the line of best fit is: C. y = 0.894x + 0.535.
How to determine the equation for the line of best fit?In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;
x y x² y² xy__
5 4 25 16 20
6 6 36 36 36
9 9 81 81 81
10 11 100 121 110
14 12 196 144 168
Sum 438 398 415
Next, we would calculate the mean of the x and y variables as follows;
Mean = [∑(x)]/n
Mean = 44/5
Mean, \(\bar{x}\) = 8.8
Mean = [∑(y)]/n
Mean = 42/5
Mean, \(\bar{y}\) = 8.4
∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)
∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4
∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²
∑(x - \(\bar{x}\))² = 50.8
Now, we can determine the slope coefficient for the line of best fit:
Slope (b) = 45.4/50.8
Slope (b) = 0.894.
Lastly, we would determine the intercept (a) as follows;
\(a = \bar{y} - b\bar{x}\)
a = 8.4 - (0.894)8.8
a = 0.535
Therefore, the required equation is y = 0.894x + 0.535.
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1. Find the equation of the image of the circle x² + y2 + 16x-24y + 183 = 0 by rotated the line mirror 4x + 7y + 13 = 0. 2. The image of the circle (x - 3)² + (y-2)² = 1 in the line mirror ax + by = 19 is (x-1)³ + (y-16)2 = 1 then, find the values of (a, b). 3. Find the equation of a line passing through the origin and making an angle with the 4 line y-3x-5. 4. A parabola is drawn with its focus at (3,4) and vertex at the focus of the parabola y²-12x - 4y + 4 = 0. The n find equation of the parabola. 5. If the line ax + by + c = 0 touches the circle x² + y² - 2x = and is normal to the circle x² + y² + 2x - 4y + 1 = 0, then find the value of (a, b). 6. If the line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x. -3 7.1² 14 231= [] then find the matrix A 8. Find the equation of the ellipse having its center at the point (2,-3), one and one vertex at (4, -3). 3 9. Find the value of x if-1 0 10. Solve the linear system using Cramer's rule a) 2 1 2 4 (6x - 4y = -12 8x - 3y = -2 X = 16 -21 3x + 2y = z = 5 b) x-y+3z = -15 (2x + y +7z = -28 one focus at (3,-3) 11. Find the value of k for which the following system of linear equations has infinite solutions: x + (k+1)y = 5 ((k+1)x + 9y = 8k - 1
Answers
Answer:
-72x - 53y + 287 = 0.
Step-by-step explanation:
To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.
The line mirror equation is given as 4x + 7y + 13 = 0.
The reflection of a point (x, y) in the line mirror can be found using the formula:
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
where A, B, and C are the coefficients of the line mirror equation.
For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.
Now, let's find the equations of the image of the circle.
The original circle equation is x² + y² + 16x - 24y + 183 = 0.
Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':
x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)
= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)
= (x - 8y - 8(4x + 7y + 13)) / 65
= (x - 8y - 32x - 56y - 104) / 65
= (-31x - 64y - 104) / 65
y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)
= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)
= (y - 14x + 8(Ax + By + C)) / 65
= (y - 14x + 8(4x + 7y + 13)) / 65
= (57x + 35y + 104) / 65
Therefore, the equation of the image of the circle is:
(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0
Simplifying the equation, we get:
-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0
-72x - 53y + 287 = 0
So, the equation of the image of the circle is -72x - 53y + 287 = 0.
Find the whole.
40% of what number is 6?
40% ofis 6.
(Type a whole number.)
Answers
Answer:
2.4
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
it is 15 I think!!!!!
The support arm, AB, is
perpendicular to a line tangent to this curve on a roller coaster at the point of tangency B.
The equation of the tangent line to the curve at B is 3x + 2y = 28.
Find the equation of the support arm, AB.
B(4,8)
Lines perpendicular to tangents to curves, at
the point of tangency, are referred to as “normals.”
Answers
Answer:
\(y = \dfrac{2}{3}x + \dfrac{16}{3}}\)
Step-by-step explanation:
The genera slope-intercept equation of a line is
y = mx + 8 where m is the slope and b the y-interecept
A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1
The equation of the tangent line is
3x + 2y = 28.
1. Convert to slope-intercept form:
Subtract 3x from both sides3x - 3x + 2y = 28 - 3x
2y = 28 - 3x
y = 14 - 3/2xy = (-3/2)x + 14
So slope = -3/2
Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3
Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:
y = (2/3)x + b
To calculate b for the complete line equation plug in the point B(4, 8) and solve for B
y = 8 when x = 4
=> 8 = (2/3)(4) + b
Switch sides: (does not change any signs)
8/3 + b = 8
Subtract 8/3 on both sides
b = 8 - 8/3
b = 24/3 - 8/3
b = 16/3
So equation of the support arm is
\(\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}\)
Which of the scenarios below are considered seller-based discounts? options are in the picture
Answers
The scenarios that can be considered a seller-based discount are:
A. The offer by Wire and Cable
B. Carfna's Fine Foods
C. Mouser Electronics offer
E. Carchex Car Maintenance
What is a seller-based discount?A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.
The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.
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Solve for x. 24= -4(x-1)
Answers
Answer:24 = 24x
Step-by-step explanation:Cross multiply:
2 * 12 = x * 24
Simplifying
2 * 12 = x * 24
Multiply 2 * 12
24 = x * 24
Reorder the terms for easier multiplication:
24 = 24x
Solving
24 = 24x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-24x' to each side of the equation.
24 + -24x = 24x + -24x
Combine like terms: 24x + -24x = 0
24 + -24x = 0
Add '-24' to each side of the equation.
24 + -24 + -24x = 0 + -24
Combine like terms: 24 + -24 = 0
0 + -24x = 0 + -24
-24x = 0 + -24
Combine like terms: 0 + -24 = -24
-24x = -24
Divide each side by '-24'.
x = 1
Simplifying
x = 1
5pts. Domain and range
Answers
Using the concept of domain and range of the functions, we have that:
The domain is: -2 < x ≤ 2.The range is: -2 < y ≤ 1.Function: Yes.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is given by the values of x.The range of a function is the set that contains all the values of the output. In a graph, it is given by the values of y.A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Hence we have that for the function graphed:
The domain is: -2 < x ≤ 2.The range is: -2 < y ≤ 1.Function: Yes.More can be learned about domain and range of functions at https://brainly.com/question/10891721
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write an equation of a line that is perpendicular to given line that passes through the given point 5y+2x=-15 T(5,-5)
Answers
Step-by-step explanation:
The answer is on the bottom if you just wanna scroll down.
The first thing that you would want to do is turn the equation of the given line into slope-intercept form (it's just easier). To do that, you would want to isolate y on either side. So subtract 2x and divide both sides by 5 and you get: y=-2/5x-3. After you do this, remember that perpendicular lines have the negative reciprical slope of the original line. So since the slope is -2/5, the slope of a perpendicular line would be 5/2. Now you have m=5/2 which is your slope! Now you can use slope point form which is y-y_1=m(x-x_1). You know your m which is 5/2. y-y_1=5/2(x-x_1). Since we know that the line passes through the point (5,-5) we can just plug the numbers in. y-(-5)=5/2(x-5). simplify everything: y+5=5/2(x-5). Remember, math is all about making things simple and easy. since the problem didn't say a specific type of equation, you can just put that as your answer!
Answer:
y+5=5/2(x-5)
Hope this helps! (If it's wrong, plz leave sum comments. thx lol)
For each graph below, state whether it represents a function.
Function?
Chuck
Graph 1
●
OYes
4-
2-
●
Graph 4
●●
No
Graph 2
OYes
O No
Graph 5
Graph 3
●
A
OYes
O No
Graph 6
Save For Later
© 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use
Answers
Answer:
a .yes
b.no
c
d.yes
e.no
f
g
h
Given that D( x ) = 2 x , select all of the following that are true statements. D( x ) is a direct variation. D( x ) is a function. D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3
Answers
The True statements are:
A ) D ( x ) is a function.D ) D ( x ) is a direct variation.E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).What is a Function?Each element of X is given exactly one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
For D (x) = 2 x:
- x is the independent variable,
- D ( 6 ) = 2 · 6 = 12.
10 = 2 · 5, 12 = 2 · 9, - 4 = 2 · ( - 2 ).
True statements are:
A ) D ( x ) is a function.
D ) D ( x ) is a direct variation.
E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).
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Someone please help me on this problem.. :(
Answers
Answer:
I believe the constant rate is 13
Step-by-step explanation:
I believe this because for each time you divided y/x you will get 13. But in the last one (146/12) it will be 12.16... So it will show a constant rate if you round the answer of (146/12) but if you aren't supposed to round then there wont be a constant.
Hope this helps! :)
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
What is the length of AD?'
Use the given information to complete the worksheet.
Thank you!
Answers
The length of side AD is,
⇒ AD = 16
We have to given that;
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
Since, Volume of right triangular prism is,
V = 1/2 (bh) x L
Substitute all the values we get;
V = 1/2 (22 × 11) × AD
1936 = 121 × AD
AD = 16
Thus, The length of side AD is, 16
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as
8
3) The volume of
a wall, 5 times
high as it is board and 8
times as long as it is high, 12.8
(a.metors) Find The Breadth of the
Wall
Answers
Answer:
0.4 meters
Step-by-step explanation:
The volume is ...
V = LHB
12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values
0.064 m³ = B³ . . . . . simplify
∛0.064 m = B = 0.4 m
The breadth of the wall is 0.4 meters.
= 9. The scale of a scientific drawing is 1 cm = 2 in. If the actual length of an object in the drawing was 4.5 inches, how long would it be in the drawing? -:lita
Answers
Answer:
2.25cm
Step-by-step explanation:
1cm = 2in
?cm = 4.5in
4.5 x 1 /2 = ?
4.5/2 = 2.25
In the drawing, it would be 2.25cm.
2. Regina Aguirre deposits $2,000 into an ordinary annuity after each 6-month period for 4 years. The account
pays 6% interest compounded semiannually. Find the a) future value, and b) total interest earned.
Answers
Solve for v. 4v = 10.24
Answers
Answer:
I believe the answer is V = 2.56
Step-by-step explanation:
10.24 divided by 4 is 2.56. And 2.56 times 4 is 10.24.
Henry's savings account has an APR of 3.65%, calculates interest daily, and
pays interest at the end of the month. If during the month of November, his
balance was $300 for the first 10 days of the month, $1200 for the next 10
days of the month, and $800 for the last 10 days of the month, how much
total interest did Henry earn in November?
Answers
First, we need to calculate the daily interest rate:
Daily interest rate = APR / 365 = 0.0365 / 365 = 0.0001
For the first 10 days, the interest earned on $300 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 300 x 0.0001 x 10 = $0.30
For the next 10 days, the interest earned on $1200 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 1200 x 0.0001 x 10 = $1.20
For the last 10 days, the interest earned on $800 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 800 x 0.0001 x 10 = $0.80
Therefore, the total interest earned by Henry in November is:
Total interest = $0.30 + $1.20 + $0.80 = $2.30
Therefore, Henry earned $2.30 interest in November.
in a semiconductor company's quality control test, a machine found that 22 out of a sample of 600 computer chips were defective how many of the 36,000 computer chips the company makes each would you expect to be defective?
Answers
Answer:
1320 should be expected
Step-by-step explanation:
22 = 600
x10
220 = 6,000
x6
1320=36,000
What is 3/11 simplified
Answers
The axis of symmetry of a quadratic equation is x = –3. If one of the zeroes of the equation is 4, what is the other zero?
Answers
Answer:
-10
Step-by-step explanation:
If the axis of symmetry is at x = -3 and one of the zeros is at 4 then the other zero must be at equal distance from the axis , but on the other side, so will be at -10.
Answer:
–10
Step-by-step explanation:
got it right
I’m terrible at percents so ...... if anybody can help that would be nice :))
Answers
Answer:
There are 625 trees in the park.
Step-by-step explanation:
Assume that there are x trees in the park
∵ The number of trees in the park = x
∵ 27% of them are oaks
∵ 16% are pins
∵ 33% of them are banyans
∵ The remaining are willows
→ The percentage of the total number of trees is 100%
∴ The percent of the remaining = 100% - (27 + 16 + 33)%
∴ The percent of the remaining = 100% - 76%
∴ The percent of the remaining = 24%
∵ The number of willows trees = 150
∴ 24% of x = 150
∴ 24% × x = 150
→ Change the percent to a decimal by divide it by 100
∵ 24% = \(\frac{24}{100}\) = 0.24
∴ 0.24 × x = 150
∴ 0.24x = 150
→ Divide both sides by 0.24
∴ x = 625
∴ There are 625 trees at the park.
After 10 years, the principal on this mortgage is $136,683. How much of the next payment will go towards interest
Answers
Answer: 13,668 i think.
7(y-5)=21 Help Please!!
Answers
Answer:
Y=8
Step-by-step explanation:
7(y-5)=21
distribute the 7
7y-35=21
get y by itself
7y=56
divide by 7
y=8
HOPE THIS HELPS YOU UNDERSTAND!
I NEED ANSWER ASAP PLEASE WITH WORK PLEASE AND TY!!!!!! In the image the question is 32!! What is the factored form of x2 + 12x - 64?
A (x-4)(x + 16)
B. (x-2)(x + 32)
C. (x + 4)(x - 16)
D. (x-6)(x + 18)
Answers
Answer:
A) (x-4)(x+16)
Step-by-step explanation:
\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)