FInd the measure of the exterior angle of a triangle if the remote interior angles are 75 degrees and 42 degrees?
Answers
In the triangle, the measure of the exterior angle is 117°.
What is a triangle's definition?
A triangle is a basic two-dimensional geometric shape that consists of three straight sides and three angles. It is a polygon with three sides and three vertices.
The sides of a triangle are usually labeled as a, b, and c, and the angles opposite to these sides are labeled as A, B, and C respectively. The sum of the interior angles of a triangle is always 180 degrees, and each angle in a triangle is less than 180 degrees.
Now,
In a triangle, the sum of the angles = 180°.
Let's denote the three interior angles of the triangle as A, B, and C.
Then we know that:
A + B + C = 180°
We're given two of the interior angles:
B = 75° (remote interior angle)
C = 42° (remote interior angle)
To find the measure of the exterior angle, let's first find the third interior angle:
A + B + C = 180°
A + 75 + 42 = 180°
A + 117 = 180
A = 63°
Now we can use the fact that the exterior angle is equal to the sum of the two remote interior angles:
Exterior angle = B + C
Exterior angle = 75 + 42
Exterior angle = 117°
Therefore, the measure of the exterior angle of the triangle is 117°.
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Related Questions
3. DETAILS SCALCETAM 7.4.050. 2/3 Submissions Used MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Make a substitution to express the integrand as a rational function and then evaluate the integrat (Remember to use absolute values where appropriate wc to the constant of integration) Tc-4*** X Submit Answer
Answers
To express the integrand as a rational function, we can make the substitution u = 1 + x^2. Then, du/dx = 2x, so dx = du/(2x).
You are asked to evaluate the integral of a function that can be expressed as a rational function using substitution. The given integrand is:
∫((Tc-4)^(-1/3) dTc)
Step 1: Make a substitution to express the integrand as a rational function
Let's perform a substitution:
u = Tc - 4
Then, differentiate both sides with respect to Tc:
du/dTc = d(Tc - 4)/dTc = 1
Now, solve for dTc:
dTc = du
Now, substitute the expressions for u and dTc into the original integrand:
∫(u^(-1/3) du)
Step 2: Evaluate the integral
Now, integrate the new expression:
∫(u^(-1/3) du) = (3/2)u^(2/3) + C
Step 3: Substitute back to the original variable, Tc
Now, substitute back the original variable, Tc, using u = Tc - 4:
(3/2)(Tc - 4)^(2/3) + C
Therefore, the integral of the given expression is:
(3/2)(Tc - 4)^(2/3) + C
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Solve the system using substitution: y + 8x = 10 and 2y - 4x = 40
PLS HURRY I NEED THIS DONE IN 10 MINS. HELP ME ASAP PLEASE
Answers
Answer:
Hence x = -1 and y = 18
Step-by-step explanation:
Given the system of equations
y + 8x = 10... 1
2y - 4x = 40 ... 2
From 1; y = 10-8x
Substitute into 2;
2(10-8x) - 4x = 40
20 - 16x - 4x = 40
20 - 20x = 40
-20x = 40 - 20
-20x = 20
x = -1
Recall that y = 10-8x
y = 10 - 8(-1)
y = 10 + 8
y = 18
Hence x = -1 and y = 18
Lacey pays $15 for each hour of golf lessons and $10 for equipment rental. Is the total cost of Lacey's lesson a function of the number of hours scheduled? Fill in the table with the correct outputs.
Answers
Answer:
60
Step-by-step explanation:
15x3=45
5x3=15
15+45=60
? That is how you write the answer.
Answers
All the possible values of x are given as follows:
26 < x < 28.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
If 27 is the greater side, we have that:
x + 1 > 27
x > 26.
If x is the greater side, we have that:
x < 27 + 1
x < 28.
Hence the interval of possible values is given as follows:
26 < x < 28.
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what is the equation of a line in point-slope form with a slope if 1/2 and the point (5,-2) is on the line?
Answers
The equation of the line in slope intercept form is y = 1 / 2x - 9 / 2.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the slope of the line is 1 / 2 and the line passes through (5, -2).
Hence,
y = 1 / 2 x + b
let's find the y-intercept using (5, -2)
Therefore,
-2 = 1 / 2 (5) + b
b = -2 - 5 / 2
b = -4 - 5/ 2
b = -9 / 2
Therefore, the equation of the line is y = 1 / 2x - 9 / 2
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what is the equation of a line parallel to y=3x-2 and goes through the point (-1,1)
Answers
Answer:
y = 3 x − 29
Step-by-step explanation:
First, let's find the slope of the line
y = 3 x + 2
As the equation is already in slope-intercept form
y = m x + c
Slope = 3
Let a point ( x , y ) be on the new line.
By finding the slope again,
y − 1 x − 10 = 3
y − 1 = 3 ( x − 10 )
y − 1 = 3 x − 30
Which can then be converted to different forms:
Standard form:
3 x − y = 29
Equation form:
3 x − y−29 = 0
Slope-intercept form:
y = 3 x − 29
graph{3x-y=29 [-32.3, 47.7, -34.1, 5.9]}
B=1 4 1 20 1 3 -40 2 6 72 9 5 -7Can every vector in R⁴ be written as a linear combination of the columns of the matrix B above? Do the columns of B span R³.
Answers
The columns of B do not span R⁴ and cannot represent every vector in R⁴.
A set of vectors spans a space if every vector in the space can be written as a linear combination of the vectors in the set. To determine whether the columns of a matrix span a space, we need to see if the rank of the matrix is equal to the dimension of the space.
In this case, the columns of B form a matrix with 4 columns, so we want to see if they span R⁴, which has a dimension of 4.
However, the rank of a matrix is equal to the number of linearly independent columns, and it is possible for a matrix to have fewer linearly independent columns than it has columns.
Therefore, we cannot conclude that the columns of B span R⁴ just by counting the number of columns. We need to perform additional computations, such as computing the rank of the matrix, to determine whether the columns of B span R⁴.
Based on the information provided, we cannot conclude that the columns of B span R⁴ and can represent every vector in R⁴.
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The area of a square field is 42025 m square. Find the perimeter of the field. Can you explain and say it answer both pls
Answers
Answer:
Step-by-step explanation:
Answer:
820 m
Step-by-step explanation:
given:
The area of a square field is 42025 m square.
Find:
perimeter of the field.
solution:
Area of square = s² where s = side of square; A = 42,025 m²
plug in values into the formula:
\(\sqrt{42,025}\) = s² ------square root
s = 205 m ---------length of each side of a square
solve for Perimeter:
Perimeter = 4 times the sides
= 4 x 205m
= 820 m
therefore, the perimeter of a square field is 820 m
a ______ is a descriptiion of the approach that is used to obtain samples from a population prior to an data collection activity.
A.
population frame
B.
sampling weight
C.
sampling plan
D.
probability interval
Answers
The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.
It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.
The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.
The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.
A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.
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Identify the solution of the two linear functions from the graph
Help plsss
Answers
Answer: (-0.5, 3)
Step-by-step explanation:
The solution of two graphed linear functions is the point of intersection, also known as the point the lines cross each other. See attached for a visual. These lines intersect at point (-0.5, 3) which means our answer is;
(-0.5, 3)
find the length of the curve. r(t) = cos(6t) i + sin(6t) j + 6 ln(cos(t)) k, 0 ≤ t ≤ π/4
Answers
The length of the curve is given by the integral of the square root of the sum of the squares of the derivatives of each component of r(t), integrated over the given interval, length is 6 units.
In this case, we have
r(t) = cos(6t) i + sin(6t) j + 6 ln(cos(t)) k, and we need to find the length of the curve from t = 0 to t = π/4.
Using the arc length formula, we have the integrand as the square root of (-6sin(6t))^2 + (6cos(6t))^2 + (-6sin(t) / cos(t))^2.
Simplifying the integrand, we get √(36sin²(6t) + 36cos²(6t) + 36sin²(t) / cos²(t)).
Further simplifying, we have √(36 + 36sin²(t) / cos²(t)).
By applying trigonometric identities, we can rewrite the integrand as √(36cos²(t) + 36sin²(t) / cos²(t)).
Simplifying further, we obtain √(36 + 36tan²(t)).
Now,
∫√(36 + 36u²) du / (1 + u²).
Now, we can simplify the integrand:
√(36 + 36u²) / (1 + u²).
Next, we can factor out 36 from the square root:
√36(1 + u²) / (1 + u²).
Simplifying further, we get:
√36 = 6, so the integral becomes:
6∫(1 + u²) / (1 + u²) du.
Notice that the expression (1 + u²) / (1 + u²) simplifies to 1, so the integral reduces to:
6∫du.
Integrating du gives us u + C, where C is the constant of integration.
Therefore, the indefinite integral of √(36 + 36tan²(t)) dt is 6(tan(t)) + C.
To evaluate the definite integral over the interval from 0 to π/4, we substitute the upper and lower limits:
[6(tan(π/4)) - 6(tan(0))] = [6(1) - 6(0)] = 6.
Hence, the length of the curve defined by the given vector function over the interval from 0 to π/4 is 6.
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1 459/500 as a decimal
Answers
Answer:
1.918
Step-by-step explanation:
1 then do 459/500 x 2 to make 918/1000 then add and convert
one half of negative five eights in numerical epression
Answers
Answer:
The answer is in the picture
Step-by-step explanation:
hope it helps!
Find the exact x-coordinate of the point on the curve parametrized by {x = t^2 + 1, y = t^2 - t where the tangent line has slope 27. Give an exact answer, do not use a decimal.
Answers
The exact x-coordinate of the point is frac{1163}{291}6
The curve is given by {x = t² + 1, y = t² - t}.
Let's find dy/dx in terms of t as follows:
frac{dy}{dx} = frac{dy/dt}{dx/dt} = frac{(2t - 1)}{(2t)} = 1 - frac{1}{2t}
Therefore, when dy/dx = 27, we have:
1 - frac{1}{2t} = 27
Rightarrow 2t - 1 = frac{2}{27}
Rightarrow t = frac{29}{54}
The x-coordinate is given by x = t² + 1, therefore, we have:
x = left(frac{29}{54}right)^2 + 1
= frac{1163}{2916}
Hence, the exact x-coordinate of the point on the curve where the tangent line has slope 27 is frac{1163}{291}6
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Which sequences of transformations could map rectangle A
onto rectangle B? Select all that apply.
A A 90° clockwise rotation around the origin, followed by a
translation to the left
B A dilation with a center of dilation at the origin, followed
by a translation down and a translation to the left
C A reflection across the x-axis, followed by a dilation with a
center of dilation at the origin and a translation to the left
B
-2
D A reflection across the y-axis, followed by a translation down and a dilation
with a center of dilation at the origin
E A 180° rotation around the origin, followed by a dilation with a center of
dilation at the origin, a translation down, and a translation to the left
Answers
The sequence of transformations of rectangle A onto rectangle B is
B) A dilation with a center of dilation at the origin, followed by a translation down and a translation to the left.
What is transformation in graphs?The graph's curve "moves to the left/right/up/down," "it expands or compresses," or "it reflects" when a function is transformed. For instance, simply advancing the graph of the function g(x) = x2 by 3 units will yield the graph of f(x) = x2 + 3. Function transformations are very useful for graphing the functions by simply moving, expanding, compressing, or reflecting the curve, as opposed to having to start from scratch with the graphing.
A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:
TranslationDilationReflectionLearn more about transformation
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Bruce has a spinner with four equal sections that are labeled A, B, C and D. He spun the spinner 8 times. It landed on A 3 times, B 1 time, and C 4 times. If he spins the spinner a 9th time, which of the following statements is true?
A. It is equally likely to be A, B, C, or D.
B. It is more likely to be D because it has not been landed on.
C. It is more likely to be C because it has landed on C the most.
D. It is not likely to be D because it has not been landed on.
Answers
All have an equal probability. One letter is not “due” because of previous spins
Answer:
the answer would be A.
Step-by-step explanation:
because it done not matter how many times the spinner has landed on a certain letter it is still always gonna be a 1/4th chance to land on any letter
1 point
Oceanside Bike Rental Shop charges a 13 dollar fixed fee plus 9 dollars an
hour for renting a bike. Carlos paid 58 dollars to rent a bike. How many
hours did he pay to have the bike checked out? *
Answers
Answer: 5 hours
Step-by-step explanation:
Carl paid $58 dollars in total and this included the fixed dollar fee and the variable amount of $9.
To find the number of hours, first deduct the fixed component:
= 58 - 13
= $45
$45 was spent as a result of hourly fee. The number of hours is therefore:
= Total hourly cost/ Cost per hour
= 45 / 9
= 5 hours
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 11 hours of burning, a candle has a height of 19.4 centimeters. after 23 hours of burning, its height is 12.2 centimeters. what is the height of the candle after 15 hours?
Answers
The height of the candle after 15 hours of burning is 17 cm.
According to the question,
We have the following information:
Height of the candle after 11 hours of burning = 19.4 cm
Height of the candle after 23 hours of burning = 12.2 cm
Now, we will find the rate at which the height of the candle is decreasing. It means that we will find the decrease in height per centimeter.
Difference between hours and height:
23-11 = 12 hours
19.4-12.2 = 7.2 cm
So, we have:
12 hours = 7.2 cm
1 hour = 7.2/12
1 hour = 0.6 cm
So, the height is decreasing at the rate of 0.6 cm per hour.
Now, we have to find the height after 15 hours.
Height at 11 hours = 19.4 cm
Difference between 15 hours and 11 hours is 4 hours.
Change in height = 0.6*4 cm
Decrease in height = 2.4 cm
So, the height after 15 hours:
19.4-2.4
17 cm
Hence, the height of the candle after 15 hours of burning is 17 cm.
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Point m is on line segment \overline{ln} ln . given mn=3x,mn=3x, ln=4x+9,ln=4x+9, and lm=2x+7,lm=2x+7, determine the numerical length of \overline{lm}. lm .
Answers
Considering the equations for the length of each segment, the numerical length of line ln is of 17 units.
What is the length of line segment ln?Line segment ln is divided by the point m, hence the length of the line can be written according to the following equation:
ln = lm + mn.
The measures are given as follows:
ln = 4x + 9.lm = 2x + 7.mn = 3x.Hence, using the equation we can solve for x, as follows:
ln = lm + mn.
4x + 9 = 2x + 7 + 3x
5x + 7 = 4x + 9
x = 2.
Hence the numerical length of line ln is given by:
ln = 4x + 9 = 4(2) + 9 = 8 + 9 = 17 units.
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The radicand in the quadratic formula, b²-4ac, is called the discriminant . How many real number solutions will the quadratic equation have if the discriminant is (a) greater than 0, (b) equal to 0, or (c) less than zero? Explain your answer.
Answers
(a) If the discrimant is > 0, the quadratic equation has 2 real solutions.
(b) If the discrimant is = 0, the quadratic equation has 1 real solution.
(c) If b^2-4ac is < 0, the quadratic equation has 0 real solution, therefore it has 2 imaginary solutions.
Why is it called discriminant?
The square root's input (i.e., its contents), which is the phrase b^2 - 4ac, is known as the "discriminant" because using its value, you may "discriminate" between (i.e., be able to distinguish between) the different solution types.
Where is the discriminant used?To determine how many possible solutions a quadratic equation has, utilize the discriminant formula.
(a) If the discrimant is > 0, the quadratic equation has 2 real solutions.
Example
x^2 - 5x + 2 = 0
where a = 1, b = -5, c= 2
D=b^2 - 4ac = (-5)^2 - 4 ×1 × 2 = 17
∴ It has two real solutions.
(b) If the discrimant is = 0, the quadratic equation has 1 real solution.
Example
x^2 + 2x + 1 = 0
where a = 1, b = 2, c= 1
D=b^2 - 4ac = (2)^2 - 4 ×1 × 1 = 0
∴ It has one real solution.
(c) If b^2-4ac is < 0, the quadratic equation has 0 real solution, therefore it has 2 imaginary solutions.
Example
3x^2 + 2x + 1 = 0
where a = 3, b = 2, c= 1
D=b^2 - 4ac = (2)^2 - 4 ×3 × 1 = -8
∴ It has two imaginary solutions.
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Brett is filling up his swimming pool. It is a cylindrical shape. How many
cubic meters of water will it take to fill the pool to a height of 1.2 meters if
the pool has a diameter of 4.5 meters?
Answers
Answer:
Hi how are you doing today Jasmine
the diameter of a circle is 4 in. find its area in terms of pi
Answers
Step-by-step explanation:
A ≈12.57in²
d = Diameter
Using the formulas
A=πr2
d=2r
Solving forA
A=1/4πd²=1/4·π·4²≈12.56637in²
Answer:
A = 4π in²
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
Here d = 4, then r = 4 ÷ 2 = 2
A = π × 2² = 4π in²
what is 345 divided by 2:3
Answers
Answer:
Est: 517
Answer: 517.499999974
Step-by-step explanation:
Multiply.
2x^4 (3x³ − x² + 4x)
Answers
Answer: A
Step-by-step explanation:
When multiplying: Numbers multiply with numbers and for the x's, add the exponents
If there is no exponent, you can assume an imaginary 1 is the exponent
2x⁴ (3x³ − x² + 4x)
= 6x⁷ -2x⁶ + 8x⁵
Answer:
A. \(6x^{7} - 2x^{6} + 8x^{5}\)
Step-by-StepLabel the parts of the expression:
Outside the parentheses = \(2x^{4}\)
Inside parentheses = \(3x^{3} -x^{2} + 4x\)
You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses
\(2x^{4}\) × \(3x^{3}\)
\(2x^{4}\) × \(-x^{2}\)
\(2x^{4}\) × \(4x\)
First, multiply the whole numbers of each value before the variables
2 x 3 = 6
2 x -1 = -2
2 x 4 = 8
Now you have:
6\(x^{4}x^{3}\)
-2\(x^{4}x^{2}\)
8\(x^{4} x\)
When you multiply exponents together, you multiply the bases as normal and add the exponents together
\(6x^{4+3}\) = \(6x^{7}\)
\(-2x^{4+2}\) = \(-2x^{6}\)
\(8x^{4+1}\) = \(8x^{5}\)
Put the numbers given above into an expression:
\(6x^{7} -2x^{6} +8x^{5}\)
Key Wordsdistribution
variable
like exponents
The probabilities in the cells of a two-way table are conditional probabilities. True or false?.
Answers
Using the conditional probability concept, it is found that the statement is true, as in a two-way probability table, we find the probability of each event B considering that each event A has happened.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula 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 problem, considering the definition of conditional probability given above, the statement is true, as in a two-way probability table, we find the probability of each event B considering that each event A has happened.
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Write an equation in slope-intercept form for the line with y-intercept 4 and slope -1/5
Answers
y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given,
y-intercept 4 and slope -1/5
Now y=-1/5x+4
Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5
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Solve for k kk. k − 7 8 = 5 2
Answers
Answer:
k = 59.8
Step-by-step explanation:
Given
k - 7.8 = 52 ( isolate k by adding 7.8 to both sides )
k = 59.8
area of the segment?
Answers
Answer:
A ≈ 34.91 m²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × \(\frac{40}{360}\) ( r is the radius )
= π × 10² × \(\frac{1}{9}\)
= \(\frac{100\pi }{9}\)
≈ 34.91 m² ( to 2 decimal places )
Answer:
34.88m²
(round 35m²)
Step-by-step explanation:
a round angle, that of the circle, is 360°, here we have a portion of 40°, we divide 360° by 40° and we have the percentage with respect to the circle
360° : 40° = 9
we now know that the wedge is 1/9 of the circlefind the area of the whole circle having the radius (10m)Area of Circle Formulas · Area = π × r2, where 'r' is the radius
Area = π × r2
Area = π × 10²
Area = π × 100
Area = 3.14 × 100
Area = 314 m²
now we divide by 9 and we have the area of the wedge314 : 9 = 34.88m² (round 35m²)
a newsletter publisher believes that more than 39% of their readers own a laptop. is there sufficient evidence at the 0.05 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
Answers
The null and alternative hypotheses for the given scenario is :
h₀ = 0.39
ha > 0.39
Given, a newsletter r publisher believes that more than 39% of their readers own a laptop.
let the proportion of readers owning a laptop be denoted by p.
We want to test the claim that more than 39% of the readers own a laptop.
Hence, we frame:
Null hypothesis is H₀: p = 0.39
Alternative hypothesis is H₁: p > 0.39
Hence there is no sufficient evidence at the 0.05 level.
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Drag the tiles to the boxes to form correct pairs.Match the palrs of equivalent expressions.(-14 +30)–(1+36)46+13(5+26)+(26+)86-15(56–3)–(8+66)16–11(-10+6)+(76–5)– 15 - 26
Answers
Kindly check below.
1) Examining the expressions inside the tiles, we can tell that:
\(\begin{gathered} (-14+\frac{3}{2}b)-(1+\frac{8}{2}b)=-\frac{5}{2}b-15 \\ 4b+\frac{13}{2} \\ (5+2b)+(2b+\frac{3}{2})=4b+\frac{13}{2} \\ 8b-15 \\ (\frac{7}{2}b-3)-(8+6b)=\frac{7}{2}b-3-8-6b\rightarrow-11-\frac{5}{2}b \\ -\frac{5}{2}b-11 \\ (-10+b)+(7b-5)=8b-15 \\ -15-\frac{5}{2}b \end{gathered}\)2) Based on this we can tell the following relationship of equivalence:
