The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. The ratio of the angles in the triangle is 1:2:3.
Define angle.When two rays are joined at one point, they produce the geometric shape known as an angle. The vertex is the shared point between the two rays, which are known as the arms or sides of the angle. When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolised by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees.
Given,
A first angle of let x
2x = 2nd angle
3x = 3rd angle
Angle sum = 180
x + 2x + 3x = 180
6x = 180
Dividing,
x = 30°
2x = 2(30)
2nd angle = 60
3x = 3(30)
3rd angle = 90
30°, 60°, and 90° are the three angles.
Ratio 1:2:3
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what's the next number 2 7 8 3 12 9 (ITS NOT 4!!!! 4 IS NOT AN OPTION!!!!!)
I'm not sure but I'd say 31
Find the term named in the problem and the explicit formula.
13) 18,14,10,6,
14) 30,0,-30,-60,
Find a₂₂
Find a₃₇
15) -34,-31,-28,-25,
Find a₂₃
The named terms in the sequence are a₂₂ = -66, a₃₇ = -1050 and a₂₃ = 32
How to determine the named term in the sequence?Sequence 1
From the question, we have the following sequence that can be used in our computation:
18,14,10,6,
In the above sequence, we can see that the 4 is subtracted from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = 18
d = -4
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 22nd term, we have
a₂₂ = 18 + (22 - 1) * -4
Evaluate
a₂₂ = -66
Sequence 2
Here, we have
30,0,-30,-60,
In the above sequence, we can see that the 30 is subtracted from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = 30
d = -30
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 37th term, we have
a₃₇ = 30 + (37 - 1) * -30
Evaluate
a₃₇ = -1050
Sequence 3
Here, we have
-34,-31,-28,-25,
In the above sequence, we can see that the 3 is added from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = -34
d = 3
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 23rd term, we have
a₂₃ = -34 + (23 - 1) * 3
Evaluate
a₂₃ = 32
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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
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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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
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.
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:
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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Pre-Calculus A
Which of the following graphs is a function?
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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5. Find CD.
B
A 9x-15D 7x-1C
Answer:
B
Step-by-step explanation:
Anna is buying a house selling for $285,000. To obtain the mortgage, Anna is required to make a 15 % down payment. Anna obtains a 25 -year mortgage with an interest rate of 5 %. Click the icon to view the table of monthly payments.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
a) Determine the amount of the required down payment.
a) The amount of the required down payment is $42,750.
b) The mortgage amount after the down payment is $242,250.
c) The monthly payment for both principal and interest is $1,416.17.
What is the down payment?The down payment refers to the upfront cash payment made to reduce the cost of the home.
After deducting the down payment from the home price the result is the loan amount.
Monthly payments pay part of the loan amount the computed interest.
The monthly payments and the down payment can be determined with an online finance calculator.
Home Price = $285,000
Down Payment = 15%
Loan Term = 25 years
Interest Rate = 5%
Monthly Pay: $1,416.17
Loan Amount $242,250 ($285,000 - $42,750)
Down Payment = $42,750 ($285,000 x 15%)
Total of 300 Mortgage Payments = $424,851 ($1,416.17 x 300)
Total Interest = $182,601
Thus, after making a down payment of $42,750 cash, Anna will be making monthly payments of $1,416.17 for 300 months.
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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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What is the equation of the line that is parallel to the line defined by the equation y = 3x−7 and goes through the point (4, 2)?
Answer:
[tex]y-2=3(x-4)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in [tex]y-y_1=m(x-x_1)[/tex].
[tex]y-y_1=3(x-x_1)[/tex]
Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].
[tex]y-2=3(x-4)[/tex]
Topic: parallel and perpendicular lines
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Help please like rn it’s so hard
Answer:
Step-by-step explanation:
u got this! try ur best
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
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
amplitude = 6
midline = -4.5
Period =5
Step-by-step explanation:
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
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:
Help with this one please x Thankyou x
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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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?
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
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
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.
what can be used to show the rank order and shape of a data set simultaneously
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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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.
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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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.]
the value of 5/32 ÷ 25/4
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]
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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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)
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?
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.
Multiple Choice You are taking guitar
•lessons. The cost of the first lesson is twice the cost of each additional lesson. You spend $360 for 8 lessons. How much did the first
lesson cost'7
A $40
(C $50
(E $80
B) $45
(D $60
The cost of the first lesson based on the information is E. $80.
How to calculate the cost?From the information, the cost of the first lesson is twice the cost of each additional lesson. Let the others lesson b represented by x.
The first lesson will be: = 2 × x = 2x
Since there are 8 lessons, this will be:
First lesson + Other lesson = Cost
2x + (7 × x) = 360
2x + 7x = 360
9x = 360
Divide
x = 360/9
x = 40
Therefore, first lesson will be:
= 2x
= 2 × 40
= 80
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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
