Answer:
$9275
Step-by-step explanation:
Selma earns 5% on the first $40,000, which is $2000.
She earns 5.5% on the next $35,000, which is $1925.
She earns 6% on the next $25,000, which is $1500.
And she earns 7% on the last $55,000 (the amount over 100,000), which is $3850.
Altogether, Selma's commission is ...
... $2000 +1925 +1500 +3850 = $9275.
_____
Comment on the sliding scale
Each of the segments of this sliding scale could be rewritten to simplify its computation. For example, for amounts above $100,000, the formula could be either of ...
7% of the amount over $22,5007% of sales, less $1575.Triangles △ABC and △DEF are similar. Find the lengths of the sides of △DEF, if AB=2 cm, BC=3 cm, CA=4 cm, DE=1.5 cm.
DE = 1.5 cm, EF = 2.25 cm, FD = 3 cm
Step-by-step explanation:Side DE corresponds to side AB and is (1.5 cm)/(2 cm) = 3/4 the length of it.
Because the triangles are similar, all pairs of corresponding sides have the same ratio. That is, the side lengths in ΔDEF are 3/4 of those in ΔABC.
... EF = (3/4)×BC = (3/4)×(3 cm)
... EF = 2.25 cm
... FD = (3/4)×CA = (3/4)×(4 cm)
... FD = 3 cm
The lengths of the sides of triangle △DEF, given that AB=2 cm, BC=3 cm, CA=4 cm, and DE=1.5 cm, would be EF = 2.25 cm and DF = 3 cm.
Explanation:If triangles △ABC and △DEF are similar, then the ratio of the corresponding sides is the same. We know AB = 2 cm which corresponds to DE = 1.5 cm in the triangle △DEF. The ratio of AB to DE is 2cm:1.5cm or 4:3. Let's compute the sides of the triangle △DEF using this ratio:
EF corresponds to BC in triangle △ABC. Using the ratio 4:3, EF = BC * (3/4) = 3cm * 3/4 = 2.25 cm DF corresponds to CA in triangle △ABC. Using the ratio 4:3, DF = CA * (3/4) = 4cm * 3/4 = 3 cmLearn more about Similar Triangles here:https://brainly.com/question/32489731
#SPJ11
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
D. There are no solutions
Step-by-step explanation:First inequality:
... -16 ≥ 8x . . . . . . . add 8x-60 to the inequality
... -2 ≥ x . . . . . . . . divide by 8
Second inequality:
... -8 < 4x . . . . . . . . add 4x-58 to the inequality
... -2 < x . . . . . . . . . divide by 4
The problem statement requires a solution satisfy both conditions on x. The two solution sets are disjoint (have no points in common), so ...
... there are no solutions.
What numbers are in between 1 and 1.01 on a number line?
There is an infinite number of numbers between 1 and 1.01 on the number line. The correct answer should theoretically be: 1 < n < 1.01.
The length of each side of a cube is increased by a factor of 4. What is the effect on the volume of the cube?
Answer:
When dealing with VOLUME, an increase in a linear quantity, produces a third power result in the volume.
Increase the sides of a cube by 2 produces an 8 times effect in the volume.
Increasing each side of a cube by 4 produces a chnage of 4 * 4 * 4 or
64 times in the volume.
Step-by-step explanation:
Increasing the length of each side of a cube by a factor of 4 results in the volume increasing by a factor of 64, since volume is proportional to the cube of the linear dimensions.
When the length of each side of a cube is increased by a factor of 4, the effect on the volume of the cube is that it increases by a factor of [tex]4^3[/tex], or 64. This is because volume is a three-dimensional measure, and when each dimension (length, width, height) of a cube is multiplied by a factor, the volume is multiplied by the factor raised to the third power (since volume is calculated by length *width * height).
Therefore, if the original length of one side of the cube is L, the original volume is L3. After increasing each side by a factor of 4, the new length becomes 4L, making the new volume [tex](4L)^3 = 4^3 \times L^3 = 64L^3[/tex]. Hence, the new volume is 64 times the original volume, not simply 4 times because the increase happens in each of the three dimensions.
HELP U WILL GET BRAINLIEST ANSWER ASAP
B. MN/LN = RS/QR
Step-by-step explanation:ΔQRS ~ ΔLMN so corresponding segments are ...
LM and QRLN and QSMN and RSCorresponding segments have the same ratio. So, ...
... LM/LN = QR/QS . . . . does not match A
... MN/LM = RS/QR . . . . matches B
... LM/MN = QR/RS . . . . does not match C
... MN/LM = RS/QR . . . . does not match D
two angles are congruent. one angle is represented by the expression (4x-2) and the other angle is (5x-3). write an equation and solve for each angle.
Answer:
4x-2=0
5x-3=0
Step-by-step explanation:
Plz help me with this ASAP Plz plz plz help me
Answer:
The graph shows that typically students with more hours of sleep(independent) had higher test scores (dependent)
Step-by-step explanation:
PLEASE HELP ASAP!!!!
System
p + m = 100.8m = 0.4·10Solution
p = m = 5 — 5 lb peanuts and 5 lb mixtureStep-by-step explanation:(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.
For the total amount of mix:
... p + m = 10
For the quantity of peanuts in the mix:
... p + 0.2m = 0.6·10
For the quantity of almonds in the mix:
... 0.8m = 0.4·10
For the ratio of peanuts to almonds:
... (p +0.2m)/(0.8m) = 0.60/0.40
Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.
So, your system of equations could be ...
p + m = 100.8m = 0.4·10___
(b) Dividing the second equation by 0.8 gives
... m = 5
Using the first equation to find p, we have ...
... p + 5 = 10
... p = 5
5 lb of peanuts and 5 lb of mixture are required.
What is 5/16 expressed as a percent?
Enter your answer in the box.
Answer:
31.25 %
Step-by-step explanation:
The fraction bar also means divide:
5 / 16
=
5 Divided By 16
=
0.3125
0.3125 * 100
= 31.25
- I.A -
The fraction 5/16 is converted to a percent by dividing 5 by 16 and then multiplying the result by 100, which equals 31.25%.
To convert the fraction 5/16 into a percent, we want to know how many parts out of 100 this fraction represents.
A percent is a way of expressing a fractional amount as a part of 100.
To do this, we can set up a proportion or multiply the fraction by 100.
So, we take 5 divided by 16 and then multiply the result by 100.
Doing the math:
= (5 / 16) x 100
= 0.3125 x 100
= 31.25%.
Therefore, the fraction 5/16 expressed as a percent is 31.25%.
Two similar pyramids A and B have surface areas of 135cm^2 and 60cm^2 respectively . The volume of pyramid A is 405 cm^3 work out the volume of pyramid B
Answer:
120 cm^3
Step-by-step explanation:
The surface areas are in the ratio 60 to 135 so the single dimensions are in the ratio √60 to √135.
Therefore the volumes are in the ratio (√60)^3 to (√135)^3 or 60^3/2 to 135^3/2.
So Volume of Pyramid B / Volume of Pyramid A
= 60^3/2 / 135^3/2.
Therefore we have the equation 60^3/2 / 135^3/2 = V / 405 where V is the volume of pyramid B.
V = (60^3/2 * 405) / 135^3/2
= 120 cm^3
Answer:
120cm³
Step-by-step explanation:
√135/√60=3/2
3/2=1.5
1.5³=3.375
405/3.375=120
120cm³
EVALUATE THE EXPRESSION WHEN P = -24 AND Q = 4
P/3Q
A. 2
B. -2
C. 24
D. -24
Answer:
B. -2
Step-by-step explanation:
We have been given an expression [tex]\frac{P}{3Q}[/tex] and we are asked to evaluate our expression, when P=-24 and Q=4.
Let us substitute P=-24 and Q=4 in our given expression.
[tex]\frac{-24}{3*4}[/tex]
Let us multiply 3 by 4.
[tex]\frac{-24}{12}[/tex]
[tex]-\frac{24}{12}[/tex]
Upon dividing 24 by 12 we will get,
[tex]-\frac{24}{12}=-2[/tex]
Therefore our expression simplifies to -2 and option B is the correct choice.
Subtract 43 from 20 raised to the 7th power; then multiply by 3.
Hi there! :)
Answer:
Subtract 43 from 20 raised to the 7th power; then multiply by 3. The answer is: 3,839,999,871
Step-by-step explanation:
"Subtract" means to take away a number from another.
" 20 raised to the 7th power" is the same thing as 20 exponent 7: [tex]20^{7}[/tex]
SO, you want to take away 43 from [tex]20^{7}[/tex] and then multiply the answer by 3:
([tex]20^{7}[/tex] - 43) × 3
[tex]20^{7} =[/tex] 1,280,000,000
(1,280,000,000 - 43) × 3
1,280,000,000 - 43 = 1,279,999,957
1,279,999,957 × 3
1,279,999,957 × 3 = 3,839,999,871
There you go! I really hope this helped, if there's anything just let me know! :)
Answer:
I got 3839999831
Step-by-step explanation:
So 20^7(calculator), then subtract and mult
Which number(s) below would NOT in scientific notation and why? 4.5 x 10^4 6 x 10^7 12.5 x 10^3 4.2 x 10^-8 2.355 x 10^6 0.45 x 10^3
Scientific notation has exactly one non-zero digit to the left of the decimal point in the mantissa. The numbers listed above do not.
_____
Comment on these numbers
There may be good reasons for writing the numbers in this form. For example, in engineering, it is often useful to have the exponent be a multiple of 3. In other instances, writing the number in these forms may facilitate arithmetic. However good the reasons may be, these numbers are not in in the form defined as "scientific notation."
need help pls. I try many ways of this answer
Answer:
3(t+2)
Step-by-step explanation:
As with any problem involving division of fractions, you can invert the denominator and multiply.
Your knowledge of the factoring of the difference of squares helps. If that doesn't work for you, you can always use synthetic division or polynomial long division to find the quotient of (t^2-4) and (t-2).
[tex]\displaystyle\frac{\frac{4t^2-16}{8}}{\frac{t-2}{6}}=\frac{4(t^2-4)}{8}\cdot\frac{6}{t-2}\\\\=\frac{3(t+2)(t-2)}{t-2}=3(t+2)[/tex]
how do I solve this (not looking for answer
Answer:
Add 78 to 54 to get 132 total patrons, then divide the number of females into the total number of patrons. Therefore, 78/132 = .5909 = 59%
Step-by-step explanation:
Answer:
Thats simple!
Step-by-step explanation:
G.o.o.g.l.e.
PLEASE HELP (Screenshot)
C. 75°
Step-by-step explanation:The sum of the three angles is 180°, as it is for the angles in any triangle.
35° + 70° + x° = 180° . . . . an equation expressing the relationship of the angles
x° = 180° -35° -70° . . . . . subtract 35° and 70°
x° = 75°
What is the result of isolating x^2 in the equation below? y^2-3x^2=6
A. x^2 = y^2/3 -2
B. x^2 = -y^2/3 -2
C. x^2 = y^2/3 + 2
D. x^2 = -y^2/3 + 2
Answer:
A. x^2 = y^2/3 -2
Step-by-step explanation:
Add 3x^2 to both sides of the equation. We do this so that the coefficient of x^2 is positive. It can be less confusing that way.
... y^2 = 3x^2 +6
Divide by 3.
... y^2/3 = x^2 +2
Subtract 2.
... y^2/3 -2 = x^2 . . . . . matches selection A.
Answer:
A. x^2 = y^2/3 -2
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The grades received by 200 students follow a normal distribution. The mean of the grades is 70%, and the standard deviation is 7%. The number of students who received a grade greater than 70% is about __ , and the number of students who got a grade higher than 84% is about __ .
Answer:
1005Step-by-step explanation:
a) The mean of a normal distribution is also the median. Half the population will have values above the mean. Half of 200 is 100, so ...
... 100 students will have grades above 70%.
b) 84% is 14% above the mean. Each 7% is 1 standard deviation, so 14% is 2 standard deviations above the mean. The empirical rule tells you 95% of the population is within 2 standard deviations of the mean, so about 5% of students (10 students) got grades higher than 84% or lower than 56%. The normal distribution is symmetrical, so we expect about 5 students in each range.
... about 5 students will have grades above 84%.
1. The number of students who received a grade greater than 70% is about 100.
2. The number of students who got a grade higher than 84% is about 195.
To find the number of students who received a grade greater than 70%,
you need to calculate the area under the normal distribution curve to the right of 70%.
Similarly, to find the number of students who got a grade higher than 84%,
you need to calculate the area under the normal distribution curve to the right of 84%.
You can use the z-score formula to convert the given grades to z-scores, then look up the corresponding areas in the standard normal distribution table.
For a grade of 70%:
[tex]\[ Z = \frac{X - \mu}{\sigma}[/tex]
[tex]= \frac{70 - 70}{7}[/tex]
= 0
For a grade of 84%:
[tex]\[ Z = \frac{X - \mu}{\sigma}[/tex]
[tex]= \frac{84 - 70}{7}[/tex]
[tex]\approx 2[/tex]
Then, you look up the corresponding areas in the standard normal distribution table:
For Z = 0, the area to the right is about 0.5000.For Z ≈ 2, the area to the right is about 0.0228.Now, to find the number of students:
Students with grades greater than 70%:
Number of students = Total students × Area to the right of 70%
= 200 × (1 - 0.5000)
= 200 × 0.5000
= 100
Students with grades higher than 84%:
Number of students = Total students × Area to the right of 84%
= 200 × (1 - 0.0228)
≈ 200 × 0.9772
≈ 195
So, the number of students who received a grade greater than 70% is about 100, and the number of students who got a grade higher than 84% is about 195.
Sarah bikes 4/5 km in 2 min. What is the unit rate and what does it mean?
Answer:
The unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.
Step-by-step explanation:
It is given that Sarah bikes [tex]\frac{4}{5}[/tex] km in 2 min. It means Sarah covers [tex]\frac{4}{5}[/tex] km in 2 min.
The units rate is defined as
[tex]\text{Unit rate}=\frac{\text{Distance covered}}{\text{Time Taken}}[/tex]
[tex]\text{Unit rate}=\frac{(\frac{4}{5})}{2}[/tex]
[tex]\text{Unit rate}=\frac{4}{5}\times \frac{1}{2}[/tex]
[tex]\text{Unit rate}=\frac{2}{5}[/tex]
Therefore the unit rate is [tex]\frac{2}{5}[/tex] km per minute. It means sarah bikes [tex]\frac{2}{5}[/tex] km in 1 minute or the speed of sarah is [tex]\frac{2}{5}[/tex] km per minute.
I kinda need to show my work so please help me out. This is due in 10 minutes
A distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/h, by a bus at 60 km/h, a truck at 50 km/h, and a bicyclist at 20 km/h. How much time did each require to travel the entire distance? Explain why the speed and the time needed to travel 150 km are inversely proportional quantities. for The motorcyclist required hours, the bus required hours, the truck required hours, the bicyclist required hours.
A)
motorcylcist: 2 hoursbus: 2.5 hourstruck: 3 hoursbicyclist: 7.5 hoursB) It is a matter of definition: speed = distance/time. Speed is proportional to distance and inversely proportional to time.
Step-by-step explanation:Speed is defined as the ratio of distance to the time required to cover that distance:
... speed = distance/time
Solving this relation for time, we have ...
... time = distance/speed
a) For each of the modes of transportation, we can find the time by using this relation.
... motorcyle: (150 km)/(75 km/h) = 2 h
... bus: (150 km)/(60 km/h) = 2.5 h
... truck: (150 km)/(50 km/h) = 3 h
... bicycle: (150 km)/(20 km/h) = 7.5 h
b) For a given distance, speed and time are inversely related as a matter of definition.
PLZ HELP ASAP. I NEED HELP PLZ
True or false will give brainliest
Probability can be written as a fraction. Is it true or false that all probability has to be somewhere between 0 & 1 when written a decimal.
If you answered "false" for the previous question, list a fraction (NOT an improper fraction) that is more than 1 when turned into a decimal. If you answered "true", explain in your own words why a fraction can not be more than 1.
Help me with Percent word problems
$67.45
Step-by-step explanation:There are a couple of ways you can go at these.
1. Compute the tip, then add that to the bill.
... 15% × $58.65 = $8.7975 ≈ $8.80
... $58.65 + 8.80 = $67.45
2. Compute the effect of adding the tip, then use that result to multiply by the bill amount.
... bill + (15% × bill) = bill × (1 +0.15) = 1.15 × bill
... 1.15 × $58.65 = $67.4475 ≈ $67.45
_____
Comment on percentages
The symbol % is a fancy (shorthand) way to write /100. The terminology "per cent" means "per hundred" or "divided by 100".
So, 15% = 15/100.
From your knowledge of place value and the meaning of decimal numbers, you know 15/100 (fifteen hundredths) = 0.15 (fifteen hundredths).
_____
Comment on 15% tip
10% = 10/100 = 1/10 of something can be computed by moving the decimal point one place left (dividing by 10).
5% of something is half of 10% of it.
15% is the sum of 10% and 5%.
Your bill is 58.65, so 10% of the bill is 5.865 ≈ 5.87. Half that is 2.9325 ≈ 2.93. The sum of 10% and 5% will be 5.87 +2.93 = 8.80, the amount that is 15% of the bill. Often, the numbers are such that this arithmetic can be done in your head.
Replace ∗ with a monomial so that the expression can be rewritten as a square of a sum or a difference: ∗ +56a+49
Answer:
[tex]\ast=16a^2[/tex]
Step-by-step explanation:
Use formula for a square of a sum:
[tex](x+y)^2=x^2+2xy+y^2.[/tex]
Note that
[tex]49=7^2;[/tex][tex]56a=2\cdot 28a=2\cdot 7\cdot 4a.[/tex]Then instead of * should be the square of the term 4a that is [tex](4a)^2=16a^2.[/tex]
Then
[tex]16a^2+56a+49=(4a+7)^2.[/tex]
To complete the pattern in the expression ∗ +56a+49 to make it a square of a sum or a difference, we can use the formula for (a+b)² as a guide. If 49 is b² and 56a is 2ab, the missing part would be a². On solving, we find that the value of a² is 16a².
Explanation:The subject of this question is finding a monomial such that the given expression can be rewritten as a square of a sum or a difference. The expression is ∗ +56a+49. We can think of the square of a sum or a difference as the result of the formula (a+b)² = a² + 2ab + b² which gives a hint that we can structure our expression in a similar way.
Let's rearrange the given expression a bit using this hint. If we look at 49, it is equal to 7². This could be our b². Additionally, 56a can be written as 2*7*a or 2ab. So the missing part would be a² which completes the pattern of the formula.
To find the value of a², we need to know the value of a. Here's where 56a comes into play. It is 2ab (or in this case, 2*7*a). Solving this equation for a, we get a=4. So, a²=16. Therefore, the monomial that completes the pattern in the expression is 16a².
Learn more about Squared terms here:https://brainly.com/question/34273316
#SPJ3
Which piece of additional information can be used to prove △CEA ~ △CDB?
∠BDC and ∠AED are right angles
AE ≅ ED
△BDC is a right triangle
∠DBC ≅ ∠DCB
∠BDC and ∠AED are right angles
Step-by-step explanation:Because ∠C ≅ ∠C, the additional bit of information above can be used to show AA similarity.
____
None of the other offered choices says anything about both triangles. In order to show similarity, you need information about corresponding parts of the two triangles. Information about one triangle alone is not sufficient.
Answer:
I think it's A. ∠BDC and ∠AED are right angles
Step-by-step explanation:
I hope this helps.
A wire is attached to the top of a 45-foot telephone pole and anchored to the ground. The angle of elevation is 64 degrees. How long is the wire to the nearest foot?
Answer:
Length of wire = 50 ft
Step-by-step explanation:
In the figure below AB is the telephone pole and C is the point on the ground where wire is anchored.
so we have
AB= 45 ft
∠ACB= 64°
Let is assume the length of the wire be x ft
now in Δ ABC
[tex]sin C = \frac{AB}{AC}[/tex]
we can plug AB= 45, ∠C= 64°and AC=x
so we have
[tex]sin(64)[/tex]°[tex]=\frac{45}{x}[/tex]
[tex]xsin(64)[/tex]°[tex]=45[/tex]
[tex]x=\frac{45}{sin(64)}[/tex]
now we have sin 64°=0.8988
[tex]x=\frac{45}{0.8988}[/tex]
[tex]x=50.07[/tex] ft
rounding to nearest foot
x= 50 ft
Final answer:
To find the length of the wire attached to a telephone pole at a 64-degree angle, we use the tangent function, resulting in an approximate wire length of 22 feet to the nearest foot.
Explanation:
The question asks how long a wire is if it's attached to the top of a 45-foot telephone pole and anchored to the ground, with an angle of elevation of 64 degrees.
To solve this, we can use trigonometry, specifically the tangent function, because we know the opposite side (height of the pole) and are trying to find the hypotenuse (length of the wire).
The tangent of an angle in a right triangle is the opposite side divided by the adjacent side. In this scenario, the angle of elevation is 64 degrees and the opposite side (height of the telephone pole) is 45 feet.
To find the length of the wire (hypotenuse), we use the formula: length of wire = opposite side / tan(angle), which translates to length of wire = 45 / tan(64 degrees).
Using a calculator, we find that tan(64 degrees) is approximately 2.05.
Therefore, the length of the wire is approximately 45 / 2.05, which equals about 21.95 feet.
To the nearest foot, the wire would be 22 feet long.
Find the reference angle, theta prime, when theta=5 radians. Write your answer in radians.
(2π-5) radians ≈ 1.2831853 radians
Step-by-step explanation:The reference angle is the magnitude of the acute angle made with the x-axis. The value of θ is greater than 3π/2, so the reference angle is ...
... θ' = abs(θ -2π) = 2π-5 . . . . radians
Drag each equivalent expression to the box where it belongs. Some expressions may not belong in either box.
Yes:
-3(4x + 12)
-4(3x -9)
4(2x - 6)
-4(-2x - 6)
3(-4x +12)
2(4x - 12)
-12x + 36
8x - 24
No:
Assuming your target boxes are (-12x +36) and (8x -24), here are the classifications of the expressions with parentheses.
-3(4x + 12) = -12x -36 (neither)
-4(3x -9) = -12x +36
4(2x - 6) = 8x -24
-4(-2x - 6) = 8x +24 (neither)
3(-4x +12) = -12x +36
2(4x - 12) = 8x -24
_____
The distributive property applies:
... a(b+c) = ab +ac
Same signs multiply to give positive. Different signs multiply to give negative.
Expressions like -3(4x + 12), -4(3x -9), and 3(-4x +12) are equivalent to -12x + 36 while 4(2x - 6) and 2(4x - 12) are equivalent to 8x - 24. The expression -4(-2x -6) is not equivalent to others.
Explanation:The question is asking to categorize the expressions whether they are equivalent or not. Two expressions are equivalent if they have the same value for all values of their variables. Let's evaluate each expression:
-3(4x + 12) simplifies to -12x - 36-4(3x -9) simplifies to -12x +364(2x - 6) simplifies to 8x - 24-4(-2x - 6) simplifies to 8x + 243(-4x +12) simplifies to -12x + 362(4x - 12) simplifies to 8x - 24So we see that -3(4x + 12), -4(3x -9), and 3(-4x +12) are equivalent to -12x + 36, while 4(2x - 6) and 2(4x - 12) are equivalent to 8x - 24. The expression -4(-2x -6) doesn't match any other expression.
Learn more about Equivalent Expressions here:https://brainly.com/question/28170201
#SPJ2
Draw and classify the given vertices. Find the perimeter and area of the polygon to the nearest tenth.
QUESTION 1a
The given polygon has vertices [tex]A(-2,3),B(3,1),C(-2,-1),D(-3,1)[/tex].
We plot the points and connect them to obtain the figure as shown in the attachment.
The polygon has four sides and two pairs of adjacent sides equal.
Therefore Polygon ABCD can be classified as a quadrilateral, specifically a kite.
QUESTION 1b
We can find the perimeter by adding the length of all the sides of the kite
[tex]Perimeter=|AB|+|BC|+|CD|+|AD|[/tex]
Or
[tex]Perimeter=2|AB|+2|AD|[/tex]
Recall the distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We use the distance formula to find the length of each side.
[tex]|AB|=\sqrt{(3--2)^2+(1-3)^2}[/tex]
[tex]|AB|=\sqrt{(3+2)^2+(1-3)^2}[/tex]
[tex]|AB|=\sqrt{(5)^2+(-2)^2}[/tex]
[tex]|AB|=\sqrt{25+4}[/tex]
[tex]|AB|=\sqrt{29}=5.385[/tex]
Length of side AD
[tex]|AD|=\sqrt{(-3--2)^2+(1-3)^2}[/tex]
[tex]|AD|=\sqrt{(-3+2)^2+(1-3)^2}[/tex]
[tex]|AD|=\sqrt{(-1)^2+(-2)^2}[/tex]
[tex]|AD|=\sqrt{1+4}[/tex]
[tex]|AD|=\sqrt{5}=2.24[/tex]
[tex]Perimeter=2(5.1)+2(2.236)[/tex]
[tex]Perimeter=10.77+4.472[/tex]
[tex]Perimeter=15.242[/tex]
The perimeter of the kite to the nearest tenth is 15.2 units
QUESTION 1c
The area of kite ABCD is twice the area of ΔABD
[tex]Area\:of\:ABD=\frac{1}{2}\times |BD| \times |AE|[/tex]
[tex]Area\:of\:ABD=\frac{1}{2}\times 6 \times 2[/tex]
[tex]Area\:of\:ABD=6\:square\units[/tex]
Therefore the are of the kite is
[tex]=2\times 6=12[/tex]
The area of the kite is 12 square units.
QUESTION 2a
The vertices of the given polygon are
[tex]P(-3,-4),Q(3,-3),R(3,-2),S(-3,2)[/tex].
We plot all the four points as shown in the diagram in the attachment.
The polygon has one pair of opposite sides parallel and has four sides.
The polygon is a quadrilateral, specifically a trap-ezoid.
QUESTION 2b
The area of the trap-ezoid can be found using the formula
[tex]Area=\frac{1}{2}(|RQ|+|PS|)\times |RU|[/tex].
We use the absolute value method to find the length of RQ,PS and RU because they are vertical and horizontal lines.
[tex]|RQ|=|-3--2|[/tex]
[tex]|RQ|=|-3+2|[/tex]
[tex]|RQ|=|-1|[/tex]
[tex]|RQ|=1[/tex]
The length of PS is
[tex]|PS|=|-4-2|[/tex]
[tex]|PS|=|-6|[/tex]
[tex]|PS|=6[/tex]
The length of RU
[tex]|RU|=|-3-3|[/tex]
[tex]|RU|=|-6|[/tex]
[tex]|RU|=6[/tex]
The area of the trap-ezoid is
[tex]Area=\frac{1}{2}(1+6)\times 6[/tex].
[tex]Area=(7)\times 3[/tex].
[tex]Area=21[/tex].
Therefore the area of the trap-ezoid is 21 square units.
QUESTION 2c
The perimeter of the trap-ezoid
[tex]=|PQ|+|RS|+|QR|+|PS|[/tex]
We use the distance formula to determine the length of RS and PQ.
[tex]|RS|=\sqrt{(3--3)^2+(-2-2)^2}[/tex]
[tex]|RS|=\sqrt{(3+3)^2+(-2-2)^2}[/tex]
[tex]|RS|=\sqrt{(6)^2+(-4)^2}[/tex]
[tex]|RS|=\sqrt{36+16}[/tex]
[tex]|RS|=\sqrt{52}[/tex]
[tex]|RS|=7.211[/tex]
We now calculate the length of PQ
[tex]|PQ|=\sqrt{(3--3)^2+(-3--4)^2}[/tex]
[tex]|PQ|=\sqrt{(3+3)^2+(-3+4)^2}[/tex]
[tex]|PQ|=\sqrt{(6)^2+(1)^2}[/tex]
[tex]|PQ|=\sqrt{36+1}[/tex]
[tex]|PQ|=\sqrt{37}[/tex]
[tex]|PQ|=6.083[/tex]
We already found that,
[tex]|PS|=6[/tex]
and
[tex]|RQ|=1[/tex]
We substitute all these values to get,
[tex]Perimeter=6+1+7.211+6.083[/tex]
[tex]Perimeter=20.294[/tex]
To the nearest tenth, the perimeter quadrilateral PQRS is 20.3 units.
QUESTION 3a
The given polygon has vertices
[tex]E(-4,1),F(-2,3),G(-2,-4)[/tex]
We plot all the three points to the polygon shown in the diagram. See attachment.
The polygon has three unequal sides, therefore it is a triangle, specifically scalene triangle.
QUESTION 3b
We can calculate the area of this triangle using the formula,
[tex]Area=\frac{1}{2} \times |FG| \times |EH|[/tex] see attachment
We can use the absolute value method to find the length of FG and EH because they are vertical or horizontal lines.
[tex]|FG|=|-4-3|[/tex]
[tex]|FG|=|-7|[/tex]
[tex]|FG|=7[/tex]
Now the length of EH is
[tex]|EH|=|-4--2|[/tex]
[tex]|EH|=|-4+2|[/tex]
[tex]|EH|=|-2|[/tex]
[tex]|EH|=2[/tex]
The area is
[tex]Area=\frac{1}{2} \times 7 \times 2[/tex]
[tex]Area=7[/tex]
Therefore the area of the triangle is 7 square units.
QUESTION 3c
The perimeter of the triangle can be found by adding the length of the three sides of the triangle.
[tex]Perimeter=|EF|+|FG|+|GE|[/tex]
The length of EF can be found using the distance formula,
[tex]|EF|=\sqrt{(-2--4)^2+(3-1)^2}[/tex]
[tex]|EF|=\sqrt{(-2+4)^2+(3-1)^2}[/tex]
[tex]|EF|=\sqrt{(2)^2+(2)^2}[/tex]
[tex]|EF|=\sqrt{4+4}[/tex]
[tex]|EF|=\sqrt{8}[/tex]
[tex]|EF|=2.828[/tex]
The length of EG can also be found using the distance formula
[tex]|EG|=\sqrt{(-4--2)^2+(1--4)^2}[/tex]
[tex]|EG|=\sqrt{(-4+2)^2+(1+4)^2}[/tex]
[tex]|EG|=\sqrt{(-2)^2+(5)^2}[/tex]
[tex]|EG|=\sqrt{4+25}[/tex]
[tex]|EG|=\sqrt{29}[/tex]
[tex]|EG|=5.385}[/tex]
We found [tex]|FG|=7[/tex]
The perimeter of the triangle is
[tex]Perimeter=5.385+7+2.828[/tex]
[tex]Perimeter=15.213[/tex]
Therefore the perimeter of the triangle is 15.2 units to the nearest tenth