Possible length of the third side of the Triangle must be between 11 and 23.
What is the Range of third side of Triangle ?As the third side of the triangle is between the sum of the sides and difference of the sides excluding both the numbers.
As triangle consist of three sides and it should must be in between two extreme values.
As by the property of Triangle
Third side should be less than sum of the sides and,
it should be greater than difference of the sides.
Sum of the sides = AB + BC = 6 + 17 = 23
Difference of the sides = 17 - 6 = 11
Then the third side will be between 11 and 23 excluding 11 and 23.
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A new Youth Activity Center is being built in Ook Valley. The perimeter of the rectangular playing field is 272 yards. The length of the field is 8 yards less than double the width. What
are the dimensions of the playing field?
Answer:
w = 48 and l = 88
Step-by-step explanation:
A new Youth Activity Center is being built in Ook Valley. The perimeter of the rectangular playing field is 272 yards. The length of the field is 8 yards less than double the width. What are the dimensions of the playing field?
P = 2w + 2l
w = w
l = 2w - 8
272 = 2w + 2(2w - 8)
272 = 2w + 4w - 16
272 = 6w - 16
288 = 6w
w = 48
remember that: l = 2w - 8
l = 2w - 8 when w = 48
l = 2(48) - 8
l = 96 - 8
l = 88
CHECK: w = 48 and l = 88
P = 2w + 2l
272 = 2(48) + 2(88)
272 = 96 + 176
272 = 272
so: w = 48 and l = 88
7 divided by 1 over 2
Answer: 3.5
Step-by-step explanation: hope it helps :)
Answer: 14
Step-by-step explanation: using cross multiplication, 7 times 2=14 and 1 time 1=1. so it would be 14/1 which can be simplified to 14.
5. Mila is preparing to travel from the United States to Belgium, a member of the European Union, and wants to exchange $80 USD to euros. She finds that the curren exchange rate is €0.85 EUR to $1 USD. If Mila exchanges $80 USD, how much mone will she receive in euros? (Example 4)
Mila will receive 68 EUROS of money after the exchange of 80 US dollar.
What is meant by USD?USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.
What is meant by EURO?Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.
According to the given data in the question,
1 USD =0.85 EURO
80 USD = 0.85*80 EURO
80 USD= 68 EURO
Hence 80USD will be converted to 68 EUROS
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In the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 105 fewer people went to the pool than in the first week. In the third week, 140 more people went to the pool than in the second week. In the fourth week, 315 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease of people who went to the pool is…
PLEASE I NEED A FAST ANSWER
TY‼️
The percent decrease of people who went to the pool is 25%.
Define percentage.Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.
Given
In first week = 1120
In second week
Subtracting,
1120 - 105
1015
In third week,
Sum
1015 + 140
1155
In fourth week
1155 - 315
840
The percentage of fewer persons that visited the pool during these four weeks,
1120 - 840/1120
280/1120
1/4
For percentage,
1/4 × 100%
25%
The percent decrease of people who went to the pool is 25%.
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Dylan has $14.00 to spend at the book fair. He decides to buy two paperbacks for $4.50 each. Then, he sees some sticker books. At most, how much can he spend on sticker books?
A $5.50
B $6.00
C $5.01
D $5.00
Answer:
B because I had learned this at school.
(10)
Write the equation
of the line in
Slope-Intercept
Form.
Answer:
y = -x
Step-by-step explanation:
The slope of this line is -1 (rise/run = -1/1 = -1). We can plug this value into the slope-intercept form equation:
y = mx + b
y = -1x + 0
and simplify.
y = -x
A cashier gets a $100 bonus for working on a holiday plus $11/h. The total holiday salary is given by the function y = 11x + 100. How will the graph change if the bonus is raised to $150 and the hourly rate is lowered to $10/h? Choose the answers that describe these transformations.
HELP PLEASE
(50,650) the graph evolve if the hourly rate is reduced to $10/h and the incentive is increased to $150.
Given that,
For working on a holiday, a cashier is given a $100 bonus in addition to $11/h. The equation y = 11x + 100 yields the entire holiday salary.
We have to find how would the graph evolve if the hourly rate is reduced to $10/h and the incentive is increased to $150.
We know that,
We get,
A cashier is given a $100 bonus in addition to $11/h is y=11x+100
The hourly rate is reduced to $10/h and the incentive is increased to $150 is y=10x+150
Now we subtract those two equation
11x+100-10x-150=0
x-50=0
x=50
We get y as y=10x+150
y=10(50)+150
y=500+150
y=650
Therefore, (50,650) the graph evolve if the hourly rate is reduced to $10/h and the incentive is increased to $150.
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Pls Help Got to do this right now!!!
Which expression is the additive inverse of - 13/6?
A) 13/6
B) 6/13
C) - 6/13
D) - 13/6
WILL MARK BRAINLIEST!!
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
Me. Ramirez writes the equation shown. He asks four students to slice the equation for y 8x-4y=20
The slicing of the equation 8x - 4y = 20 for y is y = 2x - 5
How to slice the equation for yFrom the question, we have the following parameters that can be used in our computation:
8x-4y=20
Rewrite the above equation properly
So, we have the following representation
8x - 4y = 20
Divide through the equation by 4
So, we have the following representation
2x - y = 5
Make y the subject of the equation in the above equation
This gives
y = 2x - 5
Hence, the solution is y = 2x - 5
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The equation x² - 4x + y2-2y = 16 describes a circle. What is the y-coordinate of
the center of the circle?
The y-coordinate of the center of the circle is 1.
What is a coordinate?
In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates. A coordinate system is a framework for specifying how objects are situated in relation to one another within a specified space, such as a specific region of the earth's surface or the entire surface of the planet.
Solution Explained:
After completing the square for x and for y, you should get
(x+2)^2 + (y-1)^2 = 21
Center (x,y) = (-2,1)
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Which function represents the graph below?
The graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6.
Option(B) is the correct answer.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
From the given graph we can conclude that
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
Hence, the graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
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The graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6.
Option(B) is the correct answer.
What is a graph of a function?
A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
From the given graph we can conclude that
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
Hence, the graph represents the function
y = -1 if -6 < x ≤ -4
y = 0 if -4 < x ≤ -2
y = 1 if -2 < x ≤ 0
y = 2 if 0 < x ≤ 2
y = 3 if 2 < x ≤ 4
y = 4 if 4 < x ≤ 6
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. Is x + 2 a factor of the polynomial f(x)=2x^4-3x²-4x+1?
Of(2)=13, so (x + 2) is not a factor.
O f(-2)=29, so (x + 2) is not a factor.
O f(-2)=0,so (x + 2) is a factor.
Of(2)=0,so (x+2) is a factor.
(x + 2) is not a factor of the given polynomial f(x).
What is factor of polynomial?
A polynomial with coefficients in a specific field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
Consider, the given polynomial
f(x)=2x^4-3x²-4x+1
We have to check that (x + 2) is a factor of polynomial or not.
Since, if (x - a) is a factor of polynomial then 'a' is a zero of polynomial.
Here if (x + 2) is a factor of f(x) then f(-2) = 0
Plug x = -2 in f(x).
⇒
f(-2) = 2(-2)^4 - 3(-2)^2 - 4(-2) + 1
= 32 - 12 + 8 + 1
= 20 + 9
f(-2) = 9
f(-2) ≠ 0
Hence, (x + 2) is not a factor of the given polynomial f(x).
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you are to build a rectangular pen with three parallel partitions using 500 feet of fencing. what dimensions will maximize the total area of the pen?
The dimensions required are 125 feet and 50 feet.
The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables.
The total length will be x and the height will be y.
Perimeter = 500 = 2x + 5y
Total Area = A = xy
Solve for y using the equation of perimeter:
5y = 500 - 2x
y = 100 - 2x/5
Put y in the equation of the Area
A = x(100 - 2x/5)
A = -2x²/5 +100x
To find the maximum area, find the derivative:
A' = -4x/5 + 100
To maximise the area, we equate A' to zero.
A' = 0
-4x/5 +100 = 0
∴ x = 125
A' is positive when x < 125 and A' is negative when x >125, therefore meaning that x=125 is a maximum. Since this value is a maximum, the area is maximized when the total length is 125ft.
Put x = 125 in equation of perimeter:
500 = 2(125) + 5y
500 = 250 + 5y
5y = 250
∴ y = 50 ft
Thus, the dimensions required are 125 feet and 50 feet.
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Silvia puts $1000 in an account. She puts 10% of the account each month for a year how much is in her account at the end of the year?
At the end of the year, there will be $2200.in her account
Describe account.A list of debit and credit entries for transactions involving a specific object (such as cash or notes payable), a certain person or business, or both. a financial period's transaction statement that displays the final balance
The most typical kinds of bank accounts are as follows: Checking accounts and Savings accounts
Silvia invests $1,000 in an account over the course of a year, contributing 10% per month.
Because there are 12 months in a year,
She puts 10% of the account each month for a year
that is 10 * 1000/100 = 100 each month she puts in her account.
so for 12months in a year 100*12 = $1200
$1200 in her account over the course of the year she has deposited
Thus, at the end of the year,
Silvia has $1000 + $1200 = $2200 in her account.
At the end of the year, there will be $2200.in her account.
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Really need help on this I do not understand how to do anything
Answer:
y = 6x + 12
Step-by-step explanation:
(2, $24)
(4, $36)
(6, $48)
Find slope (y2-y1) / (x2-x1)
m = ($36 - $24) / (4 - 2)
m = 12 / 2
m = 6
Put into formula y = mx + b
y = 6x + b
Substitute values to find b (the y offset)
$24 = 6(2) + b
$24 = 12 + b
b = $12
y = 6x+12
8. Graph the function
f(x)=-5/4x+6.
Label the point on the graph that is the
solution to f(x) = -4 by writing
solution" next to it. Then, write the
solution below.
Solution
Show your work
The graph for the given function f(x)=-5/4x+6. is obtained.
What is meant by the term function?A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.For the stated question, the function is defined as;
f(x) = -5/4x + 6.
Put x = 0,
f(0) = -5/4(0) + 6.
f(0) = 6
Coordinate (0, 6)
For, the solution of f(x) = -4, put f(x) = -4
-4 = -5/4x + 6
x = 8
Coordinate (8, -4)
Plot the graph using the obtained points for the function.
Thus, the graph for the given function is obtained.
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The diameter of a circle is 15 cm. Find its area to the nearest whole number.
Answer:
177
Step-by-step explanation:
A=3.14r^2
A=3.14(7.5)
A=~177
Pls help with thissss
2tan^2x+tanx=0
Find all angles that satisfy the equation below
The angles that satisfy the given trigonometric equation are 0°, 153.5°, 333.5°
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.
2tan^2∅ + tan∅ = 0
let k = tan∅
so that we have
2k^2 +k = 0
factorizing,
k( 2k + 1) = 0
Therefore,
k = 0, or 2k + 1 = 0
2k = -1
k = -1/2
so k = 0 or k = -1/2
recall that tan∅ = k
which means
tan∅ = 0 or tan∅ = - 1/2
∅ = arc(tan) 0 or arc(tan) -1/2
∅ = 0° 0r -25.6°
but tan ∅ = -1/2 at 90° to 180° and 270° to 360°
∅ = 0°, (180 - 25.55°), (360 - 25.55°)
∅ = 0°, 153.5°, 333.5°
In conclusion the angles that satisfy the equation are 0°, 153.5° and 333.5°
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Given: ∠BCD is right; BC ≅ DC; DF ≅ BF; FA ≅ FE
Triangles A C D and E C B overlap and intersect at point F. Point B of triangle E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C D. Line segments B C and C D are congruent. Line segments B F and F D are congruent. Line segments A F and F E are congruent.
Which relationships in the diagram are true? Select three options.
△ACF ≅ △ECF by HL
ΔCBF ≅ ΔCDF by SSS
ΔBFA ≅ ΔDFE by SAS
ΔCFD ≅ ΔEFD by SSS
ΔCBE ≅ ΔCDA by HL
SAS
The three relationships in the diagram that are true include the following;
B. ΔCBF ≅ ΔCDF by SSS
C. ΔBFA ≅ ΔDFE by SAS
E. ΔCBE ≅ ΔCDA by HL
What is the Right Triangles Similarity Theorem?In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.
Based on the Right Triangles Similarity Theorem, we have the following;
ΔCBF ≅ ΔCDF by side, side, side (SSS).ΔBFA ≅ ΔDFE by side, angle, side (SAS).What is HL?In Mathematics, HL is an abbreviation for hypotenuse leg and it can be defined as a theorem which states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent.
By applying the hypotenuse leg (HL) theorem across right-angle BCD (∠BCD), we have the following;
ΔCBE ≅ ΔCDA
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What is the equation of the blue line
Answer:
y = -1/2 x + 2
Step-by-step explanation:
A (0,2)
B (4,0)
(y-2)/(0-2) = (x-0)/(4-0)
(y-2)/-2 = x/4
(-y+2)/2 = x/4
4 * (-y+2)/2 = x/4 * 4
-2y+4 = x
-2y = x -4
2y = -x + 4
y = - 1/2 x + 4/2
y = -1/2 x + 2
Which of the following statements must be true about the polynomial function f(x)
For a polynomial function statements that need to be true are different end behavior for different degree and different sign of leading coefficient.
What is polynomial function?A function that can be expressed as a polynomial is referred to as a polynomial function.
A polynomial equation's definition can be used to derive the definition.
A polynomial is typically denoted by P (x).
The degree of the variable in P(x) is its maximum power.
The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large.
Whole real numbers make up a polynomial function's domain (R).
For a polynomial function following statements to be true:
Function that has different degrees have different end behaviors because due to different degrees the graph will be different, and their x-intercept will be different.Function that has leading coefficient of different sign have different end behavior because if we take even degree polynomial leading coefficient.To know more about polynomial follow link:
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when the philies play the dodgers, the tickets for three adults and three children are $75. for two adults and four children the total admission cost is $62. find the cost of each adult and each child ticket.
when the philies play the dodgers, the tickets for three adults and three children are $75. for two adults and four children the total admission cost is $62. So, by using equation formula:
the cost of each adult is $19
and each child ticket is $6
What is an equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
The relationship between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
Let us assume,
tickets for adults = a
tickets for children = c
Now,
3a + 3c = $75 ........ (i)
2a + 4c = $62 ......... (ii)
Multiply the equation (i) ×2 and equation (ii) × 3, we get -
6a + 6c = $150 ........ (iii)
6a + 12c = $186 .........(iv)
Now, subtract equation (iv) from (iii) we get -
or, 6c = $36
or, c = $6
Now, putting the value of c in equation (iii) we get -
6a + 6×6 = $150
6a = $114
a = $19
Thus, the cost of each adult is $19
and each child ticket is $6
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If 8% of a liquid is 56 mL, what is the whole
amount?
Please help
Answer:
700 mL
Step-by-step explanation:
You want to know the whole amount if 8% of it is 56 mL.
RelationThe problem statement tells you ...
8% × whole = 56 mL
Divide by the coefficient ...
whole = (56 mL)/(0.08) = 700 mL
The whole amount is 700 mL.
What is the value of g(5)-2g(1)
Answer:
3 grams
Step-by-step explanation:
g(5)-2g(1)
g × 5- 2g(1)
5g - 2g×1
5g - 2g
3g
According to online realtor Zillow a 30 year $200,000, 4. 5%, fixed rate mortgage on your house will currently set your estimated monthly payments at about $1,020 per month. A 15-year fixed rate $200,000 mortgage would drop to 4. 0% with monthly payments of $1,480. Approximately how much would the 15-year fixed rate mortgage save you over the length of both loans?
The 15-year fixed rate mortgage save $ 100,800 more than in the case of the 30-year mortgage.
We must compute the total payments to be made in order to determine the amount saved by getting a 15-year mortgage rather than a 30-year mortgage.
Payments for a 30-year mortgage with a fixed rate of 4.5% are due every month in the amount of $1,020. The total payment is then determined as follows:
Total payment = 1020 * 12* 30 = 367,200
Difference according to lone = 367,200 - 200,000
difference = $167,200
Now, the monthly payments for the 15-year mortgage at a 4% rate will be $1,480.
Then total final payment = 1480*12*20 = $266,400
so in this case, the difference from The loan will be
266,400 - 200,000 = $66,400
Thus, we can draw the conclusion that, when comparing the two loans, the 15-year option will result in savings of $ 100,800 more than the 30-year mortgage.
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write an eqation of the line that passes throught the points (0,-2), (4,-2),
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is y = -2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is given as,
y = mx + c
The line passes through the points (0, -2) and (4, -2).
Now,
Slope = m
m = (-2 + 2) / (4 - 0)
m = 0 / 4
m = 0
Now,
(x, y) = (0, -2)
y = mx + c
-2 = 0 x 0 + c
c = -2
Now,
m = 0 and c = -2
y = 0x -2
y = -2
Thus,
The equation of the line is y = -2.
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Find compound interest on 15,625 at 4% for 3 years.
Help! With steps
Answer:
P=15,625
Rate=4%
Time=3 years
CI=P(1+R/100)^T
=15,625(1+4/100)^3
=15,625*1.124864
=17576 Ans
Step-by-step explanation:
hope it helps
The spinner shown has eight congruent sections the spinner is spun 144 times what is a reasonable prediction for the spinner will land on an even number.
Prediction for the spinner will land on an even number is 54 times.
What do you mean by permutation and combination?
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.
There are 3 even numbers out of A total of 8 numbers.
Each spin would have a 3/8 chance of landing in an even number.
Multiply the chance of landing on even by number of spins:
144 x 3/8 = 432/8 = 54
The answer would be 54 times.
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Can 2/3 turn into an improper fraction
Answer:no
Step-by-step explanation:
Answer: no
Step-by-step explanation: cuz u need a number thats bigger such as the numerator is bigger than the denominator