Answers
Answer:
124.5°
Step-by-step explanation:
Let the smallest angle be x. Then, the sum of the angles is an arithmetic sequence with first term x, common difference 7, and 8 terms.
Using the sum of an arithmetic series formula,
\(\frac{8}{2}(2x+(8-1)(7))=1080 \\ \\ 4(2x+49)=1080 \\ \\ 2x+49=270 \\ \\ 2x=221 \\ \\ x=110.5\)
So, the third angle is 110.5+14=124.5
Related Questions
find the value of x. SIMPLEST RADICAL FORM
Answers
For given triangle, x is 4√5 using Pythagorean theorem.
What is Pythagorean Theorem?
Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.
The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.
The Pythagoras Theorem formula is presented in the definition as:
Perpendicular² + Base² = Hypotenuse²
c² = a² + b²
Now,
Given that perpendicular =19
Hypotenuse=21
then Base²=21²-19² using Pythagoras theorem
Base=√441-361
=√80
=4√5
Hence,
x is 4√5
To know more about Pythagorean theorem visit the link
https://brainly.com/question/343682?referrer=searchResults
#SPJ1
Don’t know how to solve, help ?
Answers
Step-by-step explanation:
180 - 120 = 60
32 + 60 = 92
180 - 92 = 88
Help me asap and need the answer quick
Answers
Answer:20 m/s
Step-by-step explanation:
Answer:
20 m/s
Step-by-step explanation:
700 ÷ 35 = 20 m/s
Scientists are preparing two satellites to be launched. The equation y = 4600x represents the number of miles, y, that the satellite, Space Explorer A, flies in x. The Table below represents the number of miles, y, that the satellite, Space Explorer B, flies in x hours.Hours (x) Miles (y)5 1500020 6000022 6600024 72000How many fewer miles does Space Explorer B travel in one hour than Space Explorer A?
Answers
Answer: We have a linear equation that represents the number of miles that satellite A flies in one hour, which is:
(A)
\(y(x)=4600x\)So, In one hour this satellite flies:
\(y(1)=4600(1)=4600\text{ miles}\)(B)
The linear equation for satellite B can be extracted from the given table as follows:
Slope:
\(\begin{gathered} y_B(x)=mx+b \\ \rightarrow\therefore\rightarrow \\ m=\frac{\Delta y}{\Delta x}=\frac{60,000-15,000}{20-5}=\frac{45,000}{15}=3000 \\ \end{gathered}\)Y-Intercept:
\(\begin{gathered} y_B(x)=mx+b \\ \rightarrow\therefore\rightarrow \\ y_B(5)=3000(5)+b=15,000 \\ \rightarrow\therefore\rightarrow b=15,000-36,000=-21,000 \\ \\ \therefore\rightarrow \\ y_B(x)=3000x-21,000 \end{gathered}\)Miles, that the Satellite (B) travels in one hour are:
\(y_B(1)=3000(1)-21,000=3000-21,000=-18,000\)The difference in the miles traveled by these two space explorers are:
\(y_B(1)-y_A(1)=-18,000mi-3000mi=-15,000\)Therefore this is the answer
.
Describe The expression 2 + x represents a number. This number can be
located on a number line.
a. When is 2 + x located to the right of 2? When is it located to the left of 2?
Note: Also if you can make the answers in sentences
Answers
In conclusion Cheryl's statement is true, When x is positive, 2 + x is located to the right of 2 on the number line, The distance between 2 + x and 2 is the absolute value of (2 + x) - 2, which simplifies to the absolute value of x.
Why it is?
Cheryl's statement is true. When you add two negative numbers, the sum is always negative. For example, -3 + (-4) = -7, -2 + (-5) = -7, and so on. The reason for this is that a negative number represents a quantity less than zero. When you add two negative quantities together, you are essentially adding two numbers that are less than zero, which results in a number that is even more negative.
When x is positive, 2 + x is located to the right of 2 on the number line. For example, if x = 3, then 2 + x = 5 and 5 is located to the right of 2 on the number line. When x is negative, 2 + x is located to the left of 2 on the number line. For example, if x = -1, then 2 + x = 1 and 1 is located to the left of 2 on the number line.
The distance between 2 + x and 2 is the absolute value of (2 + x) - 2, which simplifies to the absolute value of x. The distance is the same when x is positive or negative because the absolute value of a number is always positive, regardless of whether the number itself is positive or negative. For example, if x = 3, then the distance between 2 + x and 2 is |5 - 2| = 3. If x = -1, then the distance between 2 + x and 2 is |1 - 2| = 1.
To know more about Equation related questions, visit:
https://brainly.com/question/29538993
#SPJ1
HI PLEASE HELPP REFER TO PICTURE STATISTICS
Answers
We are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
Hence, Using a t-distribution with 86 degrees of freedom (n-1), and a 95% confidence level (α=0.05), the critical value for the two-tailed test is 1.992.
The standard error can be calculated as:
SE = SD / √n = 15.6 / √100 ≈ 1.56
The margin of error (ME) can be calculated as:
ME = t x SE = 1.992 x 1.56 ≈ 3.11
The 95% confidence interval (CI) is then:
CI = mean ± ME = 5.9 ± 3.11 = (2.79, 9.01)
Therefore, we are 95% confident that the true mean incubation period of the SARS virus lies between 2.79 and 9.01 days.
This means that if we were to sample many times from the same population, 95% of the intervals we construct would contain the true mean value.
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ1
Identify the inflection points and local maxima and minima of the function graphed to the right. Identify the intervals on which it is concave up and concave down. y = - x+ sin 2x, Find the inflection point(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The point(s) is/are ,(0,0), 2'2 (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no inflection points. Find each local maximum. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. There is one local maximum value of f at x = O B. There are two local maxima. In increasing order of x-value, the values are 5x + 3/3 and 6. T + 3/3 at x = at x = 6. OC. There are no local maxima.
Answers
∴ F is concave up on [-2π/3, 0) , F is concave down on (0,2π/3]
Inflection points are points on a graph where the curvature of the g\(f(x)= y = x+sin2x\\f'(x) = 1+cos2x\\f"(x) = -4sin2x\\f"(x) = 0= -4sin2x=0\\sin2x = 0\\2x= sin^{-1}(0)\\2x = 0\\x= 0\\\)
There is an inflection point at x=0
\(f'(x)=0 = 1+2cos2x=0\\2cos2x =-1\\cos2x = \frac{-1}{2} \\2x = cos^{-1} (\frac{-1}{2})\\\)
2x = 2π/3
x = π/3
There is only one critical point, x= π/3
f"(π/3) = -4 × sin(2π/3)
= -4 × \(\frac{\sqrt{3} }{2}\)
= \(-2\sqrt{3}\) <0
There is one local maximum at x= π/3.
There is no local minimum.
There is an inflection point at x = 0 is 0.
F"(-π/4) =4sin (2x -π/4)
= -4 sin (-π/2)
= 4sin(π/2)
= 4>0
∴ F is concave up on [-2π/3, 0)
f" (π/4) = -4sin (2 × π/4)
= -4<0
∴ F is concave down on (0,2π/3]
Inflection points are points on a graph where the curvature of the graph changes from concave to convex or vice versa. For example, in a quadratic equation, the inflection point is where the graph changes from having a 'U' shape to having an 'inverse U' shape. In other words, the point at which the graph changes from being concave down to being concave up (or vice versa). Inflection points can also occur in higher-order polynomials and in trigonometric functions.
In addition, inflection points can be used to identify local extrema or points at which the function attains either a minimum or maximum value. In general, an inflection point is a point at which the concavity of a function changes. This can be observed by examining the second derivative of the function at the point: if the second derivative is positive, then the function has a convex curvature; if the second derivative is negative, then the function has a concave curvature.
To learn more about Inflection points visit here:
brainly.com/question/29017999
#SPJ4
number 3: big ideas 3.5 (find the coordinates of point P along the directed line segment AB, from A(8,0) to B(3,-2), so that the ratio of AP to PB is 1 to 4)
Answers
Point P(x,y) divides the segment AB in the ratio m:n if it has coordinates:
\(P(x,y)=(\frac{m_{}x_2+n_{}x_1}{m+n},\frac{my_2+ny_1}{m+n})\)where A(x1,y1) and B(x2,y2).
In this case we have the ratio 1:4, this means that m=1 and n=4. Plugging this and the coordinates of points A and B we have:
\(\begin{gathered} P(x,y)=(\frac{1\cdot3+4\cdot8}{1+4},\frac{1\cdot(-2)+4\cdot(0)}{1+4}) \\ P(x,y)=(\frac{3+32}{5},\frac{-2}{5}) \\ P(x,y)=(\frac{35}{5},-\frac{2}{5}) \\ P(x,y)=(7,-\frac{2}{5}) \end{gathered}\)Therefore the coordinates of the point P are (7,-2/5)
Nao and Arban drive to work.
Nao drives 95 miles in 2.5 hours.
Arban drives 128 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h.
1 mile = 1.6 km
Thank You.
Answers
Answer:
41.6 km/h
Step-by-step explanation:
Nao drives 95mi/2.5hr or 38 miles per hour, or 60.8 km/h
1 hr 15 min is the same as 1.25 hours
Arban drives 128km/1.25hr or 102.4 km/h
The difference is 102.4-60.8 = 41.6
which of the following instructional adjustments can the teacher make to best assess all of the students' understanding of multiplying two-digit numbers?
Answers
the following instructional adjustments or educational adjustments can the teacher make to best assess all of the students' understanding of multiplying two-digit numbers : Asking multiple students to share and defend their solutions before acknowledging the correct answer.
The discussion allows the teacher to observe how students solve the problems that involves multiplying two-digit numbers. It will also allow students to express themselves before they realize their answer is incorrect.
Educational Adjustments to teaching could be described as the continuing adjustments that teachers develop to adjust teaching and learning based on research in order to enhance students' attainment of intended instructional aims.
Educational Adjustments are steps or changes that facilitate students to receive educational content and results on a comparable level to facilitate students to receive educational content and results on a comparable level as their peers.
For more information on Educational Adjustments, visit :
https://brainly.com/question/21882452?
#SPJ4
Complete question :
Which of the following instructional adjustments can the teacher make to best assess all of the students' understanding of multiplying two-digit numbers?
1. Allowing students to write their answers on paper, then collecting the papers at the end of the lesson
2. Asking multiple students to share and defend their solutions before acknowledging the correct answer
3. Asking students who did not hold up their thumbs to share their answer and explain
4. Having Billy work the problem out on the board in front of the class
HELPPPP AHHHH
I been stuck on this for over 20 mins
Answers
simplify the expression -1.1 + (-3.9). On the test, when tom simplified the expression he got -2.8. What mistake did tom likely make when he simplified the expression?
Answers
Answer:
the answer is -5.0
Step-by-step explanation:
Tom subtracted -1.1 from -3.9 instead of adding them together
For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
For similar question on cuboid.
https://brainly.com/question/29568631
#SPJ8
I apologize for the messy photo but please help me with this, I’m really confused! Thank you so so so much.
Answers
1)+4
2)-4
3) 2
4) i don't know
5)
Answer: (-2)²=4
-2²=-4
square root of 4 is 2
1 over the square root of 8 is -2
1 aquare root of -8 is 2,-2
Step-by-step explanation:plug them into calculator
a service company charges a 5% service fee
Answers
Answeis is that
is that the whole qeustion
Step-by-step explanation:
where is the image
There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula T=0.33c+38T=0.33c+38, where TT represents the temperature in degrees Fahrenheit and cc represents the number of times the cricket chirps in one minute. What could the number 38 represent in the equation?
Answers
The temperature at which the crickets do not chirp is represented by the number 38, which serves as the y-intercept of the linear equation.
The equation is as follows:
T = 38 + 0.3*c
The temperature is denoted by T, while the number of chirps in a minute is denoted by c.
We want to know what the number 38 means.
Take c = 0 to demonstrate this as there are no chirps.
Then:
T = 38 + 0.33*0 = 38
T = 38
This is the temperature where crickets cease to chirp.
The temperature at which the crickets do not chirp is represented by the number 38, which is the y-intercept of the linear equation.
To learn more about linear equation from given link
https://brainly.com/question/22686146
#SPJ1
Make a frequency table using five classes.
class 31-38 39-46 47-54 55-62 63-70
f
11
24
15
7
3
Then estimate the mean and sample standard deviation using the frequency table. (Round s to two decimal places.)
Answers
Answer: C
Step-by-step explanation:
4.25-1.25x=0 what is x someone help please
Answers
Answer:
3.4
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
Steps
1. Isolate the variable subtract 4.25 since it's positive.
4.25 - 1.25x = 0
- 4.25 - 4.25
- 1.25x = - 4.25
2. Divide by - 1.25 in both sides of equation.
- 1.25x = - 4.25
--------- ---------- <------- fraction bar/ divide
-1.25 -1.25
x = 3.4
Check:
4.25 - 1.25 (3.4) = 0
4.25 - 4.25 = 0
0 = 0
True statement.
The local carnival grounds are in the shape of a rectangle. The area of the grounds is 0.125 square mile. The length of the grounds is twice the width. What is the width of the grounds in miles? Do not include units in your answer. Please help right away! Thank you so much!
Answers
Answer:
Step-by-step explanation:
Width = x
Length = 2x
Area of the ground = 0.125 square mile
length * width = 0.125
2x * x = 0.125
2x² = 0.125
x² = \(\frac{0.125}{2}\\\\\)
= 0.0625
\(x^{2}=\frac{625}{10000}\\\\x=\sqrt{\frac{625}{10000}}\\\\ x=\frac{25}{100}\\\\x=0.25\)
Width = 0.25 miles
Length = 2* 0.25 = 0.50 miles
What goes into the boxes
Answers
Answer:
See explanation
Step-by-step explanation:
\(6 {c}^{2} + 2 {c}^{4} - c \\ \\ standard \: form = \red{ \boxed{ \bold{2 {c}^{4} + 6 {c}^{2} - c}}} \\ \\ degree = \purple{ \boxed{ \bold{4}}} \\ \\ leading \: coefficient = \orange{ \boxed{ \bold{1}}}\)
20 points & Brainliest
Why are rotations a rigid motion?
Answers
Answer:
RC,\α is a rigid motion.
Here C, is the rotacenter which is the fixed point and around C all other points move in a fixed distance by the definition of rotation.
the motion follows in a circularmanner with C as the center.
consider a point Q which changes to Q1 after rotation by an angle\alpha
Step-by-step explanation:
When considering rotational motion and subsequently rotational mechanics every point on the body must have same angular velocity and angular acceleration. If the body is not rigid different points on the body will have different angular velocity and angular acceleration.
a triangular field has boundaries of lengths 170m,195m and 210m,find the size of the largest interior angle of the field
Answers
The size of the largest interior angle of the field is 69.86°
What is cosine law?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Given that, a triangular field has boundaries of lengths 170m, 195m and 210m, we need to find the size of the largest interior angle of the field,
We know that, angle opposite to the largest side is largest,
Therefore,
The largest angle is opposite is 210 m side, (say c)
Using the cosine rule,
210² = 170²+195²-2(170)(195)cosC
CosC = 170²+195²-210² / 2(170)(195)
CosC = 22825 / 66300
CosC = 0.344268477
C = 69.86°
Hence, the size of the largest interior angle of the field is 69.86°
Learn more about cosine rule, click;
https://brainly.com/question/26952873
#SPJ9
Clayton opens a savings account with 11 dollars he got from his grandmother
Answers
Answer:
The answer is "$3640.58"
Step-by-step explanation:
This question is incomplete, that's why we add another question in the attached file. Please find it.
P = \(\$ \ 1300\) and effective per year is = interest rate per year = 7.2
Total \(\$ \ 1300\) due after 8 years is P+PRT:
\(\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8\)
\(\to Total \ X = \$ \ (7000-2048.8) \\\\\)
\(= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\\)
The number of dollars is X \(= \frac{4951.2}{1.36} = \$ \ 3640.58\)
Find the equation for the line through the point (7/5,1/12) that is perpendicular to the line 3x-4y=7. You may leave your answer in the point-slope form if you wish. If you use slope-intercept form, all fractions must be combined and reduced wherever possible.
Answers
The equation of the line is (y - 1/12) = -4/3(x - 7/5).
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.
Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be depicted by
tan θ = Δy/Δx
So, the slope of a line is tan.
The given equation of a line is:
3x-4y=7
-4y = -3x + 7
y = 3/4 x - 7/4
The slope of the line is 3/4.
The slope of the line perpendicular to the given line is - 1/m = - 4/3
The point-slope of a line is y - y₁ = m(x - x₁).
The given point is (7/5,1/12)
The equation of the line is
(y - 1/12) = -4/3(x - 7/5)
To learn more about equation of line, click on the below link:
https://brainly.com/question/10853937
#SPJ1
super easy one to one function!!! 50 POINTS HELP!!
Answers
The correct value of the given function is (E) g⁻¹(-3) = 3.
What are functions?A mathematical expression, rule, or law establishes the relationship between an independent variable and a dependent variable (the dependent variable). A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
So, g⁻¹(-3):
x = -1g(x) = -3Then, g(x)·x = (-1)(-3) = 3
Then, g⁻¹(-3) = 3.Therefore, the correct value of the given function is (E) g⁻¹(-3) = 3.
Know more about functions here:
https://brainly.com/question/25638609
#SPJ13
n Circle E, if measure of arc AB = 140, find the m
Answers
Answer:
noob
Step-by-step explanation:
lol imagine not knowing, u noob
Cystic fibrosis (CF) is a hereditary lung disorder that often results in death. It can be inherited only if both parents are carriers of an abnormal gene. In 1989, the CF gene that is abnormal in carriers of cystic fibrosis was identified. The probability that a randomly chosen person of European ancestry carries an abnormal CF gene is 1/25. (The probability is less in other ethnic groups.) The CF20m test detects most, but not all, harmful mutations of the CF gene. The test is positive for 90% of people who are carriers. It is never positive for people who are not carriers.
Required:
Compute the probability that a randomly chosen person of European ancestry does not carry an abnormal CF gene given that he /she tested negative.
Answers
Answer:
0.9959 = 99.59% probability that a randomly chosen person of European ancestry does not carry an abnormal CF gene given that he /she tested negative.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Tested negative
Event B: Does not carry an abdornal CF gene.
Probability of a negative test:
10% of 1/25 = 0.04 = 4%
100% of 100 - 4 = 96%. So
\(P(A) = 0.1*0.04 + 1*0.96 = 0.964\)
Negative test and not carrying an abdornal gene:
100% of 96%. So
\(P(A \cap B) = 1*0.96 = 0.96\)
Compute the probability that a randomly chosen person of European ancestry does not carry an abnormal CF gene given that he /she tested negative.
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.96}{0.964} = 0.9959\)
0.9959 = 99.59% probability that a randomly chosen person of European ancestry does not carry an abnormal CF gene given that he /she tested negative.
b) 6q + 4-q + 5 simplify
Answers
Answer:
5q + 9
Hope that helps! :)
-Aphrodite
Step-by-step explanation:
i need help! please, this is confusing
Answers
The cost of the 28 inches and 36 inches diagonal Smart TVs, based on the quadratic cost function are;
28 - inch diagonal; $134
36 - inch diagonal; $165
What is a quadratic function?A quadratic function is a function of the form f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.
The cost of the Smart TV as a function of the diagonal length is C(d) = 0.322·d² - 16.776·d + 351.444
The above function indicates that the cost of a Smart TV that is 28 inches long is; C(28) = 0.322 × 28² - 16.776 × 28 + 351.444 ≈ 134
A Smart TV with a diagonal of 28 inches costa about $134The cost of a Smart TV with a diagonal of 36 inches is therefore;
C(36) = 0.322 × 36² - 16.776 × 36 + 351.444 ≈ 165
A Smart TV with a diagonal of 36 inches costs about $165Learn more on the evaluation of a function here: https://brainly.com/question/2284360
#SPJ1
P(Q) = 1/4
P(R) = 2/3
If Q and R are independent events, find the P(Q Ind R).
Answers
Answer: 7/30
Step-by-step explanation: