John's present age is 15 years, and his sister's present age is 10 years.
We have,
Let's denote John's sister's age as x.
According to the given information,
John is five years older than his sister, so John's age would be x + 5.
The product of their present ages is 150, which means:
x * (x + 5) = 150
Expanding the equation:
x² + 5x = 150
Rearranging the equation to standard quadratic form:
x² + 5x - 150 = 0
Now we can solve this quadratic equation.
Factoring or using the quadratic formula will give us the values of x, representing the sister's age.
Factoring the equation:
(x - 10)(x + 15) = 0
Setting each factor to zero:
x - 10 = 0 or x + 15 = 0
Solving for x:
x = 10 or x = -15
Since ages cannot be negative, we can discard the solution x = -15. Therefore, the sister's present age is x = 10.
John's present age is then calculated by adding 5 years to his sister's age:
John's age = x + 5 = 10 + 5 = 15 years.
Thus,
John's present age is 15 years, and his sister's present age is 10 years.
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By forming a quadratic equation from the given problem, we determine that John's present age is 15 years and his sister's present age is 10 years.
Let's designate John's age as J and his sister's age as S. We've been given two pieces of information: John is five years older than his sister, and the product of their present ages is 150. Mathematically, these can be expressed as:
J = S + 5J * S = 150Substituting the first equation into the second gives us:
(S + 5) * S = 150
Expanding and rearranging, we get a quadratic equation:
S2 + 5S - 150 = 0
To solve for S, we can either factor the quadratic equation or use the quadratic formula. Factoring seems simpler in this case:
(S + 15)(S - 10) = 0
This gives us two possible values for S: -15 and 10. Since ages cannot be negative, we discard S = -15 and keep S = 10. Now we can find John's age:
J = S + 5 = 10 + 5 = 15
Therefore, John's present age is 15 years, and his sister's present age is 10 years.
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
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....
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.
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
(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.
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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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
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!
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!
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]
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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a classroom is 19 ft long 2 ft wide and 10 feet high find the number of cubic feet of air in the room
Answer:
380 cubic feet of air
Step-by-step explanation:
Volume = height * width * length.
So
Volume = 10 * 2 * 19 = 380 cubic feet of air
Answer:
[tex]380\text{ ft}^3[/tex]
Step-by-step explanation:
We have been that a classroom is 19 ft long 2 ft wide and 10 feet high. We are asked to find the number of cubic feet of air in the room.
To find the number of cubic feet of air in the room, we will find the volume of the given room by multiplying all of its side as:
[tex]\text{Volume of the room}=\text{19 ft}\times \text{2 ft}\times\text{10 ft}[/tex]
[tex]\text{Volume of the room}=380\text{ ft}^3[/tex]
Therefore, there are 380 cubic feet of air in the room.
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
1.
From a total yearly budget of
$360,000, the Kimball Foundation
spends $30,000 on leasing office
space. What is the ratio of dollars
spent on office space to dollars spent
on other costs?
A. 12:1
B. 11:1
C
Answer:
I think it would be 11:1.
Step-by-step explanation:
360,000 / 30,000 = 12
11/12 of the yearly budget was used on other costs
1/12 of the yearly budget was used for leasing office
space.
Answer:
Step-by-step explanation:
Okay so I may be wrong BUT since it's asking for the other costs, I'm assuming we're subtracting the $30,000 from the $360,000 first. Therefore the original ratio would be 30,000: 330,000 which is simplified to 1:11 ($ on office space: $ on other costs)
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 :)
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
Round off 600341 to the nearest a) tens b) hundreds c) thousands
a) 600340
b) 600300
c) 600000
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
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 !
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]
7a3+56b3 factorize it plsss
Answer:
7(a + 2b)(a² - 2ab + 4b²)
Step-by-step explanation:
Given
7a³ + 56b³ ← factor out 7 from each term
= 7(a³ + 8b³) ← sum of cubes which factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
8b³ = (2b)³ ⇒ b = 2b
a³ + 8b³ = (a + 2b)(a² - 2ab + (2b)²) = (a + 2b)(a² - 2ab + 4b²)
Hence
7a³ + 56b³ = 7(a + 2b)(a² - 2ab + 4b²) ← in factored form
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
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]
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]
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.
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.(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
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.
Please Help........................................................
[tex]2(n-5)\geq2n+10\\2n-10\geq2n+10\\-10\geq 10\\n\in\emptyset[/tex]
Which of these are the intercepts of y = 2x − 6?
A. (3, 0), (0, 6)
B. (3, 0), (0, -6)
C. (4, 0), (0, 6)
D. (6, 0), (0, 12)
Answer:
B. (3, 0), (0, -6)
Step-by-step explanation:
Plug 0 in for each variable one at a time, and you will get both intercepts.