Answer:
y=-1/3x+7
Step-by-step explanation:
put it in y-y1=m(x-x1)
perpendicular means the slope is opposite
slope is -1/3
y-9=-1/3 (x+6)
y-9=-1/3x -2
+9 +9
y=-1/3x +7
write an equation in form of y=mx+b for a line with slope =7 and y-intercept =4
Trixie exclaimed , “hey! Arithmetic sequences are just name for linear functions.” What do you think ? justify your idea based on multiple representations
An arithmetic progression is a sequence in which each number is a fixed amount larger (or smaller) than the one before it. The common difference is the sum in question.
"Arithmetic sequences are just name for linear functions", what you think?An arithmetic progression is a sequence in which each number is a fixed amount larger (or smaller) than the one before it. The common difference is the sum in question.
By picking two consecutive words in the sequence and deducting the first from the second, we may get the common difference for a particular sequence.
The graph of linear function is a straight line. A function with the formula y=f(x)=ax+by=f(x)=ax+b is said to be linear.
Although not quite the same, arithmetic progressions resemble linear functions.
If the value nn is a full number, then the expression t(n)=2n-4t(n)=2n4 denotes a series, and the graph of this sequence will have distinct points (as shown below).
The expression f(x)=2x-4f(x)=2x4, where xx is any real number, on the other hand, denotes a function, and this function's line graph will be continuous (as shown below).
Although not quite the same, arithmetic progressions resemble linear functions.
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Thenegative interval(3) of the functiony=-X²+1 are
We are given the following function
[tex]y=-x^2+1[/tex]We are asked to find the negative interval of this function.
A negative interval means that where the y values of the function are negative.
Let us have a look at the graph of this function.
As you can see,
For x = 0, the interval is positive.
For x = 1 and x = -1 the y value is 0 (we don't consider 0 as either positive or negative that's why 0 is not included in the negative or positive interval)
The y values of the function are negative for
x > 1 and x < -1
Therefore, the negative interval of the function y = x² + 1 is
[tex]1Write an equation of the line passing through point P(-2, 6) that is parallel to the line x =-5 X Graph the equations of the lines to check that they are parallel.
The equation of the line passing through the point P(-2,6) that is parallel to the line x = -5 is x = -2 .
In the question ,
it is given that
the required line is parallel to x [tex]=[/tex] -5
means the line x [tex]=[/tex] -5 , is a vertical line parallel to y axis , it makes an angle of 90° with the x axis .
so , slope will be tan(90°) = 1/0
hence the slope of the required line is 1/0.
The equation of the line passing through point P(-2,6) and with slope = 1/0 , is
y-6 = (1/0)*(x-(-2))
0 = 1 * (x + 2)
0 = x + 2
x = -2
the graph is drawn below .
Therefore , The equation of the line passing through the point P(-2,6) that is parallel to the line x = -5 is x = -2 .
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please help me on this
what is 7.6 x 10^4 in standard form?
Answer: 76,000
Step-by-step explanation:
You move the decimal point to the right 4 times because of the positive exponent.
3. Is x^5 + x² + x? a polynomial? Explain why or why not.
ANSWER:
A polynomial is an algebraic expression of ordered addition, subtraction, and multiplication made up of variables, constants, and exponents.
Polynomials are made up of finite terms. Each term is an expression that contains one or more of the three elements they are made of variables, constants, or exponents.
In this case, for each term, the variable is x, the constant is 1, and the exponents are 5, 2, and 1, respectively.
This means that we have a sum of monomials, that is, that the expression is a polynomial.
Given the equations y=x+7 and y=x^2+4 how many times do they intercept?
According to the following graph, the equations y=x+7 and y=x²+4 will intercept 2 times at the points (-1.3, 5.7) and (2.3, 9.3).
Intercept:
The point where the line or curve crosses the axis of the graph is known as intercept.
That is, if a point crosses the x-axis, then it is known as the x-intercept. Similarly, if a point crosses the y-axis, then it is called as the y-intercept.
Given,
Here we have the equation y=x+7 and y=x²+4.
Now, we need to find the number of times the equation is intercepts.
First, we have to plot the graph for the given equations,
Then based on that one we have easily identify the intercepting points in order to get the results.
In the following graph, the blue line represents the equation y=x²+4 and the red line represents the equation y = x + 7.
While we looking into the graph we have identified that the two lines are intersecting at two point they are (-1.3, 5.7) and (2.3, 9.3).
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Can someone give me the answer to this pls?
Answer: x= -3
Step-by-step explanation:
1) Set up the equation with triangle sum
35 + x + 58 + 90 = 180
2) Solve
183 + x = 180
x = -3
the product of a number and -3 increased by 16 is 31
Ax+By=C form with slope of 14 over 13 with points (5,6) and (-8,-8)
[tex]\displaystyle\\Answer:\ -\frac{14}{13} x+y=\frac{8}{13}[/tex]
Step-by-step explanation:
Ax+By=C the slope is 14/13 (5,6) (-8,-8)
The slope m equil 14/13
[tex]\displaystyle\\By=mx+C\\\\By=\frac{14}{13} x+C\ \ \ \ (1)[/tex]
Substitute the coordinates of the points into equation (1) and obtain a system of equations:
[tex]\displaystyle\\\left \{ {{B(6)=\frac{14}{13}(5)+C } \atop {B(-8)=\frac{14}{13}(-8)+C }} \right.\\\\\left \{ {{6B=\frac{70}{13} +C\ \ \ \ \ \ \ (2)} \atop {-8B=-\frac{112}{13}+C\ \ \ (3) }} \right.[/tex]
Multiply both parts of the equation (3) by -1:
[tex]\displaystyle\\\left \{ {{6B=\frac{70}{13}+C \ \ \ \ (4)} \atop {8B=\frac{112}{13}-C }} \right.[/tex]
Add these equations :
[tex]14B=\frac{182}{14}\\\\ 14B=14[/tex]
Divide both parts of the equation by 14:
[tex]B=1[/tex]
Hence, let's substitute the value of B into equation (4):
[tex]\displaystyle\\6(1)=\frac{70}{13}+C \\\\6=\frac{70}{13}+C\\6-\frac{70}{13} =\frac{70}{13} +C-\frac{70}{13}\\\\\frac{6*13-70}{13}=C\\\\\frac{78-70}{13}=C\\\\\frac{8}{13}=C\\[/tex]
[tex]\displaystyle\\Thus,\ C=\frac{8}{13}\\\\ So,\ 1(y)=\frac{14}{13} x+\frac{8}{13} \\ -\frac{14}{13} x+y=\frac{8}{13}[/tex]
hellppppp meeee pleaseeee
Answer:
a) x+4
b) a = 1, b = 10
Step-by-step explanation:
a) You can read the lenght of AB, which is 4 + x
b) The lenght of AD is 6+x
The area of the rectangle ABCD is lenght AB * lenght CD,
so (4+x)*(6+x) = 24 + 6x + 4x + x^2 = x^2 + 10x +24
Since this must equal 28, it follows that
x^2 + 10x + 24 = 28,
so 1*x^2 + 10x = 4
(note that 1*x^2 is just x^2)
so a = 1 and b = 10
2334567Happy Paws charges $19.00 plus $2.50 per hour to keep a dog during the day. Woof Watchers charges$10.00 plus 53.75 per hour. Complete the equation and solve it to find for how many hours the total costof the services is equal. Use the variable h to represent the number of hours.The equation isThe total cost of the services will be equal athours.
Let h be the hours and y the total charge. Then, for Happy Paws, we have
[tex]y=2.50h+19[/tex]and for Woof Watches, we have
[tex]y=3.75h+10[/tex]Then, we need to solve these equations.
Solving by elimination method.
If we multiply by -1 the first equation, we have the equivalent system of equations:
[tex]\begin{gathered} -y=-2.50h-19 \\ y=3.75h+10 \end{gathered}[/tex]If we add both equations, we obtain
[tex]0=(3.75-2.50)h+10-19[/tex]because y-y=0. Then, it yields,
[tex]0=1.25h-9[/tex]If we move -9 to the left hand side as -9, we have
[tex]\begin{gathered} 9=1.25h \\ h=\frac{9}{1.25} \\ h=7.2 \end{gathered}[/tex]Hence, to find the total cost, we must substitute this values into one of the 2 equations. If we choose the first one, we obtain
[tex]\begin{gathered} y=2.50(7.2)+19 \\ y=18+19 \\ y=37 \end{gathered}[/tex]Then, the answers are:
The equation is
[tex]2.50h+19=3.75h+10[/tex]and, the total cost of the services will be equal at 7.2 hours
Solve for the value of w. * (8w+8)(9w-5)°
The solution for the value w is 13 in the equation 8w+8 = 9w-5.
What is an angle?Two rays, referred to as the angle's sides and vertex, come together to form an angle. Angles created by two rays are located in the plane where the rays are located.
Dihedral angles are formed when two planes intersect. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can also be used to define an angle between two intersecting curves.
Angle is a term used to describe the size of an angle or of a rotation. This metric represents the proportion of a circular arc's length to radius. In the case of a geometric angle, the arc is centred at the vertex and is bound by the sides.
We know that vertical angles of intersection are equal, so here
⇒ (8w+8) = (9w-5)
⇒ 8w+8 = 9w-5
⇒ 9w - 8w = 8 + 5
⇒ w = 13
Angle measure = 8(13)+8
= 112°
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Five rays share a common endpoint. Set up an equation to find the value of x.
The equation that can be set up is, 2x° + 3x° + 36.5° + 36.5° + 2x° = 360°.
The value of x is: x = 41.
What are Angles around a Point?Angles that are formed around an endpoint but several rays will have a sum of 360 degrees when each of the angles formed around the endpoint is added together.
The diagram shows the angles that are formed by the five rays at a common endpoint. The angles are, 2x°, 3x°, 36.5°, 36.5°, and 2x°.
The sum of all these angles formed will give us 360 degrees. Therefore, the equation that would be created to find the value of x would be written as:
2x° + 3x° + 36.5° + 36.5° + 2x° = 360° [equation set up to find x]
Combine like terms
7x° + 73° = 360°
Subtract 73 from each side
7x° + 73° - 73° = 360° - 73° [subtraction property of equality]
7x = 287
Divide both sides by 7:
7x/7 = 287/7 [division property of equality]
x = 41
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If f (x) = x/2 - 3 and g(x) = 4 x^2 + x-4, find (f+g)(x).
The sum of the two functions can also be expressed as follows;
[tex](f+g)(x)=f(x)+g(x)[/tex]This is not a difficult process. We just put the terms of the two functions together.
We have to be careful to add or subtract the coefficients of similar terms, taking into account their signs.
[tex]f(x)=\frac{x}{2}-3[/tex][tex]g(x)=4x^2+x-4[/tex][tex](f+g)(x)=f(x)+g(x)[/tex][tex](f+g)(x)=4x^2+x+\frac{x}{2}-7[/tex]Answer:
Step-by-step explanation:
x2 – 2x – 8
A and B together can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, in how many days will A alone need to finish the work.
Answer:
it's 21 something like that
Step-by-step explanation:
im 14
What type of reasoning is used to find the next amount of train cars? Explain your answer.
Answer: It's using the table of 2 to continue the pattern of trains.
in the first fig the no. of carton is 0.
for the next one it is 2 and the next 4.
the pattern will thus continue with the multiplication table of 2.
Write a condition Pls
At a restaurant, Hamburgers cost $2.50 each and French Fries cost $1.20 each. If I went to this restaurant, and bought $8.60 worth of food,
write an equation which models how many hamburgers and french fries I purchased.
Let H represent Hamburgers
Let F represent French Fries.
Answer:
2.50h+1.20f=8.60
Step-by-step explanation:
Since the total cost of food costs $8.60, add together the costs of however many burgers and however many fries you bought. 2.50 and 1.20 are multiplied by the amount of food you purchase
-2 1/3+ 1 4/7 what is the solution of this equation?
Answer:
[tex]-\frac{16}{21}[/tex]
Step-by-step explanation:
lets organize the equation so it becomes easier to see
[tex]-2\frac{1}{3} + 1\frac{4}{7}[/tex]
switch the spots so that it becomes even easier to read (this does not affect the result in any way)
[tex]1\frac{4}{7}-2\frac{1}{3}[/tex]
now make them both improper fractions
[tex]\frac{11}{7} -\frac{7}{3}[/tex]
and make them both have the same denominator (21)
[tex]\frac{33}{21} -\frac{49}{21}[/tex]
and solve
([tex]33-49= -16[/tex])
[tex]\frac{33}{21} -\frac{49}{21} =\frac{-16}{21}[/tex]
can we simplify [tex]\frac{-16}{21}[/tex]? does 16 and 21 have a common factor?
No.
so our result is
[tex]-\frac{16}{21}[/tex] or 0.761904762
What is the remainder of 5x3 - 7x² + 2x + 1 divided by (x - 3)?
A.) 126
B.) 79
C.) 203
D.) 205
Answer: A
Step-by-step explanation:
2x - 3y = -6please solve and graph
2x - 3y = -6
Solve for y:
-3y= -6-2x
y= (-2x-6) /-3
y= 2/3x+2
Slope intercept form:
y= mx+b
Where:
m= slope (2/3)
b= y-intercept (2)
So, to graph the function, we have to draw a line that crosses the y axis at 2, and for every 3 units moved to the right along the x-axis it goes up 2 units along the y-axis.
The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 3≤x≤7 goes from least to greates
Given
Function f(x) , g(x) and h(x)
Find
Order of the function according to average rate of change
Explanation
Average rate of change can be given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex][tex]3\leq x\leq7[/tex]for f(x)
[tex]\begin{gathered} \frac{f(7)-f(3)}{7-3} \\ \\ \frac{-10-(-8)}{4} \\ \\ -\frac{2}{4} \\ \\ -\frac{1}{2} \end{gathered}[/tex]for g(x)
[tex]\begin{gathered} \frac{g(7)-g(3)}{7-3} \\ \\ \frac{7-(27)}{4} \\ \\ -\frac{20}{4} \\ \\ -5 \end{gathered}[/tex]for h(x)
[tex]\begin{gathered} \frac{h(7)-h(3)}{7-3} \\ \\ \frac{60-24}{4} \\ \\ \frac{36}{4} \\ 9 \end{gathered}[/tex]Final Answer
least to greatest = g(x) , f(x) . h(x)
correct option is 2.
simplify the expression 22(5) − 8
Answer:The answer to the expression is 102.
Step-by-step explanation:
Answer:
102
Step-by-step explanation:
22(5)-8=102
Multiply and divide (left to right) 22(5) : 110
= 110 - 8
Add and subtract ( left and right) 110 - 8 : 102
what is 14+7.2n=11+7.5n (whole number)
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\14+7.2n=11+7.5n\\\\\\\text{Move all the variables to one sides and constants to the other}\\14-11=7.5n-7.2n\\7.5n-7.2n = 14-11\\0.3n = 3\\\\\\\text{Divide both sides by 0.3}\\\dfrac{0.3n}{0.3} =\dfrac{3}{0.3} \\\\n = 10[/tex]
Answer: 10
Hope that helps!
The mass of Mars is 6.42 x 1023 kilograms. The mass of Mercury is 3.3 x 1023 kilograms.
Answer:
Im unaware what you are asking?
Step-by-step explanation:
hmmmm
2.if the m∠5 is 63° , find the measure of ∠3.
Show your work
Answer:
117°
Step-by-step explanation:
180-63=117°
so hope it help
Write your answer as a fraction in simplest form. 4/25x10
x/8 = 12.8 solve for x
Answer:
x = 102.4
Step-by-step explanation:
x/8 = 12.8 | * 8
x = 12.8 * 8
x = 102.4
Answer: x=102.4
Step-by-step explanation:
(x/8)*8=12.8*8
x=102.4