Answers
Answer: 4.3 meters
Step-by-step explanation:
Let the angle opposite the 3-meter side be [tex]\alpha[/tex].
Using the Law of Sines,
[tex]\frac{\sin \alpha}{3}=\frac{\sin 25^{\circ}}{2}\\\\\sin \alpha=1.5 \sin 25^{\circ}\\\\\alpha=\arcsin(1.5 \sin 25^{\circ})[/tex]
Using the sum of the angles in a triangle, the angle opposite the side [tex]\ell[/tex] is [tex]155^{\circ}-\arcsin(1.5 \sin 25^{\circ})[/tex].
Using the Law of Sines,
[tex]\frac{\ell}{\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}=\frac{2}{\sin 25^{\circ}}\\\\\ell =\frac{2\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}{\sin 25^{\circ}}\\\\\ell \approx 4.3[/tex]
Answer: The correct answer is 4.3
Step-by-step explanation:
This is an Obtuse Scalene Triangle
Side a = 2
Side b = 3
Side c = 4.26571
Angle ∠A = 25°
Angle ∠B = 39.34°
Angle ∠C = 115.66°
Area = 2.70415
Perimeter p = 9.26571
Semiperimeter s = 4.63285
Calculate c, ∠B, and ∠C based on given a, b, and ∠A.
∠B = arcsin(b·sin(A)/a)
= 0.68662 rad = 39.34°
∠C = 180° - A - B = 2.01864 rad = 115.66°
c = a·sin(C)/sin(A) = 4.26571 = 4.3
Related Questions
Give two examples of functions that include an absolute value expression and have a vertex of (-1,3).
Select all that apply.
A. f(x)= |x-1| +3
C. f(x)=2x+1| +3
DE. f(x)= |x-1|-3
G. f(x)=2x+11-3
B. f(x)=x+1-3
D. f(x)=2|x-1| +3
OF. f(x)=x+1| +3
H. f(x)=2x-1|-3
Answers
Answer:
B and G
Step-by-step explanation:
f(x) = a|x-h|+k
The number inside the absolute value argument "h" represents the x-value of the vertex. For -1, the number inside has to be +1.
k represents the y-value of the vertex, in this case 3.
The only two expressions that have an h value of 1 and k value of 3 are B and G.
Convert 7.5 miles to yds
Answers
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)
the measure of one angle of a triangle is 66°. of the remaining two angles, one is twice the measure of the other. how could you find the measures of the two unknown angles?
Answers
Answer:
below
Step-by-step explanation:
x = one angle and the other = 2x
solve this to find 'x' and '2x'
x + 2x + 66 = 180 because all of the angles of a triangle = 180
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.
Answers
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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the value of 5/32 ÷ 25/4
Answers
Answer: [tex]\frac{1}{40}[/tex] or 0.025
Step-by-step explanation:
[tex]\frac{5}{32}[/tex] ÷ [tex]\frac{25}{4}[/tex] = [tex]\frac{5}{32}*\frac{4}{25} =\frac{5}{4(8)} *\frac{4}{5(5)} =\frac{1}{40}[/tex]
At 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?
Answers
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.
Find the missing exponent p^2 x p^0 x p^3 x p^? = P^9
Answers
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
Question Progress
Rectangles ABCD and DEFG are congruent.
AB = 7cm
AD = 17cm
Work out the length of CE.
Optional working
Answers
Answer:
CE=7cm
Step-by-step explanation:
because if AB is the same half of CD is equal to 7
Solve for f(-2).
f(x) = 24
6
f(-2) =「?1
Answers
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
Emilia invests $10,000 in an account that compounds continuously. She plans to leave it in the account untouched. The table shows the balance of the account over 30 years. Enter the data into the graphing tool to plot these values on a scatter plot, with x representing the number years invested and f(x), or y, representing the account balance. Time Invested (years) Account Balance 5 $12,840 10 $16,487 15 $21,170 20 $27,183 25 $34,903 30 $44,817 Which equation most likely represents the curve of best fit for this data set? Select the correct answer.
Answers
The scatter plot is given by the image at the end of the answer, and the exponential function of best fit is given by:
y = 10000(1.0513)^x.
How to built the scatter plot?The scatter plot is built inserting all the points of the data-set in a graph, which are in the following input-output format:
(time in years, balance in dollars).
Hence the points for this problem are given as follows:
(5, 12840), (10, 16487), (15, 21170), (20, 27183), (25, 34903), (30, 44817).
From the graph given at the end of the answer, we can see that the function is exponential.
The exponential function of best fit is found inserting the points into a calculator, and is given as follows:
y = 10000(1.0513)^x.
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3) Find the measure of angle A.
Answers
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)
Help please like rn it’s so hard
Answers
Answer:
Step-by-step explanation:
u got this! try ur best
i need help asap, please don’t tell me the wrong answer
Answers
Answer:
C
Step-by-step explanation:
a relative maximum is a point from which the function starts decreasing
what can be used to show the rank order and shape of a data set simultaneously
Answers
A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a stem-and-leaf display. The Option C is correct.
What is the stem-and-leaf display?This is a device used for presenting quantitative data in a graphical format to assist in visualizing the shape of a distribution. They evolved in the early 1900s and are very useful in exploratory data analysis.
Also known as stem-and-leaf plot, was invented by John Tukey (but the idea can be traced back to the work of Arthur Bowley in the early 1900s.) in his work titled “Some Graphic and Semigraphic Displays” in 1972.
Missing options "a. relative frequency distribution b. pie chart c. stem-and-leaf display d. pivot table
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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
Answers
Answer:
25% were knives
Step-by-step explanation:
From the observation deck of a skyscraper, Dominic measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 984 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Answers
The horizontal distance from the base of the skyscraper is 984 feet.
What is height and distance application?A study on the uses of trigonometry is called Heights and Distances. It can be used in many real-world situations to measure things like an object's height, depth, or the separation between two heavenly objects, among other things.
Given that,
Height of deck h = 984 feet,
Angle of depression θ= 45°
Let horizontal distance is x,
To find horizontal distance of base, use height and distance formula,
tanθ = h/x
Substitute, the values of h and θ,
tan45 = 984/x
∵tan45 = 1
1 = 984/x
⇒x = 984 feet
The horizontal distance from the base of the skyscraper is 984 feet.
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Answer: The answer is 984
Step-by-step explanation:
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)
Answers
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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Pre-Calculus A
Which of the following graphs is a function?
Answers
The graph represents a function is graph a
What is a function?A function is a relationship between two sets or groups that maps each one of the elements contained in the first set to exactly one of the elements of the second set.
The graph a is a linear function, in which when we take any x value or y value, it gives the x and y value.
Hence, The graph that is a function is graph a.
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Solve the system for 20 points. :)
Answers
Answer: C
Step-by-step explanation:
x ∈ R
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
Answer:
amplitude = 6
midline = -4.5
Period =5
Step-by-step explanation:
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
Answers
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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An AP has first term as 3 and Common difference of 2 how many terms are needed to make the sum to 99
Answers
Answer:
9
Step-by-step explanation:
The [tex]n[/tex]term is [tex]2n+1[/tex].
[tex]S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)[/tex]
The number of terms that needed to make the sum to 99 is 9
The first term of the arithmetic progression = 3
The common difference = 2
The sum of n term is = (n/2) [2a+(n-1)d]
Where a is the initial term
d is the common difference
Substitute the values in the equation
(n/2) [2(3)+(n-1)2] = 99
(n/2) [6 + 2n - 2] = 99
(n/2)[4+2n] = 99
n(2 + n) = 99
2n + [tex]n^2[/tex] = 99
[tex]n^2[/tex] + 2n - 99 = 0
Split the terms
[tex]n^2[/tex] - 9n +11n - 99 =0
n(n -9) + 11(n - 9) = 0
(n + 11)(n - 9) = 0
n = -11 or 9
Since n cannot be a negative number, therefore n = 9
Hence, the number of terms that needed to make the sum to 99 is 9
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5. Find CD.
B
A 9x-15D 7x-1C
Answers
Answer:
B
Step-by-step explanation:
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
Answers
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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Solve the system by substitution.
y = -6x +8
7x + 2y = -14
Answers
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
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
Answers
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
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
Answers
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.]
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
Answers
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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Please help will mark Brainly
Answers
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.
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
Answers
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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