The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
The given coordinate are (8, -1) and (2, -5).
What is the slope of an equation?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].
The standard form of an equation is Ax + By = C.
The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].
Multiply each term by 3 of the equation.
[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]
⇒3y + 3 = 2x - 16
Subtract 2x from both sides of a equation.
That is, -2x + 3y + 3 = - 16
Subtract 3 from both sides of a equation.
That is, -2x + 3y = - 19
Multiply each term by - 1 from both sides of an equation.
That is, 2x - 3y = 19
Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
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Marsha has 132 books.
They are divided
equally between three
shelves. Each book
weighs 0-2 kg.
How much weight
does each shelf
support?
Answer:
Step-by-step explanation:
=132/3
=44 books per shelf
since maximum weight of a book is 2kgs,
=44(2)
=88
What is the range of the function y=-x² +1?
Oys-1
Oy2-1
Oyst
y21
The range of the function is
[tex]y \leqslant 1[/tex]
What is the factored form of the expression?
24g2 – gh – 10h2
The factored form of the expression is 2(g-h)(12g+5h)
What is a Quadratic Expression ?A quadratic Expression is what can be written in the form of
ax²+bx +c
The given quadratic expression is
24g² -gh -10h²
10g² - 10h² +14g² -gh
10(g+h)(g-h) +14 g(g -h)
(g-h)(10 g +10h +14g)
2(g-h)(12g+5h)
Therefore the factored form of the expression is 2(g-h)(12g+5h).
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What is the solution to the system of equation
Answer:
[tex]x=(-2,\frac{5}{3} )[/tex]
Step-by-step explanation:
1) We will use the matrix method to solve this problem.
[tex]\left[\begin{array}{ccc}-2/3&1&3\\1&0&-2\\\end{array}\right][/tex]
2) Swap Row₁ and Row₂ to make row reduction easier.
[tex]\left[\begin{array}{ccc}1&0&-2\\-2/3&1&3\\\end{array}\right][/tex]
3) Apply to Row₂ : Row₂ + [tex]\frac{2}{3}[/tex] Row₁.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\end{array}\right][/tex]
4) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
5) Apply Row₁ : Row₁ - 0 Row₂.
[tex]\left[\begin{array}{ccc}1&0&-2\0\\0&1&5/3\end{array}\right][/tex]
6) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in reduced row echelon form.
7) Therefore,
[tex]x=-2\\x=\frac{5}{3}[/tex]
Use the factorization to find the values of x for which p(x) = 0. (x – 1)(x 1)(x 5) = 0 x – 1 = 0, so x = x 1 = 0, so x = x 5 = 0, so x =
Answer: (x – 1)(x + 1)(x + 5) = 0
x – 1 = 0, so x = 1
x + 1 = 0, so x = -1
x + 5 = 0, so x = -5
A number is 5 more than 3 times another number. the sum of the two numbers is 33. as an equation, this is written x 3x 5 = 33, where x represents the smaller number. plug in the numbers from the set {3, 5, 7, 9} to find the value of x. the value of x that holds true for the equation is . so, the smaller number is and the larger number is .
Answer:
Step-by-step explanation:
Equation
x + 3*x + 5 =33
Solution
4x + 5 = 33
x = 3
4*3 + 5 =? 33
12 + 5 = ? 17 x is not 3
x = 5
4*5 + 5 = ? 33
20 + 5 = 25 x is not 5
x = 7
4*7 + 5 =? 33
28 + 5 = 33 x = 7 is the answer
The value of the variable x will be 7 that holds true for the equation.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A number is 5 more than 3 times another number.
The sum of the two numbers is 33.
Let the number be x.
Then the another number will be 3x + 5.
Then the equation will be
x + 3x + 5 = 33
Then the value of x will be
4x + 5 = 33
4x = 28
x = 7
Then the value of the variable x will be 7 that holds true for the equation.
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find the area and perimeter of the figures
Answer:
6x+6 or 4x+10
Step-by-step explanation:
hope u like it
Answer:
a) 196cm^2
b) 225cm^2
c) 180 cm^2
Step-by-step explanation:
a) The figure is a square, so you can use the formula: a = l^2, or area equals length of one side squared.
a = (14cm)^2
a = 196cm^2
b) a = (15cm)^2
a = 225cm^2
c) This one is a parallelogram, so it's trickier. However, we can imagine the figure as a rectangle by taking the small triangle that sticks out on the right and putting it into the gap in the left. Now, we can solve this using the formula for a rectangle: a = l x w.
a = l x w
a = 18cm x 10 cm = 180 cm^2
:)
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
(x minus 1) + x + (x + 1) = 42
(x minus 2) + x + (x + 2) = 42
x + 2 x + 3 x = 42
PLS HELP
Answer:
x+(x+1)+(x+2)=42
3x+3=42
3x=42-3
3x/3=39/3
x=13
Step-by-step explanation:
hope I helped
Which equation represents the line that is parallel to y= 3 and passes through (-2,-8) ?
Answer:
y = - 8
Step-by-step explanation:
y = 3 is a horizontal line that includes all of the x coordinates
just need to find parallel
y = - 8
The ratio table shows the numbet of miles karen can drive for 1,2,3 and 4 gallons of gasoline.Based on the table, How far would she be able to drive on 8 gallons of gasoline
Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:
D(n) = 30n.
She has n = 8 gallons, hence the distance is given by:
D(8) = 30 x 8 = 240 miles.
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Parent Functions
Question 4 of 10
On a piece of paper, graph:
{1 if -1 < x≤0
f(x) = {2 if 0 < x≤1
{3 if 1 < x≤2
Then determine which answer choice matches the graph you drew.
The graph of the parent function is given below;
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given function is;
1, if -1<x≤0
f(x) = 2, if 0<x≤1
3, if 1<x≤2
Now, the graph of given function is given below.
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Answer:
The correct graph is in the image below
Step-by-step explanation:
Does this graph represent a function? Why or why not?
10.
8
6
4
2
-10 8 6 4 2
88
-8
10
2468 10
A. No, because it fails the vertical line test.
O B. No, because it is not a straight line.
OC. Yes, because it passes the horizontal line test.
OD. Yes, because it passes the vertical line test.
Answer:
D.) Yes, because it passes the vertical line test.
Step-by-step explanation:
For a function to be a function, there must be one output for every input. IN other words, there must be one "y" value for every "x" value. One can see if a graph passes this test by performing the vertical line test.
In this case, the line on the graph passes the test and represents a function. Again, this is because each "x" value has only one "y" value.
Yes, The graph is function because it passes the vertical line test.
We have to given that,
A graph of function is shown in image.
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
And, The vertical line test is used to determine if a graph of a relationship is a function or not. if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.
Hence, By given graph,
it passes the vertical line test.
So, Graph shown is a function.
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A sample of 50 11th graders were asked to select a favorite pattern out of 6 choices. The data list below shows what their favorite color patterns were, and the accompanying frequency table and bar graph represent these data. In the bar graph, the height of the blue-gray bar is 4, the height of the green bar is 9, and so on.
Suppose that, rather than being just a bar graph, the display you see above is a relative frequency bar graph. The vertical axis of the graph will be marked off in percentages, from 0 percent up to 30 percent. What will be the height of the green bar?
A.
15
B.
25
C.
9
D.
18
Answer:
D 18
Step-by-step explanation:
100% = 50 (all students)
1% = 100%/100 = 50/100 = 1/2 = 0.5
we get any percentage for any number by dividing the number by 1% (0.5) to see how often it fits in.
there are 9 votes for green.
9/ 0.5 = 18%
Examine Carmen's plans for rail lines at a train station.
2
(6x + 5)°
X
48%
What is the measure of angle 2? m/2 =
K
m
(7x-4)°
t
The measure of angle 2 is 73.
What is angle?An angle is a combination of two rays (half-lines) with a common endpoint.
Given:
As, angle 1 and 2 are supplementary
<1 + <2 + (6x +5) =180
And, by corresponding angle, <1= 48
So, 48 + <2 + (6x +5)= 180
<2 + (6x +5) = 132
Also x= 9
then, <2 = 132 - 59
<2= 73.
Hence, measure of <2 is 9.
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Which transformation would be a horizontal reflection and a dilation of scale factor ½ of the L shape?
The transformation which would be a horizontal reflection and a dilation of scale factor ½ of the L shape is as in the attached image.
What is horizontal reflection and dilation?The term horizontal reflection with respect to transformation in mathematical context simple means that the shape is reflected over the vertical axis(y-axis as mirror). The dilation of a scale factor of ½ simply means that the shape reduces to half it's original size.
Hence, it follows that the attached image represents the transformation.
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Match each figure to the number of lines of reflection that will reflect the figure onto itself.
The lines of symmetry for all the figures have been determined.
What is Reflection Symmetry ?A symmetry in which one half of the object is symmetrical to thew other half
A square has 4 lines of reflection symmetry , 2 along its sides and 2 along its diagonals
A regular hexagon has 6 reflection symmetry , three along the midpoints of the sides and three along the daigonals
A Trapezium can have 0 or 1 lines of symmetry depending upon the length of the non parallel sides.
An equilateral Triangle has 3 lines of reflection symmetry , an isosceles has 2 lines of symmetry and a scalene triangle has no lines of symmetry.
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Answer:
Step-by-step explanation:
got it right
if each element in the input is mapped to one element in the output, then the relation is called as a
Answer:
function
Step-by-step explanation:
what is the answer for this please 23÷23
Answer:
1
Step-by-step explanation:
Any number divided by itself equals 1. So, 23 divided by 23 is 1.
Sal's Sandwich Shop sells wraps and
sandwiches as part of its lunch specials. The
profit on every sandwich is $2 and the profit on
every wrap is $3. Sal made a profit of $1,470
from lunch specials last month. The equation
2x + 3y = 1,470 represents Sal's profits last
month, where x is the number of sandwich
lunch specials sold and y is the number of wrap
lunch specials sold.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Answer:
it will be something like that
Step-by-step explanation:
u should modify the equation to be
y = (1470-2x)/3
The following set of random numbers represents 20 simulations of three daily
flights from New York to Los Angeles, with 0, 1, 2, or 3 representing a late
departure and 4, 5, 6, 7, 8, or 9 representing an on-time departure. In how
many of the simulations was there an on-time departure for all three flights?
The number of simulations in which was there was an on-time departure for all three flights is; 6
How to carry out number simulations?
We are given;
Number of Simulations = 20
Numbers that represent late departure = 0, 1, 2 or 3
Numbers that represent On-time departure = 4, 5, 6, 7, 8 or 9.
Now, the 20 simulations as seen online are;
339 931 317 444 432 858 194 192 649 709
742 626 702 258 955 880 505 854 774 132
To know the number of simulations that were on-time departure, we need to find the ones that don't include 0, 1, 2 or 3.
Looking at the simulations, the ones that represent on-time departure are 444, 858, 649, 955, 854, 774.
Thus, there are 6 simulations in which was there an on-time departure for all three flights
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Triangle △ABC is reflected across line n to create △ A'B'C', What is the measure of ∠C?
The measure of ∠C is 54°.
To solve the problem :let us assume that line n is a mirror.
∴ ∠A = ∠A' = 59°
∠B = ∠B' = 67°
∠C = ∠C'
According to property of triangles :
Sum of all angles of a triangle is 180°.
∴ A + B + C = 180°
59 + 67 + C = 180
C = [tex]180 - (59 +67)[/tex]
C = 54°
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Answer:
54 degrees
Step-by-step explanation:
Question 3 of 10
What else would need to be congruent to show that AABC= AXYZ by ASA?
B
A
C Z
Y
X
Given:
help i need for tomorrow
Answer:
The three bags for 92.50 pounds (offer B)
Step-by-step explanation:
Offer A:
[tex] \frac{35}{2 \times 25} = \frac{35}{50} = .7[/tex]
Offer B:
[tex] \frac{92.50}{3 \times 50} = \frac{92.50}{150} = .617[/tex]
Offer B has the lower unit price.
3 photos are printed in 1 minute. How many minuted would it take to print 600 photos
Answer:200 minutes
Step-by-step explanation:
1 minute = 60 seconds.
6/3 = 2 (20 seconds) 1 photo every 20 seconds.
600x20 = 12000. seconds.
12000/60 = 200 (200 minutes)
Answer:
200 photos
Step-by-step explanation:
1 min = 3 photos
X min = 600 photos
therefore3 X = 600
X = 600/3
X = 200
a bag contains 4 white marbles , 7 red marbles , and 5 black marbles. you randomly select 3 marbles from the bag. without replacement.the random variable represents the number of black marbles
find the y intercept
Answer:
(0,-2)
Step-by-step explanation:
y intercept is that line that intercepts with the y axis
when x is 0 then y value.
f(x) = 3x + 6, find the ordered pair when x = -1.
(-1,-3)
(-1,3)
(-1,-9)
(-1,9)
Answer:
(-1 ; 3)
Step-by-step explanation:
when they say find the ordered pair they simply mean find the corresponding y value when x = -1
* where you see x substitute-1 *
f(-1) = 3(-1) + 6
=3
Which ordered pair is included in the solution set to the following system?
y > x2 + 1
y < x2 – x + 1
(–3, 4)
(–2, 6)
(0, 2)
(2, 4)
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The ordered pair which will satisfy both the inequalities will be the solution to the system of inequalities. Therefore, let's substitute each solution in the given inequalities,
A.) (–3, 4)
y > x² + 14 > (-3)² + 1
Since the first inequality is not satisfied this is not a part of the solution.
B.) (–2, 6)
y > x² + 16 > (-2)² + 1
6 > 5
y < x² – x + 16 < (-2)² - (-2) + 1
6 < 7
Since both the inequalities are satisfied this is the solution to the given system of inequalities.
C.) (0, 2)
y > x² + 12 > 0 + 1
2 > 1
y < x² – x + 12 < (0)² - (0) + 1
2 < 1
Since the second inequality is not satisfied this is not a part of the solution.
B.) (2,4)
y > x² + 14 > (2)² + 1
4 > 5
Since the first inequality is not satisfied this is not a part of the solution.
Hence, the correct option is B.
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what is the answer in system form
y=-2x
5x-7y=-38
Answer:
x = -2
y = 4
Step-by-step explanation:
To solve the system of equations, you want to plug one equation into the other and then simplify. You can do this by setting one equation equal to a variable (like in the first equation), and then substituting the function into the variable into the second equation.
First Equation: y = -2x
Second Equation: 5x - 7y = -38
5x - 7y = -38 <----- Second equation
5x - 7(-2x) = -38 <----- Plug first equation into "y"
5x + 14x = -38 <----- Multiply -7 and -2x
19x = -38 <----- Add 5x and 14x
x = -2 <----- Divide both sides by 19
Now that you know the value of one variable, you can use it to find the value of the second variable. This can be done by plugging x = -2 in to one of the equations.
y = -2x <----- First equation
y = -2(-2) <----- Plug -2 in "x"
y = 4 <----- Multiply -2 and -2
como identifico una X Cubica en un polinomio
la componente "cubica" será aquella que tenga un exponente igual a 3.
¿como identifico una X Cubica en un polinomio?
Un polinomio tiene la forma general:
[tex]p(x) = a_n*x^n + ... + a_1*x^1 + a_0[/tex]
Donde todos los exponentes de x son numeros naturales.
Particularmente, la componente "cubica" será aquella que tenga un exponente igual a 3.
Entonces, por ejemplo, en:
[tex]p(x) = 4*x^5 + 2*x^4 + 5*x^3[/tex]
La parte cubica será:
[tex]5*x^3[/tex]
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