In the triangle LMN the length of the side l as per given measures of side and angles is equal to 42.4 inches ( nearest tenth )
In triangle LMN,
Let us consider side length opposite to ∠L, ∠M, and ∠N be l , m , and n respectively.
Measure of side m = 450 inches
Measure of ∠M = 74°
Measure of ∠N = 41°
Sum of all the angles in a triangle is equal to 180°
m ∠M + m ∠N + m ∠L = 180°
⇒ 74° + 41° + m ∠L = 180°
⇒ m ∠L = 180° - 115°
⇒ m ∠L = 65°
Using sine law of triangle we have,
sin L / l = sin M / m = sin N / n
⇒sin L / l = sin M / m
Substitute the value we get,
⇒ sin 65° / l = sin 74° / 450
⇒ l = sin 65° × ( 450 / sin 74°)
⇒ l = 0.9063 × ( 450 / 0.9613 )
⇒ l = 42.43 inches
⇒ l = 42.4 inches ( nearest tenth )
Therefore, the measure of the side length l in a triangle LMN is equal to 42.4 inches ( nearest tenth ).
The above question is incomplete, the complete question is:
In ΔLMN, m = 450 inches, m ∠M=74° and m ∠N=41°. Find the length of l, to the nearest 10th of an inch.
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Answer: 424.3
Step-by-step explanation: n ΔLMN, m = 450 inches, m∠M=74° and
m∠N=41°. Find the length of l, to the nearest 10th of an inch.
A.A.S.→Law of Sines
Plug in. Opposite sides go together. 450 sin, 65 sin 74 ≈ 424.2742 ≈ 424.3
l=
sin74
450sin65
≈424.2742≈424.3
What will be the new position of minute hand if it starts from 1 and turns 210. Degree
The new position of minute hand if it starts from 1 and turns 210° will be at the 40 minutes mark on the clock face.
The minute hand of a clock completes a full rotation every 60 minutes, or 360°. This means that each minute on the clock face corresponds to an angle of 6 degrees. (360 divided by 60 minutes). If the minute hand starts from the 1 and turns 210 degrees, we can calculate the number of minutes it has moved by dividing 210 by 6, which gives us 35. Therefore, the new position of the minute hand will be 35 minute mark on the clock face. However, since the minute hand started at the 1, we need to add 5 minutes in the final answer.
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Parallelogram CDEF is shown below.
Find the length of the segments and the measure of the angles: CF, FE, ∠D, and ∠
Length of the segments are 11 units and 10 units and measures of the angles are 54° and 126°.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Since, CDEF is a parallelogram, opposite angles are equal.
(9y)° = (7y + 28)°
9y - 7y = 28
2y = 28
y = 14
∠C = ∠E = 9y = 126°
Sum of the angles of a quadrilateral is 360°.
∠D = ∠F = (360° - (126°×2)) / 2 = 54°
Opposite sides are also equal for a parallelogram.
2x = x + 5
2x - x = 5
x = 5
CF = DE = 2x = 10 units
CD = FE = 3x - 4 = 11 units
Hence opposite sides are equal with lengths 10 units and 11 units and opposite angles are equal with measures 54° and 126°.
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What is AE
See the attachment for the problem to be answered.
The length of the segment AE is 10 units.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
The two triangles triangle ABE and triangle CDE are similar triangles.
We know that, the ratio of segments of similar triangle are equal thus:
10 / 8 = 2x + 6 / x+ 6
10(x + 6) = 8(2x + 6)
10x + 60 = 16x + 48
60 - 48 = 16x - 10x
12 = 6x
x = 2
Substitute the value of 2 in 2x + 6:
2(2) + 6 = 10 units.
Hence, the length of the segment AE is 10 units.
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Asunta's Candle Store ordered 750 candles at a total wholesale cost of $8,660.34.
The soy candles cost $12.83 each and the specialty candles cost $10.72 each.
How many of each type of candle were ordered?
The soy candles cost $12.83 each and the specialty candles cost $10.72 each then the Asunta's Candle Store ordered 293 soy candles and 457 specialty candles.
What is system of linear equations?
Let's use the following variables:
Let x be the number of soy candlesLet y be the number of specialty candlesWe have two equations based on the information given in the problem:
x + y = 750 (the total number of candles ordered)12.83x + 10.72y = 8660.34 (the total wholesale cost of the candles)To solve for x and y, we can use a system of linear equations. One way to do this is to solve for one variable in one equation, and substitute that expression into the other equation. For example, we can solve for x in the first equation:
x + y = 750
x = 750 - y
Then we substitute this expression for x in the second equation:
12.83x + 10.72y = 8660.34
12.83(750 - y) + 10.72y = 8660.34
Simplifying and solving for y:
9622.5 - 2.11y = 8660.34
-2.11y = -962.16
y = 456.5
We can then substitute this value for y in the first equation to find x:
x + y = 750
x + 456.5 = 750
x = 293.5
Therefore, Asunta's Candle Store ordered 293 soy candles and 457 specialty candles.
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for todays free brainiest what is 6+9 here's a hint: its not 15 first to answer get brainlest
Answer:
12
Step-by-step explanation:
6 with 9 figers
Answer:
Let x be 6 and y be 9.
x + y = 6 + 9 = 15.
However, x + y does not equal 15. Hence, we can deduce that:
x + y = 15 [tex]\neq[/tex] 15.
15 does not equal 15, so if 15 is 15 and not equal to 15, we can prove that since 6 does not equal 9, 6 is 9. We can therefore conclude that we need to solve for x + x. Since we proved that something is something by not being something, 2x ix 2x but not 2x.
2x isn't 2x but is 2x, so the answer isn't the answer but is still the answer. Therefore, this question isn't a question when it is a question.
:) I am teaching you Maths in Ohio.
calculate the interest and maturity value.
Interest Rates Term
Ordinary Exact (Days)
4%
Purpose
Drum Set
Used Car
Used Dirt Bike
School Tuition for Twins
Principal
$ 900.00
1,960.00
4,800.00
9,675.00
-
10
6%
9
Interest
45 a.$
30 a.
a.
123
275
a.
Maturity
Value
b. S
b.
b.
b.
The answers are:
a. For Drum Set: Interest = $0.98, Maturity Value = $900.98b. For Used Car: Interest = $2.88, Maturity Value = $1,962.88c. For Used Dirt Bike: Interest = $5.23, Maturity Value = $4,805.23d. For School Tuition for Twins: we can't calculate the interest or maturity value without the time period.How to calculate the interest and maturity valueTo calculate the interest and maturity value, we need to use the formula:
Interest = Principal x Rate x Time
Maturity Value = Principal + Interest
Where:
Principal is the initial amount investedRate is the interest rate as a decimalTime is the time period in yearsFor the given information, we have:
Drum Set:
Principal = $900.00
Rate = 4% = 0.04
Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)
Interest = $900.00 x 0.04 x 0.0274 = $0.98
Maturity Value = $900.00 + $0.98 = $900.98
Used Car:
Principal = $1,960.00
Rate = 6% = 0.06
Time = 9/365 = 0.0247 years (assuming an exact interest calculation based on days)
Interest = $1,960.00 x 0.06 x 0.0247 = $2.88
Maturity Value = $1,960.00 + $2.88 = $1,962.88
Used Dirt Bike:
Principal = $4,800.00
Rate = 4% = 0.04
Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)
Interest = $4,800.00 x 0.04 x 0.0274 = $5.23
Maturity Value = $4,800.00 + $5.23 = $4,805.23
School Tuition for Twins:
Principal = $9,675.00
Rate = 6% = 0.06
Time = not specified
We don't have the time period for this investment, so we can't calculate the interest or maturity value without that information.
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Which transformation maps △UVW to △EFG?
The transformation that maps △UVW to △EFG is (d) (x, y) = (-2x, -2y)
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we can see that
Triangle EFG is twice the triangle UVW in side lengths
This means that
(x, y) = (2x, 2y)
The orientations are 180 degrees apart
So, we have
(x, y) = (-2x, -2y)
Hence, the transformation is (d) (x, y) = (-2x, -2y)
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please help ASAP !!!!
First, use the equation for a hemisphere. Since a sphere's equation is [tex]\frac{4}{3}\pi r^{3}[/tex], and a hemisphere is half a sphere, we can use the equation [tex]\frac{2}{3}\pi r^{3}[/tex]. We know the radius is 6 inches, and we can approximate pi as 3.14, so now let's plug in our values:
[tex]\frac{2}{3}\ (3.14) 6^{3}=\frac{2}{3} \ (3.14)(216)= \frac{2}{3}(678.16)= 452.16[/tex]
The volume of the hemisphere is about [tex]452.16 in^{3}[/tex].
The formula for the volume of a cone is [tex]\pi r^{2}\frac{h}{3}[/tex]. Again, let's plug in our values:
[tex](3.14)(36)\frac{6}{3} =(3.14)(36)(2)=(3.14)(72)=226.08[/tex]
The volume of the cone is about [tex]226.08 in^{3}[/tex].
Subtract 226.08 from 452.16 and you get 226.08.
The volume of the remaining solid will be [tex]226.08 in^{3}[/tex].
what is the mad for 21, 25, 16, 8, 16, 10
The mean absolute deviation, mad, of the given data, 21, 25, 16, 8, 16, 10, is 4.83
Calculating Mean Absolute Deviation(MAD)From the question, we are to calculate the mean absolute deviation, mad, of the given data
First, we will calculate the mean of the data
21, 25, 16, 8, 16, 10
Mean = (21 + 25 + 16 + 8 + 16 + 10)/6
Mean = 96/6
Mean = 16
Now, we will determine the positive differences of each number from the mean
Positive differences
21 5
25 10
16 0
8 8
16 0
10 6
Now, we will find the mean of the positive differences
Mean absolute deviation =(5 + 10 + 0 + 8 + 0 + 6)/6
Mean absolute deviation = 29/6
Mean absolute deviation = 4.83
Hence, the mad is 4.83
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Question 6: Question 6 E 0/2 pts Which source of bias is most relevant to the following situation: A group of first time offenders are asked to rate their court-appointed defense attorney while their case is still being argued in court. Self-interest study voluntary response bias O nonresponse bias or missing data perceived lack of anonymity loaded or leading question Question 7: Question 7 < > In a study, the data you collect is Mood on a Happy/OK/Sad scale. This data is: Quantitative Qualitative (Categorical) Question 8: Question 8 < > Does this describe an observational study or an experiment? The gender of children born in January were tallied Experiment Observational Study
Perceived lack of anonymity is the source of bias that is most relevant to the given situation.
The data collected in the study, which is Mood on a Happy/OK/Sad scale, is qualitative or categorical data.
This describes an observational study.
What is Statistics?
Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and statistical methods to extract meaningful insights from data and to draw conclusions or make decisions based on the findings.
When individuals are asked to provide feedback on a court-appointed defense attorney while their case is still being argued in court, they may feel that their responses are not anonymous and that the attorney or the court may retaliate against them if they provide negative feedback. This can lead to a perceived lack of anonymity, which can influence their responses and bias the feedback they provide. They may feel pressured to provide positive feedback or may choose not to provide any feedback at all, leading to nonresponse bias or missing data.Therefore, the perceived lack of anonymity can introduce bias into the feedback collected in this situation.Qualitative data is data that represents characteristics or qualities, rather than quantities or numbers. In this case, the mood of the respondents is being measured using categories or labels, such as Happy, OK, or Sad. This type of data cannot be easily measured or expressed in numerical terms, and therefore is considered qualitative.On the other hand, quantitative data is data that can be measured and expressed in numerical terms. This type of data is usually represented by numbers and can be analyzed using statistical methods to draw meaningful conclusions. Examples of quantitative data include age, weight, temperature, and number of hours worked.In an observational study, the researcher observes and records data on the subjects without intervening or manipulating any variables. In this case, the researcher is simply tallying the gender of children born in January, which does not involve any intervention or manipulation of variables.On the other hand, in an experiment, the researcher manipulates one or more variables to observe the effect on the outcome variable. The researcher randomly assigns participants to different groups or conditions and controls one or more variables to determine cause-and-effect relationships.Since the gender of children born in January is being observed and recorded without any intervention or manipulation of variables, it is an observational study.Learn more about Statistics click here:
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Need help with this question urgent please
Answer:
x=4.5
Step-by-step explanation:
2 [x-3]-5=7
2x - 3 - 5 =7
2x - -2 =7
7+2=9
9/2=4.5
i may be wrong <3
A. A fish is 12 m below the surface of the ocean. What is its elevation?
B. A seabird is 28 m above the surface of the ocean. What is its elevation?
C. If the bird is directly above the fish, how far apart are they?
We can say that by equation 12 metres below the ocean's surface, a fish may be found. 28 metres above the ocean's surface, a sea bird may be seen and distance between them is 40 meters.
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
We require knowledge about an object's elevation to tackle such issues.
12 metres below the ocean's surface, a fish may be found.
28 metres above the ocean's surface, a sea bird may be seen.
A fish is 12 metres below the ocean's surface.
The fish's elevation is negative since it is below sea level. Consequently, the fish's elevation is -12 metres.
B.) A marine bird flies 28 metres above the water's surface.
given that the seabird is above the water. The sea bird is 28 metres above sea level.
If the bird soars straight over the fish, (C),
If the fish and the bird are immediately above one another,
Distance between fish and bird = |(elevation of the fish)| + |(elevation of the sea bird)|
= |-12| + |28|
= 12 + 28
= 40 meters
distance between them is 40 meters.
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betermine if ABCD is a rhombus, rectangle, square or none
A(-6,-1) B(4,-6) C(2,5) D(-8,10)
Answer:
ABCD forms a rhombus
Step-by-step explanation:
When you graph it out on a graph, the points make a rhombus
Need help on these question with step by step. What are the values of x?
-1/2-4x/5 = 1/2-2x
2x-3x/2=-x+1/3
5/3-x/5=-1
-2x-4=-1/5+3x/4
-6x+1=x-1
The values of x for each equation is given below:
5/14, 2/3, 10, -39/20, 0.How to solve for thisTo find the value(s) of x, you will need to solve each equation for x.
1. -1/2 - 4x/5 = 1/2 - 2x
Add 1/2 to both sides:
-1/2 - 4x/5 + 1/2 = 1/2 - 2x + 1/2
Combine like terms on the left side:
0 - 4x/5 = 1 - 2x
Multiply both sides by 5:
0 - 4x = 5 - 10x
Add 4x and 10x to both sides:
4x + 10x = 5
Combine like terms:
14x = 5
Divide both sides by 14:
x = 5/14
2. 2x - 3x/2 = -x + 1/3
Multiply both sides by 2:
4x - 3x = -2x + 2/3
Combine like terms:
x = 2/3
3. 5/3 - x/5 = -1
Add x/5 to both sides:
5/3 - x/5 + x/5 = -1 + x/5
Combine like terms on the left side:
5/3 = -1 + x/5
Add 1 to both sides:
5/3 + 1 = -1 + x/5 + 1
Combine like terms:
6/3 = x/5
Multiply both sides by 5:
30/3 = x
Divide both sides by 3:
10 = x
4. -2x - 4 = -1/5 + 3x/4
Add 2x to both sides:
-4 = 2x - 1/5 + 3x/4
Add 1/5 to both sides:
-4 + 1/5 = 2x + 3x/4 + 1/5
Combine like terms:
-39/5 = 5x/4
Multiply both sides by 4/5:
-39/5 * 4/5 = 5x/4 * 4/5
Combine like terms:
-39/5 = 5x/4
Multiply both sides by 4:
-39 = 20x/4
Divide both sides by 20:
-39/20 = x
5. -6x + 1 = x - 1
Add 6x to both sides:
-6x + 6x + 1 = x - 1 + 6x
Combine like terms:
0 = 7x
Divide both sides by 7:
0/7 = 7x/7
Combine like terms:
0 = x
The values of x are: 5/14, 2/3, 10, -39/20, and 0.
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m<1=103. Find m<2.
Answer quick!!!
Because angles 1 and 2 are adjacent, we will see that the measure of angle 2 is 77°.
How to find the measure of angle 2?Here we know that m∠1 = 103°, and we want to find the measure of angle 2, which is an angle adjacent to angle 1.
That means that if we add their measures, then we will get a plane angle, this means that:
m∠1 + m∠2 = 180°
Then we can write:
103° + m∠2 = 180°
m∠2 = 180° - 103° = 77°
That is the measure of angle 2.
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Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answer:
$19
Step-by-step explanation:
calculate 94-18/4 = 19
suppose you drive 0.6 miles on a road so that the vertical distance changes from 0 to 150 feet. what is the angle of elevation of the road? (note there are 5280 feet in a mile)
Angle of elevation = tan-1 (150/3168).Angle of elevation = 5.0°The angle of elevation of the road is 5.0°.
In order to calculate the angle of elevation of a road, we need to know the vertical distance it has changed and the horizontal distance it has travelled. In this case, we have a vertical distance of 150 feet and a horizontal distance of 0.6 miles. Since there are 5280 feet in a mile, this is equivalent to 3168 feet .Using the formula for angle of elevation, we can calculate the angle of elevation for this road Angle of elevation = tan-1 (vertical distance/horizontal distance)Angle of elevation = tan-1 (150/3168).Angle of elevation = 5.0°Therefore, the angle of elevation of the road is 5.0°.
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convert 26kg 45g into kg
Answer:
As 1000g=1 kg ⟹1g=
1000
1
kg.
26 kg 50 g.
=26 kg+50 g
=26 kg+50(
1000
1
)kg.
=26+0.05 kg.
=26.05 kg.
Answer: 26kg, 0.045kg
Step-by-step explanation:
does -8(v+1)=2(1-4v)-9 have no solutions one solution or all numbers are solutions if its one solve for v
Answer:
No solutions
Step-by-step explanation:
[tex]-8(v+1)=2(1-4v)-9\\-8v-8=2-8v-9\\8=-7\\8\neq-7[/tex]
Hence, there are no solutions to make both sides of the equation true.
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $7,000, annual interest: 3%, interest periods: 6 , number of years: 17
The difference between the investment below and one with the same principal at the same rate compounded yearly is $18123.29.
How would you compare investments?The Payback Period is the most straightforward metric to use when contrasting investment options. Simply defined, this is the minimal amount required for you to recoup your initial investment.
compound interest, which is referred to as
[tex]A = P(1+r/n)^n×t[/tex]
Where
A = amount at the end of t years
r = interest rate.
n = periodic interval
P = principal amount deposited
Considering investment compounded annually
P = 7000
r = 3% = 3/100 = 0.03
n = 1
t = 17 years
[tex]A = 7000(1 + 0.03/1)^1× 12A = 7000(1.03)^12[/tex]
A = $9980.32
For the second investment,
n = 6
[tex]A = 7000(1 + 0.08/6)^6 × 12A = 7000(1 + 0.0133)^72A = 7000(1.0133)^72A = $18123.29[/tex]
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i need help with this one?
After dilation, the coordinates of image will be (-1,3).
What exactly is dilation?
Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:
Rotation Translation ReflectionDilation or ResizingDilation Properties
Some characteristics of forms that stay constant during dilation changes are:
The figure's angles are all the same.The midpoints of the figure's sides stay the same as the midpoint of the dilated form.The figure's parallel and perpendicular lines stay the same as the dilated figure's parallel and perpendicular lines.The visuals stay unchanged.Now,
As given dilation factor= -3
that means the image will be small and x coordinate will displace from its current value - 3 that is -1.
and y coordinate will be same that is 3
Hence,
After dilation, the coordinates of image will be (-1,3).
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ted has a part time job, he is paid £7.90 per hour,
last week he worked for 15 1/2 hours
what is ted total pay for last week
Answer: £122.45
Step-by-step explanation: 7.90*15.5
Answer: 109?
Step-by-step explanation:
the distribution of the amount of money undergraduate students spend on books for a term is right-skewed, with a mean of $400 and a standard deviation of $80. in a simple random sample of 100 undergraduate students, what is the expected value of the sample mean amount of money spent on books?
The expected value of the sample mean amount of money spent on books is equal to the population mean, which is $400.
This is a property of the sampling distribution of the sample mean, which states that the mean of all possible sample means is equal to the population mean.
In other words, if we take all possible random samples of size 100 from the population of undergraduate students, and calculate the mean amount of money spent on books for each sample, then the average of all these sample means will be $400.
The expected value of the sample mean amount of money spent on books can be calculated using the formula:
E(X) = μ
where X is the sample mean, and μ is the population mean.
In this case, the population mean is given as $400. Therefore, the expected value of the sample mean amount of money spent on books is also $400.
However, we can also calculate the standard error of the mean (SE) to get a measure of the variability of the sample mean. The formula for SE is:
[tex]SE = σ / sqrt(n)[/tex]
where σ is the population standard deviation, and n is the sample size.
Substituting the values, we get:
[tex]SE = 80 / sqrt(100) = 8[/tex]
This property is true regardless of the sample size, as long as the sample is randomly selected and independent. However, as the sample size increases, the sampling distribution of the sample mean becomes more normal and the standard error of the mean decreases, making the sample mean a more precise estimate of the population mean.
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Can someone please help me??
NEED THIS ASAP……………
……………..
The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.
Solving a function:We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'
Here we have
f(x) = - 6x + 14 and g(x) = - 2ˣ + 6
The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows
=> - 6x + 14 = - 2ˣ + 6
=> - 6x + 8 = - 2ˣ
=> - 6x + 8 = - 2ˣ
=> - 6x + 2ˣ = - 8
By using the trial and error method
At x = 2
=> - 6(2) + 2² = -8
=> - 12 + 4 = -8
Therefore,
The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.
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What’s the slope of a line perpendicular to 3x-5y=45
Answer:
-5/3.
Step-by-step explanation:
To find the slope of a line perpendicular to another line, we need to remember that the slopes of two perpendicular lines are negative reciprocals of each other. To find the slope of the line perpendicular to 3x - 5y = 45, we need to first convert it to slope-intercept form, which is y = mx + b, where m is the slope of the line.
First, isolate the y-term:
3x - 5y = 45
5y = -3x + 45
y = -(3/5)x + 9
So the slope of the original line is -3/5. The slope of the line perpendicular to it would be the negative reciprocal of this slope, which is -5/3.
Therefore, the slope of a line perpendicular to 3x - 5y = 45 is -5/3.
Answer:
3/5
Step-by-step explanation:
Quadrilateral QRST is shown. Lynn draws quadrilateral WXYZ, which is similar to quadrilateral QRST, with WX = 5 inches.
What is the measure of angle Y?
Since angle S is 65°, angle Y will also be 65°
What are similar shape ?Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.
Since angle S is 65° from the diagram shown, angle will be measured as 65°.
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What are the names of these polygons?
a)
b)
c)
D)
Answer:
b) octogon
c) irregular pentagon
d) irregular hexagon
Step-by-step explanation:
March each function formula with the corresponding transformation of the parent function y=-x^2-1. 1. Y=-x^2
y = -x²: vertical translation 1 unit upwards, y = x² + 1: vertical translation 1 unit upwards, y = -x² - 2: vertical translation 2 units downwards, y = -(x+1)² - 1: horizontal translation 1 unit to the left, reflected across the x-axis, y = -(x-1)² - 1: horizontal translation 1 unit to the right, reflected across the, y-axis, y = -x²: no transformation (same as the parent function)
The parent function is y = -x² - 1.
The function y = -x² is obtained by removing the constant term "-1" from the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = -x² is the same as the parent function, except that it does not shift downwards by 1 unit.
The function y = x² + 1 is obtained by adding a constant term "1" to the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = x² + 1 is the same as the parent function, except that it shifts upwards by 1 unit.
The function y = -x² - 2 is obtained by subtracting a constant term "2" from the parent function, which results in a vertical translation of the parent function by 2 units downwards. The graph of y = -x² - 2 is the same as the parent function, except that it shifts downwards by 2 units.
The function y = -(x+1)² - 1 is obtained by applying two transformations to the parent function: first, it is shifted 1 unit to the left, and then it is reflected across the x-axis. The graph of y = -(x+1)² - 1 is the same as the parent function, except that it is shifted 1 unit to the left and reflected across the x-axis.
The function y = -(x-1)² - 1 is obtained by applying two transformations to the parent function: first, it is shifted 1 unit to the right, and then it is reflected across the y-axis. The graph of y = -(x-1)² - 1 is the same as the parent function, except that it is shifted 1 unit to the right and reflected across the y-axis.
The function y = -x² is obtained by removing the constant term "-1" from the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = -x² is the same as the parent function, except that it does not shift downwards by 1 unit.
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Complete question provided in the image attached
A 13-ft by 27-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 384 ft^2, how wide is the walkway?
Answer:
w = 25 / 4 feet wide.
Step-by-step explanation:
Let's call the width of the walkway "w."
The area of the rectangular pool is 13 * 27 = 351 ft^2.
The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:
2 * (13 + w) * w + 2 * (27 + w) * w = 384
Expanding the equation:
2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384
Combining like terms:
2w^2 + 40w = 384
Solving for w^2:
2w^2 + 40w - 384 = 0
Using the quadratic formula:
w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)
Simplifying:
w = (-40 ± √(1600 + 3072)) / 4
w = (-40 ± √4272) / 4
w = (-40 ± 65) / 4
w = (25 / 4) or (-105 / 4)
Since w must be a positive value, w = 25 / 4 feet wide.
Answer:look it up frfr
Step-by-step explanation:
