A possible length, in inches, of the third side is equal to 4 inches.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:
b - c < n < b + c
7 - 4 < n < 7 + 4
3 < n < 11.
Therefore, n could be 4, 5, 6, 7, 8, 9, and 10 inches.
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Please answer these for 100 points
The area of a trapezoid with the given parallel sides and height is 4x+8 square units. Therefore, option B is the correct answer.
What is area of the trapezoid?The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (b₁+b₂)×h.
where (A) is the area of a trapezoid, 'b₁' and 'b₂' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between b₁ and b₂).
1) Given that, b₁=x-3, b₂=x+7 and the height=4
Now, area of a trapezoid = 1/2 (x-3+x+7)×4
= 2×(2x+4)
= 4x+8 square units
Hence, option B is the correct answer.
2) The given polynomials are -3x²-7x+9 and -5x²+6x-4.
Here, sum = -3x²-7x+9+(-5x²+6x-4)
= -3x²-7x+9-5x²+6x-4
= -8x²-x+5
Hence, option 1 is the correct answer.
Therefore, the area of a trapezoid is 4x+8 square units.
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11. A) A mobile price is tagged Rs 5,000. If a customer gets 12% discount and adding certain
percent VAT reaches as Rs 4,972, find out the VAT percentage.
The VAT percentage of a mobile price is tagged Rs 5,000 with a 12% discount and adding a certain percentage of VAT reaches Rs 4,972 is a 13% VAT Percentage.
The solution to the problem is as follows:
Step 1: Find the price of the mobile after the discount. The discount is 12% of the original price, which is Rs 5,000. So, the discount amount is:
12% of Rs 5,000 = (12/100) * 5000 = Rs 600
Step 2: Subtract the discount amount from the original price to get the price after the discount:
Rs 5,000 - Rs 600 = Rs 4,400
Step 3: Now, we need to find the VAT percentage that was added to the price after the discount to get the final price of Rs 4,972. Let the VAT percentage be x%. Then the equation is:
Rs 4,400 + x% of Rs 4,400 = Rs 4,972
Step 4: Simplify the equation and solve for x:
4400 + (x/100) * 4400 = 4972
4400 + 44x = 4972
44x = 4972 - 4400
44x = 572
x = 572/44
x = 13
Therefore, the VAT percentage is 13%.
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My age 2 years ago plus my age 2 years from now equals 24. How old am I
Answer:
= 6 years old.
Step-by-step explanation:
Let your age 2 year ago be = x
= 2x
again
Let your age 2 years from now be x
= 2x
therefore
= 2x +2x = 24
= 4x = 24
= 4x/4 = 24/4
= x = 6
therefore you're 6 years old.
Determine the interval(s) on which the given function is increasing.
Polynomial going up from the left and passing through the point negative 1 comma 0 and going to a relative maximum at the point 0 comma 5 and then going down to a relative minimum at the point 1 comma 4 and then going up to the right
(–∞, –1) ∪ (1,∞)
(–1, ∞)
(–∞, 0) ∪ (1, ∞)
(0, 1)
The intervals on which the function is increasing is (0, 1). Option D
What is a polynomial?A polynomial is a type of mathematical expression that has variables that are raised to whole number powers.
Since the factors of 5 are 1 and 5, we'll try to factor the polynomial by assuming that (x-1) and (x-5) are factors.
The product of (x-1) and (x-5) is (x² - 6x + 5), which is the polynomial we're given.
⇒ (x² - 6x + 5) is the factored form of the polynomial.
A polynomial is increasing on the intervals where it's greater than zero. So we just need to look at the sign of (x² - 6x + 5) for values between 1 and 5.
For values between 1 and 5, the function is always positive, so it's increasing on the interval (1, 5). Therefore, the increasing interval is (1, 5).
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Find any points of discontinuity for the rational function. y=(x+3)(x-5)(x+7)/(x+1)(x+4)
Points of discontinuity for the rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4) are x = -1 and x = -4.
A rational function is a function that can be expressed as the ratio of two polynomial functions. In the case of the given rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4), the numerator is a polynomial of degree 3, and the denominator is a polynomial of degree 2.
To find any points of discontinuity for a rational function, we need to determine where the denominator is equal to zero. Division by zero is undefined, so any value of x that makes the denominator equal to zero will be a point of discontinuity for the function.
In this case, we set the denominator (x+1)(x+4) equal to zero and solve for x:
(x+1)(x+4) = 0
This equation is true if either (x+1) = 0 or (x+4) = 0. So we have two solutions:
x+1 = 0 or x+4 = 0
x = -1 or x = -4
These values of x make the denominator of the function equal to zero, which means that the function is undefined at these points. These points are known as vertical asymptotes of the function, since the function approaches infinity as x approaches these points from either side.
It's important to note that the numerator of the function does not affect the points of discontinuity, since it is always defined for any value of x. Therefore, the points of discontinuity only depend on the denominator of the function.
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Help!!! I don't understand this question..
Step-by-step explanation:
I want to say Marisella. Here's my argument.
5 seats in the front row, so 5/20. Before the first person enters, 5 seats are open making it 5/20.
Once the first person sits.. now there are 4 spots in the front and only 19 total seats left, making it 4/19
What is the percent composition of water in the compound magnesium sulfate heptahydrate, MgDO4•7H2O?
A. 7.3%
B. 24.8%
C. 48.8%
D. 51.2%
Answer:51. 2%
Step-by-step explanation:
24+32+(16×4)+7(2+16)=24+32+64+126=246
26g of Epsom salt contains 126g of water of crystallisation.Hence, 100g of Epsom salt contains 100×126/246The % of H2O in MgSO4.7H2O=
A bag contains only pink sweets, white sweets, green sweets and red sweets.
The table gives each of the probabilities that, when a sweet is taken at random from
the bag, the sweet will be green or the sweet will be red.
Answer:
Below
Step-by-step explanation:
Since : .35 x = 28 Given ( where x = total sweets)
x = 80 sweets total
28 are red ( given ) then 02. * 80 = green = 16
80 - 28 - 16 = 36 remaining
and are divided between pink : white in ratio of 2:1
pink are 2 out of (2+1) = 2/3
2/3 * 36 remaining = 24 pink
then 12 are white
Melanie is given two hours to complete a science test that has two sections. If she takes forty-three minutes to complete the first section, how many minutes does she have remaining on the second section?
Type a numerical answer only no words, symbols, or variables.
She have 1 hour 17 minutes remaining for the second section.
what is total time ?
Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.
Given:
Total time : two hours
Time taken to complete the first section = forty-three minutes
Now , minutes she have remaining on the second section
= Total time - Time taken to complete the first section
= 2 hours - 43 minutes
= 1 hour 17 minutes
Hence , she have 1 hour 17 minutes remaining for the second section.
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The table shows the world birth rates y number of births ler thousands people) in r years since 1960
Identify an equation that models the birth rate as a function of the number years since 1960
An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35. Thus, option 3 is correct.
What do you mean by equation?It represents a relationship between variables and constants and is used to describe the behavior of a function or system. Equations can be linear or nonlinear and can have one or multiple variables. They can be used to solve real-world problems, such as finding the slope of a line, calculating distances, or determining the minimum or maximum value of a function. Equations are also used in advanced mathematical disciplines, such as calculus, algebra, and geometry.
When x = 0, y-intercept = 35.4 ≈ 35
And when x increases, the value of y decreases, so slope is negative
From the given options
There is only two negative slope equation but only one with y-intercept = 35. i.e.
y = -0.3x + 35
Thus, An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35.
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Step 2 Use the answers from Step 1 to find the total distance Sonja's ball traveled during her warm
up. Show your work (4 points)
I need help on the whole page if anyone knows the answer to this
Answer: step 1:
wickets 2 and 9, (16,18) and (15,43) = 25.02ft
wickets 9 and 8, (15, 43) and (37,65) = 31.11 ft
wickets 8 and 5, (37, 65) and (63,39) = 36.7 ft
wickets 5 and 3, (63, 39) and (41, 17) = 31.11 ft
wickets 3 and 2, (41, 17) and (16, 18) = 25.02 ft
If P = 14 x 36, what is the prime factorization of P?
A. 2^3 x 3 x 7^2
B. 2^4 x 3 x 7
C. 2^3 x 3^2 x 7
D. 2 x 3^3 x 7
E.2 x 3 x 7^2
The prime factorization of P is given as follows:
C. 2³ x 3² x 7.
How to obtain the prime factorization of P?The number P in this problem is defined as follows:
P = 14 x 36.
Hence we must obtain the prime factorization of each number in this problem, as follows:
14 = 2 x 7.36 = 4 x 9 = 2² x 3².Then the prime factorization of the multiplication is given as follows:
14 x 36 = 2 x 7 x 2² x 3² = 2³ x 3² x 7.
Meaning that the correct option is given by option C.
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Thomas won $16,000 on a game show, and he put all of the money in a checking account (which does not give interest). Each month, he takes $400 out of the account for "spending" money.
The equation that describes this situation is M=16000−400t
, where t
is the time in months since opening the account, and M
is the amount of money left in the account.
In how many months will Thomas empty the account (which means that there will be no money left)?
It will take Thomas 40 months to empty the account if he continues to take out $400 each month of $16,000.
To find out how many months it will take for Thomas to empty the account, we need to set M to 0 and solve for t. This will give us the number of months it will take for Thomas to spend all of the $16,000 he won on the game show. The equation we need to solve is:
0 = 16000 - 400t
First, we'll isolate the variable t on one side of the equation by adding 400t to both sides:
400t = 1600
Next, we'll divide both sides of the equation by 400 to get the value of t:
t = 16000/400
Simplifying the right side of the equation gives us:
t = 40
So, it will take Thomas 40 months to empty the account if he continues to take out $400 each month for spending money.
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In a company, 70% of the workers are. If 1170 people work for the company who aren't women, how many workers are there in all?
The number of workers in the company is given as follows:
3900 workers.
How to obtain the number of workers in the company?The number of workers in the company is obtained applying the proportions in the context of the problem.
From the problem, we have that:
70% of the workers are women.1170 of the workers are not women.Hence 30% of the workers is equivalent to 1170, hence the number of workers in the company is obtained as follows:
0.3x = 1170
x = 1170/0.3
x = 3900 workers.
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Pixflix online video charges $5.95 to view a movie. Movie Prime video service charges $150 per year membership and $3.95 per movie. Assuming Minda views the same number of movies each month, what is the fewest number of movies per month Minda must view to make Movie Prime the better deal?
Minda must view 76 movies to make Movie Prime the better deal
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let, The number of movies be 'x' and from the given information the two equations can be formed as,
5.95x and 150 + 3.95x.
And to make Movie Prime the better deal,
150 + 3.95x < 5.95x.
2x > 150.
x > 75.
So, Minda must watch greater than 75 movies.
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Need answer quick !!!
The sector area is equal to: B. 54π yd².
How to calculate the area of a sector?Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = θr²/2
Where:
r represents the radius of a circle.θ represents the central angle.Substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = θr²/2
Area of sector = 240(π/180) × (9)²/2
Area of sector = 120(π/180) × 81
Area of sector = 54π yd².
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PLEASE ONLY ANSWER IF YOU KNOW
The value of AB in the triangle is 2.5 cm and the value of x in the triangle is 10 units
How to determine the value of ABFrom the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following equivalent ratio
AB : 4 = 10 : 16
Express as fraction
So, we have
AB/4 = 10/16
This gives
AB = 4 * 10/16
Evaluate
AB = 2.5
How to determine the value of xHere, we understand that the line bisects the angle BAC
This means that
x = 20 - x
So, we have
2x = 20
Divide
x = 10
Hence, the value is 10
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FIND THE LENGTH OF arc AB
thanks
Answer: D, 9.4
Step-by-step explanation:
(pi*2*12) *45/360 = 9.4
Answer:
9.4 is correct
Step-by-step explanation:
C=2πr = 2x3.14x12=75.36
arc AB=(45/360)x75.36=9.42
9) Before hibernation, a bear weighs 990 pounds. Its weight decreases by 32% during hibernation. How much does the bear weigh when it comes out of hibernation? Show your work.
The weight of the bear after hibernation is 673.2 pounds
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Before hibernation, a bear weighs 990 pounds.
Its weight decreases by 32% during hibernation.
We need to find how much the bear weigh when it comes out of hibernation.
Lets find what is 32% of 990
32/100×990
0.32×990
316.8
Now let us subtract 316.8 from 990 pounds, to find the weight after hibernation.
990-316.8
673.2
Hence, 673.2 pounds is the weight of the bear after hibernation.
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A B What is the converse of the following statement? "If I studied for it, then I did well on the exam." "If I did well on the exam, then I studied for it." "If I did not do well on the exam, then I did not study for it."
Answer:
A
I believe because p→q
q→p
can someone please help me with this work sheet
1. Adjacent angles and 1 degree is missing angle.
3. Complementary angles are missing angle is 177 degrees.
4. Adjacent angles and missing angle is 10 degrees.
5. Adjacent angles and missing angle is 104 degrees.
6. Adjacent angles and missing angle is 10 degrees.
6. Vertical angles and missing angle is 57 degrees.
What are Angles?an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
1. The angles are Adjacent
54+10x+16=180
10x=180-70
x=1
So the unknown angle is 10+16=26 degrees.
3. The angles are complementary
22+4x=90
4x=68
Divide both sides by 4
x=17
So, the angle is 4(17)=68 degrees
4. The angles are Adjacent
110+7x=180
7x=70
x=10, the other angle is 7(10)=70 degrees
5. The angles are Adjacent
72+x+4=180
x=104
The other angle is 104+4=108 degrees.
6. 92+x+78=180
x=10
The unknown angle is 10 degrees.
7. The angles are vertical.
72=x+15
x=57 degrees.
Hence,
1. The angles are Adjacent and missing angle is 1 degrees.
3. The angles are complementary and missing angle is 177 degrees.
4. The angles are Adjacent and missing angle is 10 degrees.
5. The angles are Adjacent and missing angle is 104 degrees.
6. The angles are Adjacent and missing angle is 10 degrees.
6. The angles are Vertical and missing angle is 57 degrees.
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What does it mean by the nearest cent?
Answer:
Rounding to the nearest cent implies approximating a money amount to two decimals (which represent the number of cents), applying the following rules: If the third decimal digit is lower than 5, we leave the second decimal digit as it is. E.g., $4.563 ≈ $4.56.
PLEASE HELP AS FAST AS POSSIBLE
Answer:
l is parallel to m and u is parallel to t
Step-by-step explanation:
Parallel line means that never meet each other
solve the following systems of equations by graphing y=2x-4
y=-1/2x+6
Answer:
(4,4)
By using a graphing we can see that the lines intersect at (4,4).
therefore, 4 is the solution
don't forget to say thanks
An equation is shown below.
4.3(3.4z-19.2) = 5.3z + 10.7-2.4z
Which of the following statements describes a step that can be used to solve the equation for ?
O Subtract 4.32 from both sides of the equation.
O Add 10.7 to both sides of the equation.
O Divide both sides of the equation by 4.3.
O Multiply both sides of the equation by 10.7.
Answer:z=4663/586
Step-by-step explanation:
322 Out of 450 is What Percent?
The percentage of 322 out of 450 using the percentage formula was found out to be approximately 71.56%.
To find the percentage of 322 out of 450, we can use the following formula:
percentage = (part/whole) x 100
where, "part" is the value we want to express as a percentage (in this case, 322), "whole" is the total value (in this case, 450), and "x" means "multiply".
Using the formula mentioned above, we get:
percentage = (322/450) x 100
percentage = 0.7156 x 100
percentage = 71.56%
Therefore, percentage of 322 out of 450 is approximately 71.56%.
A percentage is a way to express a number as a fraction of 100. It is often denoted using the "%" symbol.
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Python formats all floating point numbers to two decimal places when outputting using the print statement O True O False 1 pts >> Question 9 The if statement causes one or more statements to execute only when a Boolean expression is true. O True O False
Python formats all floating point numbers to two decimal places when outputting using the print statement. (FALSE)
The if statement causes one or more statements to execute only when a Boolean expression is true. ( TRUE)
What are Floating Points?Floating point is a number format that can be used to represent a large or small value.
In writing this number is done by writing it in exponential form, so that the number has a base number, the exponential number and the base number.
The following is writing scientific notation in floating point. example in decimal numbers
261,000,000,000 written 2.61 x 10¹¹
0.000000000261 is written 2.61 x 10^-10
The Floating point representation itself has two parts, namely the mantissa part and the exponent part. The mantissa determines the digits, while the exponent determines the value of how many powers the mantissa is, as follows:
±S * B±E
S = Significant also called mantissa
E = Exponent
B = Base
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Step-by-step answer please, thanks! :)
The amount of money you'll have at the end of 5 years is $4,060.
How to calculate the simple interest and future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 3,500 × 3.2/100 × 5
S.I = 3,500 × 0.03.2 × 5
S.I = $560.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = $560 + $3,500
Future value, A = $4,060.
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There are 96 birds at the Parkdale Zoo. of the birds are penguins. How many penguins are at Parkdale Zoo?
The number of penguins at the zoo is 48.
How many penguins are at the zoo?Percentage is a measure of frequency that determines the value of a number as an amount out of hundred. The sign that is used to represent percentage is %. In order to convert a number to percentage, multiply by 100.
Number of penguins = percentage of penguins x number of birds
50% x 96
(50/100) x 96 =
0.5 x 96 = 48
Here is the complete question:
There are 96 birds at the Parkdale Zoo. 50% of the birds are penguins. How many penguins are at Parkdale Zoo?
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An object is launched at 19. 6 meters per second (m/s) from a 58. 8-meter tall platform.
The item reached its highest point at 78.4 meters by quadratic form of equation.
Suppose a quadratic form of equation has the following form
y=a[tex](x-h)^2[/tex] + k
Once in vertex form, it is said to be. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)
Using the data shown above, we can determine that
-4.9[tex]t^2[/tex] + 19.6 t + 58.8 = 0
The equation will naturally be converted to vertex form after the square is finished:
where h is the amount of time needed to reach a height of k.
Next, square the half of the linear term and add it to both sides.
-4.9([tex]t^2[/tex]-4t)=-58.8
-4.9([tex]t^2[/tex]-4t+4)=-58.8-19.6
-4.9([tex](t-2)^2[/tex])=-78.4
s(t)=-4.9([tex](t-2)^2[/tex])+78.4
As can be seen, the vertex is (2,78.4).
The maximum height is 78.4m.
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Question: An object is launched at 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s(t)=−4.9[tex]t^2[/tex]+19.6t+58.8. What is the maximum height of the object?