INSTRUCTIONS: INSTRUCTIONS: Find the slope of the line and enter it here: 1. Find the slope of the line and enter it here: Find the y-intercept of the line & enter it here: Find the y-intercept of the line the enter it here: Write the equation of the line in form y=mx +b Write the equation of the line in form y=x+h 126 27 17
Answers
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]from the graph we notice that the line passes through the points (0,2) and (3,0), plugging this values into the equation above we have:
[tex]\begin{gathered} m=\frac{0-2}{3-0} \\ m=-\frac{2}{3} \end{gathered}[/tex]therefore the slope is m=-2/3.
The y intercept is the value of y when x=0; from the graph we conclude that b=2.
The equation of the line is:
[tex]y=-\frac{2}{3}x+2[/tex]Related Questions
2 subtracted from the product of 5 and a number
Answers
Answer:
5x-2
Step-by-step explanation:
the 'x' is "a number"
write an expression
1. Richie makes $40 per hour doing web design and $20 per hour doing logo design.
Answers
Answer:
Step-by-step explanation:
40x+20y x is for the amount of hours he spends on web design and y for 20 obviously
Which expression does not belong? 2^3 8 3^2 2^2*2^1
Answers
What is the domain
of the function?
Answers
The domain of the function is found as [-7, 6].
What is termed as the domain?A function is an mathematical object that accepts input, appears to apply a rule to it, and returns the result. A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result. The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs. The range refers to the outputs which are actually used.For the given question,
The graph of the function is given.
By the definition of the domain, the maximum and minimum values of the graph on x axis are 6 and -7 respectively.
Thus, the domain of the function is found as [-7, 6].
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Find the area of the triangle I’ll send a picture of the triangle
Answers
Ok, so
We want to find the area of the following triangle:
Remember that the area of a trangle is given by the following equation:
[tex]A=\frac{bh}{2}[/tex]Where b is the base of the triangle and h is its height.
If we replace our values:
[tex]A=\frac{(11)(2)}{2}=11[/tex]Therefore, the area is equal to 11 square units.
1. Given that U = {1, 2, 3, ..., 10}, S = {3, 5, 7, 9} and T = {4, 5, 6, 7}, find S-T
Answers
The set of, S - T = {3, 9}
Define Set Operation.
To obtain a combination of components according to the operation done on them, the set operations are conducted on two or more sets.
In a set theory, there are three major types of operations performed on sets, such as:
1) Union of sets (∪)
2) Intersection of sets (∩)
3) Difference of sets ( – )
We know, S -T = S ∩ T'
Given, universal set is U = {1, 2, 3, ..., 10}
S = {3, 5, 7, 9} and T = {4, 5, 6, 7}
Now, find T' (T's compliment),
The complement of set T is defined as a set that contains the elements present in the universal set but not in set T.
T' = {1, 2, 3, 8, 9, 10}
given, S = {3, 5, 7, 9}
Find, S ∩ T'
S ∩ T' = {3, 5, 7, 9} ∩ {1, 2, 3, 8, 9, 10}
The intersection of two sets S and T is a subset of the universal set U and contains elements that are present in both sets S and T. It is represented by the symbol "∩".
so, S ∩ T' = {3, 9}
Hence, S - T = S ∩ T' = {3, 9}
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which expression is equivalent to 3(x-y)
Answers
MULTIPLY EVERY TERM IN THE BRACKETS BY 3
[tex] = 3(x) + 3( - y) \\ = 3x - 3y[/tex]
ATTACHED IS THE SOLUTION
Question 6 of 10Which choice is equivalent to the fraction below when x is an appropriatevalue? Hint: Rationalize the denominator and simplify.Please help
Answers
Drag the red and blue dots along the x-axis and y-axis to graph 3x-5y=20
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Answer:
what red and blue dots?
Step-by-step explanation:
The resting heart rates for a sample of 15 students are recorded in the following stemplot.
A stemplot titled heart rates has values 55, 63, 65, 69, 69, 69, 69, 70, 71, 73, 73, 74, 75, 76, 77.
What is the mean resting heart rate for this sample?
66.0 beats per minute
69.0 beats per minute
69.9 beats per minute
70.0 beats per minute
Answers
Answer:
C) 69.9 beats per minute
Step-by-step explanation:
Mean is the average.
It is calculated as:
mean = sum of samples/ number of samplesFind it using the equation above:
(55 + 63 + 65 + 69*4 + 70 + 71 + 73*2 + 74 + 75 + 76 + 77)/15 = 1048/15 = 69.866 ≈ 69.9Correct choice is C
Answer:
c
Step-by-step explanation:
If the size of an object is 5.0 cm, and the size of the image formed by a lens is 15.0 cm, what is the magnification of the system?
Answers
The magnification of the system with an object distance of 5 cm and an image distance of 15 cm is 0.33.
A lens is a transmissive optical tool that employs refraction to focus or disperse a light beam.
In optics, magnification refers to the image's size in relation to the item that produced it. The ratio of the image length to the object length, as measured in planes perpendicular to the optical axis, is referred to as linear magnification, also known as lateral or transverse magnification.
The size of an object is u = 5 cm
The size of the image formed by the lens is v = 15 cm
Then the magnification M will be:
Magnification = Image distance/ Object distance
M = v/u
M = 5/15
M = 1/3
M = 0.33
Hence, the magnification of the system is 0.33.
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what is the answer use the slope intercept form to graph the equation y=7/4x-1
Answers
The equation y = 7/4x - 1 is in slope-intercept form, with a slope of 7/4 and a y-intercept of -1.
To graph it, you need to locate the point (0, -1) - the y-intercept -, and then use the slope to find another point. From (0, -1) you have to move 4 units to the right, and 7 units up, reaching the point (4, 6). Then, you have to draw the line that passes through theses points, as follows:
the volume of the prism below is 264 in3. what is the height of the prism
Answers
The volume of any prism = base area x height
Given Volume = 264 in^3
The prism is triangular based
Therefore, its base area = 1/2 x base x height
The base of the triangle= 8in
Height of the triangle = 6in
[tex]\begin{gathered} \text{ Base area = }\frac{1}{2}\text{ x 8 x 6} \\ \text{Base area= 24in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ Recall, Volume = Base area x height} \\ H\text{eight = }\frac{\text{Volume}}{\text{Base area}} \\ \text{ Height=}\frac{264in^3}{24in^2} \\ \\ \text{Height}=11\text{ in} \end{gathered}[/tex]The height of the prism is 11 in.
What is the function g(x) that What is the results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis?
g(x) =
Answers
The function g(x) that results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis is g(x) = -|x + 12|
Translating to left ≡ f(x + 12)
Translation up 12 units means g(x)=f(x)+5g(x)=f(x)+5. Reflecting this across the x-axis means g(x)=-(f(x)+12)g(x)=−(f(x)+12)
-(x+12)=-x-12
f(x + 12) = |x + 12|
Reflection of a function f(x) about the x - axis is keeping the x value same but negating the y values
Reflected f'(x) = -y = -f(x)
Taken together
g(x) = -(|x + 12|)
The function g(x) that results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis is g(x) = -|x + 12|
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In the circle below, G is the center, LM Is a diameter, HF intersects the circle at M, and JN intersects the circle at K and L. Useblanks.
Answers
HF, JN
1) Examining this question, we can state that a tangent line is the one that "touches" the circle in one single point.
So, in this diagram we can state that the tangent line is HF
2) On the other hand, a secant line crosses the circle in two points at least. So the one that fits in this definition is the line defined by points JN
3) In Euclidian Geometry, a chord is a line segment that connects two points in a circle or curve. Examning the diagram again, we can state that KM is a chord.
Nazir was given 5over7 of the fruit basket what fraction of the fruit basket was left over?
Answers
The fraction of the fruit basket is 2/7.
What is fraction?
Fraction represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator.
Total fraction = 1 or can be written as 7/7
Nazir given 5/7 of the fruit basket
1-5/7 = 7-5/7
= 2/7
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Use the appropriate form of the percentage formula.What percent of 14.4 is 11.7? Round to the nearest hundredth of a percent.
Answers
Hello there. To solve this question, we'll have to compare the values with two fractions:
To see how much of 14.4 is 11.7, in percentage, we start by considering 14.4 represents 100%, or 100, since we want to find the answer in percent as well.
Then we make:
[tex]\frac{11.7}{x}=\frac{14.4}{100}[/tex]Cross multiply the numbers:
[tex]11.7\cdot100=14.4\cdot x[/tex]Divide both sides of the equation by a factor 14.4
[tex]x=\frac{11.7\cdot100}{14.4}[/tex]Using a calculator, we get that x is equal to:
[tex]81.25[/tex]Therefore, 11.7 is 81.25% of 14.4!
I need help on 8 please it says find the value of x round each answer to the nearest tenth
Answers
Step 1
Redraw the diagram and use the Pythagoras theorem to find the value of c\x.
Step 2:
Find the value of y from the right-angle triangle of sides: 10, 25 and y using the Pythagoras theorem
Opposite = y
Adjacent = 10
Hypotenuse = 25
[tex]\begin{gathered} \text{Pythagoras theorem} \\ \text{Opposite}^2+adjacent^2=hypotenuse^2 \\ y^2+10^2=25^2 \\ y^2\text{ + 100 = 625} \\ y^2\text{ = 625 - 100} \\ y^2\text{ = 525} \\ y\text{ = }\sqrt[]{525} \\ y\text{ = 5}\sqrt[]{21} \end{gathered}[/tex]Step 3
Next, use the Pythagoras theorem to find x from the triangle with sides
28, x and y
Hypotenuse = 28
Opposite = x
Adjacent = y
[tex]\begin{gathered} x^2+y^2=28^2 \\ x^2\text{ + (5}\sqrt[]{21})^2=28^2 \\ x^2\text{ + 525 = 784} \\ x^2\text{ = 784 - 525} \\ x^2\text{ = 259} \\ \text{ x = }\sqrt[]{259} \\ x\text{ = 16.1} \end{gathered}[/tex]Final answer
x = 16.1
Instructions: Select all of the methods that will find both real andimaginary solutions.Select one or more:Quadratic FormulaCompleting the SquareFactoringSquare RootsCheck
Answers
Let's begin by identifying key information given to us:
Imaginary solutions
What is the word for added and subtracted parts of an expression
Answers
The word for added and subtracted parts of an expression is known as the term.
What is an expression?An expression in math is an arithmetic set of numbers and variables with signs and calculations. For example, 4x - 2x = 2x is an expression. The parts that are connected with addition or subtraction or other signs are called terms.
Terms that have the same base exponent can be joined with addition and subtraction. These are called like terms. For example, 3 x 3 and 5 x 3 are like terms.
Therefore, the term is the term for the added and removed components of an equation.
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A man sold 4 times as many tie dyed T shirts as silk screened shirts. He sold 190 shirts altogether. how many tie dyed shirts did he sell?
Answers
Answer: 152 tie dyed T shirts
Let the number of dyed T shirts be = x
Let the number of silk screened shirts be = y
He sold sold 4 times as many tie dyed T shirt as screened shirts
Since x = Tie dyed T shirt
Therefore, x = 4y
x = 4y ------------------- equation 1
He sold 190 shirts all together
x + y = 190 ------------ equation 2
Substitute the value of x = 4y into equation 2
4y + y = 190
5y = 190
Divide both sides by 5
5y/5 = 190/5
y = 38
Since x = 4y
x = 4(38)
x = 152 tie dyed T shirts
Therefore, 152 tie dyed T shirts was sold
According to the question, the man sold 4 times as many tie dyed T shirt as silk screened shirt
This implies that for 1 silk screen shirt sold, he would also sell 4 tie dyed T shirt
Since, x = tie dyed T shirt and y = silk screened shirts
Then, x= 4 x y
x = 4y
The man sold 190 shirts altogether
This implies that, he sold a total of 190 of both tie dyed T -shirt and silk screened shirts
Mathematically,
x + y = 190
Since x = 4y
Then, 4y + y = 190
This Implies that for 1
x +3 +7 = 2x -10 -x how many solutions does it have
Answers
Answer:
no solution
Step-by-step explanation:
x + 3 + 7 = 2x + 10 - x ( simplify both sides )
x + 10 = x - 10 ( subtract 10 from both sides )
x = x - 20 ( subtract x from both sides )
0 = - 20 ← not possible
this indicates the equation has no solution
in a class of students the following data table summarizes how many students pass a test and completed the homework due the day of the test what is the possibility that a student chosen randomly from the class failed the test
Answers
From the table,
Total number of students that failed the test = 2 + 7 = 9
The total number of students that participated = 10 + 3 + 2 + 7 = 22
The possibility that a student chosen randomly from the class failed the test = Total number of students that failed the test divided by the total number of students that participated
= 9/22
Hence, the possibility that a student chosen randomly from the class failed the test is 9/22
numbe
Pls explain I have a test on this number 2
Answers
Hello there. To solve this question, we have to remember some properties about equations of circles.
Given the following equation:
[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]It is called the equation of a circle with center at
[tex](x_0,\,y_0)[/tex]And radius R.
In the question, it gives us two equations that we might describe the shape of the equation, considering its key features (center, foci, asymptotes, semi-major and semi-minor axes, if applicable).
We have that
[tex](x+4)^2+(y-2)^2=16[/tex]Is the equation of a circle with center at (-4, 2) and radius equal to
[tex]R=\sqrt{16}=4[/tex]For the other equation
[tex](x-2)^2+(y-5)^2=64[/tex]Is also the equation of a circle, with center at (2, 5) and radius equal to
[tex]R=\sqrt{64}=8[/tex]Which type of wave does the illustration depict?
Answers
which fact below has the same difference as 18-6= ?8-1614-814-716-8
Answers
18-6=12
8-16=-8 not equal 18-6
14-8=6 not equal 18-6
14-7=7 not equal 18-6
16-8=8 not equal 18-6
Hence none of the options has the same difference as 18-6
What is the range of the function f(x)=√x-8 + 6?Of(x) ≥-8O f(x) ≥-6Of(x) ≥ 6O f(x) ≥ 8
Answers
Hello!
We have the function below:
[tex]f(x)=\sqrt{x-8}+6[/tex]Let's analyze the graph of it:
Note that for the domain, it starts when x = 8.
For the range, it starts when y = 6.
So, the range of this function is:
[tex]\begin{gathered} [6,+\infty) \\ \text{ or} \\ \boxed{f(x)\geqslant6} \end{gathered}[/tex]Third alternative.
Find the coordinates of the vertices of each figure after the given transformation REFLECTION ACROSS y=-x
Answers
The coordinates of the vertices after the reflection are V'(-3,2), U'(0,-2), W'(-1,3) and T'(1,2) .
A reflection in mathematics is a mapping from a Cartesian coordinates to itself which is an isometry with such a set of fixed points known as the hyperplane, also known as the axis or plane of reflection.
The mirror image of a figure in the axis or plane of reflections is the image produced by a reflection. For instance, the minuscule Latin letter p would appear like the letter q when reflected with regard to a vertical axis. It would appear like b when reflected on a horizontal axis. Every object goes back to its original place and every geometric object is returned to its initial condition when a reflection is applied twice consecutively.We know that when a figure is reflected along the line y = -x then the coordinates change their places and they are negated.
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picture to the problem sented
Answers
Answer:
Explanation:
For the matrix equation
[tex]2X+A=B[/tex]We first subtract A from both sides to get
[tex]2X=B-A_{}[/tex]Now,
[tex]B-A=\begin{bmatrix}{-7} & {-8} & {} \\ {-2} & {6} & {} \\ {4} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-3} & {0} & {} \\ {0} & {3} & {} \\ {-6} & {6} & {}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-7--3} & {-8-0} & {\square} \\ {-2-0} & {6-3} & {\square} \\ {4--6} & {4-6} & {\square}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]Hence, we have
[tex]2X=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]Dividing both sides by 2 gives
[tex]\begin{gathered} X=\frac{1}{2}\cdot\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix} \\ \end{gathered}[/tex][tex]X=\begin{bmatrix}{-5} & {-4} & {} \\ {-1} & {-\frac{3}{2}} & {} \\ {5} & {-1} & {}\end{bmatrix}[/tex]which is our answer!
Solve the system using the elimination.
Answers
On solving the system of equation using elimination method , the value of x is 1 and value of y is 3 .
in the question ,
the two equations are given as
3x+y=6 ...(i)
and
-8x+2y= -2 ...(ii)
In elimination method, the equation is multiplied by some constant and then add/subtract the equations to eliminate any variable x or y.
multiplying equation(i) by 2 we get
6x+2y=12 ....(iii)
subtracting , the equation (ii) from equation (iii) , we get
(6x+2y) - (-8x+2y) = 12-(-2)
6x+2y+8x-2y = 12+2
14x = 14
x = 1
We eliminate 'x' from equation (ii) by replacing the value of 'x' with 1 ,
we get
-8x+2y= -2
-8(1)+2y= -2
-8 + 2y = -2
2y = -2 + 8
2y = 6
y = 3
Therefore , On solving the system of equation using elimination method , the value of x is 1 and value of y is 3 .
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