Raj is 3 years older than Zia. The sum of the squares of their ages is 369. How old are they?
Answers
x--------------> ages of Raj
y--------------> age of Zia
we know that
x=y+3-------------> equation 1
x²+y²=369-----------> equation 2
I substitute 1 in 2
(y+3)²+y²=369----------> y²+6y+9+y²=369---------> 2y²+6y-360=0
2y²+6y-360=0
using a graph tool-----------> to calculate the quadratic equation
see the attached figure
the solution is
y=12
x=y+3--------> x=12+3--------> x=15
the answer is
Raj is 15 years old
Zia is 12 years old
Final answer:
Zia's age is 12 and Raj's age is 15
Explanation:
To solve this problem, we can set up two equations using the given information. Let's assume Zia's age is x. Since Raj is 3 years older than Zia, Raj's age can be represented as x + 3.
The first equation is [tex]x^2 + (x + 3)^2 = 369.[/tex]
Simplifying this equation, we get [tex]x^2 + x^2 + 6x + 9 = 369.[/tex]
Combining like terms, we have [tex]2x^2 + 6x + 9 = 369.[/tex]
Next, we can rearrange the equation by subtracting 369 from both sides and combining like terms to get [tex]2x^2 + 6x - 360 = 0.[/tex]
Now, we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula. The solutions are x = -15 and x = 12.
Since age cannot be negative, Zia's age is 12 and Raj's age is 12 + 3 = 15.
Related Questions
Write an expression to represent: The sum of ten and the quotient of a number x and 6.
Answers
+10
Then, we will add that to the quotient (which is the number after dividing) of a number x and 6. We can write that as
+ x/6
The slash means division here. Thus your final answer is
10 + x/6
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to .
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
5n = 3d and n - 2 = 2d - 4
5n = 3d and 2n - 4 = d - 2
3n = 5d and 2n - 4 = d - 2
Answers
The numerator of the fraction is "n" and the denominator of the fractions is "d". Initially the numerator and denominator are in the ratio 3 to 5. In equation form we can state this as:
[tex]n:d=3:5 \\ \\ \frac{n}{d}= \frac{3}{5} \\ \\ 5n=3d [/tex]
When both numerator and denominator are decreased by 2, the new numerator will be n-2 and denominator will be d-2. These numerator and denominators are in ratio 1 to 2. In equation form we can write this as:
[tex]n-2:d-2=1:2 \\ \\ \frac{n-2}{d-2} = \frac{1}{2} \\ \\ 2(n-2)=1(d-2) \\ \\ 2n-4=d-2 [/tex]
This is our second equation. Thus the two equation which can be used to solve the problem are:
5n = 3d
and
2n - 4 = d - 2
Answer:
A 5n=3d and n-2=2d-4
Step-by-step explanation:
It costs $3.15 for a pack of 15 pencils.Find the unit price in dollars per pencil.If necessary, round your answer to the nearest cent.
Answers
We have then that the unit price is:
P = (3.15) / (15)
P = 0.21 $ / pencil
Answer:
The unit price in dollars per pencil is:
P = 0.21 $ / pencil
Using 70 POINTS NEED YOUR HELP NOT SPAMMERS. To make an ice-cream cone, employees at an ice-cream shop completely fill the cone and then add one scoop of ice cream on top. The cone has a height of 6 inches and a diameter of 2 inches.
To the nearest cubic inch, how much ice cream is in the cone before the scoop is added on the top?
6 in³
19 in³
25 in³
75 in³
Answers
Answer:
6in^3
sorry this is late. but i put 19in^3 and got it wrong. the k12 test said the correct answer is 6in^3
if it isnt correct for you, im sorry
Find the length of the second base of a trapzoid with one base measuring 12 feet a height of 4 feet and a area of 58 square feet
Answers
b1+b2 x h / 2 = 58
12+ b2 x 4 / 2 = 58
12+b2 x 4 = 116
12 + b2 = 29
b2 = 17 feet is the length of the second base
:p
A rectangle has a width of 3 cm and a length of 10 cm. What is the effect on the perimeter when the dimensions are multiplied by 10?
A) The perimeter is increased by a factor of 10.
B) The perimeter is increased by a factor of 40.
C) The perimeter is increased by a factor of 100.
D) The perimeter is increased by a factor of 400.
I think it's 'A'.. but would really appreciate if someone else double checked it cause I'm an idiot and exhausted and can't think.
Answers
Sean has $65 to spend on CDs. If each CD costs $6.98, about how many CDs can he buy?
Answers
Answer:
9 (did it on college board)
Step-by-step explanation:
Identify the polynomial written in descending order. (1 point) 9 − 14x − 7x2+ x3 x3− 7x2− 14x + 9 −7x2+ 9 + x3− 14x −14x + x3+ 9 − 7x2
Answers
Answer:
Option 2.
Step-by-step explanation:
We need to find a polynomial which is written in descending order.
Polynomial written in descending order: If the terms are written in a manner such that the powers on the variables go from highest to lowest, then it is called polynomial in descending order.
In option 1, the given polynomial is
[tex]9-14x-7x^2+x^3[/tex]
In option 2, the given polynomial is
[tex]x^3-7x^2-14x+9[/tex]
In option 3, the given polynomial is
[tex]-7x^2+9+x^3-14x[/tex]
In option 3, the given polynomial is
[tex]-14x+x^3+9-7x^2[/tex]
Only in option 2, the terms are arranged in descending order of powers.
Therefore, the correct option is 2.
30 POINTS + BRAINLIEST! SHOW ALL WORK PLEASE
Answers
cos(2x - 7) = cos(2x)*cos(7) + sin(2x)*sin(7)
cos(2x - 7) = [cos^2(x) - sin^2(x)]*cos(7) + 2sin(X)*cos(x)*sin(7)
Somebody sure doesn't like you guys very much. A weak joke. I think the best you can do to start with is graph this relationship. The best I can do is get an answer that is somewhere around 145 degrees. - 61 degrees, - 214 degrees and 255 degrees.
If you are intended to solve this any other way by using the double angle formulas as I started to get above and sin(x) or cos(x) I would take the 0 and hope to make it up some other way.
The domain is between -360 and plus 360. The range is between +/- 1.
Answer
25
Explanation
sin (x + 22)° = cos (2x - 7)°
In trigonometry for any equation where sinθ = cosΦ, θ and Φ are complementary. That is they add up to 90°
sinθ = cosΦ ⇒ θ + Φ = 90
∴ sin (x + 22)° = cos (2x - 7)°
(x + 22) + (2x - 7) = 90
x + 22 + 2x - 7 =90
3x + 15 = 90
3x = 90 - 15
3x = 75
x = 25°
X^2/ 100 + Y^2/ 25 =1
(x squared over 100 plus y squared over 25 equals 1)
The y-intercepts are at:
(-10, 0) and (10, 0)
(0, 10) and (0, 5)
(0, -5) and (0, 5)
Answers
Every y-intercept has an x-coordinate of 0. Substituting 0 in for x we have:
[tex]\frac{0^2}{100}+\frac{y^2}{25}=1 \\ \\0+\frac{y^2}{25}=1 \\ \\\frac{y^2}{25}=1 \\ \\y^2=25 \\\sqrt{y^2}=\sqrt{25} \\y=\pm5[/tex]
Which number is written in scientific notation? A. 6x10^11 B. 12x10^-8 C. 0.2x10^5 D. 8x7^2
Answers
Answer:
A!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Step-by-step explanation:
write the resulting function if the transformation f(x+3)+9 is applied on the function f(x)=x^2+1
a) x^2+13
b)x^2+19
c)x^2+6x+19
d)x^2+3x+13
Answers
f (x) = x ^ 2 + 1
We apply the transformation f (x + 3) +9:
g (x) = (x + 3) ^ 2 + 1 + 9
Rewriting we have:
g (x) = (x + 3) * (x + 3) + 1 + 9
g (x) = (x ^ 2 + 3x + 3x + 9) + 1 + 9
g (x) = (x ^ 2 + 6x + 9) + 1 + 9
g (x) = x ^ 2 + 6x + 9 + 1 + 9
g (x) = x ^ 2 + 6x + 19
Answer:
the resulting function if the transformation f (x + 3) +9 is applied on the function f (x) = x ^ 2 + 1 is:
c) x ^ 2 + 6x + 19
draw and label an example of two parallel lines that are perpendicular to a third line.
Answers
The larger of two numbers is 10 more than three times the smaller number is larger number decreased by the smaller number is 80 what are the two numbers
Answers
Smaller number = x
Larger number = 3x+10
When you have those two equations down, you have another data section that tells you the value of the two numbers. In your case:
Larger number - Smaller number = 80.
Plugging in what we have:
(3x+10)-x=80
3x+10-x=80
2x+10=80
2x=70
2x/2=70/2
x=35...
Plugging back in for the larger number, since we found the smaller one:
3(35)+10=105+10=115
Your numbers are 115 and 35
Hope this helps.
HELP PLEASE!
A manufacturer uses a mold to make a part in the shape of a triangular prism The dimensions of this part are shown below.
which estimate is closest to the volume in cubic millimeters of the part
306
768
1,008
2,016
Answers
This answer may be wrong.. But I'm trying to make sure it's not!!
C. 1,008 :)
The Volume of the triangular prism is 124.74 cubic mm.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill. Volume is a three-dimensional quantity used to calculate the capacity of a container.
Given:
Base of the triangle (b) = 12.3 mm
Height of the triangle (h) = 8.2 mm
Length of the prism (l) = 20.5 mm
So, the volume of the triangular prism formula:
= 1/2 x b x h x l
= 1/2 x 14.4 x 2.1 x 8.25
= 7.2 x 2.1 x8.25
= 124.74 cubic mm.
Learn more about Volume here:
https://brainly.com/question/14851358
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What two numbers add to 2 and multiply to -14
Answers
is your answer
Algebra 2!..!!!! please help
Answers
(x - 2)(x^2 + 9x + 10)
x^3 + 9x^2 + 10x - 2x^2 - 18x - 20
x^3 + 7x^2 - 8x - 20.
Since the product just found is not the original expression given, Jimmy is wrong.
I will complete the work on paper by synthetic division and post my answer.
After using synthetic division, the correct quotient is x^2 + 9x + 20.
What is 43.29 rounded to the nearest 10th
Answers
The answer is "40.30".
Reason:
First you fine the tenths place:
43.29
Then look at the number next to it:
43.29
Its greater than 5 therefore it does round:
=40.30
If you need anymore help feel free to ask me!
Hope this helps!
What the answer plz help it dividing
Answers
[tex] \frac{9y^{3} - 9y^{2}}{y} \\ \frac{9y^3}{y} - \frac{9y^2}{y} \\ 9y^2 - 9y[/tex]
Simplify (5y^6u^-7)*(5u^9v^-6)*(3v^5y)
Answers
Simplify the following expression:
[tex](5y^6u^{-7})(5u^9v^{-6})(3v^5y)[/tex]
First, multiply the terms
[tex]=(5y^6u^{-7})(5u^9v^{-6})(3v^5y)[/tex]
[tex]=(25y^6u^{2}v^{-6})(3v^5y)[/tex]
[tex]=(75y^7u^{2}v^{-1})[/tex]
Rearrange the negative exponent:
[tex]=(75y^7u^{2}v^{-1})[/tex]
[tex]= \frac{75y^7u^{2}}{v} [/tex]
Rearrange to follow the correct form:
[tex]= \frac{75u^{2}y^7}{v} [/tex]
This is the most you can simplify this expression:
[tex]\boxed{=\frac{75u^{2}y^7}{v} }[/tex]
I hope this helped!
-Benjamin
Simplify (6x^2+11x-3) + (2x^2-17x-4)
Answers
36+11+4= 51, -17= 34x
-3+-4= -7
The simplified expression would be 34x+-7.
(This could be wrong though, I'm sorry if it is ^^)
5 . which of the following is NOT considered a low intensity cardiovascular activity ? ( 1point )
A . walking
b. bicycling
c. hiking
d. leisurely paced swimming,
Answers
If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?
A) π
B) 11π
C) 5π
D) 11/45π,
Answers
A spinner has 8 equal sectors with different letters for each sector, as shown below: a spinner with 8 equal sectors is shown. the sectors are labeled b, y, g, p, o, v, m, and r. hamlet spins the spinner 13 times, and it stops at the letter r 9 times. if he spins the spinner a 14th time, what is the theoretical probability that this time it will stop at the letter r? 1 over 14 1 over 13 1 over 9 1 over 8 question 4(multiple choice worth 1 points)
Answers
Answer:
The theoretical probability of obtaining letter 'r' at the 14th spin is:
[tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
It is given that:
A spinner has 8 equal sectors with different letters for each sector.
The sectors are labeled b, y, g, p, o, v, m, and r.
Hamlet spins the spinner 13 times, and it stops at the letter r 9 times.
We are asked to find the theoretical probability that we will get letter r at the 14th spin.
The theoretical Probability is given as the ratio of number of favorable outcomes to the total number of outcomes.
Hence, the theoretical probability of obtaining letter 'r' at the 14th spin is:
[tex]\dfrac{1}{8}[/tex]
( As there are a total of 8 outcomes( or 8 sectors) out of which there is only one sector which is red)
30 Points! Please Help!
Please explain your answer.
Answers
Cos is adjacent over hypotenuse tangent is sin over cos and cotangent is cos over sin
A single die is rolled twice. find the probability of rolling an odd number and a number greater than 4 in either order.
Answers
The probability of rolling an odd number and a number greater than 4 in either order is 1/6.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, a single die is rolled twice,
∴ The 36 outcomes are
(1,1),(1,2)...(1,6),(2,1)...(2,6),(3,1)...(3,6),(4,1)...(4,6)...(5,1)...(5,6)...(6,1)...(6,6).
So, N(S) = 36.
The no of favorable outcomes N(F) an odd number and a number greater than 4 in either order are [{(1,5),(1,6),(3,5)(3,6),(5,5),(5,6)} as given they can occur in either order so (1,5) and (5,1) are one combined.
∴ N(F) = 6.
So, The probability P(F) of rolling an odd number and a number greater than 4 in either order is,
P(F) = N(F)/N(S).
P(F) = 6/36.
P(F) = 1/6.
learn more about probability here :
https://brainly.com/question/795909
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The probability of rolling an odd number and a number greater than 4 in either order when a single die is rolled twice is 1/18.
To find the probability of rolling an odd number and a number greater than 4 in either order when a single die is rolled twice, we need to first identify the possible outcomes. The odd numbers on a die are 1, 3, and 5. Since we are also looking for a number greater than 4, the only possible outcomes that meet both conditions are 5 and 6.
When the die is rolled twice, there are 6 x 6 = 36 possible outcomes. There are two favorable ways to achieve the goal: Roll a 5 (odd) first and then a 6 (greater than 4), or roll a 6 first and then a 5. Thus, there are two successful outcomes: (5, 6) and (6, 5). The probability of each individual outcome is 1/36, so the combined probability is 2/36, which simplifies to 1/18.
Therefore, the probability of rolling an odd number and a number greater than 4 in either order with a single die rolled twice is 1/18.
Can someone help fast? I will give 20 points. Thx
1. The Empire State Building in New York CIty is 1,454 feet tall. A model of the building is 24 inches tall. What is the ratio of the height of the model to the height of the actual Empire state Building? A) 727:12 B) 727:1 C: 12/727 D) 1:727
Are the polygons similar? If they are, write a similarity statement and give the scale factor. The figure is not drawn to scale. A) JKML ~ PSRQ; 8:1.5 B) JKML ~ PQRS; 8:4.8 C) JKML ~ PQRS; 2.5:4.8 D) The polygons are not similar.
3. What similarity statement can you write relating the three triangles in the diagram? A) GHF ~ GIH ~ HIF B) HIF ~ GIH ~ GFH C) GFH ~ GHI ~ HIF D) GHF ~ IGH ~ HIF
4. What are the values of x and y? A) x=9/4, y=3/4 B) x=9/4, y=15/4 C) x=15/4, y=5/4 D) x=3/4, y=15/4
5. What is the value of x to the nearest tenth? The figure is not drawn to scale. A) x=15.7 B) x=4.4 C) x=13.9 D) x=1.9
6. Are the two triangles similar? How do you know? A) No B) Yes; by AA ~ C) Yes; by SAS ~ D) Yes; by SSS ~
7. What is the geometric mean of 6 and 13? A) 2_/13 B) 2_/26 C) _/78 D) 78
8. A salsa recipue uses green pepper, onion, and tomato in the extended ratio 3:7:11. How many cups of green pepper are needed to make 189 cups of salsa? A) 9 B) 27 C) 63 D) 99
9. What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale. A) 24 B) _/24 C) 143 D) _/143
10. What is the solution to the proportion? 6/11 = m/121 A) 66 B) 11 C) 1/66 D) 1 11. What is the value of x, given PQ || BC? A) 10 B) 5 C) 7 D) 8
Answers
Answer:This may not help but 1 is 1:727
2is they are not similar
Step-by-step explanation:
Fk
PLEASE HELP A flight across the US takes longer east to west then it does west to east. This is due to the plane having a headwind flying westward (thus slowing it down) and a tailwind flying eastward (thus pushing it along faster). Suppose you are flying from Philadelphia, PA to San Diego, CA. The distance between the cities is 2,400 miles and the plane's speed is 450 mi/hr. What is the speed of the wind?
Complete the chart
Going westward- Distance - Rate- Time
Going Eastward-
Write an equation to represent the total time if the round trip takes 11 hours.
Solve your equation to find the speed of the wind. Round to the nearest mph.
PLEASE HELP!
PLEASE ANSWER CORRECTLY TO GET BRAINLIEST ANSWER
Answers
where
[tex]d[/tex] is distance
[tex]v[/tex] is speed
[tex]t[/tex] is time
1. Let [tex]v_{w}[/tex] be the speed of the wind, [tex]t_{w}[/tex] be time of the westward trip, and [tex]t_{e}[/tex] the time of the eastward trip. We know from our problem that the distance between the cities is 2,400 miles, so [tex]d=2400[/tex]. We also know that the speed of the plane is 450 mi/hr, so [tex]v=450[/tex]. Now we can use our equation the relate the unknown quantities with the quantities that we know:
Going westward:
The plane is flying against the wind, so we need to subtract the speed of the wind form the speed of the plane:
[tex]d=vt[/tex]
[tex]2400=(450-v_{w})t_{w}[/tex]
Going eastward:
The plane is flying with the wind, so we need to add the speed of the wind to the speed of the plane:
[tex]d=vt[/tex]
[tex]2400=(450+v_{w})t_{e}[/tex]
We can conclude that you should complete the chart as follows:
Going westward -Distance: 2400 Rate:[tex]450-v_w[/tex] Time:[tex]t_w[/tex]
Going eastward -Distance: 2400 Rate:[tex]450+v_w[/tex] Time:[tex]t_e[/tex]
2. Notice that we already have to equations:
Going westward: [tex]2400=(450-v_{w})t_{w}[/tex] equation(1)
Going eastward: [tex]2400=(450+v_{w})t_{e}[/tex] equation (2)
Let [tex]t_{t}[/tex] be the time of the round trip. We know from our problem that the round trip takes 11 hours, so [tex]t_{t}=11[/tex], but we also know that the time round trip is the time of the westward trip plus the time of the eastward trip, so [tex]t_{t}=t_w+t_e [/tex]. Using this equation we can express [tex]t_w[/tex] in terms of [tex]t_e[/tex]:
[tex]t_{t}=t_w+t_e [/tex]
[tex]11=t_w+t_e[/tex] equation
[tex]t_w=11-t_e[/tex] equation (3)
Now, we can replace equation (3) in equation (1) to create a system of equations with two unknowns:
[tex]2400=(450-v_{w})t_{w}[/tex]
[tex]2400=(450-v_{w})(11-t_e)[/tex]
We can conclude that the system of equations that represent the situation if the round trip takes 11 hours is:
[tex]2400=(450-v_{w})(11-t_e)[/tex] equation (1)
[tex]2400=(450+v_{w})t_{e}[/tex] equation (2)
3. Lets solve our system of equations to find the speed of the wind:
[tex]2400=(450-v_{w})(11-t_e)[/tex] equation (1)
[tex]2400=(450+v_{w})t_{e}[/tex] equation (2)
Step 1. Solve for [tex]t_{e}[/tex] in equation (2)
[tex]2400=(450+v_{w})t_{e}[/tex]
[tex]t_{e}= \frac{2400}{450+v_{w}} [/tex] equation (3)
Step 2. Replace equation (3) in equation (1) and solve for [tex]v_w[/tex]:
[tex]2400=(450-v_{w})(11-t_e)[/tex]
[tex]2400=(450-v_{w})(11-\frac{2400}{450+v_{w}} )[/tex]
[tex]2400=(450-v_{w})( \frac{4950+11v_w-2400}{450+v_{w}} )[/tex]
[tex]2400=(450-v_{w})( \frac{255011v_w}{450+v_{w}} ) [/tex]
[tex]2400= \frac{1147500+4950v_w-2550v_w-11(v_w)^2}{450+v_{w}} [/tex]
[tex]2400(450+v_{w})=1147500+2400v_w-11(v_w)^2 [/tex]
[tex]1080000+2400v_w=1147500+2400v_w-11(v_w)^2[/tex]
[tex](11v_w)^2-67500=0[/tex]
[tex]11(v_w)^2=67500[/tex]
[tex](v_w)^2= \frac{67500}{11} [/tex]
[tex]v_w= \sqrt{\frac{67500}{11}} [/tex]
[tex]v_w=78[/tex]
We can conclude that the speed of the wind is 78 mi/hr.
Which rule can be used to describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3?
Answers
"Which rule ..." suggests you have some rules to choose from to describe the growth. Since you refer to "each interval from x=-1 to x=3", we assume your rule is concerned with more than one interval. With no further clues as to what you may be looking for, we can compute the factor by which the function grows from x=-1 to x=3.
The growth factor over that interval is the ratio of final value to initial value:
.. (12^3)/(12^-1) = 12^(3 -(-1)) = 12^4 = 20,736
Answer:
The rule "multiply by 12" describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3.
Step-by-step explanation:
The given function is
[tex]y=12^x[/tex]
The initial value is 1 and the growth factor is 12.
It is an exponential function.
At x=-1
[tex]y=12^{-1}=\frac{1}{12}[/tex]
At x=0
[tex]y=12^{0}=12^{-1}\times 12=1[/tex]
At x=1
[tex]y=12^{1}=1 \times 12=12[/tex]
At x=2
[tex]y=12^{2}=12 \times 12=144[/tex]
At x=3
[tex]y=12^{3}=144 \times 12=1728[/tex]
Therefore the rule "multiply by 12" describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3.
A store has 20% off sale on coats.With this discount, the price of one coat is 34.50 Whats the price of the coat?
Answers
20% = 0.20
34.50 / 0.20 = 172.50