How does this get solved? I am a bit confused on what to do next. Help is very appreciated.
Answers
Answer:
The Proof is given below.
Step-by-step explanation:
Given:
AD ≅ BD ≅ FD ≅ GD
To Prove:
AC ≅ GE
Proof:
In Δ ADF and Δ GDB
AD ≅ DG ……….{Given}
∠ ADF ≅ ∠ BDG …………..{Vertically Opposite angles are equal}
FD ≅ BD ……….{Given}
Δ ADF ≅ Δ GDB ….{Side-Angle-Side test}
∴∠ FAD ≅ ∠ BGD .....{corresponding angles of Congruent Triangle ( c.p.c.t}
i.e ∠ CAD ≅ ∠ EGD.....{ F-C-A and B-E-G straight line}.......( 1 )
Now ,
In Δ CAD and Δ E GD
∠ CAD ≅ ∠ EGD ……….{From ( 1 ) above}
AD ≅ GD ……….{Given}
∠ ADC ≅ ∠ EDG …………..{Vertically Opposite angles are equal}
Δ ADF ≅ Δ GDB ….{Angle-Side-Angle test}
∴ AC ≅ GE .....{corresponding sides of Congruent Triangle ( c.p.c.t}
[tex]\overline {AC} \cong \overline{GE}\ \textrm{......Proved}[/tex]
Related Questions
answer this for me please and quick!!
Answers
you can multiply or put it in a proportion
Answer:
24.3
Step-by-step explanation:
The difference of c and 13 is less than -19.
Answers
Answer:
If you want the inequality, c - 13 < -19
If you want the inequality simplified, c < -6
Sheldon needs to buy 8 gallons of coleslaw for a family reunions the table shows the prices for different size of two brands of coleslaw use the table for exercises 11 and 12
Answers
Nancy is taking inventory in the pharmacy to make sure there is enough eye medication in the pharmacy. She counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in stock. Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes. Calculate how many boxes of each Nancy needs to order.
Answers
Answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy.
Step-by-step explanation:
Nancy counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in the stock.
So, there is a need to order (15 - 10) = 5 boxes of travoprost.
Again, Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes.
So, there is a need to order (12 - 3) = 9 boxes of latanoprost.
Therefore, Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy. (Answer)
Final answer:
Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost to fulfill the pharmacy's minimal stock requirement.
Explanation:
Nancy needs to order more boxes of eye medication to meet the pharmacy's minimal stock levels. For travoprost, the pharmacy requires 15 boxes but currently has only 10 boxes. So, Nancy needs to order:
15 boxes (required amount) - 10 boxes (current amount) = 5 boxes of travoprost.
For latanoprost, the pharmacy needs 12 boxes, but only has 3 boxes in stock, meaning Nancy needs to order:
12 boxes (required amount) - 3 boxes (current amount) = 9 boxes of latanoprost.
3) 8p + 7q= 43
2p-7=-q
I need to solve using substitution. thanks.
Answers
Answer:
p=1, q=5. (1, 5).
Step-by-step explanation:
8p+7q=43
2p-7=-q
------------------
q=-2p+7=7-2p
8p+7(7-2p)=43
8p+49-14p=43
8p-14p=43-49
-6p=-6
6p=6
p=6/6=1
2(1)-7=-q
2-7=-5=-q
q=5
Which graph shows the solution set to this inequality? 4x < 12
Answers
Answer:
x=1,2
Step-by-step explanation:
we show that 4x is <12
if x=1,,,4x=4*1=4
if x=2,,,4x=4*2=8
if x=3,,,4x= 4*3=12
so 1 &2 is right ans
what is the probability that a randomly-selected driver fatality who was female was less than 16 years old the probability that a randomly-selected driver fatality who was female was less than 16 years old is approximately _____.
Answers
Answer:
0.19%
Step-by-step explanation:
To know what is the probability that a female who is less than 16 in involved in a driver fatality, we have to compare the cases of fatalities for females who are less than 16 years old, with the total cases of fatalities, commited by all kind of persons. Then, to know the proportion of the population of driver fatalities represented by female who are less than 16, we divide the amount of cases that happend under the characteristics mentioned (females <16) and the total amount of fatalities: [tex]\frac{100}{Total_{fatalities}} =\frac{100}{141+100+4970+2331+11009+....} =\frac{100}{52693}=0.0019=0.19\%[/tex], which is the probability that a randomly-selected driver fatality were commited by a females who is less than 16.
Higher Order Thinking
Mrs. Dryson
divided her collection of 52 glass bears
into equal groups. She had 1 bear
left over. How many groups did
Mrs. Dryson make? How many bears
are in each group?
Answers
Answer:
There are 26 glass bears in each group and there are 2 equal groups.
Step-by-step explanation:
i hope that help but your problem was kind of werid at first but i foud the answer i hope you enjoy!!!...
Help me find the value of the missing variable
Answers
Answer:
Its isosceles, so the the 2 sides other than st are equal. 2x+6=3x-6
Moves to one side. 12=x
x=12
Step-by-step explanation:
x=12
Step-by-step explanation:
You know that angles T and S are equal, meaning the lengths of the lines TV and SV are also equal. That means 2x+6=3x-6. You transfer the xs and get 6=x-6. You undo the negative 6, receiving 12=x.
PLEASE ANSWER NOW
Stephen, Paul & Bridget share some money in the ratio 3 : 4 : 2. In total, Stephen and Bridget receive £50. How much does Paul get?
Answers
Answer:
The money receive by Paul is [tex]\pounds 40[/tex].
Step-by-step explanation:
Given as :
The ratio of share of money among three people as
Stephen : Paul : Bridget = 3 : 4 : 2
The total money receive by Stephen and Bridget = [tex]\pounds 50[/tex]
Let The money receive by Stephen = 3 x
Let The money receive by Paul = 4 x
Let The money receive by Bridget = 2 x
Now, According to question
The total money receive by Stephen and Bridget = [tex]\pounds 50[/tex]
I.e 3 x + 2 x = [tex]\pounds 50[/tex]
i.e 5 x = [tex]\pounds 50[/tex]
∴ x = [tex]\frac{\pounds 50}{5}[/tex]
x = [tex]\pounds 10[/tex]
So, The money receive by Stephen = 3 × [tex]\pounds 10[/tex] = [tex]\pounds 30[/tex]
Let The money receive by Paul = 4 × [tex]\pounds 10[/tex] = [tex]\pounds 40[/tex]
Let The money receive by Bridget = 2 × [tex]\pounds 10[/tex] = [tex]\pounds 20[/tex]
Hence The money receive by Paul is [tex]\pounds 40[/tex]. Answer
10. A square picture has a 1-inch frame around it. If the
area of the frame alone is 80 in.2, what is the area of the
picture?
Answers
Answer:
361 sq, inches.
Step-by-step explanation:
Let us assume that the dimensions of the square picture are P in × P in.
So, the area of the picture alone is, A = P²
Now, if the photo has a frame of 1 inch wide, then the dimensions of the photo with frame are (P + 2) in × (P + 2) in.
So, the area of the photo with frame is A' = (P + 2)(P + 2) = (P + 2)²
Now, the area of the frame alone is 80 sq. inches.
Hence, A' - A = 80
⇒ (P + 2)² - P² = 80
⇒ 4P + 4 = 80
⇒ 4P = 76
⇒ P = 19 inches.
So, the area of the picture is = 19² = 361 sq. inches. (Answer)
361 sq, inches.
Step-by-step explanation:
The owner of a new restaurant is ordering tables and chairs. he wants to have only tables for two and tables for 4. the total number of people can be seated in rest is 120, then write an equation to represent the situation. What do the variables represent?
Answers
Answer:
4 M + 2 N = 120
Step-by-step explanation:
If we name "M" the number of tables for four people, and "N" the number of tables for two people, then the total number of people to be seated using M tables (of four people) would be the product "4 * M".
Similarly, the total number of people to be seated if the owner has N number of two person tables, would be: "2 * N".
Therefore, if the owner has M four people tables and N two person tables, the total number of people seated at the restaurant would be the addition:
4 * M + 2 * N. Since he wants this number to be 120, we complete the equation making this expression equal to 120:
4 * M + 2 * N = 120
The equation that represents this situation is 2x + 4y = 120, where x represents the number of tables for two and y represents the number of tables for four. Thus, this mathematical equation reflects the owner's seating arrangement plans for his restaurant.
Explanation:Let's use x to represent the number of tables for two and y to represent the number of tables for four. Since each table for two can seat 2 people and each table for four can seat 4 people, the total number of people that can be seated is 2x + 4y. The owner of the restaurant wants to seat a total of 120 people, so the equation that represents this situation is 2x + 4y = 120.
In this equation, x and y are the variables. The x value represents the number of tables for two and the y value represents the number of tables for four.
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Can someone actually answer this question please QUICK
A+b=c>4
b=7
a= 2
what is c?
Answers
Answer:
9
Step-by-step explanation:
The value of c is found by adding a (2) and b (7) together, which equals 9.
Explanation:The question a + b = c is asking for the value of c when a is 2 and b is 7. To find c, we simply add the values of a and b together. In mathematics, this is known as solving for the unknown variable.
In this case:
a + b = c
2 + 7 = c
c = 9
Therefore, the value of c when a is 2 and b is 7 is 9.
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y = 3x - 1
12x – 4y = 12
Answers
Answer:
8 and 23
Step-by-step explanation:
let the 1st equation be i and 2nd be ii
now putting the value of x in eqn ii, we get
12x -4×(3x-1) = 12
12x-12x+4=12
x=12-4
x=8
again,
y=3×8-1
y=23
Which graph best represents the function f(x) = (x - 1)(x + 3)(x – 3)?
Answers
Answer:
The graph you posted was Incorrect! An easy way you can check is like this:
Insert the function "f(x) = (x - 1)(x + 3)(x – 3)" into desmos, you get this which should perfectly match the function shown.
The graph that represents the function is attached to the answer.
What is a Graph?The graph is a mathematical representation of the relation between two objects.
It helps in determining the function that fits best for the data obtained.
A function is a mathematical statement that defines a relationship between a dependent and an independent variable.
A function always has a defined range and domain, domain is all the value a function can have as input and range is all the value that a function can give as output.
The function is f(x) = (x-1)(x+3)(x-3)
The graph for the function will be determined by plotting,
The graph is plotted and attached with the answer.
The parent function is a cubic function, which is also plotted along with the function graph.
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A carpenter charges $30 per hour for up to eight hours each day and increases this rate by 50% for additional hours. The carpenter will not work more than ten hours per day. If this daily cost function is modeled by y = f(x) and graphed, which statement is not correct?
A) f(0) = 0, f(8) = 240, and f(10) = 330.
B) The domain is [0, 10] and the range is [0, 330].
C) The graph is increasing on the interval (8, 10) with a slope of 45.
D) If a $20 trip charge is added, the new x-intercept will be (20, 0).
Answers
Answer:
D. If 20$ a trip charge is added, the new x-intercept will be (20,0)
This statement is false. The original graph started at (0,0), the x-intercept. Adding a 20$ trip charge moves the graph up 20 so there would not be an x-intercept.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Haley wrote the expression 24m – 6n. Kensi wrote an expression equivalent to Haley’s. Which expression could Kensi have written? 2(6m – 4n) 4(6m – 6n) 6(4m – n) 12(2m – 2n)
Answers
Answer:
C) 6(4m-n)
Step-by-step explanation:
Because 6(4m-n)=24m-6n.
Supposed charity received a donation of $23.9 million. If this represents 54% of the charity donated funds what is the total amount of its donated funds? round your answer to the nearest million dollars.
Answers
Total amount of funds is $44.26 million.
Step-by-step explanation:
Given,
Donation received = $23.9 million
As it represents 54% of charity.
Let,
Total amount = x
Therefore,
54% of x = 23.9 million
[tex]\frac{54}{100}*x=23.9\\0.54x=23.9[/tex]
Dividing both sides by 0.54
[tex]\frac{0.54x}{0.54}=\frac{23.9}{0.54}\\x=\$44.26\ millions[/tex]
Total amount of funds is $44.26 million.
Keywords: percentage, division
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Given the equation square root of quantity 3x plus 6 end quantity equals 3, solve for x and identify if it is an extraneous solution. 1; solution is extraneous 1; solution is not extraneous 3; solution is extraneous 3; solution is not extraneous
Answers
Answer:
1; solution is not extraneous
Step-by-step explanation:
the value 3=3 is true, meaning its not extraneous and also I got it correct on the test
The value of x is 1, and the solution is not extraneous.
Given that,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
We have to determine,
The value of x and identify if it is an extraneous solution.
According to the question,
Equation; [tex]\sqrt{3x+6 } = 3[/tex]
To find the value of the x following all the steps given below.
Squaring both the sides to solve the equation,
[tex]\sqrt{3x+6 } = 3\\\\(\sqrt{3x + 6 })^2= 3^2\\\\3x + 6 = 9\\\\3x = 9-6\\\\3x = 3\\\\x = \dfrac{1}{1}\\\\x = 1[/tex]
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, The solution is not extraneous.
Hence, The value of x is 1, and the solution is not extraneous.
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What is CD?
6 units
12 units
18 units
24 units
Answers
Answer: 18 units
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
6 times 2 = 12
12+6=18
Choose a system of equations with the same solution as the following system:
6x + 2y = −6
3x − 4y = −18
---------------------
A: 8x + 4y = −4
17x + 2y = −28
B: 12x + 4y = 12
21x + 2y = −36
C: 6x + 8y = −36
15x + 6y = −60
D: 6x + y = 15
15x − y = −9
Answers
Answer
______________
The same solution of the given system of equations will be same as the solution of below system of equations;
⇒ 8x + 4y = −4
17x + 2y = −28
Option A is true.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The System of equation is,
6x + 2y = - 6 ..(i)
3x - 4y = - 18 ..(ii)
Now,
Solve the given system of equation as;
The System of equation is,
6x + 2y = - 6 ..(i)
3x - 4y = - 18 ..(ii)
By equation (i);
6x + 2y = - 6
2(3x + y) = - 6
3x + y = - 3 ..(iii)
Subtract equation (ii) from (iii), we get;
3x - 4y - (3x + y) = - 18 - (-3)
3x - 4y - 3x - y = - 18 + 3
- 5y = - 15
y = 3
And, By equation (i), we get;
6x + 2y = - 6
6x + 2 × 3 = - 6
6x + 6 = - 6
6x = - 6 - 6
6x = - 12
x = - 2
Thus, The solution of given system of equation are;
x = - 2 and y = 3
Now,
Substitute the value of x and y in all the given options and find the same solution of given system of equation as;
A: 8x + 4y = −4
17x + 2y = −28
Substitute the value of x = - 2 and y = 3;
8x + 4y = −4
8 × - 2 + 4 × 3 = - 4
- 16 + 12 = - 4
- 4 = - 4
17x + 2y = −28
17 × - 2 + 2 × 3 = - 28
- 34 + 6 = - 28
- 28 = - 28
Thus, This system of equation has same solution.
Therefore, The same solution of the given system of equations will be same as the solution of below system of equations;
⇒ 8x + 4y = −4
17x + 2y = −28
Option A is true.
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-3x+12y=24 What is the Y intercept
Answers
Answer:
(0,2)
Step-by-step explanation:
y-intercept: when x = 0
-3(0) + 12y = 24
12y = 24
y = 2
12. What is the equation of a line perpendicular to the x-axis that passes through the point (-2,-4)? What is the slope of
this line?
what answer?
Answers
Answer: the vertical line with the equation "x=-2"
Step-by-step explanation:
if you are perpendicular to the x axis, you will be looking for vertical lines that pass through (-2,-4)
the vertical line with the equation "x=-2" will pass though the point because (-2,-4) has an x coordinate of -2
Help!!
Kerry has a bag containing white and yellow marbles. Kerry randomly selects one marble from the bag, records the result, and returns the marble to the bag. The results of the first 65 selections are shown below.
- A white marble was selected 41 times
- A yellow marble was selected 24 times.
Based on these results what is the probability that the next marble Kerry selects will be white?
A. 41%
B. 50%
C. 59%
D. 63%
Answers
The probability that the next marble Kerry selects will be white is; D: 63%
Probability of Selection
The results of Kerry randomly selecting one marble from the bag out of 65 selections are;
White marble = 41Yellow Marble = 24Now, these numbers of marbles represents the amount of times the respective colors are gotten for every 65 selections. Thus;
P(next marble that Kerry selects will be white) = 41/65 * 100
P(next marble that Kerry selects will be white) ≈ 63%
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Each gift bag has to contain atleast 15 candies and/or chocolate was total worth must not exceed 30 dollars. Each candy costs 1 dollar while each chocolate costs 3 dollars.
a. Write a system of inequalities that shows the various ways candies and chocolates can be combined in the bag.
b. Graph.
c. Write 3 possible combinations of candies & chocolates that can be placed in the bag.
Answers
Answer:
the answer is b
In the world balloons the ratio of wolves to consonant is
Answers
Answer:
The ratio of consonants to is 4:3. 4 consonants and 3 wolves.
the ratio of potatoes to turnips is 1:1 if there are are 473 potatoes how many turnips are there
Answers
Answer:
473 turnips
Step-by-step explanation:
well if its 1 to 1 that means how ever meany you have of one you will have the same exact amount of the other food
473x1 = 473x1
Final answer:
To find the number of turnips, set up a proportion using the given ratio and cross multiply to solve for the number of turnips.
Explanation:
To find the number of turnips, we can set up a proportion using the given ratio:
Number of potatoes / Number of turnips = Ratio of potatoes to turnips.
Since the ratio of potatoes to turnips is 1:1, the proportion will be:
473 / Number of turnips = 1 / 1.
To solve for the number of turnips, cross multiply:
473 * 1 = Number of turnips * 1.
Number of turnips = 473.
Therefore, there are 473 turnips in this scenario.
F(x)= 5x^2+6, g(x)= 7x find (f o g)(x), find (g o f)(x), find f(g(-4)), fine g(f(5))
Answers
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x^2+6\\g(x) = 7x[/tex]
So
[tex](f o g)(x) = 5(7x)^2+6\\= 5(49x^2)+6\\=245x^2+6\\(g o f)(x) = 7(5x^2+6)\\= 35x^2+42\\(fog(x))=245x^2+6f(g(-4)) = 245(-4)^2+6 \\=245(16)+6\\=3920+6\\=3926\\g(f(x)) = 35x^2+42\\g(f(5)) = 35(5)^2+42\\=35(25)+42\\=875+42\\=917[/tex]
Hence,
[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]
Keywords: functions, Function composition
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Consider this function. f(x) = 2x - 2 Which graph represents the inverse of function f?
Answers
Answer:
W
Step-by-step explanation:
If its the graphs I got then yeah
The Graph that represents the inverse of function f is attached below.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
We have been given a function of x as; f(x) = 2x - 2
If function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
y = 2x - 2
x = 2y - 2
x + 2 = 2y
y = (x + 2)/2
It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f' function here.
To Graph the inverse, Simply use a graphing calculator and the correct graph is attached below.
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a first plus twice a second number is one. twice the first number plus the second totals fourteen.
Answers
Answer:
First Number = 9
Second Number = -4
Step-by-step explanation:
Let the first number be "x" and the 2nd number be "y"
First number PLUS twice 2nd is 1, so we can write:
x + 2 y = 1
Twice First number PLUS the 2nd number is 14, so we can write:
2x + y = 14
We can write:
y = 14 - 2x
We put this into 1st equation and solve for x:
x + 2y = 1
x + 2(14 - 2x) = 1
x + 28 - 4x = 1
-3x = -27
x = 9
And now y:
y = 14 - 2(x)
y = 14 -2(9)
y = 14 - 18
y = -4
First Number = 9
Second Number = -4