The corresponding sides and angles of both the triangles [pre-image and the image] are congruent
what is congruency?Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent. If two angles have the same measure, they are said to be congruent. If the matching sides and angles of two triangles are the same, they are said to be congruent. In this post, we will learn more about congruence and congruent figures.The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.Hence,The corresponding sides and angles of both the triangles [pre-image and the image] are congruent
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JaRhondaLyn bought a Nissan Sentra about 4 years ago. Her car depreciates at a rate of 7% annually. The current value of her Nissan is 4 $18,701.30. What was the value of her car when she first purchased it?
PLEASE SHOW ME THE STEPS!!!
THANK YOU VERY MUCH!!!
The value of the car when she first purchased is $25001.73
Given,
current value of car =$18701.30
rate of depreciation annually=7%
time period =4 years
let the value of car when she first purchased be'x'
To find the value of car when she first purchased when it depreciated exponentially at constant rate ,use formula,
[tex]a(1-\frac{r}{100})^t=b[/tex]
Where,
a=value of car when she purchased
r=rate of depreciation annually
t=time period
b=current value of car
[tex]x(1-\frac{7}{100})^4=18701.30\\\\x(1-0.07)^4=18701.30\\\\x(0.93)^4=18701.30\\\\x(0.748)=18701.30\\\\x=\frac{18701.30}{0.748}\\\\x=25001.73[/tex]
Thus, the value of the car when she first purchased is $25001.73
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A catering company loses $110 as a result of a delay.
The 5 owners of the company must share the loss equally.
Which quotient represents each owner's share of the loss?
I know the answer but, is 110 negative or positive??
Answer: Positive
Step-by-step explanation: It would be positive because the question is asking how much money they lost. The lost a positive amount of money.
Statistics and
Probability
Jonathan earned the following
scores on his math tests:
82, 79, 85, 100, 46, 92, 88
What is his mean test score?
Could someone help quick
The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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The value of constant proportionality is 2.5. The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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Please help I will give the brainiest for the fastest answer.
Answer: Campbell to Hillsboro to Richmond to Winchester
(Note: Not taking the Washington route)
Step-by-step explanation:
Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi
12.2+5.2=17.4 mi while the other choice is only 15.7 mi
So taking the 15.7 mi option is faster
Five sisters each bought matching scarves and two pairs of socks. the scarves were priced at $15.00.if the total bill for all 5 sisters was $125.00 what was the price of one pair of socks?
Price of one pair of socks are $5.00
The total of 5 sisters each bought scarves and 2 pairs of socks.
Socks price variable defined as x.
Total scarves bought by the sisters are:
5 × 1 = 5
Total socks bought by the sisters are:
5 × 2 = 10
Equation for total bill:
$125.00 = 5 × $15.00 + 10 × x
$125.00 = $75.00 + 10x
10x = $125.00 - $75.00
10x = $50.00
x = $50.00/10
x = $5.00
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What sequence equation would represent this graph?
Equation of the given data y = 1750x -20,000 and graph of the equation is attached.
As given in the question,
Data of the table :
Year : 1 2 3 4 5
Investment : $20,000 $21,750 $23,500 $25,250 $27,000
(x₁, y₁) = ( 1, 20,000)
(x₂, y₂) = ( 2, 21,750)
Equation of the given graph is :
( y - 20,000)/ (x -1) = (21,750 - 20,000)/ (2 -1)
⇒ ( y - 20,000)/ (x -1) = 1750
⇒ y = 1,750x -18,250
Graph of the equation y = 1,750x -18,250 s represented by the graph.
Graph is attached.
Therefore, equation of the given data y = 1750x -20,000 and graph of the equation is attached.
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Salem and Eugene, Oregon, are 65 miles apart.If the distance on the map is 31 inches, find the scale of the map.
The scale on the map is of 1 mile: 0.477 inches.
From the question, we have
65 miles - 31 inches
1 mile - x inches
Applying cross multiplication:
65x = 31
x = 31/65
x=0.477
The ratio of inches on a map to feet, miles, or another unit of measurement on the ground is known as the scale.
Scale (map):
The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary across a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of scale significant in two different ways.
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Write these numbers in standard form.
a) 200000
b) 80000
c) 900 000 000
d) 10 000 000 000
Answer:
a) 2.0 x 10^5
b) 8.0 x 10^4
c) 9 x 10^9
d) 1 x 10^10
On May 1st, the temperatures at midnight in five European cities were
measured and the results were as follows.
Glasgow 2°C,
Nice 6°C,
Berlin 0°C,
London 4°C, Oslo -3°C
List the cities in order of the temperature at midnight, starting with the lowest.
Alan travels eight and two thirds kilometers to get to school. He ran one and ten elevenths kilometers and walked the rest. How many kilometers were left to walk? (4 points)
a
six and two thirty thirds kilometers
b
five and twenty five thirty thirds kilometers
c
six and twenty five thirty thirds kilometers
d
six and twenty thirty thirds kilometers
The Kilometer that Alan was left to walk is given as c six and twenty five thirty thirds kilometers
How to solve for the kilometerIn order to solve for the solution, we would have to write out the expressions in mathematical forms first
eight and two thirds kilometers = [tex]8\frac{2}{3}[/tex]
This is is the time that Alan is said to travel for him to get to school
The expression one and ten elevenths is written mathematically as [tex]1\frac{10}{11}[/tex]
This is the kilometer that he spent running.
We are to find the time that was used to walk to school.
To get this we have to subtract the kilometer that he ran from the total kilometer that he traveled.
[tex]8\frac{2}{3} - 1\frac{10}{11}[/tex]
we have to express as a mixed fraction then we would subtract
26/3 - 21/11
= 286 - 63 / 33
= 223/33
= 6.75
= 6 25/33
Hence the solution is C.
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a rectangular storage area is to be constructed along a side of a building. a security fence is required along the remaining three sides of the area. what is the maximum area that can be enclosed with 703 ft of fencing?
The largest area that may be surrounded by fencing is 61776.13 m².
A building's side will have a rectangular storage room built into it. The remaining three corners of the space need security fencing.
The maximum area is enclosed within 703ft of fencing.
Let x = width
L = length
The perimeter with 3 sides;
L + 2x = 703
L = (703 - 2x)
Let, Area = x * L
Now, replace L with (703 - 2x);
A = x * (703 - 2x)
A = 703x - 2x²
To get the max area by finding the axis of symmetry;
x = -b/2a
In this equation a = -2; b = 703
x = -703 / (2*-2)
x = 175.75m, ( width for the max area )
To get the max area, x=175.75;
A = -2(175.75²) + 703(175.75)
A = -61776.12 + 123552.25
A = 61776.13 m² is a max area
Hence, The maximum area that can be enclosed with 703ft of fencing is 61776.13 m².
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you want to obtain a sample to estimate a population proportion. based on previous evidence, you believe the population proportion is approximately 40%. you would like to be 90% confident that your estimate is within 1.5% of the true population proportion. how large of a sample size is required?
The largest sample size required is 2886.4.
Here we have to calculate how large of a sample size is required.
The formula:
(Z ∝I2/ E)² × P( 1- P)
The given data:
Margin error (E) = 1.5%
=0.015
As it is given that 90% confident that your estimate is within 1.5% of the true population proportion, therefore we have:
The level of significance(∝) = 1 - 0.90
= 0.10
The z value for the 90% confidence is 1.645
Therefore the largest of a sample size is required = ( 1.645/ 0.015)²× ( 0.4)(1- 0.4)
= 2886.4
The largest a sample size required is 2886.4
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A hat factory makes 3 types of hats. Each day, the factory makes 4,000 of each type of hat. How many hats does the factory make each day?
Answer:
The factory makes 12,000 (12k) hats each day
Step-by-step explanation:
4000
× 3
--------
12,000
Each bag of grass seed covers 55 square
yards. How many bags of grass seed will
Sasha need to purchase to cover her
backyard?
38 yd
28 yd
The area of Sasha's backyard is 1064 yard square. So the number of bags required would be 20.
What is area?
The measurement that expresses the size of a region on a plane or curved surface is called area. It's S.I. unit is m².
Main Body:
The area of Sasha's backyard = 38*28
= 1064 yd square
Now 1 bag covers 55 yd square
so, bag required for 1064 yd = 1064/55
= 19.3 approximately
Therefore the amount of required bags are 20.
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students and courses have ....... relationship: a. one to one b. one to many c. many to many d. none. mcq answer
The students and courses have one to many relationship.
A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.
In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.
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Please help me with this question. the m is 6 and the d is 8
Step-by-step explanation:
so, we have
6x² + 8xy + 8y²
and
5x² + 3xy + 16y²
we can combine only terms of the same kind (defined by the type and exponent of the used variables).
this is like adding fruit.
e.g. when we have a mixture of 3 apples, 4 oranges and 5 plums, and we add a mixture of 6 apples, 2 oranges and 3 plums - what do we get ?
we get a new mixture of
3+6 = 9 apples
4+2 = 6 oranges
5+3 = 8 plums
and exactly the same thing happens with mixing terms when adding them up.
so, we get
6+5 = 11x²
8+3 = 11xy
8+16 = 24y²
so, the result is
11x² + 11xy + 24y²
it is really that simple.
List all of the integer values that could take that would satisfy the inequality shown on the number line below.
Answer:
-2 ; -1 ; 0 ; 1
Step-by-step explanation:
the inequality is satisfied in this interval [-2.5,1].
We are searching the integers: -2 ; -1 ; 0 ; 1
All the values of x that satisfy the inequality will be;
⇒ x = - 2, - 1, 0, 1
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is given.
Now,
The solution of the inequality are given as;
⇒ x ∈ [- 2.5, 1]
But we can find the integers which satisfy the inequality.
Hence, All the values of x that satisfy the inequality will be;
⇒ x = - 2, - 1, 0, 1
Thus, All the values of x that satisfy the inequality will be;
⇒ x = - 2, - 1, 0, 1
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Estimate the measure of
Answer: 110°
Step-by-step explanation:
Looks like a bit more than 100°.
which expressions are equivalet to the one below check all that apply (7^3) * (7^x)
A. 49^3x
B. (7 * x)^3
C. 343 * 7^x
D. 7^(3+x)
E. 7^(3x)
F. 7^(3-x)
For given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
In this question, we have been given an expression (7^3) * (7^x)
We need to find expressions that are equivalent to given expression.
Consider given expression (7^3) * (7^x)
We know that 7^3 = 343
So given expression becomes, (7^3) * (7^x) = 343 * (7^x)
For given expression, the bases of the exponents are equal.
so, by the properties of exponents
(7^3) * (7^x) = 7^(3 + x)
Therefore, for given expression (7^3) * (7^x) equivalent expressions are:
343 * 7^x and 7^(3+x)
The correct options are option (C) and option (D)
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will give u brainliest!
Answer:
3.46
Step-by-step explanation:
[tex]\sqrt{21-9}[/tex]
[tex]\sqrt{12}[/tex]
3.46
Hopes this helps please mark brainliest
Would you classify the number 200 as a perfect square, a perfect cube, both, or neither? Explain.
Answer:200 is a perfect square
Step-by-step explanation:
because when divided by two it give a whole number being divided
The fastest cheetah on record is Sarah who lives at the Cincinnati Zoo in Ohio. The fastest human on record is Usain Bolt. Sarah can
run 161 meters in the same time that Usain can run 100 meters. If Sarah's speed is 6.4 meters per second faster than Usain's, how
fast do Sarah and Usain run? Round values to one decimal place.
sarah’s speed:
usains speed:
Sarah can run = 100 metres.
Speed of usain bolt.It takes several steps to convert between the two rates of meters per second and miles per hour in this task.Since the units in this case are measured in meters per second, we do not know what this translates to in miles per hour. Since the speedometers in our cars utilize these numbers, the majority of us are accustomed to thinking of speeds in terms of miles per hour; therefore, it is advantageous for students to be able to convert between miles per hour and other units of speed that naturally arise.The first approach displays all units used in the calculations but waits until the very end to perform any calculations. The second option takes a step-by-step approach and offers anacc to our question=
Usain Bolt traveled 100 meters in 9.63 seconds. 1 meter is 3.28 feet, so 100 meters is.Usain Bolt traveled 1 foot in 0.02936 seconds. 1 mile is 5280 feet, so at this speed, he would travel 1 mile in 5280×0.02936=155 seconds.learn more about speed,distance,time click here:
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Jane is counting the cars going by her house. There are 3 blue cars, 12 white cars, and 1 red car. What is the ratio of white cars to blue cars?
Answer:
4:1
Step-by-step explanation:
12÷3=4
3÷3=1
white to blue
12 : 1
how to determine the decision rule for rejecting the null hypothesis h0. round the numerical portion of your answer to two decimal places.
The p-value for a Z of 1.34 for a two-tailed test is 0.18025. Since the worth of p is greater than 0.05, we has fail to reject the null hypothesis.
What is hypothesis testing?
In hypothesis testing, we'll find to know whether we should reject or fail to reject some hypothesis.
To hold the decision, we should always compare the p-value in the test statistic to the significance level we have chosen to use the test. If the p-value is a smaller amount than the significance level, we'll reject the null hypothesis. Otherwise, we'll fail to reject the null hypothesis.
This calculations will tells you whether you ought to reject or fail to reject a null hypothesis based on the value of the test , the format of the test are going to be (one-tailed or two-tailed), and therefore the significance level you have chosen to use.
One-tailed or two-tailed ?
Value of the test statistic
1.34
Decision Rule say that : fail to reject the null hypothesis
The p-value for a Z of 1.34 for a two-tailed test is 0.18025. Since the worth of p is greater than 0.05, we has fail to reject the null hypothesis.
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in the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.4 inches, and standard deviation of 1.2 inches. what is the probability that the height of a randomly chosen child is between 50.5 and 53.7 inches? do not round until you get your your final answer, and then round to 3 decimal places.
Answer:
0.591
Step-by-step explanation:
You want the probability that a height falls between 50.5 and 53.7 when the distribution of heights is normal with mean 53.4 and standard deviation 1.2. All measurements are in inches.
ProbabilityThe area under the normal distribution curve with mean 53.4 and standard deviation 1.2 can be found using a suitable calculator. The one in the attachment shows the area between 50.5 and 53.7 is about 0.591
P(50.5 < X < 53.7) ≈ 0.591
__
Additional comment
Any spreadsheet and most graphing calculators have the necessary probability functions. Many special-purpose apps also can answer this question. A calculator answer is shown in the second attachment.
Jackson has saved $174.
He wants to purchase an electric dirt bike that costs $459.
If he saves $15 each week from the money he earns doing yard work and another $4 each week from his allowance, how many weeks will it take Jackson to save enough money to buy the bike?
Answer:
15 weeks.
Step-by-step explanation:
is y=7-3x a linear function
Answer:
no
Step-by-step explanation:
because the equation is supposed to be y=mx+b and the x comes after slope which is after m
Answer: Yes
Step-by-step explanation:
Linear functions are functions whose graph is a straight line. The function has to be in the form y=a+bx in order to be linear. Second, for any given change in x, the change in y will always be the same value.
It is given that AC ≅ AD and ∠CAB ≌ ∠DAB
Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
Step-by-step explanation:
the triangle above is an isosceles triangle,
two sides and angles are equal
AC=AD
triangle ACB=triangle ABD(because it is an isosceles triangle )
What is the SLOPE?
Which is the slope of a line that is perpendicular to the line that passes through the points (-9,-4) and (3,4)? Type your response as an integer or fraction.
Answer:
y = -1.5
Step-by-step explanation:
use the method y2 - y1 / x2 - x1
