The area of a triangle with the given set of vertices is 12 square units, which is obtained using the concepts of coordinate geometry and the area of triangles.
What is the area of a triangle?
The area of a triangle is defined as the total region bounded by the three sides of a triangle. For a right-angled triangle, the area is given by ½ * (base * height).
Calculation of the area of the given triangle
Given:
P(7,6), Q(1,6), R(4,2) be the three vertices of a triangle PQR
Let PQ be the base parallel to the x-axis
b = 7 - 1 = 6
And altitude is the difference of y coordinates of the point Q and R, h = 6 - 2 = 4
The area of triangle PQR is equal to half the product of base and height
Area = (6 × 4) / 2
= 24 / 2
= 12 square units
Hence, the area of the triangle with given vertices is 12 square units.
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12 1/2 divided by 5 1/2
Answer:
25/11
Step-by-step explanation:
Convert to improper fractions
25/2 ÷ 11/2
take reciprocal of divisor and multiply
25/2 x 2/11
50/22
25/11
You have $100 in your bank account. If it doubles every month and you started back in Jarwary.
how much money will you have by May?
Answer:
I think 1,600
Step-by-step explanation:
What is 943,158,670.3491 rounded to the 10 millions? PLEASE ANSWER ASAP!
Answer:
I believe the answer is 943,158,670.349
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Answer:
940,000,000
Step-by-step explanation:
943,158,670.3491
The leftmost 4 is the 10,000,000 place.
943,158,670.3491 rounded to the 10 million is:
940,000,000
Help me with this please
Answer:
5555
Step-by-step explanation:
because it was the highest in there
I think this is the answer but i can't confirm because your theory and my theory can be different
for the data in the excel file grade point averages, find 90%, 95%, and 99% confidence intervals for the mean gpa. compute the confidence intervals using the appropriate formulas and verify your results using the excel confidence intervals template.
The labels in the spreadsheet are in column B, while the score values are in column A. Column C's cells are where the command operations take place. The test results are distributed between 82.516 and 87.85 by adding and subtracting the test score confidence value of 2.667 from the mean of 85.183. Excel instantly translates the formula to the result when you enter the command functions and press "Enter," giving the confidence level of 97% given the alpha value of 0.03, or 3%.
What is excel confidence interval function ?The Excel Statistical Functions section contains the CONFIDENCE Function. The confidence interval for a population mean will be calculated using the normal distribution, and it will then be returned. For financial analysis, Excel's confidence interval tool is quite helpful. That enhances financial decision-making by enabling financial analysts to anticipate and adjust for a variety of financial goals. To do this, financial data is graphically represented together with a set of distribution parameters. Based on the statistical data offered by the normal distribution, analysts can make better financial decisions. For example, they can determine the relationship between revenue made and income spent on luxuries.
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A bee flies at 15 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 16 minutes, and then flies directly back to the hive at 12 feet per second. It is away from the hive for a total of 18 minutes. Whats the distance?
Answer:
The distance between hive and flower bed is 2250 feet
Step-by-step explanation:
Pls pls help whoever gets it right gets a crown
Answer:
[tex]\frac{15}{56} a^2[/tex]
Step-by-step explanation:
Predict whether atoms of chlorine or atoms of sulfur would be more likely to attract electrons and, therefore, be more reactive. Explain your reasoning.
Chlorine will be more reactive.
Reactivity of elementsFrom the question, we are to predict whether the atoms of chlorine or atoms of sulfur would be more likely to attract electrons
The electronic configuration of chlorine (Cl) is
2,8,7
This means Cl needs only one electron to complete its octet configuration
and
The electronic configuration of sulfur (S) is
2,8,6
This means sulfur needs two more electrons to complete its octet configuration
Since chlorine needs fewer electrons to complete its octet configuration, then it will be more likely to attract electrons.
Thus, chlorine will be more reactive.
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MatemáticasJavier pagó $92 por 5 libretas y 3 lápices. Laura compró 2 libretas y 6 lápices, y pagó $56, ¿cuál es el
precio de cada libreta y de cada lápiz?
A) $11 por una libreta y $5 por un lápiz.
B)
$13 por una libreta y $9 por un lápiz.
C)
$16 por una libreta y $4 por un lápiz.
D) $10 por una libreta y $6 por un lápiz.
If Javier paid $92 for 5 notebooks and 3 pencils and Laura paid $56 for 2 notebooks and 6 pencils, then the price of each notebook is $16 and that of each pencil is $4, calculated using linear equations.
As per question statement, Javier paid $92 for 5 notebooks and 3 pencils while Laura paid $56 for 2 notebooks and 6 pencils.
We are required to calculate the price of each notebook and each pencil.
To solve this question, let us assume that the price of each notebook is "x" and that of each pencil is "y". Now, we will form two linear equations, each with the two assumed variables, based on the conditions mentioned in the question statement, and solving the equations, we will obtain our desired answer.
Since Javier bought 5 notebooks and 3 pencils for $92 and the price of each notebook is assumed to be "x" and that of each pencil is assumed to be "y", we can write that
[tex][(5x+3y)=92]...(1)\\or,5x = 92-3y\\or,x=\frac{(92-3y)}{5}...(2)[/tex]
And in Laura's case, she bought 2 notebooks and 6 pencils for $56, i.e.,
[tex][(2x+6y)=56]...(3)\\or, 2(x+3y)=56\\or, (x+3y)=\frac{56}{2}\\ or,(x+3y)=28\\or,x=(28-3y)...(4)[/tex]
Now, equating (2) and (4), we get,
[tex]x=\frac{(92-3y)}{5}=(28-3y)\\ or, \frac{(92-3y)}{5}=(28-3y)\\ or, (92-3y)=5(28-3y)\\or, 92-3y=140-15y\\or,(15y-3y)=140-92\\or,12y=48\\or,y=\frac{48}{12}=4[/tex]i.e., Price of each pencil is $4.
Now, using (y = 4) in the equation (4), we get,
[tex]x=[28-(3*4)]\\or,x=(28-12)\\or,x=16[/tex]i.e., Price of each notebook is $16.
Hence, the correct answer is
option(C) $16 for a notebook and $4 for a pencil.
linear equations: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and hence comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.Variable: n Mathematics, a variable is a symbol or a representative of a value, which is unknown.To learn more about Linear Equations, click on the link below.
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A soap manufacturer advertises that it has increased the size of their bottle of dishwashing soap to 18.4 ounces, which is 5% more than the original size.
What is the original size of the bottle?
Round your answer to the nearest tenth.
The diagram shows a rectangle.
The area of the rectangle is 12b²-30b
Write an expression for
a
b
the length of the rectangle
the perimeter of the rectangle.
6b
A
length
N
Answer: The diagram shows a rectangle.
The area of the rectangle is 12b²-30b long a+b+a your answer is aStep-by-step explanation:
A rectangle Expression for "a": a = 12b - 30,Expression for "b": b = (12b² - 30b) / (12b - 30),Length of the rectangle: Length = a = 12b - 30,Perimeter of the rectangle: Perimeter = 2 × (13b - 30)
Let's break down the given information step by step:
The area of the rectangle is given as 12b² - 30b.
The expression for "a":
The area of a rectangle is equal to its length (a) multiplied by its width (b). So, set up the following equation:
Area = Length ×Width
12b² - 30b = a × b
To find the expression for "a," divide both sides of the equation by "b":
a = (12b² - 30b) / b
Simplify the expression for "a":
a = 12b - 30
The expression for "b":
From the same equation as above, that:
Area = Length × Width
12b² - 30b = a × b
To find the expression for "b," divide both sides of the equation by "a":
b = (12b² - 30b) / a
Substitute the value of "a" from the previous expression:
b = (12b² - 30b) / (12b - 30)
The length of the rectangle:
The length of the rectangle is represented by "a," so the expression for the length is: a = 12b - 30
The perimeter of the rectangle:
The perimeter of a rectangle is given by the formula: Perimeter = 2 ×(Length + Width)
Since the rectangle has two pairs of equal sides (opposite sides are equal in a rectangle), the expression for the perimeter will be:
Perimeter = 2 × (a + b)
Substitute the value of "a" from the expression we found earlier:
Perimeter = 2 × ((12b - 30) + b)
Simplify the expression for the perimeter:
Perimeter = 2 ×(13b - 30)
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Elementary and middle school groups typically run for __________, depending on administrator and teacher support for allowing students to miss class for the group sessions.
Elementary and middle school groups typically run for 6 to 8 weeks, depending on administrator and teacher support for allowing students to miss class for the group sessions.
What is elementary education?
Elementary education, can as well be described as the primary education, which is the first stage of education that is followed in the traditional formal education, children at about age 5 to 7 are those that are usually found in the elementary seetings of school.
Its should be noted that Elementary and middle school groups typically run for 6 to 8 weeks, depending on administrator .
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a block of pine wood, 4.0cm on each side, has a mass of 27g. What is the density of this block show your work
Step-by-step explanation:
The block of wood is 3cm on each side so it is a cube.
The volume of a cube is given by s^3. So the volume of this block is 3cm x 3cm x3 cm = 27 cm^3.
density = mass/volume =27 g / 27 cm^3 = 1 g/cm^3.
the answer is 1 g/cm^3. I hope this helps!
i need help with thisxx
Using translation concepts, we have that:
The x-coordinates in the image are the opposite of the y-coordinates in the pre-image.The y-coordinates in the image are the same as the x-coordinates of the pre-image.Therefore, the triangle was rotated clockwise 270º about the origin.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the vertices of the pre-image are given as follows:
D(-5,2), E(1,5), F(0,-1).
The vertices of the transformed image are given by:
D'(-2, -5), E'(-5,1), F(1,0).
From this, we the rule is given by:
(x,y) -> (-y,x).
Which is equivalent to the rotation rule of a rotation of 270º clockwise.
Hence:
The x-coordinates in the image are the opposite of the y-coordinates in the pre-image.The y-coordinates in the image are the same as the x-coordinates of the pre-image.Therefore, the triangle was rotated clockwise 270º about the origin.More can be learned about translation concepts at https://brainly.com/question/4521517
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If f(x) = 4x12, what is f(2)?
The value of function comes out to be - 4
In the question x is the independent variable and f ( x ) = y is the dependent variable , which is dependent on x .
Given : f ( x ) = 4 x - 12
To find : f ( 2 )
Substituting value of x as 2 in function , we get
f ( 2 ) = ( 4 * 2 ) - 12
= - 4
Hence , value of function comes out to be - 4 .
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What is the slope of the line shown in the graph?
Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]
a 5-letter password is to be constructed from the following letters: {a, b, c, d, e}. the password must contain exactly 3 of the letters. (obviously at least one of them will need to be used more than once to create a 5-letter password.)
If A,B, and C are the letters selected and we use A twice, B twice, and C once. The number of ways different passwords exist in this scenario are 30.
What is a password?
A password, sometimes known as a passcode (in devices made by Apple, for instance), is a hidden piece of information that is typically a long string of characters and is used to verify a user's identity. Passwords were always thought to be memorized, but today's average person has access to a huge number of password-protected services, making it difficult to remember a different password for each one. The secret is kept by a party known as the claimant, and the person confirming the claimant's identity is known as the verifier, according to the nomenclature of the NIST Digital Identity Guidelines. The verifier can determine the identity of the claimant when the claimant successfully uses a recognized authentication technique to show the verifier that they know the password.
A, B and C are selected
A is used twice B is used twice and C is once
Total ways = 5!/2!.2! = 30
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Which of the following is equivalent to the expression 6z - 9?
A. The quotient of 6 times a number z and 9
B. 6 times the difference of a number z and 9
C. 6 less than the product of 9 and a number z
D. 9 less than 6 times a number z
Answer:
c is the correct answer!
[tex]\left[\begin{array}{ccc}1&&10\\2&&15\\3&&20\end{array}\right][/tex]Whats the verbal rule and the tenth term?
Answer:
أنا بصراحة لا أعرف
Step-by-step explanation:
أنا بصراحة لا أعرف
أنا بصراحة لا أعرفأنا بصراحة لا أعرفأنا بصراحة لا أعرفأنا بصراحة لا أعرفأنا بصراحة لا أعرف
A repair company's charge for repairing a certain type of copy machine fits the model where y is the number of dollars charged and x is the number of minutes the repair person is on the job. how many minutes would it take for the cost of repair to reach $140? (round to the nearest minute.)
It will take 138 minutes for the repair cost to reach $140
Although part of your question is missing, you might be referring to this full question: A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 +0.617x. Where y is the number of dollars charged and x is the number of minutes the repair person is on the job. how many minutes would it take for the cost of repair to reach $140? (round to the nearest minute.)
As per the question:
Number of dollars charged by the company = y dollars
Number of minutes the repair person is on the job = x minutes
The cost that needs to be achieved = 140 dollars
Equation:
y = 47.38 + 0.617x------(1)
For the cost of repair to reach $140, substituting $140 in y in equation (1)
140 = 47.38 + 0.617x
Solving further and finding the value of x
140 - 47.38 = 0.617x
92.62 = 0.617x
x = 138 minutes (rounded to the nearest minute)
So, it will take 138 minutes for the repair cost to reach $140
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When 18 is subtracted from six times a certain number, the result is − 42. What is the number?
Answer: the unknown number is -4.
Step-by-step explanation:
Hope this helps!
Answer:
-4
Step-by-step explanation:
6x-18=-42
6x=-42+18
6x=-24
x=-24/6
x=-4
which expressions can we use to describe how many more seconds tatenda spends than ciara spends mowing lawns during 4 weeks?
The expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks is 4(700t- 750c) .
What is an expression in math example?
2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient, or a value multiplied by the variable. The number 2 is the coefficient of x in the formula 2x + 3, which indicates 2 times x plus 3.time taken by tatenda to mow a square meter of lawn = t seconds
time taken by Ciara to mow a square meter of lawn = c seconds
area mowed by tatenda in a week = 700 square meters
area mowed by Ciara in a week = 750 square meters
the expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks
time taken by tatenda for mowing in 4 weeks = 4 * 700 * t seconds
time taken by Ciara for mowing in 4 weeks = 4 * 750 * c seconds
more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks = [4 * 700 * t ] - [4 * 750 * c]
= 4(700t- 750c)
Therefore, the expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks is 4(700t- 750c).
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Harry tosses a nickel 4 times. The probability that he gets at least as many heads as tails is.
The answer is 4/8 or 1/2 or 0.5 or 50%
Step-by-step explanation:
A nickel has two faces, heads and tails
Equation of probability = Number of chances/Total Numbers of chances
So, 4 chances of heads / 8 chances of heads or tails, thus, there is a chance of 50% if Harry tosses the coin 4 times to get a head
Divide The quantity 3.185 times ten raised to the seventeenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.. Write the final answer in scientific notation.
3.5 x 10 8
0.35 x 10 9
3.5 x 10 9
0.35 x 10 25
The quantity 3.185 times ten raised to the seventeenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity written in scientific notation is 0.35 x 10^9. option B
Scientific notation(3.185 × 10^17) ÷ (9.1 × 10^8)
= (3.185 ÷ 9.1) × 10^(17-8)
= (0.35 × 10^9)
Therefore, the quantity (3.185 × 10^17) ÷ (9.1 × 10^8) written in scientific notation is (0.35 × 10^9).
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Proof diagram (50 points)!
Use the proof diagram to complete the question. State the missing reason in this proof for the letter given
The converse of corresponding angles theorem that proves that p║r is stated in the proof explained below (see proof below).
What is the Converse of Corresponding Angles Theorem?If two corresponding angles are congruent to each other, the converse of the corresponding angles theorem states that the lines on which both corresponding angles lie are parallel to each other.
What is the Vertical Angles Theorem?The vertical angles theorem is the theorem that justifies that when two angles are vertically opposite to each other, then they are congruent angles.
Given that, angle 1 is congruent to angle 5, to prove that lines p and r are parallel to each other, the statements and reasons stated below explains why they are parallel lines:
Statement Reason
1. <1 ≅ <5 Given
2. <4 ≅ <1 a. vertical angles theorem
3. <4 ≅ <5 b. transitive property
4. p║r c. converse of corresponding angles
theorem
Therefore, the converse of corresponding angles theorem that proves that p║r is stated in the proof explained above.
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Directions Round each amount to the nearest cent, dime and dollar
1. $32.518
Answer:
$32.52
Step-by-step explanation:
Hope it helps! =D
Determine if the lines are parallel, perpendicular or neither.
y= -4x - 2 and 12x + 3y = 27
jamie and imani each play softball. imani has won 5 fewer games than jamie. is it possible for jamie to have won 11 games if the sum of the games imani and jamie have won together is 30? yes; jamie could have won 11 games because 2x − 5
The total number of games won by Jamie is not 11 according to the conditions given in the question.
What is an equation?
The equation is illustrated as a mathematical statement having an equal symbol in between two expressions, '='. It depicts that both sides of the equal sign are equal to each other.
Calculation of the number of games played by Jamie
Let us assume that x and y be the number of games that Jamie and Imani have won
According to the question, Imani has won 5 fewer games than Jamie i.e.
y = x - 5 —-- 1
The total number of games won by Jamie and Imani together is 30
x + y = 30
Using equation 1, put the value of y,
x + x - 5 = 30
2x - 5= 30
Now, substitute x by 11, and we get that the equality does not net
Thus, we can conclude that 11 is not the number of games won by Jamie
Hence, the total number of games won by Jamie is not 11 using the given equations.
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is there an ordered pair that is in the solution to both of these linear equations
Answer:
(- 4, 2 )
Step-by-step explanation:
y = 3x + 14 → (1)
2x - 3y = - 14 → (2)
substitute y = 3x + 14 into (2)
2x - 3(3x + 14) = - 14 ← distribute parenthesis on left side and simplify
2x - 9x - 42 = - 14
- 7x - 42 = - 14 ( add 42 to both sides )
- 7x = 28 ( divide both sides by - 7 )
x = - 4
substitute x = - 4 into (1)
y = 3(- 4) + 14 = - 12 + 14 = 2
solution is (- 4, 2 )
a basketball player recorded the number of baskets he could make depending on how far away he stood from the basketball net. the distance from the net (in feet) is plotted against the number of baskets made as shown below.
If a player is standing 10 feet from the net, he could make approximately option (b) 5 baskets.
What is Distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.A basketball player recorded the number of baskets he could make depending on how far away he was standing from the net.
The distance from the net in feet is plotted against the number of baskets made.
Now, we see from the graph that when the distance from the net in feet is 10, the ordinate of the point is 5.
So, he could make approximately 5 baskets.
So, the answer is
Using the best fit line, if a player is standing 10 feet from the net, he could make approximately option (b) 5 baskets.
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The complete question is -
A basketball player recorded the number of baskets he could make depending on how far away he stood from the basketball net. The distance from the net (in feet) is plotted against the number of baskets made as shown below. Distance from Net vs. Number of Baskets 25 20 15 . Number of Baskets 10 5 0 0 2 10 12 4 6 8 Distance from Net (feet) Using the best-fit line, approximately how many baskets can the player make if he is standing ten feet from the net?