Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below: A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line. The length of AD is equal to 4, the length of DB is equal to 5, the length of AE is equal to 6 and the length of EC is equal to 7. She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption? 4:9 ≠ 6:13 4:9 ≠ 6:7 4:13 ≠ 6:9 4:5 ≠ 6:13
Answers
Please see attached file for the triangle’s figure:
Going with the image attached, if DE is parallel to BC
then
4: (4 + 5) = 6 : (6 + 7).
Therefore, the inequality that she will use to contradict the assumption
is 4:9 ≠ 6:13.
To add, a relation that holds
between two values when they are different in mathematics is called an inequality. A is not equal to b also means the notation a ≠ b.
Inequalities are governed by the following properties:
Transitivity
Converse
Addition and subtraction
Multiplication and division
Additive inverse
Multiplicative inverse
Applying a function to both sides
Answer:
4:9 ≠ 6:13.
Step-by-step explanation:
Related Questions
How to find the x intersept
Answers
For problem 22, the x intercept is the point (-4,0) as this is where the S shaped curve crosses through the horizontal x axis. See the attached diagram for a visual of what I'm talking about. Note the highlighted point in red.
The diffrence between a term and
coefficient
Answers
- A coefficient tells you how many times to multiply a variable.
· Ex: 4xy = Coefficient: 4
- A term is each of the numbers in an equation, ratio, etc.
· Ex: 5x + 7y + (4x - 4y) + 2 = Terms: 5x, 7y, (4x - 4y), and 2
I am 99.9% sure this is the correct answer, but if it isn't I am truly sorry, and please forgive me.
Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 4 - (x - 6)^2 ??
Answers
g(x)=4-(x-6)^2
g(x)=4-(x^2-12x+36)
g(x)=4-x^2+12x-36
g(x)=-x^2+12x-32
dg/dx=-2x+12
So g(x) will be increasing when dg/dx>0
-2x+12>0
-2x>-12
x<6
So g(x) is increasing on the interval (-oo, 6)
g(x) will be decreasing when dg/dx<0
-2x+12<0
-2x<-12
x>6
So g(x) will be decreasing on the interval (6, +oo)
The local theater has three types of seats for broadway plays: main floor, balcony, and mezzanine. main floor tickets are $59, balcony tickets are $50, and mezzanine tickets are $40. one particular night, sales totaled $73,785. there were 435 more main floor tickets sold than balcony and mezzanine tickets combined. the number of balcony tickets sold is 78 more than 33 times the number of mezzanine tickets sold. how many of each type of ticket were sold?
Answers
Final answer:
10 mezzanine tickets, 408 balcony tickets, and 853 main floor tickets were sold.
Explanation:
Let's solve this problem step-by-step to find out how many of each type of ticket were sold:
Let's assume that the number of mezzanine tickets sold is x. Therefore, the number of balcony tickets sold is 33x + 78 (since it is 78 more than 33 times the number of mezzanine tickets sold).
The number of main floor tickets sold is 435 + (33x + 78) + x = 435 + 34x + 78 = 34x + 513 (since there were 435 more main floor tickets sold than balcony and mezzanine tickets combined).
The total sales amount is $73,785.
Now, we can set up an equation to solve for x:
$40x + $50(33x + 78) + $59(34x + 513) = $73,785
Simplifying the equation:
40x + 1650x + 3900 + 59(34x + 513) = 73785
40x + 1650x + 3900 + 2006x + 30567 = 73785
3696x + 34467 = 73785
3696x = 39318
x = 39318/3696
x = 10.65
Since we can't have a fraction of a ticket, we can round down to the nearest whole number. So, x = 10.
Therefore, 10 mezzanine tickets were sold, 33x + 78 = 408 balcony tickets were sold, and 34x + 513 = 853 main floor tickets were sold.
Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans. Plan A: Raise the price by $0.05 each week until the price reaches $8.00. Plan B: Raise the price by 10 percent each week until the price reaches $8.00. Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00. Plan D: Raise the price by $0.25 each week until the price reaches $8.00. Which plan will result in the price of the bagels reaching $8.00 fastest? plan A plan B plan C
Answers
Hope This Helps
Correct If I'm Wrong
Answer:
Plan B is correct answer.
Step-by-step explanation:
Raise the price by 10 percent each week until the price reaches $8.00.
Week 1. Starting price $5
[tex]0.1\times5=0.5[/tex]
price becomes = [tex]5+0.5=5.5[/tex]
Week 2.
[tex]0.1\times5.5=0.55[/tex]
Price becomes = [tex]5.5+0.55=6.05[/tex]
Week 3.
[tex]0.1\times6.05=0.605[/tex]
Price become = [tex]6.05+0.605=6.655[/tex]
Week 4.
[tex]0.1\times6.655=0.6655[/tex]
Price becomes = [tex]6.655+0.6655=7.320[/tex]
Week 5.
[tex]0.1\times7.320=0.732[/tex]
Price becomes = [tex]7.320+0.732=8.052[/tex]
So, we can see that in 5 weeks the price becomes $8 from $5. Therefore, plan B is the best plan.
Tell which equation you would use to isolate a variable in order to solve the system using substitution. Explain your reasoning.
2x + y=-10
3x-y=0
Answers
Multiply both side by 3
2x*3+y*3=-10*3
6x+3y=-30
3x-y=0
Multiply both side by 2
3x*2-y*2=0*2
6x-2y=0
Next, use substitute property
6x+3y=-30
-
6x-2y=0
=
y=-30
3x-y=0
Substitute y with -30
3x-30=0
Add 30 to each side
3x-30+30=0+30
3x=30
Divided both side by 3
3x/3=30/3
x=10, so the solution pair is (10,-30). In this case, there is the first way to solve these two equation.
Then, I would use equation 3x+1.5y=-15 in this question by multiply 2x+y=-10 by multiplying both side by 3/2 to eliminate x and to solve variables for y. Hope it help!
last question
help me pls c:
Answers
Consider the relation y = 4|x + 2| + 7. What are the coordinates of the vertex?
(7, −2)
(2, 7)
(4, −2)
(−2, 7)
Answers
x + 2 = 0
Then, we solve for the value of x.
x + 2 - 2 = 0 - 2
Hence, the value of x from the equation above is equal to -2.
Then, substitute the value of x to the equation and drop the absolute value symbol.
y = 4(x + 2) + 7
Substituting,
y = 4(-2 + 2) + 7
y = 4(0) + 7
y = 7
Thus, the vertex of the absolute value equation is equal to (-2,7). The answer is the last choice.
What is the answer? (Tip- to undo multiply both sides by 4/7)
x|4/7 = 28
Answers
x / |4/7| = 28
Multiply by |4/7|
x = |4/7| x 28
Ignore the absolute for a second and note 4/7 x 28 is 16 because...
28 / 7 = 4
4 x 4 = 16
x = |16|
The length of a rectangle is 2 yd longer than its width. if the perimeter of the rectangle is 40 yd , find its area.
Answers
perimeter = 2L+2W
L=2+w
40 = 2L+2W
40= 2(2+w)+2W
40=4+2w+2w
36=4w
w=9
L=9+2=11
2(9) = 18, 2(11) = 22, 22+18 = 40
L=11
W=9
Area = L x w
area = 11x9= 99 square yards
[tex] \frac{x}{5}+\frac{3x}{15}=\frac{2x}{3} } [/tex]+2 Answer plz math help
Answers
3x+3x= 10x+30
Combine like terms
6x=10x+30
Subtract 10x from both sides
-4x=30
Divide both sides by -4
x= -7.5
Final answer: -7.5
Find the surface area of a sphere with a volume of 36π in3.
SHOW WORK
will give medals and mark brainliest
its 113.10 inches squared
Answers
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
[tex]r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
[tex]r=\sqrt[3]{\frac{3(36\pi)}{4\pi}}[/tex]
[tex]r=\sqrt[3]{27}[/tex]
[tex]r=3[/tex]
Then use the radius to get the surface area:
[tex]A_{surf}=4 \pi r^{2}[/tex]
[tex]A_{surf}=4 \pi 3^{2}[/tex]
[tex]A_{surf}=4 \pi 9[/tex]
[tex]A_{surf}=36\pi\approx113.09[/tex]
To find the surface area of a sphere given the volume, first solve for the radius using the volume formula (4/3πr³). In this case, the radius is 3. Then, use the surface area formula (4πr²), which gives the surface area as 36π square inches, or an approximate value of 113.10 square inches.
Explanation:The volume of a sphere is given by the formula V = 4/3 * π * r³. First, we need to find the radius of the sphere. Set the volume of the sphere (36π in³) equal to the volume formula and solve for r:
36π = 4/3πr³
From this, we find that r = 3. Now, we use the radius to find the surface area with the formula A = 4πr²:
A = 4π * 3² = 36π in²
So, the surface area of a sphere with a volume of 36π in³ is 36π square inches or approximately 113.10 square inches.
Learn more about Surface Area of Sphere here:https://brainly.com/question/31756500
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can you help me????????
Answers
now, if AC is that much, recall, BD is the midsegment, thus AB = BC, so AB is just one of the equal halves of AC, so, AB is AC/2.
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
(−5, 2)
(5, −2)
(−5, −2)
(5, 2)
Answers
Answer: Second option : (5, −2)
Step-by-step explanation: Given system of inequalities
y ≤ x − 5
y ≥ −x − 4
Plugging x=5 and y=-2 in first inequality
-2 ≤ 5 − 5
-2 ≤ 0 : True.
Plugging x=5 and y=-2 in second inequality
-2 ≥ −5 − 4
-2 ≥ -9 : Also true.
Point (5, −2) satisfied both of the given inequalities in the system.
Therefore, (5,-2) is correct option.
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours). Which is an appropriate range for this situation?
Answers
The appropriate range for John's distance in miles (d) during the marathon is A. [tex]$0 \leq d \leq 26.2$[/tex].
In a marathon, the distance (d) John covers depends on the time (t) he spends running. The distance is fixed at 26.2 miles, so we need to find the appropriate range for the time (t) he spends running.
Let's calculate John's average speed (v) during the marathon. We know that speed is given by:
[tex]\[ v = \frac{d}{t} \][/tex]
Where:
- v = average speed (miles per hour)
- d = distance covered (miles)
- t = time spent running (hours)
Given that John's distance is 26.2 miles, and the marathon covers this distance, we have:
[tex]\[ 26.2 = \frac{26.2}{t} \][/tex]
Solving for t:
[tex]\[ t = \frac{26.2}{26.2} = 1 \][/tex]
So, John takes 1 hour to cover the 26.2 miles.
Now, let's consider the maximum and minimum possible times for John to complete the marathon:
- Minimum time: John completes the marathon in the fastest time possible. Let's say this is 0. This implies he runs the marathon in 0 hours.
- Maximum time: John takes his time and completes the marathon at the slowest pace possible. Let's use the average time for a marathon, which is around 4.5 hours.
Thus, the appropriate range for the time (t) is:
[tex]\[ 0 \leq t \leq 4.5 \][/tex]
This corresponds to option C: [tex]$0 \leq t \leq 4.5$[/tex].
Complete Question:
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours) Which is an appropriate range for this situation?
A. [tex]$0 \leq d \leq 26.2$[/tex]
B. [tex]$0 \leq d \leq 4.5$[/tex]
c. [tex]$0 \leq t \leq 4.5$[/tex]
D. [tex]$0 \leq t \leq 26.2$[/tex]
Find PS if ABC=PQR, AD is an altitude of ABC, PS is an altitude of PQR, AD=12, AC=16 and PR=10
a. 7.5
b. 19.2
c. 4.62
d. 19.5
Answers
First you need to find how they're similar.
16/10 = 1.6
Then, multiply 12 (AD) by 1.6 to find PS.
12 * 1.6 = 19.2
The answer is B. 19.2
(05.02)
What is the y-intercept of the line shown?
−1
0
0.5
1
Answers
Determine whether the equation represents y as a function of x 16x-y^4=0
Answers
[tex]16x-y^4=0 \\ \\ \Rightarrow y^4=16x \\ \\ \Rightarrow y= \sqrt[4]{16x} =2 \sqrt[4]{x} [/tex]
For any value of x, there are two possible values of y, thus the equation does not represent y as a function of x.
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
The best approximation for the square root of 10 is.. A).5 B).100 C).3.1 D).25
Answers
Answer:
It is approximately 3.1
Step-by-step explanation:
Convert this percent into decimal form.
Answers
Then move the decimal place two places to the left to divide by 100 (percent means per 100),
Final answer: 0.1225
what is the inverse of the function f(x)=1/9x+2
Answers
y = 1/9x + 2,
you should swap the places of x and y and find y again, in this case it will be
x = 1/9y + 2 => x-2 = 1/9y => (x-2) * 9y = 1 => 9y = 1/(x-2)
and finally we got y = [tex] \frac{1}{(x-2)*9} [/tex]
Cost to rent a bicycle is $5 plus $3 per hour for x hours what equation represents the total cost for c hours
Answers
Hope I helped :)
A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?
Answers
A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?
Answer: 1/25
Answer:
The answer would be 1/25 Hopefully this any T4L students!
Conditional probabilities are based on some event occurring given that something else has already occurred?
Answers
The answer is true. A conditional probability is a measure of the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A in the condition B", is usually written as P (A|B). The conditional probability of A given B is well-defined as the quotient of the probability of the joint of events A and B, and the probability of B.
Which of the following is a solution of x2 + 4x + 10?
2 + i times the square root of 6
−2 + i times the square root of 24
−2 + i times the square root of 6
2 + i times the square root of 24
Answers
x^2+4x=-10
x^2+4x+4=-6
(x+2)^2=-6
x+2=±i√6
x=-2±i√6
So the correct answer is the third one down from the top.
Answer:
[tex]x=2+-i \sqrt{6}[/tex]
Step-by-step explanation:
[tex]x^2 + 4x + 10[/tex]
To find out the solution we set the expression =0 and solve for x
[tex]x^2 + 4x + 10=0[/tex]
Apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=1, b=4, c=10 plug in the values in the formula
[tex]x=\frac{-4+-\sqrt{4^2-4(1)(10)}}{2a}[/tex]
[tex]x=\frac{-4+-\sqrt{-24}}{2(1)}[/tex]
The value of square root (-1) is 'i'
[tex]x=\frac{-4+-2i\sqrt{6}}{2}[/tex]
Divide each term by 2
[tex]x=2+-i\sqrt{6}[/tex]
Which function below is the inverse of f(x) = The quantity of four x minus three, over two.?
Answers
Given f(x) = x2 + 4x − 1 and g(x) = 5x − 7, identify (fg)(x).
Answers
(fg)(x) = (x^2 + 4x − 1)(5x − 7)
(fg)(x) = 5x^3 + 20x^2 - 5x - 7x^2 - 28x + 7
(fg)(x) = 5x^3 + 13x^2 - 33x + 7
answer is C. third choice
(fg)(x) = 5x^3 + 13x^2 - 33x + 7
The product of the functions[tex]\( f(x) = x^2 + 4x - 1 \) and \( g(x) = 5x - 7 \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
To find the product[tex]\( (f \cdot g)(x) \)[/tex], where [tex]\( f(x) = x^2 + 4x - 1 \)[/tex] and [tex]\( g(x) = 5x - 7 \),[/tex]we need to perform the multiplication of these two functions.
Start by expanding [tex]\( f(x) \cdot g(x) \):[/tex]
1. Write down ( f(x) ):
[tex]\[ f(x) = x^2 + 4x - 1 \][/tex]
2. Write down ( g(x) ):
[tex]\[ g(x) = 5x - 7 \][/tex]
3. Perform the multiplication [tex]\( f(x) \cdot g(x) \)[/tex]:
[tex]\[ f(x) \cdot g(x) = (x^2 + 4x - 1)(5x - 7) \][/tex]
4. Distribute [tex]\( x^2 + 4x - 1 \)[/tex] across ( 5x - 7 ):
[tex]\[ f(x) \cdot g(x) = x^2 \cdot (5x - 7) + 4x \cdot (5x - 7) - 1 \cdot (5x - 7) \][/tex]
5. Perform the multiplications:
[tex]\[ x^2 \cdot (5x - 7) = 5x^3 - 7x^2 \][/tex]
[tex]\[ 4x \cdot (5x - 7) = 20x^2 - 28x \][/tex]
[tex]\[ -1 \cdot (5x - 7) = -5x + 7 \][/tex]
6. Combine all the terms:
[tex]\[ f(x) \cdot g(x) = 5x^3 - 7x^2 + 20x^2 - 28x - 5x + 7 \][/tex]
7. Simplify by combining like terms:
[tex]\[ f(x) \cdot g(x) = 5x^3 + (20x^2 - 7x^2) + (-28x - 5x) + 7 \][/tex]
[tex]\[ f(x) \cdot g(x) = 5x^3 + 13x^2 - 33x + 7 \][/tex]
Therefore, the product [tex]\( (f \cdot g)(x) \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]
Three cities lie along a perfectly linear route: Springfield, Clarksville, and Allentown. Molly lives in Springfield and works in Allentown. She makes it to work using two gallons of gas in her car. Her friend Edgar lives in Allentown and works in Clarksville. It takes Edgar one gallon of gas to get to work. If Molly's car averages 26 miles per gallon, and Edgar's car averages 17 miles per gallon, about how far apart are Springfield and Clarksville?
Answers
Now, since Molly travelled from Springfield to Allentown, the total distance she covered is the distance Edward travelled and the unknown distance between Springfield and Clarksville, denoted as x in the picture. So, the equation is then
Molly's distance = x + Edgar's distance
26 miles/gal(2 gal) = x + 17 miles/gal(1 gal)
x = 35 miles
99 POINTS!!! Find the equation for an ellipse with vertices at (-6, 0) and (6, 0) and foci at (-4, 0) and (4, 0).
Answers
a>b
a=6, a^2=36
foci=(a^2-b^2)^(1/2)
4=(36-b^2)^(1/2)
16=36-b^2
b^2=36-16
b^2=20
b=2(5)^(1/2) or (20)^(1/2)
1=(x^2/36)+(y^2/20)
(x^2)/a^2+(y^2)/b^2=1
a>b
a=6, a^2=36
foci=(a^2-b^2)^(1/2)
4=(36-b^2)^(1/2)
16=36-b^2
b^2=36-16
b^2=20
b=2(5)^(1/2) or (20)^(1/2)
1=(x^2/36)+(y^2/20)
What is the solution of sqrt 2x + 4 = 16 ? x = 6 x = 72 x = 126 no solution
Answers
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]\sqrt{2x+4}=16[/tex]
We need to find the value of 'x'.
First we squaring the both sides:
[tex](\sqrt{2x+4})^2=16^2\\\\2x+4=256\\\\2x=256-4\\\\2x=252\\\\x=\dfrac{252}{2}\\\\x=126[/tex]
Hence, the value of x is 126.
Therefore, Third option is correct.
Answer:
C on Edge
Step-by-step explanation:
Received a 100% on the quiz.