Chapter 15 Questions 4) In the diagram below, ABCD is a rectangle and triangle DEF is formed by joining the midpoints of AB and BC. a) determine the area of rectangle ABCD in terms of x and y, b) If the shaded area of triangle DEF is 15m², determine the value of xy. c) Hence, determine the area of triangle EBF
Answers
a) The area of rectangle ABCD in terms of x and y = 4xy.
b) xy = 10
c) area of triangle EBF = 5 m².
What is defined as the rectangle?A rectangle is a covered two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal as well as parallel. Because a rectangle is a 2-D shape, it has two dimensions: length and width. The length of the rectangle is the longer side, and the width is really the shorter side.Part A) The area of rectangle ABCD:
See the diagram;
The length of rectangle is 2x.
The width of breadth is 2y.
Area = length×breadth
Area = 2x × 2y
Area of ABCD = 4xy m².
Part b) value of xy.
The area of the triangle DEF is 15m².
area ΔDEF = area ABCD - area ΔADE - area ΔBEF - area ΔDFC.
Put the values;
area ΔDEF = 4xy - 2xy/2 - 2xy/2 - xy/2
area ΔDEF = 3xy
equate;
ΔDEF = 3xy and DEF = 15m².
3xy/2 = 15
xy = 10
Thus, the value of xy = 10.
Part c) area of triangle EBF:
area ΔEBF = xy/2
Put the value of xy = 10.
area ΔEBF = 10/2 = 5
Thus, the area of the triangle EBF 10m².
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Related Questions
find the HCF of: 6(p² +p-2), 15(p³ + 8) and 18(4p²-p-18)
Answers
Answer:
Hello,
[tex]answer=\boxed{HCF=3*(p+2)}[/tex]
Step-by-step explanation:
[tex]6(p^2+p-2)=6(p+2)(p-1)\\\\15(p^3+8)=15(p+2)(p^2-2p+4)\\\\18(4p^2-p-18)=18(p+2)(4p-9)\\\\\boxed{HCF=3*(p+2)}[/tex]
angle q and angle r are complementary. the measure of angle q is 26 degrees less than the measure of r. find the measure of each ang;e
Answers
Based on the definition of complementary angles, the measures are:
m<q = 32°
m<r = 58°
What are Complementary Angles?Tow angels are complementary if both angles give a sum of 90 degrees.
The sum of angle q and angle r would give 90 degrees because they are complementary angles. Therefore, we would have the following:
m<r = ?
m<q = m<r - 26
Plug in the values
m<r - 26 + m<r = 90
2(m<r) - 26 = 90
2(m<r) = 90 + 26
2(m<r) = 116
2(m<r)/2 = 116/2
m<r = 58°
m<q = m<r - 26 = 58 - 26
m<q = 32°
Therefore, based on the definition of complementary angles, the measures are:
m<q = 32°
m<r = 58°
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An altitude is drawn to the base of equilateral triangle abc. if ac=13, find the length of the altitude.
Answers
The length of the altitude of the equilateral triangle ABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
Equilateral Triangle is defined as the triangle with all the sides equal and all the angles = 60 deg.
Altitude of a Triangle can be defined as the perpendicular drawn from the vertex of a triangle to the opposite side.
According to the question
In the figure given below
In ΔADC
Since ΔADC is a right angle triangle we can apply Pythagoras Theorem.
Let the sides of the equilateral triangle be "a". and "h" be the altitude.
Since the altitude is of equilateral triangle it divides the base i.e. DC=a/2
[tex](AC)^{2} =(AD)^{2}+(DC)^{2}[/tex]
[tex]a^{2} =h^{2}+(\frac{a}{2})^{2}\\ \\ h^{2}=\frac{4a^{2}-a^{2}}{4} \\ \\ h=\sqrt{3} *\frac{1}{2} *a[/tex]
Substituting the value of a=13 we get
Altitude [tex]h=\frac{13\sqrt{3} }{2}[/tex]
Therefore , The length of the altitude of the equilateral ΔABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
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In a class of 30 students, 15 students have taken English, 10 students have taken English but not French. Find the number of students have taken: (i) French, and (ii) French but not English.
Answers
By using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
What do you mean by arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Given:
Total no. of students is [tex]30[/tex]
Number of students taken English is [tex]15[/tex]
Number of students taken English but not French is [tex]10[/tex]
(i) Number of students taken French = Total no. of students - Number of students taken English but not French
[tex]= 30-10\\=20[/tex]
(ii) Number of students taken French not English = Number of students taken French - Number of students taken English
[tex]=20-15\\=5[/tex]
Therefore, by using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
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Answer:
By using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
What do you mean by arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Given:
Total no. of students is
Number of students taken English is
Number of students taken English but not French is
(i) Number of students taken French = Total no. of students - Number of students taken English but not French
(ii) Number of students taken French not English = Number of students taken French - Number of students taken English
Therefore, by using arithmetic operation, we get Number of students taken French is 20 and Number of students taken French not English is 5
Thirty-six friends are renting a party bus to the school prom. Rental of the
party bus will cost $300 up front plus $18 per hour. The friends have the
bus from 5:00 PM to 3:00 AM.
Each friend has agreed to chip in $12. One of the teachers at the high
school, Mr. Jones, has offered to chip in the rest. If he does, how much will
he pay
Answers
Answer:
$48
Step-by-step explanation:
The friends have the bus from 5:00 PM to 3:00 AM, so:
3 + 18 − 5 = 15 − 5 = 10 hours.
The cost of renting the bus will be:
$300 + $18 × 10 = $300 + $180 = $480.
The thirty-six students will contribute $12 each for a total of:
$12 × 36 = $432.
So Mr. Jones will pay:
$480 − $432 = $48.
Hope this helped :)
Using the digits 1-9 , at most one time each, to fill the blanks. how many ways can you find to do this? lim
Answers
[tex]Solution(1)Digit 1 to 9Lef $x \rightarrow 1, x^{\prime}$$$\lim _{x \rightarrow 1}=1^{\prime}=1$$$\lim _{\lim ^9}=(1)^9=1$$[9$ ways $]$Similarlyt$$\lim _{x \rightarrow 2} x^{\prime}=2^{\prime}=2$$$\lim _{x \rightarrow 2} x^9=\lim _{x \rightarrow 2} 2^9=512 \quad[9$ ways $]$Total no. of ways $=9 \times 9=81$ ways.Required No, of ways $=81$ Ans[/tex]
What is limit?This article discusses the idea of limit in general. See Limit of a sequence and Limit of a function for additional detailed situations. See Mathematics (limit) for further usage.
Limits are crucial to calculus and mathematical analysis because they are needed to determine continuity, derivatives, and integrals. Limits are the value that a function (or sequence) approaches when the input (or index) approaches some value.
In addition to being closely connected to limit and direct limit in category theory, the idea of a limit of a sequence is further expanded to include the idea of a limit of a topological net.
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In golf, scores are often stated as the number of stroked above or below par for the course. Four golfers played two rounds of golf during the weekend. The table list their scores for each round in relation to par (0).
Golfers Patrick Diane James Judy
Round 1 -6 +1 +2 -3
Round 2 -2 -4 +7 +6
A. What was Judy's total after both rounds of golf?
B. What is the difference between the lowest and highest scores earned? Write and solve an expression.
C. What was the combined total of everyones score for round 1 Write and solve an expression
Answers
Judy's total score is 3.
The difference between the lowest and highest score is -12.
The combined total of the scores from round 1 is -5.
What are the scores?The mathematical operations that would be used to solve this question are addition and subtraction. Addition is the process used to determine the sum of two or more number. The sign used to represent addition is +. Subtraction is the process used to determine the difference between two or more numbers. The sign used to represent subtraction is -.
Judy's total score is the sum of the score in round one and round one.
Judy's total score = -3 + 6 = 3
For negative numbers, the further the number is from 0, the smaller the number. For example, -10 is smaller than -5. For positive numbers, the closer the number is to zero, the smaller the number. For example,1 is smaller than 5.
Looking at the table, the smallest number is -6 and the largest number is 6
The difference : -6 - 6 = -12
The total scores from round 1 = 1 -6 +1 +2 -3 = -5
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Express2a powered −5 with a positive exponent.
Answers
Answer:
To make a negative exponent positive you put it over 1
[tex]\frac{2}{a^{5} }[/tex]
Step-by-step explanation:
2[tex]a^{-5}[/tex] = [tex]\frac{2}{a^{5} }[/tex]
After performing an experiment to determine what time of day adults are
most productive, you display your data as a graph to be analyzed. Which
phase of inferential statistics is this?
O A. Survey
B. Data organization
OC. Probability-based inference
OD. Data gathering
Answers
The phase of inferential statistics is B. Data organization.
What is data organization?The process of arranging raw data in a form that makes sense is known as data organization. Classification, frequency distribution charts, image and graphical representations, among other methods, are used to organize data. Data organization enables us to arrange the information so that it is simple to read and use.
This was illustrated after performing an experiment to determine what time of day adults are most productive, you display your data as a graph to be analyzed. This is data organization.
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Write an indirect proof of each statement.
Given: x y is an odd integer.
Prove: x and y are both odd integers.
Answers
By assuming that one of the two integers is even we will reach an absurd, and in that way, prove the given statement.
How to prove the statement?
Remember that an odd integer number is written as:
A = (2n + 1)
While an even number would be written as:
B = 2n
Where n is a random integer.
Then if x times y is an odd integer we can write:
x*y = (2n + 1)
Where n, m ∈ Z.
Where Z is the set of integer numbers.
Now, let's do find an absurd. Let's suppose that one of the two numbers is even, then we can write:
x = 2m
And y can be even or odd, it does not matter, but it is an integer.
Replacing that we get:
x*y = (2m)*y
We can rewrite that as:
(2m)*y = 2*(m*y)
We know that integer numbers are closed under the product, and here m and y are integers, then m*y is also an integer.
Thus, 2*(m*y) is 2 times an integer, then that is an even number, which is absurd because we know that it should be odd. So, if at least one of the two integers is even, then the product will also be even.
Then if the product is odd, neither of the integers can be even, then we conclude that both of the integers are odd integers.
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Jerry is planting white daisies and red tulips in his garden and he wants to choose a pattern in which the tulips surround the daisies. He uses tiles to generate patterns starting with two rows of three daisies. He surrounds these daisies with a border of tulips. The design continues as shown.
a1mtxese346734a011006tai
Jerry writes the expression 8(b − 1) + 10 for the number of tulips in each border, wherein b is the border number and b ≥ 1. Complete the explanation to explain why Jerry's expression is correct.
For Border 1, tulips are added above and below the daisies, which gives a total of 6 tulips. A tulip is then added to the end of each row of daisies, which gives 4 tulips. So, there is a total of
tulips in Border 1.
For Border 2, there are
additional tulips added to the garden plus the 10 original tulips from Border 1.
8 + 10
For Border 3, there are
additional tulips added to the garden plus the 10 original tulips from Border 1 and 8 additional tulips from Border 2.
8(2) + 10
So, the expression for the number of tulips in the garden with Border b is .
Answers
In linear equation ,Jerry's expression is correct.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."As you can see, starting with border 1, we have 6 daises (white squares) surrounded by 10 tulips (colored squares). Through Jerry's expression we expected:
= 8(b − 1) + 10
= 8(1 − 1) + 10
= 0 + 10
= 10 tulips.
When considering border 2, we expect:
= 8(b − 1) + 10
= 8(2 − 1) + 10
= 8 + 10
= 18 tulips.
Indeed, we have the 10 tulips from border 1 and 8 additional tulips, for a total of 18 tulips.
Then, consider border 3, we expect:
= 8(b − 1) + 10
= 8(3 − 1) + 10
= 16 + 10
= 26 tulips.
Again, this is correct: we have the 10 tulips used in border 1 plus other 16 tulips, for a total of 26.
Therefore, Jerry's expression is correct.
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Solve the system.
4x-y+z=2
5x-2y + 4z=-9
2x+y-52=24
Answers
Answer:
4x-y+z=2
Step-by-step explanation:
the answer is simple
Can someone explain this im trying to get it but I can’t
Answers
Step-by-step explanation:
2x=x+9
subtract the x from both sides
(2x - 1x) (1x-1x)
1x 1-1= 0 so x cancels out
1x=9
divide both sides by 1x
(1x/1x) (9/1x)
1/1 cancels out so that becomes x by its self
9/1 = 9
x=9
First, you would group your like terms together by circling them.
(2x)(-x)+9
Pretend the parentheses are circles.
Your -x will act as -1x because if you ever see a +x or -x there is always an invisible 1 there.
Next you would do like you would normally do to subtract something except you just have x right there. 2-1 is 1. So 1x.
Lastly, you put 9 and 1x together, so therefore your answer will be 1x+9, or x+9. I tried my best to explain this and I really hope it helped.
∠A and \angle B∠B are vertical angles. If m\angle A=(7x+22)^{\circ}∠A=(7x+22)
∘
and m\angle B=(8x+20)^{\circ}∠B=(8x+20)
∘
, then find the measure of \angle A∠A.
Answers
Based on the definition of vertical angles, m<A = 36°.
What are Vertical Angles?Two angles that are vertically opposite to each other are called vertical angles, and they have congruent angle measures. That is, vertical angles are equal.
Angles A and B are vertical angles, then, they are equal to each other.
m<A = (7x + 22)°
m<B = (8x + 20)°
m<A = m<B
Substitute
7x + 22 = 8x + 20
7x - 8x = -22 + 20
-x = -2
x = 2
m<A = 7x + 22
Plug in the value of x
m<A = 7(2) + 22
m<A = 14 + 22
m<A = 36°
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suppose your group measures the following three numbers in some experiment: 12.4,7.8,10.2. if you use half the range as an estimate of the standard deviation, what is the standard error on the mean of these numbers?
Answers
The standard error on the mean of these numbers is 1.08
For given question,
suppose your group measures the following three numbers in some experiment: 12.4,7.8,10.2
Mean of these numbers is:
[tex]\bar x=\frac{ 12.4+7.8+10.2}{3}\\\\ \bar x=10.13[/tex]
So the standard deviation would be,
[tex]\sigma=\sqrt{\frac{(12.4-10.13)^2+(7.8-10.13)^2+(10.2-10.13)^2}{3} }\\\\\sigma=1.88[/tex]
Now we find the standard error on the mean of these numbers.
[tex]\sigma_M=\frac{\sigma}{\sqrt{N} }[/tex]
where, [tex]\sigma_M[/tex] = standard error of the mean
σ = the standard deviation of the original distribution
N = the sample size
[tex]\sigma_M=\frac{1.88}{\sqrt{3} }\\\\\sigma_M=1.08[/tex]
Therefore, the standard error on the mean of these numbers is 1.08
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Which of the following is an equivalent expression of 15x2 +12x + 8?
27x3 + 8
15x2(12x + 8)
12x + 15x2 + 8
8(15x2 + 12x)
Answers
The expression which is equivalent to the expression given in the task content is; 12x +15x² +8.
Which expression is an equivalent expression of 15x2 +12x + 8?It follows from the task content that the expression which is an equivalent of the given expression is to be identified.
Given;
15x² +12x + 8
Hence, by re-arranging the terms of the expression; we have;
12x + 15x² +8.
Ultimately, the required equivalent expression is; 12x + 15x² +8.
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find the sum (3x^2+2x+3)+(x^2+x1)
Answers
The sum of (3x² + 2x + 3) + (x² + 1) will be 4x² + 2x + 4.
How to calculate the sum?The sum of (3x² + 2x + 3) + (x² + 1) will be calculated by simply adding the values.
This will be:
= (3x² + 2x + 3) + (x² + 1)
= 3x² + x² + 2x + 3 + 1
= 4x² + 2x + 4
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What is the value of x in the system of equations below?
3x +y+2z=-10
x+5y+2z=-12
-2x+3y=-1
Answers
Answer:
Step-by-step explanation:
A. 1
B. -3
C. 3
D. -1
The value of x = -1
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
3x +y+2z=-10 equation 1
x+5y+2z=-12 equation 2
-2x+3y=-1 equation 3
Subtracting equation 1 to equation 2, we get
3x +y+2z - (x+5y+2z)=-10 - (-12)
3x +y+2z - x -5y -2z = -10 + 12
2x - 4y = 2 equation 4
Adding equation 4 to equation 3, we get
2x - 4y -2x+3y = 2 - 1
- y = 1
y = -1
Putting the value of y in equation 4, we get
2x - 4y = 2
2x - 4(-1) = 2
2x +4 = 2
2x = -2
x = -1
Therefore, the value of x = -1
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"a comparison of nine confidence intervals for a poisson parameter when the expected number of events is ≤ 5,
Answers
The exact interval for researchers who want real coverage that is at least nominal and a modified version of the variance stabilized interval for those who are OK with approximative coverage.
Let [tex]{ X_{i} }^{n} _{i = 1}[/tex] be a group of independent variables with Poisson distribution and the same distribution. Confidence intervals for can be created using a variety of methods, including the Wald method, precise inference, a variance stabilizing transformation, and many others. Actual and nominal coverage can differ significantly when n is small. For a Poisson mean, we compare nine confidence intervals in terms of coverage and expected width of the confidence bounds. We demonstrate that, for small n, only the exact interval maintains coverage probabilities; the scores interval maintains coverage probabilities roughly, but its expected width is greater than that of the exact interval.A modified confidence interval based on the variance stabilized confidence interval has coverage properties close to the nominal and an expected width that is not particularly large. Therefore, we advise using the exact interval for researchers who want real coverage that is at least nominal and a modified version of the variance stabilized interval for those who are OK with approximative coverage.
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Rita bakes pies at a bakery. the number of pies she can bake, x, is limited by the ingredients they have in stock. this situation is represented by 2x - 3 < 7 and 5 - x < 8 solve the compound inequality and write the viable solutions.
Answers
The viables solutions for the given compound inequality are x ∈ (-3, 5).
According to the given question.
The number of pies baked by Rita is x which is limited by ingredients.
Also, the inequalities which represent the situation are
2x - 3 < 7
And, 5 - x < 8
Since, we have to solve the above inequality and find its solutions.
From the given inequality
2x - 3 <7 we can say that,
2x < 7 + 3
⇒ 2x < 10
⇒ x < 5 ..(i)
And, 5 - x < 8
⇒ 5 - 8 < x
⇒ - 3 < x
or, x < -3 ..(ii)
From i and ii we can say that the solution of the given compound inequality are the numbers which lies in between -3 and 5 or x ∈ (-3, 5).
Hence, the viables solutions for the given compound inequality are
x ∈ (-3, 5).
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Please answer fast.
Thank you to who ever answers it!
Answers
Answer:
see explanation
Step-by-step explanation:
using the formula V = lwh , then
(a)
volume of first box = 3x × x × 2x = 6x³ units³
(b)
volume of second box = 4x × 2x × x = 8x³ units³
(c)
volume of 2 boxes = 6x³ + 8x³ = 14x³
(d)
if x = 6 , then
volume of 2 boxes = 14x³ = 14(6)³ = 14 × 216 = 3024 units³
It costs $5820 to get new windows for a certain house. Each of the 28 windows costs the same amount. Determine an estimate for the cost of each window. Justify your reasoning. What is the cost of each window, rounded to the nearest dollar? Show your work. Leave the remainder undivided.
Answers
Answer:
1. Determine the estimate.: Without solving I'd say 200, but you could try to think of your own estimate.
2. Justify.: 5820 rounds up to 6000, and 28 rounds up to 30. 6000/30 = 200
3. 207.85 (I don't know if your teacher makes you do the new way of rounding up, but if it says round to the nearest dollar I'd do $207.)
Step-by-step explanation:
Then you divide. Sorry I can't show you that!!! But I really hope this helped.
What is the answer to 3/10=15/50
Answers
Answer: 3/10 times 5 equals 15/50
Step-by-step explanation: First you do 3 times 5 which equals 15 and then 10 times 5 to get 50, which together make 15/50 and to make sure it's right check it by finding the greatest common factor they both have.
Answer:
5/5
Step-by-step explanation:
3 will enter 15, 5 times
n 10 will enter 50, 5 times
Mandy has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will she have in 2 years
Answers
Amount after 2 years is $44.1
Compound interest formula
[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]
A= Amount after t years.
P= Principal amount.
r= Interest rate (decimal)
n=Period of compounding
t= Time
So ,
[tex]A=40(1+\frac{0.05}{1}) ^{1*2}\\ =40(1.05) ^{2}\\ = 40*1.1025\\ = 44.1[/tex]
Amount after 2 years is $44.1
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
For each function, what is the output of the given input?
For f(x) = 4x + 7, find f(4)
Answers
f(4) = 23
Please help
Evaluate.
(-3)³-4²=
Answers
Answer:
-43
Step-by-step explanation:
(-3)³ - 4² = -27 - 16 = -43
Find missing length.
A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base?
Answers
Answer:
good luckkkkkkkkkkkkkkk
Find the value of z.
X
7
Y
Z
3
Z = ✓[?]
Please helppppp
Answers
Answer:
z = [tex]\sqrt{30}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it) × ( whole hypotenuse) , so
z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )
z = [tex]\sqrt{30}[/tex]
A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $275 each, and the desktop computers cost $150 each. How much would it cost to buy 14 notebooks and 16 desktop computers? How much would it cost to buy n n notebooks and d d desktop computers?
Answers
Answer
14 notebook computers: 3850$
16 desktop computers: 2400$
Step-by-step explanation:
275x14=3850
150x16=2400
For how many integers will 4x + 5 be greater than 4 and less than 175?
Answers
The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.
How many integers are within a linear inequality?
Herein we must find what integers are within the interval of a simultaneous linear inequality, whose definition is shown below:
4 < 4 · x + 5 < 175
Which is equivalent to the following two inequalities:
4 · x + 5 > 4 (2)
4 · x + 5 < 175 (3)
By (2):
4 · x + 5 > 4
4 · x > - 1
x > - 1 / 4
x > - 1
By (3):
4 · x + 5 < 175
4 · x < 170
x < 170 / 4
x < 85 / 2
x < 42.5
x < 43
Then, the number of integers within the simultaneous inequality is:
n = 1 + (42 - 1)
n = 42
The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.
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