Using the Pythagorean theorem, we can calculate the distance between a small plane 20 miles north of an airport and a jet 64.5 miles west of the airport as 67.5 miles to the nearest tenth.
Given that a small plane is 20 miles due north of the airport and a jet is 64.5 miles west of the airport, the scenario forms a right-angled triangle with the legs representing the distances from the airport to each aircraft. To find the distance between the small plane and the jet, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
The equation for the distance (d) between the two planes can be expressed as:
d² = north side² + west side²
d² = 202 + 64.52
d² = 400 + 4160.25
d² = 4560.25
d = √4560.25
d = 67.5 miles (rounded to the nearest tenth)
Thus, the distance between the small plane and the jet is 67.5 miles to the nearest tenth.
Mr. Berger assigned the following system of equations to be solved for homework. 2x-3y = -12
4x+ y= -10
Which is the x-coordinate of the correct solution?
Answer:
A: x= -3
Step-by-step explanation:
The x- coordinate is of solution is -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
2x-3y = -12...........(1)
4x+ y= -10..............(2)
Now, multiply Equation (1) by 2 we get
4x - 6y = -24
4x + y = -10
________
-7y = -14
y= 2
and, 4x+ y= -10
4x + 2 = -10
4x = -12
x= -12/4
x= -3.
Hence, the x- coordinate is -3.
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Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly distributed between 1.0 and 2.1 minutes. (a) determine the mean of x. (round your answer to 2 decimal places.)
Answers anybody?????
Given cos A = 0.25 find angle A in degrees. Round your answer to the nearest hundredth.
34.12°
123.98°
56.78°
75.52°
Use the quadratic formula to determine the exact solutions to the equation.
x^2−2x−4=0
Enter your answers in the boxes.
x=__ or x=___
Are the two triangles are congruent ?
Johnny is five years older than his brother. the sum of their ages is 37. how old is Johnny
Calculus HELP PLEASE? A highway runs due north. A car traveling at 50 mph exits the highway at a 30° angle. After driving another 1.5 hours at the same speed and direction, how far away is the car from the highway?
Answer:
37.5 miles is the answer.
Step-by-step explanation:
Since car is travelling with a speed = 50 mph
Angle between the highway and the track on which the car is travelling = 30°
Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track
Distance traveled by the car in 1.5 hours = speed × time
= 50 × 1.5 = 75 mi.
Therefore sin 30° = x/75
x = 75×sin30° = 75 × 1/2 = 37.5 mi.
Therefore the answer is 37.5 mi away.
what is the approximate distance between the points (-5 1) and (-2 3) on a coordinate grid
Solve x + y + z = 12
2x – y – z = -6
x + 3y + 5z = 44
(4, 3, 5)
no solutions
(2, 4, -6)
(2, 4, 6)
Explain why the function f(x)=x^2 is not invertible
Use the chart above to determine the premium for 10-year term insurance. $10,000 policy for a 35-year-old male. Premium = _____?
6.11
61.10
611.00
6,110.00
Answer:
Option B 61.10
Step-by-step explanation:
Given is a chart giving the premium to be paid for 10 year term insurance for different age groups for an amount of 1000 policy.
We have to calculate the premium for a 35 year old man for 10 year term insurance for 10000 policy.
From the chart we find that for a 35 year old man premium = 6.11
This premium is for 1000 dollars.
Since here sum assured is 10000 dollars, we get the premium
=6.11(10) = 61.10 dollars
Option B is correct
Premium = 61.10 dollars
The formula represents the surface area S of a cube with side lengths x.
S=6x^2
Solve for x.
The solution of x is √(S/6).
The formula to find the surface area of a cube with side lengths x is:
S = 6x2
To solve for x:
Divide both sides by 6: S/6 = x2
Take the square root of both sides to isolate x: x = √(S/6)
A circle has an arc of length 24pi that is intercepted by a central angle of 80 degrees. what is the radius of the circle?
Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.
Complete the statement If x/7 = 5/3, then x+7/7 =?
How do you do x ^4-4? What is the x values?
The measure of dispersion which is not measured in the same units as the original data is the
a. variance
b. standard deviation
c. median
d. coefficient determination
Variance is not expressed in the same units as the original data.
Variance is measured by:
Finding the difference between the mean of a data set and the variables in the data set Squaring this difference Summing up the squaresBecause variance is squared, it is no longer the same units as the rest of the data set. For instance, if the data set is in centimeters, the variance will be in centimeters².
In conclusion, the variance of a data set is not measured in the same unit as the data set.
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Final answer:
The measure of dispersion which is not measured in the same units as the original data is the variance.
Explanation:
The measure of dispersion which is not measured in the same units as the original data is the variance. The variance is a squared measure and does not have the same units as the data. On the other hand, the standard deviation is derived from the variance and it measures the spread in the same units as the data.
Then again, the standard deviation, which is the square foundation of the fluctuation, is estimated in similar units as the first information. It gives a proportion of the spread of the information that is all the more effectively interpretable. The middle is a proportion of focal inclination and doesn't give data about the scattering or spread of the information.
The coefficient of assurance, otherwise called R-squared, is a proportion of how well the relapse line fits the information and isn't straightforwardly connected with scattering.
Consider the quadratic equation. x^2=4x-5. How many solutions does the equation have? a.) one real solution b.) two real solutions c.)no real solutions d.)cannot be determined
This figure shows circle Z with chords AB and RS . mAR=55° mRB=66° AB=8 m RS=8 m What is mRS?
Answer:
The correct answer is, mRs = 121°
Step-by-step explanation:
From figure we get ,
mAR=55° mRB=66° AB=8 m RS=8 m
To find mRS
Using given information we can write,
mAB = mAR + mRB = 55 + 66 = 121°
Since AB=8 m RS=8 m,
AB = RS
⇒ mAB = mRS
mAB = 121°
Therefore mRS = 121°
The correct answer is given by,
mRS = 121°
describe the vertical asymptotes) and holes) for the graph of y=(x+2)(x+4)/(x+4)(x+1)
A. asymtotes: x=-1 and hole: x=4
B. asymtotes: x=2 and hole: x=-1
C. asymtotes: x= -1 and hole: x=-4
D. asymtotes: x=1 and hole: x=4
Can someone plzzzz help me!??
A rectangular prism has a volume of 360 in3. If the height measures 4 in., which base measurements could the prism have? 4 in. by 20 in. 45 in. by 45 in. 6 in. by 15 in. 5 in. by 19 in.
An angle measures 72° less than the measure of a complementary angle. What is the measure of each angle?
Answer: [tex]81^{\circ}\ \text{ and }\ 9^{\circ}[/tex]
Step-by-step explanation:
We know that the sum of two complementary angles is [tex]90^{\circ}[/tex].
Given : An angle measures 72° less than the measure of a complementary angle.
Let x be the angle , then the measure of other angle will be x-72.
Since they area complementary , then we have
[tex]x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=\dfrac{162}{2}=81[/tex]
Therefore, the measure of angles are :
[tex]81^{\circ}\ \text{ and }\ (81-72)^{\circ}=9^{\circ}[/tex]
Algebraically prove that X^3+10/x^3+9=1+ 1/x^3+9 where x is not equal to -3
The ratio of zoya's age to nelya's age is 1:4. twenty years from now, nelya will be twice as old as zoya will be then. find their present ages.
Answer:
Zoya is 10 years old. Nelya is 40 years old.
What number is 22 spaces to the right of negative 7?
Final answer:
By adding 22 to -7, we find that the number 22 spaces to the right of -7 on the number line is 15.
Explanation:
The question asks for the number that is 22 spaces to the right of negative 7 on a number line. To find this, you can simply add 22 to negative 7. Here's the calculation: -7 + 22 = 15. Therefore, the number that is 22 spaces to the right of negative 7 is 15. To determine the number that is 22 spaces to the right of -7 on the number line, we need to add 22 to -7. Moving 22 spaces to the right indicates an increase in value by 22. Therefore, when we add 22 to -7, we get the final answer of 15. This calculation reflects the concept that moving to the right on the number line corresponds to increasing the numerical value, while moving to the left corresponds to decreasing it. In this case, starting from -7 and moving 22 spaces to the right results in a value of 15. Hence, 15 is the number that is 22 spaces to the right of -7.
The volume, V, of a soap bubble is related to its surface area, A. In cubic centimeters, this relationship is shown by the formula V = 0.094A 3/2. What is the surface area of a bubble with a volume of 5 cm3 ?
The surface area of a soap bubble with a volume of 5 cm³, given the relationship V = 0.094 [tex]A^{3/2[/tex], can be calculated by rearranging and solving the formula, resulting in an approximate surface area of 36.3 cm².
To find the surface area of a soap bubble with a volume of 5 cm³, using the given relationship V = 0.094 [tex]A^{3/2[/tex], we need to rearrange the formula to solve for A (the surface area). We will take the following steps to find A:
First, divide both sides of the equation by 0.094 to isolate [tex]A^{3/2[/tex] on one side:
[tex]A^{3/2[/tex] = V / 0.094
Next, substitute V = 5 cm³ into the equation:
[tex]A^{3/2[/tex] = 5 / 0.094
Calculate the right-hand side:
[tex]A^{3/2[/tex] ≈ 53.19
Finally, raise both sides of the equation to the power of 2/3 to solve for A:
A = [tex](53.19)^{2/3[/tex]
Calculating the right-hand side gives us the surface area A. After performing these calculations, we find that the surface area of a bubble with a volume of 5 cm³ is approximately 36.3 cm².
look at the pictures below
Does the function model exponential growth or decay? g(t)=1.7 * 0.8^t
Answer:
decay
just answered this question.
Step-by-step explanation:
Answer:
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Step-by-step explanation:
. (02.02 HC) Dominic earns $18 an hour plus $25 an hour for every hour of overtime. Overtime hours are any hours more than 35 hours for the week. Part A: Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 35 hours. (3 points) Part C: Dominic earned $730 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points) (10 points)