The area of △ABC is 22 square units.
How to determine the area of △ABC?From the question, we have the following parameters that can be used in our computation:
△ABC has vertices at A(5,1), B(−3,1), and C(−2,5).
The area of △ABC is then calculated as
Area = |(1/2)(x1)(y2 - y3) + (x2)(y3 - y1) + (x3)(y1 - y2)|
Plugging in the given vertices for △ABC, the area can be calculated as follows:
Area = |(1/2)(5)(1 - 5) + (-3)(5 - 1) + (-2)(1 - 1)|
This gives
Area =|-22|
= 22
The area of △ABC is 22 square units.
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Richard and Teo have a combined age of 48. Richard Is 12 years older than twice Teo’s age. How old are Richard and Teo?
Answer: Richard is 36 and Teo is 12
Step-by-step explanation:
Let Richard be "R" and Teo be "T",
R + T = 48 (1)
R = 2T + 12 (2)
2T + 12 + T = 48 <-- Plug (2) into (1)
3T = 36
T = 12
R + 12 = 48 <-- Plug T=12 into (1)
R = 36
Therefore Richard is 36 and Teo is 12
Answer: 12 and 36
Step-by-step explanation:
(12x2)+12=36
12=36=48
12 and 36
a cylinder has a volume of 600 in3. find the volume of a cone with the same radius and height as the cylinder.
The volume of the cone is 600 cubic inches.
A cylinder has a volume of 600 inches.
We have to find the volume of a cone with the same radius and height as the cylinder.
Volume of cone: A cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.
Formula= [tex]\frac{1}{3}\pi r^{2} h[/tex].Where,
‘r’ is the base radius of the cone
‘l’ is the slant height of a cone
‘h’ is the height of the cone.
Volume of cylinder: A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. Thus, the volume of the cylinder can be given by the product of the area of base and height.
Formula=[tex]\pi r^{2} h[/tex]Where,
‘r’ is the base radius of the cylinder.
‘h’ is the height of the cylinder.
Volume of cylinder=[tex]\pi r^{2} h[/tex]=600 cubic inches.
Volume of cone= [tex]\frac{1}{3}\pi r^{2} h[/tex].
=[tex]\frac{1}{3}*(600)=200[/tex] cubic inches.
Therefore, the volume of the cone is 600 cubic inches.
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During a volleyball lounge, a team scored 36 goals. If the team had played five matches less, its goal average would have been exactly four goals per game. How many matches had the team played?
Answer: 14
Step-by-step explanation:
Let's call the number of matches the team played "x".
We know that the team scored 36 goals in total, and if they had played five matches less, their goal average would have been exactly four goals per game. We can use this information to set up the following equation:
(36 goals) / (x - 5 matches) = 4 goals per match
To solve for x, we need to isolate x on one side of the equation. To do this, we can multiply both sides of the equation by (x - 5):
36 = 4(x - 5)
36 = 4x - 20
56 = 4x
Now we can divide both sides of the equation by 4:
x = 14
Therefore, the team played 14 matches in total.
what is the area of the shaded portion in the figure? If, it is a square and the lines are parts of a circle and the side of the square is 10 unit. Give answers in terms of pi.
Answer:
Step-by-step explanation:
The shaded portion in the figure is a quarter-circle with a radius of half the side length of the square, or 10/2 = 5 units.
The area of a circle can be calculated using the formula:
A = πr^2
Where r is the radius and π is pi (approximately equal to 3.14).
So the area of a quarter-circle with a radius of 5 is:
A = (π * 5^2) / 4 = (π * 25) / 4 = 25π / 4
This is the area of the shaded portion in the figure.
Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points negative 10, negative 6, and negative 5, negative 1. Line g of x passes through points negative 2, negative 6, and negative 1, negative 1.
The value of k is 1/5.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x) and
g(x) = f(k⋅x)
We have to find the value of f(x) and g(x)
For f(x), we have:
(x, y)={(-10, -6)(-5, -1)}
Slope=-1+6/-5+10
=5/5=1
For g(x), we have:
(x, y)={(-2, -6)(-1, -1)}
Slope=-1+6/-1+2=5
g(x)=kf(x)
5=k(1)
k=1/5
Hence, the value of k is 1/5.
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Items 3-5. A triangle has vertices at
(1, 10), (-5, 2), and (7, 2).
3) What is the circumcenter?
4) What is the orthocenter?
Perpendicular bisectors of a triangle's sides meet at the circumcenter. It is situated at the equator of a triangle.
What is Circumcenter?The circumcenter is where the perpendicular bisectors of a triangle's sides meet. It is located in the middle of a triangle's perimeter. Draw the perpendicular bisectors of the sides and extend them to determine the circumcenter of any triangle. The circumcenter of the triangle will be determined by where the perpendiculars cross.
Here,
Given : (1, 10), (-5, 2), and (7, 2).
=> Perimeter of given triangle is:6
=> √(6)² + (8)² = √100 = 10
=>√(12)² = 12
=> √(6)² +(-8)² = 10
Perimeter = 10+ 12+ 10 = 32
The orthocenter is the location where the altitudes traced from a triangle's vertices intersect.
The place where the triangle's three elevations converge is known as the orthocenter. A line that goes through the triangle's vertices and is parallel to the other side is said to be an altitude. A triangle's orthocenter is the intersection of the perpendiculars that connect its vertices to its two sides.
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* Show your work and write the rule used to solve each problem
In the given Geometric shape/figure ∠1=∠4 i.e. C.
What are geometric shapes?
In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.
Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.
In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc. In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.
Now,
As we know, If two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°.
The same theorem is applied here
hence
The opposite angles ∠1 and ∠4 equal.
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Write down the percentage multiplier to decrease a price by 48%
give simple woriking out :)
Answer: 0.48
Step-by-step explanation: To get your percentage multiplier, divide the desired percentage by one hundred. In this case, 48/100.
Answer: The percentage multiplier to decrease a price by 48% is 0.52. :)
Step-by-step explanation:
Assume that you graph lines f and g on the same coordinate plane and they intersect at point (4, 5). Which of the following statements is NOT true.
1. (4,5) is on both lines
2. if you plug 4 in for x and 5 in for y in each equation you will get true statements form both equations
3. (4,5) is the solution to the linear system
4. other points that are on line f will also be solutions to the linear system
5. None. all statements are true.
Other points that are on line f will also be solutions to the linear system. Therefore, option 4 is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, graph lines f and g on the same coordinate plane and they intersect at point (4, 5).
When two lines intersect at (4, 5), then the point is the solution of system of linear equations.
When substitute x=4 and y=5 in the system of equations, both the equations will be true.
Therefore, option 4 is the correct answer.
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Danika live 5 block from her chool. If he walk to and from chool 5 day each week how many block doe he walk in one week?
Danika walks 50 blocks in one week.
Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.
As per the data given,
We have,
Danika lives at 5 blocks from her school.
As Danika walks 5 blocks to and from school, making her round trip
So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.
As Danika walks to and from school 5 days a week,
Hence, she walks 10 blocks * 5 days = 50 blocks in one week.
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Lines m and n are perpendicular lines. If line m has a slope of 1/3, find the slope of line n. Type a numerical answer in the
space provided. If necessary, use the / key as a fraction bar. Do not type spaces in your answer.
If slope of the line is 1/3, then slope of the perpendicular line should be negative reciprocal, and so it is equal -3.
What is perpendicular line?Lines that cross at a straight angle (90 degrees) are said to be perpendicular. Two geometric objects in basic geometry are perpendicular if they intersect at a right angle. The perpendicular sign,, is a graphic representation of the perpendicularity criterion.
Between two lines, between a line and a plane, or between two planes, it can be defined. slope, An evaluation of a line's inclination with respect to the horizontal using numbers.
The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line ("slope equals rise over run"). The slope or gradient of a line in mathematics is a number that indicates the line's steepness and direction.
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let p be defined as in the previous problem. is ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)) true or false? explain.
The statement ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)) is false.
Let's start by understanding what "p" is. "p" is a function that takes in two arguments, x and y. It tells us whether the relationship between x and y is true or false.
Now, let's look at the statement
=>∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).
This statement says that for every x, there exists a y and a z such that y is not equal to z and both p(x, y) and p(x, z) are true.
This statement is actually false.
Why? Imagine if p(x, y) only returned true when y was equal to x. Then, there would be no y and z such that y is not equal to z and both p(x, y) and p(x, z) are true.
Therefore, it is possible for the function "p" to return false for the statement
=> ∀x∃y∃z(y 6= z → p(x, y) ∧ p(x, z)).
It depends on the definition of the function. To determine if the statement is true or false, we need to know what the function "p" is.
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how to create a vector that ranges from 0 to π and contains 32 evenly spaced elements.
The process of creating a vector that ranges from 0 to π and contains 32 evenly spaced elements is illustrated below.
A vector is a mathematical concept that is used to represent a set of numbers in an ordered manner.
To create a vector that ranges from 0 to π and contains 32 evenly spaced elements, you first need to determine the step size.
This is done by dividing the range (π - 0) by the number of elements (32) and subtracting 1. In this case, the step size is
=> (π - 0) / (32 - 1) = π / 31.
Next, you will create a variable to represent the starting value of the vector, which is 0.
Finally, you can use the append function to add the elements of the vector to the list or array.
To ensure that the vector contains 32 evenly spaced elements, you can check the length of the vector using the len() function, and you can also check the spacing of the elements by printing the values of the vector.
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A triangular land having area of 336 sq meter and perimeter 84 meter has length of an edge 26 meter. Calculate the measurement of remaining two sides.
true or false if the correlation between two varaible is positvie the slope of the linear model will be positive
Se introduce agua (1 g/cm^3) y
aceite (0,9 g/cm^3) en un tubo con
forma de U, como se muestra en la
figura, si la altura alcanzada por la
columna de agua es de 0,30 m.
Hallar: ¿Cuál es la altura que alcanza
la columna del aceite?
Debemos tener la misma masa en ambos brazos del tubo, entonces veremos que la altura que alcanza la columna de aceite es 0.33m
¿Cuál es la altura que alcanza la columna del aceite?La altura de la columna de aceite será de tal forma que la masa en ambos brazos sea igual.
Recordar que la masa es el producto entre la densidad y el volumen, para el caso de cilindros, el volumen es el producto entre la altura H y el area circular A.
Para que las masas sean iguales debemos tener que:
A*(0.30 m)* (1 g/cm^3) = A*(H)*(0.9 g/cm^3)
Podemos remover A de ambos lados para obtener:
(0.30 m)* (1 g/cm^3) = (H)*(0.9 g/cm^3)
Resolviendo esto para H obtendremos:
H = (0.30 m)* (1 g/cm^3)/(0.9 g/cm^3)
H = 0.33m
Esa es la altura que alcanza el aceite.
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what is the breaking point of -10+5x?
The factorized form of the expression is 5(-2 + x).
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
We have an expression,
-10 + 5x.
To factorize the expression:
Simplifying,
-10 + 5x,
= 5(-2 + x)
Therefore, the required expression is 5(-2 + x).
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which of the following best describes the independent variable in this research design? responses the sample of material chosen as the potential container material is the variable being tested, so it is the independent variable. the sample of material chosen as the potential container material is the variable being tested, so it is the independent variable. the flow time, which is related to the porosity of each sample, is the variable that is measured, so it is the independent variable. the flow time, which is related to the porosity of each sample, is the variable that is measured, so it is the independent variable.
The flow duration is regarded the independent variable in the proposed research design.The independent variable is the element that the researcher manipulates or changes in order to observe its influence on another component, known as the dependent variable. .
It is controlled or quantified to explore its influence on the porosity of the sample material chosen as the possible container. The flow time is the variable in the experiment that is being manipulated, and its influence on porosity is being observed, making it the independent variable.
The idea of independent and dependent variables is critical in experimental design because it allows researchers to investigate causality and anticipate how changes in one component will impact another.
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what is the exact distance between the coordinates (1,11) and (7,18)? leave your answer in radical form
The distance between the given pair of points (1,11) and (7,18) is √85.
What is the distance between the coordinates?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given that;
Point 1 (1,11)
x₁ = 1y₁ = 11Point 2 (7,18)
x₂ = 7y₂ = 18Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( 7 - 1 )² + ( 18 - 11 )² )
D = √( ( 6 )² + ( 7 )² )
D = √( 36 + 49 )
D = √85
Therefore, the value of the distance is √85.
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PLS- ANSWER ITS DUE SOON
Answer:
23.) x = 111
24.) x = 53
25.) x = 32
26.) x = 66
Step-by-step explanation:
The sum of the exterior angles of a polygon is 360°.
23.)
65 + 106 + 78 + x = 360
249 + x = 360
x = 111
24.)
50 + 48 + 59 + x + x + 58 + 39 = 360
254 + 2x = 360
2x = 106
x = 53
25.)
85 + 44 + 3x + 2x + 71 = 360
200 + 5x = 360
5x = 160
x = 32
26.)
40 + x + 77 + 2x + 45 = 360
162 + 3x = 360
3x = 198
x = 66
Craig likes to collect vinyl records but decided to sell a few. Last year he had 120 records in his collection. Now he has 100 records. What is the percent change and is it an increase or a decrease?
Salut/Hello!
Answer: 16,(6)% and it's a decrease
Step-by-step explanation:
/ - fraction line
initial records = 120
after selling = 100
=> records sold = 120 - 100 = 20
We know that:
100% = 120/100 => 1% = 1.2/100
120 - 100 = 20
So we can find: 20 : 1.2 = 16,(6)%
Because 5% = 6 and 6 : 1.2 = 5%
So by knowing the amount of records sold and the percentage per record we divide them and find out the percentage of records sold.
I hope it'll be useful! :]
An amount of money has been divided betweeb ali bob and Caleb in the ration 2:5:3. If Caleb received $42more than bob, what’s the original amount of money
Answer:
$210
Step-by-step explanation:
42/2=21 5+3+2=10 21*10=210
explain how the ratio sy/sx affects the slope of the regression line through the original data.
The formula for the slope a of the regression line is:
a = r(sy/sx)
The reason for the connection between the value of r and the slope of the least squares line has to do with the formula that gives us the slope of this line. For paired data (x,y) we denote the standard deviation of the x data by sx and the standard deviation of the y data by sy.
The formula for the slope a of the regression line is:
a = r(sy/sx)
The calculation of a standard deviation involves taking the positive square root of a non-negative number. As a result, both standard deviations in the formula for the slope must be nonnegative. If we assume that there is some variation in our data, we will be able to disregard the possibility that either of these standard deviations is zero. Therefore the sign of the correlation coefficient will be the same as the sign of the slope of the regression line.
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find the average rate of change of the function over the given interval. p(θ)=θ3−5θ2 6θ; [1,2]
The average rate of change of the function p(θ) over the interval [1,2] is 0.
The average rate of change of a function over an interval is given by the slope of the secant line that connects the two points on the function at the endpoints of the interval.
For the function p(θ)=θ^3−5θ^2 + 6θ and the interval [1,2], the average rate of change can be calculated as:
(p(2) - p(1)) / (2 - 1) = ((2^3 - 5 × 2^2 + 6 × 2) - (1^3 - 5 × 1^2 + 6 × 1)) / (2 - 1) = ((8 - 20 + 12) - (1 - 5 + 6)) / (2 - 1) = (0) / (1) = 0.
So, the average rate of change of the function p(θ) over the interval [1,2] is 0.
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What is the equation of the line that
passes through the point (8, 3) and has a
slope of -1/4
Answer:
y = -1/4x + 5
Step-by-step explanation:
(y - y1) = m(x - x1) Point - slope form
y - 3 = -1/4(x - 8)
y - 3 = -1/4x + 2
y = -1/4x + 2 + 3
y = -1/4x + 5
Write this 4th degree polynomial in simplified factored form
Therefore , the solution of the given problem of polynomial comes out to be (x-4)²(x-1)(x+2) is a four degree polynomial.
Describe polynomials.A polynomial is a mathematical statement with coefficients or uncertainty that uses only additions, erasures, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to a phrase in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that can be added, deducted, multiplied, then raised to negative number powers of non-variables.
Here,
Given :
=> (x-4)(x-1)(x+2)
=>(x-4)²(x-1)(x+2)
So,
=> (x-4)²(x-1)(x+2) is a four degree polynomial.
The two zeros of the degree four polynomial presented are x = 2 and x = 4. The two components of the above polynomial are (x - 2) and since x = 2 and x = 4 are its two zeros (x - 4).
The quadratic expression with the coefficients 1, 8, and 15 can be factored to find additional components. This equals x2 + 8x + 15.
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Josh had a weekly gross earnings amount of $487.29 and earns a regular hourly rate of
$10.95. Determine the total number of hours Josh worked during the week if the
company pays time-and-a-half for any hours worked exceeding 40 in one week. (5
points)
The total number of hours Josh worked during the week is 44.7 hours.
How to determine the total number of hours Josh worked during the week
We first need to calculate his regular pay by dividing his weekly gross earnings by his hourly rate:
$487.29 / $10.95 = 44.7 hours
Since the company pays time-and-a-half for any hours worked exceeding 40 in one week, we need to determine if Josh worked more than 40 hours during the week. If he did, we'll calculate his overtime pay by multiplying his regular pay by 1.5.
If Josh worked 44.7 hours, then he worked 44.7 - 40 = 4.7 hours of overtime.
His overtime pay would be 4.7 hours * $10.95 * 1.5 = $81.48
His regular pay would be 40 hours * $10.95 = $438.00
So his total weekly pay would be $438.00 + $81.48 = $519.48
The total number of hours Josh worked during the week is 44.7 hours.
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please help me i'm desperate
The measure of ∠BDC = 79°
Option B is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of
2 x pi x r.
The area of a circle is given as:
We have,
∠BDC = (BC + AT) / 2
∠BDC = (95 + 63) / 2
∠BDC = 158 / 2 = 79°
Thus,
∠BDC = 79°
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of
annum
$20) At what rate percent
simple interest per
will a sum a of,
money earn interest
equal to 3/5 of the
principals is in4years ears?
Please simplify the picture
The simplified expression is 3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[ 5/(x - 3) - 5/(x + 3) ] / 10/(x² - 9)
= [ {5(x + 3) - 5(x - 3)} / (x + 3)(x - 3) ] x (x² - 9)/10
Using [ (a² - b²) = (a + b) (a - b) ]
= [(5x + 15 - 5x + 15) / (x + 3)(x - 3)] x [(x - 3)(x + 3) / 10]
= (5x + 15 - 5x + 15) / 10
= 30/10
= 3
Thus,
The value of the expression is 3.
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