The equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1
Equation of a lineA line is the shortest distance between two points. The equation of a line in point-slope form and perpendicular to a line is given as;
y - y1 = -1/m(x-x1)
where
m is the slope
(x1, y1) is the intercept
Given the following
Point = (4, -1)
Line: 2x-y - 7 = 0
Determine the slope
-y = -2x + 7
y= 2x - 7
Slope = 2
Substitute
y+1 = -1/2(x -4)
Write in slope-intercept form
2(y + 1) = -(x - 4)
2y+2 = -x + 4
2y = -x + 2
y = -1/2 + 1
Hence the equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1
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Answer:
y = - (1/2) x + 1
What is the LCM and HCF of 4 and 10?
The Least Common Multiple (LCM) of 4 and 10 is 20, and the Highest Common Factor (HCF) of 4 and 10 is 2.
HCF is the highest integer that can divide 4 and 10 is 2. HCF stands for Highest Common Factor.
Now, 4 and 10 can be expressed as:
4 = 2 × 2
10 = 2 × 5
The common prime factor is 2.
Therefore HCF (4, 10) = 2
The Least Common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers.
Similarly, Calculating the LCM, 4 and 10 can be expressed as;
4 = 2 x 2
10 = 2 x 5
LCM (4, 10) = 2 x 2 x 5 = 20
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Solve 6 sin² (x) - 5 cos(x) — 7 = 0 for all solutions 0 < x < 2π
x =
6 sin² (x) - 5 cos(x) — 7 = 0 for all solutions 0 < x < 2π : x = π
What is meant by integer?Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of the equivalent positive numbers, which are additive, are the negative numbers. The blackboard bold mathbb Z or boldface Z is a common way to represent the set of integers in mathematical terminology. Only positive and negative whole numbers as well as natural numbers are included in the category of integers, a form of real number. Integers cannot include fractions, but real numbers can because of rational and irrational numbers.[tex]& \sin ^2 x-5 \cos x=5 \\[/tex]
[tex]& 1-\cos ^2 x-5 \cos x=5 \\[/tex]
[tex]& \cos ^2 x+5 \cos x+4=0 \\[/tex]
[tex]& \cos ^2 x+\cos x+4 \cos x+4=0 \\[/tex]
[tex]& \cos x(\cos x+1)+4(\cos x+1)=0 \\[/tex]
[tex]& (\cos x+1)(\cos x+4)=0 \\[/tex]
[tex]& \cos x+1=0 \quad(\because \cos x \neq-4) \\[/tex]
[tex]& \cos x=-1 \\[/tex]
[tex]& \cos x=\cos \pi \\[/tex]
[tex]& x=(2 k+1) \pi[/tex]
Where, k is any integer i.e k = 0 ± 1, ± 2, ± 3,....
But x ∈[0,2π) hence setting k = 0 we get the solution
x = π
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Someone please help!
Answer:
v/202
Step-by-step explanation:
formula: leg² + leg² = hyp²
11² + 9² = hyp²
121 + 81 = hyp²
202 = hyp²
v/202 = v/hyp²
hope this makes sense
Jorge completed the obstacle course in 18.2 seconds. Kaitlyn finished 3.5 seconds in front of Jorge. Which equation shows Kaitlyn's time?
The equation will be [tex]x-3.2=18.2[/tex] by simple calculation.
What are equations in one step?An algebraic equation that only requires one step to solve is known as a one-step equation. Once you've figured it out, you'll know what the variable's value is that makes the equation true. In order to obtain the variable by itself when solving one-step equations, we perform the inverse (opposite) of the operation that is being applied to the variable.
How do two step equations work?An equation that must be solved in two steps is referred to as a two-step equation. Any constant that is on the same side as the variable must be removed first. To solve, isolate the variable on its own using inverse operations. Keep in mind that anything you do to one side must also be done to the other.
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Sandra drops a brick into a beaker filled with water. Volume increases by 2 liters. Then she uses the density to make a prediction about its weight in kilograms. If the density of the brick is approximately 2 grams per millimeters, what should the prediction be?
The weight of the brick that Sandra dropped is 40 N.
What is the density?We must know that we can be able to define the density as the ratio of the mass to the volume of the object. We know that the density can be regarded as an intrinsic property of the substance.
We can see that;
Density = mass/volume
mass = Density * volume
Volume = 2 L or 2000 mL
Density = 2 grams per millimeters
Mass = 2 * 2000
Mass = 4000 g or 4 Kg
Weight = mass * acceleration due to gravity
Weight = 4 Kg * 10 m/s^2
Weight = 40 N
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Suppose a function f(x) has a domain of (−[infinity],[infinity]) and range [-11,3]. If we define a new function g(x) by g(x) = f(6x) +1, then what is the range of g(x)? Express your answer in interval notation.
We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3].
Let's start by defining our function f(x):
f(x) = [-11,3]
Now, let's define our new function g(x):
g(x) = f(6x) + 1
This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. In interval notation, this can be expressed as [-67, 19].
We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3]. To generate a new function, g(x), we can define it by g(x) = f(6x) +1. This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. To express this in interval notation, we can write [-67, 19]. This means that the output of g(x) lies between the values -67 and 19. This new range can be found by multiplying each value in the range of f(x) by 6 and then adding 1 to each value. Therefore, the range of g(x) is [-67, 19] in interval notation.
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B. Exercises
Find the sums or differences.
21, 2,973+56 +37,468 +784
22. 37,205-19,804
23. 861,519-179,321
24. 1,733,642 +18,082+43,605
Perform the indicated operations. Do those inside the parentheses first.
29, (736-565)+189
30. 600-(718-453)
31. (3,264-1,628)+4,356
25. 19+73,048 +314+ 5,080
26. 8,496-6,338
27) 4,000,000-832,971
28. 46,525+273,199 +5,636,024
32. 894+ (1,036-478)
33. 2,457-(986+759)
34. (61,432-38,617)-15,674
Answer:
21. 41,281
22. 17,401
23. 682,198
24. 1,795,329
29. 360
30. 335
31. 5,992
25. 78,461
26. 2158
27. 3167029
28. 5955748
32. 1452
33. 612
34. 7141
Your welcome
how many even 5 digit whole numbers are there
Answer:
Below
Step-by-step explanation:
From 10 000 to 99 999 there are 90 000 numbers of which half are even = 45 000 even 5-digit numbers
Latoya' Coffee Shop make a blend that i a mixture of coffee type A and B. In one bag of the blend, there are 6 kilogram of type A. Four bag of the blend are a total of 36 kilogram. How many kilogram of type B are there in one bag?
The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg
What is a mixture?
A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.
The coffee blend of LaToya shop = Type A and B
A bag of the coffee blend = 6kg of Type A.
4 bags of coffee blend = 36kg
Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A
Type B in each bag = 36 - 24 = 12/4 = 3kg.
We are tasked with finding the amount in kilograms of type B coffee present in a bag of coffee.
We already know that in a bag , there are 4kg of type A coffee. Hence, in 6 bags, what we will be having would be 6 * 4kg = 24kg of type A coffee
The total kilograms of coffee in 6 bags of coffee is 48kg. Now we know we have 24kg of type A, the amount of type B coffee present is thus 48kg -24kg = 24kg
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Why might squaring a number and taking the square root of a number be thought of as opposite operations give an example to justify your answer?
Finding a number's square root is the equivalent as squaring it, or the opposite process. When you multiply the square root of a given integer by itself, you get the original number. Since 8 x 8 equals 64, as fact, 8 is the square root of 64.
What is square roots?It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse.
For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.
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make model of corresponding, co-interior and alternate by using toothpick, straw etc. Please say how to do it
To make a model of corresponding angles using toothpicks or straws, you can take two pieces of the material and place them next to each other at the same angle.
What are corresponding angles?When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal.
To make a model of co-interior angles, you can place the two pieces of material on top of each other, with one inside the other at the same angle. To make a model of alternate angles, you can place the two pieces of material on opposite sides of a straight line, with one angle facing up and the other angle facing down.
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Complete question
make a model of corresponding angles using toothpicks or straws
mr smith gives her class clues about 5 digit mystery numbers the 4 is in a place that is 10 times greater than the 9.
Answer:
Step-by-step explanation:
40
ava read 99 books in 11 months how many books per a month did she read
Question 1 of 25
Which is an equation of the line through (0, 0) and (-3,-7)?
OA. y=-7x
O B. y = x
OC. y=-3x
OD. y = x
SUBMIT
The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x
What is Coordinate Geometry ?A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.
The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
The points are (0,0) and (-3, - 7)
The equation of the line will be
y - 0 = (-7 - 0)/(-3-0) * (x - 0)
⇒y = 7/3 * x
The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x
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What is the ratio of a circles area?
The ratio of the area of a circle to the area of a square with sides of length equal to the circle's diameter is π/4.
This can be expressed mathematically as A_circle/A_square = π/4, where A_circle is the area of the circle and A_square is the area of the square.
To calculate the area of the circle, use the formula A_circle = πr^2, where r is the radius of the circle. To calculate the area of the square, use the formula A_square = (d^2)/4, where d is the diameter of the circle. Therefore, the ratio of the area of the circle to the area of the square is A_circle/A_square = πr^2/(d^2/4) = 4πr^2/d^2.
For example, if the radius of the circle is 4 cm, then the diameter is 8 cm, and the ratio of the area of the circle to the area of the square is A_circle/A_square = 4π(4^2)/(8^2) = 16π/64 = π/4.
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Help asap
Write a function that has an amplitude that is two and half times the size of the function
f(x) = 2 + 3 sin(x/3 + pi/4)
Answer:
f(x) = 2 + 7.5 sin(x/3 + pi/4)
Step-by-step explanation:
f(x) = 2 + 3 sin(x/3 + pi/4)
Amplitude: 3
2.5 * 3 = 7.5
Function that has an amplitude that is two and half times the size of the function f(x) = 2 + 3 sin(x/3 + pi/4)
f(x) = 2 + 7.5 sin(x/3 + pi/4)
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Which statements and reasons are true and can be used in a proof that m∠8 Select all that apply.
The statements and reasons that are true and can be used in a proof that m∠8 < m∠6 are:
A) m∠6+m∠2+ m∠3 = 180° because the sum of the measures of the interior angles of a triangle is 180°.
C) m∠8+m∠1+m∠2+m∠3+m∠4 = 180° because the sum of the measures of the interior angles of a triangle is 180°.
What is interior angles?Interior angles can be created in geometry in two different ways. In one, parallel lines are cut by a transversal, and in the other, they are inside a polygon. Depending on how large they are, angles are divided into various types. Other angles fall into the category of pair angles because they need to be present in pairs in order to display a particular characteristic. One type of these is interior angles.
Interior angles can be outlined in two different ways:
Angles inside a polygon are referred to as interior angles because they are found inside a polygon, typically. The angles a, b, and c are interior angles in the following figure (a).Interior Angles of Parallel Lines: The angles that are located in the space bounded by two parallel lines intersected by a transversal are also called interior angles.Learn more about Interior angles
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Solve the following system of equations: x = 60 + 4y 7x + 12y = 500 a (68, 2) b (50, 12.5) c (12.5, 50) d (2, 68)
The value of x and y in the equation is (x,y) = (68,2) (optionA)
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
x= 60+4y equation 1
7x + 12y = 500 equation 2
rearranging the equation
x- 4y = 60
7x+12y = 500
using elimination method
7x-28y = 420 equation 3
7x+12y = 500 equation 4
subtract equation 4 from 3
-40y = -80
divide both sides by -40
y = -80/-40
y= 2
substitute 3 for y in equation 1
x = 60+4(2)
x= 60+8
x= 68
Therefore the value of x and y is 68 and 2 respectively.
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A 2 column table with 5 rows. The first column, yards of red fabric, x, has the entries 1, 2, 3, 4. The second column, yards of blue fabric, y, has the entries 27, 26, 25, 24.
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.
The answer choices which correctly represent equations which model the total yards of fabric Sophie will buy is; x + y = 28, 28 - x = y and 28 - y = x.
Which equations correctly model the total yards of fabric Sophie will buy?It follows from the attached table, where x represents the yards of red fabric she buys and y represents the yards of blue fabric she buys.
It follows that the following x and y pairs are possible; (1, 27), (2, 26), (3, 25) and (4, 24).
On this note, it can be inferred that in each of the red and blue fabric pairs; x + y = 28.
Ultimately, the equations which model the total yards of of fabric Sophie will buy as required are; x + y = 28, 28 - x = y and 28 - y = x.
Complete question; The given answer choices are; x+y=28, 28+x=y, x-y=28, 28-x=y and 28-y=x.
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Find the output, h, when the input,
is -18.
h = 17+ 6
h=?
When the input x is -18, the output h is 14. The answer is obtained using substitution method.
What is substitution method?
One of the algebraic techniques for solving simultaneous linear equations is the substitution approach. It entails changing any variable's value from one equation to the other by substituting it in. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.
Now, we are given h = 17+x/6
So, when the input x is -18, using substitution method,
h=17+(-18/6)
=17+(-3)
=17-3
=14
Hence, when the input x is -18, the output h is 14.
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Use elimination to find the solution to the system of equations.
4x+y=8
3x-2y=6
A. x=6, y=6
B. x=2, y=0
C. x=-3, y=20
D. x=6, y=-16
Answer: To use the elimination method to solve the system of equations, we'll try to eliminate one of the variables by adding or subtracting the equations.
We have:
4x+y=8
3x-2y=6
multiplying the first equation by -2:
-8x-2y=-16
and adding it to the second equation:
3x-2y+(-8x-2y)=6+(-16)
-5x = -10
x = 2
substituting x=2 in the first equation:
4(2)+y = 8
8+y = 8
y = 0
So the solution is x=2 and y=0, that corresponds to the option B.
Mark loads a crate that weighs 22.5 pounds and 12 boxes that each weigh 11.25 pounds onto a truck . what is the total weight of the crate and the boxes
Answer:
157.5 pounds
Step-by-step explanation:
11.25×12=135 then add 135 to 22.5
How do you find the center of a transformation?
The center of a transformation refers to the fixed point through which the transformation takes place.
The center of a transformation can be found by the following methods:
Translation: The center of a translation is the point that remains fixed during the transformation.
Rotation: The center of rotation is the point around which the object rotates.
Reflection: The center of reflection is the line of reflection or the point of symmetry.
Dilation: The center of dilation is the point that remains fixed during the transformation and all the distances from it are multiplied by a scale factor.
Combination of Translations, Rotation, Reflection, and Dilation: The center of transformation will be the point of intersection of all the fixed points of above mentioned four transformations.
It is important to note that not all transformations have a center, and some may have multiple centers.
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In the equation 33.7 divided by 9.5 what would you round each number to
need help finding the m
Answer:
79 degree
Step-by-step explanation:
A triangle is 180 degrees
We know that angle D and F is equal to each other
180 - 22 = 158 degree
158 / 2 = 79 degree
So, m<F = 79 degree
In ΔOPQ, o = 10 cm, p = 67 cm and ∠Q=24°. Find ∠P, to the nearest degree.
In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.
What are triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.
The vertex is the intersection of two straight lines. The triangle therefore has three vertices.
Hence, In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.
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evaluate the integral ( 4 to 1) 6 + x2 / x^2 dx
So the value of integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex] is 0.51
Define integral:An integral is a mathematical concept used to calculate area or change over an interval, represented by ∫. It is opposite of derivative, with two types: definite and indefinite. Used in many areas of mathematics and physics.
The integral of x/(x^2+13) from x=1 to x=4 can be evaluated using the method of substitution.
Let u = x^2+13, then du/dx = 2x dx
so x dx = du/2
now the integral becomes 1/2 * integral (1/u) du
so intergral is 1/2* [tex]\int\limits {\frac{1}{u} } \, du[/tex]
=> 1/2 [tex]\left \{ {{x=4} \atop {x=1}} \right.[/tex] ln([tex]x^2[/tex]+13)
=> 0.5 ( ln(39)-ln(14))
=>0.51
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Complete question:
evalute integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex]
How many triangles are there in a 7 piece?
A collection of seven geometric objects known as the Tangram is composed of five triangles (two tiny, one medium, and two large), a square, and a parallelogram.
In the given question, we have to find how many triangles are there in a 7 piece.
As we know that a collection of seven geometric objects known as the Tangram is composed of five triangles (two tiny, one medium, and two large), a square, and a parallelogram.
A dissection problem called a tangram is made up of seven flat polygons, or tans, that are combined to make various shapes. The goal is to use each of the seven parts separately to duplicate a pattern that is typically found in a puzzle book.
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please help me!! i need it asap
Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees for R? Explain.
Polynomial function R is the difference of two degree-2 polynomial functions P and Q. the possible degree of Polynomial R is
D. The possible degree(s) is/are 2, 1, and 0 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancelWhat is a polynomial function?A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.
A polynomial function of degree 2 is a quadratic function.
The degree of polynomials can only increase during multiplication, when polynomials are added or subtracted the result will have a degree which is at most the degree of the functions operated on.
Polynomial of degree zero are constants and hence is possible in the case
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complete question
Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees for R? Explain.
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Use a comma to separate answers as needed)
A. The possible degree(s) is/are because it must be equal to the greater of the degrees of P and Q.
B. The possible degree(s) is/are because it must be equal to the lesser of the degrees of P and Q.
C. The possible degree(s) is/are because it must be less than the degree of either P or Q
D. The possible degree(s) is/are because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel