The distance between the points Q and R is 7.211 units.
What is an ellipse?In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base. It has two focal points.
Given an equation of ellipse x²/8+y²/18 =1, a line 2y = 3x intersect the ellipse at points Q and R,
x²/8+y²/18 =1........ (i)
2y = 3x....... (ii)
Use eq 2 in 1, we get
x²/8+(3x/2)²/18 = 1
On solving, we get,
x²/4 = 1
x = ±2
And,
(2y/3)²/8+y²/18 = 1
On solving, we get,
y = ±3
Therefore, we got, y1 = 3, y2 = -3, x1 = 2 and x2 = -2
Using the distance formula, D = √(x1-x2)²+(y2-y1)²
QR = √(-2-2)²+(-3-3)² = 7.211
|QR| = 7.211
Hence, The distance between the points Q and R is 7.211 units.
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Question Progress
Rectangles ABCD and DEFG are congruent.
AB = 7cm
AD = 17cm
Work out the length of CE.
Optional working
Answer:
CE=7cm
Step-by-step explanation:
because if AB is the same half of CD is equal to 7
Un tren va a 70 km/h debe reducir su velocidad a 30 km/h al pasar por un puente si realiza la operación en cinco segundos qué camino ha recorrido ese tiempo
The total path length covered in 5 second will be 69.45 meter.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge. It performs the operation in five seconds.
Using the first equation of motion -
v = u + at
(30 x 5/18) = (70 x 5/18) + 5a
(30 x 5/18) - (70 x 5/18) = 5a
- (5/18) x 40 = 5a
- (200/18) = 5a
a = - (40/18)
a = - 2.22 m/s²
S = 19.44 x 5 + 0.5 x (- 2.22) x 25
S = 97.2 - 27.75
S = 69.45 meter
Therefore, the total path length covered in 5 second will be 69.45 meter.
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[Question translation in english -
A train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge if it performs the operation in five seconds what total path has been traveled in that time.]
Predict the cost of a meal for a family of four between $55 and $100. Be sure to include dollars and cents. Part A: If the family has a 15% off coupon, calculate the new price of the meal. Show all work or explain your steps. (6 points) Part B: Calculate a 22% tip using the new price. What is the final cost of the meal? Show all work or explain your steps. (6 points)
The final cost is lie between the amount $46.00 and $92.00.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The coupon is given = 15% off
New price = Cost of meal (1 - coupon)
Now Substitute the known values in the equation;
New price = between 55(1 - 15%) and 100.00 (1 - 15%)
Evaluate;
The final cost of the meal is between $40.00 and $80.00
Tip = 22%
Thus Final cost = New price (1 + tip)
Now Substitute the known values in the equation
Final cost = Between 40.00 (1 + 22%) and 80.00 (1 + 22%)
The Final cost is Between $46.00 and $92.00
Hence, the final cost is lie between the amount $46.00 and $92.00
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How many liters of milk will jamal need to make 15 milkshake
Answer:
where are the numbers?
Step-by-step explanation:
Jax bought a package of plastic utensils for a picnic. There are a total of 40 utensils,
and 10 of them are knives. What percent of the plastic utensils are knives?
4) Pick the model that represents the problem.
0%
0%
?
Submit
10
10
What percent of the plastic utensils are knives?
100%
40
100%
40
Answer:
25% were knives
Step-by-step explanation:
Line K has an undefined slope. Line M is parallel to Line K, and passes through the point (-5, 6). What is the equation of Line M?
The equation of line M that is parallel to line K is: x = -5.
What is the Equation of a Vertical Line?A vertical line has a slope that is undefined. Therefore, it has no slope, hence, the equation of the line is expressed as x = b, where b is the point on the x-axis where the line intercepts.
Since line K and line M are parallel to each other, their slope will be the same. Line K has an undefined slope, so also will the slope of line M be undefined. This means line M is a vertical line.
Given that line M passes through (-5, 6), b = -5. To write the equation of the line M, substitute b = -5 into x = b:
x = -5.
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Solve the system by substitution.
y = -6x +8
7x + 2y = -14
Answer:
y=-28 and x=6
Step-by-step explanation:
y=-6x+8...... eqn(1)
7x+2y=-14.......eqn(2)
Two times equation (1)
2y=-12x+16..... eqn(3)
2y=-14-7x........ eqn (2)
eqn(3) - eqn(2)
0=-5x+30
5x=30
x=6
from eqn (1) where x=6
y=-6(6)+8
y= -36+8
y=-28
Please help meeeeee!!!!!
For the points A(-2,-3), B(0,5), C(2,5), D(4,9) and E(6,13) the slope of the line is 2.
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
y - y₁ = m(x - x₁)
In the given table, the points are,
A(-2,-3), B(0,5), C(2,5), D(4,9) and E(6,13)
To find the slope of a line which passes through the given points,
The slope of the line will always the same for any pair of points,
So slope of line having points (-2,-3) and (0,1)
Use slope formula = (y₂-y₁)/(x₂-x₁)
slope = (1-(-3))/0-(-2)
= 1+3/2
= 2
The slope of the line is 2.
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Need help dragging the dot on the graph as well
The height of a building is 1957 feet. How long would it take an object to fall to the top? Use the formula d=16t^2
It will take 2.76 seconds an object to fall to the top.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given that The height of a building is 1957 feet.
S = the distance
Given d = 16t² is the function for the height as a function of time. It will hit the ground when h=0 so:
16t² - 1957 =0
16t² - 1957 =0
16t² =1957
t² =1957 /16
t=√(1957 /16) seconds
t≈ 2.76 seconds (to nearest hundredth of a second)
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Convert 7.5 miles to yds
Answer: 13200 yards
Step-by-step explanation: 1 mile is equivalent to 1760 yards. If you multiply 1760 by 7.5, you get 13200 yards.
method 2: algebra
1. if you set the problem up as an equation, it's y/7.5=1760. Then you cross multiply, so y=13200. (Both methods are different but will get you to the same answer)
Pre-Calculus A
Which of the following graphs is a function?
Graph (a) represent the equation x+2y=4, and it is a function.
What is function?A function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
To determine the function, solve with the help of option,
(A) The graph define the equation of line x+2y = 4
For any value of x, y gives a unique value,
This satisfies the definition of function,
Therefore, graph (A) is a function.
(B)
The graph defines the function x = |y-2|
For one value of x, y has two values,
Thus, values of y are not unique.
(C)
The graph defines the equation of circle x²+y² = 1
For one value of x, y has two values,
Thus, values of y are not unique.
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Please help and thank you
Daniella: Were you thinking of perpendicular lines?
Ori: It seems like you've got the basic idea, but your definition could be more precise.
Kaori: Yes! Well done. Here, have a cookie. You've earned it.
Josh Is 9 years old and 129 cm tall. Medical chart shows that a boy's height at age 9 is 3/4 of his predicted adult height. Predict Josh's Adult height
Answer:
172 cm
Step-by-step explanation:
a=Adult height. n=9 year-old height
a*3/4=n
a*3/4=129
a*3/4 / 3/4 = 129 / 3/4
a = 129 * 4/3 ==> dividing by a number is equal to multiply by its reciprocal
a = 516/3
a = 172 cm
Find the missing exponent p^2 x p^0 x p^3 x p^? = P^9
Answer:
4
Step-by-step explanation:
[tex]p^{2}[/tex][tex]p^{0}[/tex][tex]p^{3}[/tex][tex]p^{x}[/tex] = [tex]p^{9}[/tex]
When you multiply powers with the same bases, you add the exponents.
9 - 2 - 0 - 3 = 4
Solve the system for 20 points. :)
Answer: C
Step-by-step explanation:
x ∈ R
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
amplitude = 6
midline = -4.5
Period =5
Step-by-step explanation:
Please help will mark Brainly
Answer:
f(x) = - 2x + 4
Step-by-step explanation:
Since we are only trying to move the graph up 3 units, the slope does not change. So, it would be -2.
We also know that the 1 in f(x)= -2x + 1 is the y-intercept (y=mx+b). But again, we are moving the graph 3 units up, so we have to add 3. That makes it 4 (3+1=4).
So, the new equation would be f(x) = -2x + 4
Step-by-step explanation:
it simply means that g(x) is f(x) just shifted 3 units upwards.
that means nothing else changes, only whatever y result f(x) produces is increased by 3.
so,
g(x) = f(x) + 3 = -2x + 1 + 3 = -2x + 4
therefore, as domain and range were the whole set of real numbers, the addition of 3 does not make any difference in relation to infinity. so, they remain unchanged.
the slope stays the same (g(x) is simply a parallel line to f(x)).
the y-intercept (the y-value when x = 0) also increases by 3, and is 4.
the x-intercept (the x-value when y = 0) changes :
0 = -2x + 4
2x = 4
x = 2
the x-intercept is 2.
please help answer these 5 attached questions⬇️
Answer:
The order of the answers provided are in the order of the photos uploaded in the question :)
Step-by-step explanation:
To find the perimeter we have to add the lengths of all the sides together
To find the area we have to subtract the area of the gaps by the area of the whole shape if it were to be a rectangle or square
1)
Perimeter: 4 + 2 + 2 + 4 + 2 + 6 = 20 mArea: (4 x 6) - (4 x 2) = 16 m²2)
Perimeter: 4 + 2 + 4 + 3 + 6 + 1 = 20 cmArea: (4 x 6) - (1 x 4) = 20 cm²3)
Perimeter: 8 + 6 + 2 + 2 + 6 + 8 = 32 mArea: (8 x 8) - (2 x 2) = 60 m²4)
Perimeter: 5 + 5 + 3 + 1 + 2 + 6 = 22 cmArea: (6 x 5) - (3 x 1) = 27 cm²5)
Perimeter: 6 + 2 + 3 + 3 + 2 + 3 + 1 + 2 = 22 kmArea: (6 x 5) - (3 x 1) - (3 x 3) = 18 km²Hope this helps, have a great day!!
of 16 Step 1 of 1
Teagan wants to buy a new generator. The generator costs $2050. Teagan decides to finance the generator for 24 months at an APR of 11.5%.
Determine Teagan's monthly payment. Round your answer to the nearest cent, if necessary.
01:11:21 0
Formulas
With an APR of 11.5%, Teagan decides to finance the generator for 24 months. 1.29% is Teagan's Rate.
Explain about the Interest?In its most basic form, interest is computed as a percentage of the principle. The interest you would pay, for instance, would only be 5% of $100 if you borrowed $100 from a friend and agreed to reimburse it with 5% interest: $100(0.05) = $5.
An expense associated with borrowing money or other assets is interest. The principal, which represents the amount borrowed, is what's referred to as interest, which is calculated as a percentage of the principal over a specified period of time.
The interest rate for the loan is denoted by this proportion. When you place money in a high-yield savings account, for instance, a bank will give you interest.
= 11.5 x 1/100 = 0.155
= 0.155 ÷ 12 = 0.01291
= 1.29% Rate
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Ernesto brings his dog to training classes. The equation -60x+2y-120 = 0 relates y, the total cost of a pet's training, and x, the number of classes taken. Ernesto states that the y-intercept of the line represented by the equation is 30. Is he correct? Explain your reasoning.
Answer:
Step-by-step explanation:
i need help asap, please don’t tell me the wrong answer
Answer:
C
Step-by-step explanation:
a relative maximum is a point from which the function starts decreasing
(√9)³× (√30)² what is the value of this answer
Answer:
(√9)³× (√30)²=810
Step-by-step explanation:
Lets first solve (√9)³
√9=3
3^3=27
(√9)³=27
In (√30)², the "²" and the "√" cancel out resulting in 30.
(√30)²=30
So (√9)³× (√30)² can be simplified into 27 x 30
Simplify:
27x30
10(27x3)
10(81)
810
PLEASE MARK BRAINLIESTAt the city meusum, child admission is $5.10 and the adult admission is $8.30. On Saturday, four times as many adult tickets were sold, for a total of sales of $9119.20. How many child tickets were sold that day?
Answer:
238
Step-by-step explanation:
child: $5.10
adult: $8.30
4 times as many adult as children
total: $9119.20
Let c = number of child tickets.
Let a = number of adult tickets.
5.1c + 8.30a = 9119.2
a = 4c
5.1c + 8.3(4c) = 9119.2
38.3c = 9119.2
c = 238.099
There must be a mistake with the numbers because the number of child tickets must be a whole number.
The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that a random sample of 34 smoke detectors will have a mean lifetime between 58 and 63 months. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places.
The probability that a random sample of 34 smoke detectors will have a mean lifetime between 58 and 63 months, using the normal distribution, is of:
0.9135 = 91.35%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters in the context of this problem are given as follows:
[tex]\mu = 60, \sigma = 8, n = 34, s = \frac{8}{\sqrt{34}} = 1.37[/tex]
The probability that a random sample of 34 smoke detectors will have a mean lifetime between 58 and 63 months is the p-value of Z when X = 63 subtracted by the p-value of Z when X = 58, hence:
X = 63:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (63 - 60)/1.37
Z = 2.19
Z = 2.19 has a p-value of 0.9857.
X = 58:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (58 - 60)/1.37
Z = -1.46
Z = -1.46 has a p-value of 0.0722.
0.9857 - 0.0722 = 0.9135 = 91.35%.
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Find the equation of the line that satisfies the conditions given in each of the following: 1. Through (3, 2) and (5, 7) 2. Through (-3, 4), m = 2 3. m = -3, b = 5 4. x-intercept = 3, y-intercept
The equation of each line that satisfies the given conditions are:
1. y - 2 = 5/2(x - 3)
2. y - 4 = m(x + 3)
3. y = -3x + 5
What is the Equation of a Line?If we know the slope (m) and the y-intercept (b) of a line, we can write the equation of the line as y = mx + b in slope-intercept form.If we know the point (a, b) and the slope (m) of the line, we can write the equation of the line in point-slope form as y - b = m(x - a).1. Given the points, (3, 2) and (5, 7), find the slope (m):
Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)
m = 5/2
Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):
y - 2 = 5/2(x - 3)
2. Given:
A point = (-3, 4)
Slope (m) = 2
Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):
y - 4 = m(x + 3) [equation of the line]
3. Given:
Slope (m) = -3
Y-intercept (b) = 5
Substitute m = -3 and b = 5 into the equation y = mx + b:
y = -3x + 5
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3) Find the measure of angle A.
Answer:
60
Step-by-step explanation:
First set up your equation
All triangles have angles that add up to 180, this means that you can make an equation where all your sides = 180
here is the equation: 7x-3+9x-1+40= 180 (i just wrote all the sides we can see)
Then you'll want to solve for x
7x-3+9x-1+40= 180
first combine like terms. We have a 7x and a 9x, so add them together
This will give you 16x-3-1+40=180
Now since your plain numbers (no variable) are on the same side of the = sign, you can just deal with them now. You can do -3-1+40 which is 36.
Now you have 16x+36=180
Now you'll want to take 36 from both sides. 36 is positive right now so you should do the opposite and subtract it from both 180, and itself.
This leaves you with: 16x=144
You have 16x which is the same as 16 times x. You want to do the opposite again. The opposite of multiplying is dividing so divide 144 by 16. This gives you 9 which is your x value.
Now one last thing. to get A on the triangle you can plug your X value (9) into the equation it gave you (7x-3)
this looks like 7(9)-3. 7 times 9 is 63. 63 -3 is 60.
(you can check your answer by plugging 9 into the other equation and adding everything up. it will equal 180)
A Chevrolet Sonic Hatchback costs $ 14 , 800.00 $14,800.00. With a 12 12 % % down payment, you can have an amortized loan for 6 6 years at a rate of 4.5 4.5 % %. What will the monthly payment be? Car cost in total, interest will be paid money
The monthly payment, car cost in total, and the interest to be paid, based on the loan amount and the number of years are:
Monthly payment - $206.74Car cost in total - $14, 885. 52Interest to be paid - $1, 861.52How to find the interest to be paid?First, find the loan amount:
= Cost of car x ( 1 - down payment percent)
= 14, 800 x ( 1 - 12%)
= $13, 024
Then find the monthly rate and the number of periods:
Monthly rate:
= Yearly rate / 12 months per year
= 4.5% / 12
= 0.375%
Number of periods:
= Number of years x Months per year
= 6 years x 12
= 72 months
Using these, the monthly payment can be found by the formula:
= Loan amount / Present value interest factor of annuity, 72 periods , 0.375%
= 13, 024 / 62.995976235992
= $206.74
Total cost paid on loan for car:
= Monthly payment x Number of months
= 206. 74 x 72
= $14, 885. 52
This means that the total interest paid was:
= Total amount paid on cost of car - Loan amount
= 14, 885.52 - 13, 024
= $1, 861.52
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Solve for f(-2).
f(x) = 24
6
f(-2) =「?1
Answer:
f(- 2) = 0
Step-by-step explanation:
to evaluate f(- 2), substitute x = - 2 into f(x)
f(- 2) = [tex]\frac{2(-2)+4}{6}[/tex] = [tex]\frac{-4+4}{6}[/tex] = [tex]\frac{0}{6}[/tex] = 0
John Rey invests $4100 in two different accounts. The first account paid 9 %, the second account paid 7 % in interest. At the end of the first year he had earned $307 in interest. How much was in each account?
John Rey invested $1000 in the first account at 9% interest and $3100 in the second account at 7% interest .
Let he invested x in the first account at 9%.
Interest = Principal × rate × time
Here rate = 0.09 and time = 1 year
Interest earned = 0.09x
Amount invested at 7% = $(4100-x)
rate = 0.07 and time = 1 year
Interest earned = 0.07(4100-x)
Total interest earned is $307
Hence : 0.09x + 287 - 0.07x = 307
or, 0.02x = 20
or, x = 1000
Amount invested at 7% = $(4100 - 1000) = $3100
Therefore John Rey invested $1000 in the first account at 9% interest and $3100 in the second account at 7% interest .
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.
Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.
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