Answer:
x = 5
Step-by-step explanation:
the expression is "undefined" when the denominator is equal to zero
[tex]\frac{\left(5+x\right)}{25-x^2\:} \\[/tex]denominator = 25 - x²
Values of x where the equation is "undefined"
0 = 25 - x²
x² = 25
√x² = √25
x = ± 5
Nonnegative value of x where the equation is "undefined"
x = 5
An expression is said to be undefined, if it has 0 as its denominator. For [tex]\frac{5 + x}{25 - x^2}[/tex] to be undefined, x must be 5.
Given that:
[tex]\frac{5 + x}{25 - x^2}[/tex]
For the expression to be undefined, the denominator must equal 0.
i.e.
[tex]25 - x^2 = 0[/tex]
Collect like terms
[tex]-x^2 = 0 - 25[/tex]
[tex]-x^2 = - 25[/tex]
Cancel out negatives
[tex]x^2 = 25[/tex]
Take positive square root
[tex]x = 5[/tex]
This means that when [tex]x = 5[/tex], [tex]\frac{5 + x}{25 - x^2}[/tex] is undefined.
Read more about undefined expressions at:
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Suppose you buy a CD for $500 that earns 2.5% APR and is compounded quarterly. The CD matures in 3 years. How much will this CD be worth at maturity?
Answer:
A=$538.82
Step-by-step explanation:
We're going to use the compounded interest formula:
A=P(1+r/n)^n*t
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = t is the amount of time at which you're checking how much it's worth (yrs)
Using this information, we can use:
A=500(1+0.025/4)^3*4
A=500(1+0.00625)^12
A=500(1.00625)^12
A=500(1.07763259886)
A=538.82
A=$538.82....
(4x – 12) + (–x + 7)
Answer:
3x -5
Step-by-step explanation:
(4x – 12) + (–x + 7)
= 4x – 12 –x + 7
= 3x -5 (answer)
Answer:
3x-5
Step-by-step explanation:
(4x – 12) + (–x + 7)
Open the parenthesis
=4x-12-x+7
Solve the like terms:
=3x-5
The answer is 3x-5
Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of
10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?
A. 1.7 years
B. 2.0 years
C. 3.1 years
D. 5.0 years
Answer: A) 1.7 Years
Step-by-step explanation:
Answer:
A. 1.7 years
Step-by-step explanation:
Let [tex]P_1[/tex] be the original value of first car,
Since, the car depreciates at an annual rate of 10%,
Let after [tex]t_1[/tex] years the value of car is depreciated to 60%,
That is,
[tex]P_1(1-\frac{10}{100})^{t_1}=60\%\text{ of }P_1[/tex]
[tex]P_1(1-0.1)^{t_1}=0.6P_1[/tex]
[tex]0.9^{t_1}=0.6[/tex]
Taking ln on both sides,
[tex]t_1ln(0.9) = ln(0.6)[/tex]
[tex]\implies t_1=\frac{ln(0.6)}{ln(0.9)}[/tex]
Now, let [tex]P_2[/tex] is the original value of second car,
Since, the car depreciates at an annual rate of 15%
Suppose after [tex]t_2[/tex] years it is depreciated to 60%,
[tex]P_2(1-\frac{15}{100})^{t_2}=60\%\text{ of }P_2[/tex]
[tex]P_2(1-0.15)^{t_2}=0.6P_2[/tex]
[tex]0.85^{t_2}=0.6[/tex]
Taking ln on both sides,
[tex]t_2ln(0.85) = ln(0.6)[/tex]
[tex]\implies t_2=\frac{ln(0.6)}{ln(0.85)}[/tex]
[tex]\because t_1-t_2=\frac{ln(0.6)}{ln(0.90)}-\frac{ln(0.6)}{ln(0.85)}[/tex]
[tex]=1.70518303046[/tex]
[tex]\approx 1.7[/tex]
Hence, the approximate difference in the ages of the two cars is 1.7 years,
Option 'A' is correct.
what is 20% of 50?
A.) Percent=20%, Amount =50, Base =unknown
B.) Percent=50%, Amount =unknown, Base= 20
C.) percent= 20%, Amount=unknown, Base =50
D.) Percent=unknown, Amount =20, Base= 50
20% of 50 is found by multiplying the base (50) by the decimal equivalent of the percent (0.2). The calculation yields an amount of 10, which indicates that 20% of 50 is 10.
Calculating percents involves using the basic equation that relates the percent, the base (also called 'whole' or 'total'), and the amount (or 'part'). The equation can be represented as percent = (amount/base) imes 100. To find what is 20% of 50, we use this equation, where the percent is known (20%) and the base is known (50), but the amount is what we are looking for.
First, let's convert the percent to a decimal to make the calculation easier: 20% = 20/100 = 0.2. Then, we multiply the base (50) by the decimal form of the percent (0.2): 50 x 0.2 = 10. So, 20% of 50 is 10.
Therefore, the correct representation relating the Percent, Amount, and Base in this problem is option A) Percent=20%, Amount=50, Base=unknown, since we're calculating the amount based on the known percent and base.
Answer:
C.) percent= 20%, Amount=unknown, Base =50
Step-by-step explanation:
20% is the percent
50 is the amount
20% of 50 is the unknown. This is the amount.
20% of 50 = 0.2 × 50 = 10
(j-1)(-3) I need help solving the distributive property.
Answer:
Step-by-step explanation:
-3*j = -3j
(-3)(-1) = 3
Answer
-3j + 3 Notice the sign change. Be careful about that when signs are used with the distributive property.
Find the slope of the vertical line that passes through (2,-4)
Answer:
x=2
Step-by-step explanation:
Vertical lines have the same x value all the time. It is of the form x=
Their slope is undefined
The line passes through the point (2,4) and the x value is 2
x=2
Match the polygons formed by the set of points with their perimetersrounded to the nearest hundredth. Please help ASAP taking a test . Thank you so much in advance
Answer:
Polygon ABCDE = 50 units
Polygon FGHIJ = 23.4 units
Polygon KLMNO = 19.24 units
Polygon UVWXY = 38 units
Step-by-step explanation:
In order to find the perimeter, we have to find lengths of all sides of given points
The distance formula will be used to find the lengths
[tex]d = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]
where (x_1,y_1) are coordinates of first point and (x_2,y_2) are coordinates of second point)
So,
For A(1,1), B(6,13), C(8,13), D(16,-2) and E(1, -2)
AB = 13 units
BC = 2 units
CD = 17 units
DE = 15 units
EA = 3 units
Perimeter of polygon ABCDE = 13+2+17+15+3 = 50 units
For F(14,-10), G(16,-10), H(19,-6), I(14,-2) and J(11,-6)
FG = 2 units
GH = 5 units
HI = 6.40 units
IJ = 5 units
JF = 5 units
Perimeter of polygon FGHIJ = 2+5+6.40+5+5 = 23.4 units
For K(4,2), L(8,2), M(12,5), N(6,5) and O(4,4)
KL = 4 units
LM = 5 units
MN = 6 units
NO = 2.24 units
OK = 2 units
Perimeter of polygon KLMNO = 4+5+6+2.24+2 = 19.24 units
For P(7,2), Q(12,2), R(12,6), S(7,10) and T(4,6)
PQ= 5 units
QR= 4 units
RS=6.40 units
ST= 5 units
TP = 5 units
Perimeter of polygon PQRST = 5+4+6.40+5+5 = 25.40 units
For U(4,-1), V(12, -1), W(20,-7), X(8, -7) and Y(4,-4)
UV = 8 units
VW = 10 units
WX = 12 units
XY = 5 units
YU = 3 units
Perimeter of polygon UVWXY = 8+10+12+5+3 = 38 units
The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
"All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid."
As of today, Susan's movie is currently five days late. She knows that if she doesn't get the movie back tonight, she will be charged $9.99, the purchase price of the movie, plus five days' worth of late fees. A round trip cab ride to the video store will cost about $10.
Which of the following statements is true?
a.
Taking a cab to return the movie is the cheapest action. Susan should call a cab.
b.
It would cost about the same to keep or return the movie. Susan should keep it.
c.
Keeping the movie and paying the purchase price and late fees is the cheapest option.
d.
If Susan returns the movie, she should not have to pay late fees. She should return it.
Answer:
option B
Step-by-step explanation:
Given:
per day late costs= 1.50
Purchase price= 9.99
A round trip cab ride to the video store will cost = 10
5 day late cost= 5(1.50)
= 7.50
Payment after 5 day late= 5 day late cost + Purchase price
= 7.50 + 9.99
= 17.49
If she gets a cab, then total payment= 10 + 7.50
= 17.50
Hence both costs almost the same, option B is true
b.
It would cost about the same to keep or return the movie. Susan should keep it!
I have a right triangle. The hypotenuse is 12. The base is 7 and the other side is 9.7. The sin(x) is 0.014. Cos(x) is 0.99 and tan(x) is 0.02. What is the measure of angle x?
Answer:
[tex]\sin(x)=\frac{\sqrt{95}}{12}=0.8122[/tex]
[tex]\cos(x)=\frac{7}{12} \approx .5833[/tex]
[tex]\tan(x)=\frac{\sqrt{95}}{7} \approx 1.3924[/tex]
[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12}) \approx 54.3147[/tex] degrees.
I don't know what you want to round to but I can tell you are rounding...
Step-by-step explanation:
Soh Cah Toa is the acronym we will use to help us solve this.
This says sine is opposite over hypotenuse.
It also says cosine is adjacent over hypotenuse.
And finally tangent is opposite over adjacent.
Note: Opposite and adjacent can change depending on how you are looking at the triangle, like which angle you are referring to.
Let's look at x:
The side that is opposite, not touching, the angle whose measurement is x, is the side that has measurement [tex]\sqrt{95} \approx 9.7[/tex].
I see you already found this measurement. This is really good. I might use the exact value for now and round at the end.
The side that is the hypotenuse no matter the angle you are referencing is always going to be opposite the angle whose measurement is 90 degrees. It is also the longest side (since it is opposite the largest angle). This side has measurement 12.
The hypotenuse will be one of the sides touching your angle you are referencing. The other side that is touching your angle is the adjacent side. This side has measurement 7.
Anyways let's plug into the definitions we had above:
[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex] (O/H)
[tex]\cos(x)=\frac{7}{12}[/tex] (A/H)
[tex]\tan(x)=\frac{\sqrt{95}}{7}[/tex] (O/A)
Now we can solve anyone of these for x.
Take your pick.
[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex]
[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12})[/tex]
[tex]x=54.3147[/tex] degrees.
Each of the 27 turtles in the pet store needs to be fed. There is one bag of turtle food that weighs 84 ounces. If each turtle gets the same amount of food, how many ounces of turtle food will each turtle get?
Answer:
[tex]\3.11\ ounces[/tex]
Step-by-step explanation:
we know that
To find the number of ounces of food each turtle will receive, divide the total ounces of food by the total number of turtles
so
[tex]\frac{84}{27}=3.11\ ounces[/tex]
Answer: 3.1
Step-by-step explanation: which is 3.1 with the line on top!
Which of the following data sets has the mean, median, and mode as the same number?
A. 10,10,12,12,13,13
B. 2,3,4,4,5,7
C. 4,7,11,11,16,17
D. 1,2,3,3,5,6
Answer:
C
Step-by-step explanation:
MEAN:4+7+11+11+16+17=66÷6=11
MEDIAN:11+11=22÷2=11
MODE=11
Answer:
The correct answer is option C
4,7,11,11,16,17
mean = mode = median = 11
Step-by-step explanation:
Check option A
10,10,12,12,13,13
Mean = 12, mode = 12,13 , 14 and median = 12
Check option B
2,3,4,4,5,7
Mean = 4.15, mode = 4 and median = 4
Check option C
4,7,11,11,16,17
Mean = 11, mode = 11 and median = 11
Check option D
1,2,3,3,5,6
Mean = 3.33, mode =3 and median = 3
The correct answer is option C
4,7,11,11,16,17
mean = median = mode = 11
What is the value of f(x) = 9x when x = -2? A. 1 81 B. 81 C. 1 18 D. 18
Answer:
Step-by-step explanation:
The correct answer would be -18
To solve this, you would substitute x with the x value, which in this case is -2
That would make it so f(x)= 9(-2)
9*-2=-18
Therefore f(x)=-18
Note that f(x) is another way to write y, therefore...
y = 9x
To solve for this plug -2 in for x in this equation like so...
y = 9 * -2
When a positive number is being multiplied with a negative number the answer will be negative.
y = -18
C. is the answer (assuming that you meant to write -18 instead of 1 18)
Hope this helped!
~Just a girl in love with Shawn Mendes
Fuel economy estimates for automobilos built in a certain yoar predicted a mean of 26.8 mpg and a standard deviation of 72 mpg for highway driving. Assume that a normal distribution can be applied. Within what
range are 99.8% of the automobiles?
Answer:
range=u ± 3.09 sd
Step-by-step explanation:
Given:
mean, u= 26.8 mpg
standard deviation, sd=72 mpg
% contained in interval = 99.8%
the interval for 99.8% of the values of a normal distribution is given by
mean ± 3.09 standard deviation= u ± 3.09 sd
=26.8 ± 3.09(72)
=26.8 ± 222.48
= 249.28 , -195.68
range=u ± 3.09 sd = 249.28 , -195.68 !
Find the probability of each event. There are 4 red marbles, 2 black marbles, and 2 green marbles in a box. P(red) = P ( red or black) =
Answer: P(red): 1/2
P(red or black):3/4
Step-by-step explanation: Count the total number of marbles. There are 8. Since there are 4 red marbles out of the 8, put this into a fraction. It will be 4/8, but simplify to 1/2. The P(red) is 1/2.
Since there are 4 red marbles and 2 black marbles, add them. There are 6 out of the 8 marbles. The fraction is 6/8 simplify to 3/4. The P(red or black) is 3/4.
The probability of choosing a red marble from the box is 0.5 and the probability for choosing either a red or black marble is 0.75.
Explanation:The subject of this question refers to calculating probabilities which is a concept in Mathematics, specifically in the scope of Statistics. To calculate the probability of an event, we need to know the total amount of outcomes and the amount of favorable outcomes. In the context of the question, these outcomes are represented by marbles.
First, we need to add the total number of marbles, which is 4 red + 2 black + 2 green = 8 marbles in total.
To find the probability of picking a red marble, we divide the number of red marbles by the total number of marbles. Hence, P(red) = 4/8 or 0.5.
To find the probability of picking a red or black marble, we add the number of red and black marbles and divide by the total number of marbles. Hence, P (red or black) = (4 red + 2 black) / 8 total = 6/8 or 0.75.
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can someone plz help me with this!
Answer:
(arranged from top to bottom)
System #3, where x=6
System #1, where x=4
System #7, where x=3
System #5, where x=2
System #2, where x=1
Step-by-step explanation:
System #1: x=4
[tex]2x+y=10\\x-3y=-2[/tex]
To solve, start by isolating your first equation for y.
[tex]2x+y=10\\y=-2x+10[/tex]
Now, plug this value of y into your second equation.
[tex]x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4[/tex]
System #2: x=1
[tex]x+2y=5\\2x+y=4[/tex]
Isolate your second equation for y.
[tex]2x+y=4\\y=-2x+4[/tex]
Plug this value of y into your first equation.
[tex]x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1[/tex]
System #3: x=6
[tex]5x+y=33\\x=18-4y[/tex]
Isolate your first equation for y.
[tex]5x+y=33\\y=-5x+33[/tex]
Plug this value of y into your second equation.
[tex]x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6[/tex]
System #4: all real numbers (not included in your diagram)
[tex]y=13-2x\\8x+4y=52[/tex]
Plug your value of y into your second equation.
[tex]8x+4(13-2x)=52\\8x+52-8x=52\\0=0[/tex]
all real numbers are solutions
System #5: x=2
[tex]x+3y=5\\6x-y=11[/tex]
Isolate your second equation for y.
[tex]6x-y=11\\-y=-6x+11\\y=6x-11[/tex]
Plug in your value of y to your first equation.
[tex]x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2[/tex]
System #6: no solution (not included in your diagram)
[tex]2x+y=10\\-6x-3y=-2[/tex]
Isolate your first equation for y.
[tex]2x+y=10\\y=-2x+10[/tex]
Plug your value of y into your second equation.
[tex]-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2[/tex]
no solution
System #7: x=3
[tex]y=10+x\\2x+3y=45[/tex]
Plug your value of y into your second equation.
[tex]2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3[/tex]
Which graph is the solution to lxl > 10?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Note}\rightarrow[/tex] [tex]\leq \& \geq \ = \huge\text{closed circle}\\ < \& > = \huge\text{(o)(p)(e)(n)(e)(d) circle}[/tex]
[tex]\huge\text{So, we know that A or C could be our answer}.[/tex]
[tex]\huge\text{Eliminate option B and D}[/tex]
→ [tex]\huge\text{Find the absolute value of the problem}[/tex]
→ [tex]\huge\text{You can now know that it could be:}[/tex]
[tex]\huge\text{x}\large\huge{\ >}\huge\text{ 10 or x }< \huge\text{ -10}[/tex]
→ [tex]\huge\text{Possible answer \#1: x }>\huge\text{10}\\\\\huge\text{Possible answer \#2: x}<\huge\text{ -10}[/tex]
→ [tex]\boxed{\boxed{\huge\text{Answer: C}}}[/tex]
[tex]\huge\text{Option A. would be too small}[/tex] [tex]\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
what is the value of x?
[tex]x^2=40^2+9^2\\x^2=1600+81\\x^2=1681\\x=\sqrt{1681}=41[/tex]
To solve this you must use Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = 9
b = 40
c = x
^^^Plug these numbers into the theorem
[tex]9^{2} +40^{2} =x^{2}[/tex]
simplify
81 + 1600 = [tex]x^{2}[/tex]
1681 = [tex]x^{2}[/tex]
To remove the square from x take the square root of both sides to get you...
41 = x
Hope this helped!
~Just a girl in love with Shawn Mendes
What does x ^2 + y^2 = 9 mean? What about x ^2 + y ^2 = 0 ? Can a circle have a radius of − 3 ? Why or why not?
Answer:
See below.
Step-by-step explanation:
Compare our equation with one standard form of a circle:
x^2 + y^2 = r^2 where r = the radius.
So x^2 + y^2 = 9 is the equation of a circle with it's center at the origin and it's radius is 3 units.
x^2 + y^2 = 0 is not a circle because r = 0 ( a radius of 0). A circle of radius 0 is really a point!!
The value of the radius of a circle must be positive so it cannot have a radius of -3.
Answer
[tex]x ^{2} + {y}^{2} = r^{2} [/tex]
since all the terms are squared so there can be a negative number
but in number line
...... -4,-3,-2,-1,0,1,2,3.......
as we know negative sign indicates only the direction so -3 means in which coordinates will it lie.
.
.
.
[tex] {x}^{2} + {y}^{2} = 9[/tex]
it means the origin is (0,0) and radius 3
Roger has a 0.250 batting average. If he went up to bat 240 times,how many times did he fail to get any hits?( A 0.250 batting average means that he got hits 0.250 times at bat) please help me
Answer:
lol i need help with the same question
Step-by-step explanation:
Roger, with a batting average of 0.250, recorded 60 successful hits from a total of 240 attempts. Therefore, he failed to get a hit 180 times.
Explanation:In this question, we are dealing with Roger's batting average and his performance. A batting average of 0.250 means that for every 4 at-bats, Roger gets a hit on average 1 time. So, if he has been at bat a total of 240 times, we can expect that he got hits 0.250 times out of these at-bats. So to calculate the number of successful hits, we multiple 240 by 0.250 which equals 60. Therefore, Roger has hit the ball 60 times. To find out how many times he failed to get hits, we subtract his hits from his total tries. So, 240 - 60 = 180. Therefore, Roger failed to get a hit 180 times.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5. Ir there were 3822 yes votes, what was the total
number of votes?
total votes
Answer:
The total number of votes was [tex]7,007[/tex]
Step-by-step explanation:
Let
x -----> the number of yes votes
y -----> the number of no votes
we know that
[tex]\frac{x}{y} =\frac{6}{5}[/tex]
isolate variable y
[tex]y=\frac{5}{6}x[/tex] -----> equation A
[tex]x=3,822[/tex] -----> equation B
Substitute equation B in equation A and solve for y
[tex]y=\frac{5}{6}(3,822)=3,185[/tex]
therefore
To find out the total number of votes sum the number of yes votes plus the number of no votes
[tex]3,822+3,185=7,007[/tex]
Answer: 7,007 votes :)
Step-by-step explanation:
Hope that helps
Exponential functions have the form f(x)=b^x. What type of an exponential function would you have (increasing or decreasing) if the value of b is greater than one?
Answer:
Increasing
Step-by-step explanation:
Let's see what happens if we choose a value for b greater than 1.
Let's try b=2.
[tex]f(x)=2^x[/tex].
I'm going to keep increasing x. If y increases, the the function is increasing. If y decreases, the function is decreasing.
Let's start with x=1.
[tex]y=2^1=2[/tex]
Now x=2.
[tex]y=2^2=4[/tex]
The y's got higher as you increased x so the function is increasing.
The function keep increasing for the varying value of x, hence the exponential function is increasing
Given the exponential function f(x) = [tex]b^x[/tex]
We are to check if the function is increasing or decreasing if b is greater than 1
Let b = 2 and x = 1
[tex]f(1) = 2^1\\f(1) = 2[/tex]
Let b = 2 when x = 2
[tex]f(2)=2^2\\f(2)=4[/tex]
Let b = 2 when x = 3
[tex]f(3)=2^3\\f(3)=8[/tex]
You can see that the function keep increasing for the varying value of x, hence the exponential function is increasing
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A coffee distributor needs to mix a(n) House coffee blend that normally sells for $10.50 per pound with a Kenya coffee blend that normally sells for $12.80 per pound to create 40 pounds of a coffee that can sell for $10.67 per pound. How many pounds of each kind of coffee should they mix?
Answer: They must mix
______pounds of the House Blend
______pounds of the Kenya Blend.
Round your answers to the nearest whole number of pounds.
Answer:
They must mix
37 pounds of the House Blend
3 pounds of the Kenya Blend.
Step-by-step explanation:
Let 'x' be House coffe and 'y' be Kenya Coffee. Then:
10.50x + 12.80y = 10.67(40)
Also, we knw that:
x + y = 40
Solving the system of equations above, we have that:
x ≈37.0435 ≈ 37 pounds
y ≈2.95652 ≈ 3 pounds
They must mix
37 pounds of the House Blend
3 pounds of the Kenya Blend.
What is the area of the parallelogram shown below?
A. 88 sq. units
B. 24 sq. units
C. 48 sq. units
D. 42 sq. units
Answer:
48
Let me know if this was right :)
Mary, Chau, and David have a total of $87 i their wallets. Marry has 9$ more than Chau. David has two times what Mary has. How much do they have in each wallet?
Answer:
Mary = 24
Chau = 15
David = 48
Step-by-step explanation:
The formula is
Mary + Chau + David = 87
And we know that
Chau = Mary - 9
David = Mary * 2
So when we fill this in
Mary + Mary - 9 + Mary * 2 = 87
4Mary - 9 = 87
4Mary = 96
Mary = 24
Chau = Mary - 9 = 15
David = Mary * 2 = 48
Final answer:
The problem is solved using basic algebra, yielding Chau has $15, Mary has $24, and David has $48, all adding up to the total amount of $87.
Explanation:
The question involves a three-person word problem focusing on algebraic relationships and equation solving. Mary, Chau, and David have a total of $87 in their wallets. Mary has $9 more than Chau, and David has twice what Mary has. To find out how much each person has, we'll let 'c' represent the amount that Chau has.
Accordingly, Mary has c + $9, and David has 2(c + $9). Together, they have a total of c + (c + $9) + 2(c + $9) = $87. Simplifying this, we get 4c + $27 = $87. Subtracting $27 from both sides gives us 4c = $60. Dividing both sides by 4, we find that Chau has $15.
Now, since Mary has $9 more than Chau, Mary has $24 ($15 + $9). David, having twice what Mary has, possesses $48 (2 x $24). These amounts add up to the total of $87.
how do you convert 17 1/6 to a 3 decimal place
Answer:
17.167 rounded
Step-by-step explanation:
17+(1/6)
17+0,166
17.167
well, firstly convert the mixed fraction to improper fraction, and then simply divide the numerator by the denominator and round as needed.
[tex]\bf \stackrel{mixed}{17\frac{1}{6}}\implies \cfrac{17\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{103}{6}}~\hfill \stackrel{\textit{to a decimal}~\hfill }{103\div 6 = 17.166\overline{6}}\implies \stackrel{\textit{rounded up}}{17.167}[/tex]
I’m the sixth grade class, 3/7 of the students are boys, and 5/8 of these boys are in mrs. jones’ class. What fraction of the entire sixth grade class are the boys in mrs. jones’ class??
PLEASE SHOW WORK
Answer:
15/56
Step-by-step explanation:
You just multiply 3/7 by 5/8 to get 15/56. Since you cannot simplify it more, that is the fraction of boys in mrs.jones class compared to the whole sixth grade class
Answer:
15/56
Step-by-step explanation:
Let the total number of students be x
Number of boys=[tex]\frac{3}{7}[/tex] of x
Number of boys in Mrs jones' class= [tex]\frac{3}{7}[/tex]of[tex]\frac{5}{8}[/tex]
Fraction of number of boys of Mrs jones' class to total class strength=[tex]\frac{15x/56}{x}[/tex]
Hence, the fraction is[tex]\frac{15}{56}[/tex]
HELP ASAP!!!!!
Pre-calculus
[tex]xy=\log_{5\sqrt5}{125}\cdot\log_{2\sqrt2}64\\\\xy=\dfrac{\log_5125}{\log_5 5\sqrt5}\cdot\dfrac{\log_264}{\log_22\sqrt2}\\\\xy=\dfrac{3}{\log_55^{\tfrac{3}{2}}}\cdot\dfrac{6}{\log_22^{\tfrac{3}{2}}}\\\\xy=\dfrac{3}{\dfrac{3}{2}}\cdot\dfrac{6}{\dfrac{3}{2}}\\\\xy=3\cdot\dfrac{2}{3}\cdot6\cdot\dfrac{3}{2}\\\\xy=18[/tex]
Answer:
The product of x and y is 8.
Step-by-step explanation:
It is given that
[tex]x=\log_{5\sqrt{5}}\left(125\right)[/tex]
[tex]y=\log_{2\sqrt{2}}\left(64\right)[/tex]
We need to find the product of x and y.
[tex]x\cdot y=\log_{5\sqrt{5}}\left(125\right)\cdot\log_{2\sqrt{2}}\left(64\right)[/tex]
It can be written as
[tex]xy=\log_{5\sqrt{5}}\left(5\sqrt{5}\right)^2\cdot\log_{2\sqrt{2}}\left(2\sqrt{2}\right)^4[/tex]
Using the properties of logarithm, we get
[tex]xy=2\cdot 4[/tex] [tex][\because log_aa^x=x][/tex]
[tex]xy=8[/tex]
Therefore the product of x and y is 8.
Which of the following is a key property of the absolute value parent function? A. It is in quadrants III and IV B. It is U shaped C. It’s vertex is at the origin. D. It has a slope of 1 on the left side
The key property of the absolute value parent function is:
C. It’s vertex is at the origin.
Step-by-step explanation:The absolute value parent function is given by:
[tex]f(x)=|x|[/tex]
The graph of such a function is a V-shaped graph such that the vertex of the graph is located at origin i.e. (0,0) and the function takes non-negative values for all the real numbers.i.e. the graph of the function lie in the first and second quadrant.
Also, to the left side of the y-axis the graph is decreasing continuously i.e. the graph has a negative slope.Round off 600341 to the nearest a) tens b) hundreds c) thousands
a) 600340
b) 600300
c) 600000
Please Help........................................................
[tex]2(n-5)\geq2n+10\\2n-10\geq2n+10\\-10\geq 10\\n\in\emptyset[/tex]