Given the functions f(x) = 4x + 1 and g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.
Given the functions in the question;
f(x) = 4x + 1 g(x)= x + 5( f + g )(x) = ?To evaluate f + g, replace the function designators in f + g with the actual functions and simplify
( f + g )(x) = f(x) + g(x)
( f + g )(x) = (4x + 1) + (x + 5)
Remove the parenthesis and collect like terms
( f + g )(x) = (4x + 1) + (x + 5)
( f + g )(x) = 4x + 1 + x + 5
( f + g )(x) = 4x + x + 5 + 1
( f + g )(x) = 5x + 6
Given the functions f(x) = 4x + 1 and g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.
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what is the answer for this equation
-10,844 + 9751
Answer:
-1,093
Step-by-step explanation:
-10,844 + 9751 = -1,093
Simplify
6-√√25
4
DONE
11
The simplified expression of 6 -√25 + √4 is 3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the expression?The expression is given as
6 -√25 + √4
Evaluate the exponents
So, we have
6 -√25 + √4 = 6 - 5 + 2
Evaluate the difference
So, we have
6 -√25 + √4 = 1 + 2
Evaluate the sum
So, we have
6 -√25 + √4 = 3
Hence, the simplified expression of 6 -√25 + √4 is 3
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Answer:
Step-by-step explanation:
6-√√25= 0.25
-2-√15/2= A, -2.94
x=5+√-49/6= C, 5/6+7/6i
i am do confused i am so sure I got it right but it marks it as wrong.
Answer:
Step-by-step explanation:
Try the code AEAA. Let me know if its right or not.
Answer:
CHGD
Step-by-step explanation:
You should actually solve each of these puzzles to get the right code
1. To evaluate f(-2)
We have f(x) = x³ - 2x
Substitute -2 for x
==> (-2)³ - (2 x-2)
-2³ = -8
2 x -2 = -4
==> f(-2) = -8 - (-4)
==> f(-2) = -8 + 4 (two negatives make a positive
==> f(-2) = -4 Letter C
2. Evaluate g(-10)
[tex]g(x) = \dfrac{3x}{2}[/tex]
[tex]g(-10) = \dfrac{3 \times -10}{2} \\= \dfrac{-30}{2} \\\\= \boldsymbol{-15}[/tex] Letter H
3. Evaluate h(-1)
h(x) = 2x² + x
h(1) = 2 x (-1)² - 1
= 2 x 1 - 1
= 1 Letter G
4. Evaluate f(3)
f(x) = x³ -2x
f(3) = 3³ - 2 x 3
= 27 - 6
= 21 Letter D
So the correct code is CHGD
You got everything right except the third :)
A flower shop sells 21 different bouquets and multiple different styles of vase. Which are the possible numbers for the total number of combinations of bouquet and vase?
The St. Catherine's football team loses 3 yards every 6 minutes.
How many yards did the team lose after 18 minutes?
12 yards
Step-by-step explanation:
18 ÷ 6=3
3 × 3=12
12 yards lost after 18 minutes
2. The vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
a. Find the equation of the perpendicular bisector of the side QR.
b. Find the slope of the median of the triangle that passes through point R.
c. Find the slope of the altitude of the triangle that passes through point Q.
The answers will be :
a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.
b. The slope of median of triangle passing through point R is 1/4.
c. The slope of the altitude of the triangle that passes through point R doesn't exists.
What is slope of a line segment ?
Slope is the ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.
It is given that the vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
a.
The midpoint (M) of QR will be equal to
( [tex]\frac{-2 + 8}{2} , \frac{-5 + 1}{2}[/tex] )
or
M = (-3 , 2)
Now , slope of line QR will be ;
[tex]m_{QR}[/tex] = [tex]\frac{1+5}{8+2}[/tex]
[tex]m_{QR}[/tex] = 6 / 10
We know that :
m × [tex]m_{QR}[/tex] = -1
m = -10 / 6
or
m = -5 / 3
Equation of line will be given as :
y + 2 = [tex]\frac{-5}{3}[/tex] ( x - 3 )
y = [tex]\frac{-5}{3}[/tex] x + 3
b.
The midpoint of PQ will be :
= ([tex]\frac{-6 - 2}{2} , \frac{1 - 5}{2}[/tex])
= ( -4 , -2)
The slope of median of triangle that passes through point R will be ;
m = [tex]\frac{-2 - 1}{-4-8}[/tex]
m = -3 / -12
m = 1/4
or
m = 0.25
c.
Slope of altitude of triangle that passes through point Q will be :
m = [tex]\frac{1 - 1}{-6-8}[/tex]
m = 0 / -14
m = 0
The slope in this case doesn't exist.
Therefore the answers will be :
a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.
b. The slope of median of triangle passing through point R is 1/4.
c. The slope of the altitude of the triangle that passes through point R doesn't exists.
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Assume you have applied for two jobs a and b. The probability that you get an offer for job a is 0. 25. The probability of being offered job b is 0. 20. The probability of getting at least one of the jobs is 0. 40. What is the probability that you will be offered both jobs? enter your answer as a decimal rounded to two places.
If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.
Probability is that branch of mathematics that deals with the numerical description of the possibility of an event to occur. The probability of any event is a number between 0 and 1 where 0 represents the impossibility of the event to occur while 1 represents certainty of that event to occur.
As the probability of the job a and job b are independent of each other, the probability that both jobs will be offered can be determined by using the formula;
P(A∩B) = P(A) × P(B)
Here, P(A∩B) represents the probability of both the events happening together
As P(A) = 0.25
P(B) = 0.20
P(A∩B) = 0.25 × 0.20
P(A∩B) = 0.05
Hence, the probability that both jobs will be offered is calculated to be 0.05.
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Factoriza
8x¹²-b⁹
....................................................................................
Expand each logarithm.
log₅ 25/x
If the expression is log₅ 25/x. then the expansion of this looks like
(log 25-log x)/ log 5.
Given that the expression is log₅ 25/x.
We are told to find the expanded value of the expression.
The change of base formula is used in writing a logarithm operation as a fraction of logarithms with a new base.
The expression is log₅ 25/x.
log₅ 25/x=log (25/x)/log 5
(We know that [tex]log_{a} b[/tex]=log b/ log a)
=(log 25-log x)/ log 5 (We know that log (u/v)=log u-log v)
Hence if the expression is log₅ 25/x. then the expansion of this looks like (log 25-log x)/ log 5.
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What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
Solution of exponential equation is , x = [tex]800. 7^4[/tex]
What is exponential equation ?In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]a^x[/tex] .
where, a = the base of function
x = main expression
Mathematically, if [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^x = N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
Some important formulas of exponential :
[tex]a^x . a^y = a^{x+y}[/tex][tex]\frac{a^x}{a^y} = a^{x-y}[/tex][tex]a^x.b^x=(ab)^x[/tex][tex](a^x)^y = a^{xy}[/tex][tex]a^{-x} = \frac{1}{a^x}[/tex]According to given statement,
[tex]7^{-4} x = 800[/tex]
=> [tex]\frac{1}{7^4} x = 800[/tex]
=> [tex]x = 800 . 7^4[/tex]
Thus solution for this equation is x = [tex]800. 7^4[/tex]
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The complete question is :
What is the solution of each exponential equation? Check your answer.
a. 7⁻⁴x=800
b. 5.2³x=400
what property is shown below (5+8)+11=5+(8+11)
The commutative property for addition just means the sum is the same no matter what order you add the terms. This property is also true for multiplication of real numbers.
If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations depend on it as a fundamental property, and numerous mathematical arguments.
A commutative property in mathematics states that if integer positions are switched around or combined while performing addition or multiplication operations, the result will remain the same.
According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the property is true, but not for division or subtraction.
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Make n the subject of this formula:
W= an + Z
Answer:
n = (W - Z)/a
Step-by-step explanation:
W = an + Z
Rearrange the equation so that the subject is alone, in the format Ax = B
W = an + Z
W - Z = an + Z - Z
W - Z = an
Isolate the subject by dividing or multiple so that the equation is in the format x = C
W - Z = an
(W - Z)/a = an/a
(W - Z)/a = n
The figure above shows a graph of a line that goes through the origin. What is the value of k/h?
A. 4 B. 3 C. 4/3 D. -4/3 E. -4
Suppose x and y vary inversely, and x=8 when y=-7 .
a. What is the function that models the inverse variation?
The function that models the inverse variation is y = -56/x.
What exactly is the inverse variation?Inverse variation refers to a relationship between two variables in which the value of one increases while the value of the other decreases.When two quantities, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa, this is known as indirect or inverse variation.So,
In an inverse function: x · y = C where C is the constant.Then,
-7 · 8 = -56 = CSince x · y = C then we obtain:
x · y = -56 ⇒ y = -56/xTherefore, the function that models the inverse variation is y = -56/x.
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Simplify each rational expression. State any restrictions on the variables.
-5 x³y / 15 x y³
According to the question, the given rational expression can be simplified and as shown below:
Rational expression = [tex]\frac{-5x^{3} y}{15xy^{3} }[/tex]
To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.
Rational expression = [tex]\frac{-x^{2} }{3y^{2} }[/tex]
The final expression of the given equation is [tex]\frac{-x^{2} }{3y^{2} }[/tex] .
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
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What is the slope of this line?
1/2
2
-2
-1/2
Multiply if possible. Then simplify. ∛-7. ∛49
The value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.
We are given the expression:
∛ - 7. ∛ 49
We need to multiply and simplify it.
We will first multiply the expression:
= ∛ - 7 × 49
Solving it, we get that:
= ∛ - 343
Now this can also be written as:
= ∛ (- 7 )³
Now, simplifying the cube root to get the value of the expression:
= - 7
Therefore, we get that, the value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.
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(Z-9) (z^2-8z+6) expand
Expand using which formula? If it is using Sum/Difference Formulas, the expanded solution would be:
Solution:
[tex]z^3-17z^2+78z-54[/tex]
Hope this helps!
HELP The entire graph of the function g is shown in the figure below.
Write the domain and range of g as intervals or unions of intervals.
The domain is (-2, -4] and the range is (3 , -5) .
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function.
As, the graph stretches from -2 to -4.
and, it is also defined at (-2)
So, the domain is (-2, -4]
Range is height of the graph.
The smallest value is -3 and highest value is 5.
So, the range is (3 , -5)
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Subject - Geometry
Please Help
Answer:
for the first question,i cannot help since the picture is not clear,but for the second one,i can.so here is the answer for the second question2(-2)+6=22(0)+6=62(2)+6=102(4)+6=14Step-by-step explanation:
u just need to replace the (x) in the equalition.on the calculator,u just write the equalation normally but when u want to replace the ( x) u have to put bracket.replace the x with number next to it or the number at x box.u can check again my answer5kg+58g+8kg+580g simplify
The sum of 5 and a number is then multiplied by two. The answer is -2 What is the number
3m² + n; m = 5, n = 3
The first three rooms took the painter a total of 9 hours to paint. If the learning curve rate is 85%, how long will it take the painter to paint all 20 rooms in stately wayne manor?.
It will take the painter more than 40 hours to paint all 20 rooms in stately wayne manor .
Time taken for the first 3 rooms =9hrs
Learning curve rate = 85%
Time taken for the next 20 rooms =?
Time taken for 1 room = 9hrs / 3 rooms = 3 hrs
If it takes 3 hrs to paint 1 room
Therefore, it will take x hrs to paint 20 rooms would take;
Hence, 20 rooms multiplied 3 hrs = 60 hours
It may take 60 hours to complete painting the 20 rooms.
At a learning curve rate of 85%, 15% will be the progress rate
Therefore, it will take additional 15% of 60 hours to paint the 20 room.
60+9(15% of 60) =69 hours
The painter would take more than 40 hours to paint the 20 rooms given his efficiency and learning curve rate. The answer is derived by relating the data provided in the question to the desired answer.
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Given f(n)=7n-5
Evaluate f(-3)
GIVING BRAINLIEST
Answer:
f(-3) = -26
Step-by-step explanation:
f(n)=7n-5; f(-3)
f(-3) = 7(-3) - 5
f(-3) = -21 - 5
f(-3) = -26
I hope this helps!
2) 87 what is two divided by 87 with a remainder
8 is subtracted from the cube of a number.
Answer:Solution
Result will not divisible by 3
5
3
×2−8=250−8=242
If we divide 242 by 3 it will leave reminder 2.
Step-by-step explanation:
The equation is given by A = n³ - 8 , where n is a number
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number be represented as n
A = 8 is subtracted from the cube of a number
Substituting the values in the equation , we get
A = n³ - 8 be equation (1)
Now , when 8 is subtracted from twice the cube of 5 , the result is not divisible by 3
So , A = 2 x 5³ - 8
A = 242 which is not divisible by 3
Hence, the equation is A = n³ - 8
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10. The distance between the points (5, 7) and (8, -5) is
a) √153
b) √ 154
c) √13
d) √53
Answer:
i THINK im not sure but i think its C please let me know if im wrong
Step-by-step explanation:
Please help me in this question
Give the answers as well as explanation
HELP ME plsss show with work ! thank u !!
Answer: .8 or 4/5
Step-by-step explanation:
You can do this a couple ways.
1) what you started is right, you can change your fraction into a decimal and divide.
2/5 = .4
.32/.4 = .8
2) you can change .32 into 32/100 and divide by 2/5
32/100 divided by 2/5
When you divide fractions, you flip the divisor and multiply
32/100 x 5/2
Multiply across
160/200
Simplify
4/5