The domain value for f(x)-g(x)+10 = - x²- x + 17
What are the domain of the function f(x)-g(x)+10 ?Given : f(x)=2 x+5
g(x)=x²-3 x+2
Solution:
f(x) - g(x) + 10 = 2 x+5 - x²-3 x+2 +10
f(x) - g(x) + 10 = 2 x+5 - x²-3 x+12
f(x) - g(x) + 10 = - x²- x + 17
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Solve each equation. Check your answers.
log (5-2 x)=0
The value of x for log (5-2 x)=0 is 2.
What is the logarithmic function?
It is established that the exponential equation x = ay and the logarithmic function y = logax are equal. Only when x = ay, a > 0, and a 1 do y and logax coincide. The base-a logarithmic function is what it is known as. Think about what it means for the exponential function to be inversed: x = ay.
Given,
log (5-2 x)=0
It can be expressed as -
5 - 2x = 10⁰
= 5 - 2x = 1
= x = 2
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Parallelogram has a base of 3.5 units and a corresponding height of 2 units what is it’s area
Answer:
The answer is 7
Step-by-step explanation:
The formula you would use is A=bxh
So you would just plug it in
3.5 x 2 which gives you 7
Hope this helps:)
Maryama bought 45 plain cookies for $2.20 each. She decorated them with icing and sold them for $3.75 each. How much profit did she make selling her decorated cookies?
45x2.20=99
meaning she spent $99
45x3.75=168.75
shows how much she made
168.75-99=69.75
shows what she profited
your answer is $69.75
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Solve the system of equations-2x+2y=-8 and -3x+y=8 by combining the equations
The required solution of the system of equations are x=-6 and y=-10.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The system of equations are
-2x+2y=-8 and -3x+y=8
According to given question we have
Consider the first equation.
-2x+2y=-8
Taking minus sign common from both sides we get
-(2x-2y)=-8
2x-2y=8
Taking 2 common from left sides, we get
2(x-y)=8
Divide by 2 on both sides we get,
x-y= 4....(i)
-3x+y=8...(ii)
By adding 2 equation we get
-2x=12
x=-6
Put the value of x in Equation (i) we get
x-y= 4
-6-y=4
-y=4+6
y=-10
Therefore, the required solution of the system of equations are x=-6 and y=-10.
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An equilateral triangle has a length of 10 inches.What is the area of the triangle in simplest radical form?
Answer: The area of Triangle is A = 43.25
Step-by-step explanation:
In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3 [tex]s^{2}[/tex]* s = √3/4([tex]s^{2}[/tex])
Define Area of Triangle:
In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4([tex]s^{2}[/tex]) . The perimeter of an equilateral triangle is 3s.
So, we can write,
A = √3/4([tex]s^{2}[/tex])
It means, A = Area of the Triangle
S = length of Triangle = 10inches.
A = √3/4([tex]s^{2}[/tex])
A = √3/4([tex]10^{2}[/tex])
A= √3/4*100
A = 1.73/4*100
A = 0.4325*100
A = 43.25
The area of Triangle is A = 43.25
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Find the values of the variables.
Greg is purchasing ink cartridges for his computer. Each ink cartridge costs $35.99 and comes with a $10 rebate. How much will Greg pay for one ink cartridge after the rebate? *Rebate is a refund of part of the amount paid for an item Greg will pay $ after the rebate
Greg will pay $25.99 for one ink cartridge after the rebate
Cost of ink cartridge: $35.99
Rebate on each ink cartridge: $10
A rebate is a portion of the purchase price that is refunded. It serves as a motivator to promote the sale of goods. For instance, if I want to spend $1,000 on a laptop/computer, the shopkeeper can offer me a $100 rebate to sweeten the bargain and convince me to buy the item.
Price Greg will pay after rebate: 35.99 - 10 = $25.99
So, Greg will pay $25.99 for one ink cartridge after the rebate of $10.
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Find the coordinates of M, the midpoint of AB, for each pair of points.
A (1,2) and B (-3,6)
Answers:
(-1,4)
(3.5,7)
(4,-1)
(7,-3.5)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-3}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -3 +1}{2}~~~ ,~~~ \cfrac{ 6 +2}{2} \right) \implies \left(\cfrac{ -2 }{2}~~~ ,~~~ \cfrac{ 8 }{2} \right)\implies (-1~~,~~4)[/tex]
Determine if each statement is true or false. Justify your answer.
log (x-2)= log x/log 2
The logarithm statement log (x - 2) = log x / log 2 is a false statement as log x / log 2 = log x - log 2.
We are given the logarithm as:
log (x - 2) = log x / log 2
We need to tell if it is true of not.
We get that, it is false statement.
We know that log a / log b = log a - log b
So, log x / log 2 = log x - log 2
So, it is not equal to log (x - 2)
Therefore, we get that, the logarithm statement log (x - 2) = log x / log 2 is a false statement as log x / log 2 = log x - log 2.
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ST lie on the coordinate plane with S located at (3,2). the midpoint of ST is Z(3,5). Can the location of T be determined
Answer:
T(3, 8)
Step-by-step explanation:
Yes, it can.
Use the midpoint formula with points S and Z, and solve for point T.
M( (x_1 + x_2)/2 , (y_1 + y_2)/2 )
Z(3, 5) = ( (3 + x)/2 , (2 + y)/2 )
(3 + x)/2 = 3
3 + x = 6
x = 3
(2 + y)/2 = 5
2 + y = 10
y = 8
T(3, 8)
The height of a ball thrown straight up from the ground with a velocity of 96ft/s is given by the quadratic function h(t)=-16 t²+96 t . What is the maximum height the ball reaches?
(a) 6ft (b) 128ft (c) 144ft (d) 160ft
The correct option is (c) 144ft
The maximum height the ball reaches is 144ft.
What is quadratic function ?A quadratic function has the form of equation as ax²+ bx + c, where a, b, and c are the numbers not equal to zero. In mathematics, the quadratic function, the quadratic polynomials , 2 degree polynomial is a polynomial function with one or more that one variables in which the highest term is of the second degree.
In the question,
h(t)=-16 t²+96 t
and velocity = 96ft/s
out the -16 from the equation.
h(t)= -16 ( t² + 6 t )
h(t) = −16(t² −6t+9−9)
= −16(t² −6t+9)+144
Factor the equation to get a perfect square ,t = 3 then h(t) = 144. The maximum height is 144.
−16(t−3)² +144
Thus, height is 144 ft.
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addie organizes the Venn diagram below showing the factors of 56 and 42. Reid says that she is incorrect. Who is corect? justify your thinking
Addie is correct because both 2 and 14 are common factors of 56 and 42.
Who is correct?The factor of a number is the number that can perfectly divide another number without leaving any remainder. For example, a factor of 20 is 10 because 10 perfectly divides 20 to 2.
A common factor is a factor that is common to two or more integers. An example of a common factor of 15 and 20 is 5.
A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. The numbers at the intersection of the two circles are common to both numbers.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28 and 56.
Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42.
Common factors = 1, 2, 7, 14
This means that Addie is correct because both 2 and 7 are common factors of 56 and 42.
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Evaluate the expression 7+(-2)•3^2
Answer:first do the exponents thats equal to 9 then times -2 is -16+7 is -11
hope that helps
Step-by-step explanation:
Answer:
-11.
Step-by-step explanation:
7+(-2)•3^2
= 7 - 2*9
= 7 - 18
= -11.
.What is the slope between
(-8,4) and (3,-1)?
What is the slope of
4x-3y=13?
How do you know a graph represents direct variation?
What is true about the slopes of parallel lines? What is true about the slopes of perpendicular lines?
The slope between (-8,4) and (3,-1) is -5/11 and the slope of 4x - 3y = 13 is 4/3
What is the slope between (-8,4) and (3,-1)?The points are given as
(-8,4) and (3,-1)
The slope between the points is calculated using
Slope = (y2 - y1)/(x2 - x1)
So, we have
Slope = (-1 - 4)/(3 + 8)
Evaluate
Slope = -5/11
Hence, the slope between (-8,4) and (3,-1) is -5/11
What is the slope of 4x - 3y = 13?The equation of the line is given as
4x - 3y = 13
Make 3y the subject of the formula
So, we have
3y = 4x - 13
Make y the subject of the formula
So, we have
y = 4/3x - 13/3
A linear equation is represented as
y= mx + c
Where
Slope = m
By comparison, we have
m = 4/3
Hence, the slope of 4x - 3y = 13 is 4/3
How do you know a graph represents direct variation?A graph that represents direct variation is a linear graph that passes through the origin
What is true about the slopes of parallel lines?The slopes of parallel lines are equal
i.e. m1 = m2
What is true about the slopes of perpendicular lines?The slopes of perpendicular lines are opposite reciprocals
i.e. m1 = -1/m2
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49
#
2. The equation x = 3 is graphed on the coordinate plane shown.
a. Graph the line perpendicular to x = 3 that passes
through (-2, 4).
The linear function y = 4, perpendicular to x = 3, is graphed at the end of the answer.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.When two linear functions are perpendicular, they intersect forming an angle of 90º between them.
For this problem, we want a line perpendicular to x = 3.
x = 3 is a vertical line.The line perpendicular to a vertical line is an horizontal line, in the format y = 4.The line passes through (-2,4), with y-coordinate of 4, hence the line is given by:
y = 4.
On the graph given at the end of the answer, it is shown that the two lines are perpendicular, forming an straight angle. The line y = 4 is graphed in blue.
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please help me (image attached)
The inequalities which shows the closest whole number range for :
a) y = √74 is 8 < y < 9.
b) z = ∛74 is 4 < z < 5.
What is an mathematical expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
it is given that for x = √28 the value of x ranges between 5 and 6 that is 5 < x < 6 because square root of 28 is approximately 5.29 which is less than 6 and greater than 5.
a) Now, for y = √74 :
the square root of 74 is approximately 8.6 which is less than 9 and greater than 8 that is the value of y ranges between 8 and 9 that is :
8 < y < 9.
b) Now, for z = ∛74 :
the cube root of 74 is approximately 4.19 which is less than 5 and greater than 4 that is the value of z ranges between 4 and 5 that is :
4 < z < 5.
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What is the solution of √4 x+1 -5=0 ?
The solution is 6
Rewriting the given equation
√(4x + 1) - 5 = 0
Now, taking square of the equation to find the solution of equation -
(√(4x + 1))² = 5²
On squaring both sides we get the equation -
4x + 1 = 25
Shifting 1 to the Right Hand Side of the equation
4x = 25 - 1
Performing subtraction on Right Hand Side of the equation
4x = 24
Shifting 4 to the Right Hand Side of the equation as denominator
x = 24 ÷ 4
Performing division on Right Hand Side of the equation
x = 6
Thus, the solution is 6
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The correct question is - sqrt(4x+1)-5=0
The time t in seconds for a swinging pendulum to complete one full cycle is given by the function t=0.2√I, where l is the length of the pendulum in centimeters. To the nearest tenth, how long is a full cycle if the pendulum is 10 cm long? 20cm long? How long, in centimeters, is a pendulum that takes 2 seconds for one full cycle?
A full cycle, if the pendulum is 10 cm, is 0.6 seconds long. A full cycle, if the pendulum is 20 cm, is 0.9 seconds long. A pendulum that takes 2 seconds for one full cycle is 100 cm long.
Given,
The time t in seconds for a swinging pendulum to complete one full cycle is given by the function t as,
t = 0.2 √I
Here, l is the length of the pendulum in centimeters.
For the first part, two lengths are given for the pendulum is given
We can obtain the value of t by substituting the value of l
This implies,
For l = 10 cm
t = 0.2 √10 = 0.632 = 0.6 seconds
For l = 20 cm
t = 0.2 √20 = 0.894 = 0.9 seconds
For the second part, time is given
We can obtain the value of l by substituting the value of t
This implies,
For t = 2 seconds
l = t² / (0.2)² = t² / 0.04 = 2² / 0.04 = 4 / 0.04 = 100 cm
Therefore, A full cycle is 0.6 seconds long if the pendulum is 10 cm long, 0.9 seconds long if the pendulum is 20 cm long, and 100 cm long if the pendulum takes 2 seconds to complete one full cycle.
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(20 POINTS)
If a polynomial f(x) has a remainder of -4 when divided by x-8, what is f(8)?
Based on the given parameters, the value of the polynomial function f(8) is -4
What are polynomials?Polynomials are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the polynomial function?The polynomial function is given as
Polynomial = f(x)
Also, we have the following statement
a remainder of -4 when divided by x-8
To start with, we set the divisor to 0
So, we have
x - 8 = 0
Add 8 to both sides of the equation
So, we have
x = 8
Express as a function
f(x) = f(8)
Set the equation to the remainder
So, we have
f(x) = f(8) = -4
Hence, the value of the polynomial function f(8) is -4
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please help me !!!!!
equivalent to 5(2a+b)+2(a+2b)−5(2a+2b)
The equivalent of the given expression 5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b ) is 2a - b.
What is the equivalent of the given expression?Given the expression in the question;
5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b )
To simplify, apply distributive property.
5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b )
5(2a) + 5(b) + 2(a) + 2(2b) − 5(2a) -5(2b )
Perform the multiplication operation.
10a + 5b + 2a + 4b − 10a - 10b
Collect like terms
10a − 10a + 2a + 5b + 4b - 10b
2a + 5b + 4b - 10b
2a + 9b - 10b
2a - 1b
2a - b
Therefore, the equivalent of the given expression 5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b ) is 2a - b.
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whats an irrational number between 7.7 and 7.9 and how did you find the answer?
Answer: I think it's 7.8.
Answer:
7.8
Explanation:
This number is irrational because it does not terminate.
Terminate
decimal that is expressed in finite figures in which all figures to the right are zero.
which in this case, that does not occur.Explain how to find a y-intercept.
To find Y-intercept
Set X=0
If the relationship is proportional, what is the missing value from the table?
x
y
8
6
16
?
24
18
Answer:
12.
Step-by-step explanation:
y /x = 6/8 = 3/4
y/x = 18/24 = 3/4
The relation is y = 3/4 x.
So, the missing value is 16 * 3/4
= 12.
-(8-11)3rdpower-3|-14|/24thpower-7
Answer: bofa
Step-by-step explanation:
REASONING
In most of the previous examples there were only two terms. Extend your work with using the distributive
property "backwards" and write the following as a product of binomials.
(a) x(x+2)+3(x+2)+4x(x+2)
(b) 2x(x-5)+3(x-5)+(x-1)(x-5)
The expression is written as a product of binomials as;
a) (x + 2) (5x + 3)
b) (x - 5) ( 3x + 2)
What is Distributive property?
Distributive property is said to be multiplying the sum of two or more number will give the same result as multiplying each addend individually by the number and then adding the products together.
Now, For solving the expression by using the distributive property "backwards" , we can find the GCD of each term using in the expression as;
(a) x(x+2) + 3(x+2) + 4x(x+2)
GCD of x(x + 2), 3(x + 2), 4x(x + 2) = (x + 2)
Hence, Firstly take (x + 2) as common term we get;
x (x + 2) + 3(x + 2)+ 4x(x + 2) = (x +2) ( x + 3 + 4x)
= (x + 2) (5x + 3)
The expression is written as a product of binomials as;
a) x (x + 2) + 3(x + 2)+ 4x(x + 2) = (x + 2) (5x + 3)
And, (b) 2x(x-5) + 3(x-5) + (x-1) (x-5)
GCD of 2x(x-5) , 3(x-5) , (x-1) (x-5) = (x - 5)
Hence, Firstly take (x - 5) as common term we get;
2x(x-5) + 3(x-5) + (x-1) (x-5) = (x - 5) (2x + 3 + x - 1)
= (x - 5) ( 3x + 2)
So, The expression is written as a product of binomials as;
b) 2x(x-5) + 3(x-5) + (x-1) (x-5) = (x - 5) ( 3x + 2)
Therefore, The expression is written as a product of binomials as;
a) (x + 2) (5x + 3)
b) (x - 5) ( 3x + 2)
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Write an expression for “3 times the sum of a number and 2”
Answer:
3*2
Step-by-step explanation:
Please i need help 5th grade math first one
[tex](4 \times 1) + (4 \times \frac{1}{1000}) \\ (4) + ( \frac{4}{1000} ) \\ 4 + \frac{1}{250 \\} \\ \frac{1000 + 1}{250 } \\ \frac{1001}{250} \\ [/tex]
I guess this is the answer
What is the answer to this question?
Answer:
visit a nearby farmer ask him about farming such as things to be considered, possible disease, benefits, challenges etc. prepare a short report and present
[tex]\displaystyle\\Answer:\ y=\frac{1}{3}x-2[/tex]
Step-by-step explanation:
(6,0) (9,1)
[tex]\displaystyle\\The\ slope=\frac{1-0}{9-6} \\\\The\ slope=\frac{1}{3}[/tex]
(0,-2)
[tex]\displaystyle\\y=\frac{1}{3} x+b\\-2=\frac{1}{3}(0)+b\\ -2=0+b\\\\-2=b\\\\Thus,\\\\y=\frac{1}{3} x-2\\\\[/tex]
There are 24 classrooms and 600 students. What is the ratio of classrooms to students written in fraction simplest form?
Answer:
1 : 25.
Step-by-step explanation:
24 : 600
= 24/24 : 600/24
= 1 : 25.