Answers
The information of ZY = 15 also gives the value of YX. ZY is the radius of the greater circle inside the big circle. So we have that:
\(\text{ZY = YX = 15}\)The radius of the circle that has the center on X (the big one) is the sum of ZY and YX. This value is also equal to UX! Therefore:
\(UX\text{ = ZY + YX = 15+15=30}\)If UX is 30 and the question says that WX is 10, we can find the following equation:
\(UW\text{ + WX = UX}\)Obs: UV = VW (radius of the circle). Then we can find UW using the equation above (UW is the diameter of the circle with center V).
\(30\text{ = UW + 15}\)\(UW\text{ = 30-15 = 15}\)The diameter of a circle is two times the radius. Thus:
\(UW\text{ = 2}\times Radius\)Then the radius of the circle V will be:
\(\text{Radius = }\frac{UW}{2}=\frac{15}{2}=7.5\)Related Questions
a clock chimes once at 1, twice at 2
Answers
Answer:
3 times at 3
Step-by-step explanation:
Graph the linear equation by finding and plotting its intercepts.
x-y=1
Answers
Answer: To graph the linear equation x - y = 1, we can find its intercepts by setting one of the variables to zero and solving for the other.
Step-by-step explanation:
Setting x = 0, we get:
0 - y = 1
Solving for y, we get:
y = -1
So the y-intercept is (0, -1).
Setting y = 0, we get:
x - 0 = 1
Solving for x, we get:
x = 1
So the x-intercept is (1, 0).
Now we can plot the intercepts on a coordinate plane and draw a straight line passing through them:
|
| .
| .
| .
| .
| .
| .
------------------------------------------
| | | | |
-2 -1 0 1 2
Therefore, the graph of the linear equation x - y = 1 is a straight line passing through the points (0, -1) and (1, 0).
Amy and Richard each solved an equation using the quadratic formula.
Amy's Equation and Method
Latex: 4x^2+7x-20=0
4
x
2
+
7
x
−
20
=
0
Step 1: Latex: x=\frac{-7\pm \sqrt{7^2-4(1)(20)}}{2(4)}
x
=
−
7
±
√
7
2
−
4
(
1
)
(
20
)
2
(
4
)
Step 2: Latex: x=\frac{-7\pm \sqrt{49-80}}{8}
x
=
−
7
±
√
49
−
80
8
Step 3: Latex: x=\frac{-7\pm \sqrt{-31}}{8}
x
=
−
7
±
√
−
31
8
Step 4: Latex: x=\frac{-7\pm i\sqrt{31}}{8}
x
=
−
7
±
i
√
31
8
Richard's Equation and Method
Latex: x^2-6x+8=0
x
2
−
6
x
+
8
=
0
Step 1: Latex: x=\frac{6\pm \sqrt{(-6)^2-4(1)(8)}}{2(1)}
x
=
6
±
√
(
−
6
)
2
−
4
(
1
)
(
8
)
2
(
1
)
Step 2: Latex: x=\frac{6\pm \sqrt{36-32}}{2}
x
=
6
±
√
36
−
32
2
Step 3: Latex: x=\frac{6\pm \sqrt{4}}{2}
x
=
6
±
√
4
2
Step 4: Latex: x=\frac{6+\sqrt{4}}{2}
x
=
6
+
√
4
2
and Latex: x=\frac{6-\sqrt{4}}{2}
x
=
6
−
√
4
2
Step 5: Latex: x=\frac{6+2}{2}
x
=
6
+
2
2
and Latex: x=\frac{6-2i}{2}
x
=
6
−
2
i
2
Step 6: Latex: x=4
x
=
4
and Latex: x=3-i
x
=
3
−
i
Both students made a mistake.
Describe the mistake each student made.
Explain what each student needs to do to fix their mistake.
Create your own quadratic equation, and explain how to use the quadratic formula to solve it. Be specific, using Latex: a\textsf{, }b\textsf{,} and Latex: c
c
of your equation and giving the solutions to the equation you chose.
Number your responses from 1 to 3 so your instructor can tell which question you're responding to. You may not receive full credit if your teacher cannot determine that you've answered each question.
Search entries or author
Answers
The mistake each student made and what each student needs to do to fix their mistake is;
Amy didn't include the negative sign for the 20, so she should include itRichard added a negative sign underneath the radicalQuadratic equationx² - 6x + 8 = 0
x = - b ± √b² - 4ac / 2a
where,
a = 1b = -6c = 8x = - b ± √b² - 4ac / 2a
= -(-6) ± √(-6)² - 4(1)(8) / 2(1)
= 6 ± √36 - 32 / 2
= 6 ± √4 / 2
= 6 ± 2 / 2
x = 6/2 + 2/2 or 6/2 - 2/2
= 3 + 1 or 3 - 1
x = 4 or 2
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Point b is at (1,1) on a graph. transformed using matrix A
Answers
In the above scenario, The point that B is transformed to are coordinates (10, 6). This means that it is translated to the right by 9 units and upwards by 5 units.
In order to derive the new location of point B after the transformation by matrix A, we need to perform matrix multiplication of A with the column vector representing point B.
\(\left[\begin{array}{cc}8&2\\7&1\\\end{array}\right]\) = \(\left[\begin{array}{cc}1\\1\\\end{array}\right]\)
\(\left[\begin{array}{cc}(8 * 1) + &(2 *1)\\(7 *1)&(1 *1)\\\end{array}\right]\) = \(\left[\begin{array}{cc}10\\6\\\end{array}\right]\)
As a result, the converted point B is situated at (10, 6). As a result of the transformation provided by matrix A, point B has been translated to the right by 9 units (from x = 1 to x = 10) and upwards by 5 units (from y = 1 to y = 6).
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Explain how to divide 42 by 2 1/3
Answers
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
First, I like to covert 2 1/3 to an improper fraction, 7/3. Then you can do Keep Change Flip. Keep the 42, change divide to multiply and flip 7/3 to 3/7. 42/1 * 3/7 = 18
if jose says that 75% of his class of 28 students rides the bus every day, how many students rides the bus?
Answers
Answer:
21 students ride the bus
Is 5,000 cm greater than 5m
Answers
Answer:
Yes
Step-by-step explanation:
5,000 cm = 50m
\(\frac{1m}{100cm} =5000cm\)
\(\frac{1m(5000)}{100}\)
\(\frac{5000m}{100}\)
= 50 m
hope this helps :)
$1,672.68
$287.84
$12.32
Answers
Answer:
$1672.68
Step-by-step explanation:
explanation:
please help asap!! im on a time limit geomtry
Answers
Answer:
\(B.\ TE\ congruent\ to\ EN\)
Step-by-step explanation:
\(As\ we\ know\ that,\\A\ median\ bisects\ the\ base\ side\ of\ a\ triangle.\\Hence,\\As\ AE\ is\ the\ median\ in\ this\ case,\\it\ bisects\ TN\ into\ congruent\ sides\ TE\ and\ EN.\\Hence,\\TE\ congruent\ to\ EN\\\)
Rewrite the following equation in standard form.
y = 3x – 8
Answers
Answer:
3x – y – 8 = 0
Step-by-step explanation:
y = 3x – 8 can be written in standard form as
3x – y – 8 = 0
-TheUnknownScientist 72
2) Ayanda wants to invest R200 000. The bank offers him 2 options for his
6 year investment.
Option 1: 12% Simple interest p.a.
Option 2: 9,5% Compound interest p.a.
4.2.1) Calculate the return on Ayanda's investment using Option 1.
●
●
4.2.2) Calculate the return on Ayanda's investment using Option 2.
4.2.3) Which option will render the most money?
Answers
Answer:
4.2.1) R140 000
4.2.2) R144 758.28
4.2.3) Option 2
Step-by-step explanation:
To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 12% = 0.12t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000 \cdot 0.12 \cdot 6\)
\(I=24000 \cdot 6\)
\(I=144000\)
Therefore, the return on Ayanda's investment using Option 1 is R144000.
\(\hrulefill\)
To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 9.5% = 0.095t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000(1+0.095)^6-200000\)
\(I=200000(1.095)^6-200000\)
\(I=200000(1.72379142...)-200000\)
\(I=344758.28426...-200000\)
\(I=144758.28426...\)
\(I=144758.28\)
Therefore, the return on Ayanda's investment using Option 2 is R144758.28.
\(\hrulefill\)
Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.
X
-1
0
1
2
3
y
1
10
1252
25
2
125
2
52:41
What is the rate of change of the function described in
the table?
ㅇ12/5
O5
ㅇ25/2
○ 25
Answers
Based on the figures given in the table, the rate of change of the function is b. 5.
What is the function's rate of change?This can be found as:
= (Y₂ - Y₁) / (X₂ - X₁)
Use points:
(0, 1/2) and (1, 5/2)
Solving gives:
= (5/2 - 1/2) / (1 - 0)
= 5
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Hello i was wondering if a sales tax is 6% and you spend $42 how much money will you spend on tax and how much money will you spend total
Answers
If $42 is the value before tax, then you can find how much you spend on tax as follows:
\(\begin{gathered} \frac{42}{100\text{ \%}}=\frac{x}{6\text{ \%}} \\ \text{ Solve for x:} \\ x=\frac{42\times6\text{ \%}}{100\text{ \%}}=2.52 \end{gathered}\)Then you spend $2.52 on tax, and the total will be 42+2.52= $44.52.
But if 42 is the value including tax, then you can find how much you spend on tax as follows:
\(\begin{gathered} \frac{42}{106\text{ \%}}=\frac{x}{6\text{ \%}} \\ \text{ Solve for x:} \\ x=\frac{42\times6\text{ \%}}{106\text{ \%}}=2.38 \end{gathered}\)Then you spend $2.38 on tax and for the sale: $42-$2.38=$39.62
74752/360 simplified as a whole fraction
Answers
Answer:
\(\frac{9344}{45}\)
Step-by-step explanation:
\(\frac{74752}{360}\)
Simplify by 8, and we get
\(\frac{9344}{45}\)
We can't simplify any more, so the answer is \(\frac{9344}{45}\)
The required answer is the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.
To simplify the fraction 74752/360 as a whole fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both of them by it.
Step 1: Find the GCD of 74752 and 360. The GCD can be calculated using various methods, such as prime factorization or the Euclidean algorithm. In this case, use the Euclidean algorithm.
Let's find the GCD using the Euclidean algorithm:
Divide 74752 by 360:
74752 ÷ 360 = 207 R 272
Divide 360 by 272:
360 ÷ 272 = 1 R 88
Divide 272 by 88:
272 ÷ 88 = 3 R 8
Divide 88 by 8:
88 ÷ 8 = 11 R 0
Since the remainder is 0, the GCD is the last non-zero remainder, which is 8.
Step 2: Divide both the numerator and denominator of the fraction by the GCD.
74752 ÷ 8 = 9344
360 ÷ 8 = 45
The simplified whole fraction is 9344/45.
A whole fraction refers to a fraction in which the numerator is equal to or greater than the denominator. It represents a whole number and a fraction together. For example, 3 1/4 is a whole fraction where the whole number part is 3 and the fractional part is 1/4.
Hence, the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.
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Sophia is younger than Mohal. Their ages are consecutive odd integers. Find Sophia's age if the product of their ages is 15.
Answers
Answer:
\(3\)
Step-by-step explanation:
\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)
\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)
6. Solve for y. 12y - 10 = 14y
02
0 5
O-5
O-2
Answers
Answer:
can you pls clear your questions?
Rosabell had 27 posters for the parade, she droppd 19 while marching in the parade. how many does she hav left.
Answers
6th grade math help me. :D.....
Answers
4x+28
question 2:
18x-27
Answer:
(1) 4x + 28 (2) 18x- 27
Step-by-step explanation:
the first question 4(x + 7) can be simplified by multiplying the number outside the parenthesis (4) by both of the values inside:
4x + 28 or the last answer choice
in the second question you can use the same method:
9 (2x) = 18x
9 ( -3) = -27
therefore the correct answer choice is 18x - 27
hope this helps :)
Three times a number x is more than 18.
Answers
Answer:
3x>18
Step-by-step explanation:
Three times the number x will be called 3x. If an expression is more or greater than a number, we use the greater symbol: >
So, we can write,
3x>18
Larry Sergio Katrina Jim Ian Tyrone Maria and Sarah are invited to a dinner party.
Answers
The number of ways they can is 40,320.
The number of ways Larry can arrive first and Sarah can arrive last is 720.
The probability that Larry arrives first and Sarah arrives last is 0.01786.
We have,
a)
Since each person can arrive at any time, the number of ways they can arrive is equal to the number of permutations of 8 people, which is:
= 8!
= 40,320
b)
To calculate the number of ways Larry can arrive first and Sarah can arrive last, we can fix their positions and then permute the remaining 6 people in the middle.
= 1 x 6! x 1
= 720
c)
To find the probability that Larry arrives first and Sarah arrives last, we need to divide the number of ways they can arrive in the desired order (720) by the total number of ways they can arrive (40,320):
= P(Larry first and Sarah last)
= 720 / 40,320
= 0.01786
So the probability is approximately 0.01786, or about 1.8%.
Thus,
The number of ways they can is 40,320.
The number of ways Larry can arrive first and Sarah can arrive last is 720.
The probability that Larry arrives first and Sarah arrives last is 0.01786.
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PLS ANSWER WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.
Answers
Answer:
The third option
Step-by-step explanation:
Someone answer number 10.(Both parts please.)
Answers
Angles Measures:
Top right: 86
Bottom right: 51
Bottom left: 43
plz help multiply and divide one step
Answers
Answer:
The value if y is -7
hope it helps you
Answer:
y = -7
Step-by-step explanation:
\(-4y = 28\)
\(\frac{-4y}{-4} = \frac{28}{-4}\)
\(y = -7\)
If 15% of the customers total is $98,880, then the sum total equals what
Answers
The sum total by the given data is equals to $658,880.
We are given that;
Percent=15%
Amount= $98,880
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:
15% = 0.15
To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:
$98,880 / 0.15 = $98,880 x 1/0.15
To multiply by 100, we can move the decimal point two places to the right. This gives us:
$98,880 x 1/0.15 x 100 = $658,880
Therefore, by the percentage the answer will be $658,880.
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A special drill is used at a construction site to dig holes. A hole is dug to a depth of 2.75 feet when the drill hits rock. The progress slows to 5/6 feet per hour of digging. The depth of the hole must be at least 10 1/2 feet by the end of the day to stay on schedule. What is the minimum amount of time the drill must continue at its present rate to complete the hole on schedule? Select from the drop-down menus to correctly complete the statement.
Answers
Answer:
9.3 hrs to finish
Step-by-step explanation:
(10.5 - 2.75)ft / (5/6 ft/hr) = 9.3 hrs to go
The Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile. Find a linear function which models the taxi fare F as a function of the number of miles driven, m
Answers
The equation that models the taxi fare F as a function of the number of miles driven is F = 2.40 + 0.40m
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile.
The function will be:
F = 2.40 + (0.40 × m)
F = 2.40 + 0.40m
where m = number of miles
F = taxi fare.
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HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answers
Answer:
In this case, you should check the x-intercept (y = 0).
=> (x-3)(x+4) = 0
=> Two x-intercept at x = 3 and x = -4
C, D are not right, because there is no two x-intercepts.
A is not correct, because both of x-intercepts are less than 0.
=> Option B is correct.
Hope this helps!
:)
a balance of $11,670. The bank statement indicated a balance of $13,640 on April 30. Comparing the bank statement and the accompanying canceled checks and memos with the records revealed the following reconciling items:
Checks outstanding totaled $4,910.
A deposit of $5,120, representing receipts of April 30, had been made too late to appear on the bank statement.
The bank collected $2,660 on a $2,520 note, including interest of $140.
A check for $770 returned with the statement had been incorrectly recorded by Lakeshore Gelato as $700. The check was for the payment of an obligation to Sprinkles Supply Co. for the purchase on account.
A check drawn for $40 had been erroneously charged by the bank as $400.
Bank service charges for April amounted to $50.
Answers
The balance of the bank reconciliation statement is $3,640
How to prepare a bank reconciliation statement?A bank reconciliation is is defined as the process by which the bank account balance in an entity’s books of account is reconciled to the balance reported by the financial institution in the most recent bank statement
The bank Reconciliation statement appears thus
Bank reconciliation statement
$ $
Cash book balance 11,670
Add unpresented cheque 5,120
Over cast (400-40) 360
17,150
Cheque not credited 5120
Less Uncredited cheque 4910
Notes collected 2660
Dishonored cheque 770
Bank charges 50
bank interest 140
13500
Balance as per bank statement 3640
In conclusion the balance of the Statement is $3640
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In the number 725.78, how does the value of the 7 in the tenths place compare to the value of the 7 in the hundreds place?
Answers
Answer:
C. 1/1,000
Step-by-step explanation:
yes or no ?
Given the scenario in #2 for Kevin, how much interest will he pay over the life of the
mortgage?
A. $62,283.60
B. $24,337.80
C. $28,632.60
D. $64,312.60