What is the value of x?
x =
Answer: The value of x is 2 units.
Explanation:
Since we have given that
AB and CD are two chords that are intersected externally at point E.
As we know the relation regarding the above i.e.
[tex]EA\times EB=EC\times ED[/tex]
Here,
EB=x+1
EA=x+1+11 = (x+12)
EC=x+4
ED=x+4+1 = (x+5)
Now, we put the values in the relation given above :
[tex](x+1)(x+12)=(x+4)(x+5)\\\\x^2+13x+12=x^2+9x+20\\\\12+13x=20+9x\\\\13x-9x=20-12\\\\4x=8\\\\x=\frac{8}{4}=2\\\\x=2\ units[/tex]
Hence, the value of x is 2 units.
Answer:
x = 2 is the answer.
Step-by-step explanation:
When two chords AE and ED are drawn from an external point E to a circle then by theorem we know the relation
AE×BE = DE×CE
AE = x + 1 + 11 = x + 12
BE = x + 1
CE = x + 4
DE = x + 4 + 1 = x + 5
Now putting these values in the formula
(x + 12)(x + 1) = (x + 4)(x + 5)
x² + 12x + x + 12 = x² + 5x + 4x + 20
13x + 12 = 9x + 20
13x - 9x = 20 - 12
4x = 8
x = 2
x = 2 is the answer.
HELPPPPPPPPPPPP ASAP!!!!!!!!!!
(30 points) Enter numbers to write 0.000328 in scientific notation.
what is 67912 to the nearest 10
the last digit is the ones place, if it is 5 or higher you would round up
under 5 you round down
so to the nearest 10 the number would be 67910
Brian is waiting at a park across the street from the hockey arena for his dad to pick him up. It rained most of the morning, and the streets still have puddles. At which point should Brian stand to be as far as possible from each street to avoid getting splashed? Explain your answer.
To avoid getting splashed from puddles on the street, Brian should stand in the middle of the park. This would distance him completely from the immediate spray zone of passing vehicles, like being further away from the shore reduces the impact of sprays from waves.
Explanation:To avoid getting splashed by cars driving through the puddles, Brian should stand in the middle of the park. By doing so, he establishes the maximum possible distance between himself and any part of the street. Staying as far away from the streets reduces the risk of any water reaching him when cars pass by.
Think of it like Jill delivering her flyers and retracing her steps: the farthest spot from her house during her journey was at the midpoint of her travel route.
Also consider Peter's driving scenario: The farther he is from other cars, the less likely he is to get affected by their maneuvers. In a similar way, Brian, being in the middle of the park would keep him away from the splash zone of passing cars.
Lastly, akin to Julian and his father on their surfboards, being away from the impact point of the waves (which is near the shore) they get least affected by the spray. This analogy can be compared to Brian's situation with the puddles.
Learn more about Maximizing Distance here:https://brainly.com/question/32250758
#SPJ11
every evening jenna empties her pockets and puts the changein a jar. at the end of the week she had 50 coins, all of them dimes and quarters. when she added them up, she had a totals of $10.25
d=number of dimes q=number of quarters
how many dimes did jenna have?
Which is a factor of 54xy + 45x + 18y + 15?
James is four years younger than Austin. If 2 times James age is increased by the square of austins age, the result is 28. Find the 2 ages. Use an algebraic solution
Solve this quadratic equation. x ^2 + 2x - 22 = 0
Answer:
[tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
Step-by-step explanation:
Roots of quadratic equations [tex]ax^{2}+bx+c=0[/tex] calculated as:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
First, compare [tex]ax^{2}+bx+c=0[/tex] with [tex]x^{2}+2x-22=0[/tex]
here a = 1 , b = 2 and c = -22
Now, plug the value of a,b and c in [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x=\frac{-2\pm \sqrt{2^{2}-4(1)(-22)}}{2(1)}[/tex]
[tex]x=\frac{-2\pm \sqrt{4+88}}{2}[/tex]
[tex]x=\frac{-2\pm \sqrt{92}}{2}[/tex]
[tex]x=\frac{-2\pm 2\sqrt{23}}{2}[/tex]
[tex]x=-1\pm \sqrt{23}[/tex]
Hence, [tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
The distance of saturn from the sun is 1507 million kilometers express this distance in standard form
Conjectures can always be proven true.
True or False
.help me with this please
Anderson has $50 in his savings account. He deposits $5 every week. His father also deposits $20 into the account every time Anderson mows the lawn. His savings account balance can be shown with the following expression:
50 + 5w + 20m
Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)
Part B: If Anderson saves for 10 weeks and mows the lawn 2 times, how much will he have in his account? Show your work to receive full credit. (4 points)
Part C: If Anderson had $85 in his savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)
We are given the equation of the savings (s) as:
s = 50 + 5 w + 20 m
Part A.
Coefficient = 5 and 20
Variable = w and m
Constant = 50
Part B.
w = 10
m = 2
Therefore the total savings is:
s = 50 + 5 (10) + 20 (2)
s = $140
Part C.
The coefficient and the constant values are considered as fixed value because they do not change. Therefore only the variable value would change, however the expression 50 + 5 w + 20 m would still be the same. That is only the values of the variable change.
In which expression should the exponents be multiplied?
a. (5^3)-4
b. (1/3)^4*(1/3)^7
c. 3^7/3^15
d. 4^5*4^2
Option b is the correct answer. Exponents should be multiplied in the expression (1/3)^4*(1/3)^7, resulting in (1/3)^11.
The expression where the exponents should be multiplied is Option b. (1/3)^4*(1/3)^7. This is because when you multiply two expressions that have the same base, you add their exponents. In this case, you have the base (1/3) raised to the 4th power and then to the 7th power, so you add the exponents 4 + 7, which equals 11. Therefore, (1/3)^4*(1/3)^7 simplifies to (1/3)^11.
Another case where you multiply exponents would be when raising a power to another power, like in (5^3)^4. Here the exponents 3 and 4 are multiplied, resulting in (5^12).
Perform the operation(s) and write the answer in simplest from.
2 2/5+3 1/4
A.)5 1/3
B.)25/9
C.)5 13/20
D.)12 5/9
A cell phone company charges a basic rate of $19.99 per month for 300 minutes of local usage. Any local usage over 300 minutes is charged at $.10 per minute. All long distance calls are charged at $.25 per minute. Write and simplify an expression that gives the total monthly bill if x is the number of local minutes and y is the number of long distance minutes. Evaluate the expression if local usage totals 375 minutes and long distance usage totals 54 minutes.
total = 19.99 + 0.10(x-300) + 0.25y
x = 375
y=54
total = 19.99 +0.10(375-300) +0.25(54)
total = 19.99 + 0.10(75) + 0.25(54)
total = 19.99 + 7.50 + 13.50
total = $40.99
The total monthly bill is $40.99 for 375 local minutes and 54 long distance minutes, given the cell phone company's rates.
The total monthly bill can be expressed as the sum of the basic rate, the extra charge for local minutes beyond the included 300, and the charge for all long distance minutes. The expression can be written as:
Total Monthly Bill = Basic Rate + (Local Extra Charge x Extra Local Minutes) + (Long Distance Rate x Long Distance Minutes)
Where:
Basic Rate = $19.99Local Extra Charge = $0.10 per minuteExtra Local Minutes = x - 300 (only if x > 300)Long Distance Rate = $0.25 per minuteLong Distance Minutes = yFor x = 375 local minutes and y = 54 long distance minutes, the total monthly bill is calculated as follows:
Total Monthly Bill = $19.99 + ($0.10 x (375 - 300)) + ($0.25 x 54)
Total Monthly Bill = $19.99 + $7.50 + $13.50
Total Monthly Bill = $40.99
If the following object is translated right two units and down three units. Where will the translation be located?
Copy and complete the table on the previous page into a Word document. Title your journal "Pythagorean Theorem". Discuss any relationships you see in the table? Then, look at the equation below and calculate whether a2 + b2 is >, <, or = to c2 based on the numbers you recorded in your table.
I attached the chart (in blue) and the assignment! Can someone please help, I don't understand!
Solve 2x2 + 20x = −38.
a. −5 ± square root 14
b.−5 ± square root 51
c. −5 ±square root 6
d.−5 ± square root 13
Answer:
c
Step-by-step explanation:
−5 ±square root 6
How many roots does y+x^2-6x+9 have?
A. One
B. Two
C. Zero
D. Three
recursive function f(n+1)=1/3 f(n) if f (3)=9 what is f(1)
(6.04)The scatter plot shows the relationship between the number of hours spent jogging and the number of minutes spent stretching, by the students on a track team:
What is the y-intercept of the line of best fit and what does it represent?
1 minute; the number of minutes students stretch when they do not jog
1 hour; the number of hours students jog when they do not stretch
4 hours; the number of hours students jog when they do not stretch
4 minutes; the number of minutes students stretch when they do not jog
How do you convert .444444444 to a fraction?
Vanessa typically works 8 hours per day in a normal 5 day work week. last week, however, vanessa had to take 90 minutes off on tuesday, 45 minutes off on thursday, and she left two and a half hours early on friday. how many hours did vanessa work last week?
The total number of hours Vanessa work in a week is:
total work hours = (8 hours / day) * 5 day / week
total work hours = 40 hours per week
The total number of hours she did not work:
total hours did not work = (90 minutes)(1 hour / 60 minutes) + (45 minutes)(1 hour / 60 minutes) + 2.5 hours
total hours did not work = 4.75 hours
The amount of hours Vanessa work last week can be calculated using the formula:
work hours = total work hours - total hours did not work
work hours = 40 hours – 4.75 hours
work hours = 35.25 hours
How do you simplify squats roots
Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281
Final answer:
To find the nth term equation of an arithmetic sequence, we first determined the common difference to be 92 by given terms, and then found the first term by using the formula for arithmetic sequences. The nth term equation for the sequence is: an = -1489 + (n-1)(92).
Explanation:
To find the nth term equation of the arithmetic sequence, we need to determine the common difference and the first term of the sequence. Since we know the 18th term, a18 = 97, and the 20th term, a20 = 281, we can find the common difference, d, by subtracting the two given terms and dividing by the number of terms between them:
d = (281 - 97) / (20 - 18) = 184 / 2 = 92.
Once we have the common difference, we can use the following formula to find the first term (a1):
an = a1 + (n-1)d.
Let's substitute n = 18 and d = 92 into the formula:
97 = a1 + (18-1)(92)
a1 = 97 - (17)(92) = -1489.
Now we can write the equation for the nth term of the arithmetic sequence:
an = -1489 + (n-1)(92).
Submit a positive integer. the winner is the person who submits the lowest number that isn't submitted by anyone else.
You are given the mass of CaH₂ which is 14 grams and H₂O which is 28 grams. You are required to find the maximum volume of H₂ gas at STP. The balanced chemical reaction is CaH₂ + 2H₂O → Ca(OH)₂ + H₂. Note that for every one mole of CaH₂, 2 moles of H₂O is needed to completely react and produce Ca(OH)₂ + H₂. So the CaH₂ and H₂O are at equal proportions. At STP, temperature is at 0°C(273K) and pressure at 1 atm. The molar mass of CaH₂ is 42 grams per mole.
14g CaH₂(1mol CaH₂/42 grams CaH₂)(1mol H₂/1mol CaH₂) = 0.333 moles H2
The ideal gas equation is PV = nRT, with R(gas constant) = 0.08206 L-atm/mol-K. get the equation for volume, we have
V = nRT/P
V = (0.333mol H₂)(0.08206 L-atm/mol-K)(273K)/1atm
V = 7.47L
The answer is a positive integer.
Let $s$ be the set of points with polar coordinates $(r,\theta)$ such that $ 2 \le r \le 6$ and $\frac{\pi}{3} \le \theta \le \frac{5 \pi}{6} $. find the area of $s$.
which one of the following sets of numbers represents the lengths of the sides of a right triangle ?
a. 13 35 37
b. 6 9 10
c. 5 12 13
d. 9 40 42
5, 12, 13 are the sides representing lengths of sides of a right triangle.
What is Pythagoras theorem?The theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Given that, lengths of sides of triangles.
If a triangle is a right triangle, then it should follow Pythagoras theorem,
Using Pythagoras theorem,
13² = 169
12² + 5² = 144 + 25 = 169
Therefore, 13² = 12² + 5² is following Pythagoras theorem.
Hence, 5, 12, 13 are the sides representing lengths of sides of a right triangle
For more references on Pythagoras theorem, click;
https://brainly.com/question/343682
#SPJ2
A box with a square base and open top must have a volume of 32,000 cm3. find the dimensions of the box that mini- mize the amount of material used.