This is a two part question just need help figuring out what exactly it is I need to mark up for the first section up on top and also on the second part of it I need help figuring out if both triangles are congruent and if they are need help stating the congruency
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Given the triangles CDE and JLM
For the triangles we have the following:
1) CD = JL
2) CE = JM
3) DE = LM
So, there 3 pairs of congruent sides
So, the triangles are congrurent by S.S.S ( Side-Side-Side) postulate
C is corresponding to J
D is corresponding to L
E is corresponding to M
So,
[tex]\triangle\text{CDE}\cong\triangle\text{JLM}[/tex]For marking the triangles, see the following figure:
Related Questions
Decide whether the relation defines y as a function of x. Give the domain.y=√(x-3)Is the equation a function?1)No 2)Yes
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By definition, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
In our equation, for each x value we have exactly one corresponding y-value, therefore, the following equation
[tex]y=\sqrt{x-3}[/tex]is indeed a function of x. The domain is the set of all possible inputs. The argument of a square root can't be negative, therefore, we have the following restriction:
[tex]x-3\geq0\implies x\geq3[/tex]In interval notation, our domain is:
[tex]\lbrack3,\infty)[/tex]PLEASE ANSWER QUICK I WILL GIVE BRAINLIEST IF ITS RIGHT
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Step-by-step explanation:
try this option, all the details are in the attachment.
look at the Pentagonal figure with the dimensions shown in the diagram what is area of the figure ?.
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Area of Pentagonal figure = 368 feet²
Explanation:To find the area of the Pentagonal figure, we need to divide the shape into figures we can easily find their areas.
The Pentagonal figure comprise of a triangle and a rectangle.
Area Pentagonal figure = Area of triangle + Area of rectangle
Area of triangle = 1/2 base × height
base = 5 ft, height = 12 ft
Area = 1/2 × 5 × 12 = 30
Area of triangle = 30 feet²
Area of rectangle = length × width
length = 26ft, with = 13 ft
Area of rectangle = 26 × 13
Area of rectangle = 338 feet²
Area of Pentagonal figure = 30 feet² + 338 feet²
Area of Pentagonal figure = 368 feet²
Which reason justifies step 2 of the proof?
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JG is common line between both triangle so both triangle's are equal .
What is known as a triangle?
A triangle is a polygon with three vertices and three sides. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to 180 degrees in total.Given, ∠FJG = ∠HGJ
FG ║ JH
In ΔFJG & ΔGJH
∠FJG = ∠HGJ ( Given)
FG ║ JF ( Given)
∴ JG = JG ( Common )
∵ ΔFJG = ΔGJH
JG is common line between both triangle so both triangle's are equal .
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Need ASAP, explanation if you can :)
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The probability of the complement of event E is 0.56,
How to find the probability?For any event A, we define the complement of A as:
[tex]A^c[/tex]
Where the complement refers to all the elements in the sample space that are not A, and the relation between the probabilities is:
P([tex]A^c[/tex]) = 1 - P(A).
In this case, we have an event E and we know that:
P(E) = 0.44
Then the probability of the complement will be:
P([tex]E^c[/tex]) = 1 - P(E) = 1 - 0.44 = 0.56
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3/3 - 9/10
make sure the answer is a fraction pls
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Step-by-step explanation:
look for the LCM of 3 and 10 and since it does not have a LCM you will multiply the two variables. After multiplying, you will then divide your answer by the denominator and multiply it with the denominator
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if you borrow 500 dollars for 4 years at a 6 percent intrest rate how musch will you pay all together
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Altogether, you will pay $631.24 if the interest is compounded at the end of every year for 4 years or $620 if it is based on simple interest.
What is the difference between compound interest and simple interest?Compound interest accumulates the interest and adds it to the principal for calculating subsequent interest.
On the other hand, simple interest does not accumulate the interest to add to the principal before computing the next year's.
N (# of periods) = 4 years
I/Y (Interest per year) = 6%
PV (Present Value) = $500
PMT (Periodic Payment) = $0
Results:
FV = $631.24
Total Interest = $131.24
Simple interest = $120 ($500 x 6% x 4)
Future value at simple interest = $620 ($500 + $120)
Thus, depending on how interest is calculated, you will repay between $620 and $631.24.
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The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= .2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012,to 2004, and so on, and y is in millions of students(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is 16.9 millions. This is answered. (Type an integer or decimal rounded to the nearest tenth as needed.)(b) Use the model to determine the year in which enrollment is projected to reach 17 million.(Round down to the nearest year)2008. This is answered(c) they are quite close. This is answered. This is the one i need help with part D.(d) The enrollment in Fall 1993 was 14.3 million. The model here is based on data from 2003 to 2012. If you were to use the model for 1993, what would the enrollment be?
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Solution
We are given the relation
[tex]y=0.2145x+15.79[/tex]A dog breeder has 14 puppies for sale, of which 7 are yellow Labrador retrievers. If 2 puppies are selected at random,
determine the probability they are all yellow Labrador retrievers. Assume that selection is to be done without
replacement.
Set up the problem as if it were to be solved, but do not solve.
P(2 yellow Labradors selected) =
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The total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the randomly selected dogs are yellow Labradors:
Probability formula: P(E) = Favourable events/Total eventsProbability in 1st selection:
P(E) = Favourable events/Total eventsP(E) = 7/14P(E) = 1/2Probability in 2nd selection: Without replacement
P(E) = Favourable events/Total eventsP(E) = 6/13Total Probability: 1/2 × 6/13 = 6/26 ⇒ 3/13
Therefore, the total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.
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Using the indicated slopes of lines and L1 and L2, determine whether the lines are parallel, perpendicular, or neither.Assume that the lines are not the same. M1= 4/7, M₂= -7/4 Choose the correct answer below. a)Parallel b)Perpendicular c)Neither
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the lines are perpendicular (option B)
Explanation:
For L1 and L2 to be parallel, their slopes must be equal
That is: M1 = M₂
The given slope: M1= 4/7, M₂= -7/4
Hence, they are not parallel as they are not equal
For the lines to be perpendicular, one of the the slope will be the negative reciprocal of the other one:
M1 = 4/7
Reciprocal of M1 = 7/4
Reciprocal means inverse. For
Negative Reciprocal of M1 = -7/4
This is equal to M₂
Hence, the lines are perpendicular (option B)
We want to fill a basin 3m wide, 5m long and 1m deep using atap with a flow rate of 2m^3 / h.1 °) How long does it take to fill the basin?2 °) Express the flow rate of the tap in L / min. We will round to the hundredth.
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Part 1
First we have to find the volume of the basin. We must multiply the dimensions to do so.
V= (3)(5)(1) m^3
V= 15 m^3
If the tap has a flow of 2 m^3 per hour it means that it would take 7.5 hours to fill the basin. ( Dividing 15 m^3 by 2 m^3/h)
The answer of the first part is 7.5 hours.
Part 2
To express the flow rate in L/min we would have to multiply 2m^3 by 1000 ( Since 1000 L= 1 m^3) and then divide the result by 60 minutes ( Since 1 hour has 60 minutes). Doing so, we have:
[tex]2\frac{m^3}{h}\cdot\frac{1000\text{ L}}{1m^3}\cdot\frac{1h}{60\text{ min}}=33.33\text{ L/min}[/tex]The answer of part 2 is 33.33 L/min (Rounding to the hundredth).
given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=590(1.061)^x
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Given the exponential function:
[tex]y=590(1.061)^x[/tex]Let's determine if the exponential function represents growth or decay.
Take the exponential function:
[tex]y=a(b)^x[/tex]Where b is the base.
• If the base of an exponential function is greater than one, the exponential function represents growth
• If the base of an exponential function is between 0 and 1, the function represents a decay function.
Here, the base of the exponential function, b is 1.061 which is greater than 1, the function represents a growth function.
SInce it is represents a growth function, let's determine the percentage rate of increase.
The general formula for exponential growth is:
[tex]y=a(1+r)^x[/tex]Where r is the growth rate.
Thus, we have:
[tex]\begin{gathered} y=590(1+(1-1.061)^x \\ \\ y=590(1+0.061)^x \end{gathered}[/tex]The growth rate, r is = 0.061
The percentage rate of increase is:
[tex]\text{percentage rate of increase = }0.061\ast100=6.1\text{\%}[/tex]Therefore, the percentage rate of increase is 6.1%
ANSWER:
The function represents growth
Percentage rate of increase = 6.1%
Solve 3x + 23 + x = 7.
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The answer is x = - 4. The value refers to the worth of each digit in relation to its position in the number.
What is meant by values?We compute it by multiplying the digit's place and face values. Values are benchmarks or ideals against which we judge actions, people, things, or situations. Many people support values such as beauty, honesty, justice, peace, and generosity.
Seven has the numerical value of 7. In the place value chart, seven is in the one column. The number seven can be written as 7% or 7%. By moving the decimal point two places to the left, you can convert 7% to a decimal. 5 has a place value of 500 and is in the hundreds.
Therefore,
Solving 3x + 23 + x = 7
Combine like terms
3x + 23 + x = 7
4x + 23 = 7
Subtract 23 from both sides4x +23 = 7
4x+ 23 - 23 = 7-23
4x = -16
Divide both sides by the same factor4x = -16
4x/ 4 = -16/4
Cancel terms that are in both the numerator and denominator4x/ 4 = -16/4
x = -16/4
Divide the numbersx = -16/4
x = -4
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Proving the Congruent Supplements Theorem
Given <1 and <2 are suplements
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By using the supplementary relations and the fact that angle 2 is congruent to angle 3, we will get that:
∠1 ≈ ∠4
How to prove this?Here we know that:
∠1 and ∠2 are supplements.∠3 and ∠4 are supplements.∠2 ≈ ∠3With the first two, we can write the equations:
∠1 + ∠2 = 180°
∠3 + ∠4 = 180°
Both equations have the same value in the right, then we can write:
∠1 + ∠2 = ∠3 + ∠4
Now, we know that ∠2 ≈ ∠3, then we can rewrite the equation as:
∠1 + ∠2 = ∠3 + ∠4
∠1 + ∠2 - ∠3 = ∠4
And ∠2 - ∠3 ≈ 0, then:
∠1 + ∠2 - ∠3 = ∠4
∠1 + 0 ≈ ∠4
∠1 ≈ ∠4
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Suppose 4.2 liters of water come out of the faucet each minute. For how many minutes was the faucet on if 52.5 liters of water came out
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Answer:
12.5 minutes
Explanation:
Given that:
Number of liters of water come out of the faucet each minute = 4.2 liters
To find the time(in minutes) required for 52.5 liters of water to come out from the faucet.
Number of minutes required = Quantity of water come out from the faucet/ Number of liters of water come out per minute
[tex]\begin{gathered} =\frac{52.5}{4.2} \\ =12.5\text{ minutes} \end{gathered}[/tex]12.5 minutes required for 52.5 litres of water to come out from the faucet.
A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118.Find a linear equation for the monthly cost of the cell plan as a function of x, the number of monthly minutes used. Type your answer in slope intercept form (y=mx+b) without any spaces between the characters. The function is C(x)=AnswerUse your equation to find the total monthly cost if 687 minutes are used. The cost will be $Answer
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The cost for 410 minutes is $71.50 and cost for 720 minutes is $118.
Determine the equation for (410,71.50) and (720,118).
[tex]\begin{gathered} y-71.50=\frac{118-71.50}{720-410}(x-410) \\ y-71.50=\frac{46.5}{310}(x-410) \\ y=0.15(x-410)+71.50 \\ y=0.15x-61.5+71.50 \\ =0.15x+10 \end{gathered}[/tex]So function is C(x) = 0.15x + 10.
Substitute 687 for x in equation to determine the cost for 687 minutes.
[tex]\begin{gathered} C(687)=0.15\cdot687+10 \\ =103.05+10 \\ =113.05 \end{gathered}[/tex]So monthly cost if 687 minutes used is 113.05.
hello please help me out with this and provide an explanation. thanks
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We are given the following equation that models the height of a ball:
[tex]h(t)=15t-4.9t^2[/tex]part a) is to find the distance traveled by the ball in the interval [1,3], to do that we replace the values of t=1 and t=2 in the equation, like this
[tex]\begin{gathered} h(1)=15(1)-4.9(1)^2=11 \\ h(3)=15(3)-4.9(3)^{2^{}}=0.9 \end{gathered}[/tex]The total distance is the difference between the two points, that is:
[tex]h(1)-h(3)=11-0.9=10.1[/tex]Coordinate of point x on the coordinate plane for each situation
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The horizontal distance between points A and B is:
[tex]x_B-x_A=2-(-5)=7[/tex]1/5 of this distance is:
[tex]\frac{1}{5}\cdot7=\frac{7}{5}[/tex]Then, the x-coordinate of point X is:
[tex]x_X=x_A+\frac{7}{5}=-5+\frac{7}{5}=-3.6[/tex]The vertical distance between points A and B is:
[tex]y_B-y_A=9-(-5)=14[/tex]1/5 of this distance is:
[tex]\frac{1}{5}\cdot14=\frac{14}{5}[/tex]Then, the y-coordinate of point X is:
[tex]y_X=y_A+\frac{14}{5}=-5+\frac{14}{5}=-2.2[/tex]Finally, the coordinates of X are (-3.6, -2.2)
One month Lamar rented 3 movies and 8 video games for a total of $58. The next month he rented 5 movies and 2 video games for a total of $23. Find the rental cost for each movie and each video game.
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Let x represent the rental cost for each movie.
Let y represent the rental cost for each video game.
From the information given,
Lamar rented 3 movies and 8 video games for a total of $58. The equation representing this scenario would be
3x + 8y = 58
Also,
he rented 5 movies and 2 video games for a total of $23. The equation representing this scenario would be
5x + 2y = 23
We would solve both equations by applying the method of elimination. To elimimate x, we ould multiply the first equation by 5 and the second equation by 3. We have
15x + 40y = 290
15x + 6y = 69
Subtracting the second equation from the first, we have
15x - 15x + 40y - 6y = 290 - 69
34y = 221
Dividing both sides by 34,
34y/34 = 221/34
y = 6.5
Substituting y = 6.5 into 5x + 2y = 23, we have
5x + 2(6.5) = 23
5x - 13 = 23
Adding 13 to both sides, we have
5x - 13 + 13 = 23 - 13
5x = 10
x = 10/5
x = 2
Rental cost for each movie = $2
Rental cost for reach video = $6.5
given triangle ABC with C= 90 degree is given and B = 30 degree, then we have to calculate the value of sin 30 degree
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Answer:
do you have picture if the question so I can help I
13 over 11 equals 4 over uWhat is the proportion of u?
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Margaret has a monthly clothes budget of 50 she maps the Amy of money she spends each month to the number of items of clothing she buys what constraints are there on the domain
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It is said that the graph plotted is the money spent to the number of items of clothing bought.
It will look like this:
The domain by definition is the set of inputs.
The constraint on the domain here is the monthly spending cannot be greater than $50.
So the domain will be [0,50] in dollars on the x-axis.
A babysitter charges $8 per hour for each job sheworks and charges a travel allowance of $10 for eachjob. Which of the following equations gives the numberof hours worked h, the babysitter worked at a job forwhich she charged $78?a) 18h = 78b) 10h + 8 = 78c) 8h + 10 = 78d) 8(10 + h) = 78
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A babysitter charges $8 per hour for each job she works, then after h hours, she charges 8h dollars
Also, she charges a travel allowance of $10 for each job, then after h hours in one job, she charges 8h + 10 dollars
If she charged $78, then the equation is:
c) 8h + 10 = 78
Exit Ticket in the triangles below, name all corresponding parts AND find "y. A ABD ACDB. Find y. A 7 y B D 3y + 20 C С tudents, write your response! Pear Deck In
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Given that triangle ABD= traingle CDB then;
side AB= DC and
side AD = BC
thus equate side AB and DC as;
7y =3y +20
collect like terms as;
7y-3y = 20
4y = 20
y= 20/4 = 5
help me please, i need help
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Considering the equation for the circumference of a circle, we have that:
1.
Circle D has a Circumference/Diameter ratio of 3.14.Circle E has a Circumference of 628.Circle F has a Diameter of 300.2. The circumference of the circle is given as follows:
Circumference = 3.14 x 10 in = 31.4 in.
What is the circumference of a circle?Considering a circle of diameter d, it's circumference is given by the diameter d multiplied by the number π, as follows:
C = πd.
Hence, for Circle D, as for any circle, the ratio is given as follows:
C/d = π = 3.14 (rounding π).
For Circle E, the circumference is given as follows:
C = 200 x 3.14 = 628
For Circle F, the diameter is given as follows:
3.14d = 942.5
d = 942.5/3.14
d = 300.
For item 2, the diameter is of 10 inches, hence the circumference of the circle is found applying the rule as follows:
Circumference = 3.14 x 10 in = 31.4 in.
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You want to be able to withdraw $30,000 from your account each year for 30 years after you retire.You expect to retire in 20 years.If your account earns 6% interest, how much will you need to deposit each year until retirement to achieve your retirementgoals?$Round your answer to the nearest cent.Question Help: Video Post to forum
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In this case we are making deposits each year in out account. This will be compounded at a 6% interest.
After 20 years of working and making deposits, the principal accumulated has to be able to give $30,000 per year for 30 years.
We can start with the principal. We assume that during retirement, the account yield 6% interest from the capital still in the account.
Then, we can calculate this principal as the present value of an annuity with payments PMT = $30,000, rate of interest r = 0.06 and n = 30 years.
The calculation is:
[tex]\begin{gathered} PV=PMT\cdot\frac{1-(1+r)^{-n}}{r} \\ PV=30000\cdot\frac{1-(1.06)^{-30}}{0.06} \\ PV\approx30000\cdot\frac{1-0.17411}{0.06} \\ PV\approx30000\cdot\frac{0.82589}{0.06} \\ PV\approx30000\cdot13.7648 \\ PV\approx412944.93 \end{gathered}[/tex]Now we know the amount of capital that has to be accumulated with the deposits.
This value is the future value of an annuity of n = 20 years at a rate r = 0.06.
But now, we need to calculate the yearly deposit D.
We can calculate it as:
[tex]\begin{gathered} D=\frac{FV\cdot r}{(1+r)^n-1} \\ D=\frac{412944.93\cdot0.06}{(1.06)^{20}-1} \\ D\approx\frac{24776.70}{3.207-1} \\ D\approx\frac{24776.70}{2.207} \\ D\approx11225.73 \end{gathered}[/tex]Answer: the yearly deposit has to be $11,225.73.
7. The relationship between the latitude Lof a city in the Northern Hemisphere and its average annual temperature Tis modeled by the function T = -0.68L + 89.5. The slope of this linear function means (A) That temperature at the equator would be 89.5°. (B) For every degree increase in latitude, the average annual temperature increases by 89.5º. (C) For every degree increase in latitude, the average annual temperature increases by 0.68 (D) For every degree increase in latitude the average annual temperature decreases by 0.68º.
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We are given the following function that models the temperature T as a function of the latitude L:
T = - 0.68 L + 89.5
We see that the temperature is in fact a linear function of slope -0.68 degrees/latitude.
Since the latitude of the Equator is 0 degrees, then, the equation tells us that the temperature at the Equator is:
T = - 0.68 (0) + 89.5 = 89.5 degrees of annual temperature. But this is NOT related to the slope.
The other two statements (B and C) are not correct,
The last statement D is correct, since for every degree increase in latitude, there is an annual decrease of temperature by 0.68 degrees, and this is what the slope expresses.
Please select answer D.
Y = 3 x -3+4 graphed
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The graph for y = 3x + 1 is given below
What is coordinate plane ?Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.
Y = 3 x -3+4
y = 3x +1
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what is 1,988 times 130
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5,9460.
1) Let's multiply 1988 by 30:
Notice that we multiplied the units, 0 x 1988 and then 3 x 1988 and then we added both numbers.
2) Hence, 1,988x 30 is equal to 5,9460.
Vector v is shown in the graph.Which are the magnitude and direction of v? Round the answers to the thousandths place.
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Step 1:
First, draw and label the vertical and the horizontal units of the vector.
Step 2:
Write the column vector
[tex]v\text{ = }\begin{bmatrix}{4} & \\ {8} & {}\end{bmatrix}[/tex]Step 3:
[tex]\begin{gathered} \text{Magnitude of v = }\sqrt[]{v^2_x+v^2_y} \\ v_x\text{ = 8 } \\ v_y\text{ = }4 \\ \text{Magnitude of v = }\sqrt[]{8^2+4^2} \\ =\text{ }\sqrt[]{64\text{ + 16}} \\ =\text{ }\sqrt[]{80} \\ MagnitudeofV=\text{ 8.944} \end{gathered}[/tex]Step 4:
Find the direction using the formula below
[tex]\begin{gathered} tan\theta\text{ = }\frac{v_y}{v_x} \\ \tan \theta\text{ = }\frac{4}{8} \\ \tan \theta\text{ = 0.5} \\ \theta=tan^{-1}(0.5) \\ \theta\text{ = }26.565 \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \text{Magnitude = 8.944} \\ \text{Direction = 26.565} \\ \mleft\Vert v\mleft\Vert\text{ = 8.944 , }\theta\text{ = 26.565}\mright?\mright? \end{gathered}[/tex]