Answers
To solve this problem, we need to calculate the midpoint for the two points in each option and check if it corresponds to the given midpoint (-3,4).
Calculating the midpoint for the two points of option A.
We have the points:
\((-1,7)and(2,3)\)We label the coordinates as follows:
\(\begin{gathered} x_1=-1 \\ y_1=7 \\ x_2=2 \\ y_2=3 \end{gathered}\)And use the midpoint formula:
\((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)Substituting our values:
\((\frac{-1_{}+2_{}}{2},\frac{7_{}+3_{}}{2})\)Solving the operations:
\((\frac{1_{}}{2},\frac{10_{}}{2})=(\frac{1_{}}{2},5)\)Since the midpoint is not the one given by the problem, this option is not correct.
Calculating the midpoint for the two points of option B.
We have the points:
\((-2,6)and(-4,2)\)We follow the same procedure, label the coordinates:
\(\begin{gathered} x_1=-2 \\ y_1=6 \\ x_2=-4 \\ y_2=2 \end{gathered}\)And use the midpoint formula:
\(\begin{gathered} (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{Substituting our values} \\ (\frac{-2-4_{}}{2},\frac{6+2_{}}{2}) \\ \text{Solving the operations:} \\ (\frac{-6}{2},\frac{8}{2}) \\ (-3,4) \end{gathered}\)The midpoint for the two points in option B is (-3,4) which is the midpoint given by the problem.
Answer: B (-2,6) and (-4,2)
Related Questions
Use this pattern when a binomial
can be written as the square of
one number minus the square of
another number.
4x² - 49 = (2x-7)(2x + 7)
a² + 2ab + b² = (a + b)²
Answers
The square of a binomial, when the binomials are subtracted, is defined as follows:
(a - b)² = a² - 2ab + b².
How to obtain the square of a binomial?When the two binomials are added, the square is given as follows:
(a + b)².
Expanding the square, we have that:
(a + b)² = (a + b) x (a + b).
(a + b)² = a² + ab + ab + b².
(a + b)² = a² + 2ab + b².
Which is the result presented in this problem.
Now, when the binomial has a minus sign, involving a subtraction, the pattern is obtained as follows:
(a - b)² = (a - b) x (a - b).
(a - b)² = a² - ab - ab + b².
(a - b)² = a² - 2ab + b².
More can be learned about the square of a binomial at https://brainly.com/question/12336181
#SPJ1
what are prime factors of 1000?
Answers
Answer:
1,2,4,5,8,10,20,25,40,50,10,125,200,250,500,1000
Step-by-step explanation:
prime factorization is
1000=2*2*2*5*5*5
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
For more questions on prime number
https://brainly.com/question/145452
#SPJ8
The height of a cylinder is 9.5 cm. The diameter is 1.5 cm longer than the height. Which is closest to the volume of the cylinder?
Answers
Answer:
853.8cm^3
Step-by-step explanation:
\(h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3\)
Evan collected 45 trading cards. Jessica collected 3 times as many trading cards as Evan. How many trading cards did Jessica collect?
Answers
Answer: Jessica collected 135 trading cards.
Step-by-step explanation:
you just multiply 45 by 3 to get 135
What is the difference between a subset and a proper subset?
{5,8}
{2,5,8}
is {5,8} a subset of {2,5,8} ? yes or no ? Please explain.
Answers
Answer:
it is a subset
Step-by-step explanation:
since elementsof these set{5,8} can found in {2,5,8}
if 50% is 30 what is 25%
Answers
Answer:
15
Step-by-step explanation:
25% is half of 50%, half of 30 is 15
A college student is taking two courses. The probability she passes the first course is 0.7. The probability she passes the second course is 0.67. The probability she passes at least one of the courses is 0.79. Give your answer to four decimal places. a. What is the probability she passes both courses
Answers
Answer:
0.58 = 58% probability she passes both courses
Step-by-step explanation:
We have two events, A and B.
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
In which:
\(P(A \cup B)\) is the probability of at least one of these events happening.
P(A) is the probability of A happening.
P(B) is the probability of B happening.
\(P(A \cap B)\) is the probability of both happening.
In this question:
Event A: Passes the first course.
Event B: Passes the second course.
The probability she passes the first course is 0.7.
This means that \(P(A) = 0.7\)
The probability she passes the second course is 0.67.
This means that \(P(B) = 0.67\)
The probability she passes at least one of the courses is 0.79.
This means that \(P(A \cup B) = 0.79\)
What is the probability she passes both courses
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
\(0.79 = 0.70 + 0.67 - P(A \cap B)\)
\(P(A \cap B) = 0.58\)
0.58 = 58% probability she passes both courses
Prove: If a matrix A is not square, then either the row vectors or the column vectors of A are linearly dependent.
Answers
As we have proven that if a matrix A is not square, then either its row vectors or column vectors are linearly dependent.
To prove this statement, we need to use the definition of linear independence.
Now, suppose that A is a matrix that is not square. This means that A has more columns than rows or more rows than columns.
To show that either the row vectors or the column vectors of A are linearly dependent, we can use the fact that the solutions of Ax = 0 form a vector space. This vector space is called the null space or kernel of A, denoted by null(A).
Suppose, for the sake of contradiction, that both the row vectors and column vectors of A are linearly independent. This means that null(A) has dimension zero, which implies that the only solution of Ax = 0 is the zero vector.
However, we know that there are infinitely many solutions, which contradicts our assumption. Therefore, either the row vectors or the column vectors of A must be linearly dependent.
To know more about matrix here
https://brainly.com/question/28180105
#SPJ4
Ava answered 95/100 questions correctly on the test, and therefore believes to have earned a 95%. Is Ava correct?
Answers
Answer:
yes
Step-by-step explanation:
idk how to explain but, yes
Answer:
Yes, Ava is correct because percentages are always going to be out of one hundred.
In this case, there is 95%, which can also be put as .95 or 95 over 100 (95/100).
Hope this helps!
A, B and C are collinear points. B is between A and C. AB=12 BC=18 AC=3x Find X.
Answers
Answer:
\(x =10\)
Step-by-step explanation:
Given
\(AB = 12\)
\(BC = 18\)
\(AC = 3x\)
Required
Solve for x
Since B is in between both points, then:
\(AC = AB + BC\)
This gives
\(3x = 12 + 18\)
\(3x = 30\)
Divide by 3
\(x =10\)
Krista designs quilts using the pattern shown. The table of values describes the shaded area of the pattern in square units, y, as a function of the length of a side,X units. Which equation describes this relationship?
Answers
The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²
Modeling relationship between two variablesSide length, x = 1,3,4,5,8
Shaded Area, y = 0.5, 4.5, 8, 12.5, 32
The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c
a = 0.5 ; b = 0 ; c = 0
Therefore, the quadratic function can be written as y = 0.5x²
Learn more on quadratic functions ; https://brainly.com/question/1214333
#SPJ1
PLZ HELP ASAP!!! IM STUCK!!!!!
Answers
Answer:
78.5% chanceStep-by-step explanation:
the area of the square is 16 in² and the area of the circle is 12.566in² divide the two to get 0.7852 and then multipy by 100 to make a percentage
Can someone help me?
Answers
Answer:
e
..
..................................
find the equation of the tangents to the curve (9x^(2)+16y)/(2)=26 that are parallel to 4.5x-4y=0.5
Answers
The equation is 9x + 8y = 81.
Given the function h(x)=120−7.5x−−−−−−−−−√
, find h(2.8)
.
9.95
14.95
17.75
49.50
Answers
The value of h at 2.8 would be equivalent to 9.95 rather than 14.95, 17,75, or 49.50.
How to find the value of h?We are given the function h(x)=\(\sqrt{120-7.5x}\) which describes the value of h having as reference different x values. Based on this principle, to find out the value of h in 2.8 all we need to do is to replace x for 2.8 and calculate the result as it follows:
\(h = \sqrt{120 - 7.5x\\\)
\(h =\sqrt{120 - 7.5x}\)
\(h= \sqrt{120-7.5 2.8}\)
\(h =\sqrt{120 -21}\)
\(h= \sqrt{99}\)
\(h = 9.95\)
According to this, the value of h when x is 2.8 would be 9.95, which makes the first option the correct option.
Learn more about functions in https://brainly.com/question/12431044
#SPJ1
I need help IMMEDIATELY! I'm so confused and this is due in 7 minutes!!
I won't hesitate to give brainliest to whoever answers fastest! Please please please show work
1. Given \(f(x)= 2x^2-4x+2\), what is the value of \(f(2/3)\)?
2. Given \(f(x)= 4x^2+2x-6\), what is the value of \(f(1/4)\)?
Answers
The values of the functions are:
1. f(2/3) = 2/9
2. f(1/4) = -21/4
How to Find the Value of a Function?If we are given the a function to find the value for which x assumes a given value, substitute the given value of x into the function and solve.
1. To find the value of f(2/3), substitute x = 2/3 into the function f(x) = 2x² - 4x + 2.
f(2/3) = 2(2/3)² - 4(2/3) + 2
f(2/3) = 2(4/9) - 8/3 + 2
f(2/3) = 8/9 - 8/3 + 2
f(2/3) = (8 - 24 + 18)/9
f(2/3) = 2/9
2. To find the value of f(1/4), substitute x = 1/4 into the function f(x) = 4x² + 2x - 6.
f(1/4) = 4(1/4)² + 2(1/4) - 6
f(1/4) = 4(1/16) + 1/2 - 6
f(1/4) = 1/4 + 1/2 - 6
f(1/4) = (1 + 2 - 24)/4
f(1/4) = -21/4
Learn more about function on:
https://brainly.com/question/2284360
#SPJ1
Identify the constant of proportionality from the graph
A. 3
B. 9
C. 1/3
D. 6
Answers
For this one, you should get 3
a researcher wants to know the average growth of a certain plant one week after germination. The greenhouse where he grows plants has 12 trays with 36 plants in each tray l. He picks one tray from the greenhouse and measures the heights of each plant. The results are shown in the dot plot.
When analyzing the data, he sees that the heights of the plants are clustered around in 2 in. Could this be the result of bias in his sampling method? Explain.
Answers
Answer:
Sampling bias can occur when the procedure leads to a favoring of one population over another.
When the researcher wants to know on average how a certain plant will grow; given that they have been germinated for a week's time. By oy using a certain plant, assuming t
Answer:
Yes, he sampled plants from only one tray, so the sample is not random.
The local women's club baked 196 pies. One pie dropped onto the floor and
was thrown away. If they give equal amounts of the remaining pies to each
of two schools, how many whole pies would each school receive?
100 pies
96 pies
97 pies
98 pies
Answers
Answer:
97
Step-by-step explanation:
196 ÷ 2 = 97.5
you cannot include the .5, so each school gets 97 pies
Write a function for the sinusoid (the curve).
У
(2,5)
14
(1, -1)
3
1
Choose...
3 cos x + 2
The function is f(x) = 3 sin x
3 sin x
3 cos x
2 X
Answers
The equation of the sinusoid function is:
3 Sin πx + 2.
Let's analyze the given options to find the correct equation:
a. 3 Cos πx + 2:
This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.
b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.
c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:
To determine if the period is correct, we need to calculate the x-values when the function repeats itself.
In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.
sin(πx) = 0 when πx = 0, π, 2π, 3π, ...
Solving for x, we have:
πx = 0 ⟹ x = 0
πx = π ⟹ x = 1
πx = 2π ⟹ x = 2
πx = 3π ⟹ x = 3
From this, we can see that the function repeats itself every integer value of x, which matches the given information.
Therefore, option (c) is the correct equation: 3 Sin πx + 2.
Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.
Hence, the equation of the sinusoid function is:
3 Sin πx + 2.
Learn more about sinusoid function click;
https://brainly.com/question/21008165
#SPJ1
determine the values of x when f(x)=40 for the function f(x)=2(x-3)^2-8
Answers
Answer:
x = 3 ± \(\sqrt{24}\)
or
x = 3 + \(\sqrt{24}\), x = 3 - \(\sqrt{24}\)
Step-by-step explanation:
given f(x) = 2(x - 3)^2 - 8, find when f(x) = 40
So, we plug in 40 for f(x) in the 1st equation and solve for x. (Aim to got x on its own)
40 = 2 (x - 3)^2 - 8
+ 8 + 8
-----------------------------
48 = 2 (x - 3)^2
/2 /2
-----------------------------
24 = (x - 3)^2
square root both sides
--------------------
\(\sqrt{24}\) = x - 3
x = 3 ± \(\sqrt{24}\)
Francis used the distributive property of multiplication to help him solve the equation 6 x 2 = ________. Francis did not get the same answer for each side of the expression. Explain the steps required to correct his mistake.
Answers
Answer:
12
Step-by-step explanation:
well i dont get the qiustion but i can explain it
6x2=12
12/2=6
so
12 is the answer this is the best it can explain it
Find the solution to the system
5x+4y=-34 and y=3x
Answers
Answer:
x = -2 ; y = -6
Step-by-step explanation:
Let y = 3x be eqn.1
So putting eqn.1 in 5x + 4y = -34 gives ,
\(5x + 4y = - 34\)
\( = > 5x + 4(3x) = - 34\)
\( = > 5x + 12x = - 34\)
\( = > 17x = - 34\)
\( = > x = \frac{ - 34}{17} = - 2\)
Putting the value of x in eqn.1 gives :-
\(y = 3x = 3 \times ( - 2) = - 6\)
Can you guys help me out ps hurry im timed
Answers
Answer:
If it's supposed to have no solution, I think you can just use an extreme number, like -30 or something.
(- 6x + 7) + (2x - 6) = - 4x + 1
Answers
Answer:
Step-by-step explanation:
-4x + 1 = -4x + 1
1 = 1
infinitely many solutions
rewrite each of the following expressions without using absolute value:
∣4r-12∣if r<3
Answers
Answer:
12-4r
Step-by-step explanation:
4r<12 because r<3 so you flip it.
27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
Answers
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
Learn more about determining the percentage at https://brainly.com/question/24877689.
#SPJ1
what makes 3 + 7 + 2 equals box + 2 true
A. 10
B. 14
C. 12
Answers
Answer:
b
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
12
At the local Theatre of the Arts, tickets cost $4 for children and $5 for adults. In the opening Saturday night of a play, the theater made $540. The second day was a matinee and the prices were lower for children at $3 and the same price as Saturday for adults. They made $440 at the matinee.
A) Write a system of equations in standard form that represents the prices at the Theatre on Saturday and the second day.
B) Rewrite the system of equations in slope-intercept form. What are the y-intercepts of both equations?
Answers
A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.
B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.
A) Let's define the variables:
Let x represent the number of children attending.
Let y represent the number of adults attending.
On Saturday night:
The equation for the revenue generated on Saturday night is:
4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).
Matinee on the second day:
The equation for the revenue generated at the matinee is:
3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).
Therefore, the system of equations in standard form is:
4x + 5y = 540
3x + 5y = 440
B) Let's rewrite the system of equations in slope-intercept form:
On Saturday night:
4x + 5y = 540
Rearranging the equation, we get:
5y = -4x + 540
Dividing both sides by 5, we get:
y = (-4/5)x + 108
The y-intercept of this equation is 108.
Matinee on the second day:
3x + 5y = 440
Rearranging the equation, we get:
5y = -3x + 440
Dividing both sides by 5, we get:
y = (-3/5)x + 88
The y-intercept of this equation is 88.
For such more question on equation:
https://brainly.com/question/17145398
#SPJ8