Answers
The distance of the intersection of 3 perpendicular bisectors of a triangle to the 3 vertices are equal.
In other words, HF = HE = HG.
Therefore, we see that 3 isosceles triangles are identified : HFE, HFG, HGF.
We're given HF = 15, therefore HE = 15.
Since HJ is the perpendicular bisector of line EG, JE = JG.
Therefore, JE = 12.
Now, we use the Pythagorean theorem in the right triangle HJE :
[tex]HE^{2} = HJ^{2} + JE^{2} - > HJ = \sqrt{15^{2} - 12^{2} } =\sqrt{81} = 9.[/tex]
Related Questions
Leah keeps ducks and buffalo in their farm and there are 35 animals with a total if 110 legs. How many ducks and buffalo are there?
Answers
GIVEN :
35 animals110 legsTO FIND :
the number of ducks and buffalo are there.OPTIONS :
(A) 20 ducks, 15 buffalo
(B) 15 ducks, 20 buffalo
CASE (i) - 20 ducks, 15 buffalo
= 20·2 + 15·4
= 40 + 60
= 100
CASE (ii) - 15 ducks, 20 buffalo
= 15·2 + 20·4
= 30 + 80
= 110
FINAL ANSWER :
Therefore, the number of ducks are 15 and 20 buffalo.
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Ahlee i riding her bike to the beach. If the beach i 17 mile from her home, and he ha already travelled 3/5 of the way, how much farther doe he have to cycle?
Answers
The distance yet to be covered by Ashlee is 6.8 miles.
Ashlee is riding her bike to the beach. The beach is 17 miles from her home. She has already travelled 3/5 of the total distance. We need to find out how much farther she has to cycle.
Let the distance left to be covered by Ashlee be represented by the variable "D". The distance already covered by Ashlee on her cycle is calculated below.
d = (3/5)×17
d = 10.2
So she has already covered a distance of 10.2 miles. The distance yet to be covered is the difference between the total distance and the distance covered.
D = 17 - 10.2
D = 6.8
Hence, the distance yet to be covered by Ashlee is 6.8 miles.
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in abc, m/_ A is thirteen less than m/_ C and m/_b is eleven less than 4 times m/_c find the measure of each angle
Answers
After solving the equation made for a triangle, the value of angle A will be equal to 21.
What is a Triangle?Simple polygons with three sides and three internal corners make up triangles. Being one of the fundamental geometric shapes, it is symbolized by the symbol and consists of three connected vertices.
As per the given data in the question,
Angle A is 13 less than angle C.
Let angle C is x then angle A is equal to (x - 13) and,
Angle B is 11 less than 4 times of angle C then,
B = 4x - 11
Add all the angles and equate them with 180.
(x -13) + (4x - 11 ) + x = 180
6x -24 = 180
6x = 180 + 24
x = 204/6
x = 34.
Substitute x = 34 in angle A
A = (x - 13)
A = 21.
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Write the first four terms of two different arithmetic sequences with a common difference of −3. The first sequence starts with −12 and the second sequence starts with 12.
Answers
Answer:
Step-by-step explanation:
The first arithmetic sequence would be -12, -15, -18, -21. The second sequence would be 12, 9, 6, 3.
Find the value of c so that the polynomial p(x) s divisible by (x+2).[tex]p(x)=4x^3+cx^2+x+2\pi[/tex]
Answers
If a polynomial is divisible by another then that will be a factor of the polynomial. The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8.
What is an algebraic factor?An algebraic factor is the multiplication of two algebraic terms.
That term could be in the form of summation multiplication or in subtraction.
The root of the quadratic equation formed by the algebraic factor is always real.
As per the given polynomial,
p(x) = 4x³ + cx² + x + 2
Divide 4x³ + cx² + x + 2 by (x+2)
First quotient = 4x²
Then, (4x³ + cx² )- (4x³ + 8x²)
Now in order to become it zero c must be the same as 8.
c = 8
Then, the second quotient = 1
(x + 2) - (x + 2) = 0
So, 4x³ + cx² + x + 2 = (x + 2)(4x² + 1)
Hence "The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8".
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find the product and represent in the simplest form of 12/17 × 3/8
Answers
Answer:
9/34
Step-by-step explanation:
I find when multiplying fractions, its easier to separate them into the numerator and denominator.
So we have 12 x 3, and 17 x 8
12 x 3 = 36
17 x 8 = 136
So we have 36/136
Simplified, that is 9/34
Use synthetic division to divide x^3+8x^2+11x-20 by (x+4). Explain steps
Answers
Answer:
X²+4X-5 without a reminder
the product of three consecutive positive integers is times their sum. what is the sum of their squares?
Answers
77 is the sum of their integers squares .
What in math is an integer?
A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.Three types of integers exist: 0 (zero), positive integers (natural numbers), and negative integers.Let the numbers be ( n - 1 ), n , ( n + 1 )
according to question
( n - 1 ) (n) ( n + 1 ) = 8( n + n - 1 + n + 1 )
n( n² - 1 ) = 8(3n)
( n² - 1 ) = 24
n²= 25
n = 5
since n is positive integer n = 5
thus required numbers are 4,5,6
4² + 5² + 6² = 77
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Determine the coordinates of the preimage given the image below and the composition of a rotation 180 about the origin and a translation 3
units up.
Answers
The coordinates of the preimage given in the image below and the composition of a rotation 180 about the origin and a translation 3 units up are: (2, -3), (3, 1), and (-5, 0).
What is a rotation?In Geometry, the rotation of a geometric figure 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
From the graph of the image of triangle A'B'C', we have the following coordinates and they would be reversed to obtain the coordinate of triangle ABC before a translation:
(-x, -y) → (x, y)
Points at A' = (-2, 5) → Points at A = (2, -5)
Points at B' = (-3, 1) → Points at B = (3, -1)
Points at C' = (5, 2) → Points at C = (-5, -2)
Next, we would apply a translation of 3 units up:
Points at A = (2, -5) → (2, -5 + 2) = (2, -3)
Points at B = (3, -1) → (3, -1 + 2) = (3, 1)
Points at C = (-5, -2) → (-5, -2 + 2) = (-5, 0)
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Segment RS is reflected over the line y = x and then translated by (x+3, y + 4). The resulting segment
RS" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
Answers
The original coordinates are R= (-6,-6) and S = (-4,0)
What is translation?
Translation in mathematics is a property in which we shift each coordinate on a line by a constant value.
We are given that we originally had a segment RS which is reflected over the line y = x and then translated by (x+3, y+4) after this the segment we get the coordinates are R'' (-1,4) and S( -3,-2)
We are asked to find the coordinates of R and S
To find the coordinates we first reverse the process we subtract 3 from both x coordinate and 4 from both y coordinate
Hence we get,
R' = (-1,4)-(3,4)
R' = (-4,0)
And
S' = (-3,-2)-(3,4)
S' = (-6,-6)
Now to find the original coordinates we reverse the coordinates
Hence we get,
R= (-6,-6) and S = (-4,0)
Therefore the coordinates are R= (-6,-6) and S = (-4,0)
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solve the question
4+4=
8+8=
Answers
Answer:1. 8
2. 16
Step-by-step explanation:
4+4=8
8+8=16
a homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
write an expression to find the area of the fenced region.
Answers
The required expression for the fenced region is lw = 650.
Given that,
A homeowner wants to fence in a rectangular space in her yard along one side of her house for her dogs. the total area she can fence in is 650 square feet.
What is a rectangle?
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
Here,
Let the length of the area be l and the width of the area be w,
The total area she can fence in is 650 square feet.
lw = 650
Thus, the required expression for the fenced region is lw = 650.
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after euclid high school's last basketball game, it was determined that 1/4 of the team's points were scored by alexa and 2/7 were scored by brittany. chelsea scored 15 points. none of the other 7 team members scored more than 2 points. what was the total number of points scored by the other 7 team members?
Answers
The total number of points scored by the other 7 team members in Euclid high school's last basketball game is 11.
What is defined as the term two variable equation?If an equation is written in the form ax + by + c=0, where a, b, and c are real integers as well as the coefficients of x and y, i.e., a and b, respectively, really aren't equal to zero, then it is said to be a linear function in two variables.For the given question.
Let 't' be the total points scored.
Alexa = 1/4 t.
Brittany = 2/7 t
Chelsea = 15
Let 'x' be the points scored by remaining 7 team.
Thus, the two variable equation becomes.
1/4 t + 2/7 t + 15 + x = t .....eq 1
Where, x ≤ 14 ( for 7 terams)
Simplifying eq 1.
15 + x = 13/ 28 t
28x + 28 = 13 t
Now, t must be divisible by 28.
Let t = 28 u, u ≥ 0 and divisible by 28.
Thus,
x + 15 = 13u.
Then, u = 2( t = 56) has been the only candidates for which x = 11.
Thus, the total number of points scored by the other 7 team members is 11.
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Allie is playing basketball. She takes a shot 17 ft away from the basket. When the ball is 2 ft away from her, it is at a height of 10 ft above the floor. The ball reaches its highest height of 17 ft above the
floor when it is 9 feet away from her.
a. Find the value of a.
b. If the hoop is 10 ft high, how close would Allie have to be in order to make the basket?
a. The value of a is
(Simplify your answer.)
Answers
According to the vertex form of the parabola,
a) The value of a is -1/7.
b) And If the hoop is 10 ft high, the distance close to Allie have to be in order to make the basket should be 16 feet.
Vertex form of the parabola
The vertex form of the parabola can be given as,
y = a(x - h)² + k
Where
h,k are the coordinates of the vertex.
Given,
Allie is playing basketball. She takes a shot 17 ft away from the basket. When the ball is 2 ft away from her, it is at a height of 10 ft above the floor. The ball reaches its highest height of 17 ft above the floor when it is 9 feet away from her.
Here we need to find the following:
a. The value of a
b. If the hoop is 10 ft high, how close would Allie have to be in order to make the basket?
We know that, Allie takes a shot of 17 ft away and at the distance of 2 feet the ball achieve the height of 10 feet from the ground.
And the greatest height achieved by the ball is 17 ft above the floor.
Then the value of a is calculated by using the point that is obtained thorough the given details is,
=> (2, 10)
And the vertex of the equation are (9, 17)
When we apply these on the vertex form, then we get,
10 = a(2 - 9)² + 17
-7 = a(-7)²
49a = -7
a = -1/7
Therefore, the value of a is 1/7.
Now we have to find if the hoop is 10 ft high, The distance close to Allie have to be in order to make the basket-
Here the value of y is 10 and x is not known.
Now, we have to put these values on the equation then we get,
=> 10 = -1/7 (x - 9)² + 17
=> -7 = -1/7 (x -9)²
=> 49 = (x - 9)²
=>√49 = x - 9
=> x = 16
Therefore, if the hoop is 10 ft high, the distance close to Allie have to be in order to make the basket should be 16 feet.
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1. [-/1 Points]
DETAILS
Find the x- and y-intercepts.
7x - 6y = 1
x-intercept (x, y) = (
y-intercept (x, y) = (
(x, y) = (
Answers
multiply x times y divide by 6 on both sides and you got your answer
x-12.5=95 ''solve'' ..................
Answers
Using the simplification, the solution of the given expression for x is 107.5.
In the given question we have to solve the given expression.
The given expression is x-12.5=95.
Now solving the expression.
x-12.5=95
To solve the expression we add 12.5 on both side
x-12.5+12.5=95+12.5
x=107.5
The solution of the given expression for x is 107.5.
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which number line shows -4, -1, 1, and 2 correctly plotted.
Answers
A number line which shows -4, -1, 1, and 2 correctly plotted on a graph is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical values -4 and -1 would be plotted on the left hand side of zero (0) while the numerical values 1 and 2 would be plotted on the right hand side of zero (0) using a number line.
In this scenario, a number line would be used for the comparison of two or more numbers such as -4, -1, 1, and 2, and this is plotted in the graph shown in the image attached below.
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A local candy shop sells boxes of chocolate for $3.75 each. If a customer purchases six or more boxes, the cost is only $3.25 per box, plus the customer has an additional $5 fee per order. C(x) represents the total cost and x represents the number of boxes, which can be modeled by the function below.
A piecewise function c of x in two pieces. The function is defined by part 1, which is 3 point 75 times x for x greater than 6, and part 2, which is 3 point 25 times x plus 5 for x is greater than or equal to 6.
Predict the cost of an order with 6 boxes.
$14.50
$22.50
$24.50
$27.50
Answers
Answer:
$24.50
Step-by-step explanation:
In order to predict the cost of an order with 6 boxes, x has to be equal to 6.
So we have to use the function 3.25x + 5 for [tex]x\geq 6[/tex].
Then, plug in 6 for x and solve.
3.25(6) + 5 = 19.50 + 5 = 24.50
The cost of hiring a car is $40 plus a charge of $30 per day. How much will it cost to hire the car for 2 days?
Answers
Step-by-step explanation:
we have a basic fee of $40 just for renting the car.
and we rent it for 2 days for $30 per day.
so, this costs
40 × 2×30 = 40 + 60 = $100
A function is shown. F(x) = -7/8x + 11
What's the x-intercept?
What's the y-intercept?
Answers
Answer:
x-intercept (88/7,0), y-intercept (0,11)
Answers:
x intercept = 88/7
y intercept = 11
===============================================
Explanation:
To find the y intercept, we replace f(x) with 0 and solve for x.
f(x) = (-7/8)x + 11
0 = (-7/8)x + 11
(7/8)x = 11
7x = 8*11
7x = 88
x = 88/7 is the x intercept
It is located at (x,y) = (88/7, 0)
The x intercept always occurs when y = 0.
88/7 = 12.5714 approximately, but I would stick to the fraction form since it's most exact.
-------------------------------
The y intercept always occurs when x = 0.
f(x) = (-7/8)x + 11
f(0) = (-7/8)*0 + 11
f(0) = 0 + 11
f(0) = 11 is the y intercept
It is located at (0,11)
The y intercept is much easier to find since we just need to read off the last value of the function (aka the constant value).
The first six numbers of a sequence are shown below. Which function can be used
to find the nth term?
-7, -1, 5, 11, 17, ...
Please Help Asap! Tysm if u do!
Answers
Answer:
41
Step-by-step explanation:
the pattern is +6 so the next few would be 23, 29, 35, 41, 47...
the ninth term would be 41
thanks to anyone who answers!
The sum of three consecutive numbers is 84. What is the largest of these numbers?
a 26
b 27
c 28
d 29
Answers
amy gets 7 our of 8 math problems correct, mark gets 7 out of 11 problems correct ,and carol gets 7 out of 9 math problems corect. order these fractions from least to Greatest
Answers
Answer:
[tex]\frac{7}{11}[/tex], [tex]\frac{7}{9}[/tex], [tex]\frac{7}{8}[/tex]
Hope this helps!
Step-by-step explanation:
One way to find this out is by just plain dividing the numbers, 7 ÷ 11 is 0.636363..., 7 ÷ 9 is 0.7777777..., and 7 ÷ 8 is 0.875. 7/11 is the smallest of all of them, then 7/9, and then 7/8.
The graph below illustrates the decay of a radioactive substance over t days.
Use the graph to estimate the average decay rate from t = 5 to t = 15 Note: Your answer will be negative.
Answers
The estimate of the average decay rate of change is -0.6
How to estimate the average decay rate of the function?From the question, we have the graph and the interval is given as
t = 5 to 15
This can also be represented and expressed as
(a, b) = [5, 15]
From the attached graph, we have
f(5) = 12
f(15) = 6
The estimate of the average decay rate of change is calculated as
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(15) - f(5)]/[15 - 5]
So, we have
Rate = [6 - 12]/[15 - 5]
Evaluate
Rate = -0.6
Hence, the average decay rate of change is -0.6
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Antoinette spends 3 hours reading each day.
What is the total amount of time (in hours) that
Antoinette spent reading after 6 days?
Answers
Answer:
The answer is 18 hours
Step-by-step explanation:
3 hours x 6 days
3x6 = 18
Kayden just accepted a job at a new company where he will make an annual salary of
$48000. Kayden was told that for each year he stays with the company, he will be
given a salary raise of $4500. How much would Kayden make as a salary after 4 years
working for the company? What would be his salary after t years?
Salary after 4 years:
Salary after t years:
Answers
The salary of Kayden after 4 years will be $ 221,952.00
The annual salary is $48000
Salary rise is $4500
The rate of the this salary can be found out by [tex]\frac{48,000- 4500}{48000}[/tex]
= [tex]\frac{43,500}{48,000}[/tex] × 100
= 90.6 %
The time interval is 4 years
thus the prinicipal amount is given as $48000.
thus simple interest is P × R × T/ 100
which when calculated will give us
simple interest = $221,952.00
$221,952.00 is the total amount accrued from simple interest on a principal of $48,000.00 at a rate of 90.6% per year for 4 years. This includes both principal and interest.
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20 PIONTS
Suppose you have a $6-off coupon at a fabric store. You buy fabric that costs $9.50 per yard. Write an equation that models the total amount of money y you pay if you buy x yards of fabric. What is the graph of the equation?
Answers
The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6
Given,
You have a coupon for a $6 discount at a fabric shop. You purchase fabric for $9.50 per yard.
We have to find an equation that models the total amount of money y you pay if you buy x yards of fabric.
Here,
The equation for the situation be like;
y = 9.50x - 6
Where,
y is the total amount paid
x is the number of yards of fabric you bought
That is,
The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6
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A triangle with two sides that measure 5 cm and
8 cm with an included angle of 39º.
Answers
Answer:
the other 2 sides equal 70.5 ...but I am not for sure because you did not give me enough information (like a picture)
1) suppose the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane. how many possible states are there? how many paths are there to the goal? provide assumptions for your answer
Answers
There will be infinite number of states and paths when the state space is (x,y) as the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane.
What is state space?The collection of every possible setup for a system is its state space. It is a common abstraction in the study of artificial intelligence and game theory because it can be used to reason about the behavior of a specific system. A state space is typically introduced into a system description without being given any thought to its precise physical meaning. However, it is well known that choosing an appropriate state space representation makes it simpler for us to comprehend or control a system's property.
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. Which is the better investment?
a. $1,200 at 9% simple interest for 2 years
b. $1,200 at 8% compound interest for 2 years
Answers
Answer:
200 at 9% simple interest for 2 years
Answer:
a
Step-by-step explanation:
Hope it helps and have a nice day!!!! :)