please help
1. Draw a triangle.
2. Plot a midsegment of the triangle in the image with number 11. Include work to verify that the segment drawn is the midsegment. Make sure to include the midsegment in the image.
Answers
1. Triangle ABC with the vertices, A(0, 2), B(6, 4), and C(4, -2) is drawn and attached below.
2. The midsegment is EF. This is verified using the triangle midsegment theorem which states that EF = 1/2(AC).
What is the Midsegment of a Triangle?The midsegment of a triangle is the line segment that joins the midpoints of two sides of a triangle together. Every triangle typically has three midsegments.
According to the triangle midsegment theorem, the length of the midsegment is half the length of the third side of the triangle that it is parallel to.
What is the Midpoint of a Line?The midpoint of a line is its middle, which can be calculate using the formula:
M(x, y) = [tex](\frac{x_2 - x_1}{2}, \frac{y_2 - y_1}{2})[/tex].
1. The coordinate of the three vertices that is used to draw a triangle are:
A(0, 2), B(6, 4), and C(4, -2).
The triangle is in the attachment below.
2. To plot the midsegment of the triangle, determine the midpoints of AB and BC, then plot the coordinate where both midpoints would be joined.
Midpoint of AB = (x, y) = (0+6)/2, (2+4)/2
= (6/2, 6/2)
= (3, 3) (let this be point E)
Midpoint of AB = (x, y) = (4+6)/2, (−2+4)/2
F = (5, 1)
The midsegment will have the endpoints, E(3, 3) and F(5, 1).
To verify the segment draw is the midsegment according to the triangle midsegment theorem, find the length of the midsegment, EF, and the length of the third side, AC using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
EF = √[(5−3)² + (1−3)²]
EF = √8 units
AC = √[(4−0)² + (−2−2)²]
AC = √32 units
Based on the triangle midsegment theorem:
EF = 1/2(AC)
Plug in the values:
√8 = 1/2(√32)
√8 = 1/2(4√2)
√8 = 2√2
2√2 = 2√2 (true)
This means that EF is a midsegment of triangle ABC.
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Related Questions
27
Question
A hula hoop has a diameter of 44 inches. What is the circumference of the hula hoop? Use 3.14 for pi
Answers
Answer:
138.16 inches
Step-by-step explanation:
C=Circumference. r=radius. d=diameter
C=2πr
C=2π(d/2) ==> a radius is half of a diameter
C=2(d/2)π
C=dπ ==> simplify
C=44π
C=44*3.14
C=138.16 inches
Last Sunday 1575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under. Find the number of adults, teenagers, and children that visited the park
Answers
The number of adults is 882 adults.
The number of teenagers is 252 teenagers.
The number of children is 441 children.
How to calculate the number of people?From the information, 1575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under.
The number of adults will be:
= 56% × 1575.
= 882 adults
The number of teenagers will be:
= 16% × 1575
= 252 teenager
The number of children will be:
= 28% × 1575
= 441 children
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Answer:
Number of adults
56/100×1575=882
Number of teenagers
16/100×1575=252
Number of children
28/100×1575=441
Find the AGI and taxable income.
O $19,007 and $7,822
O $19,007 and $6,362
O $20,222 and $7,822
$20,222 and $6,362
Gross income
Adjustments
1 Exemption
Deduction
$20,467
$245
$12,400
$1460
Answers
Answer:
406$
Step-by-step explanation:
Answer:
$20,222 and $6,362
Step-by-step explanation:
I took the test
A table is on sale for 100.80 , which is 76% less than the regular price. What is the regular price?
Answers
The regular price of the table based on the information is $177.41.
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Let the regular price be x.
Since the table is on sale for 100.80, which is 76% less than the regular price, that will be illustrated as:
x = 100.80 × (100% + 76%)
x = 100.80 × 1.76
x = 177.408
The value is $177.41.
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ACME insurance company estimates that the probability of the owners' of a house a
worth between $120,000 to $170,000 making a claim for $5000 is 0.09, and that
the probability of the house and contents being totally destroyed is 0.0040. Should
that tragedy happen, the company will have to pay $150,000. The company charges
$1300 for the insurance policy.
What is the expected value of this policy to the insurance company?
Round your answer to two decimal places.
Answers
Answer: -$250.00
Step-by-step explanation:
[tex][(5000)(0.09)+150000(0.0040)]-1300 =-\$250[/tex]
The expected value of the policy to the insurance company is -$ 250
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the value of probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 = 0.09
Let the value of probability of the house and contents being totally destroyed = 0.0040
Now , the tragedy happens and the company pays = $ 150,000
The amount the insurance company charges = $ 1300
So , the equation will be
The expected value of this policy to the insurance company =
( probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 x $ 5000 ) + ( the amount company pays x 0.0040) - amount the insurance company charges
So , the equation will be
The expected value of this policy to the insurance company =
( ( 0.09 x 5000 ) + ( 150000 x 0.0040 ) - 1300 )
The expected value of this policy to the insurance company =
( ( $ 450 + $ 600 - $ 1300 )
The expected value of this policy to the insurance company = - $ 250
Hence , The expected value of policy to the insurance company is -$ 250
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The height of a building is proportional to the number of floors. The figure shows the height of a building with 8 floors. Complete parts a and b.
Answers
a. The ratio of the height of the building to the number of floor is 14:1
b. the unit rate is 14ft per floor and this means that each floor is 14ft high.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.
if h is the height of the building and n is the number of floor.
Therefore h:n= h/n
h:n = 112/8
divide through by 8
h:n= 14/1=14:1
the unit rate is therefore 14feet per floor and this means that one floor has a height of 14 feet.
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Part A: A bakery sells specialty pumpkin pies during the month of October. One pumpkin pie contains 187.64 grams of sugar. The bakery wants each slice of pie to contain less than 22 grams of sugar. What is the minimum number of slices the bakery will have to cut the pie into in order for each slice to contain less than 22 grams of sugar ? Show your work. Part B: If the bakery cuts the pie into that minimum number of slices, how much sugar, in grams, will each slice of pumpkin pie contain? Round your answer to the nearest hundredth.
Answers
Answer:
9 slices20.85 gStep-by-step explanation:
You want the minimum number of pie slices and the amount of sugar in each such that the sugar in each slice is less than 22 grams when the whole pie has 187.64 grams of sugar.
A: SlicesThe sugar in each of n slices is 1/n times the sugar in the whole pie. You want ...
(187.64 g)/n < 22 g
Multiply by n/(22 g) to get
n > 187.64/22
n > 8.53
The smallest whole number that satisfies this inequality is n = 9.
The minimum number of pie slices is 9.
B: SugarWhen the sugar in the pie is divided into 9 equal parts, each part is ...
(187.64 g)/(9 slices) = 20.85 g/slice
Each slice of pumpkin pie will contain about 20.85 grams of sugar.
Answer:
Step-by-step explanation:
the answer is 9
please help if u can
Game Station 2: Amazing Race- Each team has to match 9 of the 20 banners with the word “Hello” in different languages with the 9 countries that speak that language
9/20
A. Determine the number of ways of selecting and matching nine banners with a country.
B. Determine the number of ways of selecting nine banners without having to match them with a
Answers
the number of ways of selecting and matching nine banners with a country is 36.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
Given, 9 of the 20 banners with the word “Hello” in different languages with the 9 countries
Toatl ways for arranging the 9 banners will be 9C2
And as the matching nine banner with the country is 9/20
So the number of ways of selecting is 9c2 = 36.
Hence the number of ways to select and matching the banner is 36.
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Working simultaneously, six fudge machines complete a big order in 36 hours. All the machines at the fudge factory work at the same pace. How many hours would it take to complete the order with twice the number of working machines?
Answers
Answer: 18 hours
Step-by-step explanation: There are 6 working machines at first, and it takes 36 hours to complete this.
If there are double the machines, it takes half the time to complete the order, because double the amount of fudgemaking is being done per hour.
36 divided by 2 = 18 hours with twice the machines.
Are the linear expressions equivalent?
Drag the choices to the boxes to correctly complete the table.
3x-2(2,3x+2.5)=-1.6x-5
5-3(-1.6x-2.1)=4.8x-1.3
Answers
Comparing the linear expressions it shows that
3x - 2(2,3x + 2.5) = -1.6x - 5 - equivalent
5 - 3(-1.6x - 2.1) = 4.8x - 1.3 - not equivalent
How to check if the expressions are equivalentInformation given in the question include
3x - 2(2,3x + 2.5) = -1.6x - 5
5 - 3(-1.6x - 2.1) = 4.8x - 1.3
The equations are equivalent if the values on the left hand side of the equation is equal to the values on the right hand side of the equation
3x - 2(2,3x + 2.5) = -1.6x - 5
expending gives
3x - 4.6x - 5 = -1.6x - 5
-1.6x - 5 = -1.6x - 5
The expression above is equivalent
5 - 3(-1.6x - 2.1) = 4.8x - 1.3
expending gives
5 + 4.8x + 6.3 = 4.8x - 1.3
4.8x + 11.3 = 4.8x - 1.3
The expression above is not equivalent
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A relation that shows that one expression equals another expression is a(n) __________. equation function rate inequality
Answers
Answer:
Equation.
Step-by-step explanation:
The term equation state that the two expression are equal that means left hand side of the expression and right hand side of expression are equal.
Whereas if the two equation are not equal then it is known as inequality.
Thus, the given statement is correctly filled with equation.
Use the give information to find the value of x.
Answers
30 = x + 25
subtract 25 from both sides
x = 5
hope this helps !
Select the correct answer. Which graph shows the solution region of this system of inequalities?
y ≥ 2(1.3)^x
y_<-x^2+4x+5
Answers
Answer: The solution set of the system of inequalities is the region above the dashed line (y=-2x-2) and below the solid line (y=x+4).
A triangle is shown. The table names different transformations that can be applied to the triangle.
Drag a graph to each spot in the table to show where the triangle moves after each transformation is applied.
Answers
The answer will be (1,3), (3,2), and (4,5), reflation along the x-axis and so on when we did the transformation.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
After reflation along the x-axis, the triangle's vertices are (1,3), (3,2), and (4,5).
Upon reflation along the y-axis, the triangle's vertices are (-1,-3), (-3,-2), and (-4,-5).
The triangle's vertices are (-3,1), (-2,3), and (-2,4) following reflation across y=x (-5,4).
Hence the transformation have done and all the points have to mentioned above.
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need help ASAP please
Answers
B.) It is a flat and closed shape. A rectangle is a quadrilateral.
The opposite sides are parallel and equal to each other.
Answer:
Step-by-step explanation:
know it isnt the best but here gives
Please help! Correctly match the descriptions with the given transformation.
f(x) + 5.5
5.5 f(x)
f(x + 5.5)
Answers
The transformations are:
f(x) + 5.5 → translation of 5.5 units upwards.5.5*f(x) → vertical dilation of scale factor 5.5f(x + 5.5) → translation of 5.5 units to the left.How to define each of the transformations?The transformations that appear here are:
Vertical dilation:
For a function f(x), a vertical dilation of scale factor k is written as:
g(x) = k*f(x)
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.
so:
f(x) + 5.5 is a translation of 5.5 units upwards.
5.5*f(x) is a vertical dilation of scale factor 5.5
f(x + 5.5) is a translation of 5.5 units to the left.
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The population of a country was 64 million in 1993 and the continuous exponential growth rate was
estimated at 2.7% per year. Assuming that the population of the country continues to follow an
exponential growth model, find the projected population in 2008. Round your answer to 1 decimal
place.
The approximate population in 2008 is
million people
Answers
Answer: 104.1
Step-by-step explanation:
If [tex]P(t)[/tex] represents the initial population in millions. [tex]t[/tex] years after 1990, then [tex]P(t)=64e^{0.027t}[/tex].
2008 is 18 years after 1990, so [tex]P(18)=64e^{0.027 \cdot 18} \approx 104.1[/tex]
The exponential growth of population in 2008 is 95.4 million
What is exponential growth factor?
The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the population of the country in 1993 be = 64 million
The exponential growth rate r = 2.7 %
So , the population of the country in 2008 is calculated by
The time t in years = 2008 - 1993
= 15 years
So , the equation for exponential growth rate is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
And substituting the values in the equation , we get\
x ( 15 ) = 64 × ( 1 + 0.027 )¹⁵
x ( 15 ) = 64 × ( 1.027 )¹⁵
x ( 15 ) = 64 × 1.49127
x ( 15 ) = 95.4413
So , the value of x ( 15 ) = 95.4 million
Hence , The exponential growth of population in 2008 is 95.4 million
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Solve.
x-(-2 7/8)=-1/2
What is the solution to the equation?
Enter your answer as a simplified mixed number in the box.
X =
Answers
Answer:1/2
Step-by-step explanation:
Answer:
x = 3 3/8
Step-by-step explanation:
I believe you would have to solve it with the reverse operation. If
x - (-2 7/8) = -1/2, than x has to be -1/2 more than -2 7/8. Because they are both negative numbers, the answer will be positive.
-2 7/8 + -1/2 = 3 3/8 x = 3 3/8
3 3/8 - (-2 7/8) = -1/2
Feel free to correct me. I hope you do well.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answers
2. Vertical
3. Alternating exterior
4. Corresponding
5. Supplementary
−2−(−10) in a addtition expression
Answers
The value of -2−(−10) in a addtition expression is 8.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, -2 - (-10) will be:
= -2 -(-10)
= -2 + 10
= 8
The value is 8.
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i need help in this question plsss
Answers
Answer:
a) (-9)/10
Step-by-step explanation:
Given number,
→ -(9/10)
Now the equivalent number is,
→ -(9/10)
→ -9/10
→ (-9)/10
Hence, the answer is (-9)/10.
008
Clear all
Find the quotient.
12a² - 3
ба - 3
Enter the correct answer.
ADO
?
DONE
Answers
Answer:
6a - 3
Step-by-step explanation:
Dividend: A number/expression that is divided by the divisor.
Divisor: The number/expression that divides the dividend.
Quotient: The result obtained by the division.
Remainder: The number/expression left behind.
Long division method
Divide the first term of the dividend by the first term of the divisor, and put that in the answer.Multiply the divisor by that answer, put that below the dividend.Subtract to create a new dividend.Repeat.The solution is the quotient plus the remainder divided by the divisor.
Given dividend:
12a² - 3Given divisor:
6a - 3[tex]\large \begin{array}{r}2a+1\phantom{)}\\6a-3{\overline{\smash{\big)}\,12a^2\phantom{))..)))}-3\phantom{)}}}\\{-~\phantom{(}\underline{(12a^2-6a)\phantom{)))))}}\\6a-3\phantom{)}\\-~\phantom{()}\underline{(6a-3)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]
Therefore, the quotient is 6a - 3.
!!PLEASE HURRY!!
Find the missing length indicated.
Answers
Answer:
Step-by-step explanation:
17
Explanation step - by -step
15/12 = x/28
Rewrite equation
x/28 = 15/12
Multiply both sides of equation 28
28(x/28) = 28(15/12)
Cancel common factor
x = 28(15/12)
x = 28 ( 5/4)
x = 7•5
x = 35
Dan’s dog-walking job pays $15 per hour. His job as a car-wash attendant pays $400 each week. Dan wants to know how many hours he needs to spend walking dogs to earn more than $520 in a week. Which three inequalities can model this situation? Select all the correct answers. x(15 + 400) > 520 520 < 400 + 15x 15x > 120 15x + 520 > 400 520 < 15x + 400x 15x + 400 > 520
Answers
The three inequalities will be :
1) 400 + 15x > 520
2) 520 < 400 + 15x
3) 15x > 120
Given,
In the question:
Dan’s dog-walking job pays $15 per hour.
His job as a car-wash attendant pays $400 each week.
Walking dogs to earn more than $520 in a week.
To find the which three inequalities can model this situation?
Now, According to the question:
Car wash = $400 per week
Dog - walking = $15per hour
To earn more than $520 in a week .
Let the hour be = x hour
Based on the given conditions:
Hence, The three inequalities will be :
1) 400 + 15x > 520
2) 520 < 400 + 15x
3) 15x > 120.
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find the slope. help please
Answers
Answer:
-2
Step-by-step explanation:
Look at the bottom right point. To get to the point above it only moving vertical and horizontally, you would move 2 units up (or vertically) and one unit left (or horizontally).
The slope is negative. Imagine a person starting on the very left side of the line and he starts walking. As he walks on the line, he is going down hill. That tells us that the slope is negative.
A ( x ) = 4 − ( x + 3 )^5
Answers
The solution for A(3) in the function when the function A(x) = 4 − (x + 3)⁵ is -772
How to determine the solution for A(x) in the function?From the question, we have the following equation that can be used in our computation:
A ( x ) = 4 − ( x + 3 )^5
To make the equation legible, we need to rewrite it
So, we have the following representation
A(x) = 4 − (x + 3)⁵
Also from the question, we have
A(3)
This means that the value of x is 3, and we calculate A(x) when x = 3
Substitute the known values in the above equation, so, we have the following representation
A(3) = 4 − (x + 3)⁵
So, we have the following equation
A(3) = 4 − (3 + 3)⁵
There are constants to add or subtract to both sides of the equation
However, there is no factor to multiply or divide from both sides of the equation
So, we have the following representation
A(3) = 4 − (6)⁵
Solving further, we have
A(3) = 4 − 7776
Evaluate the difference
A(3) = −7772
Hence, the solution is −7772
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Possible question
Given A ( x ) = 4 − ( x + 3 )^5, find A(3).
Help please answer the question.
Answers
The graph of the function g(x) is described as 5 units translation down.
What is a graph?A visual representation or diagram that represents data or values is known as a graph.
The function equations are provided as
f(x) = 1/3x+1
f(x) - 1 = 1/3x
g(x) = 1/3(6x) + 1
g(x) = (1/3x)6 + 1
In the equation g(x) = (1/3x), replace f(x) with f(x) - 1 = 1/3x.
6 + 1
Thus, we have
g(x) = (f(x) - 1)
6 + 1
g(x) = 6f(x) - 6 + 1
g(x) = 6f(x) - 5
The rule mentioned above means that:
A translation of the function f is the function g(x) (x)
As a result, the translation's unit is 5 and its direction is downward.
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Express the function graphed on the axes below as a piecewise
function. Help please
Answers
The equation of the line is 1st line f(x)= y=x+5 for -3≤x≤4, 2nd line f(x)=y=2/3x for -6≤x≤-3.
Given that,
In the picture we have a graph with 2 lines.
We have to find the equation of the lines and the limits.
What is an equation of the line?The slope of the line and a point on the line can be used to create the equation of a line. Let's learn more about the line's slope and the crucial point on the line in order to better understand how the equation for a line is created.
y=mx+b
We can see the lines,
The 1st lines has -3≤x≤4
The 2nd line has -6≤x≤-3
First we find the 1st line
The points are (0,5) and (1,6)
Slope of the line is m is rise/ run
m = 6-5/1-0
m =1
Take the equation of the line
y=mx+b
5=1(0)+b
b=5
We get the first equation of the line as y=x+5.
Second we find the 2nd line
The points are (-3,-2) and (-6,-4)
Slope of the line is m is rise/ run
m = -4+2/-6+3
m =-2/-3
m=2/3
Take the equation of the line
y=mx+b
-2=2/3(-3)+b
-2=-2+b
b=0
We get the first equation of the line as y=2/3x.
Therefore, the equation of the line is 1st line f(x)= y=x+5 for -3≤x≤4, 2nd line f(x)=y=2/3x for -6≤x≤-3.
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sarah invests $8200 in a new savings account which earns 5.8% annual interest, compounded semi-annually.
what will be the value of her investment after four years?
Answers
Answer:
The value after 4 years is $10307.11--------------------------------
GivenInvested amount P = $8200,Interest rate r = 5.8% = 0.058,Compound number n = 2,Time t = 4 years.Find the future amount[tex]A = P(1+r/n)^{nt}[/tex][tex]A = 8200(1+0.058/2)^{2*4}=8200*1.029^8=10307.11[/tex]Answer:
$10,307.11
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given:
P = $8,200r = 5.8% = 0.058n = 2 (semi-annually)t = 4 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=8200\left(1+\dfrac{0.058}{2}\right)^{2 \times 4}[/tex]
[tex]\implies \sf A=8200\left(1+0.029\right)^{8}[/tex]
[tex]\implies \sf A=8200\left(1.029\right)^{8}[/tex]
[tex]\implies \sf A=8200\left(1.25696445...\right)[/tex]
[tex]\implies \sf A=10307.10856...[/tex]
Therefore, the value of Sarah's investment after four years is $10,307.11 (nearest cent).
Joanna has $25 to spend at the zoo. Admission costs $12.25, and she plans to buy
Answers
Using mathematical operations, Joanna needs an additional $2.25 to meet her requirements for the zoo visit.
How is the difference determined?
The additional amount that Joanna requires is calculated with mathematical operations of addition and subtraction.
First, when you add $12.25 to $15.00, the sum is $27.25. This sum is subtracted from $25 or vice versa to get a difference of $2.25, which is the additional amount required to pay for her expenses at the zoo.
Another way to work out the difference is to first subtract the entrance fee of $12.25 from Joanna's amount. The difference becomes the minuend from which the amount of the snacks (the subtrahend) is deducted to obtain the difference as -$2.25.
Thus, with mathematical operations, Joanna's required additional amount is $2.25.
Learn more about mathematical operations at https://brainly.com/question/20628271
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Complete Question:Joanna has $25 to spend at the zoo. Admission costs $12.25, and she plans to buy snacks worth $15.00. How much more does she require to meet her needs at the zoo?
