The measures of angle possible for of an isosceles triangle when one angle given is 140° then other two angles is 20°.
In an isosceles triangle, two of the angles have the same measure. Let's call this measure x. Since the sum of the angles of a triangle is 180 degrees, we can set up an equation:
x + x + 140° = 180°
Simplifying the equation, we get:
2x + 140° = 180°
Subtracting 140° from both sides, we get:
2x = 40°
Dividing both sides by 2, we get:
x = 20°
So the other two angles in the isosceles triangle each measure:
x = 20°
Therefore, the measures 28°, 22°, 26° are not possible for the other two angles of the isosceles triangle, but the measure 20° degrees is possible.
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if 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that
The probability that the dictionary is selected is 0.417, 3 novels and 2 books of poems are selected is 0.707. The probability that 4 novels are selected is 0.354.
The probability that the dictionary is selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select the dictionary and 4 other books.
The total number of ways to select 5 books from the shelf is:
C(12,5) = 12! / (5! * 7!) = 792
The number of ways to select the dictionary and 4 other books is:
C(1,1) * C(11,4) = 11! / (4! * 7!) = 330
Therefore, the probability that the dictionary is selected is:
P(dictionary) = 330/792 = 0.417
The probability that 3 novels and 2 books of poems are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 3 novels and 2 books of poems.
The total number of ways to select 5 books from the shelf is:
C(12,5) = 12! / (5! * 7!) = 792
The number of ways to select 3 novels and 2 books of poems is:
C(8,3) * C(3,2) = (8! / (3! * 5!)) * (3! / (2! * 1!)) = 560
Therefore, the probability that 3 novels and 2 books of poems are selected is:
P(3 novels, 2 books of poems) = 560/792 = 0.707
The probability that 4 novels are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 4 novels and 1 other book.
The total number of ways to select 5 books from the shelf is:
C(12,5) = 12! / (5! * 7!) = 792
The number of ways to select 4 novels and 1 other book is:
C(8,4) * C(4,1) = (8! / (4! * 4!)) * (4! / (1! * 3!)) = 280
Therefore, the probability that 4 novels are selected is:
P(4 novels) = 280/792 = 0.354
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_____ The given question is incomplete, the complete question is given below:
If 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that a. the dictionary is selected? b. 3 novels and 2 books of poems are selected? c. 4 novels are selected?
The length of a rectangle is twice its width. The perimeter is 60 ft. Find its area.
Answer:
Step-by-step explanation:
From a hot-air balloon, Violet measures a 24
∘
∘
angle of depression to a landmark that’s 806 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
Answer:
Area = 200ft²
Step-by-step explanation:
Perimeter of a rectangle = 2(length+width)
Area of a rectangle = length * width
Then:
g = 2w Eq. 1
60 = 2(g+w) Eq. 2
g = length
w = width
From Eq. 2
60 = 2g + 2w
60 - 2g = 2w Eq. 3
matching Eq. 1 and Eq. 3
g = 60 - 2g
g + 2g = 60
3g = 60
g = 60/3
g = 20 ft
From Eq. 1
g = 2w
20 = 2w
20/2 = w
w = 10 ft
Area
area = length * width
area = 20ft * 10 ft
area = 200ft²
. Find the coordinates of the center and the measure of the radius for a circle whose equation is
(x-8)2 + (y+4)² =12 (3 points)
Answer:
Radius is 2√3 units
Center is (8,-4)
Step-by-step explanation:
Compared to the standard form equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], then the radius would be [tex]r=\sqrt{12}=2\sqrt{3}[/tex] and the center would be [tex](h,k)\rightarrow(8,-4)[/tex].
1/4 of the sum of 18 and 6. What does that mean? It it like converting 18 plus 6 to a fraction?
Answer:
See below
Step-by-step explanation:
Sum of 18 and 6 = 24
1/4 of the sum of 18 and 6 is asking you what is the result of dividing 24 by 4
In a way you can think of it as a fractional question but the answer is a whole number
[tex]\dfrac{1}{4} \cdot (18 + 6) = \dfrac{1}{4} \cdot 24 = \dfrac{24}{4} = 6\\[/tex]
Tina and her friends started a project called Lemonade for Lions. Every Saturday, they sell lemonade to raise money for lion conservation. One Saturday evening, they share the day's leftover lemonade evenly among the 4 of them. Each person gets 1/8 of a gallon of lemonade.
Find the slope of the line through each pair of points. ) (11, 8), (- 13, 11)
The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.
Slope of a line:The slope of a line is defined as the change in y- coordinate with respect to x - coordinate. The slope of a line represents the direction and steepness of a line. The formula for the slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by
Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]Here we have
The pair of points (11, 8), (- 13, 11)
By the given formula,
Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]
The slope from (11, 8) to (- 13, 11) can be calculated as follows
Slope = [ 11 - 8 ]/ [ -13 -11 ] = 3/-24 = -1/8
Therefore,
The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.
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A bowling alley charges $2.00 per game and will rent a pair of shoes for $1.00 for any number of games the bowling alley has an earnings goal of $300 for that day write a linear equation that describes the problem
The linear equation that describes the problem is: 2x + y = 300.
How to Write a Linear Equation for a Problem?A linear equation can be defined in standard form as Ax + By = C, where:
A, B, and C are integers
x and y are variables.
From the information given, we have the following:
number of games = x
rent for a pair of shoes for any number of games = y
total earnings goal for that day = 300
Therefore, the linear equation would be: 2x + y = 300
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Malik just got hired for a new job and will make $96, 000 in his first year. Malik was
told that he can expect to get raises of $5,000 every year going forward. How much
money in salary would Malik make in his 11th year working at this job?
The amount of money Jamar will make in his 18th year working at this job is = $107,500
What is salary outcome?A salary is a form of periodic payment from an employer to an employee, which may be specified in an employment contract. It is contrasted with piece wages, where each job, hour or other unit is paid separately, rather than on a periodic basis.
here, we have,
Calculation of yearly salary outcome
The amount of money Jamar made in his first year= $48,000
The salary rise per year = $3,500
The amount of money he will make for the extra 17 years is
= 17 × $3,500
= $59,500
Therefore the amount he will receive as his salary in the 18th year working at this job = $48,000 + $59,500
= $107,500
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What quantity must be added to 3-7x+4 to obtain - +4x-2?
A-4x2+3x+2
B.-412 + 11x + 2
C.-4x² + 11x-6
D. 2x²-3x+2
E. 2x²-3x+6
Answer:
Step-by-step explanation: (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient
Hope it helps =}
Answer:
b
Step-by-step explanation:
Which equations are correct? select each correct answer. 8x3(3x2)=24x6 4x3(6x2)=24x6 6b3(−2b3)=−12b6 3a3(−3a4)=−9a7?
The correct equations are:8x^3 * (3x^2) = 24x^5, 6b^3 * (-2b^3) = -12b^6, 3a^3 * (-3a^4) = -9a^7. The equations are correct because they follow the rules of algebra. The equation 4x^3 * (6x^2) = 24x^5 is not correct.
The distributive property of multiplication over addition allows us to multiply a factor by each term inside a set of parentheses. In the equation 8x^3 * (3x^2), we can use the distributive property to multiply 8x^3 by each term inside the parentheses, giving us 24x^5.
Similarly, the product of two negative numbers is positive, which explains why the equation 6b^3 * (-2b^3) equals -12b^6.
Finally, multiplying two terms with the same base means we add the exponents, so in the equation 3a^3 * (-3a^4), we get -9a^7.
Therefore, these equations are correct and follow the rules of algebra.
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Tanya is renting a bounce house for a birthday party. The graph shows the time in hours (x)
compared to the total cost in dollars (y). Determine rate and initial value to write a linear equation.
=mx+b): _____
Find the rate (M). Find the initial value (B).
Equation (y=mx+b).
the equation of the straight line will be y = 10x+10.
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The initial value 10
slope m = 30-20/2-1
m = 10/1=10
So the equation of the straight line will be y = 10x+10.
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a fitness club leases space at a major shopping center. the club has 10,500 square feet which represents 16% of the total leasable space at the shopping center. calculate the total leasable space at the center?
The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.
According to the information provided, a fitness club occupies 10,500 square feet or 16% of the total leasable area at a sizable shopping mall. We can use the proportional and percentage approaches to determine the total leasable area.
Let's assume that the variable "x" stands for the whole amount of leasable space. Since we are aware that the area leased by the gym is 16% of the total leasable area, we can create the following equation:
10,500 = 0.16x
To solve for "x", we can divide both sides of the equation by 0.16:
10,500 / 0.16 = x
Simplifying this expression gives us:
x = 65,625
Therefore, The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.
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Choose a method that can be used to solve this system of equations by elimination 2x – 2y = 24 4x + 7y = –40
Answer: x = 4, y = -8
Step-by-step explanation:
Because 2 is a multiple of four, multiply the first equation by two to eliminate the x value and effectively isolate y.
4x - 4y = 48
4x + 7x = -40
If we were to subtract the x values, that gives us -11y = 88, or y = -8.
Then, just plug y into your equation of choice.
2x - 2(-8) = 24
2x + 16 = 24
2x = 8
x = 4
One way you can check whether the values is right is plug the y value into the other equation and see if you receive the same answer.
4x + 7(-8) = -40
4x = -40 + 56
4x = 16
x = 4
In circle M, m/NMO = 144º and the area of the shaded sector = 107. Find the
length of MN.
In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.
What is the sector of the circle?
That the portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.
The area of the shaded sector of circle M can be represented as follows:
Area of sector = (m/NMO / 360) * π * r²
We know that m/NMO = 144° and the area of the sector is 107, so we can substitute these values into the equation and solve for the radius:
107 = (144 / 360) * π * r²
Multiplying both sides of the equation by 360 / 144 gives:
360 * 107 / 144 = π * r²
Dividing both sides of the equation by pi gives:
r² = 360 * 107 / (144 * π)
Taking the square root of both sides of the equation gives:
r = √(360 * 107 / (144 * π))
Now that we know the radius, we can use it to find the length of MN.
The length of the minor arc MN is equal to the length of the central angle NMO in radians times the radius:
MN = m/NMO * π * r / 180
Substituting in the values for m/NMO and r gives:
MN = 144 * π * √(360 * 107 / (144 * π)) / 180
Hence, In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.
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A number divided by 14
Answer:
it could be either 1, 2 or 7
Step-by-step explanation:
1×14=14
2×7=14
7×2=14
An athletic track is given in the figure.
The two straight parts are 80 m long.
The total length of the track is 400 m.
Find the radius of the curved part of the track
on both sides.
Subtract the length of the two straight parts
from the entire length of the track.
The radius of the curved part of the track will be 37.3m.
Solution:
Given that
The length of straight parts = 80m each
The total length of the track = is 400m
So, the total length of curved parts = 400 - (80*2) = 240m
Therefore, the radius of the curved parts =
[tex]2\pi r = 240\\r = 240/2\pi \\[/tex]
Hence, r = 37.3m.
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The distance to the nearest exit door is at most 100 feet. Write an inequality
Answer:
The distance to the nearest exit door is at most 100 feet can be written as an inequality as:
d ≤ 100
George ate a meal that included a steak, a loaded baked potato, and coleslaw. The coleslaw had 50 fewer calories than the baked potato. The steak had twice as many calories as the baked potato. The total number of calories in the meal was 1550 calories. Write an equation that could be used to find the number of calories in the loaded baked potato (where P presents the calories in the loaded baked potato). Then, SOLVE the equation.
Answer:
400 calories
Step-by-step explanation:
Let's call the number of calories in the loaded baked potato as P. Then the coleslaw had P-50 calories and the steak had 2P calories.
So the equation for the total number of calories in the meal is:
P + (P-50) + 2P = 1550
4P = 1600
P = 400
Therefore, the loaded baked potato had 400 calories.
Answer:
Below
Step-by-step explanation:
c oleslaw = p - 50
p = potato
s = 2 p Summed these = 1550
p-50 + p + 2p = 1550 Gather 'like' terms
4p - 50 = 1550 add 50 to both sides of the equation
4p = 1600 divide both sides by 4
p = 400 calories
Your Assignment
Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
2. Simplify both sides. Show your work.
3. Is x = 6 a solution to the equation? Why or why not? (3 points
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
please help me!
Answer:
5(x – 3) = x + 13 with x = 6 substituted: 5(6 – 3) = 6 + 13
Simplifying both sides: 5(3) = 6 + 13
15 = 19
x = 6 is not a solution to the equation because when you substitute it, the left side of the equation (15) does not equal the right side of the equation (19).
To find a value of x that is a solution to the equation, we can start by solving for x:
5(x – 3) = x + 13
5x – 15 = x + 13
4x = 28
x = 7
So, x = 7 is a solution to the equation 5(x – 3) = x + 13. To find this solution, we first substituted x = 7 into the equation and simplified both sides to see if they were equal.
Step-by-step explanation:
true or false: the rule of thirds is the process of dividing an image into thirds, using two horizontal lines and two vertical lines, and positioning the most important elements inside the squares the lines create.
True. The rule of thirds is a photography and visual arts guideline that involves dividing an image into thirds using two horizontal lines and two vertical lines, and then placing the image's most important elements at the intersection points or along the lines.
This aids in the creation of a balanced and visually appealing composition. This results in nine rectangular areas of equal size, with four intersection points where the lines cross.
The rule of thirds principle suggests that the points of intersection or the lines themselves are ideal places to position the composition's most important elements. The resulting image is more visually balanced and pleasing to the eye as important elements are placed in these areas.
It is important that, however, that the rule of thirds is not a hard and fast rule, and that there were times when breaking it can result in more dynamic and interesting compositions. The rule of thirds is merely a tool for artists and photographers to use in order to create more effective and engaging images.
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Solve the system of equations:
Answer:
The solution is (x = 6, y = -3)
Step-by-step explanation:
[tex]\sf \frac{x}{y + 1} = - 3 \: \: ........(1) \\ \\ \sf \frac{y}{x - 3} = - 1 \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \sf x + 3y = - 3 \: ........(1) \\ \\ \sf x + y = 3 \: \: \: \: \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \: \: \: \sf x + 3y = - 3 \: \: \: \: \: | \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x + y = 3 \: \: \: \:\: \: \: \: | \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Someone help, please!
The appropriate response will be (A). The first equation of motion gives the link between "velocity and time."
What are the names of equations?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
What are the uses of equations?An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. Pre-algebra concepts contain the fundamentals of mathematics.
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Completing a Proof
Given: ABCD is a parallelogram.
Prove: mZA+mZB+mZC+mZD=360*
A
D
B
C
By the definition of a parallelogram, AD // BC and
AB/DC. Using, AD as a transversal, ZA and Z
are same-side interior angles, so they are
By the definition of supplementary,
mZA+mZD=180. Using side [
as a
transversal, ZB and ZC are same-side interior angles,
so they are supplementary. By the definition of
supplementary, mZB+mZC=180. So, mZA+mZD
+ m2B+mZC=180+180 by the [
property. Simplifying, we have mZA+mZB+mZC+
mZD=360°.
27
A
The required, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.
Given: ABCD is a parallelogram. To prove: mZA + mZB + mZC + mZD = 360 degrees
What is parallelogram?A parallelogram is a quadrilateral consisting of pairs of parallel sides.
Here,
The proof you provided is correct! Here's a step-by-step explanation of the proof:
By the definition of a parallelogram, AD // BC and AB/DC.
Using AD as a transversal, ZA and ZD are same-side interior angles, so they are supplementary (meaning their measures add up to 180 degrees).
Using side AB as a transversal, ZB and ZC are same-side interior angles, so they are supplementary as well.
By the definition of supplementary angles, mZA + mZD = 180 degrees and mZB + mZC = 180 degrees.
Adding the two equations together, we get:
mZA + mZD + mZB + mZC = 180 degrees + 180 degrees
Simplifying the right side of the equation, we get:
mZA + mZB + mZC + mZD = 360 degrees
Therefore, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.
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The staff at a company went from 40 to 29 employees. What is the percent decrease in staff
Answer:
27,5%
Step-by-step explanation:
To find the percent decrease, we need to calculate the difference between the original number and the new number and then divide it by the original number and multiply by 100%.
The difference is 40 - 29 = 11.
The percent decrease is (11/40) * 100% = 27.5%
So the percent decrease in staff is 27.5%
The price of a gallon of unleaded gas was $2.81 yesterday. Today, the price rose to $2.88. Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase of the gas would be 2.5%.
How to calculate a percentage increase?We can calculate the value of the percentage increase by the following formula,
percentage increase = (final value - initial value) / initial value × 100%
As per the given question, we have
initial value = $2.81 , and final value = $2.88
Substitute the values in the above formula, and we get
percentage increase= (2.88 - 2.81 ) / 2.81 × 100%
percentage increase = (0.07) / 2.81× 100%
percentage increase = 0.0249 × 100%
Apply the multiplication operation, and we get
percentage increase = 2.49%
Thus, the percentage increase of an item would be 2.5%.
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Find the measure of two complementary angles, ZA and ZB, if
mA=7x+4 and mZB=4x+9.
The measure of ∠A is 53.
The measure of ∠B is 37.
What is an expression?An expression contains one variable or more than one variable with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∠A and ∠B are complementary.
This means,
∠A + ∠B = 90
Now,
∠A = 7x + 4
∠B = 4x + 9
7x + 4 + 4x + 9 = 90
11x + 13 = 90
11x = 90 - 13
11x = 77
x = 7
Now,
∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53
∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37
Thus,
∠A = 53
∠B = 37
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4 Natasha is foot taller than her little
brother. Natasha is no more than 5-½ feet
tall. Which inequality can be used to
find the possible height of her little
brother, b?
The possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as: b ≤ 4.5
How to find the inequalityLet's denote the height of Natasha as "n" and the height of her little brother as "b".
We know that Natasha is one foot taller than her little brother, so we can write:
n = b + 1
We also know that Natasha's height is no more than 5-1/2 feet, so we can write:
n ≤ 5.5
Now we can substitute the first equation into the second equation and get:
b + 1 ≤ 5.5
Simplifying this inequality, we get:
b ≤ 4.5
Therefore, the possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as:
b ≤ 4.5
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The height, h, of the triangle is 11 cm greater than its corresponding base.
What is the area of the triangle?
A=
cm²
33 cm
10 cm
Answer:
If the height of the triangle is 11 cm greater than its corresponding base, we can represent the base as b and the height as h = b + 11.
Using the formula for the area of a triangle, A = (1/2) bh, we can substitute the values of b and h:
A = (1/2) (b)(b + 11)
A = (1/2) b^2 + (1/2) 11b
If the base of the triangle is 10 cm, then we can substitute b = 10 into the equation:
A = (1/2) (10^2) + (1/2) 11 * 10
A = 50 + 55
A = 105 cm^2
So, the area of the triangle is 105 cm^2.
Step-by-step explanation:
assume that there are 60 students in a class and they will be seated in a classroom where there are 62 seats. in how many different ways this can be done?
There are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.
If there are 60 students and 62 seats, then there will be 2 empty seats in the classroom. We need to find out the number of ways to seat the 60 students in these 62 seats.
To solve this problem, we can use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects we want to arrange.
In this case, we want to arrange 60 students in 62 seats, so we can use the formula as follows:
62P60 = 62! / (62 - 60)!
= 62! / 2!
= 62 x 61 x 60 x ... x 3 x 2 x 1
= 4,431,621,036,503,680
Therefore, there are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.
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A water bottle holds 72 ounces of water. How many cups does the water bottle hold? (1 cup = 8 fluid ounces) 4 cups 8 cups 9 cups 64 cups
Answer:
9 cups
Step-by-step explanation:
1 cup is 8 ounces
72/8 is 9
