Find the measures of two complementary angles if the measure of the larger angle is 2 less than 3 times the measure of the smaller angle. The measure of the smaller angle is
°,
and the measure of the larger angle is
°
Answers
The measure of the smaller angle is 23⁰ and the measure of the larger angle is 67⁰.
What are complementary angles?
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
So we can say that two angles are complementary if they sum up to 90 degrees.
From the given statement;
let the larger angle = ylet the smaller angle = xy = 3x - 2 -------(1)
y + x = 90 --------(2) (since they are complementary)
substitute for y in equation (2)
3x - 2 + x = 90
4x = 92
x = 92/4
x = 23 ⁰
y = 3(23) - 2
y = 67⁰
Thus, the measure of the smaller angle is 23⁰ and the measure of the larger angle is 67⁰.
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Related Questions
20. Find the domain and range for the following graph.
Domain:
Range:
Pls help
Answers
9514 1404 393
Answer:
both are (-∞, ∞)
Step-by-step explanation:
The domain and range of any odd-degree polynomial are both "all real numbers." They go from -infinity to +infinity.
Your polynomial is of degree 3, so is of odd degree. The arrows on the ends of the curve indicate it extends to infinity in that direction.
y → +∞ for x → +∞
y → -∞ for x → -∞
prove algebraically that 0.5 recurring = 5/9
Answers
Answer and Step-by-step explanation:
We want to prove that 0.5555... = 5/9.
First, let's set 0.555... equal to x:
x = 0.555...
Now multiply this by 10:
10x = 5.555...
Now subtract the original from this new one:
10x = 5.555...
- x = 0.555...
______________
9x = 5
Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.
We now have 9x = 5, so divide both sides by 9:
x = 5/9, as desired
Giving brainliesttttt help pls pls
Answers
Answer:
option a. 7y + 6 + 5m and option e. 6 + 5m + 7y
Step-by-step explanation:
5y and 2y are like terms
After drinking, the body eliminates 37% of the alcohol present in the body per hour.
a) The amount of alcohol in grams in the body on an hourly basis is described by a discrete time dynamical system (DTDS) of the form xn+1=f(xn), where xn is the number of grams of alcohol in the body after n hours. Give the updating function f (as a function of the variable x).
b) Peter had three alcoholic drinks that brought the alcohol content in his body to 41 grams, and then he stopped drinking. Give the initial condition (in grams) for the DTDS in (a).
c) Find the solution of the DTDS in (a) with the initial condition given in (b). (Your answer will be a function of the variable n, which represents time in hours.)
Answers
The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.
a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.
Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:
f(x) = x - 0.37x
Simplifying the equation:
f(x) = 0.63x
b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:
x0 = 41 grams
c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.
For n hours, the solution is given by:
xn = f^n(x0)
Applying the updating function f(x) repeatedly for n times:
xn = f(f(f(...f(x0))))
In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:
xn = (0.63)^n * x0
Substituting the initial condition x0 = 41 grams, the solution becomes:
xn = (0.63)^n * 41 grams
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Please check your answer cause this is my last question
Answers
The interest rate would be 13%.
What is the simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest. For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.
To find the interest rate, we can use the formula for simple interest:
I = Prt
where I is the amount of interest earned, P is the principal (the initial amount of money deposited), r is the interest rate, and t is the time in years.
In this case, we know that I = $3,900, P = $10,000, and t = 3 years. We can use this information to solve for r:
I = Prt
$3,900 = $10,000r3
r = $3,900/($10,000*3)
r = 0.13 or 13%
Hence, the interest rate is 13%.
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Question 7 of 10
Is the graph increasing, decreasing, or constant where 8 < x < 10?
Answers
Answer:
Increasing
Step-by-step explanation:
because 8 is on the left side and the left side is negative and the side ten is on is positive
(121÷11)-√49
125+9×7
Answers
Answer:
-18176
Step-by-step explanation:
6. Which of the following is true about the
graph of the equation y = -5x + 10?
A. The graph would increase from left to right.
B. The graph would pass through the origin.
C. The graph would have a positive y-intercept.
D. The graph would have a slope of 10.
Answers
Y=mx + b is the formula (M being slope, and B being the y intercept) always start by going up or down by what the y-intercept number is, if it’s -9 you go down the y axis 9 numbers from the origin (0,0) and slope (m) is always better put in a fraction-5x is better put in -5/1x
Think of the top number of the fraction as ‘up/down’ and the bottom number as ‘over’ if the top number is negative you will go down from the y-intercept number that many times, the bottom number is how many spots you go over from that number , it is always to the right.
A company can make 12 printing presses for $78,600. It can make 19 printing presses for $82,380. Find the linear equation that models the cost to produce x printing presses. Use slope-intercept form
Answers
Answer:
\(C(x) = 540x + 72120\)
Step-by-step explanation:
Given
Cost = $78,600 when Printing Press = 12
Cost = $82,380 when Printing Press = 19
Required
Determine the linear equation
From the given parameters; Cost is a function of Printing Press
Represent Cost by C and Printing press by x;
This implies that C = f(x)
The given parameters can then be modeled as; \((x, C)\)
\((x_1, C_1) = (12,78600)\)
\((x_2, C_2) = (19,82380)\)
The first step is to calculate the slope, m;
\(m = \frac{C_1 - C_2}{x_1 - x_2}\)
\(m = \frac{78600 - 82380}{12 - 19}\)
\(m = \frac{-3780}{-7}\)
\(m = 540\)
The linear equation can then be calculated using slope formula
\(m = \frac{C- C_2}{x - x_2}\)
Substitute 540 for m and \((x_2, C_2) = (19,82380)\)
\(540 = \frac{C- 82380}{x - 19}\)
Multiply both sides by x - 19
\(540 * (x-19)= \frac{C- 82380}{x - 19} * (x-19)\)
\(540 * (x-19)= C- 82380\)
Open bracket
\(540x - 10260 = C - 82380\)
Add 82380 to both sides
\(540x - 10260 + 82380= C - 82380 + 82380\)
\(540x - 10260 + 82380= C\)
\(540x + 72120= C\)
\(C = 540x + 72120\)
Hence;
\(C(x) = 540x + 72120\)
What is d in the following arithmetic sequence? 5, 7, 9, 11, 13....
(A)5
(B)-2
(C)+2
(D)13
Answers
give: ∠BDE ≅ ∠CDE and BD ≅ CD.
Prove ∠ABD ≅ ∠ACD
Answers
3) \(\angle ADB\) and \(\angle BDE\) are supplementary (if two angles form a linear pair, they are supplementary)
4) \(\angle ADC\) and \(\angle CDE\) are supplementary (if two angles form a linear pair, they are supplementary)
5) \(\angle ADB \cong \angle ADC\) (supplements of congruent angles are congruent)
6) \(\triangle ADB \cong \triangle ADC\) (SAS)
7) \(\angle ABD \cong \angle ACD\) (CPCTC)
Find the first three nonzero terms of the Maclaurin series for the function and the values of x for which the series converges absolutely. f(x) = 4 sin x . ln(1 + x)
Answers
The interval of convergence is given as: ⟹|x|<1
What is Maclaurin series?
Given the values of the function's successive derivatives at zero, a Maclaurin series is a power series that enables one to construct an approximation of a function with input values close to zero.
We will utilize the common power series representation of the functions, such as sine and the logarithmic function, to find the first three non-zero terms of the Maclaurin series representation for the function. We shall multiply the terms of each expression to obtain the final expression.
\(sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}\)
\(ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}\)
The series representation shown above is only accurate when ⇒|x| < 1.
Given that;
f(x) = 4 sin(x) ln(1+x)
We are familiar with how functions are represented by power series:
\(sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}\)
\(ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}\)
The series representation shown above is only accurate when ⇒|x| < 1.
\(sin(x) ln(1+x) = [x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........][x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........]\)
\(sin(x) ln(1+x) = x^2 -\frac{x^3}{3}+\frac{x^4}{4} +\frac{x^5}{5} +........\)
Finally, the function's power series representation is given as:
⇒ \(f(x) = 4 sin(x) ln(1+x) = 4 [x^2 - \frac{x^3}{2}+\frac{x^4}{6} +\frac{x^5}{6}+..... ]\)
The interval of convergence is given as: ⟹|x|<1.
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50 POINTS! Use the Parabola tool to graph the quadratic function.
f(x)=(x+4)^2 −6
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
General equation
y=a(x-h)²+kBy observing y=(x+4)²-6
Vertex is at (-4,-6)a is 1So
The parabola graph is attached
Answer:
See below ~
Step-by-step explanation:
Given :
f(x) = (x+4)² − 6
f(x) = a(x + h)² + k
The vertex of the graph is (-4, -6)Compressibility factor (a) is equal to 1Another point on the parabola :
Take x = 1f(1) = (1 + 4)² - 6f(1) = 25 - 6f(1) = 19The second point is (1, 19)Graph :
i need help!! thank you in advance
Answers
Write an equation of the line that passes through the given point P and has the given slope m.
P(9,4)
m = -1/3
Answers
9514 1404 393
Answer:
y -4 = -1/3(x -9)
Step-by-step explanation:
The point-slope form of the equation for a line is useful for this.
y -k = m(x -h) . . . . . . . line through point (h, k) with slope m
You are given (h, k) = (9, 4) and m = -1/3. Putting these values into the form gives the equation ...
y -4 = -1/3(x -9)
6,926,300,000 in scientific notation.
Answers
Answer:
6.9263 × 109
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Marisa wants to buy an iPad. She
already saved $25 and plans to
save an additional $10 each week.
Write an expression that represents
the total amount of money Marisa
has saved after any number of
weeks. Use w for number of weeks.
Answers
Answer:
f(w)(or y)=10w+25
Step-by-step explanation:
The 25 is how much you have saved up and the 10 is how much you get each week
(1, 1) and (4, 3) slope
Answers
Answer:
\( \huge \boxed{ \boxed{ \frac{2}{3} }}\)
Step-by-step explanation:
The slope of a line given two points can be found by using the formula
\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)
From the question we have
\(m = \frac{3 - 1}{4 - 1} = \frac{2}{3} \\ \)
We have the final answer as
\( \frac{2}{3} \\ \)
Hope this helps you
Find an equation of the level curve of f(x y) = x2 y2 that contains the point (3 5)
Answers
The equation of the level curve described above that contains the points (3,5) is -2u/[u + v]²
What is the explanation for the above result?F(x1, y1) = = √[x² + y²]
contains
f(3, 5)
F(3, 5) = √(3² + 5²)
= √34
= 5.83095
g(u,v) = [u-v]/[u+v]
gu = [(1) (u + v) - (u-v) (1)]/(u+v)²
= 2v/(u+v)²
gv = [(-1) (u + v) - (u-v) (1)]/(u+v)²
= -2u/(u + v)²
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Full Question:
Find an equation of the level curve of f(x y) = √x² + y² that contains the point (3, 5)
The winning team
in a 400-meter relay race had a time of
198.608 seconds. Suppose all 4 of the split
times were the same. Write and solve an
equation to find the split times.
Answers
The equation for split times is 4x= 198.608 and the value of x is 49.652
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x be the split time
all 4 of the split times were the same.
4x= 198.608
=> x= 198.608/4 = 49.652
The equation for split times is 4x= 198.608 and the value of x is 49.652
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A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that apply.
Answers
The correct statements are:
The triangle and trapezoid area formulas have 1/2.
The parallelogram and rectangle formulas are both the same.
In the trapezoid formula, the bases are added.
What is a triangle?A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.
Area of a triangle = 1/2 x base x height
A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2 x (sum of the lengths of the parallel sides) x height
A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width
A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length
Area of a parallelogram = base x height
Hence, the correct statements are options (A), (B), and (D).
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The question seems to be incomplete the correct question would be:
A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is
considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that
apply.
A. The triangle and trapezoid area formulas have 1/2.
B. The parallelogram and rectangle formulas are both the same.
C. In the parallelogram formula, the bases are added.
D. In the trapezoid formula, the bases are added.
E. In the triangle formula, the sides are added, then multiplied by 1/2
There were 280 members in the ski
club last year. The membership
DECREASED by 25%. How many
total members are in the club now?
Answers
The club decreased to 7 ski members
Answer:
210
Step-by-step explanation:
25% can also be written as .25. If you multiply .25 by 280 you get 70. 70 is 25% of 280. If you take 70 from 280 you get 210.
Only answer if you will help thank you
A manufacturer is considering building a new and better mousetrap. She estimates the probability that the new mousetrap will be successful is . If it is successful, it would be able to make $120,000. Of course, she would make nothing if it were unsuccessful. The development costs for the mousetrap are $98,000. What is the expected value?
8,000
-$8,000
$22,000
-$32,000
Answers
Answer:
$22,000
Step-by-step explanation:
Subtract the development cost from the amount it would make.
And boy, that's one expensive mousetrap.
Two angles of a quadrilateral measure 133⁰ and 188°. The other two angles are in a ratio of
6:7. What are the measures of those two angles?
Answers
Answer:
18 and 21
Step-by-step explanation:
We take those two angles as 6x and 7x
133⁰ + 188° + 6x + 7x = 360(Sum of angles of a quadrilateral)
321+13x=360
13x=360-321
13x=39
x=39/13
x=3
6x=6x3=18
7x=7x3=21
The orbital period, p, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula p = a superscript three-halves. if saturn’s orbital period is 29.5 years, what is its distance from the sun? 9.5 au 19.7 au 44.3 au 160.2 au
Answers
The distance of Saturn from the sun is 9.5 astronomical units.
Orbital period p of a planet and the planet’s distance from the sun, a in astronomical units are related by:
\(p = a^{3/2}\)
What is the orbital period?The orbital period is the time a given astronomical object takes to complete one orbit around the sun.
Given that Saturn's orbital period is 29.5 years.
So, \(29.5 = a^{3/2}\)
\(a = 29.5^{2/3}\)
a = 9.5 au
Therefore, the distance of Saturn from the sun is 9.5 astronomical units.
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35°
46"
65"
30"
2x
What is the perimeter? This is a little tougher problem,
and to solve it you'll need to know the lengths of the
segments on either side of the perpendicular height
(which is whyt I gave you the numbers in smaller font).
Submit
Answers
The perimeter of the triangle is 170 inches.
How to calculate the valueTo solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:
sin(35°) = 46/x
x = 46/sin(35°) = 65 inches
Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:
cos(35°) = 65/x
x = 65/cos(35°) = 75 inches
The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:
P = 65 + 75 + 30
= 170 inches
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It costs $22 to get a pass at a ski report, plus $5.50 each hour to rent skis. Another ski resort charges $18 for a pass and $7.20 per hour to rent skis. Find the number of hours for which the costs are the same. Round your answer to the nearest half hour.
Answers
ski resort 1: 5.50x +22
ski resort 2: 7.20x +18
(x represents the number of hours)
set the equations equal to find when the costs are the same
5.50x+22=7.20x+18
solve for x (subtract 5.50x from both sides, subtract 18 from both sides)
4=1.7x (divide by 1.7)
2.4=x
in 2 and a half hours the cost would be the same
(−2/3) x (5/4) =
test pls help
Answers
Next, it’ll be (-2 over 3) x 5 over 4
Then it’ll be -1 over 3 x 5 over 2,
Multiply and your final answer will be -5 over 6, or 0.83333…
a shipping box has the dimensions shown. what is the volume of the cubic yards
Answers
Answer:
The answer is 32
a boy has 5 red , 3 yellow and 4 green marbles. in how many ways can the boy arrange the marbles in a line if: a) marbles of the same color are indistinguishable?
Answers
There are 11550 different ways that the line of marbles could be formed in this scenario.
Define combination.Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
As a result, there are (4 + 3 + 4) spots on the line, which equals 11 spots for the 11 marbles.
Given that identical-colored marbles cannot be distinguished.
This means that, for instance, if there are four red marbles in the first, second, third, and fourth positions, moving the four red marbles around these positions won't result in a different arrangement.
Solving by combination,
The total number of ways that four spots can be assigned to red marbles is thus = ¹¹C₄ = 330 ways
The number of ways three yellow marbles can be placed in each allocation of red marbles is equal to ⁷C₃ = 35 ways
The number of ways four slots can be allocated to green marbles for each allocation of red and yellow marbles is equal to ⁴C₄ way = 1
As a result, there are (330 × 35 × 1) = 11550 different ways that the line of marbles could be formed in this scenario.
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