Answers
Answer: 130 Tbsp.
Step-by-step explanation:
Related Questions
Help me with this please?
Answers
A surveyor standing on a horizontal plain can see a volcano in the distance. The angle of elevation
to the top of the volcano is 23°. If the surveyor moves 750 m closer, the angle of elevation is
now 37°. Determine the height of the volcano above the plain.
Answers
Height of the volcano = 729
The elevation angle to the peak of the volcano is 23 degrees.
The surveyor goes 750 feet closer to the volcano, and the angle of elevation now equals 37 degrees.
It forms an ABC triangle.
Point A = the volcano's summit
Point B is the volcano's lowest point.
Point C = height of 23 degrees to the volcano
Point D = going 750 towards the volcano and establishing a 37-degree elevation angle
BD = ?
DC = 750
Tan 23 degrees AB/BC
Tan 23 degrees AB = BC
Tan 37 degrees AB/BD
Tan 37 degrees = AB
23 degrees BC Tan 37 degrees BD Tan
(BD +750)
BD (.7536-.4245) = 318.356
BD = 967.35
Height of the volcano = 729
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-1,9)
(0.-2)
(4,7)
Answers
The coordinates of the fourth vertex of the parallelogram are given as follows:
How to obtain the coordinates of the fourth vertex?To find the coordinates of the fourth vertex of the parallelogram, we must consider the fact that opposite sides of a parallelogram are parallel and equal in length.
Considering the side formed by the vertices (-1,9) and (4,7), the difference of the coordinates is given as follows:
x-coordinate: -1 - 4 = -5.y-coordinate: 9 - 7 = 2.Hence, compared to the vertex (0,-2), the coordinates of the remaining vertex are given as follows:
x-coordinate: subtract 5 from 0 -> 0 -5 = -5.y-coordinate: add 2 to -2 -> -2 + 2 = 0.Then the coordinates of the fourth vertex are given as follows:
(-5,0).
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There were 432 million mobile users in India last year and it went up to 540 million mobile users this year. Find the percent increase.
Answers
The Percent increase in the number of mobile users in India from last year to this year is 25%.
The percent increase in the number of mobile users in India from last year to this year, we can use the following formula:
Percent Increase = (New Value - Old Value) / Old Value * 100
Given that there were 432 million mobile users last year and it increased to 540 million mobile users this year, we can substitute these values into the formula:
Percent Increase = (540 million - 432 million) / 432 million * 100
Simplifying the calculation:
Percent Increase = 108 million / 432 million * 100
Percent Increase = 0.25 * 100
Percent Increase = 25
Therefore, the percent increase in the number of mobile users in India from last year to this year is 25%.
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what is the next two term in the sequence 6, 10, 14, 16
Answers
Answer:
Next two terms of the sequence is 20 and 24.Step-by-step explanation:
The arithmetic sequence is 6, 10, 14 , 16
First term (a) = 6
Subtract the first term from the second term:
10 - 6 = 4Subtract the second term form the third term:
14 - 10 = 4Subtract the third term from the Fourth term:
16 - 14 = 4Here, You will notice that each time you move from one number to the next one it increases by four. So, the difference between one and the next term is four.
So,
Next two terms are:
⟶ 16 + 4 = 20
⟶ 20 + 4 = 24
Hence,
Next two terms of the sequence is 20 and 24.Step-by-step explanation:
Given Sequence :- 6 , 10 , 14 , 16 To find :- Next 2 terms in the sequenceSolution :-
D( common difference ) = a2 - a1
D = 10 – 6
D = 4
Next two terms ,
16 + D ; 16 + 4 = 20
20 + D ; 20 + 4 = 24
Find the y-intercepect of the graph of: y-6=3/8x also find the slope
Answers
We are given the following equation:
\(y-6=\frac{3}{8}x\)The general form of a line equation in slope-intercept form is the following:
\(y=mx+b\)Where "m" is the slope and "b" is the y-intercept.
To take the given equation to the slope-intercept form we need to add 6 to both sides:
\(\begin{gathered} y-6+6=\frac{3}{8}x+6 \\ y=\frac{3}{8}x+6 \end{gathered}\)Therefore, the y-intercept is 6, and the slope is 3/8.
what is the length x of a side of the small inner square?
Answers
The length x of a side of the small inner square can be determined using the properties of similar triangles.
To find the length x, we can set up a proportion between the small inner square and the larger outer square.
Let's denote the side length of the small inner square as s and the side length of the larger outer square as S.
Since the small inner square is completely contained within the larger outer square, the ratio of their side lengths will be the same as the ratio of their corresponding sides.
Therefore, we can set up the following proportion:
s / S = x / (x + 10)
Here, the x + 10 represents the side length of the larger outer square, as it is 10 units longer than the side length of the small inner square.
To solve for x, we can cross-multiply the proportion:
s * (x + 10) = x * S
Expanding the equation:
sx + 10s = xS
Rearranging the equation to isolate x:
sx - xS = -10s
Factoring out the common term x:
x(s - S) = -10s
Dividing both sides by (s - S):
x = -10s / (s - S)
Now, we have an expression for x in terms of s and S.
It's important to note that the given information is insufficient to find the exact value of x without additional measurements or equations. The value of x will depend on the specific dimensions of the small inner square and the larger outer square.
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Write the \( 2^{\text {nd }} \) degree Taylor polynomial for \( f(x)=\ln x \) about \( x=2 \).
Answers
The second degree Taylor polynomial for f(x) = ln x about x = 2 is given by:T2(x) = f(2) + f′(2)(x − 2) + f′′(2)(x − 2)2/2where f′(x) = 1/x and f′′(x) = −1/x2. Therefore, we have:T2(x) = ln 2 + 1/2(x − 2) − 1/8(x − 2)2.
A Taylor polynomial is a polynomial approximation of a function f(x) that is centred at some point c. Specifically, the nth degree Taylor polynomial for f(x) about c is defined as:Tn(x) = f(c) + f′(c)(x − c) + f′′(c)(x − c)2/2 + ⋯ + f(n)(c)(x − c)n/n!where f(n)(c) is the nth derivative of f evaluated at c.
The Taylor polynomial provides an approximation of f(x) that becomes more accurate as n increases.
The second degree Taylor polynomial for f(x) = ln x about x = 2 is given by:
T2(x) = f(2) + f′(2)(x − 2) + f′′(2)(x − 2)2/2
where f′(x) = 1/x and f′′(x) = −1/x2. Therefore, we have:T2(x) = ln 2 + 1/2(x − 2) − 1/8(x − 2)2Thus, the second degree Taylor polynomial for f(x) = ln x about x = 2 is given by ln 2 + 1/2(x − 2) − 1/8(x − 2)2.
The second degree Taylor polynomial for f(x) = ln x about x = 2 is given by ln 2 + 1/2(x − 2) − 1/8(x − 2)2.
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Let F=⟨xy,y
2
⟩ and let C be the closed curve x
2
+6x+y
2
−2y=26, oriented counterclockwise. (a) Calculate ∫
C
F
⋅
T
ds. (b) Is it possible to determine - using only the result from Part (a), and without doing any further computations - whether F is or is not conservative? Explain. 4. Extra Credit. (10 Points.) Consider a rectangle (in the plane) whose lower left corner is (a,c) and upper right corner is (b,d). For any vector field
F
=⟨P(x,y),Q(x,y)), we can define its "divergence"(written "div
F
") to be: div
F
=
∂x
∂P
+
∂y
∂Q
, (as usual, assume P and Q are differentiable). Note that this is a 2-variable function. Show that the integral of div
F
over the interior of the rectangle is equal to the flux of
F
across the boundary of the rectangle (oriented counterclockwise). How is this, in spirit, a version of the Fundamental Theorem of Calculus?
Answers
Since 0 ≠ 1, there is no solution for C. This means that the given initial value problem does not have a unique solution.
To solve the given initial value problem, we'll use the Laplace transform method. The Laplace transform of the given differential equation is:
s^2Y(s) + 6sY(s) + 34Y(s) = e^(-πs)
Applying the initial conditions y(0) = 1 and y'(0) = 0, we get:
Y(0) = 1/s
sY(0) = 0
Simplifying the equation, we have:
(s^2 + 6s + 34)Y(s) = e^(-πs) + (1/s)
Now, let's find the Laplace transform of the right-hand side:
L[e^(-πs)] = 1/(s + π)
L[1/s] = 1/s
Substituting these Laplace transforms into the equation, we get:
(s^2 + 6s + 34)Y(s) = 1/(s + π) + 1/s
To solve for Y(s), we'll rearrange the equation:
Y(s) = [1/(s + π) + 1/s] / (s^2 + 6s + 34)
Now, we can use partial fraction decomposition to express Y(s) in terms of simpler fractions:
Y(s) = A/(s + π) + B/s + C/(s^2 + 6s + 34)
Multiplying through by the denominator, we have:
1 = A(s^2 + 6s + 34) + B(s + π) + C(s^2 + 6s + 34)
Expanding and collecting like terms, we get:
1 = (A + C)s^2 + (6A + B + 6C)s + (34A + πB + 34C)
Comparing the coefficients of each power of s, we can solve for A, B, and C:
A + C = 0 (coefficients of s^2)
6A + B + 6C = 0 (coefficients of s)
34A + πB + 34C = 1 (constant term)
From the first equation, we have C = -A. Substituting this into the second equation, we get:
6A + B - 6A = 0
B = 0
Substituting A = -C into the third equation, we have:
34(-C) + π(0) + 34C = 1
34C - 34C = 1
0 = 1
Since 0 ≠ 1, there is no solution for C. This means that the given initial value problem does not have a unique solution. Please double-check the problem statement and initial conditions provided.
If you have any additional information or corrections, please provide them so that I can assist you further.
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Which function represents g(x), a reflection of f(x) = 6
H
across the y-axis?
) = −6(-3)*
O g(x) =
©_g(x) = −6[³]*
O g(x) = 6(3)*
O g(x) = 6(3)*
Answers
Step-by-step explanation:
Answer: D.) g(x) = 6(3)^{-x}g(x)=6(3)
−x
Step-by-step explanation: We are given an exponential function f(x).
g(x) is an exponential function that is being reflected across y-axis.
According to rules of transformations y=f(-x).
That is variable x is being multiplied by a negative sign.
In the given options g(x) = 6(3)^{-x}g(x)=6(3)
−x
, the variable x is being multiplied by a negative sign.
Therefore, correct option is D option.
The function represents the reflection is g(x) = 6 (3\()^{-x\).
What is Function?A function is a type of rule that produces one output for a single input.
a mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependent variable (the dependent variable).
We are given an exponential function f(x).
Also, g(x) is an exponential function that is being reflected across y-axis.
Here the rule of transformations y=f(-x).
The x-coordinate and y-coordinate swap places and the signs if you deflect across the line y = -x.
Reflections: By multiplying by -1, a function can be mirrored about an axis.
So, the function after reflection is
g(x) = 6 (3\()^{-x\)
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Let Ω=[0,1]. Let S={[0,1]}∪{[ 2 n+1
1
, 2 n
1
):n=0,1,2,…}. Let F S
be the σ-field generated by S, that is, the smallest σ-field that contains S. Which of the following events belong to F S
and why (or why not) (a) {0}, (b) {1}, (c) {1/2}, (d) {1/3}, (e) {0,1}, (f) (1/4,1],(g)[0,1/2],(h)[1/4,1),(i)(0,1/2)?
Answers
The events (a) {0}, (c) {1/2}, (d) {1/3}, (f) (1/4,1], and (i) (0,1/2) belong to the σ-field F_S. The events (b) {1}, (e) {0,1}, (g) [0,1/2], and (h) [1/4,1) do not belong to F_S.
In this case, the σ-field F_S is generated by the collection of sets S, which consists of the interval [0,1] and half-open intervals of the form [2n+1/2^n, 2n/2^n] where n is a non-negative integer.
(a) {0}: This event belongs to F_S because it is a subset of the interval [0,1] in S.
(b) {1}: This event does not belong to F_S because it is not a subset of any interval in S.
(c) {1/2}: This event belongs to F_S because it is a subset of the interval [0,1] in S.
(d) {1/3}: This event belongs to F_S because it is a subset of the interval [0,1] in S.
(e) {0,1}: This event does not belong to F_S because it is not a subset of any interval in S.
(f) (1/4,1]: This event belongs to F_S because it is a union of intervals [2n+1/2^n, 2n/2^n] in S.
(g) [0,1/2]: This event does not belong to F_S because it is not a union of intervals in S.
(h) [1/4,1): This event does not belong to F_S because it is not a union of intervals in S.
(i) (0,1/2): This event belongs to F_S because it is a union of intervals [2n+1/2^n, 2n/2^n] in S.
In summary, events (a), (c), (d), (f), and (i) belong to the σ-field F_S because they are subsets or unions of subsets of the intervals in S. Events (b), (e), (g), and (h) do not belong to F_S because they are not formed by subsets or unions of subsets of the intervals in S.
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The equation d=11t models the distance a mouse can travel when it runs at top speed. In the equation,d is the distance in feet and t is the time in second. Complete the table WILL GIVE BRAINLIEST FOR CORRECT ANSWER
Answers
Answer:
t = 0 , d = 0
t = 2, d = 22
t= 4, d = 44
t = 6, d = 66
Step-by-step explanation:
Here, given the equation that relates the time in seconds to the distance in feet, we want to complete the given table
From the equation, we have that d = 11t
This mean that by multiplying the time by 11, we get the distance
Thus, we have that ;
when t = 0
d = 11 * 0 = 0
when t = 2
d = 11 * 2 = 22 ft
when t = 4
d = 11 * 4 = 44 ft
when t = 6
d = 11 * 6 = 66 ft
Given the equation that models the proportional relationship, the missing values in the table are: 0, 22, 44, and 66.
Equation of a Proportional RelationshipEquation that models a proportional relationship between two variables, "t" and "d" can be expressed as: d = kt.k is the constant of proportionality.Given:
d = 11t
Find the corresponding values of d by plugging in the given values of t:
When t = 0,
d = 11(0) = 0
When t = 2,
d = 11(2) = 22
When t = 4,
d = 11(4) = 44
When t = 6,
d = 11(4) = 66.
Therefore, given the equation that models the proportional relationship, the missing values in the table are: 0, 22, 44, and 66.
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An experienced bricklayer can work twice as fast as an apprentice bricklayer. after the bricklayers work together on a job for 4 hours, the experienced bricklayer quits. the apprentice requires 14 more hours to finish the job. how long would it take the experienced bricklayer, working alone, to do the job?
Answers
The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.
As given in the question,
Let the time taken by experienced bricklayer be 't' hours
Then time taken by apprentice bricklayer be '2t' hours
Time to complete 1 complete work is
Experienced bricklayer worked for 4 hours
Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours
Required equation to complete 1 work is :
( 4/x) + ( 18 /2x) = 1
⇒( 8 + 18 )/ 2x = 1
⇒26/2 = x
⇒ x = 13 hours
Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.
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The table displays the mean name length for seven samples of students.what can be said about the variation between the sample means?the variation between the sample means is small. the variation between the sample means is large. the variation shows that the values are far apart. the variation cannot be used to make predictions.
Answers
The variation between the sample means is small.
The variation between the sample means provides insight into the spread or dispersion of the data. In this case, if the variation between the sample means is small, it indicates that the mean name lengths across the seven samples are relatively similar and close together. This suggests that there is not much variability or difference in the average name lengths among the different samples of students. Therefore, the variation between the sample means is small, indicating a certain level of consistency in the mean name length across the samples.
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GIVING BRAINLIST PLEASE HELP (see picture above) !!!!
Answers
Answer:
Im sure that the answer is c
Answer:
C) 1 and 2
Plzzzz give me Brainliest!!!!!
I need help ASAP please
Answers
Answer:
true
Step-by-step explanation:
65-(-35)=100
in other words 65+35=100
Answer:
the answer is true
Step-by-step explanation:
Please help!!
ABCD ~ FECG
z = [ ? ]
![Please help!!ABCD ~ FECGz = [ ? ]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/qT2vTcNjvzyFst4D4t2TDInlhXvNz3d3.jpeg)
Answers
Answer:
Z=80°
Step-by-step explanation:
If the quadrilaterals are similar, they have the same angle measurements.
∠Z=∠F
Since all interior angles of a quadrilateral add up to 360°, we can subtract ∠E, ∠C, and ∠G's measurements from 360°.
360°-100°-120°-60°=∠Z
260°-120°-60°=∠Z
140°-60°=∠Z
80°=∠Z
∠Z=80°
The measure of angle z in quadrilateral ABCD is 80 degrees.
When two quadrilaterals are similar?Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same.
What is the sum of the interior angles of a quadrilateral?The sum of interior angles of a quadrilateral is 360 degrees.
According to the given question
We have two quadrilaterals ABCD and FECG, and they are similar to each other.
Since, ABCD and FECG are similar to each other.
Therefore, ∠BAD = ∠EFG
⇒ z = ∠EFG
Now, In quadrilateral FECG
We have
∠EFG + 100 + 120 + 60 = 360
( sum of the interior angles of a quadrilateral is 360 degrees)
⇒ ∠EFG + 280 = 360
⇒ ∠EFG = 360 - 280
⇒ ∠EFG = 80 degrees
Therefore, z = 80 degrees
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if x is a continuous random variable with the uniform distribution u(5.5,20.5), what is p(x<8)?
Answers
The correct value of p(x<8) is 1.875.
Define probabilityTo determine how probable something is gonna occur, use probability. It is a number between 0 and 1, where 0 denotes the absence of a possibility and 1 denotes the existence of one. By dividing the number of favorable outcomes by the entire number of potential possibilities, the probability of an occurrence is determined.
To find the probability that is greater than 8, we need to integrate this probability density function from 5.5 to 20.5:
P(X < 8) = ∫[5.5,20.5] f(x) dx
= ∫[5.5,20.5] (1/8) dx
= [x/8] from 5.5 to 20.5
= (20.5/8) - (5.5/8)
= 15/8
= 1.875.
Therefore, the correct probability is 1.875.
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A box of 8 crayons costs $0.96. How much does each crayon cost? At the unit price, how much would a box of 30 crayons cost.
Answers
Answer:
the price of 30 crayons is 3.6$.
Step-by-step explanation:
Given that
price of 8 crayons is 0.96$
so the price of 1 crayon is
0.96÷8=0.12$
now we have to find the cost of 30
crayons
we know that price of 1 crayon is 0.12$
so the price of 30 crayons is
0.12$×30= 3.6$.
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Answer:Given the cost of a box of 8 crayons, the cost of each crayon is 0.12. a box containing 30 cryaons will cost 3.6
Step-by-step explanation: Given that ,
box of 8 crayons cost=0.96 cost of each crayon=? cost of each 30 crayon box=? first, we determine the cost of abox with 30 crayons . 8 crayons cost 0.96. 1crayon cost x. x=0.96÷8=0.12 Next we determine the cost of abox with 30 crayons . 1 cryaon cost 0.12 30 crayons cost y y=30×0.12 y=3.6
given a sample of size of 36 how large does the population standard deviation have to be in order for the standard error to be
Answers
If you provide the desired standard error value, I can help you calculate the corresponding population standard deviation.
The standard error is a measure of the variability or uncertainty of a sample mean. It is calculated by dividing the population standard deviation by the square root of the sample size. Therefore, if we want the standard error to be smaller, the population standard deviation should be larger.
To determine how large the population standard deviation needs to be, we need to specify a desired standard error value. Without that information, it is not possible to provide a specific answer. The relationship between the population standard deviation and the standard error is inversely proportional, so as the population standard deviation increases, the standard error decreases.
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On a city map, 1/3 inch represents 2 city blocks in real life. If city Hall and the library are 4 1/3 inches apart on the map, what is the actual distance between the two?
Answers
26 city blocks
Explanation:\(\begin{gathered} \frac{1}{3}\text{inch = 2 city blocks} \\ \\ \text{the distance betw}een\text{ the city hall and Library = 4}\frac{1}{3}inches\text{ apart} \end{gathered}\)\(\begin{gathered} \text{let the actual distance betw}een\text{ the city hall and Library = y} \\ \frac{1}{3}inch\text{ = 2 city blocks} \\ 4\frac{1}{3}inch\text{ = y} \\ \text{cross multiply:} \\ y(\frac{1}{3})\text{ = 2(4}\frac{1}{3}) \end{gathered}\)\(\begin{gathered} \frac{y}{3}\text{ = 2(}\frac{13}{3}) \\ \frac{y}{3}\text{ =(}\frac{26}{3}) \\ 3(y)\text{ = 26(3)} \\ y\text{ = }\frac{26(3)}{3} \\ y\text{ = 26} \end{gathered}\)Hence, the actual distnce between the city Hall and library is 26 city blocks apart
The circumference of a circular garden is 106.76 feet. What is the radius of the garden?
Answers
Answer:
16.9659
Step-by-step explanation:
you have to divide the circumference by pi, then you will have your diameter, after that you have to divide the diameter by 2 to get your radius
a. One half of 1% converted to a decimal is __________
b. 0.184 rounded to the hundredths place is ____________
c. The first three place values to the right of the decimal point are the tenths place, the hundredths place, and the thousandths place __________
Answers
a. One-half of 1% converted to a decimal is 0.005
b. 0.184 rounded to the hundredths place is 0.18
c. The thousandth place is the third digit after the decimal point.
We are given that;
To convert one-half of 1%
Number= 0.184
Now,
a. One-half of 1% converted to a decimal is 0.005.
b. 0.184 rounded to the hundredth place is 0.18.
c. The first three place values to the right of the decimal point are the tenths place (the first digit after the decimal point), the hundredths place (the second digit after the decimal point), and the thousandths place (the third digit after the decimal point).
Therefore, by algebra, the answer will be the third digit after the decimal point.
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Stacy sold half of her doll collection and then bought 12 more. She now has 28 dolls. With how many did she begin?
Answers
(Minus 12)
x/2 = 16
(Multiply by 2)
x = 32
32 dolls
Out of 80 workers surveyed at a company, 17 walk to work.
a. What is the experimental probability that a randomly selected worker at that company walks to work?
b. Predict about how many of the 3100 workers at the company walk to work.
Answers
Answer:
a. The experimental probability of a randomly selected worker at the company walking to work is the ratio of the number of workers who walk to work to the total number of workers surveyed.
Experimental probability = Number of workers who walk to work / Total number of workers surveyed
Experimental probability = 17/80
Experimental probability = 0.2125 or 21.25%
Therefore, the experimental probability that a randomly selected worker at the company walks to work is approximately 21.25%.
b. To predict about how many of the 3100 workers at the company walk to work, we can use the experimental probability we calculated in part (a).
If 21.25% of the 80 workers surveyed walk to work, we can estimate that approximately 21.25% of the entire workforce walks to work as well.
Number of workers who walk to work = 0.2125 x 3100
Number of workers who walk to work = 659.75
Therefore, we can predict that about 660 workers out of the 3100 workers at the company walk to work.
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I need help pls help me
Answers
The quadratic equation y = x² - 2x - 3 have ordered points at (0, -3), (2, -3), (-2, 5) and (4, 5)
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Quadratic equation is a polynomial that have a degree of 2. The degree of a polynomial is the highest exponent of the variables.
Given that:
y = x² - 2x - 3
When x = 0; y = (0)² - 2(0) - 3 = -3
When x = 2; y = (2)² - 2(2) - 3 = -3
When x = -2; y = (-2)² - 2(-2) - 3 = 5
When x = 4; y = (4)² - 2(4) - 3 = 5
The equation y = x² - 2x - 3 is a quadratic equation.
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List the key features of this exponential function: y= -2(1/3)x
Increasing or decreasing? Y-int? Common ratio? Horizontal asymptote?
What would happen if the equation was: y= -2(1/3)x -1?
Answers
The given exponential function is y = \(-2(1/3)^x\). Its key features include being a decreasing function, a y-intercept of -2, a common ratio of 1/3, and a horizontal asymptote at y = 0.
The given exponential function, y = \(-2(1/3)^x\), is decreasing because the base (1/3) is between 0 and 1. As x increases, the exponent becomes more negative, causing the value of the function to decrease. The y-intercept occurs when x = 0, resulting in y = \(-2(1/3)^0\) = -2(1) = -2.
The common ratio of the exponential function is 1/3, which means that each successive term is multiplied by 1/3. This ratio determines the rate of decay or decrease in the function.
The function does not have a horizontal asymptote. As x approaches negative infinity, the function approaches zero, but it never actually reaches it. This is because the exponential function continuously approaches but never reaches zero as x approaches negative infinity.
If the equation were y = \(-2(1/3)^x\) - 1, the only difference would be the subtraction of 1 after evaluating the exponential term. This would shift the entire function downward by one unit. The y-intercept would then be at
y = -2 - 1 = -3, and the function would still exhibit the same decreasing behavior with a common ratio of 1/3. The presence of the constant term -1 affects the vertical position of the graph but does not change the other key features of the exponential function.
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Two balls have their centers 3.0 m apart. One ball has a mass of 2.7 kg. The other has a mass of 4.5 kg. What is the gravitational force between them? Assume G = 6.67 x 10 -11 N m?/kg? -11 a. 1.3 x 10 N -10 b. 9.0 x 10 N -10 c. 2.7 x 10 N -11 d. 9.0 x 10 N 46. If you weigh 440.0 N on Earth's surface, how much would you weigh on the planet Mars? Mars has a mass of 6.42 x 1023 kg and a radius of 3.40 x 10ºr m. a. 557 N b. 235 N C. 1.4 x 10°N d. 166 N
Answers
Your weight on Mars would be approximately 166 N (option d).
To calculate the gravitational force between two objects, we can use the formula:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67 x 10^(-11) N m^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between their centers.
In the given scenario:
Mass of the first ball (m1) = 2.7 kg
Mass of the second ball (m2) = 4.5 kg
Distance between their centers (r) = 3.0 m
Gravitational constant (G) = 6.67 x 10^(-11) N m^2/kg^2
Substituting these values into the formula, we can calculate the gravitational force:
F = (6.67 x 10^(-11) N m^2/kg^2 * 2.7 kg * 4.5 kg) / (3.0 m)^2
F ≈ 1.35 x 10^(-10) N
Therefore, the gravitational force between the two balls is approximately 1.35 x 10^(-10) N (option a).
For the second question:
To calculate your weight on Mars, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Here:
Mass of Mars (m2) = 6.42 x 10^23 kg
Radius of Mars (r) = 3.40 x 10^6 m
Your weight on Earth's surface (F) = 440.0 N
We need to solve for m1, which represents your mass on Earth. Rearranging the formula:
m1 = (F * r^2) / (G * m2)
Substituting the given values:
m1 = (440.0 N * (3.40 x 10^6 m)^2) / (6.67 x 10^(-11) N m^2/kg^2 * 6.42 x 10^23 kg)
m1 ≈ 4.65 x 10^22 kg
Finally, we can calculate your weight on Mars using the formula:
Weight on Mars = (G * m1 * m2) / r^2
Weight on Mars = (6.67 x 10^(-11) N m^2/kg^2 * 4.65 x 10^22 kg * 6.42 x 10^23 kg) / (3.40 x 10^6 m)^2
Weight on Mars ≈ 166 N
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Please answer 5-8 ASAP I will give brainliest
Answers
Answer:
5. m∠A = 26
6. m∠D = 118
7. m∠E = 43
8. m∠H = 85
Step-by-step explanation: complementary= 90 supplementary = 180
5. (2x - 8) + (4x +4) = 90
6x - 12 = 90
6x = 102
x = 17
m∠A = 2x - 8
m∠A = 2(17) - 8 = 26
6. (2x + 18) + (5x + 8) = 180
7x + 26 = 180
7x = 154
x = 22
m∠D = 5x + 8
m∠D = 5(22) + 8 = 118
7. (2x + 15) + (3x + 5) = 90
5x + 20 = 90
5x = 70
x = 14
m∠E = 2x + 15
m∠E = 2(14) + 15 = 43
8. (5x - 20) + (4x + 7 ) = 180
9x - 27 = 180
9x = 207
x = 23
m∠H = 4x -7
m∠H = 4(23) - 7 = 85
triangle abc is congruent to triangle def . which statement must be true about the triangles? ab=ef ab=de m∠a=m∠e m∠b=m∠d
Answers
If triangle ABC is congruent to triangle DEF, then all four statements must be true about the triangles: AB=EF, AB=DE, ∠A=∠E, and ∠B=∠D.
When two triangles are congruent, it means that they have the same size and shape. To show that triangle ABC is congruent to triangle DEF, we need to show that all corresponding sides and angles are equal.
The statement AB=EF means that the lengths of side AB and EF are equal. Similarly, the statement AB=DE means that the lengths of side AB and DE are equal.
The statement ∠A=∠E means that angle A in triangle ABC is equal to angle E in triangle DEF. Similarly, the statement ∠B=∠D means that angle B in triangle ABC is equal to angle D in triangle DEF.
By the Congruence of Triangles axiom (SSS), if two triangles have three sides of equal length, then they are congruent. Therefore, since AB=EF, AB=DE, and ∠A=∠E, we can conclude that triangle ABC is congruent to triangle DEF.
Furthermore, since ∠B=∠D, we can conclude that all four statements (AB=EF, AB=DE, ∠A=∠E, and ∠B=∠D) must be true in this case.
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