Final answer:
The correct statement regarding the interior and exterior angles of the triangle is 'm∠3 + m∠4 + m∠5 = 180°'. Option b
Explanation:
When considering the properties of interior and exterior angles in a triangle, several theorems are useful to determine the correct statement among the choices provided.
Specifically, one important theorem to recall is: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Additionally, the sum of all interior angles in a triangle is always 180 degrees.
With these principles in mind, we can examine the provided statements:
m∠5 + m∠6 = m∠1 - Incorrect. The exterior angle at a vertex of a triangle is the sum of the two opposite interior angles, not an addition of an interior and its adjacent exterior angle.
m∠3 + m∠4 + m∠5 = 180° - Correct. This is true because m∠4, being an exterior angle, is equal to m∠2 + m∠5, and since the sum of the interior angles of a triangle is 180 degrees, m∠2 + m∠3 + m∠5 = 180 degrees. Replacing m∠2 + m∠5 with m∠4 gives us the correct equation.
m∠1 + m∠2 = 180° - Incorrect. This statement would imply that angle 1 and angle 2 are on a straight line, which is not the case in a triangle's exterior and interior angles.
m∠2 + m∠3 = m∠5 - Incorrect. There is no direct theorem that supports this statement as a relationship between these angles in a triangle.
The correct statement, based on the theorems regarding triangle angles, is m∠3 + m∠4 + m∠5 = 180°.
Which expression is equivalent to (−2)x + (−6)x?
A) −8x
B) −4x
C) 4x
D) 8x
20 is 22% of what number
40
50
75
100
Answer: D. 100
Step-by-step explanation:
2X plus 5 minus X plus 3X plus X -2
Answer:
=5x+3
Step-by-step explanation:
2 divided 62.2
What is the answer
The answer would be 31.1
Answer:
31.1
Step-by-step explanation:
Times 62.2 by ten to make it a whole number, which is 622. Now it looks easier! 622/2=311. But don't forget to divide it by ten again!
The stadium has a form of a rectangle with two semicircles attached to the short sides. The long side of a rectangle is 2 times longer than the short one. Construct the expression for the area of the stadium in terms of x, where x denotes a shorter side of the rectangle
Answer: [tex]2x^2+\frac{\pi x^2}{4}[/tex]
Step-by-step explanation:
The area of a rectangle can be calculated with this formula:
[tex]A_r=lw[/tex]
Where "l" is the lenght and "w" is the width.
The area of a semi-circle can be found with this formula:
[tex]A_{sc}=\frac{\pi r^2}{2}[/tex]
Where "r" is the radius.
Let be "x" the shorter side of the rectangle (which is also the diameter of the semi-circle).
Based on the information given in the exercise, you know that:
[tex]w=x\\\\l=2x[/tex]
Since the radius is half the diameter:
[tex]r=\frac{x}{2}[/tex]
Observe the figure attached, which shows the stadium.
The area of the stadium is the sum of the areas of the semi-cirlcles and the rectangle.
Therefore, you can construct the following expression for the area of the stadium is terms of "x":
[tex](2x)(x)+\frac{\pi (\frac{x}{2})^2}{2}+\frac{\pi (\frac{x}{2})^2}{2}[/tex]
Simplifying it, you get:
[tex](2x)(x)+\frac{\frac{\pi x^2}{4}}{2}+\frac{\frac{\pi x^2}{4}}{2}=2x^2+\frac{\pi x^2}{4}[/tex]
The expression for the area of the stadium in terms of x is 2x^2 + πx^2/4.
Explanation:The area of the stadium can be calculated by first finding the area of the rectangle and then adding the areas of the two semicircles. The long side of the rectangle is 2 times longer than the short side, so the dimensions of the rectangle are x for the short side and 2x for the long side. Therefore, the area of the rectangle is A = x * 2x = 2x^2. The formula for the area of a semicircle is A = πr^2/2, where r is the radius of the semicircle. In this case, the radius is x/2 since it is half of the short side of the rectangle. So, the area of one semicircle is π(x/2)^2/2 = πx^2/8. Since there are two semicircles, the total area of the semicircles is 2 * (πx^2/8) = πx^2/4.
Adding the area of the rectangle and the area of the semicircles, we get the expression for the total area of the stadium: A = 2x^2 + πx^2/4.
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Sharmaine works 30 hours at an exclusive restaurant. She earns
$3.50 per hour plus tips. In one week, she earned $1,250.00 in tips. What was Sharmaine’s total income?
Answer:
Sharmaine had an income of US$ 1,355 that week.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Hours per week Sharmaine works at an exclusive restaurant = 30
Salary of Sharmaine = US$ 3.50 per hour + tips
Tips of the week = US$ 1,250
2. What was Sharmaine’s total income?
Total income = Tips + Rate per hour
Total income = 1,250 + (3.5 * 30)
Total income = 1,250 + 105
Total income = 1,355
Sharmaine earned $105.00 from her hourly job and $1,250.00 in tips, making her total income $1,355.00 for the week.
Explanation:The student asked about Sharmaine's total income for a week. Sharmaine earns an hourly wage plus tips at a restaurant. To calculate her total income, we need to add her earnings from her hourly rate to her earnings from tips.
First, we determine her earnings from her hourly wage. She works 30 hours at $3.50 per hour. So, her income from her hourly wage is 30 hours × $3.50/hour = $105.00.
Next, we add her earnings from tips. Sharmaine earned $1,250.00 in tips for the week.
Her total income for the week is her hourly earnings plus her tips: $105.00 (hourly earnings) + $1,250.00 (tips) = $1,355.00.
Therefore, Sharmaine's total income for that week is $1,355.00.
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Can you tell which of the following triangles are right and explain
your answer? The numbers represent the lengths of the sides:
9, 12, 15
can someone please help with this.
The statement is not reversible.
A reversible statement is one where the implication goes both ways. In simpler terms, if the statement is true, its converse (reversing the hypothesis and conclusion) must also be true, and vice versa.
The statement is: "If (x=3) then (x²=9)". The converse, "If (x² = 9) then (x = 3)" is not always true. For example, if x = -3, then x² is also 9.
A biconditional statement is true if and only if both the statement and its converse are true. Because the converse of the original statement is not always true, the biconditional statement " (x = 3) if and only if (x² = 9)" is also not true.
a developer wants to develop 5 acres of land. Each lot in the develope is to be 1/12 of an acre. How many lots will the land developer have in the 5 acres?
Final answer:
The land developer can create 60 lots of 1/12 acre each from a 5-acre parcel of land.
Explanation:
The student's question asks how many lots of 1/12 acre each can be created from a 5-acre parcel of land. To find the answer, divide the total acres available (5 acres) by the size of each lot (1/12 acre). Using division for fractions, we invert the divisor and multiply:
5 ÷ (1/12) = 5 × (12/1) = 60
Therefore, the land developer will be able to create 60 lots from the 5 acres.
Help! Give me the answer. I'll give the BRAINLIEST
hi, i cant see the question :(
What is 5 times 30 I don’t know
Answer:
150
Step-by-step explanation:
5*30=150
Start by multiplying 5*3, which is 15 then add the 0 back on. =150
Answer:
5 * 30 = 150
Step-by-step explanation:
5 * 30 = 5 * 3 * 10 = 15 * 10 = 150
The first three steps in determining the solution set of the system of equations, y = x2 - 2x + 8 and y = 2x + 11, algebraically
are shown in the table.
Step
Step 1
Step 2
Step 3
Equation
-X° -2x+8 - 2x+11
0 - x² + 4x+3
0-(x + 1)(x+3)
Which represents the solution(s) of this system of equations?
(-3,-1)
(-3,5)
(-3,5) and (-1,9)
(1, 13) and (3, 20)
Answer:
(-3,5) and (-1,9)
Step-by-step explanation:
x+1 = 0 ; x + 3=0
x = -1 ; x = -3
y = 2*-1 +11 ; y = 2*-3 +11
y = -2+11 = 9 ; y = -6 +11 =5
Answer: (-3,5) and (-1,9)
Step-by-step explanation:I ain’t gonna lie stole this mans answer but for trust reasons
x + 3 + x - 8 + x = 55
Answer:
x = 20
Step-by-step explanation:
Combine like terms
3x-5=55
Add the 4 on both sides
3x-5=55
+5 +5
3x=60
Divide both sides by 3
x = 20
Julie and her brother go to Atlanta to ride the SkyView Ferris wheel. It measures 200 feet in diameter.
A)I want to know the distance around the Ferris Wheel. Would I use Circumference or Area?
B)What is the formula needed to solve this problem?Look in your notes!
C)What is the distance traveled in one rotation? Explain how you used the formula to solve the problem.
The distance around the wheel is 628 feet and distance traveled in one rotation is equal to 628 feet
Solution:
Julie and her brother go to Atlanta to ride the SkyView Ferris wheel.
It measures 200 feet in diameter
Diameter = 200 feet
We know that diameter is twice of radius
[tex]diameter = 2 \times radius\\\\200 = 2 \times radius\\\\radius = \frac{200}{2}\\\\radius = 100[/tex]
Thus radius of wheel is 100 feet
The distance around the ferris wheel is the circumference of wheel
Since, wheel is of circular shape, we can use circumference of circle formula
The circumference of circle is given as:
[tex]C = 2 \pi r[/tex]
Where "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14
Substitute r = 100 we get,
[tex]C = 2 \times 3.14 \times 100 = 628[/tex]
Thus distance around the wheel is 628 feet
Distance traveled in one rotation = circumference of wheel
The distance traveled in one rotation is equal to 628 feet
Which ordered pair is a solution of the equation? y=7x-2
Answer:
(1, 5 )
Step-by-step explanation:
To obtain a solution, substitute any value for x into the equation and solve for y, that is
x = 1 → y = 7(1) - 2 = 7 - 2 = 5 → (1, 5 )
x = - 1 → y = 7(- 1) - 2 = - 7 - 2 = - 9 → (- 1, - 9 ) is also a solution
How can I solve 764+135 faster using a different strategy?
The Answer is a calculator is best way to get an answer quickly
Step-by-step explanation:
Answer add the tens place first then after you get that number you add the hundreds place and after you get that answer you add the thousands place and then after you get that answer you have you answer!!
does this represent a function why or why not
Answer:
the answer is B.
Step-by-step explanation:
According to the x and y axis, it shouild be B.
Answer:
I cannot see the screenshot
Step-by-step explanation:
What is the steps for solving 3x-10=84 and tell me what x equals
Answer:
Step-by-step explanation:
you move the -10 to the other side of the equation
3x=84+10
3x=94
x=31 1/3
Answer:
Your goal is to get x by itself
3x-10=84
First you want to add 10 to each side
3x=94 (-10+10=0, 84+10=94)
Last step is divide each side by 3
x= 31 and 1/3 or 94/3
Hope this helps ;)
A shoreline is eroding at rate of 2 5/18 feet each year at this rate,how many feet will the shoreline erode in 8 years
The shoreline will erode approximately 22 7/9 feet in 8 years.
Explanation:To find the total erosion over 8 years, we can use the given rate of erosion per year. The rate is 2 5/18 feet each year, and to calculate the total erosion over 8 years, we can multiply this rate by the number of years.
[tex]\[ \text{Rate of erosion per year} = 2 \frac{5}{18} \text{ feet} \][/tex]
[tex]\[ \text{Total erosion over 8 years} = \text{Rate of erosion per year} \times \text{Number of years} \][/tex]
[tex]\[ \text{Total erosion} = 2 \frac{5}{18} \times 8 \][/tex]
To perform this calculation, first convert the mixed number into an improper fraction:
[tex]\[ \text{Total erosion} = \frac{41}{18} \times 8 \][/tex]
Multiply the numerators and denominators:
[tex]\[ \text{Total erosion} = \frac{328}{18} \][/tex]
Now, simplify the fraction:
[tex]\[ \text{Total erosion} = 18 \frac{2}{18} \][/tex]
Thus, the shoreline will erode approximately[tex]\(18 \frac{2}{18}\) feet in 8 years, which simplifies to \(18 \frac{1}{9}\) or \(22 \frac{7}{9}\) feet.[/tex]
HELP ITS DUE TOMORROW
The area of a circle can be found using this formula: A = πr²
A = area
π = 3.14
r = radius (half of diameter)
A = (3.14)(12.5)^2
A = (3.14)(156.25)
A = 490.63
If the first difference of a sequence is the arithmetic sequence 2, 4, 6, 8, 10,...Find the first six terms of the original sequence in each of the following cases?
Step-by-step explanation:
The first differences being [tex]2, 4, 6, 8, 10,...[/tex] means
2 is the difference between the 1st and 2nd terms4 is the difference between the 2nd and 3rd terms6 is the difference between the 3rd and 4th terms8 is the difference between the 4th and 5th terms10 is the difference between the 5th and 6th termsSo,
If
The first term of the sequence is 2.
then
The second term of the sequence is [tex]2 + 2 = 4[/tex]
The Third term of the sequence is [tex]4 + 4 = 8[/tex]
The Fourth term of the sequence is [tex]8 + 6 = 14[/tex]
The Fifth term of the sequence is [tex]14 + 8 = 22[/tex]
The Sixth term of the sequence is [tex]22 + 10 = 32[/tex]
Keywords: sequence, arithmetic sequence
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Prince is 6n years old. jordan is (3n + 10) years older than prince
a) find jordans age
b) find the total age of prince and jordan
c) kimberly is 9 yrs younger than prince. find kimberlys age
d) find the total age of three people
e) if n = 4 find the total age of the 3 people
Answer:
a) 9n + 10 years.
b) 13n + 10 years.
c) 6n - 9 years
d) 19n + 1 years.
e) 77 years.
Step-by-step explanation:
a) Prince is 6n years old. Jordan's age is (3n + 10) years more than Prince.
So, Jordan's age is (6n + 3n + 10) = 9n + 10 years.
b) The total age of Prince and Jordan will be (6n + 9n + 10) = 13n + 10 years.
c) Kimberly's age is 9 years less than Prince.
So, the age of Kimberly will be 6n - 9 years.
d) The total age of the three people will be (6n - 9 + 13n + 10) = 19n + 1 years.
e) If n = 4, then total age of three people will be 19(4) + 1 = 77 years. (Answer)
Evaluate A^2 for A = -3.
Answer:
for A = -3
A² = A×A = (-3) × (-3) Two minus negate each other
= 3 ×3
= 9
:)
LAST 2 MATH QUESTIONS FOR TODAY and if since it's two questions, I'm giving 15 pts.
Answer:
JK and CB.
JL and AB.
Step-by-step explanation:
Corresponding sides.
Name two number that are not integers but that are opposite. Explain how you know
Answer:
Decimals, fractions and mixed units are not integers.
Step-by-step explanation:
Final answer:
Opposite non-integer numbers are pairs like 1/2 and -1/2 or 3.5 and -3.5. These pairs are not integers due to their fractional parts, yet they add up to zero, confirming they are opposites.
Explanation:
When we refer to numbers that are not integers but are opposites, we are seeking pairs of numbers whose sum is zero. Integers are whole numbers such as -1, 0, and 1, which do not include fractions or decimals. On the other hand, rational numbers are ratios of integers like 2/1 or 3/4, and these can be non-integers.
Consider the rational numbers 1/2 and -1/2; these are opposite numbers because they add up to zero. Similarly, another pair could be 3.5 (which is the same as 7/2) and -3.5 (or -7/2). These numbers are not integers because they have fractional parts, yet they are opposites because their sum is zero.
In both cases, these pairs demonstrate the mathematical property that when a number is added to its opposite, the result is always zero, which is a fundamental aspect of additive inverses. This is how we can verify that 1/2 and -1/2, as well as 3.5 and -3.5, are non-integer opposites.
solve -15=3/7b ''''''''''''''''''''''''''''''''
Answer:
Therefore,
[tex]b=-35[/tex]
Step-by-step explanation:
Solve:
[tex]-15=\dfrac{3}{7}b[/tex]
To Find:
b = ?
Solution:
[tex]-15=\dfrac{3}{7}b[/tex] ..............Given
Step 1 .Multiply Both the side by 7 we get
[tex]-15\times 7=7\times \dfrac{3}{7}b\\\\-105=3b[/tex]
Step 2. Divide Both the side by 3 we get
[tex]\dfrac{-105}{3}=\dfrac{3b}{3}\\\\-35=b\\b=-35[/tex]
Therefore,
[tex]b=-35[/tex]
16. Which point is the reflection of (-3, -2)
over the x-axis?
A. (-3,-2)
B. (3, -2)
C. (-3,2)
D. (3, 2)
use the formula f=9/5c+32 to convert -20 degrees f
Answer:
c ≈ -29°
Step-by-step explanation:
To convert Fahrenheit to Celsius using the formula, substitute the degrees for Fahrenheit "f", then isolate Celsius "c".
f = [tex]\frac{9}{5}c[/tex] + 32
-20 = [tex]\frac{9}{5}c[/tex] + 32 Substitute "f" for -20
-20 - 32 = [tex]\frac{9}{5}c[/tex] + 32 - 32 Subtract 32 from both sides
-20 - 32 = [tex]\frac{9}{5}c[/tex] +32-32 cancels out to 0. Simplify left side
-52 = [tex]\frac{9}{5}c[/tex]
-52/[tex]\frac{9}{5}[/tex] = [tex]\frac{9}{5}c/\frac{9}{5}[/tex] Divide by 9/5 on both sides
-52/[tex]\frac{9}{5}[/tex] = c
-52[tex]*\frac{5}{9}[/tex] = c When dividing a fraction, flip the fraction and change to multiplication
[tex]\frac{-52*5}{9}[/tex] = c Multiply by combining into the numerator
[tex]\frac{-260}{9}[/tex] = c Use a calculator
c = -28.8888888889°
c ≈ -29° Round to the nearest degrees
Therefore -20°F is about -29°C.
Emilio borrows $1200 from a bank with 8% simple interest per year. How much will he have to pay back total in 2 years?
Answer:
Step-by-step explanation:
1200÷2=600
An angle measures 18 more than the angle of its complementary what is the measure of each angle
Answer:
71
Step-by-step explanation:
Complementary angles have measures that add to 90°.
ABC and CBD are complementary angles.
Since the angles are complementary, their measures must add to 90°. Set up an equation and solve for n.
n + 18° = 90°
n + 18° − 18° = 90° − 18°
n = 72°
The measure of the complementary angle is 72°.