Answers
[tex]10+y=5x+x^2~~~~.....(i)\\\\5x+y =1~~~....(ii)\\\\\text{From (i):}\\\\10+y = 5x +x ^2\\\\\\\implies y = 5x +x ^2 -10\\\\\text{Substitute y in equation (ii):}\\\\5x+5x+x^2-10=1\\\\\implies x^2 + 10x -11 =0\\\\\implies x^2 +11x -x -11=0\\\\\implies x(x+11) -(x+11) =0\\\\\implies (x-1)(x+11) =0\\\\\implies x =1 ~~ \text{or}~~ x = -11\\\\\text{Substitute x =~1 in equation (ii):}\\ \\5+y =1 \implies y =-4[/tex]
[tex]\\\text{Substitute}~ x =-11~ \text{in equation (ii):}\\\\\ 5(-11) + y = 1 \implies y = 1 +55 = 56 \\\\\text{Hence} (x,y) = (-11,56) ~~\text{and}~~ (x,y)=(1,-4)[/tex]
Related Questions
What is the amplitude and period of the function shown below?
Answers
The features of the sine function in this problem are given as follows:
Amplitude: 2.
Midline: y = -4.
Period: 3 units.
What is trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here, we have,
The equation is given as follows:
y = 2sin(2πx/3) - 4.
we have to define the sine function:
The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.
B: the period is 2π/B.
C: phase shift.
D: vertical shift.
The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:
2A = 4.
A = 2.
Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:
D = -4.
The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:
2π/B = 3
B = 2π/3.
The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:
y = 2sin(2πx/3) - 4.
More can be learned about trigonometric functions at brainly.com/question/21558626
#SPJ2
Jamie Lee needs to save a total of $9,000 in order to get started in her cupcake café venture. She is presently depositing $1,800 a year in a regular savings account. Calculate the future value of these deposits.
Answers
Answer: 16,200,000
Step-by-step explanation: divide both numbers
The future value of her deposit would be in 5 years.
The total amount needed to start a cupcake cafe venture
= $9,000
Deposit per year = $1,800
Therefore, if $1,800 = 1 year
$9,000 = X
[tex]x = \frac{9000}{1800} [/tex]
[tex]x = 5[/tex]
Therefore in 5 years, Jamie Lee would be able to start her cupcake café venture.
Learn more about savings here:
https://brainly.com/question/25787382
Please help thank you! Solve for x and y
Answers
Answer:
x = 2
y = 7
I aced this lesson in 6th grade.
Step-by-step explanation:
hope this helps. . . <3
good luck! uωu
Answer:
Step-by-step explanation:
All 4 sides are equal. (They are marked that way).
8x = 5x + 6 Subtract 5x from both sides
8x - 5x = 5x - 5x + 6 Combine
3x = 6 Divide by 3
3x/3 = 6/3
x = 2
Consecutive angles of a rhombus are supplementary
97 + 12y - 1 = 180 Combine
96 + 12y = 180 Subtract 86 from both sides
12y = 180 - 96
12y = 84 Divide by 12
y = 84/12
y = 7
Please help! Grade 7 math
Answers
Answer:
[tex]-\frac{5}{8}\\-9.2%\\\\-0.001[/tex]
-3/4, -5/8, -9.2%, -0.001, 4.6%, 5%, 33%
Step-by-step explanation:
[tex]-\frac{3}{4}=-75[/tex]% 4.6%
Let's do the process of elimination to find our answers
[tex]-\frac{5}{8}=-62.5[/tex]% this would be in between because - 62.5% would be after -75%
[tex]\frac{5}{100}=5[/tex]% this fraction equals to a positive percentage which would be after 4 so not this one
[tex]-0.001 = -0.1[/tex]% this number would come after -75%, -62.5%, -9.2%and before 4.6% so this would be one
[tex]-0.75= -75[/tex]% we already have the percentage so not this one
33% this number would come after 4.6% so not this one
-9.2% this would be between them because its -9 and it will be after -75% and -62.5%
Someone, please help me with this. I will give Brainliest
Answers
Explanation:
What we need to do here is to take the ratio of the distances of the planets to determine how much farther Neptune is from the sun compared to Mercury:
[tex]\dfrac{D_N}{D_M} = \dfrac{4.503×10^9\:\text{km}}{5.791×10^7\:\text{km}} = 7.776×10^1[/tex]
This means that Neptune is 77.76 times farther from the sun than Mercury is.
biografía completa de Pitágoras
Answers
Answer:
hiiiiiiiiiíiiiiiiiiiii
Explain the differences and similarities of the steps for dividing whole numbers and decimals.
Answers
Answer: Comparing a whole numbers and a decimals:
First let’s talk about the similarities of comparing whole numbers and decimals:
=> their place value always matters.
Now, let’s proceed to their differences
=> in comparing whole numbers, we don’t care about the value to the nearest decimal points or the value of ones. We always look at the highest value, not unless the highest values are all the same.
=> In comparing decimals, the value to the nearest decimal points or the tenths place value always matters.
Step-by-step explanation:
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is p = 19.00 Mbps. The sample size is n = 21 and the test statistic is t= 1.401
P-value = (Round to three decimal places as needed)
Answers
Using the t-distribution, it is found that the p-value is of 0.177.
At the null hypothesis, it is tested that for a smartphone carrier's data speeds at airports, the mean is 19 Mbps, that is:
[tex]H_0: \mu = 19[/tex]
At the alternative hypothesis, it is tested if the mean is different than 19 Mbps, that is:
[tex]H_1: \mu \neq 19[/tex]
We are testing if the mean is different from a value, hence it is a two-tailed test.The test statistic is t = 1.401.Sample size of n = 21, hence there are 21 - 1 = 20 df.Inputting this information into a calculator, the p-value is of 0.177.
A similar problem is given at https://brainly.com/question/13873630
due in an hour please help!!! :(
Answers
Answer:
Step-by-step explanation:
1,7 are same side exterior
1,8 alternate exterior
2,4 none
3,5 same side int
2,6 corrosponding
4,6 same side int
4,7 is none
5,4 alternate int
8,5 vertical
8,7 alternate exterior
In 2020, Puerto Rican rapper Bad Bunny claimed the top spot of most streamed artist globally on SPOTIFY, with more than 8.3 billion streams (8,300,000,000) this year from fans around the globe. His album YHLQMDLG—released in late February 2020, featuring collaborations with Sech, Anuel AA, and Daddy Yankee—is the number one streamed album as well. Calculate the profit earned using these numbers. (Hint: Use the slope intercept format to build this equation. Also, remember one unit = one thousand streams).
Answers
PLZZZ HELPPP
What are the domain and range of f (x) = 1/2 (x+4)^2 - 11
Domain: All real numbers
Range: f(x) > -11
Domain: 3 > -11
Range: f(x) > -11
Domain: All real numbers
Range: All real numbers
Domain: 2 > -11
Range: All real numbers
Answers
Answer:
D. Domain: 2 > -11
Range: All real numbers
Step-by-step explanation:
Correct me if I’m wrong UwU
Answer:
Domain: All real numbers
Range: f(x) ≥ - 11
Step-by-step explanation:
Given the quadratic function in vertex form, f(x) = ½(x + 4)² - 11:
The vertex, (h, k) is (-4, -11).
Range: f(x) ≥ -11.The parabola opens upward (where a = ½, which is greater than 0), and k = -11 is the minimum value for f(x). Hence, the range of the given function must be at least -11, or f(x) ≥ -11.
Domain: all real numbersThere is no restriction for the value of x. Therefore, the domain of the given function is all real numbers.
Anne bought an aquarium priced at $44.96. Shipping and handling cost an additional 25%of the price. What was the total cost of the aquarium, including shipping and handling?
Answers
Find the 6th term of the geometric sequence whose common ratio is
1/3
and whose first term is 5.
Answers
Step-by-step explanation:
geometric sequence means every new term is created by multiplying the previous term by a certain constant (here 1/3).
s1 = 5
s2 = s1 × 1/3 = 5 × 1/3
s3 = s2 × 1/3 = s1 × 1/3 × 1/3 = 5 × 1/9
sn = sn-1 × 1/3 = s1 × (1/3)^(n-1) = 5 × (1/3)^(n-1)
s6 = 5 × (1/3)⁵ = 5 × 1/243 = 5/243
29. Which set of integers is listed in order from least to greatest?
5,8,-9, -10
-5, -3, -2,7
O-5, 4, -2, -7
O 5, 4, 2, -1
Answers
Answer:
It would be the second set of numbers.
Step-by-step explanation:
Please help me with these questions. I’m genuinely confused.
Answers
Answer:
16: 5
17: 6 4/9
Step-by-step explanation:
I only will give u the answer for a few questions
) Which value is equivalent
[tex] {7}^{3} [/tex]
Answers
Answer:
343
Step-by-step explanation:
[tex]7^{3} = 7 * 7 * 7[/tex]
[tex]7^3 = 343[/tex]
-Chetan K
chapter 6.4 : Problem 4
Answers
Answer:
wdym
Step-by-step explanation:
Becca hikes 9/10 mile in 5/3 hour.
Answers
Answer:
(9/10 mile)/(5/3 hour) = 27/50 miles/hour
Step-by-step explanation:
If you are looking for the speed, then speed = distance/time
speed = (9/10 mile)/(5/3 hour)
speed = 9/10 ÷ 5/3 miles/hour
speed = 9/10 × 3/5 miles/hour
speed = 27/50 miles/hour
Answer:
1. 9/10/3/5
2. 3/2
Step-by-step explanation:
Got it correct on iReady.
A 6 sided die is rolled 2 times. What is the probability of getting a 1 both times ?
Answers
Answer:
Step-by-step explanation: If you roll the die twice, the probability of getting a even number both times is (1/2)(1/2) ... A probability experiment consists of rolling a 6 sided die
Which number line shows the solution of –5x + 10 > –15? A. B. C. D.
Answers
[tex]-5x+10>-15\\\\\implies -5x> -10 -15\\\\\implies -5x > -25\\\\\implies x< 5\\\\\text{Interval,} ~(-\infty,5)[/tex]
Answer:
add the options, then we'll talk
Step-by-step explanation:
Solve the equation for B. PLEASE SHOW YOUR WORK.
2(B + 3.5 - B = -3(6 - 2B)
Answers
9514 1404 393
Answer:
B = 5
Step-by-step explanation:
The given equation has mismatched parentheses. We assume the intent is ...
2(b +3.5) -b = -3(6 -2b)
Eliminating parentheses, we have ...
2b +7 -b = -18 +6b
25 = 5b . . . . . . . . . . . add 18-b to both sides and collect terms
b = 5 . . . . . . . . . . . . divide both sides by 5
Question 21: In January, Michelle walked 15.73 miles. In February she walked 3.6 miles. In March,
she walked 8.01 miles. How many miles did she walk in all?
Answers
Answer:
27.34 milesStep-by-step explanation:
Add all together:
15.73 + 3.6 + 8.01 = 27.3415.73miles + 3.6miles + 8.01miles = ...
= 19.33miles + 8.01miles
= 27.34miles
For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t is time in seconds. Let θ be the angle between the line of your horizon and your line of sight to the elevator. 4 (a) Find a formula for h(t), the elevator's height above the ground as it descends from the top of the hotel. h(t) = (b) Using your answer to part (a), express θ as a function of time t. θ(t) = Find the rate of change of θ with respect to t. dθ dt = (c) The rate of change of θ is a measure of how fast the elevator appears to you to be moving. At what time does the elevator appear to be moving fastest? time = seconds At what height does the elevator appear to be moving fastest?
Answers
9514 1404 393
Answer:
a. h(t) = -20t +400
b. θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)
c. 15 seconds; 100 ft
Step-by-step explanation:
a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...
h(t) = -20t +400
__
b. The tangent of the angle above the line of sight is "opposite"/"adjacent":
tan(θ) = (h(t) -100)/(150) = -2/15t +2
θ(t) = arctan(2 -2/15t) . . . . radians
The derivative of the angle function is ...
dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)
dθ/dt = -30/(1125 -120t +4t^2)
__
c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)
The elevator appears to be moving fastest at t=15 seconds.
The height at that time is ...
h(15) = 400 -20(15) = 100
The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.
If 10 candy cost $35. How much candy can I buy with $20
Answers
Answer:
6 candies
Step-by-step explanation:
(find unit rate, cost / quantity)
35/10 = 3.5
20/3.5 = = 5.7142857142857
candies cannot be in decimal so you must round to the nearest whole
For the right angle shown, the length of two sides are given. Find the third side. Leave your answer in simplified, radical form.
b=9, c=16
a=
Answers
Answer:
a is about 13.2
Step-by-step explanation:
the formula for this type equation is a²+b²=c²
plug in the numbers to make the equation a²+9²=16²
do the multiplication and it gives u a²+81=256
subtract 81 from both sides and a²=175
take the square root of both sides and it gives u 13.22
18x+5=-1+8x+46 find value of x
Answers
Answer:
3
Step-by-step explanation:
18x + 15 -8x = 8x + 45 -8x
10x + 15 = 45
10x + 15 - 15 = 45 - 15
10x = 30
10x/10 = 30/10
× = 3
the difference between factors and factor pairs
Answers
Answer:
Factors are often given as pairs of numbers, which multiply together to give the original number. These are called factor pairs. A square number will have one factor pair consisting of one factor multiplied by itself. This factor is called the square root of the given number.
Myra likes blueberry yogurt, but cherry yogurt is her favorite. Yesterday, she bought 3 cartons of cherry yogurt for every 2 cartons of blueberry yogurt. If Myra bought 3 more cartons of cherry yogurt than blueberry yogurt yesterday, how many cartons of cherry yogurt did she buy?
Answers
Answer:
9 cherry, 6 blueberry
Step-by-step explanation:
lets do a table!
cherry | blueberry
----------------------------
3 2
6 4
9 6
When there are 2 blueberry, there are 3 cherry. 3 is 1 more than 2. When there are 4 blueberry, there are 6 cherry. 6 is 2 more than 4. When there are 6 blueberry, there aare 9 cherry. 9 is 3 more than 6.
You have 2.567 grams of water. What is the volume of water(use correct units)
Answers
Answer:
16
Step-by-step explanation:
16 grams
Look at attached photo. Will give brainiest to correct answer. Trigonometry.
Answers
Answer:
Step-by-step explanation: