Answer: Deep inside Earth, between the molten iron core and the thin crust at the surface, there is a solid body of rock called the mantle. When rock from the mantle melts, moves to the surface through the crust, and releases pent-up gases, volcanoes erupt. Extremely high temperatures and pressure cause the rock to melt and become liquid rock or magma. When a large body of magma has formed, it rises through the denser rock layers toward Earth's surface. Magma that has reached the surface is called lava.
Step-by-step explanation:
Andre wanted to measure the width of a creek by his camp but cannot get to the other side of the creek. Andre decided to construct two triangles to determine the width of the creek indirectly. Sighting the position of a tree on the opposite bank of the creek and placing 4 wooden pegs at point N, O, P, and Q as shown in the figure, such that MN is perpendicular to NP, NP is perpendicular to PQ, and O is the midpoint of NP. Andre claims that triangle MNO and triangle QPO are congruent.
Part A: Provide a valid argument, using geometry theorems or postulates, to validate
Andre's claim that AMNO and APQO are congruent.
Part B: Which segment should Andre measure to determine the width of the creek? Explain why.
Use the space below to answer Parts A and B of the question above. Use the CER (Claim, Evidence, Reasoning) method as a guide to your response. You may also upload a screenshot of your work
Triangles MNO and QPO are congruent.
What is congruent triangle?When two triangles are congruent, their three sides and their three angles match precisely.If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. Therefore, if two separate plane figures on a piece of paper can be cut out and then perfectly fitted up, they are congruent.It is given that
O is the midpoint of NP,
NP is perpendicular to MN, and
NP is perpendicular to PQ.
When two lines intersect at a specific point, the opposite angles formed in this situation are equal.Then ∠MNP =∠QPO=90°∠MON=∠QOP∠MOP=∠QONTherefore, Triangles MNO and QPO are congruent.
To learn more about congruent triangle refer to:
https://brainly.com/question/1675117
#SPJ1
Help pls explain!!!!!!!!!!!!
The exact value of the logarithmic expression 12 · ㏒₃ [z⁷ / (y⁵ · t²)] is equivalent by logarithm properties to -711 / 5.
How to determine the result of logarithmic expression by logarithmic properties
In this question we must determine the exact value of a logarithmic expression by means of logarithm properties, which are described below:
Logarithm of a product
㏒ (a · b) = ㏒ a + ㏒ b
Logarithm of a division
㏒ (a / b) = ㏒ a - ㏒ b
Logarithm of a power
㏒ aⁿ = n · ㏒ a
Now we proceed to determine the exact value of the expression:
12 · ㏒₃ [z⁷ / (y⁵ · t²)]
12 · [㏒₃ z⁷ - ㏒₃ (y⁵ · t²)]
12 · (㏒₃ z⁷ - ㏒₃ y⁵ - ㏒₃ t²)
12 · (7 · ㏒₃ z - 5 · ㏒₃ y - 2 · ㏒₃ t)
12 · (7 · 7.74 - 5 · 11.03 - 2 · 5.44)
-711 / 5
To learn more on logarithm properties: https://brainly.com/question/29373972
#SPJ1
Use the Rule of 72 to figure out how long it will take a $1,000 deposit to double at 7% interest. Following this rule will give you the number of years it will take for your money to double.
Using the formula of simple interest, the time period it takes to double the principal is approximately 14.29 years
Simple InterestSimple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
The formula is given as
S.I = P(1 + rt)
S.I = Simple InterestP = Principalr = rate t = timeSubstituting the values into the simple interest formula
S.I = 1000(1 + 0.07 * t)
However, we are to calculate the time it takes to double the money
2000 = 1000(1 + 0.07 * t)
2 = 1 + 0.07t
0.07t = 2 - 1
t = 1 / 0.07
t = 14.29 years
Learn more on simple interest here;
https://brainly.com/question/3575751
#SPJ1
Question What is the decibel level of the noise from a motorcycle with intensity 10-2 watts per square inch? Use a logarithmic model to solve. Provide your answer below: 100 dB
The decibel level of the noise from a motorcycle with intensity 10⁻² watts per square inch (W/in²) is equal to 50 dB.
What is sound intensity?In Science, sound intensity can be defined as a measure of the power of a sound wave per unit area. This ultimately implies that, sound intensity is a quantity that is typically be used for measuring the energy of sound and its unit of measurement is Watts per square meter (W/m²) or .
How to calculate the sound intensity level?Mathematically, sound intensity level or decibel level can be calculated by using this formula:
[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]
Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² watts per square inch (W/in²).
Since the intensity of the noise from this motorcycle is 10⁻² W/in², the decibel level (in dB) would be calculated as follows:
Decibel level, β = 10 × log(10⁻²/10⁻¹²)
Decibel level, β = 10 × log(10¹⁰)
Decibel level, β = 10 × 10
Decibel level, β = 100 dB.
Read more on sound intensity here: https://brainly.com/question/17062836
#SPJ1
Help!! Please!!!!
Helppp
Answer: 60
Step-by-step explanation:
The square root of 144 is 12.
12 = x/5
You multiply 5 on BOTH sides (make sure when you do something to one side you do it to the other)
60 = x
1. Consider this system of linear equations: -
y=4/5 x-3
y=4/5 x+1
a. Without graphing, determine how many solutions you would expect this system of equations to have. Explain your reasoning.
b. Try solving the system of equations algebraically and describe the result that you get. Does it match your prediction
The system of linear equations have no solution
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
In the problem, given the system of linear equations are
y = 4/5x - 3 ...eq(i)
y = 4/5x + 1 ...eq(ii)
a) Since there are two unknown variables(x, y) the number of solutions expected is 2.
b)
From equation (i)
y = 4/5x - 3
Put eq(i) into equ(ii)
4/5x - 3 = 4/5x + 1
0 = 4
There's no solution for x and y
In the calculation, there's no solution for both x and y because the variables in both equation are equal to one another and hence cancel out.
Learn more on system of linear equation here;
https://brainly.com/question/13729904
#SPJ1
Adnan bought
pounds of apples for $0.72 per pound and
pounds of bananas for $1.60 per pound.
a%2Bb=12 [1]
.75a%2B1.05b=10.20 [2]
Use elimination: multiply the first equation by .75 and then compare the two equations (i.e., subtract one equation from the other):
.75a%2B.75b=9
.75a%2B1.05b=10.2
.3b=1.2
3b=12
b=4
ANSWER: He bought 4 pounds of bananas, which means 8 pounds of apples.
CHECK: 8($.75)+4($1.05) = $6+$4.20 = $10.20
what is m% of n? HII PLS HELP! :0
Answer:SLOPE
Step-by-step explanation:M in a equation is slope
A train takes 16 hours to travel a distance of 35,376 km. Find the distance travelled in one hour if it covers the same distance every hour
Find all of the prime numbers between 10 and 20
Answer:
11, 13, 17, and 19!
Step-by-step explanation:
Answer:
11, 13,17 and 19
Step-by-step explanation:
prome numbers are natural numbers that are greater than 1 and not a product of two natural numbers eg 2×5 =10 so it's not a prime number 2×6 or 3×4 =12 it's not also a prime number e.t.c
T (6,2) T’ (9,3 find the scale factor was used in the dilation shown
The scale factor of the transformation is 1.5
What is the scale factor of the dilationFrom the question, we have the following parameters that can be used in our computation:
Point T (6,2) T’ (9,3)
Also, see attachment for the missing graph in the question
This means that
The scale factor of the transformation = T'/T
Substitute the known values in the above equation, so, we have the following representation
Scale factor = (9, 3)/(6, 2)
Evaluate
Scale factor = 1.5
Hence, the scale factor is 1.5
Read more about dilation at
https://brainly.com/question/3457976
#SPJ1
When Kelsey is not on the moving sidewalk, she can walk the length of the sidewalk in 3 minutes. If she stands on the sidewalk as it moves, she can travel the length in 2 minutes. If Kelsey walks on the sidewalk as it moves, how many minutes will it take her to travel the same distance? Assume she always walks at the same speed.
Answer:
1.2 minutes
Step-by-step explanation:
Kelsey moves 1/3 length per minute. The sidewalk moves 1/2 length per minute. Walking on the sidewalk, Kelsey moves (1/3+1/2) = 5/6 lengths per minute, or 6/5 minutes per length.
So it takes Kelsey 1 1/5 minutes to walk the length on the moving sidewalk.
Find the range of the function f(x)=x^2- 6x if the domain is (-7,-2, 1)
The range of the function will be;
⇒ Range = (91, 16, - 5)
What is Domain?The set of all inputs of the function is called Domain of set.
Given that;
The function is,
⇒ f (x) = x² - 6x
And, The domain = (- 7, - 2, 1)
Now,
Since, The function is,
⇒ f (x) = x² - 6x
We know that;
The range of the function gives the value of y.
Here, The domain (x) = (- 7, - 2, 1)
Put x = - 7;
⇒ f (-7 ) = (-7)² - 6 × - 7
= 49 + 42
= 91
Put x = - 2;
⇒ f (- 2) = (-2)² - 6 × - 2
= 4 + 12
= 16
Put x = 1;
⇒ f (1) = (1)² - 6 × 1
= 1 - 6
= - 5
Thus, The range = (91, 16, - 5)
Learn more about the domain visit:
https://brainly.com/question/12188600
#SPJ1
A total of 1,043 players signed up for a citywide soccer league. Each team in the league can have up to 18 members. How many teams will be needed?
Answer:
58 teams
Step-by-step explanation:
This is a division problem. There are a total of 1043 players and there is a max number of 18 members per team. 1043 divided by 18 = 57 and a remainder. Because there is a remainder you add one more team for the remaining members.
Answer: 57.9
Step-by-step explanation:
Based on the given conditions, formulate: 1043 / 18
Evaluate the equation/expression: 57.9444
get the result: 57.9444
After rounding: 57.9
Answer: 57.9
......... i need help past due
Answer:
3,2,4
The fastest restaurant for service is the second choice. It takes 2 minutes to service each customer.
Step-by-step explanation:
27/9 = 3 minutes per customer
8/4 = 2 minutes per customer
32/8 = 4 minutes per customer
rate?
2) James Bond took 4.5 minutes to complete a Grand Prix circuit when driving at an average speed.
97 mph. How long would it take to complete one circuit driving at a speed of 112 mph.
Answer: 30 meters
Step-by-step explanation:
A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second.
Factor the expression below. x 2 − 12 x + 36 A. (x + 6)(x + 6) B. (x − 6)(x + 6) C. 6(x2 − x + 6) D. (x − 6)(x − 6)
Answer:
D) = (x - 6 )(x - 6)
Step-by-step explanation:
x^2 - 12x + 36
= x^2 -6x -6x + 36
= x(x - 6) -6(x - 6)
= (x - 6 )(x - 6)
Answer:
[tex]\boxed{\tt (x-6)(x-6)}[/tex]
Step-by-step explanation:
To factor x²−12x+36 we need to find two numbers that add together to get -12 and multiply together to get 36:-
Let's try -6 and -6:-
[tex]\tt -6+-6 = -12[/tex]
[tex]\tt -6\times -6 = 36[/tex]
[tex]\tt (x-6)(x-6)[/tex]
_________________
Hope this helps!
Have a nice day!
its a 50 50 question both A and B are wrong please help
Answer: d/ 30x +200 <= 1400
Step-by-step explanation:
It can't be the first two answers because the truck can only hold 1400
So it must be < or = 1400
It says that she loaded computers for 200 pounds and x number of books, 30 pounds each.
So the equation is 30x + 200 <=1400
PLEASE HELP SOON I NEED TO LEAVE TO MY LAB
Answer: 10: 6 is
ration add them 16
Step-by-step explanation:
(a) The area of a rectangular parking lot is 6279 m². If the length of the parking lot is 91 m, what is its width? Width of the parking lot:
Answer:
The width of the parking is 69 meters
Step-by-step explanation:
Rectangle area = L*W
6279 = 91*W
Widht = 6279/91
W = 69 m
A competition mark is worked out by doubling the sum of the middle four scores, then adding the average of the top and bottom scores.
Martha scores: 7 7 6 8 5 9
What is her competition mark?
The required competition mark is given as 60, as of the given condition.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60
Thus, the competition mark is 60.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
This Venn Diagram represents the Science subjects studied by students.
Students
Physics
Biology
CO
6
7
6
2
3
8
4
5
Chemistry
What is the probability that a student, chosen at random,
studies Physics or Chemistry or both?
The probability that a student chosen at random studies physics and chemistry or both is 35/41 = 0.85
What is the probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
What is the formula for probability?The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.
The Venn diagram shows:
There are 2 students studying both biology and physics.
Six students study biology and chemistry together.
There are 4 students who study physics and chemistry.
There are 5 students who just study physics.
There are 7 students who just study biology.
There are 8 students who just study chemistry.
There are 6 students that study none.
As a result, there are a total of 41 students, which is equal to 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 students.
There are 21 students who study chemistry, which is equal to 8 + 6 + 3 + 4 students.
The number of students that studies physics is = 14
The number of students that studies chemistry is = 21
Probability = number of favorable outcomes / total number of outcomes
To learn more about probability visit:
https://brainly.com/question/30034780
#SPJ1
use rounding or compatible numbers to estimate each product or quotient.
5 x 2 3/5
a. about 10
b. about 10 3/5
c. about 15
d. about 20
im guessing b
Answer: c.
Step-by-step explanation:
I used rounding: 3 is closer to 2 3/5 than 2 and 5 * 3 is 15, so the answer is about 15.
A movie streaming service charges a set fee for
membership each month, plus an additional fee
for the number of movies streamed each
month. If 2 movies are streamed, the cost is
$14 per month, however if 6 movies are
streamed, the cost is $20. Write an equation to
model the cost, y, based on the number of
movies streamed x.
The equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.
What is a linear equation in one variable?
The linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For the first case:
If 2 movies are streamed, the cost is $14 per month
So the cost = number of movies * cost per movie
y = 2*x
14 = 2x
For the second case:
If 6 movies are streamed, the cost is $20 per month
So the cost = number of movies * cost per movie
y = 6*x
20 = 6x
Hence the equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.
To learn more about linear equations in one variable, visit:
brainly.com/question/85774
#SPJ1
Are the two functions inverse of one another ?
Graph y=-2x+5y=−2x+5y, equals, minus, 2, x, plus, 5. NEED HELP PLS
The graph for the linear equation y = -2x + 5 is plotted and shown in the image attached below.
How to Graph an Equation?If we are given an equation of a line that is expressed in slope-intercept form as y = mx + b, it means that the graph will have a slope = rise / run = the value of m, while it would cut across the y-axis at b, that is the y-intercept.
Given the equation in slope-intercept form as y = -2x + 5, it means that the graph will have a slope that has a ratio of the rise to the run as -2, while the line will intercept the y-axis at y = 5.
Therefore, the graph in the image attached below shows the equation, y = -2x + 5.
Learn more about the graph of linear equation on:
https://brainly.com/question/4074386
#SPJ1
ANSWER ASAP PLEASE
Little Susie is standing at the top of a lighthouse. She is 96 feet above the ocean. She tosses a ball into the air. The height, h, of the ball after x seconds is given by
h = -16t + 64t + 96 . (there is no t^2 on my question but i think -16 is meant to be t^2 because it's quadratics... PLEASE help...)
a. What is the ball's height after 0.5 seconds?
b. How many seconds does it take to reach maximum height? What is the maximum height?
c. How many seconds does it take for the ball to land in the ocean?
Use complete sentences when explaining or justifying your solutions. Neatly show all algebra work, and upload any pictures or files that support your work.
When t=2+√110/4, the ball will be 50 feet height above the ocean.
What is height?Height is the measurement of someone or something from the top to toe or the base to head.height always refers to something is mesured either its high or low.
As per the given question
Because h=-16t^2+64t+96
So when h = 50
It means -16t^2+64t+96 =50
-16t^2+64+46=0
8t^2-32t-23=0
{∆=b^2-4ac,x= -b+√∆/2a}
So, ∆=(-32)^-4×8×(-23)=1760>0
So t =2- √110/4 <0
Thus tha answer is t = 2+√110/4
To know more about height click-
https://brainly.com/question/73194
#SPJ1
Pleas help me find the equation for this chart please
Answer: y = 1/12x
Step-by-step explanation:
(24, 2)
(12, 1)
find slope (y2 - y1) / (x2 - x1)
2 - 1 / 24 - 12
1 / 12
find y intercept
y = mx + b
1 = 1/12(12) + b
1 = 1 + b
b = 0
y = 1/12x + 0
y = 1/12x
Adam currently run about 20 mile per week, and he want to increae hi weekly mileage by 10%. How many mile will Adam run per week? He will run mile per week
which function has the same domain as
[tex]y = 2 \sqrt{x} [/tex]
Both have a domain of [tex][0, \infty)[/tex] which in other words, is the set of nonnegative real numbers. I recommend using a graphing calculator to verify both of these functions have the same domain.
The reason for this is because we need to avoid negative numbers under the square root. So it leads us to [tex]\text{x} \ge 0[/tex]