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Find the value of x and y.
Answers
[tex]\left\{\begin{array}{ccc}2x+3y=68&|\cdot(-15)\\30x+11y=112\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-30x-45y=-1020\\30x+11y=112\end{array}\right}\\.\ \ \ \ \ \ \ -34y=-908\ \ \ |:(-34)\\\\.\ \ \ \ \ \ \ \ \ \ \ y=\dfrac{908}{34}\to y=\dfrac{454}{17}\\\\2x+3\cdot\dfrac{454}{17}=68\ \ \ \ |\cdot17\\\\34x+1362=1156\ \ \ \ |-1362\\34x=-206\ \ \ \ |:34\\\\x=-\dfrac{206}{34}\to x=-\dfrac{103}{17}\\\\ \left\{\begin{array}{ccc}x=-\dfrac{103}{17}\\\\y=\dfrac{454}{17}\end{array}\right[/tex]
Related Questions
The angle of elevation from a boat to the top of a lighthouse is 22°. The lighthouse is 32 meters tall.
What is the distance from the boat to the base of the lighthouse?
Enter your answer as a decimal. Round only your final answer to the nearest tenth.
Answers
The distance from the boat to the lighthouse would be the base of the triangle
to find the base given the height and angle given the formula is
x = height / tan(angle)
x = 32 / tan(22)
x = 79.2 Meters
Does anyone know how to find x?
Answers
We can solve this using trigonometric functions. We will be referring to the 70 degree angle. We need to solve for the hypotenuse. We have the length of the opposite side and need to find the hypotenuse. Therefore, we use the sine.
sin70=12/x
Since we cannot immediately solve for x, we will simplify this equation. We multiply both sides by x.
x(sin70)=12
Divide both sides by sin70.
x=12/sin70
Now we solve this equation.
12/sin70≈15.51
Therefore, x=15.51 cm.
I hope this helps!
x=15.51cm
70+90+x=180
Leah pays $40 a month for cable TV, plus $4 for each movie she orders on pay-per-view. Which equation gives Leah’s total monthly cable bill as a function of the number of pay-per-view movies m that she orders?
Answers
b = bill
b = 4m + 40
I hope this helps
An equation which gives Leah’s total monthly cable bill is b=4m+40.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Leah pays $40 a month for cable TV, plus $4 for each movie she orders on pay-per-view.
Let the number of pay-per-view movies she orders be m and the total monthly cable bill be b.
Now, b=4m+40
Therefore, an equation which gives Leah’s total monthly cable bill is b=4m+40.
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Evaluate the following in polar and standard forms. Select all answers that apply. [3(cos(27°) isin(27°))]^5
Answers
if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)
Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
=================================
Part (2)
The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2 and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]
= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
===========================================
The correct answers are options (1) and (3)
option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
Question 2 (Matching Worth 4 points)
Match the sequence (term) with the correct type of sequence (definition).
Match Term Definition
128, 32, 8, 2, … A) Geometric, common ratio is 0.25
1, 3, 9, 27, … B) Geometric, common ratio is 3
5, 10, 15, 20, … C) Arithmetic, common difference is −3
20, 17, 14, 11, … D) Arithmetic, common difference is 5
Answers
Which makes it so that the common difference between 5, 10, 15, 20 is 5.
Then the difference between 20, 17, 14, 11 ... is -3.
Other than that your correct
Mr bartley is taking the theater club on a field trip he wrote the the folowing function for the school treasure 52(25+2)
Answers
Answer:
The answer is 1,404
Step-by-step explanation:
To do this operation, you should be aware of the order of operations. PEMDAS is a good way to remember the order of operations:
1. Parenthesis
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Substraction
Therefore, the first thing we have to do is the parenthesis.
(25+2) = 27
And now, we can do the multiplication
52*27 = 1,404.
1.
A. 3.75
B. 1.5
C. 3
D. 4.5
2.
A. 30
B. 16
C. 8
D. 15
Answers
1)
b: 3.75 since it is half of the segment that measures 7.5, this is proven because the line in the middle is a bisector of the top and bottom line indication that both half measure the same; 3.75
2) 15 not sure why
Find the volume of the square pyramid to the nearest cubic unit. edge 10 ft; height 11 ft 1,467 ft3 1,100 ft3 550 ft3 367 ft3
Answers
[volume of square pyramid]=(1/3)*b²*h
where
b is the length side of the square base-----> 10 ft
h is the height-----> 11 ft
[volume of square pyramid]=(1/3)*10²*11----> 366.67 ft³-----> 367 ft³
the answer is
367 ft³
Jenna uses 18 inches if ribbon for each box she wraps how many yds of ribbon does she need to wrap 4 boxes
Answers
She needs 2 yards of ribbon to wrap 4 boxes.
since 1 yard is 36 inches she will need 72/36=2 yards.
if you like my answer please rate as brainliest! thx
A pet store has two tanks of tropical fish. The first tank contains 7 blue fish and 3 yellow fish and the second tank contains 10 blue fish and 8 yellow fish. If Keisha randomly purchases a fish from each tank, what is the probability that both fish will be blue? A. 1/70 B. 17/180 C. 7/18 D. 17/28
Answers
In the first tank we have 7 blue fish and 3 yellow fish, so total number of fishes in tank 1 = 10
The probability of picking a blue fish in tank 1 = number of blue fishes/ total number of fishes = 7/10
The second tank has 10 blue fish and 8 yellow fish, so the total number of fishes in tank 2 = 18
The probability of picking a blue fish in tank 2 = number of blue fishes/ total number of fishes = 10/18
The probability that both fish will be blue = 7/10 * 10/18 = 70/180 = 7/18 (Option C)
Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town
Answers
Please Help! 16 points!
The equation 1.6x − 2.2 = 1.4x can be transformed to form which of the following expressions?
Select one:
a. 3.0x = 2.2
b. 0.2x = −2.2
c. 3.0x = −2.2
d. 0.2x = 2.2
Answers
You must simplify the equation using SADMEP, the reverse order of operations in which subtraction is the first step. Your goal is to isolate the variable.
First, subtract 1.6 from each side:
1.6x - 2.2 = 1.4x
-1.6x -1.6x
------ --------
This will get you to 0x - 2.2 = -0.2x, or -2.2 = -0.2x
This is equivalent to 2.2 = 0.2x
So, the equation can be simplified to 0.2x = 2.2
Hope this helps, let me know if you need anything else! :)
Answer:
d
Step-by-step explanation:
Using differentiation from first principles, prove that the gradient of the line y=mx + c is m
Answers
[tex] \frac{dy}{dx} = m[/tex]
because when you differentiate, only the constant of the x remains (which is m in this case), and c being another constant independent of x, is 0 when differentiated. hence, since dy/dx is the gradient of the line, m is therefore the gradient
Anyone know the answer?
Answers
What is the length of AB?
Answers
Let the center be O. So OB is the radius = 14.5
We can draw a triangle as shown in the image below. We have a right angled triangle. We know the hypotenuse and the base, we need to find the perpendicular side. This can be done using the Pythagorean theorem.
So, we can write:
[tex](14.5)^{2}=10^{2}+OA^{2} \\ \\ OA^{2}=110.25 \\ \\ OA=10.5 [/tex]
Thus, the measure of OA = 10.5
OB = OA + AB
14.5 = 10.5 + AB
⇒
AB = 4
form a right triangle with the 10 as 1st side and r as the hypotenuse.
get the length of the other side using pythagorean.
c = sqrt(14.5^2 - 10^2) = 10.5
The length from the center to point A = c = 10.5
AB = r - c = 14.5 - 10.5 = 4
length AB = 4
what is the value of this expression 3*[(7+8)*2+6] A.64 B.87 C.96 D.108
Answers
thats the answer
[tex]=3*36[/tex]
[tex]=108[/tex]
Hope this helps :)
Six years ago annabelle was twice as old as jason was. now, annabelle is four years older than jason. how old is jason now?
Answers
The present age of Jason is given as 10 years.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given problem can be solved as follows,
Suppose the age of Jason 6 years ago was x.
Then, the age of Annabelle 6 years ago was 2x.
Their present ages are x + 6 and 2x + 6 years respectively.
As per the question, the following equation can be formed as follows,
2x + 6 = x + 6 + 4
=> 2x - x = 10 - 6
=> x = 4
Thus the present age of Jason is 4 + 6 = 10 years.
Hence, the age of Jason now is 10 years.
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98 POINTS PLEASE HELP
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Determine the standard form of the equation for the circle
With center (h,k)=(-5,1/2) and radius r=1
A) (x-5)^2 + (y + 1/2)^2 = 1
B) (x-5) + (y - 1/2) = 1
C) (x+5)^2 + (y - 1/2)^2 = 1
D) (x+5)^5 + (y- 1/2)^2 = 105/2
Answers
Hello!
I believe the answer is C) (x+5)^2 + (y - 1/2)^2 = 1.
I hope it helps!
pls help with this pre-calc question on vectors!!
Answers
C. √29
The explanation of this exercise is:
To solve this problem you must apply the proccedure shown below:
1- You have that:
W (-2,8,-3) and X(1,4,-1)
2- Therefore, you can calculate the magnitude as below:
|WX|=√[(1-(-2)]²+(4-8)²+[(-1-(-3)]²)
|WX|=√29
The angle of elevation from point A to the top of a cliff is 38 degrees. If point A is 80 feet from the base of the cliff, how high is the cliff?
A.
60.50 ft.
B.
62.50 ft.
C.
63.50 ft.
D.
61.50 ft.
Answers
h = 80 tan 38 = 62.50 ft
Its B
Your brother and sister took turns driving on a 580 mile trip that took 10 hours to complete. your brother drove at a constant speed of 55 miles per hour and your sister drove at a constant speed of 60 miles per hour. how long did each person drive.
Answers
x+y=10
thus
x=10-y........i
distance=speed*time
the distance each one drove will be:
55x+60y=580....ii
substituting i in ii we get:
55(10-y)+60y=580
550-55y+60y=580
5y=30
y=6 hours
thus
x=10-6=4 hours
hence the boy drove for 4 hours and the girl for 4 hours
Using a system of equations, it is found that the brother drove for 4 hours and the sister drove for 6 hours on their 580-mile, 10-hour trip.
To solve this problem, let's assign variables to the unknown quantities. Let x be the number of hours your brother drove and y be the number of hours your sister drove. We know they drove for a combined total of 10 hours and covered 580 miles together. This gives us two equations:
Equation 1 (Total Time): x + y = 10Equation 2 (Total Distance): 55x + 60y = 580Since there are two equations with two unknowns, we can solve for x and y by using substitution or elimination method. Let's use the substitution method:
Solve Equation 1 for y: y = 10 - xSubstitute y into Equation 2: 55x + 60(10 - x) = 580Simplify and solve for x: 55x + 600 - 60x = 580, which gives us -5x = -20, so x = 4.Now substitute x back into Equation 1 to find y: y = 10 - 4, so y = 6.Therefore, your brother drove for 4 hours, and your sister drove for 6 hours.
Hi, I don't feel very confident about my work in this calculus problem and I would appreciate it if anyone else could note any corrections or ways to improve my answers. My problem is split into parts A, B, C, and D and my work is in green. Thank you!
Answers
A. Correct.
B. Correct.
C. Sign error in the boxed answer. -(-0.5) = 0.5
The graph shows c ≈ 1.855. If a is more than that and decreasing, area is increasing. The sign of dA/dt will be positive. (Compare to D)
D. Units are not shown. Numerical value is correct.
0.6704 repeating as a fraction?
Answers
Then [tex]10^4x=6704.67046704\ldots[/tex], and we have
[tex]10^4x-x=9999x=6704[/tex]
which means
[tex]x=\dfrac{6704}{9999}[/tex]
What is the value of r?
Answers
Answer:R = 4
Step-by-step explanation:
Richard can read 1/4 of a book in 3/5 of an hour. At this rate, how much can Richard read in one hour
Answers
Find 1/5 hour:
1/5 hour ⇒ 1/4 ÷ 3 = 1/4 x 1/3 = 1/12 of the book
Find 5/5 (1 hour):
5/5 hour ⇒ 1/12 x 5 = 5/12 of the book
Answer: 5/12 of the book
. Convert 5π/3 to degrees
Answers
Convert [tex] \pi [/tex] to 180 to get the following fraction:
[tex] \frac{5 * 180}{3} [/tex]
Multiply 5 and 180 together to get the following fraction:
[tex] \frac{900}{3} [/tex]
Simplify the fraction.
[tex] \frac{900}{3} [/tex] = 300
The answer is 300 degrees.
so 5π / 3 radians = 180 / π * 5 π / 3 = 900 / 3 = 300 degrees Answer
Two campers leave their campsite at point A to go on a hike. Camper one heads east for 2 miles, then heads north 1 mile to point B. Camper two heads north for 4 miles, then east for 3 miles to point C. Referencing the triangle formed by A, B, and C, m
A.
27°
B.
36°
C.
45°
D.
53°
Answers
Answer:
its not C. It's A. 27
I just did it with my math teacher
The volumes of two spheres are in a ratio of 1:8. what is the ratio of their radii?
Answers
volume of a sphere=(4/3)*pi*r³
let
A-----> smaller sphere
B-----> larger sphere
VA=(4/3)*pi*rA³
VB=(4/3)*pi*rB³
VA/VB=1/8--------> (1/8)=[(4/3)*pi*rA³]/[(4/3)*pi*rB³]
(1/8)=[rA³]/[rB³]-----> (1/8)=[rA/rB]³-----> rA/rB=∛(1/8)----> rA/rB=1/2
the answer is
the ratio of their radii is (1/2)
Maria is ordering copy paper for her office. The office is low on white paper and on blue paper. She will pay $3.50 per realm of white paper and $3.75 per realm of blue paper. If the purchase order is for $36.00 and she ordered 10 realms of paper, how many realms of white paper will she receive
Answers
x: the number of reams of white paper purchased
y:the number of reams of blue paper purchased
Then, you have the following system of equations:
x+y=10
3.50x+3.75y=36
When you solve the system shown above, you obtain:
x=6
y=4
The answer is: 6 reams of white paper
1>>> a+b=10
2>>> 3.50a+3.75b=36
a=6
b=4
There will be 6 realms of white paper that Maria will receive
A gazebo is located in the center of a large circular lawn with a diameter of 300 feet. straight paths extend from the gazebo to a sidewalk around the lawn. if two of the paths form a 45 angle, how far would you have to travel around the sidewalk to get from one path to the other? Round your answer to the nearest foot
Answers
arc length=2πr(central angle/360)
r=300 feet/2
r=150 feet
central angle=45°
2. When you substitute the values, you obtain
arclength=118 feet
The answer is: 118 feet
Answer: 118
Step-by-step explanation:
1.To solve this problem you must apply the formula for calculate the arc length, which is:
arc length=2πr(central angle/360)
r=300 feet/2
r=150 feet
central angle=45°
2. When you substitute the values, you obtain
arclength=118